hp 49g+/ hp 48gII graphing calculator
hp 49g+/ hp 48gII graphing calculator
advanced user's reference manual
H
Edition 1.1
HP part number F2228-90010
Printed Date: 2006/3/20
Notice
REGISTER YOUR PRODUCT AT: www.register.hp.com
THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT
TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND
WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.
© Copyright 1993-1998, 2005, 2006 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of HewlettPackard Company, except as allowed under the copyright laws.
Hewlett-Packard Company
4995 Murphy Canyon Rd,
Suite 301
San Diego, CA 92123
Acknowledgements
Hewlett-Packard would like to thank the following for their contribution:
Gene Wright, Tony Hutchins, Wlodek Mier-Jedrzejowicz, Jordi Hidalgo, Ted Kerber, Joe Horn, Richard Nelson,
Bruce Horrocks and Jake Schwartz.
Printing History
Edition 1 September 2005
Edition 1.1 March 2006
Contents
Contents........................................................................................................................................................................................ 1
1. RPL Programming................................................................................................................................................................. 1-1
Understanding Programming .............................................................................................................................................1-1
The Contents of a Program ......................................................................................................................................... 1-1
Calculations in a Program ........................................................................................................................................... 1-2
Entering and Executing Programs......................................................................................................................................1-3
Viewing and Editing Programs ..........................................................................................................................................1-6
Creating Programs on a Computer .....................................................................................................................................1-7
Using Local Variables........................................................................................................................................................1-7
Creating Local Variables............................................................................................................................................. 1-7
Evaluating Local Names ............................................................................................................................................. 1-8
Defining the Scope of Local Variables ....................................................................................................................... 1-9
Compiled Local Variables......................................................................................................................................... 1-10
Creating User-Defined Functions as Programs......................................................................................................... 1-10
Using Tests and Conditional Structures ...........................................................................................................................1-11
Testing Conditions .................................................................................................................................................... 1-11
Using Conditional Structures and Commands .......................................................................................................... 1-13
Using Loop Structures......................................................................................................................................................1-17
Using Definite Loop Structures ................................................................................................................................ 1-17
Using Indefinite Loop Structures .............................................................................................................................. 1-21
Using Loop Counters ................................................................................................................................................ 1-24
Using Summations Instead of Loops ........................................................................................................................ 1-25
Using Flags.......................................................................................................................................................................1-25
Types of Flags........................................................................................................................................................... 1-26
Setting, Clearing, and Testing Flags ......................................................................................................................... 1-26
Recalling and Storing the Flag States ....................................................................................................................... 1-27
Using Subroutines ............................................................................................................................................................1-28
Single-Stepping through a Program .................................................................................................................................1-29
Trapping Errors ................................................................................................................................................................1-32
Causing and Analyzing Errors .................................................................................................................................. 1-32
Making an Error Trap ............................................................................................................................................... 1-33
Input .................................................................................................................................................................................1-35
Data Input Commands............................................................................................................................................... 1-35
Using PROMPT … CONT for Input ........................................................................................................................ 1-35
Using DISP FREEZE HALT … CONT for Input .................................................................................................... 1-37
Using INPUT … ENTER for Input .......................................................................................................................... 1-38
Using INFORM and CHOOSE for Input.................................................................................................................. 1-42
Beeping to Get Attention .......................................................................................................................................... 1-45
Stopping a Program for Keystroke Input .........................................................................................................................1-46
Using WAIT for Keystroke Input ............................................................................................................................. 1-46
Using KEY for Keystroke Input ............................................................................................................................... 1-46
Output ....................................................................................................................................................................... 1-46
Data Output Commands............................................................................................................................................ 1-47
Labeling Output with Tags ....................................................................................................................................... 1-47
Labeling and Displaying Output as Strings .............................................................................................................. 1-48
Pausing to Display Output ........................................................................................................................................ 1-48
Using MSGBOX to Display Output ......................................................................................................................... 1-49
Using Menus with Programs ............................................................................................................................................1-49
Using Menus for Input .............................................................................................................................................. 1-50
Using Menus to Run Programs ................................................................................................................................. 1-50
Turning Off the hp49g+/hp48gII from a Program ...........................................................................................................1-52
2. RPL Programming Examples ................................................................................................................................................ 2-1
Fibonacci Numbers ............................................................................................................................................................2-1
Contents -1
FIB1 (Fibonacci Numbers, Recursive Version).......................................................................................................... 2-1
FIB2 (Fibonacci Numbers, Loop Version) ................................................................................................................. 2-2
FIBT (Comparing Program-Execution Time)............................................................................................................. 2-3
Displaying a Binary Integer ............................................................................................................................................... 2-5
PAD (Pad with Leading Spaces) ................................................................................................................................ 2-5
PRESERVE (Save and Restore Previous Status) ....................................................................................................... 2-6
BDISP (Binary Display) ............................................................................................................................................. 2-7
Median of Statistics Data ................................................................................................................................................. 2-10
%TILE (Percentile of a list)...................................................................................................................................... 2-10
MEDIAN (Median of Statistics Data) ...................................................................................................................... 2-11
Expanding and Collecting Completely ............................................................................................................................ 2-14
MULTI (Multiple Execution) ................................................................................................................................... 2-14
EXCO (Expand and Collect Completely)................................................................................................................. 2-15
Minimum and Maximum Array Elements ....................................................................................................................... 2-16
MNX (Minimum or Maximum Element—Version 1).............................................................................................. 2-16
MNX2 (Minimum or Maximum Element- Version 2).............................................................................................. 2-18
Applying a Program to an Array...................................................................................................................................... 2-20
Converting Between Number Bases ................................................................................................................................ 2-22
Verifying Program Arguments ........................................................................................................................................ 2-24
NAMES (Check List for Exactly Two Names) ........................................................................................................ 2-24
Converting Procedures from Algebraic to RPN .............................................................................................................. 2-27
Bessel Functions .............................................................................................................................................................. 2-29
Animation of Successive Taylor's Polynomials ............................................................................................................... 2-30
SINTP (Converting a Plot to a Graphics Object)...................................................................................................... 2-31
Techniques used in SINTP ....................................................................................................................................... 2-31
SETTS (Superimposing Taylor's polynomials) ........................................................................................................ 2-32
TSA (Animating Taylor's Polynomials) ................................................................................................................... 2-33
Programmatic Use of Statistics and Plotting.................................................................................................................... 2-34
Trace Mode ...................................................................................................................................................................... 2-37
Inverse-Function Solver................................................................................................................................................... 2-38
Animating a Graphical Image .......................................................................................................................................... 2-39
3. Full Command and Function Reference................................................................................................................................ 3-1
ABCUV.............................................................................................................................................................................. 3-4
ABS ................................................................................................................................................................................... 3-4
ACK ................................................................................................................................................................................... 3-4
ACKALL ............................................................................................................................................................................ 3-4
ACOS ................................................................................................................................................................................ 3-5
ACOS2S ........................................................................................................................................................................... 3-6
ACOSH ............................................................................................................................................................................. 3-6
ADD ................................................................................................................................................................................... 3-7
ADDTMOD ....................................................................................................................................................................... 3-8
ADDTOREAL ................................................................................................................................................................... 3-8
ALGB................................................................................................................................................................................. 3-8
ALOG ................................................................................................................................................................................ 3-8
AMORT ............................................................................................................................................................................. 3-8
AND ................................................................................................................................................................................... 3-8
ANIMATE.......................................................................................................................................................................... 3-9
ANS ................................................................................................................................................................................. 3-10
APPLY............................................................................................................................................................................. 3-10
ARC ................................................................................................................................................................................. 3-10
ARCHIVE........................................................................................................................................................................ 3-11
ARG................................................................................................................................................................................. 3-11
ARIT ................................................................................................................................................................................ 3-12
ARRY→ .......................................................................................................................................................................... 3-12
→ARRY .......................................................................................................................................................................... 3-12
ASIN ................................................................................................................................................................................ 3-12
ASIN2C ........................................................................................................................................................................... 3-14
ASIN2T ........................................................................................................................................................................... 3-14
Contents - 2
ASINH..............................................................................................................................................................................3-14
ASN .................................................................................................................................................................................3-14
ASR .................................................................................................................................................................................3-15
ASSUME.........................................................................................................................................................................3-16
ATAN ...............................................................................................................................................................................3-16
ATAN2S ..........................................................................................................................................................................3-17
ATANH ............................................................................................................................................................................3-17
ATICK ..............................................................................................................................................................................3-18
ATTACH..........................................................................................................................................................................3-18
AUGMENT......................................................................................................................................................................3-19
AUTO...............................................................................................................................................................................3-19
AXES ...............................................................................................................................................................................3-20
AXL ..................................................................................................................................................................................3-20
AXM .................................................................................................................................................................................3-20
AXQ .................................................................................................................................................................................3-20
BAR .................................................................................................................................................................................3-20
BARPLOT .......................................................................................................................................................................3-21
BASIS ..............................................................................................................................................................................3-22
BAUD...............................................................................................................................................................................3-22
BEEP ...............................................................................................................................................................................3-22
BESTFIT .........................................................................................................................................................................3-22
BIN ...................................................................................................................................................................................3-22
BINS ................................................................................................................................................................................3-23
BLANK.............................................................................................................................................................................3-23
BOX .................................................................................................................................................................................3-23
BUFLEN ..........................................................................................................................................................................3-24
BYTES.............................................................................................................................................................................3-24
B→R ................................................................................................................................................................................3-24
C2P..................................................................................................................................................................................3-24
CASCFG .........................................................................................................................................................................3-25
CASCMD ........................................................................................................................................................................3-25
CASE...............................................................................................................................................................................3-25
CEIL.................................................................................................................................................................................3-25
CENTR ............................................................................................................................................................................3-26
CF ....................................................................................................................................................................................3-26
%CH ................................................................................................................................................................................3-26
CHINREM .......................................................................................................................................................................3-27
CHOLESKY ....................................................................................................................................................................3-27
CHOOSE ........................................................................................................................................................................3-27
CHR .................................................................................................................................................................................3-27
CIRC ................................................................................................................................................................................3-28
CKSM ..............................................................................................................................................................................3-28
CLEAR ............................................................................................................................................................................3-28
CLKADJ ..........................................................................................................................................................................3-28
CLLCD.............................................................................................................................................................................3-29
CLOSEIO ........................................................................................................................................................................3-29
CLΣ ..................................................................................................................................................................................3-29
CLVAR ............................................................................................................................................................................3-29
CMPLX ............................................................................................................................................................................3-29
CNRM..............................................................................................................................................................................3-30
→COL..............................................................................................................................................................................3-30
COL→..............................................................................................................................................................................3-30
COL– ...............................................................................................................................................................................3-30
COL+ ...............................................................................................................................................................................3-31
COLCT ............................................................................................................................................................................3-31
COLLECT .......................................................................................................................................................................3-31
COLΣ ...............................................................................................................................................................................3-31
COMB..............................................................................................................................................................................3-32
Contents - 3
CON................................................................................................................................................................................. 3-32
COND.............................................................................................................................................................................. 3-33
CONIC............................................................................................................................................................................. 3-33
CONJ............................................................................................................................................................................... 3-34
CONLIB........................................................................................................................................................................... 3-34
CONST ........................................................................................................................................................................... 3-35
CONSTANTS................................................................................................................................................................. 3-35
CONT .............................................................................................................................................................................. 3-35
CONVERT ...................................................................................................................................................................... 3-35
CORR.............................................................................................................................................................................. 3-35
COS................................................................................................................................................................................. 3-36
COSH.............................................................................................................................................................................. 3-36
COV................................................................................................................................................................................. 3-37
CR.................................................................................................................................................................................... 3-37
CRDIR............................................................................................................................................................................. 3-37
CROSS ........................................................................................................................................................................... 3-37
CSWP ............................................................................................................................................................................. 3-38
CURL............................................................................................................................................................................... 3-38
CYCLOTOMIC............................................................................................................................................................... 3-38
CYLIN.............................................................................................................................................................................. 3-38
C→PX ............................................................................................................................................................................. 3-38
C→R................................................................................................................................................................................ 3-39
DARCY ........................................................................................................................................................................... 3-39
DATE............................................................................................................................................................................... 3-39
→DATE........................................................................................................................................................................... 3-39
DATE+ ............................................................................................................................................................................ 3-40
DBUG.............................................................................................................................................................................. 3-40
DDAYS............................................................................................................................................................................ 3-40
DEC ................................................................................................................................................................................. 3-41
DECR .............................................................................................................................................................................. 3-41
DEDICACE..................................................................................................................................................................... 3-41
DEF ................................................................................................................................................................................. 3-41
DEFINE........................................................................................................................................................................... 3-41
DEG................................................................................................................................................................................. 3-42
DEGREE......................................................................................................................................................................... 3-42
DELALARM .................................................................................................................................................................... 3-42
DELAY ............................................................................................................................................................................ 3-42
DELKEYS ....................................................................................................................................................................... 3-42
DEPND ........................................................................................................................................................................... 3-43
DEPTH............................................................................................................................................................................ 3-44
DERIV ............................................................................................................................................................................. 3-44
DERVX............................................................................................................................................................................ 3-44
DESOLVE....................................................................................................................................................................... 3-44
DET ................................................................................................................................................................................. 3-44
DETACH ......................................................................................................................................................................... 3-44
DIAG→............................................................................................................................................................................ 3-45
→DIAG............................................................................................................................................................................ 3-45
DIAGMAP ....................................................................................................................................................................... 3-45
DIFF................................................................................................................................................................................. 3-45
DIFFEQ........................................................................................................................................................................... 3-46
DIR................................................................................................................................................................................... 3-47
DISP ................................................................................................................................................................................ 3-47
DISPXY........................................................................................................................................................................... 3-47
DISTRIB.......................................................................................................................................................................... 3-48
DIV................................................................................................................................................................................... 3-48
DIV2................................................................................................................................................................................. 3-48
DIV2MOD ....................................................................................................................................................................... 3-48
DIVIS ............................................................................................................................................................................... 3-48
Contents - 4
DIVMOD..........................................................................................................................................................................3-48
DIVPC..............................................................................................................................................................................3-48
dn .....................................................................................................................................................................................3-48
DO....................................................................................................................................................................................3-48
DOERR ...........................................................................................................................................................................3-49
DOLIST ...........................................................................................................................................................................3-49
DOMAIN..........................................................................................................................................................................3-50
DOSUBS.........................................................................................................................................................................3-50
DOT .................................................................................................................................................................................3-50
DRAW .............................................................................................................................................................................3-51
DRAW3DMATRIX .........................................................................................................................................................3-51
DRAX...............................................................................................................................................................................3-51
DROITE...........................................................................................................................................................................3-52
DROP ..............................................................................................................................................................................3-52
DROP2 ............................................................................................................................................................................3-52
DROPN ...........................................................................................................................................................................3-52
DTAG...............................................................................................................................................................................3-52
DUP .................................................................................................................................................................................3-53
DUP2 ...............................................................................................................................................................................3-53
DUPDUP.........................................................................................................................................................................3-53
DUPN ..............................................................................................................................................................................3-53
D→R ................................................................................................................................................................................3-54
e .......................................................................................................................................................................................3-54
EDIT.................................................................................................................................................................................3-54
EDITB ..............................................................................................................................................................................3-55
EGCD ..............................................................................................................................................................................3-55
EGV .................................................................................................................................................................................3-55
EGVL ...............................................................................................................................................................................3-55
ELSE................................................................................................................................................................................3-55
END .................................................................................................................................................................................3-56
ENDSUB .........................................................................................................................................................................3-56
ENG .................................................................................................................................................................................3-56
EPSX0.............................................................................................................................................................................3-56
EQNLIB ...........................................................................................................................................................................3-56
EQW ................................................................................................................................................................................3-57
EQ→ ................................................................................................................................................................................3-57
ERASE ............................................................................................................................................................................3-57
ERR0 ...............................................................................................................................................................................3-57
ERRM ..............................................................................................................................................................................3-57
ERRN ..............................................................................................................................................................................3-58
EULER ............................................................................................................................................................................3-58
EVAL................................................................................................................................................................................3-58
EXLR ...............................................................................................................................................................................3-59
EX&LN.............................................................................................................................................................................3-59
EXP..................................................................................................................................................................................3-59
EXP2HYP .......................................................................................................................................................................3-60
EXP2POW ......................................................................................................................................................................3-60
EXPAN ............................................................................................................................................................................3-60
EXPAND .........................................................................................................................................................................3-60
EXPANDMOD ................................................................................................................................................................3-60
EXPFIT............................................................................................................................................................................3-60
EXPLN.............................................................................................................................................................................3-60
EXPM ..............................................................................................................................................................................3-60
EYEPT.............................................................................................................................................................................3-61
F0λ...................................................................................................................................................................................3-61
FACT ...............................................................................................................................................................................3-61
FACTOR .........................................................................................................................................................................3-62
FACTORMOD ................................................................................................................................................................3-62
Contents - 5
FACTORS ...................................................................................................................................................................... 3-62
FANNING ....................................................................................................................................................................... 3-62
FAST3D .......................................................................................................................................................................... 3-62
FCOEF............................................................................................................................................................................ 3-63
FC?.................................................................................................................................................................................. 3-63
FC?C ............................................................................................................................................................................... 3-63
FDISTRIB ....................................................................................................................................................................... 3-64
FFT .................................................................................................................................................................................. 3-64
FILER .............................................................................................................................................................................. 3-64
FINDALARM .................................................................................................................................................................. 3-64
FINISH ............................................................................................................................................................................ 3-65
FIX ................................................................................................................................................................................... 3-65
FLASHEVAL .................................................................................................................................................................. 3-65
FLOOR............................................................................................................................................................................ 3-66
FONT6 ............................................................................................................................................................................ 3-66
FONT7 ............................................................................................................................................................................ 3-66
FONT8 ............................................................................................................................................................................ 3-66
FONT→........................................................................................................................................................................... 3-67
→FONT........................................................................................................................................................................... 3-67
FOR ................................................................................................................................................................................. 3-67
FOURIER ....................................................................................................................................................................... 3-68
FP .................................................................................................................................................................................... 3-68
FREE............................................................................................................................................................................... 3-68
FREEZE.......................................................................................................................................................................... 3-68
FROOTS......................................................................................................................................................................... 3-69
FS? .................................................................................................................................................................................. 3-69
FS?C ............................................................................................................................................................................... 3-69
FUNCTION..................................................................................................................................................................... 3-70
FXND............................................................................................................................................................................... 3-71
GAMMA .......................................................................................................................................................................... 3-71
GAUSS ........................................................................................................................................................................... 3-71
GBASIS........................................................................................................................................................................... 3-71
GCD................................................................................................................................................................................. 3-71
GCDMOD ....................................................................................................................................................................... 3-71
GET ................................................................................................................................................................................. 3-71
GETI ................................................................................................................................................................................ 3-72
GOR ................................................................................................................................................................................ 3-73
GRAD.............................................................................................................................................................................. 3-73
GRAMSCHMIDT ........................................................................................................................................................... 3-73
GREDUCE ..................................................................................................................................................................... 3-73
GRIDMAP....................................................................................................................................................................... 3-73
→GROB.......................................................................................................................................................................... 3-74
GROB.............................................................................................................................................................................. 3-74
GROBADD ..................................................................................................................................................................... 3-74
GXOR.............................................................................................................................................................................. 3-75
HADAMARD................................................................................................................................................................... 3-75
HALFTAN ....................................................................................................................................................................... 3-75
HALT ............................................................................................................................................................................... 3-75
HEAD .............................................................................................................................................................................. 3-75
HEADER→..................................................................................................................................................................... 3-76
→HEADER..................................................................................................................................................................... 3-76
HELP ............................................................................................................................................................................... 3-76
HERMITE ....................................................................................................................................................................... 3-76
HESS............................................................................................................................................................................... 3-76
HEX ................................................................................................................................................................................. 3-76
HILBERT......................................................................................................................................................................... 3-77
HISTOGRAM ................................................................................................................................................................. 3-77
HISTPLOT ...................................................................................................................................................................... 3-77
Contents - 6
HMS–...............................................................................................................................................................................3-78
HMS+ ..............................................................................................................................................................................3-78
HMS→.............................................................................................................................................................................3-79
→HMS.............................................................................................................................................................................3-79
HOME..............................................................................................................................................................................3-79
HORNER ........................................................................................................................................................................3-79
i.........................................................................................................................................................................................3-80
IABCUV...........................................................................................................................................................................3-80
IBASIS.............................................................................................................................................................................3-80
IBERNOULLI ..................................................................................................................................................................3-80
IBP ...................................................................................................................................................................................3-80
ICHINREM ......................................................................................................................................................................3-80
IDN...................................................................................................................................................................................3-80
IDIV2................................................................................................................................................................................3-81
IEGCD .............................................................................................................................................................................3-81
IF ......................................................................................................................................................................................3-81
IFERR..............................................................................................................................................................................3-81
IFFT .................................................................................................................................................................................3-82
IFT....................................................................................................................................................................................3-83
IFTE .................................................................................................................................................................................3-83
ILAP .................................................................................................................................................................................3-83
IM .....................................................................................................................................................................................3-83
IMAGE.............................................................................................................................................................................3-84
INCR ................................................................................................................................................................................3-84
INDEP..............................................................................................................................................................................3-84
INFORM ..........................................................................................................................................................................3-85
INPUT..............................................................................................................................................................................3-86
INT ...................................................................................................................................................................................3-86
INTEGER ........................................................................................................................................................................3-87
INTVX ..............................................................................................................................................................................3-87
INV ...................................................................................................................................................................................3-87
INVMOD..........................................................................................................................................................................3-87
IP......................................................................................................................................................................................3-87
IQUOT .............................................................................................................................................................................3-87
IREMAINDER.................................................................................................................................................................3-87
ISOL.................................................................................................................................................................................3-87
ISOM................................................................................................................................................................................3-88
ISPRIME? .......................................................................................................................................................................3-88
I→R..................................................................................................................................................................................3-88
JORDAN .........................................................................................................................................................................3-88
KER .................................................................................................................................................................................3-88
KERRM ...........................................................................................................................................................................3-88
KEY..................................................................................................................................................................................3-89
KEYEVAL........................................................................................................................................................................3-89
→KEYTIME ....................................................................................................................................................................3-89
KEYTIME→ ....................................................................................................................................................................3-89
KGET...............................................................................................................................................................................3-90
KILL .................................................................................................................................................................................3-90
LABEL .............................................................................................................................................................................3-90
LAGRANGE....................................................................................................................................................................3-90
LANGUAGE→................................................................................................................................................................3-91
→LANGUAGE................................................................................................................................................................3-91
LAP ..................................................................................................................................................................................3-91
LAPL ................................................................................................................................................................................3-91
LAST................................................................................................................................................................................3-91
LASTARG .......................................................................................................................................................................3-91
LCD→..............................................................................................................................................................................3-92
→LCD..............................................................................................................................................................................3-92
Contents - 7
LCM ................................................................................................................................................................................. 3-92
LCXM .............................................................................................................................................................................. 3-92
LDEC............................................................................................................................................................................... 3-92
LEGENDRE ................................................................................................................................................................... 3-92
LGCD .............................................................................................................................................................................. 3-92
LIBEVAL ......................................................................................................................................................................... 3-92
LIBS................................................................................................................................................................................. 3-93
lim .................................................................................................................................................................................... 3-93
LIMIT ............................................................................................................................................................................... 3-93
LIN ................................................................................................................................................................................... 3-93
LINE................................................................................................................................................................................. 3-93
ΣLINE .............................................................................................................................................................................. 3-93
LINFIT ............................................................................................................................................................................. 3-94
LININ ............................................................................................................................................................................... 3-94
LINSOLVE ...................................................................................................................................................................... 3-94
LIST→ ............................................................................................................................................................................. 3-94
→LIST ............................................................................................................................................................................. 3-94
∆LIST............................................................................................................................................................................... 3-95
ΠLIST .............................................................................................................................................................................. 3-95
ΣLIST............................................................................................................................................................................... 3-95
LN .................................................................................................................................................................................... 3-95
LNAME............................................................................................................................................................................ 3-96
LNCOLLECT .................................................................................................................................................................. 3-97
LNP1 ............................................................................................................................................................................... 3-97
LOCAL ............................................................................................................................................................................ 3-97
LOG ................................................................................................................................................................................. 3-97
LOGFIT ........................................................................................................................................................................... 3-98
LQ .................................................................................................................................................................................... 3-98
LR .................................................................................................................................................................................... 3-98
LSQ ................................................................................................................................................................................. 3-99
LU .................................................................................................................................................................................... 3-99
LVAR ............................................................................................................................................................................. 3-100
MAD............................................................................................................................................................................... 3-100
MAIN ............................................................................................................................................................................. 3-100
MANT ............................................................................................................................................................................ 3-100
MAP............................................................................................................................................................................... 3-100
↓MATCH....................................................................................................................................................................... 3-100
↑MATCH....................................................................................................................................................................... 3-101
MATHS ......................................................................................................................................................................... 3-101
MATR ............................................................................................................................................................................ 3-101
MAX............................................................................................................................................................................... 3-101
MAXR............................................................................................................................................................................ 3-102
MAXΣ ............................................................................................................................................................................ 3-102
MCALC ......................................................................................................................................................................... 3-102
MEAN............................................................................................................................................................................ 3-103
MEM .............................................................................................................................................................................. 3-103
MENU............................................................................................................................................................................ 3-103
MENUXY ...................................................................................................................................................................... 3-104
MERGE......................................................................................................................................................................... 3-104
MIN ................................................................................................................................................................................ 3-104
MINEHUNT .................................................................................................................................................................. 3-104
MINIFONT→ ................................................................................................................................................................ 3-105
→MINIFONT ................................................................................................................................................................ 3-105
MINIT............................................................................................................................................................................. 3-105
MINR ............................................................................................................................................................................. 3-106
MINΣ.............................................................................................................................................................................. 3-106
MITM ............................................................................................................................................................................. 3-106
MKISOM ....................................................................................................................................................................... 3-106
Contents - 8
MOD ..............................................................................................................................................................................3-106
MODSTO ......................................................................................................................................................................3-107
MODULAR....................................................................................................................................................................3-107
MROOT.........................................................................................................................................................................3-107
MSGBOX ......................................................................................................................................................................3-107
MSLV.............................................................................................................................................................................3-107
MSOLVR.......................................................................................................................................................................3-107
MULTMOD....................................................................................................................................................................3-108
MUSER .........................................................................................................................................................................3-108
→NDISP........................................................................................................................................................................3-108
NDIST............................................................................................................................................................................3-108
NDUPN .........................................................................................................................................................................3-109
NEG ...............................................................................................................................................................................3-109
NEWOB.........................................................................................................................................................................3-109
NEXT .............................................................................................................................................................................3-110
NEXTPRIME ................................................................................................................................................................3-110
NIP .................................................................................................................................................................................3-110
NOT ...............................................................................................................................................................................3-110
NOVAL ..........................................................................................................................................................................3-111
NΣ ..................................................................................................................................................................................3-111
NSUB.............................................................................................................................................................................3-111
→NUM...........................................................................................................................................................................3-111
NUM...............................................................................................................................................................................3-112
NUMX ............................................................................................................................................................................3-112
NUMY ............................................................................................................................................................................3-112
OBJ→ ............................................................................................................................................................................3-113
OCT ...............................................................................................................................................................................3-113
OFF................................................................................................................................................................................3-113
OLDPRT........................................................................................................................................................................3-114
OPENIO ........................................................................................................................................................................3-114
OR..................................................................................................................................................................................3-114
ORDER .........................................................................................................................................................................3-115
OVER ............................................................................................................................................................................3-115
P2C ................................................................................................................................................................................3-115
PA2B2 ...........................................................................................................................................................................3-115
PARAMETRIC..............................................................................................................................................................3-116
PARITY .........................................................................................................................................................................3-116
PARSURFACE ............................................................................................................................................................3-117
PARTFRAC ..................................................................................................................................................................3-118
PATH .............................................................................................................................................................................3-118
PCAR.............................................................................................................................................................................3-118
PCOEF ..........................................................................................................................................................................3-118
PCONTOUR.................................................................................................................................................................3-118
PCOV ............................................................................................................................................................................3-119
PDIM..............................................................................................................................................................................3-119
PERM ............................................................................................................................................................................3-120
PEVAL...........................................................................................................................................................................3-120
PGDIR ...........................................................................................................................................................................3-120
PICK ..............................................................................................................................................................................3-121
PICK3 ............................................................................................................................................................................3-121
PICT...............................................................................................................................................................................3-121
PICTURE ......................................................................................................................................................................3-121
PINIT..............................................................................................................................................................................3-122
PIX? ...............................................................................................................................................................................3-122
PIXOFF .........................................................................................................................................................................3-122
PIXON ...........................................................................................................................................................................3-122
PKT ................................................................................................................................................................................3-122
PLOT .............................................................................................................................................................................3-123
Contents - 9
PLOTADD..................................................................................................................................................................... 3-123
PMAX ............................................................................................................................................................................ 3-123
PMIN ............................................................................................................................................................................. 3-123
PMINI ............................................................................................................................................................................ 3-124
POLAR.......................................................................................................................................................................... 3-124
POLYNOMIAL.............................................................................................................................................................. 3-125
POP ............................................................................................................................................................................... 3-125
POS ............................................................................................................................................................................... 3-125
POTENTIAL ................................................................................................................................................................. 3-125
POWEXPAND.............................................................................................................................................................. 3-125
POWMOD..................................................................................................................................................................... 3-125
PR1................................................................................................................................................................................ 3-125
PREDV.......................................................................................................................................................................... 3-126
PREDX.......................................................................................................................................................................... 3-126
PREDY.......................................................................................................................................................................... 3-127
PREVAL........................................................................................................................................................................ 3-127
PREVPRIME ................................................................................................................................................................ 3-127
PRLCD.......................................................................................................................................................................... 3-128
PROMPT ...................................................................................................................................................................... 3-128
PROMPTSTO .............................................................................................................................................................. 3-128
PROOT ......................................................................................................................................................................... 3-128
PROPFRAC ................................................................................................................................................................. 3-129
PRST............................................................................................................................................................................. 3-129
PRSTC.......................................................................................................................................................................... 3-129
PRVAR.......................................................................................................................................................................... 3-129
PSDEV .......................................................................................................................................................................... 3-130
PSI ................................................................................................................................................................................. 3-130
Psi.................................................................................................................................................................................. 3-130
PTAYL........................................................................................................................................................................... 3-130
PURGE ......................................................................................................................................................................... 3-131
PUSH ............................................................................................................................................................................ 3-131
PUT ............................................................................................................................................................................... 3-131
PUTI .............................................................................................................................................................................. 3-132
PVAR............................................................................................................................................................................. 3-133
PVARS.......................................................................................................................................................................... 3-133
PVIEW........................................................................................................................................................................... 3-134
PWRFIT ........................................................................................................................................................................ 3-134
PX→C ........................................................................................................................................................................... 3-134
→Q ................................................................................................................................................................................ 3-135
→Qπ .............................................................................................................................................................................. 3-135
qr.................................................................................................................................................................................... 3-135
QR ................................................................................................................................................................................. 3-136
QUAD............................................................................................................................................................................ 3-136
QUOT............................................................................................................................................................................ 3-136
QUOTE ......................................................................................................................................................................... 3-136
QXA ............................................................................................................................................................................... 3-137
RAD ............................................................................................................................................................................... 3-137
RAND ............................................................................................................................................................................ 3-137
RANK ............................................................................................................................................................................ 3-137
RANM............................................................................................................................................................................ 3-138
RATIO ........................................................................................................................................................................... 3-138
RCEQ............................................................................................................................................................................ 3-139
RCI................................................................................................................................................................................. 3-139
RCIJ............................................................................................................................................................................... 3-139
RCL ............................................................................................................................................................................... 3-139
RCLALARM.................................................................................................................................................................. 3-140
RCLF ............................................................................................................................................................................. 3-140
RCLKEYS..................................................................................................................................................................... 3-141
Contents - 10
RCLMENU ....................................................................................................................................................................3-141
RCLVX ..........................................................................................................................................................................3-141
RCLΣ .............................................................................................................................................................................3-141
RCWS ...........................................................................................................................................................................3-142
RDM...............................................................................................................................................................................3-142
RDZ ...............................................................................................................................................................................3-142
RE ..................................................................................................................................................................................3-143
RECN ............................................................................................................................................................................3-143
RECT.............................................................................................................................................................................3-143
RECV.............................................................................................................................................................................3-144
REF................................................................................................................................................................................3-144
REMAINDER................................................................................................................................................................3-144
RENAME.......................................................................................................................................................................3-144
REORDER....................................................................................................................................................................3-144
REPEAT........................................................................................................................................................................3-144
REPL .............................................................................................................................................................................3-144
RES ...............................................................................................................................................................................3-145
RESTORE ....................................................................................................................................................................3-146
RESULTANT ................................................................................................................................................................3-146
REVLIST .......................................................................................................................................................................3-146
REWRITE .....................................................................................................................................................................3-147
RISCH ...........................................................................................................................................................................3-147
RKF................................................................................................................................................................................3-147
RKFERR .......................................................................................................................................................................3-147
RKFSTEP .....................................................................................................................................................................3-148
RL...................................................................................................................................................................................3-148
RLB................................................................................................................................................................................3-148
RND ...............................................................................................................................................................................3-149
RNRM............................................................................................................................................................................3-149
ROLL .............................................................................................................................................................................3-150
ROLLD ..........................................................................................................................................................................3-150
ROMUPLOAD ..............................................................................................................................................................3-150
ROOT ............................................................................................................................................................................3-150
ROT ...............................................................................................................................................................................3-151
ROW–............................................................................................................................................................................3-151
ROW+............................................................................................................................................................................3-151
ROW→ ..........................................................................................................................................................................3-151
→ROW ..........................................................................................................................................................................3-152
RPL>..............................................................................................................................................................................3-152
RR..................................................................................................................................................................................3-152
RRB ...............................................................................................................................................................................3-153
rref..................................................................................................................................................................................3-153
RREF.............................................................................................................................................................................3-153
RREFMOD....................................................................................................................................................................3-153
RRK ...............................................................................................................................................................................3-153
RRKSTEP.....................................................................................................................................................................3-154
RSBERR .......................................................................................................................................................................3-155
RSD ...............................................................................................................................................................................3-155
RSWP............................................................................................................................................................................3-156
RULES ..........................................................................................................................................................................3-156
R→B ..............................................................................................................................................................................3-156
R→C ..............................................................................................................................................................................3-156
R→D ..............................................................................................................................................................................3-157
R→I................................................................................................................................................................................3-157
SAME ............................................................................................................................................................................3-157
SBRK.............................................................................................................................................................................3-157
SCALE...........................................................................................................................................................................3-158
SCALEH........................................................................................................................................................................3-158
Contents - 11
SCALEW....................................................................................................................................................................... 3-158
SCATRPLOT................................................................................................................................................................ 3-158
SCATTER..................................................................................................................................................................... 3-159
SCHUR ......................................................................................................................................................................... 3-159
SCI................................................................................................................................................................................. 3-160
SCLΣ ............................................................................................................................................................................. 3-160
SCONJ.......................................................................................................................................................................... 3-160
SCROLL ....................................................................................................................................................................... 3-160
SDEV............................................................................................................................................................................. 3-161
SEND ............................................................................................................................................................................ 3-161
SEQ ............................................................................................................................................................................... 3-161
SERIES......................................................................................................................................................................... 3-162
SERVER ....................................................................................................................................................................... 3-162
SEVAL........................................................................................................................................................................... 3-162
SF .................................................................................................................................................................................. 3-162
SHOW ........................................................................................................................................................................... 3-162
SIDENS......................................................................................................................................................................... 3-163
SIGMA........................................................................................................................................................................... 3-163
SIGMAVX ..................................................................................................................................................................... 3-163
SIGN.............................................................................................................................................................................. 3-163
SIGNTAB ...................................................................................................................................................................... 3-164
SIMP2 ........................................................................................................................................................................... 3-164
SIMPLIFY ..................................................................................................................................................................... 3-164
SIN................................................................................................................................................................................. 3-164
SINCOS ........................................................................................................................................................................ 3-164
SINH.............................................................................................................................................................................. 3-164
SINV .............................................................................................................................................................................. 3-165
SIZE............................................................................................................................................................................... 3-165
SL................................................................................................................................................................................... 3-165
SLB................................................................................................................................................................................ 3-166
SLOPEFIELD............................................................................................................................................................... 3-166
SNEG ............................................................................................................................................................................ 3-167
SNRM............................................................................................................................................................................ 3-167
SOLVE .......................................................................................................................................................................... 3-167
SOLVEQN .................................................................................................................................................................... 3-167
SOLVER ....................................................................................................................................................................... 3-168
SOLVEVX..................................................................................................................................................................... 3-168
SORT ............................................................................................................................................................................ 3-168
SPHERE ....................................................................................................................................................................... 3-168
SQ.................................................................................................................................................................................. 3-168
SR.................................................................................................................................................................................. 3-169
SRAD ............................................................................................................................................................................ 3-169
SRB ............................................................................................................................................................................... 3-169
SRECV.......................................................................................................................................................................... 3-169
SREPL .......................................................................................................................................................................... 3-170
START .......................................................................................................................................................................... 3-170
STD ............................................................................................................................................................................... 3-171
STEP ............................................................................................................................................................................. 3-172
STEQ............................................................................................................................................................................. 3-172
STIME ........................................................................................................................................................................... 3-172
STO ............................................................................................................................................................................... 3-172
STOALARM.................................................................................................................................................................. 3-173
STOF............................................................................................................................................................................. 3-173
STOKEYS..................................................................................................................................................................... 3-174
STORE.......................................................................................................................................................................... 3-174
STOVX.......................................................................................................................................................................... 3-174
STO+............................................................................................................................................................................. 3-174
STO– ............................................................................................................................................................................. 3-174
STO*.............................................................................................................................................................................. 3-175
Contents - 12
STO/ ..............................................................................................................................................................................3-175
STOΣ .............................................................................................................................................................................3-176
STR→............................................................................................................................................................................3-176
→STR............................................................................................................................................................................3-176
STREAM .......................................................................................................................................................................3-176
STURM..........................................................................................................................................................................3-177
STURMAB ....................................................................................................................................................................3-177
STWS ............................................................................................................................................................................3-177
SUB ...............................................................................................................................................................................3-177
SUBST ..........................................................................................................................................................................3-178
SUBTMOD....................................................................................................................................................................3-178
SVD ...............................................................................................................................................................................3-178
SVL ................................................................................................................................................................................3-178
SWAP ............................................................................................................................................................................3-179
SYSEVAL......................................................................................................................................................................3-179
SYLVESTER ................................................................................................................................................................3-179
SYST2MAT...................................................................................................................................................................3-179
%T..................................................................................................................................................................................3-179
TABVAL ........................................................................................................................................................................3-180
TABVAR........................................................................................................................................................................3-180
→TAG............................................................................................................................................................................3-180
TAIL ...............................................................................................................................................................................3-180
TAN................................................................................................................................................................................3-180
TAN2CS2......................................................................................................................................................................3-181
TAN2SC ........................................................................................................................................................................3-181
TAN2SC2......................................................................................................................................................................3-181
TANH.............................................................................................................................................................................3-181
TAYLOR0......................................................................................................................................................................3-181
TAYLR...........................................................................................................................................................................3-181
TCHEBYCHEFF ..........................................................................................................................................................3-182
TCOLLECT...................................................................................................................................................................3-182
TDELTA ........................................................................................................................................................................3-182
TESTS...........................................................................................................................................................................3-182
TEVAL ...........................................................................................................................................................................3-182
TEXPAND.....................................................................................................................................................................3-183
TEXT..............................................................................................................................................................................3-183
THEN.............................................................................................................................................................................3-183
TICKS ............................................................................................................................................................................3-183
TIME ..............................................................................................................................................................................3-183
→TIME ..........................................................................................................................................................................3-183
TINC ..............................................................................................................................................................................3-184
TLIN ...............................................................................................................................................................................3-184
TLINE ............................................................................................................................................................................3-184
TMENU..........................................................................................................................................................................3-184
TOT................................................................................................................................................................................3-185
TRACE ..........................................................................................................................................................................3-185
TRAN.............................................................................................................................................................................3-185
TRANSIO ......................................................................................................................................................................3-185
TRIG ..............................................................................................................................................................................3-186
TRIGCOS......................................................................................................................................................................3-186
TRIGO ...........................................................................................................................................................................3-186
TRIGSIN........................................................................................................................................................................3-186
TRIGTAN ......................................................................................................................................................................3-186
TRN ...............................................................................................................................................................................3-186
TRNC.............................................................................................................................................................................3-186
TRUNC..........................................................................................................................................................................3-187
TRUTH ..........................................................................................................................................................................3-187
TSIMP............................................................................................................................................................................3-188
Contents - 13
TSTR ............................................................................................................................................................................. 3-188
TVARS .......................................................................................................................................................................... 3-188
TVM ............................................................................................................................................................................... 3-188
TVMBEG....................................................................................................................................................................... 3-189
TVMEND....................................................................................................................................................................... 3-189
TVMROOT ................................................................................................................................................................... 3-189
TYPE ............................................................................................................................................................................. 3-189
UBASE .......................................................................................................................................................................... 3-190
UFACT .......................................................................................................................................................................... 3-190
UFL1→MINIF............................................................................................................................................................... 3-191
UNASSIGN................................................................................................................................................................... 3-191
UNASSUME................................................................................................................................................................. 3-191
UNBIND ........................................................................................................................................................................ 3-191
→UNIT .......................................................................................................................................................................... 3-191
UNPICK ........................................................................................................................................................................ 3-191
UNROT ......................................................................................................................................................................... 3-191
UNTIL............................................................................................................................................................................ 3-192
UPDIR ........................................................................................................................................................................... 3-192
UTPC............................................................................................................................................................................. 3-192
UTPF ............................................................................................................................................................................. 3-192
UTPN............................................................................................................................................................................. 3-193
UTPT ............................................................................................................................................................................. 3-193
UVAL ............................................................................................................................................................................. 3-194
V→................................................................................................................................................................................. 3-194
→V2............................................................................................................................................................................... 3-195
→V3............................................................................................................................................................................... 3-195
VANDERMONDE ........................................................................................................................................................ 3-195
VAR ............................................................................................................................................................................... 3-196
VARS............................................................................................................................................................................. 3-196
VER ............................................................................................................................................................................... 3-196
VERSION ..................................................................................................................................................................... 3-196
VISIT ............................................................................................................................................................................. 3-196
VISITB........................................................................................................................................................................... 3-197
VPOTENTIAL............................................................................................................................................................... 3-197
VTYPE .......................................................................................................................................................................... 3-197
WAIT ............................................................................................................................................................................. 3-197
WHILE........................................................................................................................................................................... 3-198
WIREFRAME ............................................................................................................................................................... 3-198
WSLOG......................................................................................................................................................................... 3-199
ΣX .................................................................................................................................................................................. 3-200
ΣX2 ................................................................................................................................................................................ 3-200
XCOL............................................................................................................................................................................. 3-201
XGET............................................................................................................................................................................. 3-201
XMIT.............................................................................................................................................................................. 3-201
XNUM............................................................................................................................................................................ 3-202
XOR............................................................................................................................................................................... 3-202
XPON ............................................................................................................................................................................ 3-202
XPUT............................................................................................................................................................................. 3-203
XQ.................................................................................................................................................................................. 3-203
XRECV.......................................................................................................................................................................... 3-203
XRNG............................................................................................................................................................................ 3-203
XROOT ......................................................................................................................................................................... 3-204
XSEND.......................................................................................................................................................................... 3-204
XSERV.......................................................................................................................................................................... 3-205
XVOL............................................................................................................................................................................. 3-205
XXRNG ......................................................................................................................................................................... 3-205
ΣXY................................................................................................................................................................................ 3-205
ΣY .................................................................................................................................................................................. 3-206
Contents - 14
ΣY2 ................................................................................................................................................................................3-206
YCOL.............................................................................................................................................................................3-206
YRNG ............................................................................................................................................................................3-206
YSLICE..........................................................................................................................................................................3-207
YVOL .............................................................................................................................................................................3-207
YYRNG..........................................................................................................................................................................3-208
ZEROS ..........................................................................................................................................................................3-208
ZFACTOR.....................................................................................................................................................................3-208
ZVOL .............................................................................................................................................................................3-208
^ (Power) ...................................................................................................................................................................3-209
|
(Where) ..................................................................................................................................................................3-209
√
(Square Root) ......................................................................................................................................................3-210
∫
(Integrate) ..............................................................................................................................................................3-211
?
(Undefined) ..........................................................................................................................................................3-212
∞
(Infinity).............................................................................................................................................................3-212
Σ
(Summation) ........................................................................................................................................................3-212
Σ+
(Sigma Plus) ....................................................................................................................................................3-212
Σ–
(Sigma Minus) .................................................................................................................................................3-213
π (Pi) ..........................................................................................................................................................................3-213
∂
(Derivative) ...........................................................................................................................................................3-213
!
(Factorial)...............................................................................................................................................................3-214
% (Percent)...............................................................................................................................................................3-214
_
(Unit attachment) ................................................................................................................................................3-215
« » (Program delimeters)......................................................................................................................................3-215
<
(Less than) ...........................................................................................................................................................3-215
≤ (Less than or Equal).............................................................................................................................................3-216
>
(Greater than) ......................................................................................................................................................3-217
≥ (Greater than or Equal)........................................................................................................................................3-218
≠ (Not equal).............................................................................................................................................................3-219
* (Multiply) ................................................................................................................................................................3-219
+
(Add) .....................................................................................................................................................................3-220
– (Subtract) ...............................................................................................................................................................3-222
/
(Divide)...................................................................................................................................................................3-223
=
(Equal) ..................................................................................................................................................................3-223
==
(Logical Equality) ............................................................................................................................................3-224
! (Store) ....................................................................................................................................................................3-225
→ (Create Local)......................................................................................................................................................3-225
4. Computer Algebra Commands .............................................................................................................................................. 4-1
Introduction ........................................................................................................................................................................4-1
CAS Operations .................................................................................................................................................................4-1
CAS Settings ......................................................................................................................................................................4-2
Selecting CAS Settings ............................................................................................................................................... 4-2
The CAS directory, CASDIR...................................................................................................................................... 4-2
Points to note when choosing settings ........................................................................................................................ 4-3
Using the CAS....................................................................................................................................................................4-4
Examples and Help ..................................................................................................................................................... 4-4
Compatibility with Other Calculators ......................................................................................................................... 4-4
Extending the CAS...................................................................................................................................................... 4-4
Dealing with unexpected CAS results or messages .................................................................................................... 4-4
ABCUV ............................................................................................................................................................................4-12
ACOS2S..........................................................................................................................................................................4-12
ADDTMOD......................................................................................................................................................................4-12
ADDTOREAL .................................................................................................................................................................4-13
ALGB ...............................................................................................................................................................................4-13
ARIT.................................................................................................................................................................................4-13
ASIN2C ...........................................................................................................................................................................4-14
ASIN2T............................................................................................................................................................................4-14
ASSUME.........................................................................................................................................................................4-14
Contents - 15
ATAN2S.......................................................................................................................................................................... 4-15
AUGMENT ..................................................................................................................................................................... 4-15
AXL.................................................................................................................................................................................. 4-15
AXM................................................................................................................................................................................. 4-16
AXQ ................................................................................................................................................................................. 4-16
BASIS.............................................................................................................................................................................. 4-16
C2P.................................................................................................................................................................................. 4-17
CASCFG......................................................................................................................................................................... 4-17
CASCMD ........................................................................................................................................................................ 4-17
CHINREM....................................................................................................................................................................... 4-17
CHOLESKY.................................................................................................................................................................... 4-18
CIRC................................................................................................................................................................................ 4-18
COLLECT ....................................................................................................................................................................... 4-19
CONSTANTS................................................................................................................................................................. 4-19
CURL............................................................................................................................................................................... 4-19
CYCLOTOMIC............................................................................................................................................................... 4-20
DEDICACE..................................................................................................................................................................... 4-20
DEF ................................................................................................................................................................................. 4-20
DEGREE......................................................................................................................................................................... 4-21
DERIV ............................................................................................................................................................................. 4-21
DERVX............................................................................................................................................................................ 4-21
DESOLVE....................................................................................................................................................................... 4-22
DIAGMAP ....................................................................................................................................................................... 4-22
DIFF................................................................................................................................................................................. 4-23
DISTRIB.......................................................................................................................................................................... 4-23
DIV................................................................................................................................................................................... 4-23
DIV2................................................................................................................................................................................. 4-23
DIV2MOD ....................................................................................................................................................................... 4-24
DIVIS ............................................................................................................................................................................... 4-24
DIVMOD ......................................................................................................................................................................... 4-25
DIVPC ............................................................................................................................................................................. 4-25
DOMAIN ......................................................................................................................................................................... 4-25
DROITE .......................................................................................................................................................................... 4-26
dn ..................................................................................................................................................................................... 4-26
EGCD.............................................................................................................................................................................. 4-27
EPSX0............................................................................................................................................................................. 4-27
EULER ............................................................................................................................................................................ 4-28
EXLR ............................................................................................................................................................................... 4-28
EXP&LN.......................................................................................................................................................................... 4-28
EXP2HYP ....................................................................................................................................................................... 4-28
EXP2POW...................................................................................................................................................................... 4-29
EXPAND ......................................................................................................................................................................... 4-29
EXPANDMOD................................................................................................................................................................ 4-30
EXPLN ............................................................................................................................................................................ 4-30
FACTOR ......................................................................................................................................................................... 4-30
FACTORMOD................................................................................................................................................................ 4-31
FACTORS ...................................................................................................................................................................... 4-31
FCOEF............................................................................................................................................................................ 4-31
FDISTRIB ....................................................................................................................................................................... 4-32
FOURIER ....................................................................................................................................................................... 4-32
FROOTS......................................................................................................................................................................... 4-33
FXND............................................................................................................................................................................... 4-33
GAUSS ........................................................................................................................................................................... 4-33
GBASIS........................................................................................................................................................................... 4-34
GCD................................................................................................................................................................................. 4-34
GCDMOD ....................................................................................................................................................................... 4-35
GRAMSCHMIDT ........................................................................................................................................................... 4-35
GREDUCE ..................................................................................................................................................................... 4-35
HADAMARD................................................................................................................................................................... 4-36
Contents - 16
HALFTAN........................................................................................................................................................................4-36
HELP ...............................................................................................................................................................................4-36
HERMITE........................................................................................................................................................................4-37
HESS...............................................................................................................................................................................4-37
HILBERT.........................................................................................................................................................................4-37
HORNER ........................................................................................................................................................................4-38
IABCUV...........................................................................................................................................................................4-38
IBASIS.............................................................................................................................................................................4-38
IBERNOULLI ..................................................................................................................................................................4-39
IBP ...................................................................................................................................................................................4-39
ICHINREM ......................................................................................................................................................................4-40
IDIV2................................................................................................................................................................................4-40
IEGCD .............................................................................................................................................................................4-40
ILAP .................................................................................................................................................................................4-41
IMAGE.............................................................................................................................................................................4-41
INT ...................................................................................................................................................................................4-41
INTEGER ........................................................................................................................................................................4-42
INTVX ..............................................................................................................................................................................4-42
INVMOD..........................................................................................................................................................................4-42
IQUOT .............................................................................................................................................................................4-43
IREMAINDER.................................................................................................................................................................4-43
ISOM................................................................................................................................................................................4-43
ISPRIME? .......................................................................................................................................................................4-44
JORDAN .........................................................................................................................................................................4-44
KER .................................................................................................................................................................................4-45
LAGRANGE....................................................................................................................................................................4-45
LAP ..................................................................................................................................................................................4-45
LAPL ................................................................................................................................................................................4-46
LCM .................................................................................................................................................................................4-46
LCXM...............................................................................................................................................................................4-46
LDEC ...............................................................................................................................................................................4-47
LEGENDRE....................................................................................................................................................................4-47
LGCD...............................................................................................................................................................................4-48
LIMIT................................................................................................................................................................................4-48
lim.....................................................................................................................................................................................4-48
LIN ...................................................................................................................................................................................4-48
LINSOLVE ......................................................................................................................................................................4-49
LNAME ............................................................................................................................................................................4-49
LNCOLLECT ..................................................................................................................................................................4-49
LOCAL.............................................................................................................................................................................4-50
LVAR ...............................................................................................................................................................................4-50
MAD.................................................................................................................................................................................4-51
MAIN................................................................................................................................................................................4-51
MATHS............................................................................................................................................................................4-51
MATR ..............................................................................................................................................................................4-52
MENUXY.........................................................................................................................................................................4-52
MKISOM..........................................................................................................................................................................4-53
MODSTO ........................................................................................................................................................................4-53
MODULAR......................................................................................................................................................................4-53
MSLV...............................................................................................................................................................................4-54
MULTMOD......................................................................................................................................................................4-54
NEXTPRIME ..................................................................................................................................................................4-55
P2C ..................................................................................................................................................................................4-55
PA2B2 .............................................................................................................................................................................4-55
PARTFRAC ....................................................................................................................................................................4-56
PCAR...............................................................................................................................................................................4-56
PMINI...............................................................................................................................................................................4-56
POLYNOMIAL................................................................................................................................................................4-57
POTENTIAL....................................................................................................................................................................4-57
Contents - 17
POWEXPAND................................................................................................................................................................ 4-57
POWMOD....................................................................................................................................................................... 4-58
PREVAL.......................................................................................................................................................................... 4-58
PREVPRIME .................................................................................................................................................................. 4-58
PROPFRAC ................................................................................................................................................................... 4-59
PTAYL............................................................................................................................................................................. 4-59
QUOT.............................................................................................................................................................................. 4-59
QXA ................................................................................................................................................................................. 4-60
RCLVX ............................................................................................................................................................................ 4-60
REF ................................................................................................................................................................................. 4-60
REMAINDER.................................................................................................................................................................. 4-61
REORDER ..................................................................................................................................................................... 4-61
RESULTANT.................................................................................................................................................................. 4-61
REWRITE ....................................................................................................................................................................... 4-62
RISCH ............................................................................................................................................................................. 4-62
RREF............................................................................................................................................................................... 4-62
rref ................................................................................................................................................................................... 4-63
RREFMOD ..................................................................................................................................................................... 4-63
SERIES........................................................................................................................................................................... 4-64
SEVAL............................................................................................................................................................................. 4-64
SIGMA............................................................................................................................................................................. 4-65
SIGMAVX ....................................................................................................................................................................... 4-65
SIGNTAB ........................................................................................................................................................................ 4-65
SIMP2 ............................................................................................................................................................................. 4-66
SIMPLIFY ....................................................................................................................................................................... 4-66
SINCOS .......................................................................................................................................................................... 4-67
SOLVE ............................................................................................................................................................................ 4-67
SOLVEVX....................................................................................................................................................................... 4-68
STORE............................................................................................................................................................................ 4-68
STOVX............................................................................................................................................................................ 4-68
STURM ........................................................................................................................................................................... 4-69
STURMAB ...................................................................................................................................................................... 4-69
SUBST ............................................................................................................................................................................ 4-69
SUBTMOD ..................................................................................................................................................................... 4-70
SYLVESTER .................................................................................................................................................................. 4-70
SYST2MAT .................................................................................................................................................................... 4-71
TABVAL .......................................................................................................................................................................... 4-71
TABVAR ......................................................................................................................................................................... 4-71
TAN2CS2 ....................................................................................................................................................................... 4-72
TAN2SC.......................................................................................................................................................................... 4-72
TAN2SC2 ....................................................................................................................................................................... 4-73
TAYLOR0 ....................................................................................................................................................................... 4-73
TCHEBYCHEFF ............................................................................................................................................................ 4-73
TCOLLECT..................................................................................................................................................................... 4-74
TESTS............................................................................................................................................................................. 4-74
TEXPAND....................................................................................................................................................................... 4-74
TLIN................................................................................................................................................................................. 4-74
TRIG................................................................................................................................................................................ 4-75
TRIGCOS ....................................................................................................................................................................... 4-75
TRIGO............................................................................................................................................................................. 4-76
TRIGSIN ......................................................................................................................................................................... 4-76
TRIGTAN ........................................................................................................................................................................ 4-76
TRUNC ........................................................................................................................................................................... 4-77
TSIMP ............................................................................................................................................................................. 4-77
UNASSIGN..................................................................................................................................................................... 4-77
UNASSUME................................................................................................................................................................... 4-78
UNBIND .......................................................................................................................................................................... 4-78
VANDERMONDE .......................................................................................................................................................... 4-78
VER ................................................................................................................................................................................. 4-79
Contents - 18
VPOTENTIAL .................................................................................................................................................................4-79
XNUM ..............................................................................................................................................................................4-79
XQ ....................................................................................................................................................................................4-80
ZEROS ............................................................................................................................................................................4-80
? .......................................................................................................................................................................................4-81
∞.......................................................................................................................................................................................4-81
5. Equation Reference ............................................................................................................................................................... 5-1
Columns and Beams (1) .....................................................................................................................................................5-3
Elastic Buckling (1, 1) ................................................................................................................................................ 5-4
Eccentric Columns (1, 2)............................................................................................................................................. 5-4
Simple Deflection (1, 3).............................................................................................................................................. 5-5
Simple Slope (1, 4)...................................................................................................................................................... 5-5
Simple Moment (1, 5) ................................................................................................................................................. 5-6
Simple Shear (1, 6)...................................................................................................................................................... 5-6
Cantilever Deflection (1, 7)......................................................................................................................................... 5-7
Cantilever Slope (1, 8) ................................................................................................................................................ 5-7
Cantilever Moment (1, 9)............................................................................................................................................ 5-8
Cantilever Shear (1, 10) .............................................................................................................................................. 5-8
Electricity (2) .....................................................................................................................................................................5-9
Coulomb's Law (2, 1)................................................................................................................................................ 5-10
Ohm's Law and Power (2, 2)..................................................................................................................................... 5-10
Voltage Divider (2, 3) ............................................................................................................................................... 5-11
Current Divider (2, 4)................................................................................................................................................ 5-11
Wire Resistance (2, 5)............................................................................................................................................... 5-11
Series and Parallel R (2, 6)........................................................................................................................................ 5-12
Series and Parallel C (2, 7)........................................................................................................................................ 5-12
Series and Parallel L (2, 8)........................................................................................................................................ 5-13
Capacitive Energy (2, 9) ........................................................................................................................................... 5-13
Inductive Energy (2, 10) ........................................................................................................................................... 5-13
RLC Current Delay (2, 11) ....................................................................................................................................... 5-14
DC Capacitor Current (2, 12).................................................................................................................................... 5-14
Capacitor Charge (2, 13)........................................................................................................................................... 5-14
DC Inductor Voltage (2, 14) ..................................................................................................................................... 5-14
RC Transient (2, 15).................................................................................................................................................. 5-15
RL Transient (2, 16).................................................................................................................................................. 5-15
Resonant Frequency (2, 17) ...................................................................................................................................... 5-16
Plate Capacitor (2, 18) .............................................................................................................................................. 5-16
Cylindrical Capacitor (2,19)...................................................................................................................................... 5-16
Solenoid Inductance (2, 20) ...................................................................................................................................... 5-17
Toroid Inductance (2, 21).......................................................................................................................................... 5-17
Sinusoidal Voltage (2, 22) ........................................................................................................................................ 5-18
Sinusoidal Current (2, 23)......................................................................................................................................... 5-18
Fluids (3) ..........................................................................................................................................................................5-18
Pressure at Depth (3, 1)............................................................................................................................................. 5-19
Bernoulli Equation (3, 2) .......................................................................................................................................... 5-19
Flow with Losses (3, 3)............................................................................................................................................. 5-20
Flow in Full Pipes (3, 4)............................................................................................................................................ 5-21
Forces and Energy (4) ......................................................................................................................................................5-21
Linear Mechanics (4, 1) ............................................................................................................................................ 5-22
Angular Mechanics (4, 2).......................................................................................................................................... 5-23
Centripetal Force (4, 3) ............................................................................................................................................. 5-23
Hooke's Law (4, 4).................................................................................................................................................... 5-23
1D Elastic Collisions (4, 5) ....................................................................................................................................... 5-24
Drag Force (4, 6)....................................................................................................................................................... 5-24
Law of Gravitation (4, 7) .......................................................................................................................................... 5-24
Mass-Energy Relation (4, 8) ..................................................................................................................................... 5-24
Gases (5) ..........................................................................................................................................................................5-25
Ideal Gas Law (5, 1).................................................................................................................................................. 5-25
Ideal Gas State Change (5, 2).................................................................................................................................... 5-26
Contents - 19
Isothermal Expansion (5, 3)...................................................................................................................................... 5-26
Polytropic Processes (5, 4)........................................................................................................................................ 5-26
Isentropic Flow (5, 5) ............................................................................................................................................... 5-26
Real Gas Law (5, 6) .................................................................................................................................................. 5-27
Real Gas State Change (5, 7) .................................................................................................................................... 5-27
Kinetic Theory (5, 8) ................................................................................................................................................ 5-28
Heat Transfer (6).............................................................................................................................................................. 5-28
Heat Capacity (6, 1) .................................................................................................................................................. 5-29
Thermal Expansion (6, 2) ......................................................................................................................................... 5-29
Conduction (6, 3) ...................................................................................................................................................... 5-29
Convection (6, 4) ...................................................................................................................................................... 5-30
Conduction + Convection (6, 5) ............................................................................................................................... 5-30
Black Body Radiation (6, 6) ..................................................................................................................................... 5-31
Magnetism (7).................................................................................................................................................................. 5-31
Straight Wire (7, 1) ................................................................................................................................................... 5-32
Force between Wires (7, 2)....................................................................................................................................... 5-32
Magnetic (B) Field in Solenoid (7, 3)....................................................................................................................... 5-33
Magnetic (B) Field in Toroid (7, 4) .......................................................................................................................... 5-33
Motion (8) ........................................................................................................................................................................ 5-34
Linear Motion (8, 1) ................................................................................................................................................. 5-35
Object in Free Fall (8, 2)........................................................................................................................................... 5-35
Projectile Motion (8, 3)............................................................................................................................................. 5-35
Angular Motion (8, 4)............................................................................................................................................... 5-36
Circular Motion (8, 5)............................................................................................................................................... 5-36
Terminal Velocity (8, 6) ........................................................................................................................................... 5-36
Escape Velocity (8, 7)............................................................................................................................................... 5-36
Optics (9) ......................................................................................................................................................................... 5-37
Law of Refraction (9, 1) ........................................................................................................................................... 5-37
Critical Angle (9, 2) .................................................................................................................................................. 5-38
Brewster's Law (9, 3)................................................................................................................................................ 5-38
Spherical Reflection (9, 4) ........................................................................................................................................ 5-39
Spherical Refraction (9, 5)........................................................................................................................................ 5-39
Thin Lens (9, 6) ........................................................................................................................................................ 5-39
Oscillations (10)............................................................................................................................................................... 5-40
Mass-Spring System (10, 1)...................................................................................................................................... 5-41
Simple Pendulum (10, 2) .......................................................................................................................................... 5-41
Conical Pendulum (10, 3) ......................................................................................................................................... 5-42
Torsional Pendulum (10, 4) ...................................................................................................................................... 5-42
Simple Harmonic (10, 5) .......................................................................................................................................... 5-42
Plane Geometry (11) ........................................................................................................................................................ 5-43
Circle (11, 1)............................................................................................................................................................. 5-44
Ellipse (11, 2)............................................................................................................................................................ 5-44
Rectangle (11, 3)....................................................................................................................................................... 5-45
Regular Polygon (11, 4)............................................................................................................................................ 5-45
Circular Ring (11, 5)................................................................................................................................................. 5-46
Triangle (11, 6) ......................................................................................................................................................... 5-46
Solid Geometry (12) ........................................................................................................................................................ 5-47
Cone (12, 1) .............................................................................................................................................................. 5-47
Cylinder (12, 2)......................................................................................................................................................... 5-48
Parallelepiped (12, 3)................................................................................................................................................ 5-48
Sphere (12, 4) ........................................................................................................................................................... 5-49
Solid State Devices (13)................................................................................................................................................... 5-49
PN Step Junctions (13, 1) ......................................................................................................................................... 5-51
NMOS Transistors (13, 2) ........................................................................................................................................ 5-52
Bipolar Transistors (13, 3) ........................................................................................................................................ 5-53
JFETs (13, 4) ............................................................................................................................................................ 5-53
Stress Analysis (14) ......................................................................................................................................................... 5-54
Normal Stress (14, 1) ................................................................................................................................................ 5-55
Shear Stress (14, 2) ................................................................................................................................................... 5-56
Contents - 20
Stress on an Element (14, 3) ..................................................................................................................................... 5-56
Mohr's Circle (14, 4) ................................................................................................................................................. 5-57
Waves (15) .......................................................................................................................................................................5-57
Transverse Waves (15,1)........................................................................................................................................... 5-58
Longitudinal Waves (15, 2) ...................................................................................................................................... 5-58
Sound Waves (15, 3)................................................................................................................................................. 5-58
References ........................................................................................................................................................................5-59
6. The Development Library ..................................................................................................................................................... 6-1
Section 1 - Introduction......................................................................................................................................................6-1
Section 2 – The tools of the development library ..............................................................................................................6-1
APEEK...............................................................................................................................................................................6-1
PEEK..................................................................................................................................................................................6-1
POKE .................................................................................................................................................................................6-1
PEEKARM.........................................................................................................................................................................6-2
POKEARM ........................................................................................................................................................................6-2
A→.....................................................................................................................................................................................6-2
→A.....................................................................................................................................................................................6-2
→RAM...............................................................................................................................................................................6-2
A→H ..................................................................................................................................................................................6-2
H→A ..................................................................................................................................................................................6-2
CD→ ..................................................................................................................................................................................6-3
→CD ..................................................................................................................................................................................6-3
→H.....................................................................................................................................................................................6-3
H→.....................................................................................................................................................................................6-3
S→H...................................................................................................................................................................................6-3
H→S...................................................................................................................................................................................6-3
SREV .................................................................................................................................................................................6-3
MAKESTR.........................................................................................................................................................................6-4
SERIAL..............................................................................................................................................................................6-4
→S2....................................................................................................................................................................................6-4
XLIB~ ................................................................................................................................................................................6-4
CRC....................................................................................................................................................................................6-4
S~N ....................................................................................................................................................................................6-4
R~SB ..................................................................................................................................................................................6-5
SB~B ..................................................................................................................................................................................6-5
LR~R..................................................................................................................................................................................6-5
LC~C..................................................................................................................................................................................6-5
COMP→ ............................................................................................................................................................................6-5
→ALG................................................................................................................................................................................6-5
→PRG ................................................................................................................................................................................6-6
→LST.................................................................................................................................................................................6-6
Section 3 - CRLIB..............................................................................................................................................................6-6
Section 4 - ASM.................................................................................................................................................................6-8
Section 5 – Disassemblers................................................................................................................................................6-34
ASM→ .............................................................................................................................................................................6-34
ARM→.............................................................................................................................................................................6-35
Section 6 – The Entry Point Library: Extable ..................................................................................................................6-35
nop....................................................................................................................................................................................6-35
GETNAME ......................................................................................................................................................................6-35
GETADR..........................................................................................................................................................................6-36
GETNAMES ....................................................................................................................................................................6-36
A. Error and Status Messages................................................................................................................................................... A-1
B. Table of Units ...................................................................................................................................................................... B-1
C. System Flags........................................................................................................................................................................ C-1
D. Reserved Variables.............................................................................................................................................................. D-1
Contents of the Reserved Variables .................................................................................................................................. D-2
αENTER............................................................................................................................................................................ D-2
ALRMDAT ....................................................................................................................................................................... D-2
Contents - 21
βENTER............................................................................................................................................................................ D-3
CST ................................................................................................................................................................................... D-3
ENVSTACK ..................................................................................................................................................................... D-4
EQ ..................................................................................................................................................................................... D-4
EXITED ............................................................................................................................................................................ D-4
EXPR ................................................................................................................................................................................ D-4
IOPAR .............................................................................................................................................................................. D-4
MASD.INI ........................................................................................................................................................................ D-6
MHpar............................................................................................................................................................................... D-6
Mpar.................................................................................................................................................................................. D-6
n1, n2, … .......................................................................................................................................................................... D-6
Nmines .............................................................................................................................................................................. D-6
PPAR ................................................................................................................................................................................ D-6
PRTPAR ........................................................................................................................................................................... D-8
REALASSUME................................................................................................................................................................ D-8
STARTED ........................................................................................................................................................................ D-8
STARTEQW..................................................................................................................................................................... D-9
STARTERR ...................................................................................................................................................................... D-9
STARTOFF ...................................................................................................................................................................... D-9
STARTRECV ................................................................................................................................................................... D-9
STARTSEND ................................................................................................................................................................... D-9
STARTUP......................................................................................................................................................................... D-9
s1, s2, … ........................................................................................................................................................................... D-9
TOFF................................................................................................................................................................................. D-9
VPAR................................................................................................................................................................................ D-9
ZPAR .............................................................................................................................................................................. D-10
ΣDAT.............................................................................................................................................................................. D-10
ΣPAR .............................................................................................................................................................................. D-11
E. Technical Reference .............................................................................................................................................................E-1
Object Sizes .......................................................................................................................................................................E-1
Symbolic Integration Patterns............................................................................................................................................E-2
Trigonometric Expansions .................................................................................................................................................E-4
Source References..............................................................................................................................................................E-5
F. Parallel Processing with Lists ............................................................................................................................................... F-1
G. Keyboard Shortcuts............................................................................................................................................................. G-1
H. The Menu-Number Table.................................................................................................................................................... H-1
I. The Command Menu-Path Table............................................................................................................................................I-1
J. ASCII Character Codes and Translations...............................................................................................................................J-1
Index .................................................................................................................................................................................. Index-1
Contents - 22
1
1.RPL Programming
If you've used a calculator or computer before, you're probably familiar with the idea of programs. Generally
speaking, a program is something that gets the calculator or computer to do certain tasks for you -- more than a
built-in command might do. In the hp49g+/hp48gII, a program is an object that does the same thing.
Understanding Programming
An hp49g+/hp48gII program is an object with « » delimiters containing a sequence of numbers, commands,
and other objects you want to execute automatically to perform a task.
For example, a program that takes a number from the stack, finds its factorial, and divides the result by 2 would
look like this: « ! 2 / » or
«
!
2
/
»
The Contents of a Program
As mentioned above, a program contains a sequence of objects. As each object is processed in a program, the
action depends on the type of object, as summarized below.
Actions for Certain Objects in Programs
Object
Command
Action
Number
Executed.
Put on the stack.
Algebraic or `Algebraic`
Algebraic put on the stack.
String
Put on the stack.
List
Put on the stack.
Program
Put on the stack.
Global name (quoted)
Put on the stack.
Global name (unquoted)
!
!
Program executed.
Name evaluated.
!
Directory becomes current.
!
Other object put on the stack.
Local name (quoted)
Put on the stack.
Local name (unquoted)
Contents put on the stack
As you can see from this table, most types of objects are simply put on the stack — but built-in commands and
programs called by name cause execution. The following examples show the results of executing programs
containing different sequences of objects.
RPL Programming 1-1
Examples of Program Actions
Program
« 1 2 »
Results
2:
1:
« "Hello" {A B}»
2:
1:
"Hello"
{ A B }
« '1+2' »
1:
'1+2'
« '1+2' NUM»
1:
3
« « 1 2 + » »
1:
« 1 2 + »
« « 1 2 + » EVAL »
1:
3
1
2
Programs can also contain structures. A structure is a program segment with a defined organization. Two basic
kinds of structure are available:
Local variable structure. The  command defines local variable names and a corresponding algebraic or
program object that's evaluated using those variables.
! Branching structures. Structure words (like DO… UNTIL…END) define conditional or loop structures to
control the order of execution within a program.
!
A local variable structure has one of the following organizations inside a program:
«  name1 … namen ' algebraic ' »
«  name1 … namen « program » »
The " command removes n objects from the stack and stores them in the named local variables. The algebraic
or program object in the structure is automatically evaluated because it’s an element of the structure – even
though algebraic and program objects are put on the stack in other situations. Each time a local variable name
appears in the algebraic or program object, the variable’s contents are substituted.
So the following program takes two numbers from the stack and returns a numeric result:
«  a b 'ABS(a-b)' »
Calculations in a Program
Many calculations in programs take data from the stack. Two typical ways to manipulate stack data are:
Stack commands. Operate directly on the objects on the stack.
Local variable structures. Store the stack objects in temporary local variables, then use the variable names
to represent the data in the following algebraic or program object.
Numeric calculations provide convenient examples of these methods. The following programs use two numbers
from the stack to calculate the hypotenuse of a right triangle using the formula x 2 + y 2.
« SQ SWAP SQ + ƒ »
«  x y « x SQ y SQ + ƒ » »
«  x y 'ƒ(x^2+y^2)' »
The first program uses stack commands to manipulate the numbers on the stack – the calculation uses stack
syntax. The second program uses a local variable structure to store and retrieve the numbers – the calculation
uses stack syntax. The third program also uses a local variable structure — the calculation uses algebraic syntax.
Note that the underlying formula is most apparent in the third program. This third method is often the easiest to
write, read, and debug.
!
!
1-2 RPL Programming
Entering and Executing Programs
A program is an object – it occupies one level on the stack, and you can store it in a variable.
To enter a program:
1. Press @%.The PRG annunciator appears, indicating program-entry mode is active.
2. Enter the commands and other objects (with appropriate delimiters) in order for the operations you want the
program to execute.
! Press # to separate consecutive numbers.
! Press ™ to move past closing delimiters.
3. Optional: Press @ë (newline) to start a new line in the command line at any time.
4. Press ` to put the program on the stack.
In Program-entry mode (PRG annunciator on), command keys aren't executed -- they're entered in the command
line instead. Only nonprogrammable operations such as ƒ and J are executed.
Line breaks are discarded when you press `.
To enter commands and other objects in a program:
Press the keyboard or menu key for the command or object. All commands can also be selected from the
@µ list.
This guide assumes that Flag -117 is clear, so that you see menus rather than choose boxes wherever possible.
Also RPN mode should be set.
or
! Type the characters using the alpha keyboard.
Refer to the hp49g+/hp48gII User’s Guide for how to use the alpha keyboard.
In this guide an abbreviated convention is used whereby invocations of the alpha keyboard are not always
shown. In the next example we show:
OVOLK where the alpha "VOL" can be entered as shown:
O~~VOL ~K (assuming Flag -60 is clear).
!
To store or name a program:
1. Enter the program on the stack.
2. Enter the variable name (with ' delimiters) and press K.
!
You can choose descriptive names for programs. Here are some ideas of what the name can describe:
The calculation or action. Examples: SPH (spherical-cap volume), SORT (sort a list).
!
The input and output. Examples: X"FX (x to f (x)), RH"V (radius-and -height to volume).
!
The technique. Example: SPHLV (spherical-cap volume using local variables).
To execute a program:
Press J then the menu key for the program name.
or
! Enter the program name (with no delimiters) and press `.
or
! Put the program name in level 1 and press N.
or
! Put the program object in level 1 and press N.
!
RPL Programming 1-3
To stop an executing program:
!
Press −.
Example: Enter a program that takes a radius value from the stack and calculates the volume of a sphere of
radius r using
V=
4
π
3
r3
If you were going to calculate the volume manually after entering the radius on the stack, you might press these
keys:
3Q!ì*4`3/*@ï
Enter the same keystrokes in a program. (@ë just starts a new line.)
@%
3Q!ì*4#3/*
@ë @ï
Put the program on the stack.
`
Store the program in variable VOL. Then put a radius of 4 on the stack and run the VOL program.
OVOL K
4 J %VOL%
The program is
« 3 ^ œ * 4 3 / * NUM »
Example: Replace the program from the previous example with one that's easier to read. Enter a program that
uses a local variable structure to calculate the volume of a sphere. The program is
«  r '4/3*œ*r^3' NUM »
(You need to include " NUM because π causes a symbolic result, unless Flag -2 or Flag -3 is set)
Enter the program. (@ë just starts a new line.)
@%
@ér #
O4 /3 *!ì*
r Q3 ™@ë@ï
Put the program on the stack, store it in VOL, and calculate the volume for a radius of 4.
OVOLK
4 %VOL%
1-4 RPL Programming
Example: Enter a program SPH that calculates the volume of a spherical cap of height h within a sphere of
radius R using values stored in variables H and R.
1 2
V = --- πh ( 3r – h )
3
In this and following chapters on programming, “stack diagrams” show what arguments must be on the stack
before a program is executed and what results the program leaves on the stack. Here's the stack diagram for
SPH.
Level 1
"
Level 1
"
volume
The diagram indicates that SPH takes no arguments from the stack and returns the volume of the spherical cap
to level 1. (SPH assumes that you've stored the numerical value for the radius in variable R and the numerical
value for the height in variable H. These are global variables — they exist outside the program.)
Program listings are shown with program steps in the left column and associated comments in the right column.
Remember, you can either press the command keys or type in the command names to key in the program. In this
first listing, the keystrokes are also shown.
Program:
Keys:
Comments:
«
@%
Begins the program.
'1/3
O1 /3
Begins the algebraic expression
to calculate the volume.
*œ*H^2
*!ì Multiplies by πh2.
*H Q2
*(3*R-H)'
*!Ü Multiplies by 3r - h, completing
3 * R - the calculation and ending the
H ™™
expression.
NUM
@ï
»
`
OSPH K
Converts the expression with π to
a number.
Ends the program.
Puts the program on the stack.
Stores the program in variable
SPH.
RPL Programming 1-5
This is the program:
« '1/3*œ*H^2*(3*R-H)' NUM »
Now use SPH to calculate the volume of a spherical cap of radius
r = 10 and height h = 3.
First, store the data in the appropriate variables. Then select the VAR menu and execute the program. The
answer is returned to level 1 of the stack.
10 O R K
3OHK
J %SPH%
Viewing and Editing Programs
You view and edit programs the same way you view and edit other objects — using the command line.
To view or edit a program:
1. View the program:
! If the program is in level 1, press ˜ (or use the EDIT command).
! If the program is stored in a variable, use the Filer (!¡) to select the variable and press EDIT (‘),
or press J, then @ and the variable's menu key (a shortcut to recall a variable's contents to level 1),
followed by ˜. Alternatively, with the variable name in level 1 press „ ˜ (or use the EDITB, VISIT
or VISITB command).
2. Optional: Make changes.
3. Press ` to save any changes (or press − to discard changes) and return to the stack, or to Filer if you
used Filer to select the program.
Filer lets you change a stored program without having to do a store operation. From the stack you can change a
program and then store the new version in a different variable.
While you're editing a program, you may want to switch the command-line entry mode between Program-entry
mode (for editing most objects) and Algebraic/Program-entry mode (for editing algebraic objects). The PRG
and ALG annunciators indicate the current mode.
To switch between entry modes:
!
Press @Í.
Example: Edit SPH from the previous example so that it stores the number from level 1 into variable H and
the number from level 2 into variable R.
Select SPH from the soft keys.
J
@%SPH% ˜
Move the cursor past the first program delimiter and insert the new program steps.
™OH ™K
OR ™K
Save the edited version of SPH in the variable. Then, to verify that the changes were saved, view SPH in the
command line.
`J!%SPH%
1-6 RPL Programming
@%SPH% ˜
Press − to stop viewing.
Creating Programs on a Computer
It is convenient to create programs and other objects on a computer and then load them into the hp49g+/hp48gII.
If you are creating programs on a computer, you can include “comments” in the computer version of the
program.
To include a comment in a program:
Enclose the comment text between two @ characters.
or
! Enclose the comment text between one @ character and the end of the line.
!
Whenever the hp49g+/hp48gII processes text entered in the command line — either from keyboard entry or
transferred from a computer — it strips away the @ characters and the text they surround. However, @
characters are not affected if they're inside a string.
Using Local Variables
The program SPH in the previous example uses global variables for data storage and recall. There are
disadvantages to using global variables in programs:
After program execution, global variables that you no longer need to use must be purged if you want to clear
the VAR menu and free user memory.
! You must explicitly store data in global variables prior to program execution, or have the program execute
STO.
!
Local variables address the disadvantages of global variables in programs. Local variables are temporary
variables created by a program. They exist only while the program is being executed and cannot be used outside
the program. They never appear in the VAR menu. In addition, local variables are accessed faster than global
variables. (By convention, this manual uses lowercase names for local variables.) A compiled local variable is a
form of local variable that can be used outside of the program that creates it. See "Compiled Local Variables" on
page 1-10 for more information.
Creating Local Variables
In a program, a local variable structure creates local variables.
To enter a local variable structure in a program:
1. Enter the " command (press @é).
2. Enter one or more variable names.
3. Enter a defining procedure (an algebraic or program object) that uses the names.
«  name1 name2 … namen ' algebraic ' »
or
«  name1 name2 … namen « program » »
When the " command is executed in a program, n values are taken from the stack and assigned to variables
name1 name2, …. namen.
For example, if the stack looks like this:
RPL Programming 1-7
then
 a creates local variable a = 20.
 ab creates local variables a = 6 and b = 20.
 abc crates local variables a = 10, b = 6, and c = 20.
The defining procedure then uses the local variables to do calculations.
Local variable structures have these advantages:
!
The " command stores the values from the stack in the corresponding variables — you don't need to
explicitly execute STO.
!
Local variables automatically disappear when the defining procedure for which they are created has
completed execution. Consequently, local variables don't appear in the VAR menu, and they occupy user
memory only during program execution.
!
Local variables exist only within their defining procedure — different local variable structures can use the
same variable names without conflict.
Example: The following program SPHLV calculates the volume of a spherical cap using local variables. The
defining procedure is an algebraic expression.
Level 2
Level 1
"
Level 1
r
h
"
volume
Program:
Comments:
«
 r h
Creates local variables r and h for the radius of the
sphere and height of the cap.
'1/3*œ*h^2*(3*r-h)' Expresses the defining procedure. In this program,
the defining procedure for the local variable
structure is an algebraic expression.
NUM
Converts expression to a number.
»
OSPHLVK
Stores the program in variable SPHLV.
Now use SPHLV to calculate the volume of a spherical cap of radius r =10 and height h = 3. Enter the data on
the stack in the correct order, then execute the program.
10 `3
J%SPHLV%
Evaluating Local Names
Local names are evaluated differently from global names. When a global name is evaluated, the object stored in
the corresponding variable is itself evaluated. (You've seen how programs stored in global variables are
automatically evaluated when the name is evaluated.)
1-8 RPL Programming
When a local name is evaluated, the object stored in the corresponding variable is returned to the stack but is
not evaluated.When a local variable contains a number, the effect is identical to evaluation of a global name,
since putting a number on the stack is equivalent to evaluating it. However, if a local variable contains a
program, algebraic expression, or global variable name — and if you want it evaluated — the program should
execute EVAL after the object is put on the stack.
Defining the Scope of Local Variables
Local variables exist only inside the defining procedure.
Example: The following program excerpt illustrates the availability of local variables in nested defining
procedures (procedures within procedures). Because local variables a, b, and c already exist when the defining
procedure for local variables d, e, and f is executed, they're available for use in that procedure.
Program:
Comments:
«
.
.
.
No local variables are available.
 a b c
Defines local variables a, b, c.
«
a b + c +
 d e f
'a/(d*e+f)'
Local variables a, b, c are
available in this procedure.
Defines local variables d, e, f.
Local variables a, b, c and d, e, f
are available in this procedure.
a c / »
.
Only local variables a, b, c are
available.
No local variables are available.
.
.
»
RPL Programming 1-9
Example: In the following program excerpt, the defining procedure for local variables d, e, and f calls a
program that you previously created and stored in global variable P1.
Program:
Comments:
«
.
.
 a b c
«
a b + c +
 d e f
'P1+a/(d*e+f)'
Defines local variables d, e, f.
Local variables a, b, c and d, e, f
are available in this procedure.
The defining procedure executes
the program stored in variable P1.
a c / »
.
.
»
The six local variables are not available in program P1 because they didn't exist when you created P1. The
objects stored in the local variables are available to program P1 only if you put those objects on the stack for P1
to use or store those objects in global variables.
Conversely, program P1 can create its own local variable structure (with any names, such as a, c, and f, for
example) without conflicting with the local variables of the same name in the procedure that calls P1. It is
possible to create a special type of local variable that can be used in other programs or subroutines. This type of
local variable is called a compiled local variable.
Compiled Local Variables
Global variables use up memory, and local variables can't be used outside of the program they were created in.
Compiled local variables bridge the gap between these two variable types. To programs, compiled local
variables look like global variables, but to the calculator they act like local variables. This means you can create
a compiled local variable in a local variable structure, use it in any other program that is called within that
structure, and when the program finishes, the variable is gone.
Compiled local variables have a special naming convention: they must begin with a Í. For example,
«
 Íy
'IFTE(Íy<0,BELOW,ABOVE)'
»
The variable Íy is a compiled local variable that can be used in the two programs BELOW and ABOVE.
Creating User-Defined Functions as Programs
The defining procedure for a local variable structure can be either an algebraic or program object.
A program that consists solely of a local variable structure whose defining procedure is an algebraic expression
is a user-defined function.
1-10 RPL Programming
If a program begins with a local variable structure and has a program as the defining procedure, the complete
program acts like a user-defined function in two ways: it takes numeric or symbolic arguments, and takes those
arguments either from the stack or in algebraic syntax. However, it does not have a derivative. (The defining
program must, like algebraic defining procedures, return only one result to the stack.)
There's an advantage to using a program as the defining procedure for a local variable structure: The program
can contain commands not allowed in algebraic expressions. For example, loop structures are not allowed in
algebraic expressions.
Using Tests and Conditional Structures
You can use commands and branching structures that let programs ask questions and make decisions.
Comparison functions and logical functions test whether or not specified conditions exist. Conditional
structures and conditional commands use test results to make decisions.
Testing Conditions
A test is an algebraic or a command sequence that returns a test result to the stack. A test result is either true —
indicated by a value of 1. — or it is false — indicated by a value of 0..
To include a test in a program:
!
!
To use stack syntax, enter the two arguments, then enter the test command.
To use algebraic syntax, enter the test expression (with ' delimiters).
You often use test results in conditional structures to determine which clause of the structure to execute.
Conditional structures are described under Using Conditional Structures and Commands, p.1-13.
Example: Test whether or not X is less than Y. To use stack syntax, enter X Y <. To use algebraic syntax,
enter 'X<Y'. (For both cases, if X contains 5 and Y contains 10, then the test is true and 1. is returned to the
stack.)
Using Comparison Functions
Comparison functions compare two objects, using either stack syntax or algebraic syntax.
Comparison Functions
Key
Programmable
Command
Description
„° %TEST% (pages 1 and 2):
%$==$%
%%´%%
%#%<%%
%#%>%%
%#%»%%
#%%¼%%
##SAME##
==
≠
<
>
≤
≥
SAME
Tests equality of two objects.
Not equal.
Less than.
Greater than.
Less than or equal to.
Greater than or equal to.
Identical. Like = =, but doesn't allow a
comparison between the numerical value of
an algebraic (or name) and a number. Also
considers the wordsize of a binary integer.
RPL Programming 1-11
The comparison commands return 1. (true) or 0. (false) based on the comparison — or an expression that can
evaluate to 1. or 0.. The order of the comparison is “level 2 test level 1,” where test is the comparison function.
All comparison commands except SAME return the following:
!
If neither object is an algebraic or a name, returns 1. if the two objects are the same type and have the same
value, or 0. otherwise. For example, if 6 is stored in X, X 5 < puts 6 and 5 on the stack, then removes them
and returns 0.. (Lists and programs are considered to have same value if the objects they contain are identical.
For strings, “less than” means “alphabetically previous.”)
!
If one object is an algebraic (or name) and the other object is an algebraic (or name) or a number, returns an
expression that must be evaluated to get a test result based on numeric values. For example, if 6 is stored in X,
'X' 5 < returns 'X<5', then "NUM returns 0..
(Note that = = is used for comparisons, while = separates two sides of an equation.)
SAME returns 1. (true) if two objects are identical. For example, 'X+3' 4 SAME returns 0. regardless of the
value of X because the algebraic 'X+3' is not identical to the real number 4. Binary integers must have the
same wordsize and the same value to be identical. For all object types other than algebraics, names, and binary
integers, SAME works just like = =.
You can use any comparison function (except SAME) in an algebraic by putting it between its two arguments.
For example, if 6 is stored in X, 'X<5' NUM returns 0..
Using Logical Functions
Logical functions return a test result based on the outcomes of one or two previously executed tests. Note that
these four functions interpret any nonzero argument as a true result.
Logical Functions
Keys
Programmable
Command
Description
!°%TEST% L
%AND%
AND
Returns 1. (true) only if both
arguments are true (0. otherwise).
%OR%
OR
Returns 1. (true) if either or both
arguments are true (0. otherwise).
%XOR%
XOR
Returns 1. (true) if either argument,
but not both, is true (0. otherwise).
%NOT%
NOT
Returns 1. (true) if the argument is 0
(false); otherwise, returns 0. (false).
AND, OR, and XOR combine two test results. For example, if 4 is stored in Y, Y 8 < 5 AND returns 1.. First, Y
8 < returns 1. to the stack. AND removes 1. and 5 from the stack, interpreting both as true results, and returns 1.
to the stack.
NOT returns the logical inverse of a test result. For example, if 1 is stored in X and 2 is stored in Y, X Y < NOT
returns 0.
You can use AND, OR, and XOR in algebraics as infix functions. For example, '3<5 XOR 4>7' NUM
returns 1.
1-12 RPL Programming
You can use NOT as a prefix function in algebraics. For example, 'NOT Z‰4' NUM returns 0. if Z =2.
Testing Object Types
The TYPE command (!°%TEST% L %TYPE%) takes any object as its argument and returns the number
that identifies that object type. For example, "HELLO" TYPE returns 2, the value for a string object. See the
table of object types in chapter 3, in the TYPE command, to find hp49g+/hp48gII objects and their
corresponding type numbers.
Testing Linear Structure
The LININ command (!°%TEST% !«%LININ%) takes an algebraic equation on level 2 and a
variable on level 1 as arguments and returns 1. if the equation is linear for that variable, or 0. if it is not. For
example, 'H+Y^2' 'H' LININ returns 1. because the equation is structurally linear for H. See the LININ
command in chapter 3 for more information.
Using Conditional Structures and Commands
Conditional structures let a program make a decision based on the results of tests.
Conditional commands let you execute a true-clause or a false-clause (each of which are a single command or
object).
These conditional structures and commands are contained in the PRG BRCH menu (!°%BRCH%):
IF … THEN … END structure.
IF … THEN … ELSE … END structure.
! CASE … END structure.
! IFT (if-then) command.
! IFTE (if-then-else) function.
!
!
The IF … THEN … END Structure
The syntax for this structure is
« … IF test-clause THEN true-clause END … »
IF … THEN … END executes the sequence of commands in the true-clause only if the test-clause evaluates to
true. The test-clause can be a command sequence (for example, A B ‰) or an algebraic (for example,'A‰B').
If the test-clause is an algebraic, it's automatically evaluated to a number — you don’t need " NUM or EVAL.
IF begins the test-clause, which leaves a test result on the stack.
THEN removes the test result from the stack. If the value is nonzero, the true-clause is executed — otherwise,
program execution resumes following END. See "Conditional Examples" on page 1-15.
To enter IF … THEN … END in a program:
!
Press !°%BRCH% !%IF% .
The IFT Command
The IFT command takes two arguments: a test-result in level 2 and a true-clause object in level 1. If the testresult is true, the true-clause object is executed — otherwise, the two arguments are removed from the stack. See
"Conditional Examples" on page 1-15.
To enter IFT in a program:
! Press !°%BRCH% L!%IFT% .
RPL Programming 1-13
The IF … THEN … ELSE … END Structure
The syntax for this structure is
« … IF test-clause
THEN true-clause ELSE false-clause END … »
IF … THEN … ELSE … END executes either the true-clause sequence of commands if the true-clause is true,
or the false-clause sequence of commands if the true-clause is false. If the test-clause is an algebraic, it's
automatically evaluated to a number — you don't need "NUM or EVAL.
IF begins the test-clause, which leaves a test result on the stack. THEN removes the test result from the stack. If
the value is nonzero, the true-clause is executed — otherwise, the false-clause is executed. After the appropriate
clause is executed, execution resumes following END. See "Conditional Examples" on page 1-15.
To enter IF … THEN … ELSE … END in a program:
Press !°%BRCH% @%#IF#% .
!
The IFTE Function
The algebraic syntax for this function is 'IFTE( test, true-clause, false-clause)'
If test evaluates true, the true-clause algebraic is evaluated — otherwise, the false-clause algebraic is evaluated.
You can also use the IFTE function with stack syntax. It takes three arguments: a test-result in level 3, a trueclause object in level 2, and a false-clause object in level 1. See "Conditional Examples" on page 1-15.
To enter IFTE in a program or in an algebraic:
!
Press !°%BRCH% L!%IFTE% .
The CASE … END Structure
The syntax for this structure is
« … CASE
test-clause1 THEN true-clause1 END
test-clause2 THEN truet-clause2 END
...
test-clausen THEN true-clausen END
default-clause (optional)
END … »
The CASE … END structure lets you execute a series of test-clause commands, then execute the appropriate
true-clause sequence of commands. The first test that returns a true result causes execution of the corresponding
true-clause, ending the CASE … END structure. Optionally, you can include after the last test a default-clause
that's executed if all the tests evaluate to false. If a test-clause is an algebraic, it's automatically evaluated to a
number — you don't need "NUM or EVAL.
When CASE is executed, test-clause1 is evaluated. If the test is true, true-clause1 is executed, and execution
skips to END. If test-clause1 is false, execution proceeds to test-clause2. Execution within the CASE structure
continues until a true-clause is executed, or until all the test-clauses evaluate to false. If a default clause is
included, it's executed if all the test-clauses evaluate to false. See "Conditional Examples" below.
1-14 RPL Programming
To enter CASE … END in a program:
1. Press !°%BRCH% !%CASE% to enter CASE … THEN …END…END
2. For each additional test-clause, move the cursor after a test-clause END and press @%CASE% to enter THEN
… END.
Conditional Examples
These examples illustrate conditional structures in programs.
Example: One Conditional Action. The programs below test the value in level 1 — if the value is
positive, it's made negative. The first program uses a command sequence as the test-clause:
« DUP IF 0 > THEN NEG END »
The value on the stack must be duplicated because the > command removes two arguments from the stack (0.
and the copy of the value made by DUP).
The following version uses an algebraic as the test clause:
«  x « x IF 'x>0' THEN NEG END » »
The following version uses the IFT command:
« DUP 0 > « NEG » IFT »
Example: One Conditional Action. This program multiplies two numbers if both are nonzero.
Program:
Comments:
«
 x y
Creates local variables x and y containing
the two numbers from the stack.
«
IF
'xŠ0'
Starts the test-clause.
Tests one of the numbers and leaves a test
result on the stack. Tests the other
number, leaving another test result on the
stack. Tests whether both tests were true.
Ends the test-clause, starts the trueclause.
Multiplies the two numbers together only
if AND returns true.
'yŠ0'
AND
THEN
x y *
END
»
Ends the true-clause.
»
The following program accomplishes the same task as the previous program:
«  x y « IF 'x AND y' THEN x y * END » »
The test-clause 'x AND y' returns “true” if both numbers are nonzero.
The following version uses the IFT command:
«  x y « 'x AND y' 'x*y'IFT » »
Example: Two Conditional Actions. This program takes a value x from the stack and calculates (sin x) /x.
At x= 0 the division would error, so the program returns the limit value 1 in this case.
«  x « IF 'x‹0' THEN x SIN x / ELSE 1 END » »
The following version uses IFTE algebraic syntax:
RPL Programming 1-15
«  x 'IFTE(x‹0,SIN(x)/x,1)' »
Example: Two Conditional Actions. This program multiplies two numbers together if they're both
nonzero — otherwise, it returns the string “ZERO”.
Program:
Comments:
«
 n1 n2
Creates the local variables.
«
IF
'n1‹0 AND n2‹0'
THEN
n1 n2 *
ELSE
"ZERO"
END
Starts the defining procedure.
Starts the test clause.
Tests n1 and n2.
If both numbers are nonzero, multiplies the two values.
Otherwise,
returns the string ZERO.
Ends the conditional.
»
Ends the defining procedure.
»
Example: Two Conditional Actions. This program tests if two numbers on the stack have the same value.
If so, it drops one of the numbers and stores the other in variable V1 — otherwise, it stores the number from
level 1 in V1 and the number from level 2 in V2.
Program:
Comments:
«
IF
DUP2
SAME
THEN
DROP
'V1' STO
ELSE
'V1' STO
'V2' STO
END
For the test clause, copies the numbers in levels 1 and
2 and tests if they have the same value.
For the true clause, drops one of the numbers and
stores the other in V1.
For the false clause, stores the level 1 number in V1
and the level 2 number in V2.
Ends the conditional structure.
»
`
OTST K
Puts the program on the stack. Stores it in TST.
Enter the numbers 26 and 52, then execute TST to compare their values. Because the two numbers aren't equal,
the VAR menu now contains two new variables V1 and V2.
26 `52 J %TST%
Example: Multiple Conditional Actions. The following program stores the level 1 argument in a variable
if the argument is a string, list, or program.
1-16 RPL Programming
Program:
Comments:
«
 y
«
CASE
y TYPE
THEN y
END
y TYPE
THEN y
END
y TYPE
THEN y
END
END
»
Defines local variable y.
Starts the defining procedure.
2 SAME
'STR' STO
5 SAME
'LIST' STO
Starts the case structure.
Case 1: If the argument is a string, stores it in STR.
Case 2: If the argument is a list, stores it in LIST.
Case 3: If the argument is a program, stores it in
PROG.
8 SAME
'PROG' STO
Ends the case structure.
Ends the defining procedure.
»
Using Loop Structures
You can use loop structures to execute a part of a program repeatedly. To specify in advance how many times to
repeat the loop, use a definite loop. To use a test to determine whether or not to repeat the loop, use an indefinite
loop.
Loop structures let a program execute a sequence of commands several times. Loop structures are built with
commands — called structure words — that work only when used in proper combination with each other. These
loop structure commands are contained in the PRG BRCH menu (!° %BRCH%):
START… NEXT and START… STEP.
! FOR … NEXT and FOR…STEP
! DO … UNTIL …END.
! WHILE… REPEAT… END.
!
In addition, the Σ function provides an alternative to definite loop structures for summations.
Using Definite Loop Structures
Each of the two definite loop structures has two variations:
!
!
NEXT. The counter increases by 1 for each loop.
STEP. The counter increases or decreases by a specified amount for each loop.
The START … NEXT Structure
The syntax for this structure is
« … start finish START loop-clause NEXT… »
START … NEXT executes the loop-clause sequence of commands one time for each number in the range start
to finish. The loop-clause is always executed at least once.
RPL Programming 1-17
Syntax
Flowchart
Start
finish
1:Start
2:finish
START
counter=start
Store finish
loop-clause
Body of loop
counter = counter + 1
NEXT
Is
counter ≤ finish?
yes
no
START … NEXT Structure
START takes two numbers (start and finish) from the stack and stores them as the starting and ending values for
a loop counter. Then, the loop-clause is executed. NEXT increments the counter by 1 and tests to see if its value
is less than or equal to finish. If so, the loop-clause is executed again — otherwise, execution resumes following
NEXT.
To enter START … NEXT in a program:
!
Press !°%BRCH% !%START%.
Example: The following program creates a list containing 10 copies of the string "ABC":
« 1 10 START "ABC" NEXT 10 LIST »
The START … STEP Structure
The syntax for this structure is
« … start finish START loop-clause increment STEP … »
START … STEP executes the loop-clause sequence just like START … NEXT does — except that the program
specifies the increment value for the counter, rather than incrementing by 1. The loop-clause is always executed
at least once.
1-18 RPL Programming
Syntax
Flowchart
Start
finish
1:Start
2:finish
START
counter=start
Store finish
loop-clause
Body of loop
increment
1:increment
counter = counter +
increment
STEP
Is
counter ≤ finish?
yes
no
START … STEP Structure
START takes two numbers (start and finish) from the stack and stores them as the starting and ending values of
the loop counter. Then the loop-clause is executed. STEP takes the increment value from the stack and
increments the counter by that value. If the argument of STEP is an algebraic or a name, it's automatically
evaluated to a number.
The increment value can be positive or negative. If it's positive, the loop is executed again if the counter is less
than or equal to finish. If the increment value is negative, the loop is executed if the counter is greater than or
equal to finish. Otherwise, execution resumes following STEP. In the previous flowchart, the increment value is
positive.
To enter START … STEP in a program:
!
Press !° %BRCH% … %START%.
Example: The following program takes a number x from the stack and calculates the square of that number
several times (x/3 times):
« DUP  x « x 1 START x SQ -3 STEP » »
The FOR … NEXT Structure
The syntax for this structure is
« … start finish FOR counter loop-clause increment NEXT … »
FOR … NEXT executes the loop-clause program segment one time for each number in the range start to
finish, using local variable counter as the loop counter. You can use this variable in the loop-clause. The
loop-clause is always executed at least once.
RPL Programming 1-19
Syntax
Flowchart
Start
finish
1:Start
2:finish
FOR
counter=start
Store finish
loop-clause
Body of loop
counter = counter + 1
NEXT
Is
counter ≤ finish?
yes
no
FOR … NEXT Structure
FOR takes start and finish from the stack as the beginning and ending values for the loop counter, then creates
the local variable counter as a loop counter. Then the loop-clause is executed — counter can appear within the
loop-clause. NEXT increments counter by one, and then tests whether its value is less than or equal to finish. If
so, the loop-clause is repeated (with the new value of counter) — otherwise, execution resumes following
NEXT. When the loop is exited, counter is purged.
To enter FOR … NEXT in a program:
!
Press !°%BRCH% ! %FOR%.
Example: The following program places the squares of the integers 1 through 5 on the stack:
« 1 5 FOR j j SQ NEXT »
Example: The following program takes the value x from the stack and computes the integer powers i of x. For
example, when x =12 and start and finish are 3 and 5 respectively, the program returns 123, 124 and 125. It
requires as inputs start and finish in level 3 and 2, and x in level 1. ( x removes x from the stack, leaving start
and finish there as arguments for FOR.)
«  x « FOR n 'x^n' EVAL NEXT » »
The FOR … STEP Structure
The syntax for this structure is
« … start finish FOR counter loop-clause increment STEP … »
FOR … STEP executes the loop-clause sequence just like FOR … NEXT does — except that the program
specifies the increment value for counter, rather than incrementing by 1. The loop-clause is always executed at
least once.
1-20 RPL Programming
Syntax
Flowchart
Start
finish
1:Start
2:finish
FOR
counter=start
Store finish
loop-clause
Body of loop
increment
1:increment
counter = counter +
increment
STEP
Is
counter ≤ finish?
yes
no
FOR … STEP Structure
FOR takes start and finish from the stack as the beginning and ending values for the loop counter, then creates
the local variable counter as a loop counter. Next, the loop-clause is executed — counter can appear within the
loop-clause. STEP takes the increment value from the stack and increments counter by that value. If the
argument of STEP is an algebraic or a name, it's automatically evaluated to a number.
The increment value can be positive or negative. If the increment is positive, the loop is executed again if
counter is less than or equal to finish. If the increment is negative, the loop is executed if counter is greater than
or equal to finish. Otherwise, counter is purged and execution resumes following STEP. In the previous
flowchart, the increment value is positive.
To enter FOR … STEP in a program:
!
Press !° %BRCH% … %FOR%.
Example: The following program places the squares of the integers 1, 3, 5, 7, and 9 on the stack:
« 1 9 FOR x x SQ 2 STEP »
Example: The following program takes n from the stack, and returns the series of numbers 1, 2, 4, 8, 16, …,
n. If n isn't in the series, the program stops at the last value less than n.
« 1 SWAP FOR n n n STEP »
The first n is the local variable declaration for the FOR loop. The second n is put on the stack each iteration of
the loop. The third n is used by STEP as the step increment.
Using Indefinite Loop Structures
The DO … UNTIL … END Structure
The syntax for this structure is
RPL Programming 1-21
« … DO loop-clause UNTIL test-clause END … »
DO… UNTIL… END executes the loop-clause sequence repeatedly until test-clause returns a true (nonzero)
result. Because the test-clause is executed after the loop-clause, the loop-clause is always executed at least once.
Syntax
Flowchart
DO
loop-clause
Body of loop
UNTIL
TEST
test-clause
END
1: test result
Is test
result non-zero?
no
yes
DO … UNTIL … END Structure
DO starts execution of the loop-clause. UNTIL marks the end of the loop-clause. The test-clause leaves a test
result on the stack. END removes the test result from the stack. If its value is zero, the loop-clause is executed
again — otherwise, execution resumes following END. If the argument of END is an algebraic or a name, it's
automatically evaluated to a number.
To enter DO … UNTIL … END in a program:
!
Press !°%BRCH% ! %DO%.
Example: The following program calculates n + 2n +3n + … for a value of n. The program stops when the
sum exceeds 1000, and returns the sum and the coefficient of n.
Program:
Comments:
«
DUP 1
 n s c
1-22 RPL Programming
Duplicates n, stores the value into
n and s, and initializes c to 1.
Program:
Comments:
«
DO
'c' INCR
n * 's' STO+
UNTIL
s 1000 >
END
s c
»
Starts the defining procedure.
Starts the loop-clause.
Increments the counter by 1. (See
Using Loop Counters.)
Calculates c × n and adds the product to s.
Starts the test-clause.
Repeats loop until s > 1000.
Ends the test-clause.
Puts s and c on the stack.
Ends the defining procedure.
»
The WHILE … REPEAT … END Structure
The syntax for this structure is
« … WHILE test-clause REPEAT loop-clause END … »
WHILE … REPEAT … END repeatedly evaluates test-clause and executes the loop-clause sequence if the test
is true. Because the test-clause is executed before the loop-clause, the loop-clause is not executed if the test is
initially false.
Syntax
Flowchart
WHILE
TEST
test-clause
1: test result
REPEAT
no
Is test
result non-zero?
yes
loop-clause
Body of loop
END
WHILE … REPEAT … END Structure
WHILE starts execution of the test-clause, which returns a test result to the stack. REPEAT takes the value from
the stack. If the value is nonzero, execution continues with the loop-clause-otherwise, execution resumes
following END. If the argument of REPEAT is an algebraic or a name, it's automatically evaluated to a number.
RPL Programming 1-23
To enter WHILE … REPEAT … END in a program:
!
Press !°%BRCH% ! %WHILE%.
Example: The following program starts with a number on the stack, and repeatedly performs a division by 2
as long as the result is evenly divisible. For example, starting with the number 24, the program computes 12,
then 6, then 3.
« WHILE DUP 2 MOD 0 == REPEAT 2 / DUP END DROP »
Example: The following program takes any number of vectors or arrays from the stack and adds them to the
statistics matrix. (The vectors and arrays must have the same number of columns.)
WHILE … REPEAT … END is used instead of DO … UNTIL … END because the test must be done before
the addition. (If only vectors or arrays with the same number of columns are on the stack, the program errors
after the last vector or array is added to the statistics matrix.)
« WHILE DUP TYPE 3 == REPEAT …+ END »
Using Loop Counters
For certain problems you may need a counter inside a loop structure to keep track of the number of loops. (This
counter isn't related to the counter variable in a FOR … NEXT/STEP structure.) You can use any global or local
variable as a counter. You can use the INCR or DECR command to increment or decrement the counter value
and put its new value on the stack.
The syntax for INCR and DECR is
« … 'variable' INCR … »
or
« … 'variable' DECR … »
To enter INCR or DECR in a program:
!
Press !° #MEM# %ARITH% %INCR% or %DECR%.
The INCR and DECR commands take a global or local variable name (with ' delimiters) as their argument
— the variable must contain a real number. The command does the following:
1. Changes the value stored in the variable by +1 or -1.
2. Returns the new value to the stack.
Examples: If c contains the value 5, then 'c' INCR stores 6 in c and returns 6 to the stack.
The following program takes a maximum of five vectors from the stack and adds them to the current statistics
matrix.
Program:
«
Comments:
0  c
Stores 0 in local variable c.
«
Starts the defining procedure.
Starts the test clause.
Returns true if level 1 contains a vector.
Increments and returns the value in c.
Returns true if the counter c≤5.
Returns true if the two previous test results are true.
Adds the vector to ΣDAT.
Ends the structure.
Ends the defining procedure.
WHILE
DUP TYPE 3 ==
'c' INCR
5 ‰
AND
REPEAT
…+
END
»
»
1-24 RPL Programming
Using Summations Instead of Loops
For certain calculations that involve summations, you can use the Σ function instead of loops. You can use Σ
with stack syntax or with algebraic syntax. Σ automatically repeats the addition for the specified range of the
index variable — without using a loop structure.
Example: The following programs take an integer upper limit n from the stack, then find the summation. One
program uses a FOR … NEXT loop — the other uses Σ.
n
∑j
2
Program:
j=1
Comments:
«
0 1 ROT
FOR j
j SQ +
NEXT
Initializes the summation and puts
the limits in place.
Loops through the calculation.
»
Program:
Comments:
«
 n
'…(j=1,n,j^2)'
Uses Σ to calculate the summation.
»
Example: The following program uses ΣLIST to calculate the summation of all elements of a vector or matrix.
The program takes from the stack an array or a name that evaluates to an array, and returns the summation.
Program:
Comments:
«
OBJ
1
+
œLIST
LIST
…LIST
Finds the dimensions of the array and
leaves it in a list on level 1.
Adds 1 to the list. (If the array is a vector,
the list on level 1 has only one element.
ΠLIST will error if the list has fewer than
two elements.)
Multiplies all of the list elements together.
Converts the array elements into a list, and
sums them.
»
Using Flags
You can use flags to control calculator behavior and program execution. You can think of a flag as a switch that
is either on (set) or off (clear). You can test a flag's state within a conditional or loop structure to make a
RPL Programming 1-25
decision. Because certain flags have unique meanings for the calculator, flag tests expand a program's decisionmaking capabilities beyond that available with comparison and logical functions.
Types of Flags
The hp49g+/hp48gII has two types of flags:
!
!
System flags. Flags -1 through -128. These flags have predefined meanings for the calculator.
User flags. Flags 1 through 128. User flags are, for the most part, not used by any built-in operations. What
they mean depends entirely on how the program uses them.
Appendix C lists the 128 system flags and their definitions. For example, system flag -40 controls the clock
display - when this flag is clear (the default state), the clock is not displayed - when this flag is set, the clock is
displayed. (When you press %CLK% in the H%MISC% menu, you are setting or clearing flag -40.)
Note that for the hp49g+/hp48gII, there are no display annunciators to indicate that user flags 1 through 5 are
set, like the hp48S-series and hp48G-series calculators.
Setting, Clearing, and Testing Flags
Flag commands take a flag number from the stack – an integer 1 through 128 (for user flags) or -1 through -128
(for system flags).
To set, clear, or test a flag:
1. Enter the flag number (positive or negative).
2. Execute the flag command – see the table below.
Flag Commands
Key
Programmable
Command
Description
!°%TEST% LL:
%SF%
SF
Sets the flag.
%CF%
CF
Clears the flag.
%FS?%
FS?
Returns 1. (true) if the flag is set, or
0. (false) if the flag is clear.
%FC?%
FC?
Returns 1. (true) if the flag is clear,
or 0. (false) if the flag is set.
%FS?C%
FS?C
Tests the flag (returns true if the
flag is set), then clears the flag.
%FC?C%
FC?C
Tests the flag (returns true if the
flag is clear), then clears the flag.
Example: System Flag. The following program sets an alarm for June 6, 2007 at 5:05 PM. It first tests the
status of system flag -42 (Data Format flag) in a conditional structure and then supplies the alarm date in the
current date format, based on the test result.
1-26 RPL Programming
Example:
Program:
Comments:
«
IF
-42 FC?
THEN
6.152007
ELSE
15.062007
END
17.05 "TEST COMPLETE"
3 LIST STOALARM
Tests the status of flag –42, the Date
Format flag.
If flag –42 is clear, supplies the date in
month/day/year format.
If flag –42 is set, supplies the date in
day.month.year format.
Ends the conditional.
Sets the alarm: 17.05 is the alarm time
and “TEST COMPLETE” is the alarm
message.
»
Example: User Flag. The following program returns either the fractional or integer part of the number in
level 1, depending on the state of user flag 10.
Program:
Comments:
«
IF
10 FS?
THEN
IP
ELSE
FP
END
Starts the conditional.
Tests the status of user flag 10.
If flag 10 is set, returns the integer part.
If flag 10 is clear, returns the fractional part.
Ends the conditional.
»
To use this program, you enter a number, either set flag 10 (to get the integer part) or clear flag 10 (to get the
fractional part), then run the program.
Recalling and Storing the Flag States
If you have a program that changes the state of a flag during execution, you may want it to save and restore
original flag states.
The RCLF (recall flags) and STOF (store flags) commands let you recall and store the states of the
hp49g+/hp48gII flags. For these commands, a 64-bit binary integer represents the states of 64 flags — each 0
bit corresponds to a flag that's clear, each 1 bit corresponds to a flag that's set. The rightmost (least significant)
bit corresponds to system flag –1 or user flag 1 for the lower groups and system flag -65 or user flag 65 for the
upper groups.
To recall the current flag states:
!
Execute RCLF (!°L %MODES% %FLAG% L%RCLF% ).
RCLF returns a list containing four 64-bit binary integers representing the current states of the lower and upper
groups of system and user flags:
{ #nsystem-lower #nuser-lower #nsystem-upper #nuser-upper }
RPL Programming 1-27
To change the current flag states:
1. Enter the flag-state argument- see below
2. Execute STOF (!°L %MODES% %FLAG% L%STOF% ).
STOF sets the current states of flags based on the flag-state argument:
#ns
Changes the states of only the system flags.
{ #ns-lower #nu-lower #ns-upper #nu-upper }Changes the states of the system and user flags.
Example: The program PRESERVE on page 2-6 uses RCLF and STOF.
Using Subroutines
Because a program is itself an object, it can be used in another program as a subroutine. When program B is
used by program A, program A calls program B, and program B is a subroutine in program A.
Example: The program TORSA calculates the surface area of a torus of inner radius a and outer radius b.
TORSA is used as a subroutine in a second program TORSV, which calculates the volume of a torus.
The surface area and volume are calculated by
2
2
2
A = π (b – a )
1 2 2
2
V = --- π ( b – a ) ( b – a )
4
(The quantity π2 ( b2 – a 2 ) in the second equation is the surface area of a torus calculated by TORSA.)
Here are the stack diagram and program listing for TORSA.
Level 2
Level 1
"
Level 1
a
b
"
surface area
Program:
Comments:
«
 a b
'‡^2*(b^2-a^2)'
NUM
Creates local variables a and b.
Calculates the surface area.
Converts algebraic to a number.
»
`
O TORSA K
1-28 RPL Programming
Puts the program on the stack.
Stores the program in TORSA.
Here is a stack diagram and program listing for TORSV.
Level 2
Level 1
"
Level 1
a
b
"
volume
Program:
«
 a b
«
a b TORSA
b a - * 4 /
»
Comments:
Creates local variables a and b.
Starts a program as the defining
procedure.
Puts the numbers stored in a and b
on the stack, then calls TORSA
with those arguments.
Completes the volume calculation
using the surface area.
Ends the defining procedure.
»
`
O TORSV K
Puts the program on the stack.
Stores the program in TORSV.
Now use TORSV to calculate the volume of a torus of inner radius a = 6 and outer radius b = 8.
6 ` 8 J %TORSV%
Single-Stepping through a Program
It's easier to understand how a program works if you execute it step by step, observing the effect of each step.
Doing this can help you debug your own programs or understand programs written by others.
To single-step from the start of a program:
1. Put the program or program name in level 1 ( or the command line).
2. Press !°LL%RUN% %DBUG% to start and immediately suspend execution. HLT appears in the status
area.
3. Take any action:
! To see the next program step displayed in the status area and then executed, press %SST%.
! To display but not execute the next one or two program steps, press %NEXT%.
! To continue with normal execution, press !=.
! To abandon further execution, press %KILL%.
4. Repeat the previous step as desired.
To turn off the HALT annunciator at any time:
!
Press !°LL %RUN% %KILL%.
RPL Programming 1-29
Example: Execute program TORSV step by step. Use a = 6 and b = 8.
Select the VAR menu and enter the data. Enter the program name and start the debugging. HLT indicates
program execution is suspended.
@· J6 `8 `O%TORSV%
!°LL%RUN% %DBUG%
Display and execute the first program step. Notice that it takes the two arguments from the stack and stored
them in local variables a and b.
%SST%
Continue single-stepping until the status area shows the current directory. Watch the stack and status area
as you single-step through the program.
%SST% … %SST%.
To single-step from the middle of a program:
1. Insert a HALT command in the program where you want to begin single-stepping.
2. Execute the program normally. The program stops when the HALT command is executed, and the HLT
annunciator appears.
3. Take any action:
! To see the next program step displayed in the status area and then executed, press %SST%.
! To display but not execute the next one or two program steps, press %NEXT%.
! To continue with normal execution, press !=.
! To abandon further execution, press %KILL%.
4. Repeat the previous step as desired.
When you want the program to run normally again, remove the HALT command from the program.
To single-step when the next step is a subroutine:
To execute the subroutine in one step, press %SST%.
! To execute the subroutine step-by-step, press %SST°%.
!
%SST% executes the next step in a program — if the next step is a subroutine, %SST% executes the subroutine in
one step. %SST°% works just like %SST% — except if the next program step is a subroutine, it single-steps to the
first step in the subroutine.
Example: In the previous example, you used %SST% to execute subroutine TORSA in one step. Now execute
program TORSV step by step to calculate the volume of a torus of radii a = 10 and b = 12. when you reach
subroutine TORSA, execute it step by step.
Select the VAR menu and enter the data. Enter the program name and start the debugging. Execute the first four
steps of the program, then check the next step.
1-30 RPL Programming
@·J 10 `12 O%TORSV%
!°LL%RUN% %DBUG%
%SST°% (4 times)
%NEXT%
The next step is TORSA. Single-step into TORSA, then check that you're at the first step of TORSA.
%SST°% %NEXT%
Press != != to complete subroutine and program execution. The following table summarizes the
operations for single-stepping through a program.
Single-Step Operations
Key
Programmable
Command
Description
!°LL%RUN% :
%DBUG%
Starts program execution, then suspends it as if HALT were the first
program command. Takes as its argument the program or program name
in level 1.
%SST%
Executes the next object or command in the suspended program.
%SST°%
Same as %SST%, except if the next program step is a subroutine, single-steps
to the first step in that subroutine.
%NEXT%
Displays the next one or two objects, but does not execute them. The display
persists until the next keystroke.
%HALT%
HALT
Suspends program execution at the location of the HALT command in
the program.
%KILL%
KILL
Cancels all suspended programs and turns off the HLT annunciator.
!=
CONT
Resumes execution of a halted program.
RPL Programming 1-31
Trapping Errors
If you attempt an invalid operation from the keyboard, the operation is not executed and an error message
appears. For example, if you execute + with a vector and a real number on the stack, the hp49g+/hp48gII
returns the message + Error: Bad Argument Type and returns the arguments to the stack (if Last
Arguments is enabled).
In a program, the same thing happens, but program execution is also aborted. If you anticipate error conditions,
your program can process them without interrupting execution.
For simple programs, you can run the program again if it stops with an error. For other programs, you can
design them to trap errors and continue executing. You can also create user-defined errors to trap certain
conditions in programs. The error trapping commands are located in the PRG ERROR menu.
Causing and Analyzing Errors
Many conditions are automatically recognized by the hp49g+/hp48gII as error conditions– and they're
automatically treated as errors in programs.
You can also define conditions that cause errors. You can cause a user-defined error (with a user-defined error
message) — or you can cause a built-in error. Normally, you'll include a conditional or loop structure with a test
for the error condition — and if it occurs, you'll cause the user-defined or built-in error to occur.
To cause a user-defined error to occur in a program:
1. Enter a string (with "" delimiters) containing the desired error message.
2. Enter the DOERR command (PRG ERROR menu).
To artificially cause a built-in error to occur in a program:
1. Enter the error number (as a binary integer or real number) for the error.
2. Enter the DOERR command (PRG ERROR menu).
If DOERR is trapped in an IFERR structure (described in the next topic), execution continues. If it's not
trapped, execution is abandoned at the DOERR command and the error message appears.
To analyze an error in a program:
To get the error number for the last error, execute ERRN (PRG ERROR menu).
To get the error message for the last error, execute ERRM (PRG ERROR menu).
! To clear the last-error information, execute ERR0 (PRG ERROR menu).
!
!
The error number for a user-defined error is #70000h. See the list of built-in error numbers in appendix A,
“Error and Status Messages”.
Example: The following program aborts execution if the list in level 1 contains three objects.
«
OBJ
IF 3 ==
THEN "3 OBJECTS IN LIST" DOERR
END
»
The following table summarizes error trapping commands.
1-32 RPL Programming
Error Trapping Commands
Key
Programmable
Command
Description
!° L L %ERROR% :
%DOERR%
DOERR
Causes an error. For a string in level 1, causes a user-defined error: the
calculator behaves just as if an ordinary error has occurred. For a binary
integer or real number in level 1, causes the corresponding built-in error.
If the error isn't trapped in an IFERR structure, DOERR displays the
message and abandons program execution. (For 0 in level 1, abandons
execution without updating the error number or message — like −.)
%ERRN%
ERNN
Returns the error number, as a binary integer, of the most recent error.
Returns #0 if the error number was cleared by ERR0.
%ERRM%
ERRM
Returns the error message (a string) for the most recent error. Returns
an empty string if the error number was cleared by ERR0.
%ERR0%
ERR0
Clears the last error number and message.
Making an Error Trap
You can construct an error trap with one of the following conditional structures:
!
!
IFERR … THEN … END.
IFERR … THEN … ELSE … END.
The IFERR … THEN … END Structure
The syntax for this structure is
« … IFERR trap-clause THEN error-clause END … »
The commands in the error-clause are executed only if an error is generated during execution of the trap-clause.
If an error occurs in the trap-clause, the error is ignored, the remainder of the trap-clause is skipped, and
program execution jumps to the error-clause. If no errors occur in the trap-clause, the error-clause is skipped and
execution resumes after the END command.
To enter IFERR … THEN … END in a program:
!
Press !°LL %ERROR% !%IFERR%.
Example: The following program takes any number of vectors or arrays from the stack and adds them to the
statistics matrix. However, the program stops with an error if a vector or array with a different number of
columns is encountered. In addition, if only vectors or arrays with the same number of columns are on the stack,
the program stops with an error after the last vector or array has been removed from the stack.
« WHILE DUP TYPE 3 == REPEAT …+ END »
In the following revised version, the program simply attempts to add the level 1 object to the statistics matrix
until an error occurs. Then, it ends by displaying the message DONE.
RPL Programming 1-33
Program:
Comments:
«
IFERR
WHILE
1
REPEAT
…+
END
THEN
"DONE" 1 DISP
1 FREEZE
END
Starts the trap-clause.
The WHILE structure repeats
indefinitely, adding the vectors
and arrays to the statistics matrix
until an error occurs.
Starts the error clause. If an error
occurs in the WHILE structure,
displays the message DONE in the
status area.
»
Ends the error structure.
The IFERR … THEN … ELSE … END Structure
The syntax for this structure is
« … IFERR trap-clause
THEN error-clause ELSE normal-clause END … »
The commands in the error-clause are executed only if an error is generated during execution of the trap-clause.
If an error occurs in the trap-clause, the error is ignored, the remainder of the trap-clause is skipped, and
program execution jumps to the error-clause. If no errors occur in the trap-clause, execution jumps to the
normal-clause at the completion of the trap-clause.
To enter IFERR … THEN … ELSE … END in a program:
!
Press !°LL %ERROR% @%IFERR%
Example: The following program prompts for two numbers, then adds them. If only one number is supplied,
the program displays an error message and prompts again.
Program:
Comments:
«
DO
"KEY IN a AND b" "
"
INPUT OBJ
UNTIL
IFERR
+
THEN
ERRM 5 DISP
2 WAIT
0
ELSE
1
END
END
»
1-34 RPL Programming
Begins the main loop.
Prompts for two numbers.
Starts the loop test clause.
The error trap contains only the + command.
If an error occurs, recalls and displays the
Too Few Arguments message for 2 seconds,
then puts 0 (false) on the stack for the main loop.
If no error occurs, puts 1(true) on the stack for the
main loop.
Ends the error trap.
Ends the main loop. If the error trap left 0 (false) on
the stack, the main loop repeats — otherwise, the
program ends.
Input
A program can stop for user input, then resume execution, or can use choose boxes or input forms (dialog
boxes) for input. You can use several commands to get input:
PROMPT (!=to resume).
DISP FREEZE HALT (!=to resume).
! INPUT (`to resume).
! INFORM
! CHOOSE
!
!
Data Input Commands
Key
Command
Description
!°L %IN% :
%INFOR%
INFORM
Creates a user-defined input form.
%NOVAL
NOVAL
Place holder for the INFORM command. Returned when a value is not present in
an input form field.
%CHOOS%
CHOOSE
Creates a user-defined choose box.
%KEY%
KEY
Returns a test result to level 1 and, if a key is pressed, the location of that key (level
2).
%WAIT%
WAIT
Suspends program execution for a specified duration (in seconds, level 1).
%INPUT%
INPUT
Suspends program execution for data input.
%PROMP%
PROMPT
Halts program execution for data input.
Using PROMPT … CONT for Input
PROMPT uses the status area for prompting, and allows the user to use normal keyboard operations during
input.
To enter PROMPT in a program:
1. Enter a string ( with "" delimiters) to be displayed as a prompt in the status area.
2. Enter the PROMPT command (PRG IN menu).
« … "prompt-string" PROMPT … »
PROMPT takes a string argument from level 1, displays the string (without the ""delimiters) in the status area,
and halts program execution. Calculator control is returned to the keyboard.
When execution resumes, the input is left on the stack as entered.
To respond to PROMPT while running a program:
1. Enter your input — you can use keyboard operations to calculate the input.
2. Press !=.
The message remains until you press `or − or until you update the status area.
RPL Programming 1-35
Example: If you execute this program segment
« "ABC?" PROMPT »
the display looks like this:
Example: The following program, TPROMPT, prompts you for the dimensions of a torus, then calls program
TORSA (from page 1-28) to calculate its surface area. You don't have to enter data on the stack prior to program
execution.
Program:
Comments:
«
"ENTER a, b IN ORDER:"
Puts the prompting string on the stack.
PROMPT
Displays the string in the status area,
halts program execution, and returns
calculator control to the keyboard.
TORSA
Executes TORSA using the just-entered
stack arguments.
»
`OTPROMPT ‰
Stores the program in TPROMPT.
Execute TPROMPT to calculate the volume of a torus with inner radius a =8 and outer radius b =10. Execute
TPROMPT. The program prompts you for data.
@·J %TPROM%
Enter the inner and outer radii. After you press `, the prompt message is cleared from the status area.
8 `10
1-36 RPL Programming
Continue the program.
!=
Note that when program execution is suspended by PROMPT, you can execute calculator operations just as you
did before you started the program. If the outer radius b of the torus in the previous example is measured as 0.83
feet, you can convert that value to inches while the program is suspended for data input by pressing .83 `12
*, then !=.
Using DISP FREEZE HALT … CONT for Input
DISP FREEZE HALT lets you control the entire display during input, and allows the user to use normal
keyboard operations during input.
To enter DISP FREEZE HALT in a program:
1. Enter a string or other object to be displayed as a prompt.
2. Enter a number specifying the line to display it on.
3. Enter the DISP command (PRG OUT menu).
4. Enter a number specifying the areas of the display to “freeze.”
5. Enter the FREEZE command (PRG OUT menu).
6. Enter the HALT command (PRG OUT menu).
« … prompt-object display-line DISP
freeze-area FREEZE HALT … »
DISP displays an object in a specified line of the display. DISP takes two arguments from the stack: an object
from level 2, and a display-line number 1 through 7 from level 1. If the object is a string, it's displayed without
the ""delimiters. The display created by DISP persists only as long as the program continues execution — if
the program ends or is suspended by HALT, the calculator returns to the normal stack environment and updates
the display. However, you can use FREEZE to retain the prompt display.
FREEZE “freezes” display areas so they aren't updated until a key press. Argument n in level 1 is the sum of the
codes for the areas to be frozen: 1 for the status area, 2 for the stack/command line area, 4 for the menu area.
HALT suspends program execution at the location of the HALT command and turns on the HALT
annunciator. Calculator control is returned to the keyboard for normal operations.
When execution resumes, the input remains on the stack as entered.
To respond to HALT while running a program:
1. Enter your input — you can use keyboard operations to calculate the input.
2. Press !=.
Example: If you execute this program segment
« "ABC
DEF
GHI" CLLCD 3 DISP 2 FREEZE HALT »
The display looks like this:
(The
in the previous program is the calculator's representation for the newline character after you enter a
program on the stack.)
RPL Programming 1-37
Using INPUT … ENTER for Input
INPUT lets you use the stack area for prompting, lets you supply default input, and prevents the user from using
normal stack operations or altering data on the stack.
To enter INPUT in a program:
1. Enter a string (with "" delimiters) to be displayed as a prompt at the top of the stack area.
2. Enter a string or list (with delimiters) that specifies the command-line content and behavior — see below.
3. Enter the INPUT command (PRG IN menu).
4. Enter OBJ" (PRG TYPE menu) or other command that processes the input as a string object.
« … "prompt-string" "command-line" INPUT OBJ … »
or
« … "prompt-string" {command-line} INPUT OBJ … »
INPUT, in its simplest form, takes two strings as arguments — see the list of additional options following.
INPUT blanks the stack area, displays the contents of the level-2 string at the top of the stack area, and displays
the contents of the level-1 string in the command line. It then activates Program-entry mode, puts the insert
cursor after the string in the command line, and suspends execution.
When execution resumes, the input is returned to level 1 as a string object, called the result string.
To respond to INPUT while running a program:
1. Enter your input. (You can't execute commands — they're simply echoed in the command line.)
2. Optional: To clear the command line and start over, press −.
3. Press `.
If you execute this program segment
« "Variable name?" ":VAR:" INPUT »
the display looks like this:
The following program, VSPH, calculates the volume of a sphere. VSPH prompts for the radius of the sphere,
then cubes it and multiplies by 4/3 π. VSPH executes INPUT to prompt for the radius. INPUT sets Programentry mode when program execution pauses for data entry.
1-38 RPL Programming
Program:
Comments:
«
"Key in radius"
Specifies the prompt string.
""
Specifies the command-line string.
In this case, the command line will be
empty.
Displays the prompt, puts the cursor at
the start of the command line, and
suspends the program for data input
(the radius of the sphere).
Converts the result string into its
component object- a real number.
Cubes the radius.
Completes the calculation.
INPUT
OBJ
3 ^
4 * 3 / ‡ * NUM
»
`OVSPH ‰
Stores the program in VSPH.
Example:
Execute VSPH to calculate the volume of a sphere of radius 2.5.
J %VSPH%
Key in the radius and continue program execution. ...............................
2.5 `
To include INPUT options:
!
Use a list (with {} delimiters) as the command-line argument for INPUT. The list can contain one more of
the following:
" Command-line string (with "" delimiters).
" Cursor position as a real number or as a list containing two real numbers.
" Operating options ALG, Œ, or V.
In its general form, the level 1 argument for INPUT is a list that specifies the content and interpretation of the
command line. The list can contain one or more of the following parameters in any order:
RPL Programming 1-39
{"command-line" cursor-position operating-options }
“Commandline”
Specifies the content of the command line when the program pauses. Embedded
newline characters produce multiple lines in the display. (If not included, the
command line is blank.)
Cursorposition
Specifies the position of the cursor in the command line and its type. (If not included,
an insert cursor is at the end of the command line.)
!
A real number n specifies the nth character in the first row (line) of the command
line. Zero specifies the end of the command-line string. A positive number specifies
the insert cursor — a negative number specifies the replace cursor.
!
A list {row character} specifies the row and character position. Row 1 is the first row
(line) of the command line. Characters count from
the left end of each row — character 0 specifies the end of the row. A positive row
number specifies the insert cursor — a negative row number specifies the replace
cursor.
operatingoptions
Specify the input setup and processing using zero or more of these unquoted names:
ALG activates Algebraic/Program-entry mode (for algebraic syntax). (If not included,
Program-entry mode is active.)
! Œ (~…a) specifies alpha lock. (If not included, alpha is inactive.)
! V verifies whether the result string (without the ""delimiters) is a valid object or
sequence of objects. If the result string isn't valid, INPUT displays the
Invalid Syntax message and prompts again for data. (if not included, syntax
isn't checked.)
!
To design the command-line string for INPUT:
For simple input, use a string that produces a valid object:
" Use an empty string
" Use a :label : tag.
" Use a @ text @ comment.
! For special input, use a string that produces a recognizable pattern.
!
After the user enters input in the command line and presses ` to resume execution, the contents of the
command line are returned to level 1 as the result string. The result string normally contains the original
command-line string, too. If you design the command-line string carefully, you can ease the process of
extracting the input data.
To process the result string from INPUT:
For simple input, use OBJ" to convert the string into its corresponding objects.
For sensitive input, use the V option for INPUT to check for valid objects, then use OBJ" to convert the
string into those objects.
! For special input, process the input as a string object, possibly extracting data as substrings.
!
!
Example: The program VSPH on page 1-39 uses an empty command-line string.
Example: The program SSEC on page 1-42 uses a command-line string whose characters form a pattern. The
program extracts substrings from the result string.
1-40 RPL Programming
Example: The command-line string "@UPPER [email protected]" displays @UPPER [email protected]´ in the
command line. If you press 200 `the return string is "@UPPER [email protected]". When OBJ" extracts the
text from the string, it strips away the @ characters and the enclosed characters, and it returns the number 200.
(See "Creating Programs on a computer" on page 1-7 for more information about @ comments.)
Example: The following program, TINPUT, executes INPUT to prompt for the inner and outer radii of a
torus, then calls TORSA (page 1-28) to calculate its surface area. TINPUT prompts for a and b in a two-row
command line. The level 1 argument for INPUT is a list that contains:
The command-line string, which forms the tags and delimiters for two tagged objects.
! An embedded list specifying the initial cursor position.
! The V parameter to check for invalid syntax in the result string.
!
Program:
Comments:
«
"Key in a, b"
The level 2 string, displayed at the top of the
stack area.
{":a:
The level 1 list contains a string, a list, and the
verify option. (To key in the string, press
@Õ!ê a ™@ë!ê b.
After you press `to put the finished program
on the stack, the string is shown on one line, with
indicating the newline character.) The
embedded list puts the insert cursor at the end of
row 1.
b:"{1 0}V}
INPUT
Displays the stack and command-line strings,
positions the cursor, sets Program-entry mode,
and suspends execution for input.
OBJ
Converts the string into its component objects —
two tagged objects.
TORSA
Calls TORSA to calculate the surface area.
»
`O TINPUT ‰
Stores the program in TINPUT.
Execute TINPUT to calculate the surface area of a torus of inner radius a = 10 and outer radius b = 20.
J %TINPU%
Key in the value for a, press ˜ to move the cursor to the next prompt, then key in the value for b.
RPL Programming 1-41
10 ˜20
Continue program execution.
`
Example: The following program executes INPUT to prompt for a social security number, then extracts two
strings: the first three digits and last four digits. The level 1 argument for INPUT specifies:
A command-line string with dashes.
! The replace cursor positioned at the start of the prompt string ( –1). This lets the user “fill in” the command
line string, using ™to skip over the dashes in the pattern.
! By default, no verification of object syntax — the dashes make the content invalid as objects
!
Level 1
"
Level 2
Level 1
"
“last four digits“
“first three digits“
Program:
Comments:
«
"Key in S.S. #"
{ "
- " -1}
Prompt string.
Command-line string (3 spaces
before the first -, 2 spaces
between, and 4 spaces after the
last -).
INPUT
DUP 1 3 SUB
SWAP
8 11 SUB
Suspends the program for input.
Copies the result string, then
extracts the first three and last
four digits in string form.
»
O SSEC ‰
Stores the program in SSEC.
Using INFORM and CHOOSE for Input
You can use input forms (dialog boxes), and choose boxes for program input. Program that contain input forms or
choose boxes wait until you acknowledge them (%OK% or −) before they continue execution.
If OK is pressed, CHOOSE returns the selected item (or its designated returned value) to level 2 and a 1 to level
1. INFORM returns a list of field values to level 2 and 1 to level 1.
Both the INFORM and CHOOSE commands return 0 if CANCEL is pressed.
1-42 RPL Programming
To set up an input form:
1. Enter a title string for the input for the input form (use @Õ).
2. Enter a list of field specifications.
3. Enter a list of format options.
4. Enter a list of reset values (values that appear when RESET is pressed).
5. Enter a list of default values.
6. Execute the INFORM command.
Example: Enter a title "FIRST ONE" `.
Specify a field { "Name:" } `.
Enter format options (one column, tabs stop width five) { 1 5 } `.
Enter reset value for the field {"THERESA"} `.
Enter default value for the field {"WENDY"} `.
Execute INFORM (!°L%IN% %INFOR%).
The screen on the left appears. Press L%RESET% %OK% and the screen on the right appears.
You can specify a help message and the type of data that must be entered in field by entering field specifications
as lists. For example, {{"Name:" "Enter your name" 2}} defines the Name field, displays
Enter your name across the bottom of the input form, and accepts only object type 2 (strings) as input.
To set up a choose box:
1. Enter a title string for the choose box.
2. Enter a list of items. If this is a list of two-element lists, the first element is displayed in the choose box, and
the second element is returned to level 2 when OK is pressed.
3. Enter a position number for the default highlighted item. (0 makes a view-only choose box.)
4. Execute the CHOOSE command.
Example: Enter a title "FIRST ONE" `.
Enter a list of items {ONE TWO THREE } `.
Enter a position number for default highlighted value 3 `.
Execute CHOOSE (!°L%IN% %CHOOS%).
Example: The following choose box appears:
Example: The following program uses input forms, choose boxes, and message boxes to create a simple
phone list database.
RPL Programming 1-43
Program:
Comments:
«
'NAMES' VTYPE
IF -1 ==
THEN{ } 'NAMES' STO
END
Checks if the name list
(NAMES) exists, if not,
creates an empty one.
WHILE
"PHONELIST OPTIONS:"
{
{ "ADD A NAME" 1}
{ "VIEW A NUMBER" 2 }
} 1 CHOOSE
While cancel is not
pressed, creates a choose
box that lists the database
options. When OK is
pressed, the second item
in the list pair is returned
to the stack.
REPEAT  c «
CASE c 1 ==
THEN
WHILE
Stores the returned value
in c.
Case 1 (ADD name),
while cancel is not
pressed, do the
following:
"ADD A NAME"
{
{"NAME:" "ENTER NAME" 2}
{"PHONE:" "ENTER A PHONE
NUMBER" 2 } }
{ } { } { } INFORM
REPEAT
Creates an input form that
gets the name and phone
number. The two fields
accept only strings (object
type 2).
DUP
IF{ NOVAL } HEAD POS
THEN
DROP
"Complete both fields
before pressing OK"
MSGBOX
Checks if either field in the
new entry is blank.
ELSE 1
LIST NAMES + SORT
'NAMES' STO
END
END
END
If neither are, adds the list
to NAMES, sorts it, and
stores it back in NAMES.
Ends the IF structure, the
WHILE loop, and the
CASE statement.
c 2 ==
Case 2 (View a Number).
THEN
IF { } NAMES SAME
THEN
"YOU MUST ADD A
NAME FIRST"
MSGBOX
Checks if NAMES is an
empty list.
If it is, displays a message.
1-44 RPL Programming
If either one is, displays a
message.
Program:
ELSE
WHILE
"VIEW A NUMBER"
NAMES 1 CHOOSE
REPEAT
STR MSGBOX
END
END
END
END
»
END
»
`OPHONES ‰
Comments:
If NAMES isn't empty,
creates a choose box using
NAMES as choice items.
When OK is pressed, the
second item in the NAMES
list pairs (the phone
number) is returned.
Makes it a string and
displays it.
Ends the WHILE loop, the
IF structure, and the CASE
statement.
Ends the CASE structure,
marks the end of the local
variable defining
procedure, ends the
WHILE loop, and marks
the end the program.
Stores the program in
PHONES.
You can delete names and numbers by editing the NAMES variable.
To improve upon this program, create a delete name routine.
Beeping to Get Attention
To enter BEEP in a program:
1. Enter a number that specifies the tone frequency in hertz.
2. Enter a number that specifies the tone duration in seconds.
3. Enter the BEEP command (!°L%OUT% L menu).
« … frequency duration BEEP … »
BEEP takes two arguments from the stack: the tone frequency from level 2 and the tone duration from level 1.
Example: The following edited version of TPROMPT sounds a 440-hertz, one-half-second tone at the prompt
for data input.
Program:
Comments:
«
"ENTER a, b IN ORDER:"
440 .5 BEEP
PROMPT
TORSA
Sounds a tone just before
the prompt for data input.
»
RPL Programming 1-45
Stopping a Program for Keystroke Input
A program can stop for keystroke input — it can wait for the user to press a key. You can do this with the WAIT
and KEY commands.
Using WAIT for Keystroke Input
The WAIT command normally suspends execution for a specified number of seconds. However, you can
specify that it wait indefinitely until a key is pressed.
To enter WAIT in a program:
!
!
To stop without changing the display, enter 0 and the WAIT command (PRG IN menu).
To stop and display the current menu, enter –1 and the WAIT command (PRG IN menu).
WAIT takes the 0 or –1 from level 1, then suspends execution until a valid keystroke is executed.
For an argument of –1, WAIT displays the currently specified menu. This lets you build and display a menu of
user choices while the program is paused. (A menu built with MENU or TMENU is not normally displayed until
the program ends or is halted.)
When execution resumes, the three-digit key location number of the pressed key is left on the stack. This
number indicates the row, column, and shift level of the key.
To respond to WAIT while running a program:
!
Press any valid keystroke. (A prefix key such as !or ~ by itself is not a valid keystroke.)
Using KEY for Keystroke Input
You can use KEY inside an indefinite loop to “pause” execution until any key — or a certain key — is pressed.
To enter a KEY loop in a program:
1. Enter the loop structure.
2. In the test-clause sequence, enter the KEY command (PRG IN menu) plus any necessary test commands.
3. In the loop-clause, enter no commands to give the appearance of a “paused” condition.
KEY returns 0 to level 1 when the loop begins. It continues to return 0 until a key is pressed — then it returns 1
to level 1 and the two-digit row-column number of the pressed key to level 2. For example, `returns 105,
and ! returns 81.)
The test-clause should normally cause the loop to repeat until a key is pressed. If a key is pressed, you can use
comparison tests to check the value of the key number. (See "Using Indefinite Loop Structures" on page 1-21
and "Using Comparison Functions" on page 1-11.)
To respond to a KEY loop while running a program:
!
Press any key. (A prefix key such as !or ~is a valid key.)
Example: The following program segment returns 1 to level 1 if + is pressed, or 0 to level 1 if any other
key is pressed:
« … DO UNTIL KEY END 95 SAME … »
Output
You can determine how a program presents its output. You can make the output more recognizable using the
techniques described in this section.
1-46 RPL Programming
Data Output Commands
Key
Command
Description
!°L%OUT%:
%PVIEW%
PVIEW
%TEXT%
TEXT
%CLLCD%
CLLCD
%DISP%
DISP
%FREEZ%
FREEZE
%MSGBO%
MSGBOX
%BEEP%
BEEP
Displays PICT starting at the given coordinates.
Displays the stack display.
Blanks the stack display.
Displays an object in the specified line.
“Freezes” a specified area of the display until a key press.
Creates a user-defined message box.
Sounds a beep at a specified frequency (in hertz, level 2) and
duration (in seconds, level 1).
Labeling Output with Tags
To label a result with a tag:
1. Put the output object on the stack.
2. Enter a tag — a string, a quoted name, or a number.
3. Enter the "TAG command (PRG TYPE menu).
« … object tag TAG … »
"TAG takes two arguments — an object and a tag — from the stack and return a tagged object.
Example: The following program TTAG is identical to TINPUT, except that it returns the result as AREA:
value.
Program:
Comments:
«
"Key in a, b"
{ ":a:
:b:" {1 0} V}
INPUT OBJ
TORSA
"AREA"
TAG
»
`OTTAG ‰
Enters the tag (a string). Uses
the program result and string
to create the tagged object.
Stores the program in TTAG.
Execute TTAG to calculate the area of a torus of inner radius a = 1.5 and outer radius b =1.85. The answer is
returned as a tagged object.
J %TTAG% 1.5 ˜1.85 `
RPL Programming 1-47
Labeling and Displaying Output as Strings
To label and display a result as a string:
1. Put the output object on the stack.
2. Enter the "STR command (PRG TYPE menu).
3. Enter a string to label the object (with "" delimiters).
4. Enter the SWAP + commands to swap and concatenate the strings.
5. Enter a number specifying the line to display the string on.
6. Enter the DISP command (PRG OUT menu).
« … object STR label SWAP + line DISP … »
DISP displays a string without its "" delimiters.
Example: The following program TSTRING is identical to TINPUT, except that it converts the program
result to a string and appends a labeling string to it.
Program:
Comments:
«
"Key in a, b"
{ ":a:
:b:" {1 0} V}
INPUT OBJ
TORSA
STR
"Area = "
SWAP +
CLLCD 1 DISP 3 FREEZE
Converts the result to a string.
Enters the labeling strings.
Swaps and adds the two strings.
Displays the resultant string, without
its delimiters, in line 1 of the display.
»
`OTSTRING ‰
Stores the program in TSTRING.
Execute TSTRING to calculate the area of the torus with a = 1.5 and b = 1.85. The labeled answer appears in the
status area.
@·J%TSTRI%
1.5 ˜1.85 `
Pausing to Display Output
To pause to display a result:
1. Enter commands to set up the display.
2. Enter the number of seconds you want to pause.
3. Enter the WAIT command (PRG IN menu).
WAIT suspends execution for the number of seconds in level 1. You can use WAIT with DISP to display
messages during program execution — for example, to display intermediate program results. (WAIT interprets
arguments 0 and –1 differently — see "Using WAIT for Keystroke Input" on page 1-46.)
1-48 RPL Programming
Using MSGBOX to Display Output
To set up a message box:
1. Enter a message string.
2. Execute the MSGBOX command.
Example: Enter the string "HELLO, WORLD" `.
Execute MSGBOX (!°L %OUT% %MSGBO%).
The following message appears:
You must acknowledge a message box by pressing %OK% or −.
Using Menus with Programs
You can use menus with programs for different purposes:
!
Menu-based input. A program can set up a menu to get input during a halt in a program and then resume
executing the same program.
!
Menu-based application. A program can set up a menu and finish executing, leaving the menu to start
executing other related programs.
To set up a built-in or library menu:
1. Enter the menu number.
2. Enter the MENU command (MODES MENU menu).
To set up a custom menu:
1. Enter a list (with { } delimiters) or the name of a list defining the menu actions. If a list of two element lists
is given, the first element appears in the menu, but it is the second element that is returned to the stack when
the menu key is pressed. This second element can itself be a list with up to 3 objects, one for the menu key,
one for the left shift menu key and one for the right shift menu key.
2. Activate the menu:
! To save the menu as the CST menu, enter the MENU command (MODES MENU menu).
! To make the menu temporary, enter the TMENU command (MODES MENU menu).
The menu isn't displayed until program execution halts.
Menu numbers for built-in menus are listed in Appendix H. Library menus also have numbers — the library
number serves as the menu number. So you can activate applications menus (such as the SOLVE and PLOT
menus) and other menus (such as the VAR and CST menus) in programs. The menus behave just as they do
during normal keyboard operations.
You create a custom menu to cause the behavior you need in your program — see the topics that follow. You
can save the menu as the CST menu, so the user can get it again by pressing !£. Or you can make it
temporary — it remains active (even after execution stops), but only until a new menu is selected — and it
doesn't affect the contents of variable CST.
RPL Programming 1-49
To specify a particular page of a menu, enter the number as m.pp, where m is the menu number and pp is the
page number (such as 94.02 for page 2 of the TIME menu). If page pp doesn't exist, page 1 is displayed (94
gives page 1 of the TIME menu).
Example: Enter 69 MENU to get page 1 of the MODES MISC menu.
Enter 69.02 MENU to get page 2 of the MODES MISC menu.
To restore the previous menu:
!
Execute 0 MENU.
To recall the menu number for the current menu:
!
Execute the RCLMENU command (MODES MENU menu).
Using Menus for Input
To display a menu for input in a program:
1. Set up the menu — see the previous section.
2. Enter a command sequence that halts execution (such as DISP, PROMPT, or HALT).
The program remains halted until it's resumed by a CONT command, such as by pressing !æ. If you
create a custom menu for input, you can include a CONT command to automatically resume the program when
you press the menu key.
Example: The following program activates page 1 of the MODES ANGL menu and prompts you to set the
angle mode. After you press the menu key, you have to press !æto resume execution.
« 65 MENU "Select Angle Mode" PROMPT »
Example: The PIE program on page 2-34 assigns the CONT command to one key in a temporary menu.
Example: The MNX program on page 2-17 sets up a temporary menu that includes a program containing
CONT to resume execution automatically.
Using Menus to Run Programs
You can use a custom menu to run other programs. That menu can serve as the main interface for an application
(a collection of programs).
To create a menu-based application:
1. Create a custom menu list for the application that specifies programs as menu objects.
2. Optional: Create a main program that sets up the application menu — either as the CST menu or as a
temporary menu.
Example: The following program, WGT, calculates the mass of an object in either English or SI units given
the weight. WGT displays a temporary custom menu, from which you run the appropriate program. Each
program prompts you to enter the weight in the desired unit system, then calculates the mass. The menu remains
active until you select a new menu, so you can do as many calculations as you want. Enter the following list and
store it in LST:
{
{ "ENGL" « "ENTER Wt in POUNDS" PROMPT 32.2 / »}
{ "SI" « "ENTER Wt in NEWTONS" PROMPT 98.1 / »}
}
OLST ‰
1-50 RPL Programming
Program:
Comments:
« LST TMENU »
Displays the custom menu
stored in LST.
`OWGT ‰
Stores the program in WGT.
Use WGT to calculate the mass of an object of weight 12.5 N. The program sets up the menu, then completes
execution.
J%WGT%
Select the SI unit system, which starts the program in the menu list.
%SI%
Key in the weight, then resume the program.
12.5 !æ
Example: The following program, EIZ, constructs a custom menu to emulate the HP Solve application for a
capacitive electrical circuit. The program uses the equation E = IZ, where E is the voltage, I is the current, and Z
is the impedance.
Because the voltage, current, and impedance are complex numbers, you can't use the HP Solve application to
find solutions. The custom menu in EIZ assigns a direct solution to the left-shifted menu key for each variable,
and assigns store and recall functions to the unshifted and right-shifted keys — the actions are analogous to the
HP Solve application. The custom menu is automatically stored in CST, replacing the previous custom menu —
you can press !£ to restore the menu.
Program:
Comments:
«
DEG -15 SF -16 SF
2 FIX
Sets Degrees mode. Sets flags
–15 and –16 to display complex numbers in
polar form. Sets the display mode to 2 Fix.
{
Starts the custom menu list.
Builds menu key 1 for E.
Unshifted action: stores the object in E. Left-shift
action: calculates I × Z, stores it in E, and
displays it with a label. Right-shift action: recalls
the object in E.
{ "E" { « 'E' STO »
« I Z * DUP 'E' STO
"E: " SWAP + CLLCD
1 DISP 3 FREEZE »
« E » } }
{ "I" { « 'I' STO»
« E Z / DUP 'I' STO
"I:"SWAP + CLLCD
1 DISP 3 FREEZE »
« I » } }
Builds menu key 2.
RPL Programming 1-51
Program:
{ "Z"{ « 'Z' STO»
« E I / DUP 'Z' STO
"Z:" SWAP + CLLCD
1 DISP 3 FREEZE »
« Z » } }
Comments:
Builds menu key 3.
}
Ends the list.
MENU
Displays the custom menu.
»
`OEIZ ‰
Stores the program in EIZ.
For a 10-volt power supply at phase angle 0°, you measure a current of 0.37-amp at phase angle 68°. Find the
impedance of the circuit using EIZ.
@·J%EIZ%
Key in the voltage value.
!Ü10 [email protected] 0
Store the voltage value. Then key in and store the current value. Solve for the impedance.
%%E%% !Ü .37 [email protected] 68 %%I%%
!%%Z%%
Recall the current and double it. Then find the voltage.
@%%I%% 2 *%%I%% !%%E%%
Press (!H)%FMT% %STD% and L %MODES %ANGLE %RECT% to restore Standard and Rectangular modes.
Turning Off the hp49g+/hp48gII from a Program
To turn off the calculator in a program:
!
Execute the OFF command (PRG RUN menu).
The OFF command turns off the hp49g+/hp48gII. If a program executes OFF, the program resumes when the
calculator is next turned on.
1-52 RPL Programming
2
2.RPL Programming Examples
The programs in this chapter demonstrate basic programming concepts. These programs are intended to improve
your programming skills, and to provide supplementary functions for your calculator.
At the end of each program, the program's checksum and size in bytes are listed to help make sure you typed the
program in correctly. (The checksum is a binary integer that uniquely identifies the program based on its
contents). To make sure you've keyed the program in correctly, store it in its name, put the name in level 1, then
execute the BYTES command (!°#MEM# %BYTES%). This returns the program's checksum to level 2, and
its size in bytes to level 1. (If you execute BYTES with the program object in level 1, you'll get a different byte
count.)
The examples in this chapter assume the hp49g+/hp48gII is in its initial, default condition – they assume you
haven't changed any of the hp49g+/hp48gII operating modes. (To reset the calculator to this condition, see
“Memory Reset” in chapter 5 of the hp49g+/hp48gII User's Guide.)
Each program listing in this chapter gives the following information:
A brief description of the program.
! A syntax diagram (where needed) showing the program's required inputs and resulting outputs.
! Discussion of special programming techniques in the program.
! Any other programs needed.
! The program listing.
! The program's checksum and byte size.
!
Fibonacci Numbers
This section includes three programs that calculate Fibonacci numbers:
!
FIB1 is a user-defined function that is defined recursively (that is, its defining procedure contains its own
name). FIB1 is short.
!
FIB2 is a user-defined function with a definite loop. It's longer and more complicated than FIB1, but faster.
!
FIBT calls both FIB1 and FIB2 and calculates the execution time of each subprogram.
FIB1 and FIB2 demonstrate an approach to calculating the nth Fibonacci number Fn, where:
F0 = 0, F1 = 1, Fn = Fn-1 + Fn-2
FIB1 (Fibonacci Numbers, Recursive Version)
Level 1
"
Level 1
n
"
Fn
RPL Programming Examples 2-1
Techniques used in FIB1
IFTE (if -then-else function). The defining procedure for FIB1 contains the conditional function IFTE,
which can take its argument either from the stack or in algebraic syntax.
! Recursion. The defining procedure for FIB1 is written in terms of FIB1, just as Fn is defined in terms of Fn-1
and Fn-2.
!
FIB1 program listing
Program:
Comments:
«
 n
'IFTE(n‰1,
n,
FIB1(n-1)+FIB1(n-2))
'
Defines local variable n.
The defining procedure, an
algebraic expression. If n ≤
1, Fn = n, else Fn = Fn-1+Fn-2.
»
Stores the program in FIB1.
`OFIB1 K
Checksum: # 14909d (press O%FIB1% !°#MEM# %BYTES%)
Bytes:
113.5
Example: Calculate F6. Calculate F10 using algebraic syntax.
First calculate F6.
J
6 %FIB1%
Next, calculate F10 using algebraic syntax.
O%FIB1% !Ü10 N
FIB2 (Fibonacci Numbers, Loop Version)
Level 1
"
Level 1
n
"
Fn
Techniques used in FIB2
!
IF…THEN…ELSE…END. FIB2 uses the program-structure form of the conditional. (FIB1 uses IFTE.)
!
START…NEXT (definite loop). To calculate Fn, FIB2 starts with F0 and F1 and repeats a loop to calculate
successive values of Fi.
2-2 RPL Programming Examples
FIB2 program listing
Program:
Comments:
«
 n
«
IF n 1 ‰
THEN n
ELSE
0 1
2 n
START
DUP
ROT
+
NEXT
SWAP DROP
END
»
Creates a local variable structure.
If n ≤ 1,
then Fn = n;
otherwise …
Puts F0 and F1 on the stack.
From 2 to n does the following loop:
Copies the latest F (initially F1)
Gets the previous F (initially F0)
Calculates the next F (initially F2)
Repeats the loop.
Drops Fn-1.
Ends the ELSE clause.
Ends the defining procedure.
»
`O FIB2 K
Stores the program in FIB2.
Checksum: # 23902d (press O%FIB2% !°#MEM# %BYTES%)
Bytes:
89
Example: Calculate F6 and F10.
Calculate F6.
J
6 %FIB2%
Calculate F10.
10 %FIB2%
FIBT (Comparing Program-Execution Time)
FIB1 calculates intermediate values Fi more than once, while FIB2 calculates each intermediate Fi only once.
Consequently, FIB2 is faster. The difference in speed increases with the size of n because the time required for
FIB1 grows exponentially with n, while the time required for FIB2 grows only linearly with n.
RPL Programming Examples 2-3
FIBT executes the TICKS command to record the execution time of FIB1 and FIB2 for a given value of n.
Level 1
"
Level 3
Level 2
Level 1
n
"
Fn
FIB1 TIME: z
FIB2 TIME: z
Techniques used in FIBT
!
!
!
Structured programming. FIBT calls both FIB1 and FIB2.
Programmatic use of calculator clock. FIBT executes the TICKS command to record the start and finish of
each subprogram.
Labeling output. FIBT tags each execution time with a descriptive message.
Required Programs
!
FIB1 (page 2-2) calculates Fn using recursion.
!
FIB2 (page 2-3) calculates Fn using looping.
FIBT program listing
Program:
Comments:
«
DUP TICKS SWAP FIB1
SWAP TICKS SWAP
- BR 8192 /
Copies n, then executes FIB1, recording the start and
stop time.
Calculates the elapsed time, converts it to a real
number, and converts that number to seconds.
Leaves the answer returned by FIB1 in level 2.
"FIB1 TIME" TAG
ROT TICKS SWAP FIB2
TICKS
SWAP DROP SWAP
- BR 8192 /
Tags the execution time.
Executes FIB2, recording the start and stop time.
Drops the answer returned by FIB2 (FIB1 returned
the same answer). Calculates the elapsed time for
FIB2 and converts to seconds.
"FIB2 TIME" TAG
Tags the execution time.
»
`OFIBT K
Checksum: # 23164d
Bytes: 129
2-4 RPL Programming Examples
Stores the program in FIBT.
Example: Calculate F13 and compare the execution time for the two methods.
Select the VAR menu and do the calculation.
J
13 %FIBT%
F13 is 233. FIB2 takes fewer seconds to execute than FIB1 (far fewer if n is large). (The times required for the
calculations depend on the contents of memory and other factors, so you may not get the exact times shown
above.)
Displaying a Binary Integer
This section contains three programs:
!
PAD is a utility program that converts an object to a string for right-justified display.
!
PRESERVE is a utility program for use in programs that change the calculator's status (angle mode, binary
base, and so on).
!
BDISP displays a binary integer in HEX, DEC, OCT, and BIN bases. It calls PAD to show the displayed
numbers right-justified, and it calls PRESERVE to preserve the binary base.
PAD (Pad with Leading Spaces)
PAD converts an object to a string, and if the string contains fewer than 22 characters, adds spaces to the
beginning of the string till the string reaches 22 characters.
When a short string is displayed with DISP, it appears left-justified: its first character appears at the left end of
the display. By adding spaces to the beginning of a short string, PAD moves the string to the right. When the
string (including leading spaces) reaches 22 characters, it appears right-justified: its last character appears at the
right end of the display. PAD has no effect on longer strings.
Level 1
"
Level 1
object
"
"object"
Techniques used in PAD
!
WHILE…REPEAT…END (indefinite loop). The WHILE clause contains a test that executes the
REPEAT clause and tests again (if true) or skips the REPEAT clause and exits (if false).
!
String operations. PAD demonstrates how to convert an object to string form, count the number of
characters, and combine two strings.
RPL Programming Examples 2-5
PAD program listing
Program:
Comments:
«
STR
Makes sure the object is in string form. (Strings
are unaffected by this command.)
WHILE
DUP SIZE 22 <
REPEAT
" " SWAP +
Repeats if the string contains fewer than 22
characters.
Loop-clause adds a leading space.
END
End loop.
»
`OPAD K
Stores the program in PAD.
Checksum: # 6577d
Bytes:
57.5
PAD is demonstrated in the program BDISP.
PRESERVE (Save and Restore Previous Status)
PRESERVE stores the current calculator (flag) status, executes a program from the stack, and restores the
previous status.
Level 1
"
Level 1
«program»
"
result of program
'program'
"
result of program
Techniques used in PRESERVE
!
Preserving calculator flag status. PRESERVE uses RCLF (recall flags) to record the current status of the
calculator in a binary integer, and STOF (store flags) to restore the status from that binary integer.
!
Local-variable structure. PRESERVE creates a local variable structure to briefly remove the binary
integer from the stack. Its defining procedure simply evaluates the program argument, then puts the binary
integer back on the stack and executes STOF.
!
Error trapping. PRESERVE uses IFERR to trap faulty program execution on the stack and to restore flags.
DOERR shows the error if one occurs.
2-6 RPL Programming Examples
PRESERVE program listing
Program:
Comments:
«
RCLF
Recalls the list of four 64-bit
binary integers representing the
status of the 128 system flags
and 128 user flags.
 f
«
IFERR
EVAL
Stores the list in local variable f.
Begins the defining procedure.
Starts the error trap.
Executes the program placed on
the stack as the level 1
argument. If the program caused
an error, restores flags, shows
the error, and aborts execution.
Ends the error routine.
Puts the list back on the stack,
then restores the status of all
flags.
THEN
f STOF ERRN DOERR
END
f STOF
»
Ends the defining procedure.
»
Stores the program in
PRESERVE.
`OPRESERVE K
Checksum: # 26834d
Bytes:
71
PRESERVE is demonstrated in the program BDISP.
BDISP (Binary Display)
BDISP displays a real or binary number in HEX, DEC, OCT, and BIN bases.
Level 1
"
Level 1
#n
"
#n
n
"
n
RPL Programming Examples 2-7
Techniques used in BDISP
!
IFERR…THEN…END (error trap). To accommodate real-number arguments, BDISP includes the
command R"B (real-to-binary). However, this command causes an error if the argument is already a binary
integer. To maintain execution if an error occurs, the R"B command is placed inside an IFERR clause. No
action is required when an error occurs (since a binary number is an acceptable argument), so the THEN
clause contains no commands.
!
Enabling LASTARG. In case an error occurs, the LASTARG recovery feature must be enabled to return the
argument (the binary number) to the stack. BDISP clears flag –55 to enable this.
!
FOR…NEXT loop (definite loop with counter). BDISP executes a loop from 1 to 4, each time
displaying n (the number) in a different base on a different line. The loop counter (named j in this program) is
a local variable created by the FOR…NEXT program structure (rather than by a  command), and
automatically incremented by NEXT.
!
Unnamed programs as arguments. A program defined only by its « and » delimiters (not stored in a
variable) is not automatically evaluated, but is placed on the stack and can be used as an argument for a
subroutine. BDISP demonstrates two uses for unnamed program arguments:
contains a main program argument and a call to PRESERVE. This program argument goes on the
stack and is executed by PRESERVE.
" BDISP also contains four program arguments that “customize” the action of the loop. Each of these
contains a command to change the binary base, and each iteration of the loop evaluates one of these
arguments.
" BDISP
When BDISP creates a local variable for n, the defining procedure is an unnamed program. However, since
this program is a defining procedure for a local variable structure, it is automatically executed.
Required Programs
PAD
!
PAD (Pad with Leading Spaces) expands a string to 22 characters so that DISP shows it right-justified.
PRESERVE
PRESERVE (S) stores the current status, executes the main nested program, and restores the status.
2-8 RPL Programming Examples
BDISP program listing
Program:
Comments:
«
«
DUP
-55 CF
IFERR
RB
THEN
END
 n
«
CLLCD
« BIN »
« OCT »
« DEC »
« HEX »
1 4
FOR j
EVAL
n STR
PAD
j DISP
NEXT
»
3 FREEZE
»
PRESERVE
Begins the main nested program.
Makes a copy of n.
Clears flag –55 to enable
LASTARG.
Begins error trap.
Converts n to a binary integer.
If an error occurs, do nothing (no
commands in the THEN clause).
Creates a local variable n and
begins the defining program.
Clears the display.
Nested program for BIN.
Nested program for OCT.
Nested program for DEC.
Nested program for HEX.
Sets the counter limits.
Starts the loop with counter j.
Executes one of the nested base
programs (initially for HEX).
Makes a string showing n in the
current base.
Pads the string to 22 characters.
Displays the string in the jth line.
Increments j and repeats the loop.
Ends the defining program.
Freezes the status and stack
areas.
Ends the main nested program.
Stores the current flag status,
executes the main nested
program, and restores the status.
»
`OBDISP K
Stores the program in BDISP.
Checksum: # 22884d
Bytes:
187
RPL Programming Examples 2-9
Example: Switch to DEC base, display #100 in all bases, and check that BDISP restored the base to DEC.
Clear the stack and select the MTH BASE menu. Make sure the current base is DEC and enter # 100.
‚·
‚ã%DEC%
!â100 `
Execute BDISP.
J %BDISP%
Return to the normal stack display and check the current base.
−
‚ã
Although the main nested program left the calculator in BIN base,
PRESERVE restored DEC base. To check that BDISP also works for
real numbers, try 144.
J
144 %BDISP%
Press − to return to the stack display.
Median of Statistics Data
This section contains two programs:
!
%TILE returns the value of a specified percentile of a list.
!
MEDIAN uses %TILE to calculate the median of the current statistics data.
%TILE (Percentile of a list)
%TILE sorts a list, then returns the value of a specified percentile of the list. For example, typing {list} 50
and pressing %©TILE% returns the median (50th percentile) of the list.
Level 2
Level 1
"
Level 1
{ list }
n
"
nth percentile of sorted list
2-10 RPL Programming Examples
Techniques used in %TILE
!
!
FLOOR and CEIL. For an integer, FLOOR and CEIL both return that integer; for a noninteger, FLOOR and
CEIL return successive integers that bracket the noninteger.
SORT. The SORT command sorts the list elements into ascending order.
%TILE program listing (Note: Use Approximate mode for this program and example)
Program:
Comments:
«
SWAP SORT
DUP SIZE
1 + ROT 100 / *
 p
«
DUP
p FLOOR GET
SWAP
p CEIL GET
+ 2 /
»
Brings the list to level 1 and sorts it.
Copies the list, then finds its size.
Calculates the position of the specified
percentile.
Stores the center position in local variable p.
Begins the defining procedure.
Makes a copy of the list.
Gets the number at or below the center
position.
Moves the list to level 1.
Gets the number at or above the center
position.
Calculates the average of the two numbers.
Ends the defining procedure.
»
`O%TILE K
Stores the program in %TILE.
Checksum: # 50559d
Bytes:
99
Example: Calculate the median of the list {8 3 1 5 2}.
!ä8 3 1 5 2`
J50 %©TILE%
MEDIAN (Median of Statistics Data)
MEDIAN returns a vector containing the medians of the columns of the statistics data. Note that for a sorted list
with an odd number of elements, the median is the value of the center element; for a list with an even number of
elements, the median is the average value of the elements just above and below the center.
Level 1
"
Level 1
"
[ x1 x2 … xm ]
RPL Programming Examples 2-11
Techniques used in MEDIAN
!
Arrays, lists, and stack elements. MEDIAN extracts a column of data from ΣDAT in vector form. To
convert the vector to a list, MEDIAN puts the vector elements on the stack and combines them into a list.
From this list the median is calculated using %TILE.
The median for the mth column is calculated first, and the median for the first column is calculated last. As
each median is calculated, ROLLD is used to move it to the top of the stack.
After all medians are calculated and positioned on the stack, they’re combined into a vector.
!
FOR…NEXT (definite loop with counter). MEDIAN uses a loop to calculate the median of each
column. Because the medians are calculated in reverse order (last column first), the counter is used to reverse
the order of the medians.
Required Program
!
%TILE (page 2-10) sorts a list and returns the value of a specified percentile.
MEDIAN program listing (Note: Use approximate mode for this program and example).
Program:
Comments:
«
RCL…
Puts a copy of the current
statistics matrix ΣDAT on the
stack.
DUP SIZE
Puts the list { n m }on the stack,
where n is the number of rows in
ΣDAT and m is the number of
columns.
OBJ DROP
Puts n and m on the stack, and
drops the list size.
 s n m
Creates local variables for s, n,
and m.
«
Begins the defining procedure.
Recalls and transposes ΣDAT.
Now n is the number of columns
in ΣDAT and m is the number of
rows. (To key in the … character,
press @½, then delete the
parentheses.)
'…DAT' TRN
1 m
FOR j
…-
2-12 RPL Programming Examples
Specifies the first and last rows.
For each row, does the following:
Extracts the last row in ΣDAT.
Initially this is the mth row, which
corresponds to the mth column in
the original ΣDAT.
(To key in the Σ– command, use
@µ.)
Program:
OBJ DROP
n LIST
50 %TILE
j ROLLD
NEXT
m ARRY
Comments:
Puts the row elements on the
stack. Drops the index list { n }.
Makes an n-element list.
Sorts the list and calculates its
median.
Moves the median to the proper
stack level.
Increments j and repeats the loop.
s STO…
Combines all the medians into an
m-element vector.
Restores ΣDAT to its previous
value.
Ends the defining procedure.
`OMEDIAN K
Stores the program in MEDIAN.
»
»
Checksum: # 50773d
Bytes:
136
Example: Calculate the median of the following data.
18 12
4 7
3 2
11 1
31 48
20 17
There are two columns of data, so MEDIAN will return a two-element vector.
Enter the matrix.
‚Ù%OK% %EDIT
18 `12 `˜šš
4 `7 `
3 `2 `
11 `1 `
31 `48 `
20 `17 `
` %OK%
The matrix is now stored in ΣDAT.
Calculate the median.
J %MEDIA%
Clear approximate mode (set exact mode) before going on to the next example.
RPL Programming Examples 2-13
Expanding and Collecting Completely
This section contains two programs:
! MULTI repeats a program until the program has no effect on its argument.
! EXCO calls MULTI to completely expand and collect an algebraic.
MULTI (Multiple Execution)
Given an object and a program that acts on the object, MULTI applies the program to the object repeatedly until
the program no longer changes the object.
Level 2
Level 1
"
Level 1
object
«program»
"
objectresult
Techniques used in MULTI
!
DO…UNTIL…END (indefinite loop). The DO clause contains the steps to be repeated. The UNTIL
clause contains the test that repeats both clauses again (if false) or exits (if true).
!
Programs as arguments. Although programs are commonly named and then executed by calling their
names, programs can also be put on the stack and used as arguments to other programs.
!
Evaluation of local variables. The program argument to be executed repeatedly is stored in a local variable.
It's convenient to store an object in a local variable when you don't know beforehand how many copies you'll
need. An object stored in a local variable is simply put on the stack when the local variable is evaluated.
MULTI uses the local variable name to put the program argument on the stack and then executes EVAL to
execute the program.
MULTI program listing
Program:
Comments:
 p
Creates a local variable p that contains the
program from level 1.
«
END
Begins the defining procedure.
Begins the DO loop clause.
Makes a copy of the object, now in level 1.
Applies the program to the object, returning
its new version.
Makes a copy of the new object.
Moves the old version to level 1.
Begins the DO test clause.
Tests whether the old version and the new
version are the same.
Ends the DO structure.
Ends the defining procedure.
`OMULTI K
Stores the program in MULTI.
«
DO
DUP
p EVAL
DUP
ROT
UNTIL
SAME
»
»
Checksum: # 22693d
Bytes:
56
2-14 RPL Programming Examples
MULTI is demonstrated in the next programming example.
EXCO (Expand and Collect Completely)
EXCO repeatedly executes EXPAN on an algebraic until the algebraic doesn't change, then repeatedly executes
COLCT until the algebraic doesn't change. In some cases the result will be a number.
Expressions with many products of sums or with powers can take many iterations of EXPAN to expand
completely, resulting in a long execution time for EXCO.
Level 1
"
Level 1
'algebraic'
"
'algebraic'
'algebraic'
"
z
Techniques used in EXCO
!
Subroutines. EXCO calls the program MULTI twice. It is more efficient to create program MULTI and
simply call its name twice than write each step in MULTI two times.
Required Programs
!
MULTI (Multiple Execution) repeatedly executes the programs that EXCO provides as arguments.
EXCO program listing
Program:
Comments:
«
« EXPAN »
Puts a program on the stack as the
level 1 argument for MULTI.
The program executes the
EXPAN command.
MULTI
Executes EXPAN until the
algebraic object doesn't change.
« COLCT »
Puts another program on the stack
for MULTI. The program
executes the COLCT command.
MULTI
Executes COLCT until the
algebraic object doesn't change.
»
`OEXCO K
Stores the program in EXCO.
Checksum: # 41162d
Bytes:
65.5
Example: Expand and collect completely the expression:
2
3x(4y + z) + (8x – 5z)
RPL Programming Examples 2-15
Enter the expression.
O3 * X *
!Ü4 *Y+Z ™+
! Ü 8 *X -5 *Z
™Q2
`
Select the VAR menu and start the program.
J %EXCO%
Minimum and Maximum Array Elements
This section contains two programs that find the minimum or maximum element of an array:
!
MNX uses a DO…UNTIL…END (indefinite) loop.
!
MNX2 uses a FOR…NEXT (definite) loop.
MNX (Minimum or Maximum Element—Version 1)
MNX finds the minimum or maximum element of an array on the stack.
Level 1
"
Level2
Level 1
[[ array ]]
"
[[ array ]]
Zmin or Zmax
Techniques used in MNX
!
DO…UNTIL…END (indefinite loop). The DO clause contains the sort instructions. The UNTIL clause
contains the system-flag test that determines whether to repeat the sort instructions.
!
User and system flags for logic control:
flag 10 defines the sort: When flag 10 is set, MNX finds the maximum element; when flag 10 is clear,
it finds the minimum element. You determine the state of flag 10 at the beginning of the program.
" System flag –64, the Index Wrap Indicator flag, determines when to end the sort. While flag –64 is clear,
the sort loop continues. When the index invoked by GETI wraps back to the first array element, flag –64 is
automatically set, and the sort loop ends.
" User
!
Nested conditional. An IF…THEN…END conditional is nested in the DO…UNTIL…END conditional,
and determines the following:
" Whether
to maintain the current minimum or maximum element, or make the current element the new
minimum or maximum.
" The sense of the comparison of elements (either < or >) based on the status of flag 10.
!
Custom menu. MNX builds a custom menu that lets you choose whether to sort for the minimum or
maximum element. Key 1, labeled %MAX%, sets flag 10. Key 2, labeled %MIN%, clears flag 10.
!
Logical function. MNX executes XOR (exclusive OR) to test the combined state of the relative value of the
two elements and the status of flag 10.
2-16 RPL Programming Examples
MNX program listing
Program:
Comments:
«
{{ "MAX"
« 10 SF CONT » }
{ "MIN"
« 10 CF CONT » }}
Defines the option menu. %MAX% sets
flag 10 and continues execution. %MIN%
clears flag 10 and continues execution.
Displays the temporary menu and a
TMENU
"Sort for MAX or MIN?" prompt message.
PROMPT
1 GETI
DO
ROT ROT GETI
Gets the first element of the array.
Begins the DO loop.
Puts the index and the array in levels 1
and 2, then gets the new array element.
4 ROLL DUP2
Moves the current minimum or
maximum array element from level 4
below 1, then copies both.
IF
> 10 FS? XOR
Tests the combined state of the relative
value of the two elements and the status
of flag 10.
THEN
SWAP
END
If the new element is either less than
the current maximum or greater than
the current minimum, swaps the new
element into level 1.
DROP
Drops the other element off the stack.
UNTIL
-64 FS?
Begins the DO test-clause.
Tests if flag –64 is set — if the index
reached the end of the array.
END
SWAP DROP 0 MENU
Ends the DO loop.
Swaps the index to level 1 and drops it.
Restores the last menu.
»
`OMNX K
Stores the program in MNX.
Checksum: # 20991d
Bytes:
194.5
Example: Find the maximum element of the following matrix:
12 56
45 1
9 14
Enter the matrix.
RPL Programming Examples 2-17
!²
12 `56 `˜šš
45 `1 `
9 `14 `
`
Select the VAR menu and execute MNX.
J %MNX%
Find the maximum element.
%MAX%
MNX2 (Minimum or Maximum Element- Version 2)
Given an array on the stack, MNX2 finds the minimum or maximum element in the array. MNX2 uses a
different approach than MNX: it executes OBJ" to break the array into individual elements on the stack for
testing, rather than executing GETI to index through the array.
Level 1
"
Level2
Level 1
[[ array ]]
"
[[ array ]]
Zmax or Zmin
Techniques used in MNX2
!
FOR…NEXT (definite loop). The initial counter value is 1. The final counter value is nm –1, where nm is
the number of elements in the array. The loop-clause contains the sort instructions.
!
User flag for logic control. User flag 10 defines the sort: When flag 10 is set, MNX2 finds the maximum
element; when flag 10 is clear, it finds the minimum element. You determine the status of flag 10 at the
beginning of the program.
!
Nested conditional. An IF…THEN…END conditional is nested in the FOR…NEXT loop, and determines
the following:
" Whether
to maintain the current minimum or maximum element, or make the current element the new
minimum or maximum.
" The sense of the comparison of elements (either < or >) based on the status of flag 10.
!
Logical function. MNX2 executes XOR (exclusive OR) to test the combined state of the relative value of
the two elements and the status of flag 10.
!
Custom menu. MNX2 builds a custom menu that lets you choose whether to sort for the minimum or
maximum element. Key 1, labeled %MAX%, sets flag 10. Key 2, labeled %MIN%, clears flag 10.
2-18 RPL Programming Examples
MNX2 program listing
Program:
Comments:
«
{{ "MAX"
« 10 SF CONT » }
{ "MIN"
« 10 CF CONT » }}
TMENU
"Sort for MAX or MIN?"
PROMPT
DUP OBJ
Defines the temporary option menu. %MAX%
sets flag 10 and continues execution. %MIN%
clears flag 10 and continues execution.
Displays the temporary menu and a
prompting message.
Copies the array. Returns the individual array
elements to levels 2 through nm+1, and
returns the list containing n and m to level 1.
1
SWAP OBJ
Sets the initial counter value.
Converts the list to individual elements on
the stack.
DROP * 1 -
Drops the list size, then calculates the final
counter value (nm - 1).
FOR n
Starts the FOR…NEXT loop.
DUP2
Saves the array elements to be tested
(initially the last two elements). Uses the last
array element as the current minimum or
maximum.
IF
> 10 FS? XOR
Tests the combined state of the relative value
of the two elements and the status of flag 10.
THEN
SWAP
END
If the new element is either less than the
current maximum or greater than the current
minimum, swaps the new element into level
1.
DROP
Drops the other element off the stack.
Ends the FOR…NEXT loop.
Restores the last menu.
NEXT
0 MENU
»
`OMNX2 K
Stores the program in MNX2.
Checksum: # 6992d
Bytes:
188.5
Example: Use MNX2 to find the minimum element of the matrix from the previous example:
12 56
45 1
9 14
Enter the matrix (or retrieve it from the previous example).
RPL Programming Examples 2-19
!²
12 `56 `˜šš
45 `1 `
9 `14 `
`
Select the VAR menu and execute MNX2.
J %MNX2%
Find the minimum element.
%MIN%
Applying a Program to an Array
APLY makes use of list processing to transform each element of an array according to a desired procedure. The
input array must be numeric, but the output array may be symbolic.
The procedure applied to each element must be a program that takes exactly one argument (i.e. the element) and
returns exactly one result (i.e. the transformed element).
Level 2
Level 1
"
Level 1
[ array ]
« program »
"
[[ array ]] or {{ array }}
Techniques used in APLY
!
Manipulating Meta-Objects. Meta-objects are composite objects like arrays and lists that have been
disassembled on the stack. APLY illustrates several approaches to manipulating the elements and dimensions
of such objects.
!
Application of List Processing. APLY makes use of DOSUBS (although DOLIST might also have been
used) to perform the actual transformation of array elements.
!
Using an IFERR…THEN…ELSE…END Structure. The entire symbolic pseudo-array case is handled
within a error structure — triggered when the "ARRY command generates an error when symbolic elements
are present.
!
Using Flags. User flag 1 is used to track the case when the input array is a vector.
APLY program listing
Program:
«
 a p
«
2-20 RPL Programming Examples
Comments:
Store the array and program in local variables.
Begin the main local variable structure.
Program:
1 CF
a DUP SIZE
DUP SIZE
IF 1 ==
THEN 1 SF 1 +
Comments:
Make sure the flag 1 is clear to begin the procedure.
Retrieve the dimensions of the array.
Determine if the array is a vector.
SWAP OBJ OBJ
DROP
Disassemble the original vector, leaving the element
count, n, in level 1.
1 + ROLL
If array is a vector, set flag 1 and add a second
dimension by treating the vector as an n × 1 matrix.
Roll the elements up the stack and bring the “matrix”
dimensions of the vector to level 1.
ELSE DROP2 a OBJ
If array is a matrix, clean up the stack and decompose
the matrix into its elements, leaving its dimension list
on level 1.
END DUP OBJ DROP * Duplicate the dimension list and compute the total
number of elements.
SWAP OVER 2 +
ROLLD LIST
Roll up the element count and combine all elements
into a list.Note that the elements in the list are in rowmajor order.
1 p DOSUBS
Recalls the program and uses it as an argument for
DOSUBS (DOLIST works in this case as well).
Result is a list of transformed elements.
OBJ 1 + ROLL
Disassembles the result list and brings the array
dimensions to level 1.
IFERR
Begins the error-trapping structure. Its purpose is to
find and handle the cases when the result list contains
symbolic elements.
Was original array a vector? If the original array was
a vector, then drop the second dimension (1) from the
dimension list.
IF 1 FS?
THEN OBJ DROP
LIST
END ARRY
THEN
OBJ
IF 1 FC?C
THEN DROP
END  n m
« 1 n
FOR i
m LIST
Convert the elements into an array with the given
dimensions. If there are symbolic elements present, an
error will be generated and the error clause which
follows will be executed.
Begin the error clause.
Put the array dimensions on levels 2 and 1. If the
array is a vector, level 1 contains a 1.
Is original array a matrix? Clear flag 1 after
performing the test.
Drop the number of matrix elements.
Store the array dimensions in local variables.
Begin local variable structure and initiate
FOR…NEXT loop for each row.
Collect a group of elements into a row (a list).
RPL Programming Examples 2-21
Program:
Comments:
'm*(n-i)+i' EVAL Computes the number of elements to roll so that the
ROLLD
next row can be collected.
NEXT
n LIST
Repeat loop for the next row. Gather rows into a list,
forming a list of lists (symbolic pseudo-array).
»
END 1 CF
Close the local variable structure and end the
IFERR…THEN...END structure. Clear flag 1 before
exiting the program.
»
»
Stores the program in APLY.
`OAPLY K
Checksum: # 11132d
Bytes:
314
Example: Apply the function, f(x) = Ax3-7 to each element x of the vector [ 3 -2 4 ].
!Ô3†2W†4`
‚å 3 QA *7 `J %APLY%
H#DISP ˜˜
(select small stack display to see
all vector elements.)
Converting Between Number Bases
nBASE converts a positive decimal number (x) into a tagged string representation of the equivalent value in a
different number base (b). Both x and b must be real numbers. nBASE automatically rounds both arguments to
the nearest integer.
Level 2
Level 1
"
Level 1
x
b
"
x baseb: "string"
Techniques used in nBASE
!
String Concatenation and Character Manipulation. nBASE makes use of several string and character
manipulation techniques to build up the result string.
!
Tagged Output. nBASE labels (“tags”) the output string with its original arguments so that the output is a
complete record of the command.
!
Indefinite Loops. nBASE accomplishes most of its work using indefinite loops — both DO...UNTIL...END
and WHILE...REPEAT...END loops.
2-22 RPL Programming Examples
nBASE program listing
Program:
Comments:
«
1 CF 0 RND SWAP 0 RND
RCLF
 b n f
«
Clear flag 1, round both arguments to
integers and recall flag settings.
Store the base, number and flag settings
in local variables.
Begin the outer local variable structure.
STD n LOG b LOG /
Sets “standard” display mode and
computes the ratio of the common
logarithms of number and base.
10 RND
Rounds result to remove imprecision in
last decimal place.
IP n 0
Find the integer part of log ratio, recall
the original number, and initialize the
counter variable k for use in the
DO...UNTIL loop.
 i m k
Store the values in local variables.
«
""
DO
'm' EVAL b i
'k' EVAL - ^
Begin inner local variable structure, enter
an empty string and begin the
DO...UNTIL...END loop.
Compute the decimal value of the
(i – k) th position in the string.
DUP2 MOD
Makes a copy of the arguments and
computes the decimal value still
remaining that must be accounted for by
other positions.
IF DUP 0 ==
'm' EVAL b Š
AND
THEN 1 SF
END 'm' STO
/ IP
Is the remainder zero and m ≥ b?
If the test is true, then set flag 1.
IF DUP 10 Š
THEN 55
ELSE 48
END + CHR
Is the “digit” ≥ 10?
Then convert the digit into a alphabetic
digit (such as A, B, C, …).
+ 'k' 1 STO+
Append the digit to the current result
string and increment the counter variable
k.
Store the remainder in m. Compute the
number of times the current positionvalue goes into the remaining decimal
value. This is the “digit” that belongs in
the current position.
RPL Programming Examples 2-23
Program:
UNTIL 'm' EVAL 0 ==
END
IF 1 FS?C
THEN "0" +
Comments:
Repeat the DO...UNTIL loop until m = 0
(i.e. all decimal value have been
accounted for).
Is flag 1 set? Clear the flag after the test.
Then add a placeholding zero to the result
string.
WHILE i 'k' EVAL
- 0 Š
Begin WHILE...REPEAT loop to
determine if additional placeholding zeros
are needed.
Loop repeats as long as i ≠ k.
REPEAT "0" +
1 'k' STO+
Add an additional placeholding zero and
increment k before repeating the testclause.
End the WHILE...REPEAT...END loop,
the IF...THEN...END structure, and the
inner local variable structure.
END
END
»
" base" b +
n SWAP + TAG f STOF
End the outermost
IF...THEN...ELSE...END structure and
create the label string and tag the result
string using the original arguments.
Also restore original flag settings.
»
»
`OnBASE K
Stores the program in nBASE.
Checksum: # 54850d
Bytes:
433
Example: Convert 100010 to base 23.
1000 `23 J %NBASE%
Verifying Program Arguments
The two utility programs in this section verify that the argument to a program is the correct object type.
!
NAMES verifies that a list argument contains exactly two names.
!
VFY verifies that the argument is either a name or a list containing exactly two names. It calls NAMES if the
argument is a list.
You can modify these utilities to verify other object types and object content.
NAMES (Check List for Exactly Two Names)
If the argument for a program is a list (as determined by VFY), NAMES verifies that the list contains exactly
two names. If the list does not contain exactly two names, an error message appears in the status area and
program execution is aborted.
2-24 RPL Programming Examples
Level 1
"
{ valid list }
"
{ invalid list }
"
Level 1
(error message in status area)
Techniques used in NAMES
!
Nested conditionals. The outer conditional verifies that there are two objects in the list. If so, the inner
conditional verifies that both objects are names.
!
Logical functions. NAMES uses the AND command in the inner conditional to determine if both objects
are names, and the NOT command to display the error message if they are not both names.
NAMES program listing
Program:
«
IF
OBJ
DUP 2. SAME
THEN
DROP
IF
TYPE 6. SAME
SWAP TYPE 6. SAME
AND
Comments:
Starts the outer conditional structure.
Returns the n objects in the list to levels 2
through (n + 1), and returns the list size n to
level 1.
Copies the list size and tests if it's 2.
If the size is 2, moves the objects to level 1 and
2, and starts the inner conditional structure.
Tests if the object is a name: returns 1 if so,
otherwise 0.
Moves the second object to level 1, then tests if
it is a name (returns 1 or 0).
Combines test results: Returns 1 if both tests
were true, otherwise returns 0.
NOT
Reverses the final test result.
THEN
If the objects are not both names, displays an
"List needs two names" error message and aborts execution.
DOERR
Ends the inner conditional structure.
END
ELSE
DROPN
"Illegal list size"
DOERR
END
If the list size is not 2, drops the list size,
displays an error message, and aborts
execution.
Ends the outer conditional.
»
`ONAMES K
Stores the program in NAMES.
Checksum: # 10752d
Bytes:
141.5
RPL Programming Examples 2-25
NAMES is demonstrated in the program VFY.
VFY (Verify Program Argument)
VFY verifies that an argument on the stack is either a name or a list that contains exactly two names.
Level 1
"
Level 1
'name'
"
'name'
{ valid list }
"
{ valid list }
{ invalid list }
"
{ invalid list } (and error message in status area)
invalid object
"
invalid object (and error message in status area)
Techniques used in VFY
!
!
Utility programs. VFY by itself has little use. However, it can be used with minor modifications by other
programs to verify that specific object types are valid arguments.
CASE…END (case structure). VFY uses a case structure to determine if the argument is a list or a name.
!
Structured programming. If the argument is a list, VFY calls NAMES to verify that the list contains exactly
two names.
!
Local variable structure. VFY stores its argument in a local variable so that it can be passed to NAMES if
necessary.
!
Logical function. VFY uses NOT to display an error message.
Required Programs
NAMES
!
NAMES (Check List for Exactly Two Names) verifies that a list argument contains exactly two names.
VFY program listing
Program:
«
DUP
DTAG
Comments:
Copies the original argument to leave on the
stack.
Removes any tags from the argument for
subsequent testing.
 argm
Stores the argument in local variable argm.
«
Begins the defining procedure.
Begins the case structure.
Tests if the argument is a list.
If so, puts the argument back on the stack and
calls NAMES to verify that the list is valid,
then leaves the CASE structure.
CASE
argm TYPE 5. SAME
THEN
argm NAMES
END
2-26 RPL Programming Examples
Program:
argm TYPE 6. SAME
NOT
THEN
"Not name or list"
DOERR
END
END
»
Comments:
Tests if the argument is not a name. If so,
displays an error message and aborts execution.
Ends the CASE structure.
Ends the defining procedure.
»
`OVFYK
Enters the program, then stores it in VFY.
Checksum: # 31403d
Bytes:
139.5
Example: Execute VFY to test the validity of the name argument BEN. (The argument is valid and is simply
returned to the stack.)
OBEN `
J %VFY%
Example: Execute VFY to test the validity of the list argument {BEN JEFF SARAH }. Use the name from the
previous example, then enter the names JEFF and SARAH and convert the three names to a list.
OJEFF `
OSARAH `
3 !° %LIST% %²LIST%
Execute VFY. Since the list contains too many names, the error message is displayed and execution is aborted.
J %VFY%
Converting Procedures from Algebraic to RPN
This section contains a program, "RPN, that converts an algebraic expression into a series (list) of objects in
equivalent RPN order.
Level 1
"
Level 1
‘symb’
"
{ objects }
RPL Programming Examples 2-27
Techniques used in "RPN
!
Recursion. The "RPN program calls itself as a subroutine. This powerful technique works just like calling
another subroutine as long as the stack contains the proper arguments before the program calls itself. In this
case the level 1 argument is tested first to be sure that it is an algebraic expression before "RPN is called
again.
!
Object Type-Checking. "RPN uses conditional branching that depends on the object type of the level 1
object.
!
Nested program Structures. "RPN nests IF…THEN…END structures inside FOR…NEXT loops inside a
IF…THEN… ELSE…END structure.
!
List Concatenation. The result list of objects in RPN order is built by using the ability of the + command to
sequentially append additional elements to a list. This is a handy technique for gathering results from a
looping procedure.
"RPN program listing
Program:
Comments:
«
OBJ
IF OVER
THEN  n f
«
Take the expression apart.
If the argument count is nonzero,
then store the count and the
function.
Begins local variable defining
procedure.
1 n
FOR i
Begins FOR…NEXT loop, which
converts any algebraic arguments to
lists.
IF DUP TYPE 9. SAME
Tests whether argument is an
algebraic.
THEN RPN
If argument is an algebraic, convert
it to a list first.
END n ROLLD
Roll down the stack to prepare for
the next argument.
NEXT
Repeat the loop for the next
argument.
IF DUP TYPE 5. ‹
Tests to see if level 1 object is a list.
THEN 1 LIST
If not a list, then convert it to one.
END
Ends the IF…THEN…END
structure.
IF n 1 >
Tests to see if there is more than
one argument.
THEN 2 n
START +
NEXT
Combine all of the arguments into a
list.
2-28 RPL Programming Examples
Program:
Comments:
END f +
Append the function to the end of
the list.
»
End the local variable defining
procedure.
ELSE 1 LIST SWAP DROP
For functions with no arguments,
converts to a simple list.
END
End the IF…THEN…
ELSE…END structure.
»
Stores the program in "RPN.
`O"RPN K
Checksum: # 1522d
Bytes:
181.0
Example: Convert the following algebraic expression to a series of objects in RPN syntax:
'A*COS(B+ƒ(C/D))-X^3'.
OA *TB +R!Ü
C /D ™™-X Q3 `%²RPN%
Bessel Functions
This section contains a program, BER, that calculates the real part Bern(x) of the Bessel function Jn (xe3πi/4).
When n = 0,
4
8
(x ⁄ 2 )
(x ⁄ 2 )
- + ----------------- – …
Ber ( x ) = 1 – ---------------2
2
2!
4!
Level 1
"
Level 1
z
"
Ber(z)
Techniques used in BER
!
Local variable structure. At its outer level, BER consists solely of a local variable structure and so has two
properties of a user-defined function: it can take numeric or symbolic arguments from the stack, or it can take
arguments in algebraic syntax. However, because BER uses a DO…UNTIL…END loop, its defining
procedure is a program. (Loop structures are not allowed in algebraic expressions.) Therefore, unlike userdefined functions, BER is not differentiable.
!
DO…UNTIL…END loop (indefinite loop with counter). BER calculates successive terms in the series
using a counter variable. When the new term does not differ from the previous term to within the 12-digit
precision of the calculator, the loop ends.
!
Nested local variable structures. The outer structure is consistent with the requirements of a user-defined
function. The inner structure allows storing and recalling of key parameters.
RPL Programming Examples 2-29
BER program listing
Program:
Comments:
«
 x
Creates local variable x.
«
Begins outer defining procedure.
'x/2' NUM 2 1
 xover2 j sum
Enters x/2, the first counter value, and
the first term of the series, then creates
local variables.
«
Begins inner defining procedure.
Begins the loop.
Recalls the old sum and calculates the
new sum.
DO
sum
'sum+(-1)^(j/2)*
xover2^(2*j)/SQ(j!)'
EVAL
2 'j' STO+
DUP 'sum' STO
UNTIL
==
END
sum
Increments the counter.
Stores the new sum.
Ends the loop clause.
Tests the old and new sums.
Ends the loop.
Recalls the sum.
»
Ends inner defining procedure.
Ends outer defining procedure.
`OBER K
Stores the program in BER.
»
»
Checksum: # 15837d
Bytes:
203
Example: Calculate BER(3).
J
3 %BER%
Calculate BER(2) in algebraic syntax.
O %BER% !Ü2
N
Animation of Successive Taylor's Polynomials
This section contains three programs that manipulate graphics objects to display a sequence of Taylor's
polynomials for the sine function.
!
SINTP draws a sine curve, and saves the plot in a variable.
2-30 RPL Programming Examples
!
SETTS superimposes plots of successive Taylor's polynomials on the sine curve plot from SINTP, and saves
the resulting graphics objects in a list.
!
TSA uses the ANIMATE command to display in succession each graphics object from the list built in SETTS.
SINTP (Converting a Plot to a Graphics Object)
SINTP draws a sine curve, returns the plot to the stack as a graphics object, and stores that graphics object in a
variable. Make sure your calculator is in Radians mode.
Techniques used in SINTP
!
Programmatic use of PLOT commands. SINTP uses PLOT commands to build and display a graphics
object.
SINTP program listing
Program:
Comments:
«
'SIN(X)' STEQ
Stores the expression for sin
x in EQ.
FUNCTION '-2*‡' NUM
DUP NEG XRNG
-2 2 YRNG
Sets the plot type and x- and
y-axis display ranges.
ERASE DRAW
Erases PICT, then plots the
expression.
PICT RCL 'SINT' STO
Recalls the resultant graphics
object and stores it in SINT.
»
`O SINTP K
Stores the program in
SINTP.
Checksum: # 41184d
Bytes:
94
SINTP is demonstrated in the program TSA.
RPL Programming Examples 2-31
SETTS (Superimposing Taylor's polynomials)
SETTS superimposes successive Taylor's polynomials on a sine curve and stores each graphics object in a list.
Techniques used in SETTS
!
Structured programming. SETTS calls SINTP to build a sine curve and convert it to a graphics object.
!
FOR…STEP (definite loop). SETTS calculates successive Taylor's polynomials for the sine function in a
definite loop. The loop counter serves as the value of the order of each polynomial.
!
Programmatic use of PLOT commands. SETTS draws a plot of each Taylor's polynomial.
!
Manipulation of graphics objects. SETTS converts each Taylor's polynomial plot into a graphics object.
Then it executes + to combine each graphics object with the sine curve stored in SINT, creating nine new
graphics objects, each the superposition of a Taylor's polynomial on a sine curve. SETTS then puts the nine
new graphics objects, and the sine curve graphics object itself, in a list.
SETTS program listing
Program:
Comments:
«
SINTP
Plots a sine curve and stores the
graphics object in SINT.
1 17 FOR n
Sets the range for the FOR loop
using local variable n.
'SIN(X)' 'X' n TAYLR Plots the Taylor's polynomial of
STEQ ERASE DRAW
order n.
PICT RCL SINT +
Returns the plot to the stack as a
graphics object and executes + to
superimpose the sine plot from
SINT.
2 STEP
Increments the loop counter n by
2 and repeats the loop.
SINT
10 LIST
'TSL' STO
Puts the sine curve graphics
object on the stack, then builds a
list containing it and the nine
graphics objects created in the
loop. Stores the list in TSL.
»
`OSETTS K
Checksum: # 41304d
Bytes:
130.5
SETTS is demonstrated in the program TSA.
2-32 RPL Programming Examples
Stores the program in SETTS.
TSA (Animating Taylor's Polynomials)
TSA displays in succession each graphics object created in SETTS.
Techniques used in TSA
! Passing a global variable. Because SETTS takes several minutes to execute, TSA does not call SETTS.
Instead, you must first execute SETTS to create the global variable TSL containing the list of graphics objects.
TSA simply executes that global variable to put the list on the stack.
!
ANIMATE. TSA uses the ANIMATE command to display in succession each graphics object from the list.
TSA program listing
Program:
Comments:
«
TSL OBJ
Puts the list TSL on the stack
and converts it to 10 graphics
objects and the list count.
{ { #0 #0 } .5 0 } +
Set up the parameters for
ANIMATE.
ANIMATE
Displays the graphics in
succession.
11 DROPN
Removes the graphics objects
and list count from the stack.
»
`OTSA K
Stores the program in TSA.
Checksum: # 24644d
Bytes:
92.5
Example: Execute SETTS and TSA to build and display in succession a series of Taylor's polynomial
approximations of the sine function.
Set Radians mode and execute SETTS to build the list of graphics objects. (SETTS takes several minutes to
execute.) Then execute TSA to display each plot in succession. The display shows TSA in progress.
!&H !ANGLE !RAD ( if necessary)
J %SETTS%
%TSA%
Press − to stop the animation. Press !&H !ANGLE !DEG to restore Degrees mode.
RPL Programming Examples 2-33
Programmatic Use of Statistics and Plotting
This section describes a program PIE you can use to draw pie charts. PIE prompts for single variable data,
stores that data in the statistics matrix ΣDAT, then draws a labeled pie chart that shows each data point as a
percentage of the total.
Techniques used in PIE
!
Programmatic use of PLOT commands. PIE executes XRNG and YRNG to define x- and y-axis display
ranges in user units, and executes ARC and LINE to draw the circle and individual slices.
!
Programmatic use of matrices and statistics commands.
!
Manipulating graphics objects. PIE recalls PICT to the stack and executes GOR to merge the label for each
slice with the plot.
!
FOR…NEXT (definite loop). Each slice is calculated, drawn, and labeled in a definite loop.
!
CASE…END structure. To avoid overwriting the circle, each label is offset from the midpoint of the arc of
the slice. The offset for each label depends on the position of the slice in the circle. The CASE…END
structure assigns an offset to the label based on the position of the slice.
!
Preserving calculator flag status. Before specifying Radians mode, PIE saves the current flag status in a
local variable, then restores that status at the end of the program.
!
Nested local variable structures. At different parts of the process, intermediate results are saved in local
variables for convenient recall as needed.
!
Temporary menu for data input.
PIE program listing
Program:
Comments:
«
RCLF  flags
Recalls the current flag status
and stores it in variable flags.
«
RAD
{{ "SLICE" …+ }
{ }
{ "CLEAR" CL… }
{ } { }
{ "DRAW" CONT }}
Sets Radians mode.
Defines the input menu: key 1
executes Σ+ to store each data
point in ΣDAT, key 3 clears
ΣDAT, and key 6 continues
program execution after data
entry.
TMENU
"Key values into
SLICE
DRAW
restarts program."
PROMPT
Displays the temporary menu.
Prompts for inputs.
represents the newline
character (… ë) after you
enter the program on the stack.
ERASE 1 131 XRNG
1 64 YRNG CLLCD
Erases the current PICT and
sets plot parameters.
2-34 RPL Programming Examples
Program:
Comments:
"Please wait...
Drawing Pie Chart"
1 DISP
Displays “drawing” message.
(66,32) 20 0 6.28
ARC
Draws the circle.
PICT RCL LCD
RCL… TOT /
Displays the empty circle.
Recalls the statistics data
matrix, computes totals, and
calculates the proportions.
DUP 100 *
Converts the proportions to
percentages.
 prcnts
Stores the percentage matrix in
prcnts.
«
Multiplies the proportion matrix
by 2π, and enters the initial
angle (0).
2 ‡ NUM * *
0
 prop angle
Stores the angle matrix in prop
and angle in angle.
«
Sets up 1 to m as loop counter
range.
Begins loop-clause.
prop SIZE OBJ
DROP SWAP
FOR n
(66,32) prop n GET Puts the center of the circle on
'angle' STO+
the stack, then gets the nth
value from the proportion
matrix and adds it to angle.
angle COS angle SIN Computes the endpoint and
RC 20 * OVER +
draws the line for the nth slice.
LINE
PICT RCL
angle prop n GET
2 / - DUP DUP
COS SWAP SIN RC
26 * (66,32) +
Recalls PICT to the stack.
For labeling the slice, computes
the midpoint of the arc of the
slice.
SWAP
CASE
Starts the CASE structure to
test angle and determine the
offset value for the label.
DUP 1.5 ‰
THEN
DROP
END
DUP 4.4 ‰
THEN
DROP 15 END
From 0 to 1.5 radians, doesn't
offset the label.
From 1.5 to 4.4 radians, offsets
the label 15 user units left.
RPL Programming Examples 2-35
Program:
5 <
THEN
(3,2) +
END
END
Comments:
From 4.4 to 5 radians, offsets
the label 3 units right and 2
units up.
Ends the CASE structure.
prcnts n GET
1 RND
STR "%" +
Gets the nth value from the
percentage matrix, rounds it to
one decimal place, and converts
it to a string with “%”
appended.
1 GROB
Converts the string to a
graphics object.
GOR DUP PICT STO
Adds the label to the plot and
stores the new plot.
LCD
NEXT
{ } PVIEW
»
»
flags STOF
» 0 MENU
Displays the updated plot.
Ends the loop structure.
Displays the finished plot.
Restores the original flag status.
Restores the previous menu.
(You must first press − to
clear the plot.)
»
`OPIE K
Stores the program in PIE.
Checksum: # 16631d
Bytes:
737
Example: The inventory at Fruit of the Vroom, a drive-in fruit stand, includes 983 oranges, 416 apples, and 85
bananas. Draw a pie chart to show each fruit's percentage of total inventory.
J %PIE%
Clear the current statistics data. (The prompt is removed
from the display.) Key in the new data and draw the pie
chart.
CLEAR
983 %SLICE%
416 %SLICE%
85 %SLICE%
%DRAW%
Press − to return to the stack display.
2-36 RPL Programming Examples
Trace Mode
This section contains two programs, αENTER and ßENTER, which together provide “trace mode” for the
hp49g+/hp48gII using an external printer. To turn on “trace mode,” set flag –63 and activate User mode. To
turn off “trace mode,” clear flag –63 or turn off User mode.
Techniques used in αENTER and ßENTER
!
Vectored ENTER. Setting flag –63 and activating User mode turns on vectored ENTER. When vectored
ENTER is turned on and variable αENTER exists, the command-line text is put on the stack as a string and
αENTER is evaluated. Then, if variable ßENTER exists, the command that triggered the command-line
processing is put on the stack as a string and ßENTER is evaluated.
αENTER program listing
Program:
Comments:
«
PR1
OBJ
Prints the command line text, then
converts the string to an object and
evaluates it.
»
`O αENTER K
Stores the program in αENTER.
(Press ~‚A to type α. You
must use this name.)
Checksum: # 127d
Bytes:
25.5
ßENTER program listing
Program:
Comments:
«
PR1 DROP
PRSTC
Prints the command that caused the
processing, then drops it and prints
the stack in compact form.
»
`O ßENTER K
Stores the program in ßENTER.
(Press ~‚B to type ß. You
must use this name.)
Checksum: # 31902d
Bytes:
28
RPL Programming Examples 2-37
Inverse-Function Solver
This section describes the program ROOTR, which finds the value of x at which f(x) = y. You supply the
variable name for the program that calculates f(x), the value of y, and a guess for x (in case there are multiple
solutions).
Level 3
Level 2
Level 1
"
Level 1
'function name'
y
xguess
"
x
Techniques used in ROOTR
!
!
Programmatic use of root-finder. ROOTR executes ROOT to find the desired x-value.
Programs as arguments. Although programs are commonly named and then executed by calling their
names, programs can also be put on the stack and used as arguments to other programs.
ROOTR program listing
Program:
Comments:
«
 fname yvalue xguess Creates local variables.
«
xguess 'XTEMP' STO
Begins the defining procedure.
Creates variable XTEMP (to be solved for).
« XTEMP fname
yvalue - »
Enters program that evaluates f(x) - y.
'XTEMP'
xguess
ROOT
Enters name of unknown variable.
Enters guess for XTEMP.
Solves program for XTEMP.
»
Ends the defining procedure.
Program:
'XTEMP' PURGE
Comments:
Purges the temporary variable.
»
`OROOTR K
Stores the program in ROOTR.
Checksum: # 4708d
Bytes:
163
Example: Assume you often work with the expression
3.7x3 + 4.5x2 + 3.9x + 5 and have created the program X"FX to calculate the value:
«  x '3.7*x^3+4.5*x^2+3.9*x+5' »
You can use ROOTR to calculate the inverse function.
2-38 RPL Programming Examples
Example: Find the value of x for which X"FX equals 599.5. Use a guess in the vicinity of 1.
Start by keying in X"FX :
@å@é x †O3.7
*x Q3 +4.5 * x Q2
+3.9 *x +5 `
Store the program in X"FX, then enter the program name, the y-value 599.5, and the guess 1, and execute
ROOTR:
O X"FX K
O J %X²FX% `
599.5 ` 1 %ROOTR%
Animating a Graphical Image
Program WALK shows a small person walking across the display. It animates this custom graphical image by
incrementing the image position in a loop structure.
Techniques used in WALK
!
Custom graphical image. (Note that the programmer compiles the full information content of the graphical
image before writing the program by building the image interactively in the Graphics environment and then
returning it to the command line.)
!
FOR…STEP (definite loop). WALK uses this loop to animate the graphical image. The ending value for
the loop is MAXR. Since the counter value cannot exceed MAXR, the loop executes indefinitely.
WALK program listing
Program:
«
Comments:
Puts the graphical image of the
walker in the command line.
(Note that the hexadecimal
GROB 9 15 E300
portion
of the graphics object is a
140015001C001400E300
8000C110AA0094009000 continuous integer
4100220014102800
E300...2800. The
linebreaks do not represent
spaces.)
 walk
Creates local variable walk
containing the graphics object.
«
ERASE { # 0d # 0d }
Clears PICT, then displays it.
PVIEW
RPL Programming Examples 2-39
Program:
Comments:
Puts the first position on the stack
{ # 0d # 25d }
and turns on the first image. This
PICT OVER walk GXOR
readies the stack and PICT for
the loop.
Starts the loop to generate
horizontal coordinates
5 MAXR FOR i
indefinitely.
Computes the horizontal
i 131 MOD RB
coordinate for the next image.
Specifies a fixed vertical
coordinate. Puts the two
# 25d 2 LIST
coordinates in a list.
Displays the new image, leaving
PICT OVER walk GXOR
its coordinates on the stack.
Turns off the old image,
PICT ROT walk GXOR removing its coordinates from the
stack.
Increments the horizontal
0.2 WAIT 5 STEP
coordinate by 5.
»
»
`OWALK K
Checksum: # 28684d
Bytes:
250.0
Example: Send the small person out for a walk.
J %WALK%
Press − when you think the walker's tired.
2-40 RPL Programming Examples
Stores the program in WALK.
3
3.Full Command and Function Reference
Introduction
This chapter details the hp49g+/hp48gII commands and functions.
These listings include the following information:
! a brief definition of what the command or function does
! additional information about how it works and how to use it
! the key to press to gain access to it
! any flags that may affect how it works
! a stack diagram showing the arguments it requires (if any)
! related commands or functions
Computer Algebra System Commands and Functions
CAS-specific commands and functions are included in this chapter with a description of what the item does. For
more detailed information on CAS-specific items, see the listing for each CAS item in the next chapter. For example,
the CAS command “ABCUV” is included in this chapter, but the only description given is:
CAS:
From polynomials a, b and constant c give polynomials u and v such that au+bv =c .
The CAS: indicates that this is a computer algebra system item and that the next chapter contains a listing
giving more information on the entry.
How to Access Commands and Functions
Many of the commands and functions in this reference are not located on the hp49g+/hp48gII keyboard and are
accessed by pressing …µ. This is the right-shifted function of the Pkey, which is the fourth key from the
left on the fourth row of keys from the top. Once accessed, the function or command’s name is found by pressing
the ~key and then using the letter keys to spell out the function or command’s name. Usually, pressing the first
letter of the command will move the catalog list close enough to the function to use the ˜key to find the function.
For functions or commands (or symbols) that are located on the hp49g+/hp48gII keyboard as shifted functions of
other keys (such as …µ above), the proper shift key is shown followed by a font symbol indicating the
function, command or symbol written above the key.
In some cases, access is shown with two keys with an ampersand (&) in between, such as !&H. This notation
means that you must press the first key and hold it down while then pressing the second key at the same time.
The next few pages explain how to read the stack diagrams in the command reference, how commands are
alphabetized, and the meaning of command classifications at the upper right corner of each stack diagram.
How to Read Stack Diagrams
Each entry in the command reference includes a stack diagram. This is a table showing the arguments that the
command, function, or analytic function takes from the stack and the results that it returns to the stack. The “"”
character (pronounced “to” as in “to list” for "List) in the table separates the arguments from the results. The stack
diagram for a command may contain more than one “argument " result” line, reflecting all possible combinations
of arguments and results for that command.
RPL Programming Examples 3-1
Consider this example:
ACOS
Arc Cosine Analytic Function: Returns the value of the angle having the given cosine.
Level 1
"
Level 1
z
"
arc cos z
'symb'
"
'ACOS(symb)'
This diagram indicates that the analytic function ACOS (Arc Cosine) takes a single argument from level 1 and returns
one result (to level 1). ACOS can take either a real or complex number or an algebraic object as its argument. In the
first case, it returns the numeric arccosine; in the second, it returns the symbolic arccosine expression of the
argument.
Some commands affect a calculator state — a mode, a reserved variable, a flag, or a display — without taking any
arguments from the stack or returning any results to the stack. No stack diagrams are shown for these commands.
Parallel Processing with Lists
This feature is discussed in greater detail in Appendix G.
As a rule-of-thumb, a command can use parallel list processing if all the following are true:
The command checks for valid argument types. Commands that apply to all object types, such as DUP, SWAP,
ROT, and so forth, do not use parallel list processing.
! The command takes exactly one, two, three, four, or five arguments, none of which may itself be a list.
Commands, such as "LIST, that have an indefinite number of arguments do not use parallel list processing.
! The command is not a programming branch command (IF, FOR, CASE, NEXT, and so forth).
!
There are also a few commands (PURGE, DELKEYS, SF and FS? are examples) that have list processing capability
built into their definitions, and so do not also use the parallel list processing feature.
How Commands Are Alphabetized
Commands appear in alphabetical order. Command names that contain special (non-alphabetic) characters are
organized as follows:
!
For commands that contain both special and alphabetic characters:
" A special character at the start of a command name is ignored. Therefore, the command %CH follows the
command CF and precedes the command CHOOSE.
" A special character within or at the end of a command name is considered to follow “Z” at the end of the
alphabet. Therefore, the command R"B follows the command RSWP and precedes the command R"C. The
only exception would be the “Σ” character which, when not the first character in the name, is alphabetized as if
it were the string “SIGMA”. An example is “NΣ”, which falls between NOVAL and NSUB.
!
Commands that contain only special characters appear at the end of the dictionary.
Classification of Operations
The command dictionary contains hp48gII/hp49g+ commands, functions, and analytic functions. Commands are
calculator operations that can be executed from a program. Functions are commands that can be included in
algebraic objects. Analytic functions are functions for which hp48gII/hp49g+ provides an inverse and a derivative.
The definitions of the abbreviations used for argument and result objects are contained in the following table,
“Terms Used in Stack Diagrams.” Often, descriptive subscripts are added to convey more information.
3-2 Full Command and Function Reference
Terms Used in Stack Diagrams
Term
arg
Description
Argument.
[ array ]
Real or complex vector or matrix.
[ C-array ]
Complex vector or matrix.
date
Date in form MM.DDYYYY or DD.MMYYYY.
{ dim }
List of one or two array dimensions (real numbers).
'global'
Global name.
grob
Graphics object.
HMS
A real-number time or angle in hours-minutes-seconds format.
{ list }
List of objects.
local
Local name.
[[ matrix ]]
Real or complex matrix.
n or m
Positive integer real number (rounded if noninteger)
:nport:
Backup identifier.
:nport: nlibrary
Library identifier.
#n
Binary integer.
{ #n #m }
Pixel coordinates. (Uses binary integers.)
'name'
Global or local name.
obj
Any object.
PICT
Current graphics object.
« program »
Program.
[ R-array ]
Real vector or matrix.
"string"
Character string.
'symb'
Expression, equation, or name treated as an algebraic.
T/F
Test result used as an argument: zero (false) or non-zero (true) real number.
0/1
Test result returned by a command: zero (false) or one (true).
time
Time in form HH.MMSSs.
[ vector ]
Real or complex vector.
x or y
Real number.
x_unit
Unit object, or a real number treated as a dimensionless object.
(x,y)
Complex number in rectangular form, or user-unit coordinate.
z
Real or complex number.
Full Command and Function Reference 3-3
ABCUV
CAS:
From polynomials a, b and constant c give polynomials u and v such that au+bv =c .
ABS
Type:
Function
Description: Absolute Value Function: Returns the absolute value of its argument.
ABS has a derivative (SIGN) but not an inverse.
In the case of an array, ABS returns the Frobenius (Euclidean) norm of the array, defined as the
square root of the sum of the squares of the absolute values of all n elements. That is:
n
∑
i=1
Access:
!Ê
Flags:
Numerical Results (-3)
Input/Output:
zi
2
( Êis the left-shift of the /key).
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
|x|
(x,y)
→
x +y
x_unit
→
|x|_unit
[array]
→
||array||
'symb'
→
'ABS(symb)'
2
2
NEG, SIGN
ACK
Type:
Command
Description: Acknowledge Alarm Command: Acknowledges the oldest past-due alarm.
ACK clears the alert annunciator if there are both no other past-due alarms and no other active
alert sources (such as a low battery condition).
ACK has no effect on control alarms. Control alarms that come due are automatically acknowledged
and saved in the system alarm list.
Access:
…Ó TOOLS ALRM ACK
(Ó is the right-shift of the 9 key).
Flags:
Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44)
Input/Output:
None
See also:
ACKALL
ACKALL
Type:
Command
Description: Acknowledge All Alarms Command: Acknowledges all past-due alarms.
ACKALL clears the alert annunciator if there are no other active alert sources (such as a low
battery condition).
ACKALL has no effect on control alarms. Control alarms that come due are automatically
acknowledged and saved in the system alarm list.
Access:
…Ó TOOLS ALRM ACKALL
( Ó is the right-shift of the 9 key).
Flags:
Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44)
3-4 Full Command and Function Reference
Input/Output: None
See also:
ACK
ACOS
Type:
Analytic Function
Description: Arc Cosine Analytic Function: Returns the value of the angle having the given cosine.
For a real argument x in the domain –1 ≤ x ≤ 1, the result ranges from 0 to 180 degrees (0 to π
radians; 0 to 200 grads).
A real argument outside of this domain is converted to a complex argument, z = x + 0i, and the
result is complex.
The inverse of COS is a relation, not a function, since COS sends more than one argument to the
same result. The inverse relation for COS is expressed by ISOL as the general solution
s1*ACOS(Z)+2*π*n1
The function ACOS is the inverse of a part of COS, a part defined by restricting the domain of
COS such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of COS are called the principal values of the inverse relation.
ACOS in its entirety is called the principal branch of the inverse relation, and the points sent by
ACOS to the boundary of the restricted domain of COS form the branch cuts of ACOS.
The principal branch used by the hp49g+/hp48gII for ACOS was chosen because it is analytic
in the regions where the arguments of the real-valued inverse function are defined. The branch cut
for the complex-valued arc cosine function occurs where the corresponding real-valued function
is undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of ACOS. The graph of the domain shows where
the branch cuts occur: the heavy solid line marks one side of a cut, while the feathered lines mark
the other side of a cut. The graph of the range shows where each side of each cut is mapped
under the function.
These graphs show the inverse relation s1*ACOS(Z)+2*π*n1 for the case s1=1 and n1 = 0. For
other values of s1 and n1, the vertical band in the lower graph is translated to the right or to the
left. Taken together, the bands cover the whole complex plane, which is the domain of COS.
View these graphs with domain and range reversed to see how the domain of COS is restricted
to make an inverse function possible. Consider the vertical band in the lower graph as the
restricted domain Z = (x, y). COS sends this domain onto the whole complex plane in the range
W = (u, v) = COS(x, y) in the upper graph.
Access:
!¾
( ¾ is the left-shift of the Tkey).
Flags:
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
acos z
'symb'
→
'ACOS(symb)'
ASIN, ATAN, COS, ISOL
Full Command and Function Reference 3-5
ACOS2S
CAS:
Transform expressions replacing acos(x) with π/2–asin(x).
ACOSH
Type:
Analytic Function
Description: Inverse Hyperbolic Cosine Analytic Function: Returns the inverse hyperbolic cosine of the
argument.
For real arguments x < 1, ACOSH returns the complex result obtained for the argument (x, 0).
The inverse of ACOSH is a relation, not a function, since COSH sends more than one argument
to the same result. The inverse relation for COSH is expressed by ISOL as the general solution:
s1*ACOSH(Z)+2*π*i*n1
The function ACOSH is the inverse of a part of COSH, a part defined by restricting the domain
of COSH such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of COSH are called the principal values of the inverse relation.
ACOSH in its entirety is called the principal branch of the inverse relation, and the points sent by
ACOSH to the boundary of the restricted domain of COSH form the branch cuts of ACOSH.
The principal branch used by the hp49g+/hp48gII for ACOSH was chosen because it is
analytic in the regions where the arguments of the real-valued inverse function are defined. The
branch cut for the complex-valued hyperbolic arc cosine function occurs where the
corresponding real-valued function is undefined. The principal branch also preserves most of the
important symmetries.
The graphs below show the domain and range of ACOSH. The graph of the domain shows
where the branch cut occurs: the heavy solid line marks one side of the cut, while the feathered
3-6 Full Command and Function Reference
lines mark the other side of the cut. The graph of the range shows where each side of the cut is
mapped under the function.
These graphs show the inverse relation s1*ACOSH(Z)+2*π*i*n1 for the case s1 = 1 and n1 = 0.
For other values of s1 and n1, the horizontal half-band in the lower graph is rotated to the left
and translated up and down. Taken together, the bands cover the whole complex plane, which is
the domain of COSH.
View these graphs with domain and range reversed to see how the domain of COSH is restricted
to make an inverse function possible. Consider the horizontal half-band in the lower graph as the
restricted domain Z = (x, y). COSH sends this domain onto the whole complex plane in the
range W = (u, v) = COSH(x, y) in the upper graph.
Access:
…ÑHYPERBOLIC ACOSH
(Ñ is the right-shift of the 8key).
Flags:
Principal Solution (–1), Numerical Results (–3)
Input/Output:
Level 1/Argument 1
z
See also:
'symb'
ASINH, ATANH, COSH, ISOL
Level 1/Item 1
→
acosh z
→
'ACOSH(symb)'
ADD
Type:
Command
Description: Add List Command: Adds corresponding elements of two lists or adds a number to each of the
elements of a list.
ADD executes the + command once for each of the elements in the list. If two lists are the
arguments, they must have the same number of elements as ADD will execute the + command
once for each corresponding pair of elements. If one argument is a non-list object, ADD will
attempt to execute the + command using the non-list object and each element of the list
argument, returning the result to the corresponding position in the result. (See the + command
entry to see the object combinations that are defined.) If an undefined addition is encountered, a
Bad Argument Type error results.
Full Command and Function Reference 3-7
Access:
!´LIST ADD
( ´ is the left-shift of the Pkey).
Flags:
Binary Integer Wordsize (–5 through –10)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
{ list1 }
{ list2 }
→
{ listresult }
{ list }
objnon-list
→
{ listresult }
objnon-list
{ list }
→
{ listresult }
+, ∆LIST, ΠLIST, ΣLIST
ADDTMOD
CAS:
Add two expressions or values, modulo the current modulus.
ADDTOREAL
CAS:
Add names to list of variables treated as real when Complex mode is set.
ALGB
CAS:
Display a menu or list of CAS algebraic operations.
ALOG
Type:
Analytic Function
Description: Common Antilogarithm Analytic Function: Returns the common antilogarithm; that is, 10 raised
to the given power.
For complex arguments: 10(x,y) = ecx cos cy + i ecx sin cy where c = ln 10.
Access:
!Â
( Â is the left-shift of the Vkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
10z
'symb'
→
'ALOG(symb)'
EXP, LN, LOG
AMORT
Type:
Command
Description: Amortize Command: Amortizes a loan or investment based upon the current amortization
settings.
Values must be stored in the TVM variables (I%YR, PV, PMT, and PYR). The number of
payments n is taken from the input together with flag –14.
Access:
@& ÎTVM AMORT
(Îis the left-shift of the 7key).
Flags:
Financial Payment Mode (–14)
Input/Output:
Level 1/Argument 1
See also:
Level 3/Item 1
→
n
principal
TVM, TVMBEG, TVMEND, TVMROOT
AND
Type:
Function
Description: And Function: Returns the logical AND of two arguments.
3-8 Full Command and Function Reference
Level 2/Item 2
Level 1/Item 3
interest
balance
When the arguments are binary integers or strings, AND does a bit-by-bit (base 2) logical
comparison.
• An argument that is a binary integer is treated as a sequence of bits as long as the current
wordsize. Each bit in the result is determined by comparing the corresponding bits (bit1 and
bit2) in the two arguments as shown in the following table.
bit1
bit2
bit1 AND bit2
0
0
0
0
1
0
1
0
0
1
1
1
• An argument that is a string is treated as a sequence of bits, using 8 bits per character (that is,
using the binary version of the character code). The two string arguments must have the same
number of characters.
When the arguments are real numbers or symbolics, AND simply does a true/false test. The
result is 1 (true) if both arguments are non-zero; it is 0 (false) if either or both arguments are
zero. This test is usually done to compare two test results.
If either or both of the arguments are algebraic expressions, then the result is an algebraic of the
form symb1 AND symb2. Execute →NUM (or set flag –3 before executing AND) to produce a
numeric result from the algebraic result.
Access:
…ãL LOGIC AND
(ã is the right-shift of the 3key).
Flags:
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
#n1
#n2
→
#n3
“string1”
“string2”
→
“string3”
T/F1
T/F2
→
0/1
T/F
'symb'
→
'T/F AND symb'
'symb'
T/F
→
'symb AND T/F''
'symb1'
NOT, OR, XOR
'symb2'
→
'symb1 AND symb2'
ANIMATE
Type:
Command
Description: Animate Command: Displays graphic objects in sequence.
ANIMATE displays a series of graphics objects (or variables containing them) one after the
other. You can use a list to specify the area of the screen you want to animate (pixel coordinates
#X and #Y), the number of seconds before the next grob is displayed (delay), and the number of
times the sequence is run (rep). If rep is set to 0, the sequence is played one million times, or until
you press − (the $ key).
If you use a list on level 1, all parameters must be present.
The animation displays PICT while displaying the grobs. The grobs and the animate parameters
are left on the stack.
Full Command and Function Reference 3-9
Access:
!°LGROBLANIMATE
Input/Output:
( °is the left-shift of the Nkey).
Ln+1.../A1
L1/An+1
L1/I1
grobn...grob1
ngrobs
→
same stack
grobn...grob1
{ n {#X#Y } delay
rep }
→
same stack
L = Level, A = Argument, I = item
See also:
BLANK, →GROB
ANS
Type:
Command
Description: Recalls the nth answer from history (algebraic mode only), where n is an integer. In RPN mode, it
performs the LASTARG command.
Access:
!î
( îis the left-shift of the `key).
Input/Output:
Level 1/Argument 1
→
n
See also:
Level 1/Item 1
objn
LAST, LASTARG
APPLY
Type:
Function
Description: Apply to Arguments Function: Creates an expression from the specified function name and
arguments.
A user-defined function f that checks its arguments for special cases often can't determine
whether a symbolic argument x represents one of the special cases. The function f can use
APPLY to create a new expression f(x). If the user now evaluates f(x), x is evaluated before f, so
the argument to f will be the result obtained by evaluating x.
When evaluated in an algebraic expression, APPLY evaluates the arguments (to resolve local
names in user-defined functions) before creating the new object.
Access:
…µAPPLY
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
{ symb1 ... symbn }
'name'
Level 1/Item 1
→
'name(symb1 ... symbn)'
QUOTE, |
ARC
Type:
Command
Description: Draw Arc Command: Draws an arc in PICT counterclockwise from xθ1 to xθ2, with its center at
the coordinate specified in argument 1 or level 4 and its radius specified in argument 2 or level 3.
ARC always draws an arc of constant radius in pixels, even when the radius and center are
specified in user-units, regardless of the relative scales in user-units of the x- and y-axes. With
user-unit arguments, the arc starts at the pixel specified by (x, y) + (a, b), where (a, b) is the
rectangular conversion of the polar coordinate (xradius, xθ1). The resultant distance in pixels from
the starting point to the centre pixel is used as the actual radius, r'. The arc stops at the pixel
specified by (r', xθ2).
3-10 Full Command and Function Reference
If xθ1 = xθ2, ARC plots one point. If |xθ1 – xθ2| >360 degrees, 2π radians, or 400 grads, ARC
draws a complete circle.
Access:
!°LPICT ARC
( °is the left-shift of the Nkey).
Flags:
Angle Mode (–17 and –18). The setting of flags –17 and –18 determine the interpretation of xθ1
and xθ2 (degrees, radians, or grads).
Input/Output:
Level 4/Argument 1 Level 3/Argument 2 Level 2/Argument 3 Level 1/Argument 4
(x, y)
See also:
{ #n,#m }
BOX, LINE, TLINE
Level 1/Item 1
xradius
xθ1
xθ2
→
#nradius
xθ1
xθ2
→
ARCHIVE
Type:
Command
Description: Archive HOME Command: Creates a backup copy of the HOME directory (that is, all variables),
the user-key assignments, and the alarm catalog in the specified backup object (:nport:name) in
RAM or flash ROM.
The specified port number can be 0 through 3, where 3 is the SD card. (This only applies to the
hp49g+.) An error will result if there is not enough memory in the specified port to copy the
HOME directory.
If the backup object is “:IO:name”, then the copied directory is transmitted in binary via Kermit
protocol through the current I/O port to the specified filename.
To save flag settings, execute RCLF and store the resulting list in a variable.
Access:
!°MEMORYLARCHIVE
( °is the left-shift of the Nkey).
Flags:
I/O Device (–33), I/O Messages (–39) if the argument is “:IO:name”.
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
:nport :name
→
:IO :name
→
RESTORE
ARG
Type:
Function
Description: Argument Function: Returns the (real) polar angle θ of a complex number (x, y).
The polar angle θ is equal to:
• atan y/x for x ≥ 0
• atan y/x + π sign y for x < 0, Radians mode
• atan y/x + 180 sign y for x < 0, Degrees mode
• atan y/x + 200 sign y for x < 0, Grads mode
A real argument x is treated as the complex argument (x,0).
Access:
…Ë
(Ë is the right-shift of the /key).
Flags:
Angle mode (–17, –18)
Full Command and Function Reference 3-11
Input/Output:
Level 1/Argument 1
Level 1/Item 1
(x, y)
→
θ
'symb'
→
'ARG(symb)'
See also:
ATAN
ARIT
CAS:
Display a menu or list showing CAS submenus for arithmetical operations
ARRY→
Type:
Command
Description: Array to Stack Command: Takes an array and returns its elements as separate real or complex
numbers. Also returns a list of the dimensions of the array.
If the argument is an n-element vector, the first element is returned to level n + 1 (not level nm +
1), and the nth element to level 2.
Access:
…µ ARRY→
Input/Output:
Level 1/Argument 1
Lnm+1/A1 ... L2/Anm
Level1/Itemnm+1
[ vector ]
→
z1 ... zn
{ nelement }
[[ matrix ]]
→
z11 ... znm
{ nrow mcol }
L = Level; I = item
See also:
→ARRY, DTAG, EQ→, LIST→, OBJ→, STR→
→ARRY
Type:
Command
Description: Stack to Array Command: Returns a vector of n real or complex elements or a matrix of n × m
real or complex elements.
The elements of the result array should be entered in row order. If one or more of the elements
is a complex number, the result array will be complex.
Access:
!°TYPE →ARRY
( °is the left-shift of the Nkey).
Input/Output:
Levelnm+1/Argument1 … Level2/Argumentnm Level1/Argumentnm+1
z1 … zn
z1 1 … zn
See also:
m
Level1/Item1
nelement
→
[ vector ]
{ nrow, mcol }
→
[[ matrix ]]
ARRY→, LIST→, →LIST, OBJ→, STR→, →TAG, →UNIT
ASIN
Type:
Analytic Function
Description: Arc Sine Analytic Function: Returns the value of the angle having the given sine.
For a real argument x in the domain –1 ≤ x ≤ 1, the result ranges from –90 to +90 degrees (–π/2
to +π/2 radians; –100 to +100 grads).
A real argument outside of this domain is converted to a complex argument z = x + 0i, and the
result is complex.
3-12 Full Command and Function Reference
The inverse of SIN is a relation, not a function, since SIN sends more than one argument to the
same result. The inverse relation for SIN is expressed by ISOL as the general solution:
ASIN(Z)*(-1)^n1+π*n1
The function ASIN is the inverse of a part of SIN, a part defined by restricting the domain of
SIN such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of SIN are called the principal values of the inverse relation.
ASIN in its entirety is called the principal branch of the inverse relation, and the points sent by
ASIN to the boundary of the restricted domain of SIN form the branch cuts of ASIN.
The principal branch used by the hp49g+/hp48gII for ASIN was chosen because it is analytic in
the regions where the arguments of the real-valued inverse function are defined. The branch cut
for the complex-valued arc sine function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of ASIN. The graph of the domain shows where
the branch cuts occur: the heavy solid line marks one side of a cut, while the feathered lines mark
the other side of a cut. The graph of the range shows where each side of each cut is mapped
under the function. These graphs show the inverse relation ASIN(Z)*(–1)^n1+π*n1 for the case
n1=0. For other values of n1, the vertical band in the lower graph is translated to the right (for n1
positive) or to the left (for n1 negative). Taken together, the bands cover the whole complex
plane, which is the domain of SIN.
View these graphs with domain and range reversed to see how the domain of SIN is restricted to
make an inverse function possible. Consider the vertical band in the lower graph as the restricted
domain Z = (x, y). SIN sends this domain onto the whole complex plane in the range
W = (u, v) = SIN(x, y) in the upper graph.
Access:
!¼
( ¼is the left-shift of the Skey).
Full Command and Function Reference 3-13
Flags:
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
z
→
asin z
'symb'
→
'ASIN(symb)'
See also:
ACOS, ATAN, ISOL, SIN
ASIN2C
CAS:
Transform expressions replacing asin(x) with π/2–acos(x).
ASIN2T
CAS:
Transform expressions replacing asin(x) with atan(x/√(1-x^2))
ASINH
Type:
Analytic Function
Description: Arc Hyperbolic Sine Analytic Function: Returns the inverse hyperbolic sine of the argument.
The inverse of SINH is a relation, not a function, since SINH sends more than one argument to
the same result. The inverse relation for SINH is expressed by ISOL as the general solution:
ASINH(Z)*(–1)^n1+π*i*n1
The function ASINH is the inverse of a part of SINH, a part defined by restricting the domain of
SINH such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of SINH are called the principal values of the inverse relation.
ASINH in its entirety is called the principal branch of the inverse relation, and the points sent by
ASINH to the boundary of the restricted domain of SINH form the branch cuts of ASINH.
The principal branch used by the hp49g+/hp48gII for ASINH was chosen because it is analytic
in the regions where the arguments of the real-valued function are defined. The branch cut for the
complex-valued ASINH function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
The graph for ASINH can be found from the graph for ASIN (see ASIN) and the relationship
asinh z = –i asin iz.
Access:
…ÑHYPERBOLIC ASINH
(Ñ is the right-shift of the 8key).
Flags:
Principal Solution (–1), Numerical Results (–3)
Input/Output:
Level 1/Argument 1
z
See also:
'symb'
ACOSH, ATANH, ISOL, SINH
Level 1/Item 1
→
asinh z
→
'ASINH(symb)'
ASN
Type:
Command
Description: Assign Command: Defines a single key on the user keyboard by assigning the given object to the
key xkey, which is specified as rc.pf.
The argument xkey is a real number rc.pf specifying the key by its row number r, column number c,
shift plane p and shift-and-hold flag f. A value of f=0 represents a normal shifted key assignment
(where the shift is released prior to pressing the key); whereby f=1 corresponds to a shift-and3-14 Full Command and Function Reference
hold key assignment indicated by “&” in the table below (where the shift is held while pressing
the key). The legal values for p and f are as follows:
Value of
.pf
Value
of .pf
Shift
Shift
.00 or .10
Unshifted [key]
.20
!(left-shifted) [key]
.21
! & [key]
.30
…(right-shifted) [key]
.31
… & [key]
.40
~(alpha-shifted) [key]
.41
~& [key]
.50
~!(alpha left-shifted) [key]
.51
~!& [key]
.60
~…(alpha right-shifted)
.61
~…& [key]
Once ASN has been executed, pressing a given key in User or 1-User mode executes the userassigned object. The user key assignment remains in effect until the assignment is altered by
ASN, STOKEYS, or DELKEYS. Keys without user assignments maintain their standard
definitions.
If the argument obj is the name SKEY, then the specified key is restored to its standard key
assignment on the user keyboard. This is meaningful only when all standard key assignments had
been suppressed (for the user keyboard) by the command S DELKEYS (see DELKEYS).
To make multiple key assignments simultaneously, use STOKEYS. To delete key assignments,
use DELKEYS.
Be careful not to reassign or suppress the keys necessary to cancel User mode. If this happens,
exit User mode by doing a system halt (“warm start”): press and hold ‡and C
simultaneously, releasing Cfirst. This cancels User mode.
Access:
…µASN OR !&H KEYS ASN
Flags:
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj
xkey
→
xkey
→
'SKEY'
DELKEYS, RCLKEYS, STOKEYS
Level 1/Item 1
ASR
Type:
Command
Description: Arithmetic Shift Right Command: Shifts a binary integer one bit to the right, except for the most
significant bit, which is maintained.
The most significant bit is preserved while the remaining (wordsize –1) bits are shifted right one
bit. The second-most significant bit is replaced with a zero. The least significant bit is shifted out
and lost.
An arithmetic shift is useful for preserving the sign bit of a binary integer that will be shifted.
Although the hp49g+/hp48gII makes no special provision for signed binary integers, you can
still interpret a number as a signed quantity.
Full Command and Function Reference 3-15
Access:
…ãL BIT ASR
( ãis the right-shift of the 3key).
Flags:
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
SL, SLB, SR, SRB
ASSUME
CAS:
Place assumptions on variables treated by CAS as real when Complex mode is set.
ATAN
Type:
Analytic Function
Description: Arc Tangent Analytic Function: Returns the value of the angle having the given tangent.
For a real argument, the result ranges from –90 to +90 degrees (–π/2 to +π/2 radians; –100 to
+100 grads).
The inverse of TAN is a relation, not a function, since TAN sends more than one argument to the
same result. The inverse relation for TAN is expressed by ISOL as the general solution:
ATAN(Z)+π*n1
The function ATAN is the inverse of a part of TAN, a part defined by restricting the domain of
TAN such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of TAN are called the principal values of the inverse relation.
ATAN in its entirety is called the principal branch of the inverse relation, and the points sent by
ATAN to the boundary of the restricted domain of TAN form the branch cuts of ATAN.
The principal branch used by the hp49g+/hp48gII for ATAN was chosen because it is analytic
in the regions where the arguments of the real-valued inverse function are defined. The branch
cuts for the complex-valued arc tangent function occur where the corresponding real-valued
function is undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of ATAN. The graph of the domain shows where
the branch cuts occur: the heavy solid line marks one side of a cut, while the feathered lines mark
the other side of a cut. The graph of the range shows where each side of each cut is mapped
under the function.
These graphs show the inverse relation ATAN(Z)+π*n1 for the case n1 = 0. For other values of
n1, the vertical band in the lower graph is translated to the right (for n1 positive) or to the left
(for n1 negative). Together, the bands cover the whole complex plane, the domain of TAN.
View these graphs with domain and range reversed to see how the domain of TAN is restricted
to make an inverse function possible. Consider the vertical band in the lower graph as the
restricted domain Z = (x, y). TAN sends this domain onto the whole complex plane in the range
W = (u, v) = TAN(x, y) in the upper graph.
3-16 Full Command and Function Reference
Access:
!À
( Àis the left-shift of the Ukey).
Flags:
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
z
→
atan z
'symb'
→
'ATAN(symb)'
See also:
ACOS, ASIN, ISOL, TAN
ATAN2S
CAS:
Transform expressions by replacing atan(x) with asin(x/√(x^2+1)).
ATANH
Type:
Analytic Function
Description: Arc Hyperbolic Tangent Analytic Function: Returns the inverse hyperbolic tangent of the
argument.
For real arguments |x| > 1, ATANH returns the complex result obtained for the argument (x,
0). For a real argument x=±1, an Infinite Result exception occurs. If flag –22 is set (no error),
the sign of the result (MAXR) matches that of the argument.
The inverse of TANH is a relation, not a function, since TANH sends more than one argument
to the same result. The inverse relation for TANH is expressed by ISOL as the general solution;
ATANH(Z)+π*i*n1
The function ATANH is the inverse of a part of TANH, a part defined by restricting the domain
of TANH such that:
Full Command and Function Reference 3-17
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of TANH are called the principal values of the inverse relation.
ATANH in its entirety is called the principal branch of the inverse relation, and the points sent by
ATANH to the boundary of the restricted domain of TANH form the branch cuts of ATANH.
The principal branch used by the hp49g+/hp48gII for ATANH was chosen because it is
analytic in the regions where the arguments of the real-valued function are defined. The branch cut
for the complex-valued ATANH function occurs where the corresponding real-valued function
is undefined. The principal branch also preserves most of the important symmetries.
The graph for ATANH can be found from the graph for ATAN (see ATAN) and the
relationship atanh z = –i atan iz.
Access:
…ÑHYPERBOLIC ATAN
(Ñ is the right-shift of the 8key).
Flags:
Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)
Input/Output:
Level 1/Argument 1
z
See also:
'symb'
ACOSH, ASINH, ISOL, TANH
Level 1/Item 1
→
atanh z
→
'ATANH(symb)'
ATICK
Type:
Command
Description: Axes Tick-Mark Command: Sets the axes tick-mark annotation in the reserved variable PPAR.
Given x, ATICK sets the tick-mark annotation to x units on both the x- and the y-axis. For
example, 2 would place tick-marks every 2 units on both axes.
Given #n, ATICK sets the tick-mark annotation to #n pixels on both the x- and the y-axis. For
example, #5 would place tick-marks every 5 pixels on both axes.
Given { x y }, ATICK sets the tick-mark unit annotation for each axis individually. For example,
{ 10 3 } would mark the x-axis at every multiple of 10 units, and the y-axis at every multiple of 3
units.
Given { #n #m } ATICK sets the tick-mark pixel annotation for each axis individually. For
example, {#6 #2 } would mark the x-axis every 6 pixels, and the y-axis every 2 pixels.
Access:
…µATICK
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
#n
→
{xy}
→
{ #n #m }
→
→
AXES, DRAX
ATTACH
Type:
Command
Description: Attach Library Command: Attaches the library with the specified number to the current
directory. Each library has a unique number. If a port number is specified, it is ignored.
3-18 Full Command and Function Reference
To use a library object, it must be in a port and it must be attached. A library object copied into
RAM (such as through the PC Link) must be stored into a port using STO.
Some libraries require you to ATTACH them.
You can ascertain whether a library is attached to the current directory by executing LIBS.
The number of libraries that can be attached to the HOME directory is limited only by the
available memory. However, only one library at a time can be attached to any other directory. If
you attempt to attach a second library to a non-HOME directory, the new library will overwrite
the old one.
Access:
…µATTACH
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
nlibrary
→
:nport :nlibrary
→
DETACH, LIBS
AUGMENT
CAS:
Concatenate lists, or vectors, with elements, or create matrices from row vectors.
AUTO
Type:
Command
Description: Autoscale Command: Calculates a y-axis display range, or an x- and y-axis display range.
The action of AUTO depends on the plot type as follows:
Plot Type
Scaling Action
FUNCTION
Samples the equation in EQ at 40 values of the independent
variable, equally spaced through the x-axis plotting range, discards
points that return ±∞, then sets the y-axis display range to include
the maximum, minimum, and origin.
CONIC
Sets the y-axis scale equal to the x-axis scale.
POLAR
Samples the equation in EQ at 40 values of the independent
variable, equally spaced through the plotting range, discards points
that return ±∞, then sets both the x- and y-axis display ranges in
the same manner as for plot type FUNCTION.
PARAMETRIC
Same as POLAR.
TRUTH
No action.
BAR
Sets the x-axis display range from 0 to the number of elements in
ΣDAT, plus 1. Sets the y-range to the minimum and maximum of
the elements. The x-axis is always included.
HISTOGRAM
Sets the x-axis display range to the minimum and maximum of the
elements in ΣDAT. Sets the y-axis display range from 0 to the
number of rows in ΣDAT.
Full Command and Function Reference 3-19
Plot Type
Scaling Action
SCATTER
Sets the x-axis display range to the minimum and maximum of the
independent variable column (XCOL) in ΣDAT. Sets the y-axis
display range to the minimum and maximum of the dependent
variable column (YCOL).
AUTO does not affect 3D plots.
AUTO actually calculates a y-axis display range and then expands that range so that the menu
labels do not obscure the resultant plot.
AUTO does not draw a plot – execute DRAW to do so.
Access:
…µAUTO
Input/Output: None
See also:
DRAW, SCALEH, SCALE, SCLΣ, SCALEW, XRNG, YRNG
AXES
Type:
Command
Description: Axes Command: Specifies the intersection coordinates of the x- and y-axes, tick-mark
annotation, and the labels for the x- and y-axes. This information is stored in the reserved
variable PPAR.
The argument for AXES (a complex number or list) is stored as the fifth parameter in the
reserved variable PPAR. How the argument is used depends on the type of object it is:
• If the argument is a complex number, it replaces the current entry in PPAR.
• If the argument is a list containing any or all of the above variables, only variables that are
specified are affected.
atick has the same format as the argument for the ATICK command. This is the variable that is
affected by the ATICK command.
The default value for AXES is (0,0).
Axes labels are not displayed in PICT until subsequent execution of LABEL.
Access:
…µAXES
Input/Output:
Level 1/Argument 1
Level 1/Item 1
(x, y)
→
{ (x, y) atick “x-axis label” “y-axis label” }
→
See also:
ATICK, DRAW, DRAX, LABEL
AXL
CAS:
Convert a list to an array, or an array to a list.
AXM
CAS:
Convert a numeric array to a symbolic matrix, or a symbolic matrix to a numeric array.
AXQ
CAS:
Convert a square matrix into the associated quadratic form.
BAR
Type:
Command
Description: Bar Plot Type Command: Sets the plot type to BAR.
3-20 Full Command and Function Reference
When the plot type is BAR, the DRAW command plots a bar chart using data from one column
of the current statistics matrix (reserved variable ΣDAT). The column to be plotted is specified
by the XCOL command, and is stored in the first parameter of the reserved variable ΣPAR. The
plotting parameters are specified in the reserved variable PPAR, which has the following form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type BAR, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is either a name specifying a label for the horizontal axis, or a list containing such a name
and two numbers, with the smaller of the numbers specifying the horizontal location of the
first bar. The default value of indep is X.
• res is a real number specifying the bar width in user-unit coordinates, or a binary integer
specifying the bar width in pixels. The default value is 0, which specifies a bar width of 1 in
user-unit coordinates.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command BAR places the
command name BAR in PPAR.
• depend is a name specifying a label for the vertical axis. The default value is Y.
A bar is drawn for each element of the column in ΣDAT. Its width is specified by res and its
height is the value of the element. The location of the first bar can be specified by indep;
otherwise, the value in (xmin, ymin) is used.
Access:
…µBAR
Input/Output: None
See also:
CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME,
YSLICE
BARPLOT
Type:
Command
Description: Draw Bar Plot Command: Plots a bar chart of the specified column of the current statistics
matrix (reserved variable ΣDAT).
The data column to be plotted is specified by XCOL and is stored as the first parameter in
reserved variable ΣPAR. The default column is 1. Data can be positive or negative, resulting in
bars above or below the axis. The y-axis is autoscaled, and the plot type is set to BAR.
When BARPLOT is executed from a program, the resulting plot does not persist unless
PICTURE, PVIEW (with an empty list argument), or FREEZE is subsequently executed.
Access:
…µBARPLOT
Input:
None
Output:
A bar chart based on ΣDAT.
See also:
FREEZE, HISTPLOT, PICTURE, PVIEW, SCATRPLOT, XCOL
Full Command and Function Reference 3-21
BASIS
CAS:
Determine the basis of a sub-space of the n-space Rn.
BAUD
Type:
Command
Description: Baud Rate Command: Specifies bit-transfer rate.
Legal baud rates are 2400, 4800, 9600 (default), 14400, 19200, 38400, 57600 and 115200.
Access:
…µBAUD
Input/Output:
Level 1/Argument 1
→
nbaudrate
See also:
Level 1/Item 1
CKSM, PARITY, TRANSIO
BEEP
Type:
Command
Description: Beep Command: Sounds a tone at n hertz for x seconds.
The frequency of the tone is subject to the resolution of the built-in tone generator. The
minimum frequency is 1 Hz and the maximum frequency in 15000 Hz. An input that doesn’t
round to an integer within this range will cause the BEEP command to be skipped. Durations
greater than 1200 seconds are automatically changed to 1200 seconds.
Access:
!°LOUT L BEEP
( °is the left-shift of the Nkey).
Flags:
Error Beep (–56)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
nfrequency
xduration
Level 1/Item 1
→
HALT, INPUT, PROMPT, WAIT
BESTFIT
Type:
Command
Description: Best-Fitting Model Command: Executes LR with each of the four curve fitting models, and
selects the model yielding the largest correlation coefficient.
The selected model is stored as the fifth parameter in the reserved variable ΣPAR, and the
associated regression coefficients, intercept and slope, are stored as the third and fourth
parameters, respectively.
Access:
…µBESTFIT
Input/Output: None
See also:
EXPFIT, LINFIT, LOGFIT, LR, PWRFIT
BIN
Type:
Command
Description: Binary Mode Command: Selects binary base for binary integer operations. (The default base is
decimal.)
Binary integers require the prefix #. Binary integers entered and returned in binary base
automatically show the suffix b. If the current base is not binary, binary numbers can still be
entered by using the suffix b (the numbers are displayed in the current base, however).
The current base does not affect the internal representation of binary integers as unsigned binary
numbers.
3-22 Full Command and Function Reference
Access:
…ãBIN
( ãis the right-shift of the 3key).
Flags:
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output: None
See also:
DEC, HEX, OCT, STWS, RCWS
BINS
Type:
Command
Description: Sort into Frequency Bins Command: Sorts the elements of the independent column (XCOL) of
the current statistics matrix (the reserved variable ΣDAT) into (nbins + 2) bins, where the left edge
of bin 1 starts at value xmin and each bin has width xwidth.
BINS returns a matrix containing the frequency of occurrences in each bin, and a 2-element
array containing the frequency of occurrences falling below or above the defined range of xvalues. The array can be stored into the reserved variable ΣDAT and used to plot a bar
histogram of the bin data (for example, by executing BARPLOT).
For each element x in ΣDAT, the nth bin count nfreq bin n is incremented, where:
n
f r e q b in n
x – x m in
= I P ------------------x w i d th
for xmin £ x £ xmax, where xmax = xmin + (nbins)(xwidth).
Access:
…µBINS
Input/Output:
L3/A1
L2/A2
L1/A3
xmin
xwidth
nbins
→
L2/I1
L1/I2
[[ nbin 1 ... nbin n ]]
[ nbin L nbin R]
L = Level; A = Argument; I = item
See also:
BARPLOT, XCOL
BLANK
Type:
Command
Description: Blank Graphics Object Command: Creates a blank graphics object of the specified width and
height.
Access:
!°LGROB BLANK
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
#nwidth
#mheight
Level 1/Item 1
→
grobblank
→GROB, LCD→
BOX
Type:
Command Operation
Description: Box Command: Draws in PICT a box whose opposite corners are defined by the specified pixel
or user-unit coordinates.
Access:
!°LPICT BOX
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
{ #n1 #m1 }
{ #n2 #m2 }
→
(x1, y1)
(x2, y2)
→
Full Command and Function Reference 3-23
See also:
ARC, LINE, TLINE
BUFLEN
Type:
Command
Description: Buffer Length Command: Returns the number of characters in the hp49g+/hp48gII 's serial
input buffer and a single digit indicating whether an error occurred during data reception.
The digit returned is 1 if no framing, UART overrun, or input-buffer overflow errors occurred
during reception, or 0 if one of these errors did occur. (The input buffer holds up to 255 bytes.)
When a framing or overrun error occurs, data reception ceases until the error is cleared (which
BUFLEN does); therefore, n represents the data received before the error.
Use ERRM to see which error has occurred when BUFLEN returns 0 to level 1.
Access:
…µBUFLEN
Input/Output:
Level 1/Argument 1
Level 2/Item 1
Level 1/Item 2
nchars
0/1
→
See also:
CLOSEIO, OPENIO, SBRK, SRECV, STIME, XMIT
BYTES
Type:
Command
Description: Byte Size Command: Returns the number of bytes and the checksum for the given object.
If the argument is a built-in object, then the size is 2.5 bytes and the checksum is #0.
If the argument is a global name, then the size represents the name and its contents, while the
checksum represents the contents only. The size of the name alone is (3.5 + n), where n is the
number of characters in the name.
Access:
!°MEMORY BYTES
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
→
obj
See also:
Level 2/Item 1
Level 1/Item 2
#nchecksum
xsize
MEM
B→R
Type:
Command
Description: Binary to Real Command: Converts a binary integer to its floating-point equivalent.
If # n ≥ # 1000000000000 (base 10), only the 12 most significant decimal digits are preserved in
the resulting mantissa.
( ãis the right-shift of the 3key).
Access:
…ãB→R
Flags:
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output:
Level 1/Argument 1
#n
Level 1/Item 1
→
See also:
R→ B
C2P
CAS:
Take a list of cycles and return the equivalent permutation.
3-24 Full Command and Function Reference
n
CASCFG
CAS:
Restore the default CAS mode settings with the modulus value set to 13.
CASCMD
CAS:
List CAS operations, provide descriptions and examples.
CASE
Type:
Command
Description: CASE Conditional Structure Command: Starts CASE … END conditional structure.
The CASE … END structure executes a series of cases (tests). The first test that returns a true
result causes execution of the corresponding true-clause, ending the CASE … END structure. A
default clause can also be included: this clause executes if all tests evaluate to false. The CASE
command is available in RPN programming only. You cannot use it in algebraic programming.
The CASE … END structure has this syntax:
CASE
test-clause1 THEN true-clause1 END
test-clause2 THEN true-clause2 END
.
.
test-clausen THEN true-clausen END
default-clause (optional)
END
When CASE executes, test-clause1 is evaluated. If the test is true, true-clause1 executes, then
execution skips to END. If test-clause1 is false, test-clause2 executes. Execution within the CASE
structure continues until a true clause is executed, or until all the test clauses evaluate to false. If
the default clause is included, it executes if all test clauses evaluate to false.
Access:
!°BRCH CASE
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
Level 1/Item 1
→
CASE
THEN
See also:
T/F
→
END
→
END
→
END, IF, IFERR, THEN
CEIL
Type:
Function
Description: Ceiling Function: Returns the smallest integer greater than or equal to the argument.
Access:
!´REAL LL CEIL
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
n
x_unit
→
n_unit
'symb'
→
'CEIL(symb)'
FLOOR, IP, RND, TRNC
Full Command and Function Reference 3-25
CENTR
Type:
Command
Description: Center Command: Adjusts the first two parameters in the reserved variable PPAR, (xmin, ymin)
and (xmax, ymax), so that the point represented by the argument (x, y) is the plot center. On the
hp49g+, the center pixel is in row 40, column 65 when PICT is its default size (131 × 80). On
the hp48gII, the center pixel is in row 32, column 65 when PICT is its default size (131 × 64).
If the argument is a real number x, CENTR makes the point (x,0) the plot center.
Access:
…µCENTR
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
(x, y)
→
x
→
SCALE
CF
Type:
Command
Description: Clear Flag Command: Clears the specified user or system flag.
User flags are numbered 1 through 128. System flags are numbered –1 through –128. See
Appendix C for a listing of hp49g+/hp48gII system flags and their flag numbers.
Access:
!°TESTLLCF
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
nflagnumber
See also:
FC?, FC?C, FS?, FS?C, SF
%CH
Type:
Function
Description: Percent Change Function: Returns the percent change from x to y as a percentage of x.
If both arguments are unit objects, the units must be consistent with each other. The dimensions
of a unit object are dropped from the result, but units are part of the calculation.
For more information on using temperature units with arithmetic functions, refer to the keyword
entry of +.
Access:
!´REAL %CH
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
x
y
→
100(y – x)/x
x
'symb'
→
'%CH(x,symb)'
'symb'
x
→
'%CH(symb,x)'
'symb1'
'symb2'
→
'%CH(symb1, symb2)'
x_unit
y_unit
→
100(y_unit – x_unit)/x_unit
x_unit
'symb'
→
'%CH(x_unit,symb)'
'symb'
x_unit
→
'%CH(symb,x_unit)'
%, %T
3-26 Full Command and Function Reference
Level 1/Item 1
CHINREM
CAS:
Solve a system of simultaneous polynomial congruences in the ring Z[x].
CHOLESKY
CAS:
Return the Cholesky factorization of a square matrix.
CHOOSE
Type:
Command
Description: Create User-Defined Choose Box Command: Creates a user-defined choose box.
CHOOSE creates a standard single-choice choose box based on the following specifications:
Variable
Function
“prompt”
A message that appears at the top of choose box. If “prompt” is an
empty string (“”), no message is displayed.
{c1 … cn}
Definitions that appear within the choose box. A choice definition
(cx) can have two formats.
• obj, any object
• { objdisplay objresult }, the object to be displayed followed by the result
returned to the stack if that object is selected.
npos
The position number of an item definition. This item is highlighted
when the choose box appears. If npos = 0, no item is highlighted, and
the choose box can be used to view items only.
If you choose an item from the choose box and press OK, CHOOSE returns the result (or the
object itself if no result is specified) to level 2 and 1 to level 1. If you press −, CHOOSE
returns 0. Also, if npos = 0, CHOOSE returns 0.
Access:
!°LIN CHOOSE
Input/Output:
( °is the left-shift of the Nkey).
L3/A1
L2/A2
L1/A3
“prompt”
{ c1 ... cn }
npos
→
“prompt”
{ c1 ... cn }
npos
→
L2/I1
L1/I2
obj or result
“1”
“0”
L = Level; A = Argument; I = item
See also:
INFORM, NOVAL
CHR
Type:
Command
Description: Character Command: Returns a string representing the character corresponding to the character
code n.
The character codes are an extension of ISO 8859/1. Codes 128 through 160 are unique to the
hp49g+/hp48gII.
The default character ! is supplied for all character codes that are not part of the normal
hp49g+/hp48gII display character set.
Character code 0 is used for the special purpose of marking the end of the command line.
Attempting to edit a string containing this character causes the error Can't Edit Null Char.
You can use the CHARS application to find the character code for any character used by the
hp49g+/hp48gII. See “Additional Character Set” in Appendix D of the hp49g+/hp48gII User's
Guide.
Access:
!°TYPE L CHR
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-27
Input/Output:
Level 1/Argument 1
See also:
n
NUM, POS, REPL, SIZE, SUB
CIRC
CAS:
Compose two permutations.
Level 1/Item 1
→
“string”
CKSM
Type:
Command
Description: Checksum Command: Specifies the error-detection scheme.
Legal values for nchecksum are as follows:
• 1-digit arithmetic checksum.
• 2-digit arithmetic checksum.
• 3-digit cyclic redundancy check (default).
The CKSM specified is the error-detection scheme that will be requested by KGET, PKT, or
SEND. If the sender and receiver disagree about the request, however, then a 1-digit arithmetic
checksum will be used.
Access:
…µCKSM
Input/Output:
Level 1/Argument 1
See also:
nchecksum
BAUD, PARITY, TRANSIO
Level 1/Item 1
→
CLEAR
Type:
Command
Description: Clear Command: Removes all objects from the stack or history.
To recover a cleared stack or history, press …¯ (the right-shift of the Mkey) before
executing any other operation. There is no programmable command to recover the stack or
history.
Access:
…·
(·is the right-shift of the ƒkey).
Input/Output:
Leveln/Argument 1 ... Level 1/Argumentn
objn ...obj1
See also:
Leveln/Item 1 ... Level 1/Itemn
→
CLVAR, PURGE
CLKADJ
Type:
Command
Description: Adjust System Clock Command: Adjusts the system time by x clock ticks, where 8192 clock ticks
equal 1 second. If x is positive, x clock ticks are added to the system time. If x is negative, x
clock ticks are subtracted from the system time. If X>10^12, it will be changed to 10^12 ticks
(which is approximately 3.87 years).
Access:
…ÓTOOLS LLCLKADJ
( Ó is the right-shift of the 9 key).
Input/Output:
Level 1/Argument 1
x
3-28 Full Command and Function Reference
Level 1/Item 1
→
See also:
→TIME
CLLCD
Type:
Command
Description: Clear LCD Command: Clears (blanks) the stack display.
The menu labels continue to be displayed after execution of CLLCD.
When executed from a program, the blank display persists only until the keyboard is ready for
input. To cause the blank display to persist until a key is pressed, execute FREEZE after
executing CLLCD. (When executed from the keyboard, CLLCD automatically freezes the display.)
Access:
!°LOUT CLLCD
( °is the left-shift of the Nkey).
Input/Output: None
See also:
DISP, FREEZE
CLOSEIO
Type:
Command
Description: Close I/O Port Command: Closes the serial port, and clears the input buffer and any error
messages for KERRM.
When the hp49g+/hp48gII turns off, it automatically closes the serial port, but does not clear
KERRM. Therefore, CLOSEIO is not needed to close the port, but can conserve power without
turning off the calculator.
Executing hp49g+/hp48gII Kermit protocol commands automatically clears the input buffer;
however, executing non-Kermit commands (such as SRECV and XMIT) does not.
CLOSEIO also clears error messages from KERRM. This can be useful when debugging.
Access:
…µCLOSEIO
Input/Output: None
See also:
BUFLEN, OPENIO
CLΣ
Type:
Command
Description: Purges the current statistics matrix (reserved variable ΣDAT).
Access:
…µCLΣ
Input/Output: None
See also:
RCLΣ, STOΣ, Σ+, Σ–
CLVAR
Type:
Command
Description: Clear Variables Command: Purges all variables and empty subdirectories in the current directory.
Access:
…µCLVAR
Input/Output: None
See also:
PGDIR, PURGE
CMPLX
Type:
Command
Description: Displays a menu of commands pertaining to complex numbers.
Access:
…µCMPLX
Input/Output: None
See also:
ARIT, DIFF, EXP&LN, SOLVER, TRIGO
Full Command and Function Reference 3-29
CNRM
Type:
Command
Description: Column Norm Command: Returns the column norm (one-norm) of the array argument.
The column norm of a matrix is the maximum (over all columns) of the sum of the absolute
values of all elements in each column. For a vector, the column norm is the sum of the absolute
values of the vector elements. For complex arrays, the absolute value of a given element (x, y) is
2
x +y
2
.
Access:
!Ø
Input/Output:
( Ø is the left-shift of the 5key).
OPERATIONS CNRM
Level 1/Argument 1
See also:
Level 1/Item 1
→
[ array ]
CROSS, DET, DOT, RNRM
xcolumnnorm
→COL
Type:
Command
Description: Matrix to Columns Command: Transforms a matrix into a series of column vectors and returns
the vectors and a column count, or transforms a vector into its elements and returns the
elements and an element count.
→COL introduces no rounding error.
Access:
!´MATRIX COL →COL
( ´ is the left-shift of the Pkey).
!Ø
Input/Output:
CREATE COLUMN →COL
Level 1/Argument 1
See also:
( Ø is the left-shift of the 5key).
Leveln+1/Item 1 ...
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]
→
[ vector ]col1
[ vector ]coln
ncolcount
[ vector ]
COL→, →ROW, ROW→
→
element1
elementn
nelementcount
COL→
Type:
Command
Description: Columns to Matrix Command: Transforms a series of column vectors and a column count into a
matrix containing those columns, or transforms a sequence of numbers and an element count
into a vector with those numbers as elements.
All vectors must have the same length. The column or element count is rounded to the nearest
integer.
Access:
!´MATRIX COL COL→
( ´ is the left-shift of the Pkey).
( Ø is the left-shift of the 5key).
!Ø CREATE COLUMN COL→
Input/Output:
Ln+1/A1 ...
L2/A2
L1/An+1
[ vector ]col1
[ vector ]coln
ncolcount
→
[[ matrix ]]
element1
elementn
nelementcount
→
[ vector ]
L = Level; A = Argument; I = item
See also:
→COL, →ROW, ROW→
COL–
Type:
Command
3-30 Full Command and Function Reference
Level 1/Item 1
Description: Delete Column Command: Deletes column n of a matrix (or element n of a vector), and returns
the modified matrix (or vector) and the deleted column (or element).
n is rounded to the nearest integer.
Access:
!´MATRIX COL COL−
( ´ is the left-shift of the Pkey).
!Ø
Input/Output:
See also:
( Ø is the left-shift of the 5key).
CREATE COLUMN COL−
Level 2/Argument 1
Level 1/Argument 2
[[ matrix ]]1
ncolumn
[ vector ]1
nelement
Level 2/Item 1
Level 1/Item 2
→
[[ matrix ]]2
[ vector ]column
→
[ vector ]2
elementn
COL+, CSWP, ROW+, ROW–
COL+
Type:
Command
Description: Insert Column Command: Inserts an array (vector or matrix) into a matrix (or one or more
elements into a vector) at the position indicated by nindex, and returns the modified array.
The inserted array must have the same number of rows as the target array. nindex is rounded to the
nearest integer. The original array is redimensioned to include the new columns or elements, and
the elements at and to the right of the insertion point are shifted to the right.
Access:
!´MATRIX COL COL+
( ´ is the left-shift of the Pkey).
( Ø is the left-shift of the 5key).
!Ø CREATE COLUMN COL+
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]1
[[ matrix ]]2
nindex
→
[[ matrix ]]3
[[ matrix ]]1
[ vector ]column
nindex
→
[[ matrix ]]2
nelement
nindex
→
[ vector ]2
[ vector ]1
COL–, CSWP, ROW+, ROW–
Level 1/Item 1
COLCT
Type:
Command
Description: Factorizes a polynomial or an integer. Identical to COLLECT.
Access:
…µCOLCT
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'symb1'
→
'symb2'
x
→
x
→
(x, y)
(x, y)
EXPAN, FACTOR, ISOL, QUAD, SHOW
COLLECT
CAS:
Factorize a polynomial or an integer. Identical to COLCT.
COLΣ
Type:
Command
Description: Column Sigma Command: Specifies the independent-variable and dependent-variable columns
of the current statistics matrix (the reserved variable ΣDAT).
Full Command and Function Reference 3-31
COLΣ combines the functionality of XCOL and YCOL. The independent-variable column
number xxcol is stored as the first parameter in the reserved variable ΣPAR (the default is 1). The
dependent-variable column number xycol is stored as the second parameter in the reserved
variable ΣPAR (the default is 2).
COLΣ accepts and stores noninteger values, but subsequent commands that use these two
parameters in ΣPAR will cause errors.
Access:
…µCOLΣ
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
xcol
ycol
Level 1/Item 1
→
BARPLOT, BESTFIT, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR, PREDX,
PREDY, PWRFIT, SCATRPLOT, XCOL, YCOL
COMB
Type:
Function
Description: Combinations Function: Returns the number of possible combinations of n items taken m at a
time. The following formula is used:
n!
C n, m = ------------------------------m! ⋅ ( n – m )!
The arguments n and m must each be less than 1012. If n<m, zero is returned.
Access:
!´L PROBABILITY COMB
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
n
m
→
Cn;m
'symbn'
m
→
'COMB(symbn,m)'
n
'symbm'
→
'COMB(n, symbm)'
'symbn'
'symbm'
→
'COMB(symbn,symbm)'
FACT, PERM, !
CON
Type:
Command
Description: Constant Array Command: Returns a constant array, defined as an array whose elements all have
the same value.
The constant value is a real or complex number taken from argument 2/level 1. The resulting
array is either a new array, or an existing array with its elements replaced by the constant,
depending on the object in argument 1/level 2.
• Creating a new array: If argument 1/level 2 contains a list of one or two integers, CON
returns a new array. If the list contains a single integer ncolumns, CON returns a constant vector
with n elements. If the list contains two integers nrows and mcolumns, CON returns a constant
matrix with n rows and m columns.
• Replacing the elements of an existing array: If argument 1/level 2 contains an array, CON returns
an array of the same dimensions, with each element equal to the constant. If the constant is a
complex number, the original array must also be complex.
• If argument 1/level 2 contains a name, the name must identify a variable that contains an array. In
this case, the elements of the array are replaced by the constant. If the constant is a complex
number, the original array must also be complex.
3-32 Full Command and Function Reference
Access:
!´MATRIX MAKE CON
!Ø
Input/Output:
See also:
( ´ is the left-shift of the Pkey).
( Ø is the left-shift of the 5key).
CREATE CON
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
{ ncolumns }
zconstant
→
[ vectorconstant ]
{ nrows mcolumns }
zconstant
→
[[ matrixconstant ]]
[ R-array ]
xconstant
→
[ R-arrayconstant ]
[ C-array ]
zconstant
→
[ C-arrayconstant ]
'name'
zconstant
→
IDN
COND
Type:
Command
Description: Condition Number Command: Returns the 1-norm (column norm) condition number of a
square matrix.
The condition number of a matrix is the product of the norm of the matrix and the norm of the
inverse of the matrix. COND uses the 1-norm and computes the condition number of the matrix
without computing the inverse of the matrix.
The condition number expresses the sensitivity of the problem of solving a system of linear
equations having coefficients represented by the elements of the matrix (this includes inverting
the matrix). That is, it indicates how much an error in the inputs may be magnified in the outputs
of calculations using the matrix.
In many linear algebra computations, the base 10 logarithm of the condition number of the
matrix is an estimate of the number of digits of precision that might be lost in computations
using that matrix. A reasonable rule of thumb is that the number of digits of accuracy in the
result is approximately MIN(12,15–log10(COND)).
Access:
!´MATRIX NORMALIZE COND
( ´ is the left-shift of the Pkey).
!Ø OPERATIONS COND
( Ø is the left-shift of the 5key).
Input/Output:
Level 1/Argument 1
[[ matrix ]]m×n
See also:
Level 1/Item 1
→
xconditionnumber
SNRM, SRAD, TRACE
CONIC
Type:
Command
Description: Conic Plot Type Command: Sets the plot type to CONIC.
When the plot type is CONIC, the DRAW command plots the current equation as a secondorder polynomial of two real variables. The current equation is specified in the reserved variable
EQ. The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type CONIC, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
Full Command and Function Reference 3-33
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a name specifying the independent variable, or a list containing such a name and two
numbers specifying the minimum and maximum values for the independent variable (the
plotting range). The default value is X.
• res is a real number specifying the interval (in user-unit coordinates) between plotted values of
the independent variable, or a binary integer specifying the interval in pixels. The default value
is 0, which specifies an interval of 1 pixel.
• axes is a complex number specifying the user-unit coordinates of the intersection of the
horizontal and vertical axes, or a list containing such a number and two strings specifying
labels for the horizontal and vertical axes. The default value is (0,0).
• ptype is a command name specifying the plot type. Executing the command CONIC places the
command name CONIC in PPAR.
• depend is a name specifying the dependent variable. The default value is Y.
The current equation is used to define a pair of functions of the independent variable. These
functions are derived from the second-order Taylor's approximation to the current equation. The
minimum and maximum values of the independent variable (the plotting range) can be specified
in indep; otherwise, the values in (xmin, ymin) and (xmax, ymax) (the display range) are used. Lines are
drawn between plotted points unless flag –31 is set.
Access:
…µCONIC
Input/Output: None
See also:
BAR, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE,
PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
CONJ
Type:
Function
Description: Conjugate Analytic Function: Conjugates a complex number or a complex array.
Conjugation is the negation (sign reversal) of the imaginary part of a complex number. For real
numbers and real arrays, the conjugate is identical to the original argument.
Access:
…ßCONJ
(ßis the right-shift of the 1key).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
x
(x, y)
→
(x, –y)
[ R-array ]
→
[ R-array ]
[ C-array ]1
→
[ C-array ]2
→
'CONJ(symb)'
'symb'
ABS, IM, RE, SCONJ, SIGN
CONLIB
Type:
Command
Description: Open Constants Library Command: Opens the Constants Library catalog.
Access:
GCONSTANTS LIBRARY
Input/Output: None
3-34 Full Command and Function Reference
See also:
CONST
CONST
Type:
Function
Description: Constant Value Command: Returns the value of a constant.
CONST returns the value of the specified constant. It chooses the unit type depending on flag
–60: SI if clear, English if set, and uses the units depending on flag –61: units if clear, no units if
set.
Access:
…µCONST
Flags:
Units Type (60), Units Usage (61)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
'name'
See also:
x
CONLIB
CONSTANTS
CAS:
Display menu or list of CAS symbolic constants.
CONT
Type:
Command
Description: Continue Program Execution Command: Resumes execution of a halted program.
Since CONT is a command, it can be assigned to a key or to a custom menu.
Access:
!æ
( æis the left-shift of the ‡key).
Input/Output: None
See also:
HALT, KILL, PROMPT
CONVERT
Type:
Command
Description: Convert Units Command: Converts a source unit object to the dimensions of a target unit.
The source and target units must be compatible. The number part x2 of the target unit object is
ignored.
Access:
!Ú UNITS TOOLS CONVERT
( Ú is the left-shift of the 6key).
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
x1_unitssource
x2_unitstarget
UBASE, UFACT, →UNIT, UVAL
Level 1/Item 1
→
x3_unitstarget
CORR
Type:
Command
Description: Correlation Command: Returns the correlation coefficient of the independent and dependent
data columns in the current statistics matrix (reserved variable ΣDAT).
The columns are specified by the first two elements in the reserved variable ΣPAR, set by XCOL
and YCOL, respectively. If ΣPAR does not exist, CORR creates it and sets the elements to their
default values (1 and 2).
The correlation is computed with the following formula:
Full Command and Function Reference 3-35
n
∑
i=1
( xin1 – xn1 ) ( xin2 – xn2 )
----------------------------------------------------------------------------------n
∑
i=1
( x in1 – xn 1 )
2 n
∑
i=1
( xin2 – xn2 )
2
where x in1 is the ith coordinate value in column n1, x in2 is the ith coordinate value in the column
n2, xn1 is the mean of the data in column n1, xn2 is the mean of the data in column n2, and n is
the number of data points.
Access:
…µCORR
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
xcorrelation
COLΣ, COV, PREDX, PREDY, XCOL, YCOL
COS
Type:
Analytic Function
Description: Cosine Analytic Function: Returns the cosine of the argument.
For real arguments, the current angle mode determines the number's interpretation as an angle,
unless the angular units are specified.
For complex arguments, cos(x + iy) = cosx coshy – i sinx sinhy.
If the argument for COS is a unit object, then the specified angular unit overrides the angle
mode to determine the result. Integration and differentiation, on the other hand, always observe
the angle mode. Therefore, to correctly integrate or differentiate expressions containing COS
with a unit object, the angle mode must be set to Radians (since this is a “neutral” mode).
Access:
T
Flags:
Numerical Results (–3), Angle Mode (–17, –18)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
cos z
'symb'
→
'COS(symb)'
x_unitangular
→
cos (x_unitangular)
ACOS, SIN, TAN
COSH
Type:
Analytic Function
Description: Hyperbolic Cosine Analytic Function: Returns the hyperbolic cosine of the argument.
For complex arguments, cosh(x + iy) = coshx cosy + i sinhx siny.
Access:
…ÑHYPERBOLIC COSH
(Ñ is the right-shift of the 8key).
!´HYPERBOLIC COSH
( ´is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
cosh z
'symb'
→
'COSH(symb)'
ACOSH, SINH, TANH
3-36 Full Command and Function Reference
COV
Type:
Command
Description: Covariance Command: Returns the sample covariance of the independent and dependent data
columns in the current statistics matrix (reserved variable ΣDAT).
The columns are specified by the first two elements in reserved variable ΣPAR, set by XCOL
and YCOL respectively. If ΣPAR does not exist, COV creates it and sets the elements to their
default values (1 and 2).
The covariance is calculated with the following formula:
1 n
------------ ∑ ( x in 1 – x n 1 ) ( x in 2 – x n 2 )
n – 1i = 1
where x in1 is the ith coordinate value in column n1, x in2 is the ith coordinate value in the column
n2, xn1 is the mean of the data in column n1, xn2 is the mean of the data in column n2, and n is
the number of data points.
Access:
…µCOV
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
xcovariance
COLΣ, CORR, PCOV, PREDX, PREDY, XCOL, YCOL
CR
Type:
Command
Description: Carriage Right Command: Prints the contents, if any, of the printer buffer.
CR sends to the printer a string that encodes the line termination method. The default
termination method is carriage-return/linefeed. The string is the fourth parameter in the reserved
variable PRTPAR.
Access:
…µCR
Flags:
I/O Device (–33), Printing Device (–34), Double-Spaced Printing (–37)
Input/Output: None
See also:
DELAY, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1
CRDIR
Type:
Command
Description: Create Directory Command: Creates an empty subdirectory with the specified name in the
current directory.
CRDIR does not change the current directory; evaluate the name of the new subdirectory to
make it the current directory.
Access:
!°MEMORY DIRECTORY CRDIR
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
'global'
HOME, PATH, PGDIR, UPDIR
Level 1/Item 1
→
CROSS
Type:
Command
Description: Cross Product Command: CROSS returns the cross product C = A × B of vectors A and B.
The arguments must be vectors having two or three elements, and need not have the same
number of elements. (The hp49g+/hp48gII automatically converts a two-element argument
Full Command and Function Reference 3-37
[ d1 d2 ] to a three-element argument [ d1 d2 0 ].)
Access:
!´VECTOR CROSS
Input/Output:
( ´ is the left-shift of the Pkey).
Level 2/Argument 1
See also:
Level 1/Argument 2
[ vector ]A
CNRM, DET, DOT, RNRM
[ vector ]B
Level 1/Item 1
→
[ vector ]A × B
CSWP
Type:
Command
Description: Column Swap Command: Swaps columns i and j of the argument matrix and returns the
modified matrix, or swaps elements i and j of the argument vector and returns the modified
vector.
Column numbers are rounded to the nearest integer. Vector arguments are treated as row
vectors.
Access:
!Ø CREATE COLUMN CSWP
( Ø is the left-shift of the 5key).
!´MATRIX COL CSWP
( ´ is the left-shift of the Pkey).
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]1
ncolumni
ncolumnj
→
[[ matrix ]]2
nelementi
nelementj
→
[ vector ]2
See also:
[ vector ]1
COL+, COL–, RSWP
CURL
CAS:
Return the curl of a three-dimensional vector function.
Level 1/Item 1
CYCLOTOMIC
CAS:
Return the cyclotomic polynomial of order n.
CYLIN
Type:
Command
Description: Cylindrical Mode Command: Sets Cylindrical coordinate mode.
CYLIN clears flag –15 and sets flag –16.
In Cylindrical mode, vectors are displayed as polar components.
Access:
!´VECTOR L CYLIN
( ´ is the left-shift of the Pkey).
Input/Output: None
See also:
RECT, SPHERE
C→PX
Type:
Command
Description: Complex to Pixel Command: Converts the specified user-unit coordinates to pixel coordinates.
The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the
reserved variable PPAR.
Access:
!°LPICT LC→PX
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
(x, y)
See also:
PX→C
3-38 Full Command and Function Reference
Level 1/Item 1
→
{ #n, #m }
C→R
Type:
Command
Description: Complex to Real Command: Separates the real and imaginary parts of a complex number or
complex array. The result in item 1/level 2 represents the real part of the complex argument.
The result in item 2/ level 1 represents the imaginary part of the complex argument.
( °is the left-shift of the Nkey).
Access:
!°TYPE LC→R
Input/Output:
Level 1/Argument 1
See also:
Level 2/Item 1
Level 1/Item 2
(x, y)
→
x
y
[ C-array ]
→
[R-array ]1
[R-array ]2
R→C, RE, IM
DARCY
Type:
Function
Description: Darcy Friction Factor Function: Calculates the Darcy friction factor of certain fluid flows.
DARCY calculates the Fanning friction factor and multiplies it by 4. xe/D is the relative roughness
– the ratio of the conduit roughness to its diameter. yRe is the Reynolds number. The function
uses different computation routines for laminar flow (Re ≤ 2100) and turbulent flow (Re > 2100).
xe/D and yRe must be real numbers or unit objects that reduce to dimensionless numbers, and
both numbers must be greater than 0.
Access:
…µ DARCY
Input/Output:
Level 2/Argument 1
xe
See also:
/
Level 1/Argument 2
D
yRe
Level 1/Item 1
→
xDarcy
FANNING
DATE
Type:
Command
Description: Date Command: Returns the system date.
Access:
…ÓTOOLS DATE
(Ó is the right-shift of the 9 key).
…&9 DATE
Flags:
Date Format (-42)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
date
DATE+, DDAYS, TIME, TSTR
→DATE
Type:
Command
Description: Set Date Command: Sets the system date to date.
date has the form MM.DDYYYY or DD.MMYYYY, depending on the state of flag –42. MM is
month, DD is day, and YYYY is year. If YYYY is not supplied, the current specification for the
year is used. The range of allowable dates is January 1, 2000 to December 31, 2090. Inputs
between January 1, 1991 and December 31, 1999 are silently rejected by →DATE; no error is
reported and the system date is left unchanged.
Full Command and Function Reference 3-39
…ÓTOOLS →DATE
…&9 →DATE
Flags:
Date Format (-42)
Input/Output:
( Ó is the right-shift of the 9 key).
Access:
Level 1/Argument 1
→
date
See also:
Level 1/Item 1
→TIME
DATE+
Type:
Command
Description: Date Addition Command: Returns a past or future date, given a date in argument 1/level 2 and a
number of days in argument 2/level 1. If xdays is negative, DATE+ calculates a past date. The
range of allowable dates is October 15, 1582, to December 31, 9999.
Access:
…ÓTOOLS L DATE+
( Ó is the right-shift of the 9 key).
…&9 LDATE+
Flags:
Date Format (-42)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
date1
xdays
Level 1/Item 1
→
datenew
DATE, DDAYS
DBUG
Type:
Operation
Description: Debug Operation: Starts program execution, then suspends it as if HALT were the first program
command.
DBUG is programmable.
Access:
…µDEBUG
Input/Output:
Level 1/Argument 1
« program » or 'program name'
See also:
Level 1/Item 1
→
HALT, NEXT
DDAYS
Type:
Command
Description: Delta Days Command: Returns the number of days between two dates.
If the argument 1/level 2 date is chronologically later than the argument 2/ level 1 date, the
result is negative. The range of allowable dates is October 15, 1582, to December 31, 9999.
Access:
…ÓTOOLS LDDAYS
( Ó is the right-shift of the 9 key).
…&9 LDDAYS
Flags:
Date Format (-42)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
date1
date2
DATE, DATE+
3-40 Full Command and Function Reference
Level 1/Item 1
→
xdays
DEC
Type:
Command
Description: Decimal Mode Command: Selects decimal base for binary integer operations. (The default base is
decimal.)
Binary integers require the prefix #. Binary integers entered and returned in decimal base
automatically show the suffix d. If the current base is not decimal, then you can enter a decimal
number by ending it with d. It will be displayed in the current base when it is entered.
The current base does not affect the internal representation of binary integers as unsigned binary
numbers.
Access:
!´BASE DEC
( ´ is the left-shift of the Pkey).
!Ú BASE DEC
( Ú is the left-shift of the 6key).
Flags:
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output: None
See also:
BIN, HEX, OCT, RCWS, STWS
DECR
Type:
Command
Description: Decrement Command: Takes a variable, subtracts 1, stores the new value back into the original
variable, and returns the new value. The contents of name must be a real number or an integer.
Access:
!°MEMORY ARITHMETIC DECR
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
'name'
See also:
xnew
INCR, STO+, STO–
DEDICACE
CAS:
Display a greeting from the CAS team.
DEF
CAS:
Define function or variable; store global variable or store expression as a function to evaluate
later.
DEFINE
Type:
Command
Description: Define Variable or Function Command: Stores the expression on the right side of the = in the
variable specified on the left side, or creates a user-defined function.
If the left side of the equation is name only, DEFINE stores exp in the variable name.
If the left side of the equation is name followed by parenthetical arguments name1 … namen,
DEFINE creates a user-defined function and stores it in the variable name.
Access:
!à
( àis the left-shift of the 2key).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
'name=exp'
See also:
'name(name1 ... namen)=exp(name1 ... namen)'
DEF, STO, UNASSIGN
→
Full Command and Function Reference 3-41
DEG
Type:
Command
Description: Degrees Command: Sets Degrees angle mode.
DEG clears flags –17 and –18, and displays the DEG annunciator.
In Degrees angle mode, real-number arguments that represent angles are interpreted as degrees,
and real-number results that represent angles are expressed in degrees.
Access:
!&H ANGLE DEG
!°L MODES ANGLE DEG
( °is the left-shift of the Nkey).
Input/Output: None
See also:
GRAD, RAD
DEGREE
CAS:
Return the degree of a polynomial expression, or –1 if expression is zero.
DELALARM
Type:
Command
Description: Delete Alarm Command: Deletes the specified alarm.
If nindex is 0, all alarms in the system alarm list are deleted.
Access:
…ÓTOOLS ALRM DELALARM
( Ó is the right-shift of the 9 key).
…&9 ALRM DELALARM
Input/Output:
Level 1/Argument 1
See also:
nindex
FINDALARM, RCLALARM, STOALARM
Level 1/Item 1
→
DELAY
Type:
Command
Description: Delay Command: Specifies how many seconds the hp49g+/hp48gII waits between sending lines
of information to the printer.
xdelay specifies the delay time in seconds. The default delay is 0 seconds. The maximum delay is
6.9 seconds. (The sign of xdelay is ignored, so –4 DELAY is equivalent to 4 DELAY.)
The delay setting is the first parameter in the reserved variable PRTPAR.
A shorter delay setting can be useful when the hp49g+/hp48gII sends multiple lines of
information to your printer (for example, when printing a program). To optimize printing
efficiency, set the delay just longer than the time the printhead requires to print one line of
information. If you set the delay shorter than the time to print one line, you may lose information.
Access:
…µDELAY
Flags:
I/O Device (–33), Printing Device (–34)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xdelay
CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1
DELKEYS
Type:
Command
Description: Delete Key Assignments Command: Clears user-defined key assignments.
The argument xkey is a real number rc.p specifying the key by its row number, its column number,
and its plane (shift). For a definition of plane, see ASN.
3-42 Full Command and Function Reference
Specifying 0 for xkey clears all user key assignments and restores the standard key assignments.
Specifying S as the argument for DELKEYS suppresses all standard key assignments on the user
keyboard. This makes keys without user key assignments inactive on the user keyboard. (You can
make exceptions using ASN, or restore them all using STOKEYS.) If you are stuck in User
mode – probably with a “locked” keyboard – because you have reassigned or suppressed the
keys necessary to cancel User mode, do a system halt (“warm start”): press and hold ‡ and
C simultaneously, releasing C first. This cancels User mode. Deleted user key assignments
still take up from 2.5 to 62.5 bytes of memory each. You can free this memory by packing your
user key assignments by executing RCLKEYS 0 DELKEYS STOKEYS.
Access:
!&H
KEYS DELKEYS
!°L MODES KEYS DELKEYS
( °is the left-shift of the Nkey).
Flags:
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard.
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
xkey
→
{ xkey1, ... ,xkey n }
→
0
→
'S'
→
ASN, RCLKEYS, STOKEYS
DEPND
Type:
Command
Description: Dependent Variable Command: Specifies the dependent variable (and its plotting range for
TRUTH plots).
The specification for the dependent variable name and its plotting range is stored in the reserved
variable PPAR as follows:
• If the argument is a global variable name, that name replaces the dependent variable entry in
PPAR.
• If the argument is a list containing a global name, that name replaces the dependent variable
name but leaves unchanged any existing plotting range.
• If the argument is a list containing a global name and two real numbers, or a list containing a
name, array, and real number, that list replaces the dependent variable entry.
• If the argument is a list containing two real numbers, or two real numbers from levels 1 and 2,
those two numbers specify a new plotting range, leaving the dependent variable name
unchanged. (LASTARG returns a list, even if the two numbers were entered separately.)
The default entry is Y.
The plotting range for the dependent variable is meaningful only for plot type TRUTH, where it
restricts the region for which the equation is tested, and for plot type DIFFEQ, where it specifies
the initial solution value and absolute error tolerance.
Access:
…µDEPND
Input/Output:
Level 2/Argument 1
ystart
Level 1/Argument 2
Level 1/Item 1
'global'
→
{ global }
→
{ global, ystart, yend }
→
{ystart, yend }
→
yend
→
Full Command and Function Reference 3-43
See also:
INDEP
DEPTH
Type:
RPL Command
Description: Depth Command: Returns a real number representing the number of objects present on the
stack (before DEPTH was executed).
Access:
!°STACK LDEPTH
( °is the left-shift of the Nkey).
I STACK LDEPTH
Input/Output:
Level n…Level 1
Level 1
→
n
See also:
CLEAR, DROPN
DERIV
CAS:
Return the partial derivatives of a function, with respect to specified variables.
DERVX
CAS:
Return the derivative of a function with respect to the current variable.
DESOLVE
CAS:
Solve first-order ordinary differential equations with respect to the current variable.
DET
Type:
Command
Description: Determinant Function: Returns the determinant of a square matrix.
The argument matrix must be square. DET computes the determinant of 1 × 1 and 2 × 2
matrices directly from the defining expression for the determinant. DET computes the
determinant of a larger matrix by computing the Crout LU decomposition of the matrix and
accumulating the product of the decomposition's diagonal elements.
Since floating-point division is used to do this, the computed determinant of an integer matrix is
often not an integer, even though the actual determinant of an integer matrix must be an integer.
DET corrects this by rounding the computed determinant to an integer value. This technique is
also used for noninteger matrices with determinants having fewer than 15 nonzero digits: the
computed determinant is rounded at the appropriate digit position to restore some or all of the
accuracy lost to floating-point arithmetic.
This refining technique can cause the computed determinant to exhibit discontinuity. To avoid
this, you can disable the refinement by setting flag –54.
Access:
!Ø OPERATIONS DET
( Ø is the left-shift of the 5key).
!´NORMALIZE DET
( ´ is the left-shift of the Pkey).
Flags:
Tiny Element (–54)
Input/Output:
Level 1/Argument 1
See also:
[[ matrix ]]
CNRM, CROSS, DOT, RNRM
Level 1/Item 1
→
xdeterminant
DETACH
Type:
Command
Description: Detach Library Command: Detaches the library with the specified number from the current
directory. Each library has a unique number. If a port number is specified, it is ignored.
3-44 Full Command and Function Reference
A library object attached to a non-HOME directory is automatically detached (without using
DETACH) whenever a new library object is attached there.
Access:
…µDETACH
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
nlibrary
→
:nport :nlibrary
→
ATTACH, LIBS, PURGE
DIAG→
Type:
Command
Description: Vector to Matrix Diagonal Command: Takes an array and a specified dimension and returns a
matrix whose major diagonal elements are the elements of the array.
Real number dimensions are rounded to integers. If a single dimension is given, a square matrix
is returned. If two dimensions are given, the proper order is { number of rows, number of columns }.
No more than two dimensions can be specified.
If the main diagonal of the resulting matrix has more elements than the array, additional diagonal
elements are set to zero. If the main diagonal of the resulting matrix has fewer elements than the
array, extra array elements are dropped.
Access:
!Ø CREATEL DIAG→
( Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
!´MATRIX L DIAG→
( ´ is the left-shift of the Pkey).
!´MATRIX MAKELL DIAG→
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
[ array ]diagonals
{ dim }
Level 1/Item 1
→
[[ matrix ]]
→DIAG
→DIAG
Type:
Command
Description: Matrix Diagonal to Array Command: Returns a vector that contains the major diagonal elements
of a matrix.
The input matrix does not have to be square.
Access:
!Ø
CREATE →DIAG
!´MATRIX L →DIAG
!´MATRIX MAKE LL →DIAG
Input/Output:
( Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
[[ matrix ]]
See also:
Level 1/Item 1
→
[ vector ]diagonals
DIAG→
DIAGMAP
CAS:
Apply an holomorphic operator to a diagonalizable matrix.
DIFF
CAS:
Display a menu or list of CAS commands for differential calculus, including series.
Full Command and Function Reference 3-45
DIFFEQ
Type:
Command
Description: Differential Equation Plot Type Command: Sets the plot type to DIFFEQ.
When the plot type is DIFFEQ and the reserved variable EQ does not contain a list, the initial
value problem is solved and plotted over an interval using the Runge–Kutta–Fehlberg (4,5)
method. The plotting parameters are specified in the reserved variable PPAR, which has the
following form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type DIFFEQ, the elements of PPAR are used as follows:
•
(xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left
corner of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9)
for the hp49g+.
•
(xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper
right corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0)
for the hp49g+.
indep is a list, { X x0 xf }, containing a name that specifies the independent variable, and two
numbers that specify the initial and final values for the independent variable. The default
values for these elements are { X 0 xmax }.
•
•
res is a real number specifying the maximum interval, in user-unit coordinates, between
values of the independent variable. The default value is 0. If res does not equal zero, then the
maximum interval is res. If res equals zero, the maximum interval is unlimited.
•
axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. If the
solution is real-valued, these strings can specify the dependent or the independent variable; if
the solution is vector valued, the strings can specify a solution component:
– 0 specifies the dependent variable (X)
– 1 specifies the dependent variable (Y)
– n specifies a solution component Yn
– If axes contains any strings other than 0, 1 or n, the DIFFEQ plotter uses the default
strings 0 and 1, and plots the independent variable on the horizontal axis and the
dependent variable on the vertical.
• ptype is a command name specifying the plot type. Executing the command DIFFEQ places
the command name DIFFEQ in PPAR.
•
depend is a list, { Y y0 xErrTol }, containing a name that specifies the dependent variable (the
solution), and two numbers that specify the initial value of Y and the global absolute error
tolerance in the solution Y. The default values for these elements are { Y 0 .0001 }
EQ must define the right-hand side of the initial value problem Y'(XF(X,Y). Y can return a real
value or real vector when evaluated.
The DIFFEQ-plotter attempts to make the interval between values of the independent variable
as large as possible, while keeping the computed solution within the specified error tolerance
xErrTol. This tolerance may hold only at the computed points. Straight lines are drawn between
computed step endpoints, and these lines may not accurately represent the actual shape of the
solution. res limits the maximum interval size to provide higher plot resolution.
On exit from DIFFEQ plot, the first elements of indep and depnd (identifiers) contain the final
values of X and Y, respectively.
3-46 Full Command and Function Reference
If EQ contains a list, the initial value problem is solved and plotted using a combination of
Rosenbrock (3,4) and Runge-Kutta-Fehlberg (4,5) methods. In this case DIFFEQ uses
RRKSTEP to calculate yf, and EQ must contain two additional elements:
•
The second element of EQ must evaluate to the partial derivative of Y' with respect to X,
and can return a real value or real vector when evaluated.
• The third element of EQ must evaluate to the partial derivative of Y' with respect to Y, and
can return a real value or a real matrix when evaluated.
Access:
…µDIFFEQ
Input/Output: None
See also:
AXES, CONIC, FUNCTION, PARAMETRIC, POLAR, RKFSTEP, RRKSTEP, TRUTH
DIR
Type:
Function
Description: Creates an empty directory structure in run mode. Can be used as an alternative to CRDIR to
create an empty directory by typing DIR ‘NAME’ STO, which will create an empty directory
‘NAME’ if it does not already exist in the current directory.
Access:
…µDIR
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
DIR …END
CRDIR
DISP
Type:
Command
Description: Display Command: Displays obj in the nth display line.
n ≤ 1 indicates the top line of the display.
To facilitate the display of messages, strings are displayed without the surrounding " " delimiters.
All other objects are displayed in the same form as would be used if the object were in level 1 in
the multiline display format. If the object display requires more than one display line, the display
starts in line n, and continues down the display either to the end of the object or the bottom of
the display. The object displayed by DISP persists in the display only until the keyboard is ready
for input. The FREEZE command can be used to cause the object to persist in the display until
a key is pressed.
Access:
!°LOUT DISP
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
obj
n
DISPXY, FREEZE, HALT, INPUT, PROMPT
Level 1/Item 1
→
DISPXY
Type:
Command
Description: Display Command: Displays obj at the specified screen coordinates using a specified font size.
The list argument expects exactly two binary integers to specify the X and Y coordinates. The
level one integer argument n will display the obj using a small font if n is 1 and using the system
font if n is 2.
To facilitate the display of messages, strings are displayed without the surrounding " " delimiters.
All other objects are displayed in the same form as would be used if the object were in level 1 in
Full Command and Function Reference 3-47
the multiline display format. If the object display requires more than one display line, the display
starts at coordinate #x #y, and continues down the display either to the end of the object or the
bottom of the display. NOTE: DISPXY is not useful for displaying GROBs.
The object displayed by DISPXY persists in the display only until the keyboard is ready for
input. The FREEZE command can be used to cause the object to persist in the display until a
key is pressed.
Access:
!°LOUT DISPXY
( °is the left-shift of the Nkey).
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
n
Level 1/Item 1
→
See also:
obj
{ list }
DISP, FREEZE, HALT, INPUT, PROMPT
DISTRIB
CAS:
Apply one step of the distributive property of multiplication and division.
DIV
CAS:
Return the divergence of a vector function.
DIV2
CAS:
Perform Euclidean division on two expressions.
DIV2MOD
CAS:
Perform euclidean division on two expressions modulo the current modulus.
DIVIS
CAS:
Return a list of divisors of a polynomial or an integer.
DIVMOD
CAS:
Divide two expressions modulo the current modulus.
DIVPC
CAS:
Return a Taylor polynomial for the quotient of two polynomial expressions.
dn
CAS:
Differential of a function with respect to its argument n, an alternative to the ∂ function.
DO
Type:
Command
Description: DO Indefinite Loop Structure Command: Starts DO…UNTIL…END indefinite loop structure.
DO … UNTIL … END executes a loop repeatedly until a test returns a true (nonzero) result. Since
the test clause is executed after the loop clause, the loop is always executed at least once. The syntax
is: DO loop-clause UNTIL test-clause END
DO starts execution of the loop clause. UNTIL ends the loop clause and begins the test clause.
The test clause must return a test result to the stack. END removes the test result from the stack.
If its value is zero, the loop clause is executed again; otherwise execution resumes following
END.
Access:
!°BRANCH DO
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
DO
→
UNTIL
→
END
END, UNTIL, WHILE
3-48 Full Command and Function Reference
T/F
→
DOERR
Type:
Command
Description: Do Error Command: Executes a “user-specified” error, causing a program to behave exactly as if
a normal error had occurred during program execution.
DOERR causes a program to behave exactly as if a normal error has occurred during program
execution. The error message depends on the argument provided to DOERR:
• nerror or #nerror display the corresponding built-in error message.
• "error" displays the contents of the string. (A subsequent execution of ERRM returns "error".
ERRN returns # 70000h.)
• 0 abandons program execution with an ‘interrupted’ error message (ERRN = #13Fh).
• 0 DOERR is equivalent to pressing −.
Access:
!°LLERROR DOERR
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
nerror
→
#nerror
→
“error”
→
0
→
ERRM, ERRN, ERR0
DOLIST
Type:
Command
Description: Do to List Command: Applies commands, programs, or user-defined functions to lists.
The number of lists, n, can be omitted when the first or level 1 argument is any of the following:
• A command.
• A program containing exactly one command (e.g. « DUP »)
• A program conforming to the structure of a user-defined function.
The final argument 1 (or level 1 object) can be a local or global name that refers to a program or
command.
All lists must be the same length l. The program is executed l times: on the ith iteration, n objects
each taken from the ith position in each list are entered on the stack in the same order as in their
original lists, and the program is executed. The results from each execution are left on the stack.
After the final iteration, any new results are combined into a single list.
Access:
!°LIST PROCEDURES DOLIST
( °is the left-shift of the Nkey).
Input/Output:
Ln+2/A1 ... L3/An–2
L2/An+1
L1/An+2
{ list }1 ... { list }n
n
« program »
→
{ results }
{ list }1 ... { list }n
n
command
→
{ results }
{ list }1 ... { list }n
n
name
→
{ results }
{ list }1 ...
{ list }n+1
« program »
→
{ results }
{ list }1 ...
{ list }n+1
command
→
{ results }
{ list }1 ...
{ list }n+1
name
→
{ results }
Level 1/Item 1
L = Level; A = Argument
See also:
DOSUBS, ENDSUB, NSUB, STREAM
Full Command and Function Reference 3-49
DOMAIN
CAS:
List the domain of real numbers for which a function is defined.
DOSUBS
Type:
Command
Description: Do to Sublist Command: Applies a program or command to groups of elements in a list.
The real number n can be omitted when the first argument is one of the following:
• A command.
• A user program containing a single command.
• A program with a user-defined function structure.
• A global or local name that refers to one of the above.
The first iteration uses elements 1 through n from the list; the second iteration uses elements 2
through n + 1; and so on. In general, the mth iteration uses the elements from the list
corresponding to positions m through m + n – 1.
During an iteration, the position of the first element used in that iteration is available to the user
using the command NSUB, and the number of groups of elements is available using the
command ENDSUB. Both of these commands return an Undefined Local Name error if
executed when DOSUBS is not active.
DOSUBS returns the Invalid User Function error if the object at level 1/argument 3 is a user
program that does not contain only one command and does not have a user-defined function
structure. DOSUBS also returns the Wrong Argument Count error if the object at level
1/argument 3 is a command that does not accept 1 to 5 arguments of specific types (DUP, ROT,
or →LIST, for example).
Access:
!°LIST PROCEDURES DOSUBS
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
{ list }1
n
« program »
→
{ list }2
{ list }1
n
command
→
{ list }2
{ list }1
n
name
→
{ list }2
{ list }1
« program »
→
{ list }2
{ list }1
command
→
{ list }2
name
→
{ list }2
{ list }1
DOLIST, ENDSUB, NSUB, STREAM
Level 1/Item 1
DOT
Type:
Command
Description: Dot Product Command: Returns the dot product A•B of two arrays A and B, calculated as the
sum of the products of the corresponding elements of the two arrays.
Both arrays must have the same dimensions.
Some authorities define the dot product of two complex arrays as the sum of the products of the
conjugated elements of one array with their corresponding elements from the other array. The
hp49g+/hp48gII uses the ordinary products without conjugation. If you prefer the alternative
definition, apply CONJ to one array before using DOT.
Access:
!Ø LVECTOR DOT
( Ø is the left-shift of the 5key).
!´VECTOR DOT
( ´ is the left-shift of the Pkey).
3-50 Full Command and Function Reference
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
[ array A ]
[ array B ]
Level 1/Item 1
→
x
CNRM, CROSS, DET, RNRM
DRAW
Type:
Command Operation
Description: Draw Plot Command: Plots the mathematical data in the reserved variable EQ or the statistical
data in the reserved variable ΣDAT, using the specified x- and y-axis display ranges.
The plot type determines if the data in the reserved variable EQ or the data in the reserved
variable ΣDAT is plotted.
DRAW does not erase PICT before plotting; execute ERASE to do so. DRAW does not draw
axes; execute DRAX to do so.
When DRAW is executed from a program, the graphics display, which shows the resultant plot,
does not persist unless PICTURE, PVIEW (with an empty list argument), or FREEZE is
subsequently executed.
Access:
…µDRAW
Flags:
Simultaneous or Sequential Plot (–28), Curve Filling (–31)
Input/Output: None
See also:
AUTO, AXES, DRAX, ERASE, FREEZE, PICTURE, LABEL, PVIEW
DRAW3DMATRIX
Type:
Command
Description: Draws a 3D plot from the values in a specified matrix.
The number of rows indicates the number of units along the x axis, the number of columns
indicates the number of units along the y axis, and the values in the matrix give the magnitudes
of the plotted points along the z axis. In other words, the coordinates of a plotted point are (r, c,
v) where r is the row number, c the column number and v the value in the corresponding cell of
the matrix.
You can limit the points that are plotted by specifing a minimum value (vmin) and a maximum
value (vmax). Values in the matrix outside this range are not plotted. If all values are included, the
total number of points plotted is r × c.
Once the plot has been drawn, you can rotate it in various ways by pressing the following keys:
™ and š rotate the plot around the x axis (in different directions)
— and ˜ rotate the plot around the y axis (in different directions)
Iand L rotate the plot around the z axis (in different directions)
Access:
…µDRAW3DMATRIX
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]
vmin
vmax
Level 1/Item 1
→
FAST3D
DRAX
Type:
Command
Description: Draw Axes Command: Draws axes in PICT.
Full Command and Function Reference 3-51
The coordinates of the axes intersection are specified by AXES. Axes tick-marks are specified in
PPAR with the ATICK, or AXES command. DRAX does not draw axes labels; execute LABEL
to do so.
Access:
…µDRAX
Input/Output: None
See also:
AXES, DRAW, LABEL
DROITE
CAS:
Return an equation for the line through two given points in a plane.
DROP
Type:
RPL Command
Description: Drop Object Command: Removes the level 1 object from the stack.
Access:
!°STACK DROP
( °is the left-shift of the Nkey).
ISTACK DROP
ƒ in RPN mode executes DROP when no command line is present.
Input/Output:
Level 1
Level 1
→
obj
See also:
CLEAR, DROPN, DROP2
DROP2
Type:
RPL Command
Description: Drop 2 Objects Command: Removes the first two objects from the stack.
Access:
!°STACK LL DROP2
( °is the left-shift of the Nkey).
ISTACK LL DROP2
Input/Output:
Level 2
See also:
obj1
CLEAR, DROP, DROPN
Level 1
obj2
Level 1
→
DROPN
Type:
RPL Command
Description: Drop n Objects Command: Removes the first n + 1 objects from the stack (the first n objects
excluding the integer n itself).
Access:
!°STACK LL DROPN
( °is the left-shift of the Nkey).
ISTACK LL DROPN
Input/Output:
Leveln+1 ... Level 2
See also:
obj1 ... objn
CLEAR, DROP, DROP2
Level 1
n
Level 1
→
DTAG
Type:
Command
Description: Delete Tag Command: DTAG removes all tags (labels) from an object.
The leading colon is not shown for readability when the tagged object is on the stack.
3-52 Full Command and Function Reference
DTAG has no effect on an untagged object.
Access:
!°TYPE LDTAG
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
Level 1/Item 1
→
tag:obj
See also:
obj
LIST→, →TAG
DUP
Type:
RPL Command
Description: Duplicate Object Command: DUP returns a copy of the argument (or the object on level 1).
Access:
!°STACK DUP
( °is the left-shift of the Nkey).
ISTACK DUP
` in RPN mode executes DUP when no command line is present.
Input/Output:
Level 1
Level 1
obj
obj
→
obj
See also:
Level 2
DUPN, DUP2, PICK
DUP2
Type:
RPL Command
Description: Duplicate 2 Objects Command: DUP2 returns copies of the two objects on levels 1 and 2 of the
stack.
Access:
!°STACK LL DUP2
( °is the left-shift of the Nkey).
ISTACK LL DUP2
Input/Output:
L2
L1
obj2
obj1
→
L4
L3
L2
L1
obj2
obj1
obj2
obj1
L = Level
See also:
DUP, DUPN, PICK
DUPDUP
Type:
RPL Command
Description: Duplicates an object twice.
Access:
!°STACK LL DUPDUP
ISTACK LL DUPDUP
Input/Output:
( °is the left-shift of the Nkey).
Level 1
See also:
obj
DUP, NDUPN, DUPN, DUP2
→
Level 3
Level 2
Level 1
obj
obj
obj
DUPN
Type:
RPL Command
Description: Duplicate n Objects Command: Takes an integer n from level 1 of the stack, and returns copies
of the objects on stack levels 2 through n + 1.
Full Command and Function Reference 3-53
Access:
!°STACK LL DUPN
( °is the left-shift of the Nkey).
ISTACK LL DUPN
Input/Output:
Li+1
Li …L3
L2
L1
obj1
obj2 … obji–1
obji
n
→
Li+n
Li+n–1 ... L2
L1
obj1
obj2 ... obji–1
obji
L = Level
See also:
DUP, DUP2, PICK
D→R
Type:
Function
Description: Degrees to Radians Function: Converts a real number representing an angle in degrees to its
equivalent in radians.
This function operates independently of the angle mode.
Access:
!´REAL LL D→R
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
(π/180)x
'symb'
→
'D→R(symb)'
R→ D
e
Type:
Function
Description: e Function: Returns the symbolic constant e or its numerical representation, 2.71828182846.
The number returned for e is the closest approximation to 12-digit accuracy. For exponentiation,
use the expression EXP(x) rather than e^x, since the function EXP uses a special algorithm to
compute the exponential to greater accuracy. Even though the calculator often displays EXP(x) as
e^x, it’s still’ EXP(x)’ intenally.
Access:
~!e
!´LCONSTANTS e
( ´ is the left-shift of the Pkey).
!´LCONSTANTS 2.718281828…
( ´ is the left-shift of the Pkey).
Flags:
Symbolic Constants (–2), Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'e'
→
2.71828182846
EXP, EXPM, i, LN, LNP1, MAXR, MINR, π
EDIT
Type:
Command
Description: Edit Command: Moves specified object to the command line where it can be edited.
Access:
!˜
I!EDIT
Input/Output: None
See also:
EDITB, VISIT
3-54 Full Command and Function Reference
EDITB
Type:
Command
Description: Edit Best Command: Opens the specified object in the most suitable editor. For example, if you
use a matrix as the specified object, the command opens it in Matrix Writer.
Access:
˜
IEDIT
Input/Output: None
See also:
EDIT, VISIT
EGCD
CAS:
From polynomials a and b, returns polynomials u, v, and c, where au+bv=c, c is the GCD of a & b.
EGV
Type:
Command
Description: Eigenvalues and Eigenvectors Command: Computes the eigenvalues and right eigenvectors for a
square matrix.
The resulting vector EVal contains the computed eigenvalues. The columns of matrix EVec
contain the right eigenvectors corresponding to the elements of vector EVal.
The computed results should minimize (within computational precision):
A ⋅ EVec – EVec ⋅ diag ( EVal )
------------------------------------------------------------------------------n⋅ A
where diag (EVal) denotes the n × n diagonal matrix containing the eigenvalues EVal.
Access:
!Ø LEIGENVECTOR EGV
( Ø is the left-shift of the 5key).
!´MATRIX LEGV
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
[[matrix ]]A
See also:
→
Level 2/Item 1
Level 1/Item 2
[[matrix ]]EVec
[vector ]EVal
EGVL
EGVL
Type:
Command
Description: Eigenvalues Command: Computes the eigenvalues of a square matrix.
The resulting vector L contains the computed eigenvalues.
Access:
!Ø LEIGENVECTOR EGVL
( Ø is the left-shift of the 5key).
!´MATRIX LEGVL
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
[[matrix ]]A
See also:
Level 1/Item 1
→
[vector ]EVal
EGV
ELSE
Type:
Command
Description: ELSE Command: Starts false clause in conditional or error-trapping structure.
See the IF and IFERR keyword entries for more information.
Access:
!°BRANCH IF ELSE
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-55
Input/Output: None
See also:
IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE
END
Type:
Command
Description: END Command: Ends conditional, error-trapping, and indefinite loop structures.
See the IF, CASE, IFERR, DO, and WHILE keyword entries for more information.
Access:
!°BRANCH IF/CASE/DO/WHILE END
( °is the left-shift of the Nkey).
Input/Output: None
See also:
IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE
ENDSUB
Type:
Command
Description: Ending Sublist Command: Provides a way to access the total number of sublists contained in the
list used by DOSUBS.
Returns an Undefined Local Name error if executed when DOSUBS is not active.
Access:
!°LIST PROCEDURES ENDSUB
( °is the left-shift of the Nkey).
Input/Output: None
See also:
DOSUBS, NSUB
ENG
Type:
Command
Description: Engineering Mode Command: Sets the number display format to engineering mode, which
displays one to three digits to the left of the fraction mark (decimal point) and an exponent that
is a multiple of three. The total number of significant digits displayed is n + 1.
Engineering mode uses n + 1 significant digits, where 0 ≤ n ≤ 11. (Values for n outside this range
are rounded up or down.) A number is displayed or printed as follows:
(sign) mantissa E (sign) exponent
where the mantissa is of the form (nn)n.(n…) (with up to 12 digits total) and the exponent has
one to three digits.
A number with an exponent of –499 is displayed automatically in scientific mode.
Access:
!&H
FMT ENG
!°L MODES FMT ENG
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
n
Level 1/Item 1
→
See also:
FIX, SCI, STD
EPSX0
CAS:
Replace coefficients in a polynomial, that have an absolute value less than EPS, with 0.
EQNLIB
Type:
Command
Description: Starts the Equation Library application.
Access:
GEQUATION LIBRARY OR G — `
Input/Output: None
See also:
MSOLVR, SOLVEQN
3-56 Full Command and Function Reference
EQW
Type:
Command
Description: Opens Equation Writer, where you can edit an expression.
Puts an object into the Equation Writer.
Access:
…µEQW
(Non-programmable access is via ˜ when there is an algebraic object on the stack. To start a
new equation when not entering a program object, press …³)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
exp1
EDIT, EDITB, VISIT, VISITB
exp2
EQ→
Type:
Command
Description: Equation to Stack Command: Separates an equation into its left and right sides.
If the argument is an expression, it is treated as an equation whose right side equals zero.
Access:
!°TYPE LEQ→
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 2/Item 1
Level 1/Item 2
'symb1=symb2'
→
'symb1'
'symb2'
z
→
z
0
'name'
→
'name'
0
'x_unit'
→
'x_unit'
0
'symb'
0
→
'symb'
ARRY→, DTAG, LIST→, OBJ→, STR→
ERASE
Type:
Command
Description: Erase PICT Command: Erases PICT, leaving a blank PICT of the same dimensions.
Access:
…µ ERASE
Input/Output: None
See also:
DRAW
ERR0
Type:
Command
Description: Clear Last Error Number Command: Clears the last error number so that a subsequent execution
of ERRN returns # 0h, and clears the last error message.
Access:
!°LLERROR ERR0
( °is the left-shift of the Nkey).
Input/Output: None
See also:
DOERR, ERRM, ERRN
ERRM
Type:
Command
Description: Error Message Command: Returns a string containing the error message of the most recent
calculator error.
ERRM returns the string for an error generated by DOERR. If the argument to DOERR was 0,
the string returned by ERRM is ‘Interrupted’.
Access:
!°LL ERROR ERRM
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-57
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
“error message”
DOERR, ERRN, ERR0
ERRN
Type:
Command
Description: Error Number Command: Returns the error number of the most recent calculator error.
If the most recent error was generated by DOERR with a string argument, ERRN returns
#70000h. If the most recent error was generated by DOERR with a binary integer argument,
ERRN returns that binary integer. (If the most recent error was generated by DOERR with a
real number argument, ERRN returns the binary integer conversion of the real number.) The
only exceptions to these rules are 0 DOERR and #0 DOERR, both of which set ERRN to
#31Fh and ERRM to ‘Interrupted’.
Access:
!°LL ERROR ERRN
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
#nerror
See also:
DOERR, ERRM, ERR0
EULER
CAS:
Return the number of integers less than an integer that are co-prime with it. (Euler’s Φ function.)
EVAL
Type:
Command
Description: Evaluate Object Command: Evaluates the object.
The following table describes the effect of the evaluation on different object types.
Object Type
Effect of Evaluation
Local Name
Recalls the contents of the variable.
Global Name
Calls the contents of the variable:
• A name is evaluated.
• A program is evaluated.
• A directory becomes the current directory.
• Other objects are put on the stack.
If no variable exists for a given name, evaluating the
name returns the name to the stack.
Program
List
Enters each object in the program:
• Names are evaluated (unless quoted).
• Commands are evaluated.
• Other objects are put on the stack.
Enters each object in the list:
• Names are evaluated.
• Commands are evaluated
• Programs are evaluated.
• Other objects are put on the stack.
3-58 Full Command and Function Reference
Object Type
Effect of Evaluation
Tagged
If the tag specifies a port, recalls and evaluates the
specified object. Otherwise, puts the untagged object
on the stack.
Algebraic
Enters each object in the algebraic expression:
• Names are evaluated.
• Commands are evaluated.
• Other objects are put on the stack.
Command, Function, XLIB Name
Other Objects
Evaluates the specified object.
Puts the object on the stack.
To evaluate a symbolic argument to a numerical result, evaluate the argument in Numerical
Results mode (flag –3 set) or execute →NUM on that argument.
Access:
N
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
obj
(see above)
See also:
→NUM, SYSEVAL
EXLR
CAS:
Return the left- and right-hand sides of an equation as separate expressions.
EX&LN
CAS:
Display a menu or list of CAS exponential and logarithmic operations.
EXP
Type:
Analytic Function
Description: Exponential Analytic Function: Returns the exponential, or natural antilogarithm, of the
argument; that is, e raised to the given power.
EXP uses extended precision constants and a special algorithm to compute its result to full 12digit precision for all arguments that do not trigger an underflow or overflow error.
EXP provides a more accurate result for the exponential than can be obtained by using e Q.
The difference in accuracy increases as z increases. For example:
z
ez
EXP(z)
3
20.0855369232
20.0855369232
10
22026.4657948
22026.4657949
100
2.68811714182E43
2.68811714191E43
500
1.40359221785E217
1.40359221809E217
1000
1.9707111402E434
1.9707111469E434
For complex arguments: e(x,y) = excosy + iexsiny
Access:
Flags:
!¸
Numerical Results (–3)
( ¸is the left-shift of the Qkey).
Full Command and Function Reference 3-59
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
ez
'symb'
→
'EXP(symb)'
ALOG, EXPM, LN, LOG
EXP2HYP
CAS:
Convert expressions with the exponential function into expressions with hyperbolic functions.
EXP2POW
CAS:
Simplify expressions involving the composition of the exponential and logarithmic functions.
EXPAN
Type:
Command
Description: Expand Products Command: Rewrites an algebraic expression or equation by expanding
products and powers. This command is equivalent to the old HP 48G series command, with
minor modifications (such as adding RISCH for integration).
Access:
…µEXPAN
Flags:
Numerical Results (–3), Exact Mode (-105)
Input/Output:
Level 1/Argument 1
See also:
EXPAND
CAS:
Level 1/Item 1
x
→
x
'symb1'
→
'symb2'
→
(x, y)
(x, y)
COLCT, EXPAND, ISOL, QUAD, SHOW
Expand and simplify an algebraic expression. More in-depth than EXPAN and often provides
better simplification.
EXPANDMOD
CAS:
Expand and simplify algebraic expressions, modulo the current modulus.
EXPFIT
Type:
Command
Description: Exponential Curve Fit Command: Stores EXPFIT as the fifth parameter in the reserved variable
ΣPAR, indicating that subsequent executions of LR are to use the exponential curve fitting
model.
LINFIT is the default specification in ΣPAR.
Access:
…µ EXPFIT
Input/Output: None
See also:
BESTFIT, LR, LINFIT, LOGFIT, PWRFIT
EXPLN
CAS:
Transform the trigonometric terms in an expression to exponential and logarithmic terms.
EXPM
Type:
Analytic Function
Description: Exponential Minus 1 Analytic Function: Returns ex – 1.
3-60 Full Command and Function Reference
For values of x close to zero, EXPM(x) returns a more accurate result than does EXP(x)–1.
(Using EXPM allows both the argument and the result to be near zero, and avoids an
intermediate result near 1. The calculator can express numbers within 10–449 of zero, but within
only 10–11 of 1.)
Access:
!´HYPERBOLIC L EXPM
( ´ is the left-shift of the Pkey).
!Ð EXPM
Flags:
Numerical Results (–3)
Input/Output:
(Ð is the left-shift of the 8key).
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
ex – 1
'symb'
→
'EXPM(symb)'
EXP, LNP1
EYEPT
Type:
Command
Description: Eye Point Command: Specifies the coordinates of the eye point in a perspective plot.
xpoint, ypoint, and zpoint are real numbers that set the x-, y-, and z-coordinates as the eye-point from
which to view a 3D plot's view volume. The y-coordinate must always be 1 unit less than the
view volume's nearest point (ynear of YVOL). These coordinates are stored in the reserved
variable VPAR.
Access:
…µEYEPT
Input/Output:
Level 3/Argument 1
See also:
Level 2/Argument 2
Level 1/Argument 3
xpoint
ypoint
zpoint
NUMX, NUMY, XVOL, XXRNG, YVOL, YYRNG, ZVOL
Level 1/Item 1
→
F0λ
Type:
Function
Description: Black Body Emissive Power Function: Returns the fraction of total black-body emissive power
at temperature xT between wavelengths 0 and ylambda. If units are not specified, ylambda has implied
units of meters and xT has implied units of K.
F0λ returns a dimensionless fraction.
Access:
…µ F0λ
Flags:
Numerical Results (–3)
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
ylambda
xT
→
xpower
ylambda
'symb'
→
'F0λ(ylambda,symb)'
'symb'
xT
→
'F0λ(symb,xT)'
'symb1'
'symb2'
→
'F0λ(symb1,symb2)'
FACT
Type:
Command
Description: Factorial (Gamma) Function: FACT is the same as !.
Full Command and Function Reference 3-61
Access:
…µFACT
Flags:
Numerical Results (–3), Underflow Exception (-20), Overflow Exception (-21)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
n
→
n!
x
→
Γ(x + 1)
'symb'
→
'(symb)!'
See also:
COMB, PERM, !
FACTOR
CAS:
Factorize a polynomial to irreducible polynomials, or an integer to primes.
FACTORMOD
CAS:
Factorize a polynomial modulo the current modulus.
FACTORS
CAS:
For a value or expression, return a list of prime factors and their multiplicities.
FANNING
Type:
Function
Description: Fanning Friction Factor Function: Calculates the Fanning friction factor of certain fluid flows.
FANNING calculates the Fanning friction factor, a correction factor for the frictional effects of
fluid flows having constant temperature, cross-section, velocity, and viscosity (a typical pipe flow,
for example). xx/D is the relative roughness (the ratio of the conduit roughness to its diameter).
yRe is the Reynolds number. The function uses different computation routines for laminar flow
(Re ≤ 2100) and turbulent flow (Re > 2100). xx/D and yRe must be real numbers or unit objects
that reduce to dimensionless numbers, and both numbers must be greater than 0.
Access:
…µFANNING
Flags:
Numerical Results (–3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
xx/D
yRe
→
xfanning
xx/D
'symb'
→
'FANNING(xx/D,symb)'
'symb'
yRe
→
'FANNING(symb,yRe)'
'symb1'
'symb2'
→
'FANNING(symb1,symb2)'
DARCY
FAST3D
Type:
Command
Description: Fast 3D Plot Type Command: Sets the plot type to FAST 3D.
When plot type is set to FAST3D, the DRAW command plots an image graph of a 3-vectorvalued function of two variables. FAST3D requires values in the reserved variables EQ, VPAR,
and PPAR.
VPAR is made up of the following elements:
{ xleft,xright, ynear, yfar,zlow,zhigh,xmin,xmax, ymin, ymax,xeye, yeye,zeye,xstep, ystep }
For plot type FAST3D, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
3-62 Full Command and Function Reference
zlow and zhigh are real numbers that specify the height of the view space.
xmin and xmax are not used.
ymin and ymax are not used.
xeye, yeye, and zeye are are not used.
xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin),(xmax, ymax),indep,res,axes,ptype,depend }
For plot type FAST3D, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command FAST3D places
the name FAST3D in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µFAST3D
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME,
YSLICE
•
•
•
•
•
FCOEF
CAS:
From an array of roots and multiplicities/poles, return a rational polynomial.
FC?
Type:
Command
Description: Flag Clear? Command: Tests whether the system or user flag specified by nflag number is clear, and
returns a corresponding test result: 1 (true) if the flag is clear or 0 (false) if the flag is set.
Access:
!°TEST LLFC?
( °is the left-shift of the Nkey).
!° LMODES FLAG FC?
( °is the left-shift of the Nkey).
!&H FLAG FC?
Input/Output:
Level 1/Argument 1
nflag number
See also:
Level 1/Item 1
→
0/1
CF, FC?C, FS? FS?C, SF
FC?C
Type:
Command
Description: Flag Clear? Clear Command: Tests whether the system or user flag specified by nflag number is clear,
and returns a corresponding test result: 1 (true) if the flag is clear or 0 (false) if the flag is set.
After testing, clears the flag.
Access:
!°TEST LLFC?C
( °is the left-shift of the Nkey).
!° LMODES FLAG FC?C
( °is the left-shift of the Nkey).
!&H FLAG FC?C
Full Command and Function Reference 3-63
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
nflag number
See also:
0/1
CF, FC?, FS? FS?C, SF
FDISTRIB
CAS:
Perform a full distribution of multiplication and division in a single step.
FFT
Type:
Command
Description: Discrete Fourier Transform Command: Computes the one- or two-dimensional discrete Fourier
transform of an array.
If the argument is an N-vector or an N × 1 or 1 × N matrix, FFT computes the one-dimensional
transform. If the argument is an M × N matrix, FFT computes the two-dimensional transform.
M and N must be integral powers of 2.
The one-dimensional discrete Fourier transform of an N-vector X is the N-vector Y where:
Yk =
N–1
∑
n=0
Xn e
2πi kn
– --------------N ,
i =
–1
for k = 0, 1, …, N – 1.
The two dimensional discrete Fourier transform of an M × N matrix X is the M × N matrix Y
where:
Y kl =
M–1 N–1
∑
∑
m=0 n=0
xm n e
2πikm 2πi ln
– ---------------- – -----------------N
M e
,
i =
–1
for k = 0, 1, …, M – 1 and l = 0, 1, …, N – 1.
The discrete Fourier transform and its inverse are defined for any positive sequence length.
However, the calculation can be performed very rapidly when the sequence length is a power of
two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast
Fourier transform (IFFT).
The FFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the
result to 12-digit precision.
Access:
!´L FFT FFT
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
[ array ]1
See also:
Level 1/Item 1
→
[ array ]2
IFFT
FILER
Type:
Command
Description: Opens File Manager.
Access:
!¡
…µFILER
Input/Output: None
FINDALARM
Type:
Command
3-64 Full Command and Function Reference
( ¡ is the left-shift of the Gkey).
Description: Find Alarm Command: Returns the alarm index nindex of the first alarm due after the specified
time.
If the input is a real number date, FINDALARM returns the index of the first alarm due after
12:00 AM on that date. If the input is a list { date time }, it returns the index of the first alarm due
after that date and time. If the input is the real number 0, FINDALARM returns the first past-due
alarm. For any of the three arguments, FINDALARM returns 0 if no alarm is found.
( Ó is the right-shift of the 9 key).
Access:
…ÓTOOLS ALRM FINDALARM
…&9 ALRM FINDALARM
!°LL TIME ALRM FINDALARM ( °is the left-shift of the Nkey).
Flags:
Date Format (-42)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
date
→
nindex
{ date time }
→
nindex
→
nindex
0
DELALARM, RCLALARM, STOALARM
FINISH
Type:
Command
Description: Finish Server Mode Command: Terminates Kermit Server mode in a device connected to an
hp49g+/hp48gII.
FINISH is used by a local Kermit device to tell a server Kermit (connected via the serial port) to
exit Server mode.
Access:
…µFINISH
Flags:
I/O Device flag (-33), I/O Messages (-39)
Input/Output: None
See also:
BAUD, CKSM, KGET, PARITY, PKT, RECN, RECV, SEND, SERVER
FIX
Type:
Command
Description: Fix Mode Command: Sets the number display format to fix mode, which rounds the display to n
decimal places.
Fix mode shows n digits to the right of the fraction mark (decimal point), where 0 ≤ n ≤ 11. (Values
for n outside this range are rounded to the nearest integer.) A number is displayed or printed as (sign)
mantissa, where the mantissa can be of any form. However, the calculator automatically displays a
number in scientific mode if either of the following is true:
• The number of digits to be displayed exceeds 12.
• A nonzero value rounded to n decimal places otherwise would be displayed as zero.
Access:
! & HFMT FIX
!°LMODES FMT FIX
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
n
See also:
Level 1/Item 1
→
SCI, STD
FLASHEVAL
Type:
Command
Full Command and Function Reference 3-65
Description: Evaluate Flash Function Command: Evaluates unnamed Flash functions.
WARNING: Use extreme care when executing this function. Using FLASHEVAL with
random addresses will almost always cause a memory loss. Do not use this function
unless you know what you are doing.
#nfunction is of the form ffffbbbh, where bbb is the bank ID, and ffff is the function number.
Access:
…µFLASHEVAL
Input/Output:
Level 1/Argument 1
See also:
#nfunction
EVAL, LIBEVAL, SYSEVAL
Level 1/Item 1
→
FLOOR
Type:
Function
Description: Floor Function: Returns the greatest integer that is less than or equal to the argument.
Access:
!´REAL LL FLOOR
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
n
x_unit
→
n_unit
'symb'
→
'FLOOR(symb)'
CEIL, IP, RND, TRNC
FONT6
Type:
Function
Description: Font Function: Returns the system FONT6 object. You use this in conjunction with the
→FONT command to set the system font to type 6.
Access:
…µ FONT6
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Font object
FONT7, FONT8, →FONT, FONT→
FONT7
Type:
Function
Description: Font Function: Returns the system FONT7 object. You use this in conjunction with the
→FONT command to set the system font to type 7.
Access:
…µFONT7
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
FONT6, FONT8, →FONT, FONT→
FONT8
Type:
Function
3-66 Full Command and Function Reference
Font object
Description: Font Function: Returns the system FONT8 object. You use this in conjunction with the
→FONT command to set the system font to type 8.
Access:
…µ FONT8
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Font object
FONT6, FONT7, →FONT, FONT→
FONT→
Type:
Function
Description: Returns the current system font.
Access:
…µ FONT→
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Font object
FONT6, FONT7, FONT8, →FONT
→FONT
Type:
Function
Description: Set font Function: Sets the system font. You use this in conjunction with one of the three font
commands to set the system font. Valid input is any font object (TYPE 30) of size 6, 7, or 8.
Access:
…µ →FONT
Input/Output:
Level 1/Argument 1
See also:
Font object
FONT6, FONT7, FONT8, FONT→
Level 1/Item 1
→
FOR
Type:
Command Operation
Description: FOR Definite Loop Structure Command: Starts FOR … NEXT and FOR … STEP definite
loop structures.
Definite loop structures execute a command or sequence of commands a specified number of
times.
• A FOR … NEXT loop executes a program segment a specified number of times using a local
variable as the loop counter. You can use this variable within the loop. The RPL syntax is this:
xstart xfinish FOR counter loop-clause NEXT
The algebraic syntax is this:
FOR (counter,xstart,xfinish)loop-clause NEXT
FOR takes xstart and xfinish as the beginning and ending values for the loop counter, then
creates the local variable counter as a loop counter. Then, the loop clause is executed; counter
can be referenced or have its value changed within the loop clause. NEXT increments
counter by one, and then tests whether counter is less than or equal to xfinish. If so, the loop
clause is repeated (with the new value of counter).
When the loop is exited, counter is purged.
• FOR … STEP works just like FOR … NEXT, except that it lets you specify an increment
value other than 1. The syntax RPL is:
xstart xfinish FOR counter loop-clause xincrement STEP
The algebraic syntax is:
Full Command and Function Reference 3-67
FOR( counter xstart xfinish)loop-clause, STEP (xincrement)
FOR takes xstart and xfinish as the beginning and ending values for the loop counter, then
creates the local variable counter as a loop counter. Next, the loop clause is executed; counter
can be referenced or have its value changed within the loop clause. STEP takes xincrement and
increments counter by that value. If the argument of STEP is an algebraic expression or a
name, it is automatically evaluated to a number.
The increment value can be positive or negative. If the increment is positive, the loop is
executed again when counter is less than or equal to xfinish. If the increment is negative, the
loop is executed when counter is greater than or equal to xfinish.
When the loop is exited, counter is purged.
Access:
!°BRANCH FOR
( °is the left-shift of the Nkey).
Input/Output:
Level 2/
Level 1
FOR xstart
xfinish
See also:
→
→
NEXT
Note:
Level 1/Item 1
FOR xstart
xfinish
→
STEP
xincrement
→
→
STEP
'symbincrement'
It should be noted that FOR inputs may also be integers (object type 28) and binary integers
(type 10). FOR actually runs fastest on binary integers, runs “normally” on reals and slightly
slower on integers.
NEXT, START, STEP
FOURIER
CAS:
Return the nth coefficient of a complex Fourier series expansion.
FP
Type:
Function
Description: Fractional Part Function: Returns the fractional part of the argument.
The result has the same sign as the argument.
Access:
!´REAL LFP
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
y
x_unit
→
y_unit
'symb'
→
'FP(symb)'
IP
FREE
Type:
Command
Description: This command, a carry-over from the HP 48GX for handling plug-in RAM cards, should not be
used.
FREEZE
Type:
Command
Description: Freeze Display Command: Freezes the part of the display specified by ndisplay area, so that it is not
updated until a key is pressed.
3-68 Full Command and Function Reference
Normally, the stack display is updated as soon as the calculator is ready for data input. For
example, when HALT stops a running program, or when a program ends, any displayed
messages are cleared. The FREEZE command “freezes” a part or all of the display so that it is
not updated until a key is pressed. This allows, for example, a prompting message to persist after
a program halts to await data input.
ndisplay area is the sum of the value codes for the areas to be frozen:
Display Area
Value Code
Status area
1
History/Stack/Command-line area
2
Menu area
4
So, for example, 2 FREEZE freezes the history/stack/command-line area, 3 FREEZE freezes
the status area and the history/stack/command-line area, and 7 FREEZE freezes all three areas.
Values of ndisplay area ≥ 7 or ≤ 0 freeze the entire display (are equivalent to value 7). To freeze the
graphics display, you must freeze the status and stack/command-line areas (by entering 3), or the
entire display (by entering 7).
Access:
!°LOUT FREEZE
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
ndisplayarea
Level 1/Item 1
→
See also:
CLLCD, DISP, HALT
FROOTS
CAS:
For a rational polynomial, return its roots and poles, with their corresponding multiplicities.
FS?
Type:
Command
Description: Flag Set? Command: Tests whether the system or user flag specified by nflag number is set, and
returns a corresponding test result: 1 (true) if the flag is set or 0 (false) if the flag is clear.
Access:
!°TEST LLFS?
( °is the left-shift of the Nkey).
!° LMODES FLAG FS?
( °is the left-shift of the Nkey).
!& H FLAG FS?
Input/Output:
Level 1/Argument 1
nflag number
See also:
Level 1/Item 1
→
0/1
CF, FC?, FC?C, FS?C, SF
FS?C
Type:
Command
Description: Flag Set? Clear Command: Tests whether the system or user flag specified by nflag number is set, and
returns a corresponding test result: 1 (true) if the flag is set or 0 (false) if the flag is clear. After
testing, clears the flag.
Access:
!°TEST LLFS?C
( °is the left-shift of the Nkey).
!° LMODES FLAG FS?C
( °is the left-shift of the Nkey).
!& H FLAG FS?C
Input/Output:
Level 1/Argument 1
nflag number
Level 1/Item 1
→
0/1
Full Command and Function Reference 3-69
See also:
CF, FC?, FC?C, FS?, SF
FUNCTION
Type:
Command
Description: Function Plot Type Command: Sets the plot type to FUNCTION.
When the plot type is FUNCTION, the DRAW command plots the current equation as a realvalued function of one real variable. The current equation is specified in the reserved variable
EQ. The plotting parameters are specified in the reserved variable PPAR, which has the form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type FUNCTION, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a name specifying the independent variable, or a list containing such a name and two
numbers specifying the minimum and maximum values for the independent variable (the
plotting range). The default value of indep is X.
• res is a real number specifying the interval (in user-unit coordinates) between plotted values of
the independent variable, or a binary integer specifying the interval in pixels. The default value
is 0, which specifies an interval of 1 pixel.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command FUNCTION
places the name FUNCTION in PPAR.
• depend is a name specifying a label for the vertical axis. The default value is Y.
The current equation is plotted as a function of the variable specified in indep. The minimum and
maximum values of the independent variable (the plotting range) can be specified in indep;
otherwise, the values in (xmin, ymin) and (xmax, ymax)(the display range) are used. Lines are drawn
between plotted points unless flag –31 is set.
If EQ contains an expression or program, the expression or program is evaluated in Numerical
Results mode for each value of the independent variable to give the values of the dependent
variable. If EQ contains an equation, the plotting action depends on the form of the equation, as
shown in the following table.
Form of Current Equation
Plotting Action
expr = expr
Each expression is plotted separately. The intersection of
the two graphs shows where the expressions are equal.
name = expr
Only the expression is plotted.
indep = constant
A vertical line is plotted.
If flag –28 is set, all equations are plotted simultaneously.
If the independent variable in the current equation represents a unit object, you must specify the
units by storing a unit object in the corresponding variable in the current directory. For example,
if the current equation is X+3_m, and you want X to represent some number of inches, you
would store 1_in (the number part of the unit object is ignored) in X. For each plotted point, the
numerical value of the independent variable is combined with the specified unit (inches in this
3-70 Full Command and Function Reference
example) before the current equation is evaluated. If the result is a unit object, only the number
part is plotted.
Access:
…µFUNCTION
Flags:
Simultaneous Plotting (-28), Curve Filling (-31)
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FAST3D, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME,
YSLICE
FXND
CAS:
Split a fractional object into its numerator and denominator.
GAMMA
Type:
Function
Description: Evaluate the Γ function at the given point. For a positive integer x, Γ(x) is equal to (x +1)!
GAMMA differs from the FACT and ! functions because it allows complex arguments. The Γ
function is defined by
Γ( x ) =
+∞ – t
∫0
e ⋅t
x–1
dt
.
Access:
Input:
Output:
Flags:
!´LSPECIAL
A real or complex number, x.
Γ(x). If the input x is an integer greater than 100, returns the symbolic expression GAMMA(x).
If the Underflow Exception (–20) or Overflow Exception (–21) flags are set then underflow or
overflow conditions give errors, otherwise they give zero or the maximum real number the calculator
can express.
Complex mode must be set (flag –103 set) if x is complex.
See also:
FACT, PSI, Psi, !
GAUSS
CAS:
Return the diagonal representation of a quadratic form.
GBASIS
CAS:
GCD
CAS:
Return a set of polynomials that are a Grœbner basis G of the ideal I of an input set of
polynomials.
Return the greatest common divisor of two objects.
GCDMOD
CAS:
Find the greatest common divisor of two polynomials modulo the current modulus.
GET
Type:
Command
Description: Get Element Command: Returns from the argument 1/level 2 array or list (or named array or
list) the real or complex number zget or object objget whose position is specified in argument
2/level 1. For matrices, nposition is incremented in row order.
Access:
!°LIST ELEMENTS GET
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-71
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
[[ matrix ]]
nposition
→
zget
[[ matrix ]]
{ nrow, mcolumn }
→
zget
'namematrix'
nposition
→
zget
'namematrix'
{ nrow, mcolumn }
→
zget
[ vector ]
nposition
→
zget
[ vector ]
{nposition }
→
zget
'namevector'
nposition
→
zget
'namevector'
{nposition }
→
zget
{ list }
nposition
→
objget
{ list }
{nposition }
→
objget
'namelist'
nposition
→
objget
{nposition }
→
objget
'namelist'
GETI, PUT, PUTI
Level 1/Item 1
GETI
Type:
Command
Description: Get and Increment Index Command: Returns from the argument 1/level 2 array or list (or
named array or list) the real or complex number zget or object objget whose position is specified in
argument 2/level 1, along with the first (level 2) argument and the next position in that
argument. For matrices, the position is incremented in row order.
Access:
!°LIST ELEMENTS GETI
( °is the left-shift of the Nkey).
Flags:
Index Wrap Indicator (-64)
Input/Output:
L2/A1
L1/A2
L3/I1
L2/I2
L1/I3
[[ matrix ]]
nposition1
→
[[ matrix ]]
nposition2
zget
[[ matrix ]]
{ nrow, mcolumn }1
→
[[ matrix ]]
{ nrow, mcolumn }2
zget
'namematrix'
nposition1
→
'namematrix'
nposition2
zget
'namematrix'
{ nrow, mcolumn }1
→
'namematrix'
{ nrow, mcolumn }2
zget
[ vector ]
nposition
→
[ vector ]
nposition2
zget
[ vector ]
{nposition1 }
→
[ vector ]
{nposition2 }
zget
'namevector'
nposition1
→
'namevector
nposition2
zget
'namevector'
{nposition1 }
→
'namevector
{nposition2 }
zget
{ list }
nposition1
→
{ list }
nposition2
objget
{ list }
{nposition1 }
→
{ list }
{nposition2 }
objget
'namelist'
nposition1
→
'namelist'
nposition2
objget
'namelist'
{nposition1 }
→
'namelist'
{nposition2 }
objget
L = Level; A = Argument; I = Item
See also:
GET, PUT, PUTI
3-72 Full Command and Function Reference
GOR
Type:
Command
Description: Graphics OR Command: Superimposes grob1 onto grobtarget or PICT, with the upper left corner
pixel of grob1 positioned at the specified coordinate in grobtarget or PICT.
GOR uses a logical OR to determine the state (on or off) of each pixel in the overlapping
portion of the argument graphics object.
If the first argument (stack level 3) is any graphics object other than PICT, then grobresult is
returned to the stack. If the first argument (level 3) is PICT, no result is returned to the stack.
Any portion of grob1 that extends past grobtarget or PICT is truncated.
Access:
!°L GROB GOR
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
grobtarget
{ #n #m }
grob1
→
grobresult
grobtarget
(x, y)
grob1
→
grobresult
PICT
{ #n #m }
grob1
→
(x, y)
grob1
→
PICT
GXOR, REPL, SUB
Level 1/Item 1
GRAD
Type:
Command
Description: Grads Mode Command: Sets Grads angle mode.
GRAD clears flag –17 and sets flag –18, and displays the GRD annunciator.
In Grads angle mode, real-number arguments that represent angles are interpreted as grads, and
real-number results that represent angles are expressed in grads.
Access:
!&HANGLE GRAD
…µ GRAD
Input/Output: None
See also:
DEG, RAD
GRAMSCHMIDT
CAS:
Find an orthonormal base of a vector space with respect to a given scalar product.
GREDUCE
CAS:
Reduce a polynomial with respect to a Grœbner basis.
GRIDMAP
Type:
Command
Description: GRIDMAP Plot Type Command: Sets the plot type to GRIDMAP.
When plot type is set GRIDMAP, the DRAW command plots a mapping grid representation of
a 2-vector-valued function of two variables. GRIDMAP requires values in the reserved variables
EQ, VPAR, and PPAR.
VPAR has the following form:
{xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep}
For plot type GRIDMAP, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
• zlow and zhigh are real numbers that specify the height of the view space.
Full Command and Function Reference 3-73
• xmin and xmax are real numbers that specify the input region's width. The default value is (–
1,1).
• ymin and ymax are real numbers that specify the input region's depth. The default value is (–1,1).
• xeye, yeye, and zeye are real numbers that specify the point in space from which you view the
graph.
• xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted. These can be used instead of (or in combination with) RES.
The plotting parameters are specified in the reserved variable PPAR, which has the following form:
{ (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend }
For plot type GRIDMAP, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is a real number specifying the interval (in user-unit coordinates) between plotted values of
the independent variable, or a binary integer specifying the interval in pixels. The default value
is 0, which specifies an interval of 1 pixel.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command GRIDMAP places
the command name GRIDMAP in PPAR.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µ GRIDMAP
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, HISTOGRAM, PARAMETRIC, PARSURFACE,
PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
→GROB
Type:
Command
Description: Stack to Graphics Object Command: Creates a graphics object from a specified object, where the
argument nchar size specifies the character size of the object.
nchar size can be 0, 1 (small), 2 (medium), or 3 (large). nchar size = 0 is the same as nchar size = 3, except
for unit objects and algebraic objects, where 0 specifies the Equation Writer application picture.
Access:
…µ→GROB
!°LGROB →GROB
Input/Output:
See also:
( °is the left-shift of the Nkey).
Level 2/Argument 1
Level 1/Argument 2
obj
ncharsize
Level 1/Item 1
→
grob
→LCD, LCD→
GROB
Type:
Command
Description: Enters GROB on the command line to help with the manual entry of a graphic object.
Access:
…µGROB
GROBADD
Type:
Command
Description: Combines two graphic objects by appending the second argument onto the bottom of the first.
Access:
PGRAPH GROBADD
!ÖGRAPH GROBADD
( Ö is the left-shift of the 4key).
3-74 Full Command and Function Reference
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
GROB1
GROB2
Level 1/Item 1
→
GROB3
GXOR
Type:
Command
Description: Graphics Exclusive OR Command: Superimposes grob1 onto grobtarget or PICT, with the upper left
corner pixel of grob1 positioned at the specified coordinate in grobtarget or PICT.
GXOR is used for creating cursors, for example, to make the cursor image appear dark on a light
background and light on a dark background. Executing GXOR again with the same image
restores the original picture.
GXOR uses a logical exclusive OR to determine the state of the pixels (on or off) in the
overlapping portion of the argument graphics objects.
Any portion of grob1 that extends past grobtarget or PICT is truncated.
If the first (level 3) argument (the target graphics object) is any graphics object other than PICT,
then grobresult is returned to the stack. If the first (level 3) argument is PICT, no result is returned
to the stack.
Access:
!°L GROB GXOR
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
grobtarget
{ #n, #m }
grob1
→
grobresult
grobtarget
(x, y)
grob1
→
grobresult
PICT
{ #n, #m }
grob1
→
PICT
(x, y)
grob1
→
GOR, REPL, SUB
HADAMARD
CAS:
Perform an element by element multiplication of two matrices (Hadamard product).
HALFTAN
CAS:
Transform an expression by replacing sin(x), cos(x) and tan(x) subexpressions with tan(x/2).
HALT
Type:
Command
Description: Halt Program Command: Halts program execution.
Program execution is halted at the location of the HALT command in the program. The HLT
annunciator is turned on. Program execution is resumed by executing CONT (that is, by pressing
!æ). Executing KILL cancels all halted programs.
Access:
!°LL RUN & DEBUG HALT ( °is the left-shift of the Nkey).
Input/Output: None
See also:
CONT, KILL
HEAD
Type:
Command
Description: First Listed Element Command: Returns the first element of a list or string.
Full Command and Function Reference 3-75
Access:
!°LCHARS LHEAD
( °is the left-shift of the Nkey).
!°LIST ELEMEN LHEAD
( °is the left-shift of the Nkey).
…± LHEAD
Input/Output:
(± is the right-shift of the Nkey).
Level 1/Argument 1
See also:
Level 1/Item 1
{ obj1, ... ,objn }
→
obj1
“string”
→
“element1”
TAIL
HEADER→
Type:
Command
Description: Header size: Returns the current size of the header in lines.
Access:
…µHEADER→
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Header size
→HEADER
→HEADER
Type:
Command
Description: Header size: Sets the current size of the header in lines: to 0, 1, or 2 lines.
Access:
…µ→HEADER
Input/Output:
Level 1/Argument 1
Header size
Level 1/Item 1
→
See also:
HEADER→
HELP
CAS:
Display CAS operations and help information for them.
HERMITE
CAS:
Return the nth Hermite polynomial.
HESS
CAS:
Return the Hessian matrix and the gradient of an expression with respect to specified variables.
HEX
Type:
Command
Description: Hexadecimal Mode Command: Selects hexadecimal base for binary integer operations. (The
default base is decimal.)
Binary integers require the prefix #. Binary integers entered and returned in hexadecimal base
automatically show the suffix h. If the current base is not hexadecimal, then you can enter a
hexadecimal number by ending it with h. It will be displayed in the current base when it is
entered.
The current base does not affect the internal representation of binary integers as unsigned binary
numbers.
3-76 Full Command and Function Reference
Access:
!´BASE HEX
( ´ is the left-shift of the Pkey).
!Ú BASE HEX
( Ú is the left-shift of the 6key).
Flags:
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output: None
See also:
BIN, DEC, OCT, RCWS, STWS
HILBERT
CAS:
Return a square Hilbert matrix of specified order.
HISTOGRAM
Type:
Command
Description: Histogram Plot Type Command: Sets the plot type to HISTOGRAM.
When the plot type is HISTOGRAM, the DRAW command creates a histogram using data from
one column of the current statistics matrix (reserved variable ΣDAT). The column is specified by
the first parameter in the reserved variable ΣPAR (using the XCOL command). The plotting
parameters are specified in the reserved variable PPAR, which has the form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type HISTOGRAM, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is either a name specifying a label for the horizontal axis, or a list containing such a name
and two numbers that specify the minimum and maximum values of the data to be plotted.
The default value of indep is X.
• res is a real number specifying the bin size, in user-unit coordinates, or a binary integer
specifying the bin size in pixels. The default value is 0, which specifies the bin size to be 1/13
of the difference between the specified minimum and maximum values of the data.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command HISTOGRAM
places the command name HISTOGRAM in PPAR.
• depend is a name specifying a label for the vertical axis. The default value is Y.
The frequency of the data is plotted as bars, where each bar represents a collection of data
points. The base of each bar spans the values of the data points, and the height indicates the
number of data points. The width of each bar is specified by res. The overall maximum and
minimum values for the data can be specified by indep; otherwise, the values in (xmin, ymin) and
(xmax, ymax) are used.
Access:
…µ HISTOGRAM
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, PARAMETRIC, PARSURFACE,
PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
HISTPLOT
Type:
Command
Full Command and Function Reference 3-77
Description: Draw Histogram Plot Command: Plots a frequency histogram of the specified column in the
current statistics matrix (reserved variable ΣDAT).
The data column to be plotted is specified by XCOL and is stored as the first parameter in the
reserved variable ΣPAR. If no data column is specified, column 1 is selected by default. The yaxis is autoscaled and the plot type is set to HISTOGRAM.
HISTPLOT plots relative frequencies, using 13 bins as the default number of partitions. The RES
command lets you specify a different number of bins by specifying the bin width. To plot a
frequency histogram with numerical frequencies, store the frequencies in ΣDAT and execute
BINS and then BARPLOT.
When HISTPLOT is executed from a program, the graphics display, which shows the resultant
plot, does not persist unless PICTURE, PVIEW (with an empty list argument), or FREEZE is
subsequently executed.
Access:
…µ HISTPLOT
Input/Output: None
See also:
BARPLOT, BINS, FREEZE, PICTURE, PVIEW, RES, SCATRPLOT, XCOL
HMS–
Type:
Command
Description: Hours-Minutes-Seconds Minus Command: Returns the difference of two real numbers, where
the arguments and the result are interpreted in hours-minutes-seconds format.
The format for HMS (a time or an angle) is H.MMSSs, where:
• H is zero or more digits representing the integer part of the number (hours or degrees).
• MM are two digits representing the number of minutes.
• SS are two digits representing the number of seconds.
• s is zero or more digits (as many as allowed by the current display mode) representing the
decimal fractional part of seconds.
Access:
…ÓTools LHMS–
( Ó is the right-shift of the 9 key).
…& 9LHMS–
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
HMS1
HMS→, →HMS, HMS+
HMS2
Level 1/Item 1
→
HMS1 – HMS2
HMS+
Type:
Command
Description: Hours-Minutes-Seconds Plus Command: Returns the sum of two real numbers, where the
arguments and the result are interpreted in hours-minutes-seconds format.
The format for HMS (a time or an angle) is H.MMSSs, where:
• H is zero or more digits representing the integer part of the number (hours or degrees).
• MM are two digits representing the number of minutes.
• SS are two digits representing the number of seconds.
• s is zero or more digits (as many as allowed by the current display mode) representing the
decimal fractional part of seconds.
Access:
…ÓTools LHMS+
( Ó is the right-shift of the 9 key).
…& 9LHMS+
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
HMS1
HMS2
3-78 Full Command and Function Reference
Level 1/Item 1
→
HMS1 + HMS2
See also:
HMS→, →HMS, HMS–
HMS→
Type:
Command
Description: Hours-Minutes-Seconds to Decimal Command: Converts a real number in hours-minutesseconds format to its decimal form (hours or degrees with a decimal fraction).
The format for HMS (a time or an angle) is H.MMSSs, where:
• H is zero or more digits representing the integer part of the number (hours or degrees).
• MM are two digits representing the number of minutes.
• SS are two digits representing the number of seconds.
• s is zero or more digits (as many as allowed by the current display mode) representing the
decimal fractional part of seconds.
Access:
…ÓTools L HMS→
( Ó is the right-shift of the 9 key).
…&9L HMS→
Input/Output:
Level 1/Argument 1
HMS
See also:
Level 1/Item 1
→
x
→HMS, HMS+, HMS–
→HMS
Type:
Command
Description: Decimal to Hours-Minutes-Seconds Command: Converts a real number representing hours or
degrees with a decimal fraction to hours-minutes-seconds format.
The format for HMS (a time or an angle) is H.MMSSs, where:
• H is zero or more digits representing the integer part of the number.
• MM are two digits representing the number of minutes.
• SS are two digits representing the number of seconds.
• s is zero or more digits (as many as allowed by the current display mode) representing the
decimal fractional part of seconds.
Access:
…ÓTools L→HMS
( Ó is the right-shift of the 9 key).
…&9L→HMS
Input/Output:
Level 1/Argument 1
x
See also:
Level 1/Item 1
→
HMS
HMS→, HMS+, HMS–
HOME
Type:
Command
Description: HOME Directory Command: Makes the HOME directory the current directory.
Access:
…µ HOME
!& J
Input/Output: None
See also:
CRDIR, PATH, PGDIR, UPDIR
HORNER
CAS:
Execute a Horner scheme;. for polynomial P, and number r, return P/(x–r), r and P(r).
Full Command and Function Reference 3-79
i
Type:
Function
Description: i Function: Returns the symbolic constant i or its numerical representation, (0, 1).
Access:
!¥
(¥is the left-shift of the Ikey).
Flags:
Symbolic Constants (–2), Numerical Results (–3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
'i'
→
(0,1)
See also:
e, MAXR, MINR, π
IABCUV
CAS:
Return a solution in integers u and v of au + bv = c, where a, b, and c are integers.
IBASIS
CAS:
Determine the basis of the intersection between two vector spaces.
IBERNOULLI
CAS:
Return the nth Bernoulli number for a given integer n.
IBP
CAS:
Integration by parts of a product of two functions, given the antiderivative of one function.
ICHINREM
CAS:
Solve a system of two congruences in integers using the Chinese Remainder theorem.
IDN
Type:
Command
Description: Identity Matrix Command: Returns an identity matrix; that is, a square matrix with its diagonal
elements equal to 1 and its off-diagonal elements equal to 0.
The result is either a new square matrix, or an existing square matrix with its elements replaced
by the elements of the identity matrix, according to the argument.
• Creating a new matrix: If the argument is a real number n, a new real identity matrix is
returned, with its number of rows and number of columns equal to n.
• Replacing the elements of an existing matrix: If the argument is a square matrix, an identity
matrix of the same dimensions is returned. If the original matrix is complex, the resulting
identity matrix will also be complex, with diagonal values (1,0).
• If the argument is a name, the name must identify a variable containing a square matrix. In
this case, the elements of the matrix are replaced by those of the identity matrix (complex if
the original matrix is complex).
Access:
!Ø CREATE IDN
( Ø is the left-shift of the 5key).
!´MATRIX MAKE IDN
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
n
[[ matrix ]]
'name'
3-80 Full Command and Function Reference
Level 1/Item 1
→
→
→
[[ R-matrixidentity ]]
[[ matrixidentity ]]
[[ matrixidentity ]]
See also:
CON
IDIV2
CAS:
For two integers, a and b, return the integer part of a/b, and the remainder, r.
IEGCD
CAS:
Given integers x and y, return integers, a, b, and c, where ax+by=c and, c is the GCD of x and y.
IF
Type:
Command Operation
Description: IF Conditional Structure Command: Starts IF … THEN … END and IF … THEN … ELSE
… END conditional structures.
Conditional structures, used in combination with program tests, enable a program to make
decisions.
• IF … THEN … END executes a sequence of commands only if a test returns a nonzero
(true) result. The syntax is:
IF test-clause THEN true-clause END
IF begins the test clause, which must return a test result to the stack. THEN removes the test
result from the stack. If the value is nonzero, the true clause is executed. Otherwise, program
execution resumes following END.
• IF … THEN … ELSE … END executes one sequence of commands if a test returns a true
(nonzero) result, or another sequence of commands if that test returns a false (zero) result.
The syntax is:
IF test-clause THEN true-clause ELSE false-clause END
IF begins the test clause, which must return a test result to the stack. THEN removes the test
result from the stack. If the value is nonzero, the true clause is executed. Otherwise, the false
clause is executed. After the appropriate clause is executed, execution resumes following
END.
In RPL mode, the test clause can be a command sequence (for example, A B ≤) or an algebraic
(for example, ‘Α ≤ Β)’. If the test clause is an algebraic, it is automatically evaluated to a number
(→NUM or EVAL isn't necessary).
Access:
!°BRANCH IF
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
Level 1/Item 1
→
IF
THEN
T/F
→
T/F
→
END
IF
THEN
ELSE
See also:
END
CASE, ELSE, END, IFERR, THEN
→
→
IFERR
Type:
Command
Description: If Error Conditional Structure Command: Starts IFERR … THEN … END and IFERR …
THEN … ELSE … END error trapping structures.
Full Command and Function Reference 3-81
Error trapping structures enable program execution to continue after a “trapped” error occurs.
• IFERR … THEN … END executes a sequence of commands if an error occurs. The syntax
of IFERR … THEN … END is:
IFERR trap-clause THEN error-clause END
If an error occurs during execution of the trap clause:
1 The error is ignored.
2 The remainder of the trap clause is discarded.
3 The key buffer is cleared.
4 If any or all of the display is “frozen” (by FREEZE), that state is cancelled.
5 If Last Arguments is enabled, the arguments to the command that caused the error are
returned to the stack.
6 Program execution jumps to the error clause.
The commands in the error clause are executed only if an error is generated during execution
of the trap clause.
• IFERR … THEN … ELSE … END executes one sequence of commands if an error occurs
or another sequence of commands if an error does not occur. The syntax of IFERR …
THEN … ELSE … END is:
IFERR trap-clause THEN error-clause ELSE normal-clause END
If an error occurs during execution of the trap clause, the same six events listed above occur.
If no error occurs, execution jumps to the normal clause at the completion of the trap clause.
Access:
!°LLERROR [IFERR] IFERR
Flags:
Last Arguments (-55)
Input/Output: None
See also:
CASE, ELSE, END, IF, THEN
( °is the left-shift of the Nkey).
IFFT
Type:
Command
Description: Inverse Discrete Fourier Transform Command: Computes the one- or two-dimensional inverse
discrete Fourier transform of an array.
If the argument is an N-vector or an N × 1 or 1 × N matrix, IFFT computes the onedimensional inverse transform. If the argument is an M × N matrix, IFFT computes the twodimensional inverse transform. M and N must be integral powers of 2.
The one-dimensional inverse discrete Fourier transform of an N-vector Y is the N-vector X
where:
1
X n = ---N
N–1
∑
k=0
Yk e
2πikn
--------------N
,i =
–1
for n = 0, 1, …, N – 1.
The two-dimensional inverse discrete Fourier transform of an M × N matrix Y is the M × N
matrix X where:
M – 1N – 1
2πi km 2πi ln
---------------- -----------------1
X mn = --------- ∑ ∑ Y kl e M e N , i =
MN k = 0 l = 0
–1
for m = 0, 1, …, M – 1 and n = 0, 1, …, N – 1.
The discrete Fourier transform and its inverse are defined for any positive sequence length.
However, the calculation can be performed very rapidly when the sequence length is a power of
3-82 Full Command and Function Reference
two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast
Fourier transform (IFFT).
The IFFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the
result to 12-digit precision.
Access:
!´LFFT IFFT
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
Level 1/Item 1
→
[ array ]1
See also:
[ array ]2
FFT
IFT
Type:
Command
Description: IF-THEN Command: Executes obj if T/F is nonzero. Discards obj if T/F is zero.
IFT lets you execute in stack syntax the decision-making process of the IF … THEN … END
conditional structure. The “true clause” is obj in argument 2 (level 1).
Access:
!°BRANCH IFT
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
T/F
obj
Level 1/Item 1
→
It depends!
IFTE
IFTE
Type:
Function
Description: IF-THEN-ELSE Function: Executes the obj in argument 2 or level 2 if T/F is nonzero. Executes
the obj in argument 3 or level 1 if T/F is zero.
IFTE lets you execute in stack syntax the decision-making process of the IF … THEN … ELSE
… END conditional structure. The “true clause” is objtrue in argument 2 or level 2. The “false
clause” is objfalse in argument 3 or level 1.
IFTE is also allowed in algebraic expressions, with the following syntax:
IFTE(test,true-clause,false-clause)
When an algebraic containing IFTE is evaluated, its first argument test is evaluated to a test result.
If it returns a nonzero real number, true-clause is evaluated. If it returns zero, false-clause is
evaluated.
Access:
!°BRANCH LIFTE
Input/Output:
( °is the left-shift of the Nkey).
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
T/F
objtrue
objfalse
Level 1/Item 1
→
It depends!
See also:
IFT
ILAP
CAS:
Return the inverse Laplace transform of an expression that evaluates to a rational fraction.
IM
Type:
Function
Description: Imaginary Part Function: Returns the imaginary part of its complex argument.
Full Command and Function Reference 3-83
If the argument is an array, IM returns a real array, the elements of which are equal to the
imaginary parts of the corresponding elements of the argument array. If the argument array is
real, all of the elements of the result array are zero.
Access:
…ß IM
(ßis the right-shift of the 1key).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
x
→
0
(x, y)
→
y
[ R-array ]
→
[ R-array ]
[ C-array ]
→
[ R-array ]
'symb'
→
'IM(symb)'
See also:
C→R, RE, R→C
IMAGE
CAS:
Compute the basis of the image (also called the range) of a linear application.
INCR
Type:
Command
Description: Increment Command: Takes a variable, adds 1, stores the new value back into the original
variable, and returns the new value.
The value in name must be a real number or an integer.
Access:
!°MEMORY ARITHMETIC INCR
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
'name'
See also:
Level 1/Item 1
→
xincrement
DECR
INDEP
Type:
Command
Description: Independent Variable Command: Specifies the independent variable and its plotting range.
The specification for the independent variable name and its plotting range is stored as the third
parameter in the reserved variable PPAR. If the argument to INDEP is a:
• Global variable name, that name replaces the independent variable entry in PPAR.
• List containing a global name, that name replaces the independent variable name but leaves
unchanged any existing plotting range.
• List containing a global name and two real numbers, that list replaces the independent
variable entry.
• List containing two real numbers, or two real numbers from levels 1 and 2, those two
numbers specify a new plotting range, leaving the independent variable name unchanged.
(LASTARG returns a list, even if the two numbers were entered separately.)
The default entry is X.
Access:
…µ INDEP
3-84 Full Command and Function Reference
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
xstart
See also:
Level 1/Item 1
'global'
→
{ global }
→
{ global xstart xend }
→
{xstart xend }
→
xend
→
DEPND
INFORM
Type:
Command
Description: User-Defined Dialog Box Command: Creates a user-defined input form (dialog box).
INFORM creates a standard dialog box based upon the following specifications:
Variable
Function
“title”
Title. This appears at the top of the dialog box.
{s1 s2 … sn}
Field definitions. A field definition (sx) can have two formats: “label”, a field
label, or { “label” “helpInfo” type0 type1 … typen }, a field label with optional help
text that appears near the bottom of the screen, and an optional list of valid
object types for that field. If object types aren't specified, all object types are
valid. For information about object types, see the TYPE command.
When creating a multi-column dialog box, you can span columns by using an
empty list as a field definition. A field that appears to the left of an empty
field automatically expands to fill the empty space.
format
Field format information. This is the number col or a list of the form { col tabs
}: col is the number of columns the dialog box has, and tabs optionally
specifies the number of tab stops between the labels and the highlighted
fields. This list can be empty. col defaults to 1 and tabs defaults to 3.
{ resets }
Default values displayed when RESET is selected. Specify reset values in the
list in the same order as the fields were specified. To specify no value, use the
NOVAL command as a place holder. This list can be empty.
{ init }
Initial values displayed when the dialog box appears. Specify initial values in
the list in the same order as the fields were specified. To specify no value, use
the NOVAL command as a place holder. This list can be empty.
If you exit the dialog box by selecting OK or `, INFORM returns the field values { vals } in
item 1 or level 2, and puts a 1 in item 2 or level 1. (If a field is empty, NOVAL is returned as a
place holder.) If you exit the dialog box by selecting CANCEL or B, INFORM returns 0.
Access:
!°LIN INFORM
Input/Output:
( °is the left-shift of the Nkey).
L5/A1
L4/A2
L3A3
L2/A4
L1/A5
“title”
{s1 s2 ... sn }
format
{resets }
{init }
→
“title”
{s1 s2 ... sn }
format
{resets }
{init }
→
L2/I1
L1/I2
{ vals }
1
0
L = Level; A = Argument; I = item
Full Command and Function Reference 3-85
See also:
CHOOSE, INPUT, NOVAL, TYPE
INPUT
Type:
Command
Description: Input Command: Prompts for data input to the command line and prevents the user access to
stack operations.
When INPUT is executed, the stack or history area is blanked and program execution is
suspended for data input to the command line. The contents of “stack prompt” are displayed at
the top of the screen. Depending on the second argument (level 1), the command line may also
contain the contents of a string, or it may be empty. Pressing ` resumes program execution
and returns the contents of the command line in string form.
In its general form, the second argument (level 1) for INPUT is a list that specifies the content
and interpretation of the command line. The list can contain one or more of the following
parameters, in any order:
• "command-line prompt", whose contents are placed on the command line for prompting when
the program pauses.
• Either a real number, or a list containing two real numbers, that specifies the initial cursor position
on the command line:
– A real number n at the nth character from the left end of the first row (line) of the
command line. A positive n specifies the insert cursor; a negative n specifies the replace
cursor. 0 specifies the end of the command-line string.
– A list that specifies the initial row and column position of the cursor: the first number in
the list specifies a row in the command line (1 specifies the first row of the command
line); the second number counts by characters from the left end of the specified line. 0
specifies the end of the command-line string in the specified row. A positive row number
specifies the insert cursor; a negative row number specifies the replace cursor.
• One or more of the parameters ALG, α, or V, entered as unquoted names:
– ALG activates Algebraic/Program-entry mode.
– α specifies alpha lock.
– V verifies if the characters in the result string "result", without the " delimiters, compose a
valid object or objects. If the result-string characters do not compose a valid object or
objects, INPUT displays the Invalid Syntax warning and prompts again for data.
You can choose to specify as few as one of the argument 2 (level 1) list parameters. The default
states for these parameters are:
• Blank command line.
• Insert cursor placed at the end of the command-line prompt string.
• Program-entry mode.
• Result string not checked for invalid syntax.
If you specify only a command-line prompt string for the second argument (level 1), you don't
need to put it in a list.
Access:
!°LIN INPUT
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
“stack prompt”
“command-line prompt”
→
“result”
“stack prompt”
{ listcommand-line }
→
“result”
See also:
PROMPT, STR→
INT
CAS:
Calculate the antiderivative of a function for a given variable at a given point.
3-86 Full Command and Function Reference
INTEGER
CAS:
Display a menu or list of CAS integer operations.
INTVX
CAS:
Find the antiderivative of a function symbolically, with respect to the current default variable.
INV
Type:
Analytic function
Description: Inverse (1/x) Analytic Function: Returns the reciprocal or the matrix inverse.
For a complex argument (x, y), the inverse is the complex number:
⎛ x
–y ⎞
----------------2 ⎟
⎜ ---------------2
2, 2
⎝x +y x +y ⎠
Matrix arguments must be square (real or complex). The computed inverse matrix A-1 satisfies A
× A-1 = In, where In is the n × n identity matrix.
Access:
Y
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
z
→
1/z
[[ matrix ]]
→
[[ matrix ]]–1
'symb'
→
'INV(symb)'
x_unit
→
1/x_1/unit
See also:
SINV, /
INVMOD
CAS:
Perform modular inversion on an object, modulo the current modulus.
IP
Type:
Function
Description: Integer Part Function: Returns the integer part of its argument.
The result has the same sign as the argument.
Access:
!´ REALL IP
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (–3)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
x
→
n
x_unit
→
n_unit
'symb'
→
'IP(symb)'
See also:
FP
IQUOT
CAS:
Return the integer (or Euclidean) quotient of integers a, b; the integer part of a/b.
IREMAINDER
CAS:
Return the remainder of the division of one integer by another.
ISOL
Type:
Command
Full Command and Function Reference 3-87
Description: Isolate Variable Command: Returns an algebraic symb2 that rearranges symb1 to “isolate” the first
occurrence of variable global.
The result symb2 is an equation of the form global = expression. If global appears more than once,
then symb2 is effectively the right side of an equation obtained by rearranging and solving symb1 to
isolate the first occurrence of global on the left side of the equation.
If symb1 is an expression, it is treated as the left side of an equation symb1 = 0.
If global appears in the argument of a function within symb1, that function must be an analytic
function, that is, a function for which the hp49g+/hp48gII provides an inverse. Thus ISOL
cannot solve IP(x)=0 for x, since IP has no inverse.
ISOL is identical to SOLVE.
Access:
!ÎISOL
( Îis the left-shift of the 7key).
Flags:
Principal Solution (-1), Numerical Results (–3)
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
→
See also:
'symb1'
'global'
COLCT, EXPAN, QUAD, SHOW, SOLVE
ISOM
CAS:
Determine the characteristics of a 2-d or 3-d linear isometry.
'symb2'
ISPRIME?
CAS:
Test if a number is prime. For large numbers test if the number is pseudoprime.
I→R
Type:
Function
Description: Converts an integer into a real number.
Access:
…Ú REWRITE
Flags:
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). The
flags affect the output only if the input is not an integer.
Input:
Level 1/Argument 1: An integer.
Output:
Level 1/Item 1: The integer converted to a real number.
See also:
→NUM, R→I, XNUM
JORDAN
CAS:
Diagonalization, or Jordan cycle decomposition, of a matrix.
KER
CAS:
Compute the basis of the kernel of a linear application.
KERRM
Type:
Command
Description: Kermit Error Message Command: Returns the text of the most recent Kermit error packet.
If a Kermit transfer fails due to an error packet sent from the connected Kermit device to the
hp49g+/hp48gII, then executing KERRM retrieves and displays the error message. (Kermit
errors not in packets are retrieved by ERRM rather than KERRM.)
Access:
…µ KERRM
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
FINISH, KGET, PKT, RECN, RECV, SEND, SERVER
3-88 Full Command and Function Reference
“error message”
KEY
Type:
Command
Description: Key Command: Returns a test result and, if a key is pressed, returns the row-column location xn
m of that key.
KEY returns a false result (0) to item 2 (stack level 1) until a key is pressed. When a key is
pressed, it returns a true result (1) to item 2 (stack level 1) and xn m to item 1 (stack level 2). The
result xn m is a two- or three-digit number that identifies the row and column location of the key
just pressed. Unlike WAIT, which returns a three-digit number that identifies alpha and shifted
keyboard planes, KEY returns the row-column location of any key pressed, including !,
…, and ~.
Access:
!°LIN KEY
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 2/Item 1
Level 1/Item 2
xn m
1
→
→
See also:
0
WAIT, KEYEVAL
KEYEVAL
Type:
Description:
Command
Actions the specified key press.
You input a number, in the format ab.c, that represents the key. In the number ab.c:
• a is the row coordinate number, where row 1 is the top-most row.
• b is the column number, where column 1 is the left-most column.
• c is the shift state of the key, i.e., whether it is normal, alpha-shifted, left shifted, etc.
The shift state representations are as follows:
1: Normal function.
2: Left-shift function.
21: Left shift-and-hold function.
3. Right-shift function.
31: Right shift-and-hold function.
4. Alpha-function.
41: Alpha shift-and-hold function.
5. Alpha-left-shift function.
51: Alpha-left-shift-and-hold function.
6. Alpha-right-shift function.
61: Alpha-right-shift-and-hold function.
The sign of the input controls whether USER mode key assignments are used. Positive inputs
specify the USER mode key definition. Negative inputs specify the default system keyboard.
Access:
…µ KEYEVAL
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
nn.n
Example:
Command:
Result:
Turn the calculator off using a command.
KEYEVAL(101.3)
The calculator is turned off.
→KEYTIME
Type:
Command
Description: This command is provided for compatibility with earlier calculators, but does nothing on the
hp49g+/hp48gII.
KEYTIME→
Type:
Command
Description: This command is provided for compatibility with earlier calculators, but does nothing on the
hp49g+/hp48gII.
Full Command and Function Reference 3-89
KGET
Type:
Command
Description: Kermit Get Command: Used by a local Kermit to get a Kermit server to transmit the named
object(s).
To rename an object when the local device gets it, include the old and new names in an
embedded list. For example, {{ AAA BBB }} KGET gets the variable named AAA but changes
its name to BBB. {{ AAA BBB } CCC } KGET gets AAA as BBB and gets CCC under its own
name. (If the original name is not legal on the hp49g+/hp48gII, enter it as a string.)
Access:
…µ KGET
Flags:
I/O Device (-33), RECV Overwrite (-36), I/O Messages (-39)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
“name”
→
{ nameold namenew }
→
{ name1 ... namen }
→
→
{{ nameold namenew } name ... }
BAUD, CKSM, FINISH, PARITY, RECN, RECV, SEND, SERVER, TRANSIO
KILL
Type:
Command
Description: Cancel Halted Programs Command: Cancels all currently halted programs. If KILL is executed
within a program, that program is also canceled.
Canceled programs cannot be resumed.
KILL cancels only halted programs and the program from which KILL was executed, if any.
Commands that halt programs are HALT and PROMPT.
Suspended programs cannot be canceled. Commands that suspend programs are INPUT and
WAIT.
Access:
!°LL RUN & DEBUG KILL
( °is the left-shift of the Nkey).
Input/Output: None
See also:
CONT, DOERR, HALT, PROMPT
LABEL
Type:
Command
Description: Label Axes Command: Labels axes in PICT with x- and y-axis variable names and with the
minimum and maximum values of the display ranges.
The horizontal axis name is chosen in the following priority order:
1. If the axes parameter in the reserved variable PPAR is a list, then the x-axis element from that
list is used.
2. If axes parameter is not a list, then the independent variable name in PPAR is used.
The vertical axis name is chosen in the following priority order:
1. If the axes parameter in PPAR is a list, then the y-axis element from that list is used.
2. If axes is not a list, then the dependent variable name from PPAR is used.
Access:
…µ LABEL
Input/Output: None
See also:
AXES, DRAW, DRAX
LAGRANGE
CAS:
Return the interpolating polynomial of minimum degree for a set of pairs of values.
3-90 Full Command and Function Reference
LANGUAGE→
Type:
Command
Description: Language: Returns the language that is currently set. 0 for English, 1 for French, and 2 for
Spanish.
Access:
…µ LANGUAGE→
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
value
→LANGUAGE
→LANGUAGE
Type:
Command
Description: Language: Sets the language for things such as error messages: 0 for English, 1 for French, and 2
for Spanish.
Access:
…µ →LANGUAGE
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
value
See also:
LANGUAGE→
LAP
CAS:
Perform a Laplace transform on an expression with respect to the current default variable.
LAPL
CAS:
Return the Laplacian of a function with respect to a list of variables.
LAST
Type:
Command
Description: Returns copies of the arguments of the most recently executed command.
LAST is provided for compatibility with the HP28S. LAST is the same as LASTARG.
Access:
None. Must be typed in.
Flags:
Last Arguments (-55)
Input/Output:
Level 1
→
See also:
Level n
…
Level 1
objn
…
obj1
ANS, LASTARG
LASTARG
Type:
Command
Description: Returns copies of the arguments of the most recently executed command.
The objects return to the same stack levels that they originally occupied. Commands that take no
arguments leave the current saved arguments unchanged. When LASTARG follows a command
that evaluates an algebraic expression or program, the last arguments saved are from the
evaluated algebraic expression or program, not from the original command.
Access:
…µ LASTARG
!°LLERROR LASTA
( °is the left-shift of the Nkey).
!îin RPN mode.
(îis the left-shift of the`key).
Flags:
Last Arguments (-55)
Full Command and Function Reference 3-91
Input/Output:
Level 1
→
See also:
Level n
…
Level 1
objn
…
obj1
ANS, LAST
LCD→
Description: LCD to Graphics Object Command: Returns the current stack and menu display as a 131 × 80
(on the hp49g+) or 131 × 64 (on the hp48gII) graphics object.
( °is the left-shift of the Nkey).
Access:
!°LGROB LLCD→
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
grob
→GROB, →LCD
→LCD
Type:
Command
Description: Graphics Object to LCD Command: Displays the specified graphics object with its upper left
pixel in the upper left corner of the display. If the graphics object is larger than 131 × 72 (on the
hp49g+) or 131 × 56 (on the hp48gII), it is truncated.
Access:
!°LGROB L→LCD
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
grob
Level 1/Item 1
→
See also:
BLANK, →GROB, LCD→
LCM
CAS:
Return the least common multiple of two objects.
LCXM
CAS:
From a program with arguments i, j, build a matrix of specified size, with elements aij .
LDEC
CAS:
Solve linear differential equation (LDE), or system of first order LDEs, with constant
coefficients.
LEGENDRE
CAS:
Return the nth degree Legendre polynomial.
LGCD
CAS:
Return the greatest common divisor of a list of expressions or values.
LIBEVAL
Type:
Command
Description: Evaluate Library Function Command: Evaluates unnamed library functions.
WARNING: Use extreme care when executing this function. Using LIBEVAL with
random addresses will almost always cause a memory loss. Do not use this function
unless you know what you are doing.
Access:
#nfunction is of the form lllfffh, where lll is the library number, and fff the function number.
…µ LIBEVAL
3-92 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
#nfunction
EVAL, FLASHEVAL, SYSEVAL
LIBS
Type:
Command
Description: Libraries Command: Lists the title, number, and port of each library attached to the current
directory. The title of a library often takes the form LIBRARY-NAME : Description. A library
without a title is displayed as " ".
Access:
…µ LIBS
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
{“title”, nlib, nport, ...,“title”, nlib, nport }
See also:
ATTACH, DETACH
lim
CAS:
Return the limit of a function as its argument approaches a specified value.
LIMIT
CAS:
Return the limit of a function as its argument approaches a specified value. Identical to lim.
LIN
CAS:
Linearize expressions involving combinations of exponential terms.
LINE
Type:
Command Operation
Description: Draw Line Command: Draws a line in PICT between the input coordinates.
Access:
!°LPICT LINE
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
(x1, y1)
See also:
{ #n1, #m1}
ARC, BOX, TLINE
Level 1/Argument 2
Level 1/Item 1
(x2, y2)
→
{ #n2, #m2}
→
ΣLINE
Type:
Command
Description: Regression Model Formula Command: Returns an expression representing the best fit line
according to the current statistical model, using X as the independent variable name, and explicit
values of the slope and intercept taken from the reserved variable ΣPAR.
For each curve fitting model, the following table indicates the form of the expression returned by
ΣLINE, where m is the slope, x is the independent variable, and b is the intercept.
Model
Access:
Form of Expression
LINFIT
LOGFIT
mx + b
m ln(x) + b
EXPFIT
bemx
PWRFIT
bxm
…µ ΣLINE
Full Command and Function Reference 3-93
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
'symbformula'
BESTFIT, COLΣ, CORR, COV, EXPFIT, LINFIT, LOGFIT, LR, PREDX, PREDY, PWRFIT,
XCOL, YCOL
LINFIT
Type:
Command
Description: Linear Curve Fit Command: Stores LINFIT as the fifth parameter in the reserved variable
ΣPAR, indicating that subsequent executions of LR are to use the linear curve fitting model.
LINFIT is the default specification in ΣPAR.
Access:
…µ LINFIT
Input/Output: None
See also:
BESTFIT, EXPFIT, LOGFIT, LR, PWRFIT
LININ
Type:
Function
Description: Linear Test Function: Tests whether an algebraic is structurally linear for a given variable.
If any two subexpressions containing a variable (name) are combined only with addition and
subtraction, and any subexpression containing the variable is at most multiplied or divided by
another factor not containing the variable, the algebraic (symb) is determined to be linear for that
variable. LININ returns a 1 if the algebraic is linear for the variable, and a 0 if not.
Access:
!°TEST !«LININ
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
'symb'
'name'
Level 1/Item 1
→
0/1
LINSOLVE
CAS:
Solve a system of linear equations.
LIST→
Type:
Command
Description: List to Stack Command: Takes a list of n objects and returns each object to a separate level, and
returns the total number of objects to item n+1 (stack level 1).
The command OBJ→ also provides this function.
Access:
…µ LIST→
Input/Output:
Level 1/Argument 1
See also:
Leveln+1/Item1 ...
→
{ obj1, ...,objn }
obj1 ...
ARRY→, DTAG, EQ→, →LIST, OBJ→, STR→
Level2/Itemn
Level1/Itemn+1
objn
n
→LIST
Type:
Command
Description: Stack to List Command: Takes n specified objects and returns a list of those objects.
Access:
!°TYPE →LIST
( °is the left-shift of the Nkey).
!°LIST →LIST
3-94 Full Command and Function Reference
( °is the left-shift of the Nkey).
Input/Output:
See also:
Leveln+1/Argument1 …Level2/Argumentn
Level1/Argumentn+1
obj1 … objn
n
Level 1/Item 1
→
{ obj1, … ,objn }
→ARRY, LIST→, →STR, →TAG, →UNIT
∆LIST
Type:
Command
Description: List Differences Command: Returns the first differences of the elements in a list.
Adjacent elements in the list must be suitable for mutual subtraction.
Access:
!´ LIST ∆LIST
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
{ list }
See also:
Level 1/Item 1
→
{ differences }
ΣLIST, ΠLIST, STREAM
ΠLIST
Type:
Command
Description: List Product Command: Returns the product of the elements in a list.
The elements in the list must be suitable for mutual multiplication.
Access:
!´ LIST ΠLIST
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
{ list }
See also:
Level 1/Item 1
→
product
ΣLIST, ∆LIST, STREAM
ΣLIST
Type:
Command
Description: List Sum Command: Returns the sum of the elements in a list.
The elements in the list must be suitable for mutual addition.
Access:
!´LIST ΣLIST
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
{ list }
See also:
Level 1/Item 1
→
sum
ΠLIST, STREAM
LN
Type:
Analytic function
Description: Natural Logarithm Analytic Function: Returns the natural (base e) logarithm of the argument.
For x = 0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set, –MAXR is returned.
The inverse of EXP is a relation, not a function, since EXP sends more than one argument to the
same result. The inverse relation for EXP is the general solution:
LN(Z)+2*π*i*n1
The function LN is the inverse of a part of EXP, a part defined by restricting the domain of EXP
such that: each argument is sent to a distinct result, and each possible result is achieved.
The points in this restricted domain of EXP are called the principal values of the inverse relation.
LN in its entirety is called the principal branch of the inverse relation, and the points sent by LN to
the boundary of the restricted domain of EXP form the branch cuts of LN.
The principal branch used by the hp49g+/hp48gII for LN was chosen because it is analytic in
the regions where the arguments of the real-valued inverse function are defined. The branch cut
Full Command and Function Reference 3-95
for the complex-valued natural log function occurs where the corresponding real-valued function
is undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of LN. The graph of the domain shows where the
branch cut occurs: the heavy solid line marks one side of the cut, while the feathered lines mark
the other side of the cut. The graph of the range shows where each side of the cut is mapped
under the function.
These graphs show the inverse relation LN(Z)+2*π*i*n1 for the case n1=0. For other values of
n1, the horizontal band in the lower graph is translated up (for n1 positive) or down (for n1
negative). Taken together, the bands cover the whole complex plane, which is the domain of
EXP.
You can view these graphs with domain and range reversed to see how the domain of EXP is
restricted to make an inverse function possible. Consider the vertical band in the lower graph as
the restricted domain Z = (x,y). EXP sends this domain onto the whole complex plane in the
range W = (u,v) = EXP(x,y) in the upper graph.
Access:
…¹
(¹is the right-shift of the Qkey).
Flags:
Principal Solution (-1), Numerical Results (-3), Inifinite Result Exception (-22)
Input/Output:
Level 1/Argument 1
z
Level 1/Item 1
→
ln z
→
'LN(symb)'
See also:
'symb'
ALOG, EXP, ISOL, LNP1, LOG
LNAME
CAS:
Return a list of variable names contained in a symbolic expression.
3-96 Full Command and Function Reference
LNCOLLECT
CAS:
Simplify an expression by collecting logarithmic terms.
LNP1
Type:
Analytic function
Description: Natural Log of x Plus 1 Analytic Function: Returns ln (x + 1).
For values of x close to zero, LNP1(x) returns a more accurate result than does LN(x+1). Using
LNP1 allows both the argument and the result to be near zero, and it avoids an intermediate
result near 1. The calculator can express numbers within 10-449 of zero, but within only 10–11 of 1.
For values of x < –1, an Undefined Result error results. For x=–1, an Infinite Result exception
occurs, or, if flag –22 is set, LNP1 returns –MAXR.
Access:
!´ HYPERBOLIC LNP1
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3), Inifinite Result Exception (-22)
Input/Output:
Level 1/Argument 1
See also:
EXPM, LN
LOCAL
CAS:
Create local variables.
Level 1/Item 1
x
→
ln (x + 1)
'symb'
→
'LNP1(symb)'
LOG
Type:
Analytic function
Description: Common Logarithm Analytic Function: Returns the common logarithm (base 10) of the
argument.
For x=0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set (no error), LOG
returns –MAXR.
The inverse of ALOG is a relation, not a function, since ALOG sends more than one argument to
the same result. The inverse relation for ALOG is the general solution:
LOG(Z)+2*π*i*n1/2.30258509299
The function LOG is the inverse of a part of ALOG, a part defined by restricting the domain of
ALOG such that 1) each argument is sent to a distinct result, and 2) each possible result is
achieved. The points in this restricted domain of ALOG are called the principal values of the
inverse relation. LOG in its entirety is called the principal branch of the inverse relation, and the
points sent by LOG to the boundary of the restricted domain of ALOG form the branch cuts of
LOG.
The principal branch used by the hp49g+/hp48gII for LOG(z) was chosen because it is analytic
in the regions where the arguments of the real-valued function are defined. The branch cut for
the complex-valued LOG function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
You can determine the graph for LOG(z) from the graph for LN (see LN) and the relationship
log z = ln z / ln 10.
Access:
Flags:
…Ã
( Ã is the right-shift of the Vkey).
Principal Solution (-1), Numerical Results (-3), Inifinite Result Exception (-22)
Full Command and Function Reference 3-97
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
log z
'symb'
→
'LOG(symb)'
ALOG, EXP, ISOL, LN
LOGFIT
Type:
Command
Description: Logarithmic Curve Fit Command: Stores LOGFIT as the fifth parameter in the reserved variable
ΣPAR, indicating that subsequent executions of LR are to use the logarithmic curve-fitting
model.
LINFIT is the default specification in ΣPAR.
Access:
…µ LOGFIT
Input/Output: None
See also:
BESTFIT, EXPFIT, LINFIT, LR, PWRFIT
LQ
Type:
Command
Description: LQ Factorization of a Matrix Command: Returns the LQ factorization of an m × n matrix.
LQ factors an m × n matrix A into three matrices:
• L is a lower m × n trapezoidal matrix.
• Q is an n × n orthogonal matrix.
• P is a m × m permutation matrix.
Where P × A = L × Q.
Access:
!Ø FACTORIZATION LQ
( Ø is the left-shift of the 5key).
!´ MATRIX FACTORS LQ
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
[[ matrix ]]A
See also:
→
Level 3/Item 1
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]L
[[ matrix ]]Q
[[ matrix ]]P
LSQ, QR
LR
Type:
Command
Description: Linear Regression Command: Uses the currently selected statistical model to calculate the linear
regression coefficients (intercept and slope) for the selected dependent and independent
variables in the current statistics matrix (reserved variable ΣDAT).
The columns of independent and dependent data are specified by the first two elements in the
reserved variable ΣPAR, set by XCOL and YCOL, respectively. (The default independent and
dependent columns are 1 and 2.) The selected statistical model is the fifth element in ΣPAR. LR
stores the intercept and slope (untagged) as the third and fourth elements, respectively, in ΣPAR.
The coefficients of the exponential (EXPFIT), logarithmic (LOGFIT), and power (PWRFIT)
models are calculated using transformations that allow the data to be fitted by standard linear
regression. The equations for these transformations appear in the table below, where b is the
intercept and m is the slope. The logarithmic model requires positive x-values (XCOL), the
exponential model requires positive y-values (YCOL), and the power model requires positive xand y-values.
3-98 Full Command and Function Reference
Model
Transformation
Logarithmic
y = b + m ln(x)
Exponential
ln(y) = ln(b) + mx
Power
ln(y) = ln(b) + m ln(x)
Access:
…µ LR
Input/Output:
Level 1/Argument 1
→
See also:
Level 2/Item 1
Level 1/Item 2
Intercept: x1
Slope: x2
BESTFIT, COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, PREDX, PREDY,
PWRFIT, XCOL, YCOL
LSQ
Type:
Command
Description: Least Squares Solution Command: Returns the minimum norm least squares solution to any
system of linear equations where A × X = B.
If B is a vector, the resulting vector has a minimum Euclidean norm ||X|| over all vector
solutions that minimize the residual Euclidean norm ||A × X – B||. If B is a matrix, each
column of the resulting matrix, Xi, has a minimum Euclidean norm ||Xi|| over all vector
solutions that minimize the residual Euclidean norm ||A × Xi – Bi||.
If A has less than full row rank (the system of equations is underdetermined), an infinite number
of solutions exist. LSQ returns the solution with the minimum Euclidean length.
If A has less than full column rank (the system of equations is overdetermined), a solution that
satisfies all the equations may not exist. LSQ returns the solution with the minimum residuals of
A × X – B.
Access:
!Ø OPERATIONS L LSQ
( Ø is the left-shift of the 5key).
!´ MATRIX LSQ
( ´ is the left-shift of the Pkey).
Flags:
Singular Values (-54)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
[ array ]B
[[ matrix ]]A
→
[ array ]x
[[ matrix ]]A
→
[[ matrix ]]x
[[ matrix ]]B
LQ, RANK, QR, /
Level 1/Item 1
LU
Type:
Command
Description: LU Decomposition of a Square Matrix Command: Returns the LU decomposition of a square
matrix.
When solving an exactly determined system of equations, inverting a square matrix, or
computing the determinant of a matrix, the hp49g+/hp48gII factors a square matrix into its
Crout LU decomposition using partial pivoting.
The Crout LU decomposition of A is a lower-triangular matrix L, an upper-triangular matrix U
with ones on its diagonal, and a permutation matrix P, such that P × A = L × U. The results
satisfy P × A ≅ L × U.
Full Command and Function Reference 3-99
Access:
!Ø
( Ø is the left-shift of the 5key).
FACTORIZATION LU
!´ MATRIX FACTOR LU
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
→
Level 3/Item 1
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]L
[[ matrix ]]U
[[ matrix ]]P
See also:
[[ matrix ]]A
DET, INV, LSQ, /
LVAR
CAS:
Return a list of variable and function names in an algebraic object.
MAD
CAS:
Return details of a square matrix, including the information needed to obtain the adjoint matrix.
MAIN
CAS:
Display the names of the main menus of CAS operations, as a menu or a list.
MANT
Type:
Function
Description: Mantissa Function: Returns the mantissa of the argument.
Access:
!´REAL LMANT
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
MAP
Type:
Description:
Level 1/Item 1
x
→
ymant
'symb'
→
'MANT(symb)'
SIGN, XPON
Command
Applies a specified program to a list of objects or values.
• Level 1/Argument 2 contains the list of objects or values
• Level 2/Argument 1 contains the program to apply to the objects or values.
Access:
…µMAP
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
{list}1
«program»
Level 1/Item 1
→
{list}2
↓MATCH
Type:
Command
Description: Match Pattern Down Command: Rewrites an expression that matches a specified pattern.
↓MATCH rewrites expressions or subexpressions that match a specified pattern 'symbpat'. An
optional condition, 'symbcond', can further restrict whether a rewrite occurs. A test result is also
returned to indicate if command execution produced a rewrite; 1 if it did, 0 if it did not.
The pattern 'symbpat' and replacement 'symbrepl' can be normal expressions; for example, you can
replace .5 with 'SIN(π/6)'. You can also use a “wildcard” in the pattern (to match any
subexpression) and in the replacement (to represent that expression). A wildcard is a name that
begins with &, such as the name '&A', used in replacing 'SIN(&A+&B)' with
3-100 Full Command and Function Reference
'SIN(&A)*COS(&B)+COS(&A)*SIN(&B)'. Multiple occurrences of a particular wildcard in a
pattern must match identical subexpressions.
↓MATCH works from top down; that is, it checks the entire expression first. This approach
works well for expansion. An expression expanded during one execution of ↓MATCH will
contain additional subexpressions, and those subexpressions can be expanded by another
execution of ↓MATCH. Several expressions can be expanded by one execution of ↓MATCH
provided none is a subexpression of any other.
Access:
…µ↓MATCH
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
'symb1'
{ 'symbpat' 'symbrepl' }
'symb1'
{ 'symbpat' 'symbrepl' 'symbcond' }
Level 2/Item 1
Level 1/Item
2
→
'symb2'
0/1
→
'symb2'
0/1
↑MATCH
↑MATCH
Type:
Command
Description: Bottom-Up Match and Replace Command: Rewrites an expression.
↑MATCH rewrites expressions or subexpressions that match a specified pattern 'symbpat'. An
optional condition, 'symbcond', can further restrict whether a rewrite occurs. A test result is also
returned to indicate if command execution produced a rewrite; 1 if it did, 0 if it did not.
The pattern 'symbpat' and replacement 'symbrepl' can be normal expressions; for example, you can
replace 'SIN(π/6)' with '1/2'. You can also use a “wildcard” in the pattern (to match any
subexpression) and in the replacement (to represent that expression). A wildcard is a name that
begins with &, such as the name '&A', used in replacing 'SIN(&A+π)' with '–SIN(&A)'. Multiple
occurrences of a particular wildcard in a pattern must match identical subexpressions.
↑MATCH works from bottom up; that is, it checks the lowest level (most deeply nested)
subexpressions first. This approach works well for simplification. A subexpression simplified
during one execution of ↑MATCH will be a simpler argument of its parent expression, so the
parent expression can be simplified by another execution of ↑MATCH.
Several subexpressions can be simplified by one execution of ↑MATCH provided none is a
subexpression of any other.
Access:
…µ↑MATCH
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
'symb1'
{ 'symbpat', 'symbrepl' }
'symb1'
{ 'symbpat', 'symbrepl', 'symbcond' }
Level 2/Item 1
Level 1/Item 2
→
'symb2'
0/1
→
'symb2'
0/1
See also:
↓MATCH
MATHS
CAS:
Display a menu or list of CAS mathematics submenus.
MATR
CAS:
Display a menu or list of CAS commands for matrix operations.
MAX
Type:
Function
Full Command and Function Reference 3-101
Description: Maximum Function: Returns the greater of two inputs.
Access:
!´REAL MAX
Flags:
Numerical Results (-3)
Input/Output:
See also:
( ´ is the left-shift of the Pkey).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
max(x,y)
x
'symb'
→
'MAX(x, symb)'
'symb'
x
→
'MAX(symb, x)'
'symb1'
'symb2'
→
'MAX(symb1, symb2)'
x_unit1
y_unit2
→
max(x_unit1, y_unit2)
MIN
MAXR
Type:
Function
Description: Maximum Real Function: Returns the symbolic constant MAXR or its numerical representation
9.99999999999E499.
MAXR is the largest real number that can be represented by the hp49g+/hp48gII.
Access:
!´L CONSTANTS LMAXR
( ´ is the left-shift of the Pkey).
Flags:
Symbolic Constants (-2), Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'MAXR'
→
9.99999999999E499
e, i, MINR, π
MAXΣ
Type:
Command
Description: Maximum Sigma Command: Finds the maximum coordinate value in each of the m columns of
the current statistical matrix (reserved value ΣDAT).
The maxima are returned as a vector of m real numbers, or as a single real number if m = 1.
Access:
…µ MAXΣ
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xmax
→
[xmax1 xmax2 ... xmaxm ]
BINS, MEAN, MINΣ, SDEV, TOT, VAR
MCALC
Type:
Command
Description: Make Calculated Value Command: Designates a variable as a calculated variable for the multipleequation solver.
MCALC designates a single variable, a list of variables, or all variables as calculated values.
Access:
…µ MCALC
3-102 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
{ list }
→
"ALL"
→
MUSER
MEAN
Type:
Command
Description: Mean Command: Returns the mean of each of the m columns of coordinate values in the current
statistics matrix (reserved variable ΣDAT).
The mean is returned as a vector of m real numbers, or as a single real number if m = 1. The
mean is computed from the formula:
1 n
--- ∑ xi
ni = 1
where xi is the ith coordinate value in a column, and n is the number of data points.
…µ MEAN OR
…ÙSingle-variable statistics, Mean
(Ùis the right-shift of the 5key and always invokes a choose box).
Input/Output:
Access:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xmean
→
[xmean1, xmean2, ..., xmeanm ]
BINS, MAXΣ, MINΣ, SDEV, TOT, VAR
MEM
Type:
Command
Description: Memory Available Command: Returns the number of bytes of available RAM.
The number returned is only a rough indicator of usable available memory, since recovery
features (LASTARG= !î, …¯, and !®) consume or release varying
amounts of memory with each operation.
Before it can assess the amount of memory available, MEM must remove objects in temporary
memory that are no longer being used. This clean-up process (also called “garbage collection”)
also occurs automatically at other times when memory is full. Since this process can slow down
calculator operation at undesired times, you can force it to occur at a desired time by executing
MEM. In a program, execute MEM DROP.
Access:
!°MEMORY MEM
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
x
BYTES
MENU
Type:
Command Operation
Description: Display Menu Command: Displays a built-in menu or a library menu, or defines and displays a
custom menu.
Full Command and Function Reference 3-103
Access:
A built-in menu is specified by a real number xmenu. The format of xmenu is mm.pp, where mm is
the menu number and pp is the page of the menu. If pp doesn't correspond to a page of the
specified menu, the first page is displayed.
Library menus are specified in the same way as built-in menus, with the library number serving as
the menu number.
Custom menus are specified by a list of the form { "label-object" action-object } or a name containing
a list (namedefinition). Either argument is stored in reserved variable CST, and the custom menu is
subsequently displayed.
MENU takes any object as a valid argument and stores it in CST. However, the calculator can
build a custom menu only if CST contains a list or a name containing a list. Thus, if an object
other than a list or name containing a list is supplied to MENU, a Bad Argument Type error will
occur when the calculator attempts to display the custom menu.
!&H [MENU] MENU
!°LMODES [MENU] MENU
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
See also:
Level 1/Item 1
xmenu
→
{ listdefinition }
→
'namedefinition'
→
obj
→
RCLMENU, TMENU
MENUXY
CAS:
Display a function key menu of computer algebra commands in a specified range.
MERGE
Type:
Command
Description: Do not use this command, a carry-over from the HP 48GX for handling plug-in RAM cards.
MIN
Type:
Function
Description: Minimum Function: Returns the lesser of two inputs.
Access:
!´REAL MIN
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
x
y
→
min(x,y)
x
'symb'
→
'MIN(x, symb)'
'symb'
x
→
'MIN(symb, x)'
'symb1'
'symb2'
→
'MIN(symb1, symb2)'
x_unit1
y_unit2
→
min(x_unit1, y_unit2)
MAX
MINEHUNT
Type:
Command
Description: Starts the MINEHUNT game.
3-104 Full Command and Function Reference
Level 1/Item 1
In this game, you are standing in the upper-left corner of an 8x16 battlefield grid. Your mission
is to travel safely to the lower-right corner, avoiding invisible mines along the way. The game
tells you how many mines are under the eight squares adjacent to your position.
Use the number or arrow keys to cross the battlefield one square at a time (use 7, 9,
1, and 3to move diagonally.) You can exit the game at any time by pressing −(the
$ key).
To interrupt and save a game, press . This creates a variable MHpar in the current directory and
ends the game. If MHpar exists when you start MINEHUNT, the interrupted game resumes and
MHpar is purged.
You can change the number of mines in the battlefield by creating a variable named Nmines
containing the desired number. Nmines must contain a real number (1 to 64). If Nmines is
negative, the mines are visible during the game (allowing you to cheat).
Access:
G EQUATION LIBRARY UTILS MINEHUNT
Input/Output: None.
MINIFONT→
Type:
Command
Description: Minifont: Returns the font that is set as the minifont.
Access:
…µ MINIFONT→
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Font object
MINFONT→
→MINIFONT
Type:
Command
Description: Minifont: Sets the font that is used as the minifont.
Access:
…µ →MINIFONT
Input/Output:
Level 1/Argument 1
Font object
See also:
Level 1/Item 1
→
→MINIFONT
MINIT
Type:
Command
Description: Multiple-equation Menu Initialization Command. Creates the reserved variable Mpar, which
includes the equations in EQ and the variables in these equations.
Access:
…µMINIT
See also:
MITM, MROOT, MSOLVER
Full Command and Function Reference 3-105
MINR
Type:
Function
Description: Minimum Real Function: Returns the symbolic constant MINR or its numerical representation,
1.00000000000E–499.
MINR is the smallest positive real number that can be represented by the hp49g+/hp48gII.
Access:
!´LCONSTANTS LMINR
( ´ is the left-shift of the Pkey).
Flags:
Symbolic Constants (-2), Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'MINR'
→
1.00000000000E–499
e, i, MAXR, π
MINΣ
Type:
Command
Description: Minimum Sigma Command: Finds the minimum coordinate value in each of the m columns of
the current statistics matrix (reserved variable ΣDAT).
The minima are returned as a vector of m real numbers, or as a single real number if m = 1.
Access:
…µ MINΣ
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
→
See also:
xmin
{ xmin 1 xmin 2 … xmin
m
}
BINS, MAXΣ, MEAN, SDEV, TOT, VAR
MITM
Type:
Command
Description: Multiple-equation Menu Item Order Command. Changes multiple equation menu titles and
order. The argument list contains the variable names in the order you want. Use "" to indicate a
blank label. You must include all variables in the original menu and no others.
Access:
…µMITM
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
"title"
{ list }
Level 1/Item 1
→
See also:
MINIT
MKISOM
CAS:
Return the matrix representation for a given isometry.
MOD
Type:
Function
Description: Modulo Function: Returns a remainder defined by: x mod y = x – y floor (x/y)
Mod (x, y) is periodic in x with period y. Mod (x, y) lies in the interval [0, y) for y > 0 and in (y, 0]
for y < 0.
Algebraic syntax: argument 1 MOD argument 2
Access:
!´REAL MOD
( ´ is the left-shift of the Pkey).
!ÞMODUL L MOD
3-106 Full Command and Function Reference
( Þ is the left-shift of the 1key).
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
x mod y
x
'symb'
→
'MOD(x, symb)'
'symb'
x
→
'MOD(symb, x)'
'symb1'
'symb2'
→
'MOD(symb1, symb2)'
FLOOR, /
MODSTO
CAS:
Change the modulo setting to the specified number.
MODULAR
CAS:
Display a menu or list of CAS modulo operations.
MROOT
Type:
Command
Description: Multiple Roots Command: Uses the multiple-equation solver to solve for one or more variables
using the equations in EQ. Given a variable name, MROOT returns the found value; with "ALL"
MROOT stores a found value for each variable but returns nothing.
Access:
…µ MROOT
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
"ALL"
→
x
MCALC, MUSER
MSGBOX
Type:
Command
Description: Message Box Command: Creates a user-defined message box.
MSGBOX displays “message” in the form of a standard message box. Message text too long to
appear on the screen is truncated. You can use spaces and new-line characters (…ë) to
control word-wrapping and line breaks within the message.
Program execution resumes when the message box is exited by selecting OK or CANCL.
Access:
!°LOUT MSGBOX
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
“message”
CHOOSE, INFORM, PROMPT
MSLV
CAS:
Multiple equation solver; numerically approximate a solution to a system of equations.
MSOLVR
Type:
Command
Description: Multiple Equation Solver Command: Gets the multiple-equation solver variable menu for the set
of equations stored in EQ.
Full Command and Function Reference 3-107
The multiple-equation solver application can solve a set of of two or more equations for
unknown variables by finding the roots of each equation. The solver uses the list of equations
stored in EQ.
Access:
…µ MSOLVR
Input/Output: None
See also:
EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, MUSER
MULTMOD
CAS:
Perform modular multiplication of two objects, modulo the current modulus.
MUSER
Type:
Command
Description: Make User-Defined Variable Command: Designates a variable as user-defined for the multipleequation solver.
MUSER designates a single variable, a list of variables, or all variables as user-defined.
Access:
…µ MUSER
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
{ list }
→
"ALL"
→
MCALC
→NDISP
Type:
Command
Description: Sets the number of program lines displayed on the screen.
The default value on the hp49g+/hp48gII is 9. On the hp49g+ a value of 12 should be set for
→NDISP, which will allow more of the hp49g+’s taller screen to be used when the font is
FONT7, FONT6, or the MINIFONT. Also, note that the →NDISP setting is reset to 9 at every
warmstart. Including << 12 →NDISP >> in 'STARTUP' will automatically reset the value to 12.
Access:
…µ →NDISP
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
n
NDIST
Type:
Command
Description: Normal Distribution Command: Returns the normal probability distribution (bell curve) at x
based on the mean m and variance v of the normal distribution.
NDIST is calculated using this formula:
2
(x – m)
– ------------------2v
e
ndist ( m, v, x ) = --------------------2πv
Access:
!´LPROBABILITY L NDIST
3-108 Full Command and Function Reference
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
m
v
x
Level 1/Item 1
→
ndist(m, v, x)
UTPN
NDUPN
Type:
RPL command
Description: Duplicates an object n times, and returns n.
Access:
!°STACK !«NDUPN
( °is the left-shift of the Nkey).
ISTACK !«NDUPN
Input/Output:
Level 2
See also:
Level 1
obj
DUP, DUPDUP, DUPN, DUP2
n
→
Leveln+1 … Level2
Level1
obj … obj
n
NEG
Type:
Analytic function
Description: Negate Analytic Function: Changes the sign or negates an object.
Negating an array creates a new array containing the negative of each of the original elements.
Negating a binary number takes its two's complement (complements each bit and adds 1).
Negating a graphics object “inverts” it (toggles each pixel from on to off, or vice-versa). If the
argument is PICT, the graphics object stored in PICT is inverted.
Access:
… ß NEG
( ß is the right-shift of the 1key).
!´L COMPLEX L NEG
( ´ is the left-shift of the Pkey).
W
Flags:
Numerical Results (-3), Binary Integer Wordsize (-5 through -10)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
–z
#n1
→
#n2
[ array ]
→
[ –array ]
'symb'
→
'–(symb)'
x_unit
→
–x_unit
grob1
→
grob2
PICT1
→
PICT2
ABS, CONJ, NOT, SIGN
NEWOB
Type:
Command
Description: New Object Command: Creates a new copy of the specified object.
NEWOB has two main uses:
• NEWOB enables the purging of a library or backup object that has been recalled from a port.
NEWOB creates a new, separate copy of the object in memory, thereby allowing the original
copy to be purged.
Full Command and Function Reference 3-109
• Creating a new copy of an object that originated in a larger composite object (such as a list)
allows you to recover the memory associated with the larger object when that larger object is
no longer needed.
!°MEMORY NEWOB
( °is the left-shift of the Nkey).
Last Arguments (-55). In order for NEWOB to immediately release the memory occupied by the
original copy, flag -55 must be set so that the copy is not saved as a last argument.
Input/Output:
Access:
Flags:
Level 1/Argument 1
→
obj
See also:
Level 1/Item 1
obj
MEM, PURGE
NEXT
Type:
Command
Description: NEXT Command: Ends definite loop structures.
See the FOR and START keyword entries for more information.
Access:
!°BRANCH START/FOR NEXT
( °is the left-shift of the Nkey).
Input/Output: None
See also:
FOR, START, STEP
NEXTPRIME
CAS:
Return the next prime number larger than a given integer.
NIP
Type:
RPL command
Description: Drops the (n–1)th argument, where n is the number of arguments or items on the stack. (that is,
the object on level 2 of the stack). This is equivalent to executing SWAP folowed by DROP in
RPN mode.
Access:
!° STACK LLNIP
( °is the left-shift of the Nkey).
I STACK LLNIP
Input/Output:
Level 2
See also:
Level 1
obj1
DUP, DUPDUP, DUPN, DUP2
obj2
Level 1
→
obj2
NOT
Type:
Function
Description: NOT Command: Returns the one's complement or logical inverse of the argument.
When the argument is a binary integer or string, NOT complements each bit in the argument to
produce the result.
• A binary integer is treated as a sequence of bits as long as the current wordsize.
• A string is treated as a sequence of bits, using 8 bits per character (that is, using the binary
version of the character code).
When the argument is a real number or symbolic, NOT does a true/false test. The result is 1
(true) if the argument is zero; it is 0 (false) if the argument is nonzero. This test is usually done
on a test result (T/F).
If the argument is an algebraic object, then the result is an algebraic of the form NOT symb.
Execute →NUM (or set flag –3 before executing NOT) to produce a numeric result from the
algebraic result.
3-110 Full Command and Function Reference
Access:
!°
TEST LNOT
( °is the left-shift of the Nkey).
…ãL LOGIC NOT
(ã is the right-shift of the 3key).
Flags:
Numerical Results (-3), Binary Integer Wordsize (-5 through -10)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
#n1
→
#n2
T/F
→
0/1
“string1”
→
“string2”
'symb'
→
'NOT symb'
AND, OR, XOR
NOVAL
Type:
Command
Description: INFORM Place Holder/Result Command: Place holder for reset and initial values in userdefined dialog boxes. NOVAL is returned when a field is empty.
NOVAL is used to mark an empty field in a user-defined dialog box created with the INFORM
command. INFORM defines fields sequentially. If default values are used for those fields, the
defaults must be defined in the same order as the fields were defined. To skip over (not provide
defaults for) some of the fields, use the NOVAL command.
After INFORM terminates, NOVAL is returned if a field is empty and OK or ` is selected.
Access:
!°L IN NOVAL
( °is the left-shift of the Nkey).
Input/Output: None
See also:
INFORM
NΣ
Type:
Command
Description: Number of Rows Command: Returns the number of rows in the current statistical matrix
(reserved variable ΣDAT).
Access:
…µ NΣ
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
nrows
ΣX, ΣXY, ΣX2, ΣY, ΣY2
NSUB
Type:
Command
Description: Number of Sublist Command: Provides a way to access the current sublist position during an
iteration of a program or command applied using DOSUBS.
Returns an Undefined Local Name error if executed when DOSUBS is not active.
Access:
!°LIST PROCEDURES NSUB
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
DOSUBS, ENDSUB
→NUM
Type:
Command
nposition
Full Command and Function Reference 3-111
Description: Evaluate to Number Command. Evaluates a symbolic argument object (other than a list) and
returns the numerical result.
→NUM repeatedly evaluates a symbolic argument until a numerical result is achieved. The effect
is the same as evaluating a symbolic argument in Numerical Result Mode (flag -3 set).
Access:
… →NUM
(→NUM is the right-shift of the `key).
Input/Output:
Level 1/Argument 1
objsymb
See also:
Level 1/Item 1
→
z
EVAL
NUM
Type:
Command
Description: Character Number Command: Returns the character code n for the first character in the string.
The character codes are an extension of ISO 8859/1.
The number of a character can be found by accessing the Characters tool (…±) and
highlighting that character. The number appears near the bottom of the screen.
Access:
!°TYPE LNUM
( °is the left-shift of the Nkey).
!° LCHARS NUM
( °is the left-shift of the Nkey).
…&N NUM
Input/Output:
Level 1/Argument 1
See also:
“string”
CHR, POS, REPL, SIZE, SUB
Level 1/Item 1
→
n
NUMX
Type:
Command
Description: Number of X-Steps Command: Sets the number of x-steps for each y-step in 3D perspective
plots.
The number of x-steps is the number of independent variable points plotted for each dependent
variable point plotted. This number must be 2 or more. This value is stored in the reserved
variable VPAR. YSLICE is the only 3D plot type that does not use this value.
Access:
…µ NUMX
Input/Output:
Level 1/Argument 1
nx
See also:
Level 1/Item 1
→
NUMY
NUMY
Type:
Command
Description: Number of Y-Steps Command: Sets the number of y-steps across the view volume in 3D
perspective plots.
The number of y-steps is the number of dependent variable points plotted across the view
volume. This number must be 2 or more. This value is stored in the reserved variable VPAR.
Access:
…µ NUMY
Input/Output:
Level 1/Argument 1
ny
See also:
NUMX
3-112 Full Command and Function Reference
Level 1/Item 1
→
OBJ→
Type:
Command
Description: Object to Stack Command: Separates an object into its components. For some object types, the
number of components is returned as item n+1 (stack level 1).
If the argument is a complex number, list, array, or string, OBJ→ provides the same functions as
C→R, LIST→, ARRY→, and STR→, respectively. For lists, OBJ→ also returns the number of
list elements. If the argument is an array, OBJ→ also returns the dimensions { m n } of the array,
where m is the number of rows and n is the number of columns.
For algebraic objects, OBJ→ returns the arguments of the top-level (least-nested) function (arg1
… argn), the number of arguments of the top-level function (n), and the name of the top-level
function (function).
If the argument is a string, the object sequence defined by the string is executed.
Access:
!°TYPE OBJ→
( °is the left-shift of the Nkey).
!°LIST OBJ→
( °is the left-shift of the Nkey).
…&NL OBJ→
!°LCHARS LOBJ→
( °is the left-shift of the Nkey).
Input/Output:
Leveln+1/Item1
Level 1/Argument 1
See also:
Level2/Itemn
Level1/Itemn+1
→
x
y
(x, y)
→
{ obj1, ... ,objn }
→
obj1
→
objn
n
[ x1, ... ,xn ]
→
x1
→
xn
{n}
[[ x1 1, ... ,xm n ]]
→
x1 1
→
xm n
{ m, n }
“obj”
→
'symb'
→
x_unit
→
evaluated object
→
arg1 ... argn
→
n
'function'
→
x
1_unit
obj
“tag”
→
:tag:obj
→
ARRY→, C→R, DTAG, EQ→, LIST→, R→C, STR→, →TAG
OCT
Type:
Command
Description: Octal Mode Command: Selects octal base for binary integer operations.
(The default base is decimal.) Binary integers require the prefix #. Binary integers entered and
returned in octal base automatically show the suffix o. If the current base is not octal, enter an
octal number by ending it with o. It will be displayed in the current base when entered. The
current base does not affect the internal representation of binary integers as unsigned binary
numbers.
Access:
…ãOCT
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output: None
See also:
BIN, DEC, HEX, RCWS, STWS
OFF
Type:
Command
Description: Off Command: Turns off the calculator.
When executed from a program, that program will resume execution when the calculator is
turned on. This provides a programmable “autostart.” ( i.e., a programmable …ç).
Access:
„°LLRUNL OFF
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-113
Input/Output: None
See also:
CONT, HALT, KILL
OLDPRT
Type:
Command
Description: Modifies the remapping string in the reserved variable PRTPAR so that the extended character
set of the calculator matches that of the HP82240A infrared printer.
To cancel OLDPRT character mapping, purge the PRTPAR variable. To print a string
containing graphics data, disable OLDPRT.
Access:
…µ OLDPRT
See also:
CR, DELAY, PRLCD, PRST, PRSTC, PRVAR, PR1
OPENIO
Type:
Command
Description: Open I/O Port Command: Opens a serial port using the I/O parameters in the reserved variable
IOPAR.
Since all hp49g+/hp48gII Kermit-protocol commands automatically effect an OPENIO first,
OPENIO is not normally needed, but can be used if an I/O transmission does not work.
OPENIO is necessary for interaction with devices that interpret a closed port as a break.
OPENIO is also necessary for the automatic reception of data into the input buffer using nonKermit commands. If the port is closed, incoming characters are ignored. If the port is open,
incoming characters are automatically placed in the input buffer. These characters can be
detected with BUFLEN, and can be read out of the input buffer using SRECV.
If the port is already open, OPENIO does not affect the data in the input buffer. However, if
the port is closed, executing OPENIO clears the data in the input buffer.
Access:
…µ OPENIO
Flags:
I/O Device (-33)
Input/Output: None
See also:
BUFLEN, CLOSEIO, SBRK, SRECV, STIME, XMIT
OR
Type:
Function
Description: OR Function: Returns the logical OR of two arguments.
When the arguments are binary integers or strings, OR does a bit-by-bit (base 2) logical
comparison.
• An argument that is a binary integer is treated as a sequence of bits as long as the current
wordsize. Each bit in the result is determined by comparing the corresponding bits (bit1 and
bit2) in the two arguments as shown in the following table:
bit1
bit2
bit1 OR bit2
0
0
0
0
1
1
1
0
1
1
1
1
• An argument that is a string is treated as a sequence of bits, using 8 bits per character (that is,
using the binary version of the character code). The two string arguments must be the same
length.
When the arguments are real numbers or symbolics, OR simply does a true/false test. The result
is 1 (true) if either or both arguments are nonzero; it is 0 (false) if both arguments are zero. This
test is usually done to compare two test results.
3-114 Full Command and Function Reference
If either or both of the arguments are algebraic objects, then the result is an algebraic of the form
symb1 OR symb2. Execute →NUM (or set flag –3 before executing OR) to produce a numeric
result from the algebraic result.
…ãL LOGIC OR
(ãis the right-shift of the 3key).
!° TEST L OR
( °is the left-shift of the Nkey).
Flags:
Numerical Results (-3), Binary Integer Wordsize (-5 through -10)
Input/Output:
Access:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
#n1
#n2
→
#n3
“string1”
“string2”
→
“string3”
T/F1
T/F2
→
0/1
T/F
'symb'
→
'T/F OR symb'
'symb'
T/F
→
'symb OR T/F'
'symb1'
AND, NOT, XOR
'symb2'
→
'symb1 OR symb2'
ORDER
Type:
Command
Description: Order Variables Command: Reorders the variables in the current directory (shown in the VAR
menu) to the order specified.
The names that appear first in the list will be the first to appear in the VAR menu. Variables not
specified in the list are placed after the reordered variables.
If the list includes the name of a large subdirectory, there may be insufficient memory to execute
ORDER.
Access:
!°MEMORY DIRECTORY L ORDER
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
{ global1 ... globaln }
See also:
VARS
OVER
Type:
RPL command
Description: Over Command: Returns a copy to stack level 1 of the object in level 2.
Access:
!°STACK OVER
( °is the left-shift of the Nkey).
Input/Output:
Level 2
Level 1
Level 3
Level 2
Level 1
obj1
obj2
obj1
→
See also:
obj1
obj2
PICK, ROLL, ROLLD, ROT, SWAP
P2C
CAS:
Decompose a permutation into lists that represent cycles.
PA2B2
CAS:
Given prime p, with p=2 or p ≡ 1 modulo 4, return Gaussian integer a + ib such that p = a2 + b2.
Full Command and Function Reference 3-115
PARAMETRIC
Type:
Command
Description: Parametric Plot Type Command: Sets the plot type to PARAMETRIC.
When the plot type is PARAMETRIC, the DRAW command plots the current equation as a
complex-valued function of one real variable. The current equation is specified in the reserved
variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has the
following form:
{ (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend }
For plot type PARAMETRIC, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a list containing a name that specifies the independent variable, and two numbers
specifying the minimum and maximum values for the independent variable (the plotting
range). Note that the default value is X. If X is not modified and included in a list with a
plotting range, the values in (xmin, ymin) and (xmax, ymax) are used as the plotting range, which
generally leads to meaningless results.
• res is a real number specifying the interval, in user-unit coordinates, between values of the
independent variable. The default value is 0, which specifies an interval equal to 1/130 of the
difference between the maximum and minimum values in indep (the plotting range).
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command PARAMETRIC
places the name PARAMETRIC in PPAR.
• depend is a name specifying a label for the vertical axis. The default value is Y.
The contents of EQ must be an expression or program; it cannot be an equation. It is evaluated
for each value of the independent variable. The results, which must be complex numbers, give
the coordinates of the points to be plotted. Lines are drawn between plotted points unless flag
-31 is set.
Access:
…µ PARAMETRIC
Flags:
Simultaneous Plotting (-28), Curve Filling (-31)
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARSURFACE,
PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
PARITY
Type:
Command
Description: Parity Command: Sets the parity value in the reserved variable IOPAR.
Legal values are shown below. A negative value means the hp49g+/hp48gII does not check
parity on bytes received during Kermit transfers or with SRECV. Parity is still used during data
transmission, however.
3-116 Full Command and Function Reference
n-Value
Meaning
0
no parity (the default value)
1
odd parity
2
even parity
3
mark
4
space
Access:
…µPARITY
Input/Output:
Level 1/Argument 1
nparity
See also:
Level 1/Item 1
→
BAUD, CKSM, TRANSIO
PARSURFACE
Type:
Command
Description: PARSURFACE Plot Type Command: Sets plot type to PARSURFACE.
When plot type is set to PARSURFACE, the DRAW command plots an image graph of a 3vector-valued function of two variables. PARSURFACE requires values in the reserved variables
EQ, VPAR, and PPAR.
VPAR is made up of the following elements:
{ xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep }
For plot type PARSURFACE, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
• zlow and zhigh are real numbers that specify the height of the view space.
• xmin and xmax are real numbers that specify the input region's width. The default value is (–
1,1).
• ymin and ymax are real numbers that specify the input region's depth. The default value is (–1,1).
• xeye, yeye, and zeye are real numbers that specify the point in space from which the graph is
viewed.
• xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend }
For plot type PARSURFACE, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command PARSURFACE
places the name PARSURFACE in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µ PARSURFACE
Input/Output: None
Full Command and Function Reference 3-117
See also:
BAR, CONIC, DIFFEQ, FAST3D, FUNCTION, GRIDMAP, HISTOGRAM,
PARAMETRIC, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME,
YSLICE
PARTFRAC
CAS:
Perform partial fraction decomposition on a partial fraction.
PATH
Type:
Command
Description: Current Path Command: Returns a list specifying the path to the current directory.
The first directory is always HOME, and the last directory is always the current directory.
If a program needs to switch to a specific directory, it can do so by evaluating a directory list,
such as one created earlier by PATH.
Access:
!°MEMORY DIRECTORY PATH
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
{ HOME directory-name1 ... directory-namen }
See also:
CRDIR, HOME, PGDIR, UPDIR
PCAR
CAS:
Return the characteristic polynomial of a square matrix.
PCOEF
Type:
Command
Description: Monic Polynomial Coefficients Command: Returns the coefficients of a monic polynomial (a
polynomial with a leading coefficient of 1) having specific roots.
The argument must be a real or complex array of length n containing the polynomial's roots. The
result is a real or complex vector of length n+1 containing the coefficients listed from highest
order to lowest, with a leading coefficient of 1.
Access:
!Þ POLYNOMIAL LL PCOEF
( Þis the left-shift of the 1key).
Input/Output:
Level 1/Argument 1
[ array ]roots
See also:
Level 1/Item 1
→
[ array ]coefficients
PEVAL, PROOT
PCONTOUR
Type:
Command
Description: PCONTOUR Plot Type Command: Sets the plot type to PCONTOUR.
When plot type is set PCONTOUR, the DRAW command plots a contour-map view of a scalar
function of two variables. PCONTOUR requires values in the reserved variables EQ, VPAR,
and PPAR.
VPAR is made up of the following elements:
{ xleft xright ynear yfar zlow zhigh xmin xmax ymin ymax xeye yeye zeye xstep ystep }
For plot type PCONTOUR, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
• zlow and zhigh are real numbers that specify the height of the view space.
• xmin and xmax are not used.
• ymin and ymax are not used.
3-118 Full Command and Function Reference
• xeye, yeye, and zeye are real numbers that specify the point in space from which the graph is
viewed.
• xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type PCONTOUR, the elements of PPAR are used as follows:
• (xmin, ymin) and (xmax, ymax) are not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command PCONTOUR
places the name PCONTOUR in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µ PCONTOUR
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
PCOV
Type:
Command
Description: Population Covariance Command: Returns the population covariance of the independent and
dependent data columns in the current statistics matrix (reserved variable ΣDAT).
The columns are specified by the first two elements in reserved variable ΣPAR, set by XCOL
and YCOL respectively. If ΣPAR does not exist, PCOV creates it and sets the elements to their
default values (1 and 2).
The population covariance is calculated with the following formula:
1 n
--- ∑ ( xkn1 – xn 1 ) ( x kn2 – x n2 )
nk = 1
where
x kn 1
is the kth coordinate value in column
n 2 x n1
column ,
is the mean of the data in column
and n is the number of data points.
n 1 x kn 2
,
is the kth coordinate value in the
n1 xn
, 2 is
the mean of the data in column
n2
,
Access:
…µ PCOV
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
xpcovariance
COLΣ, CORR, COV, PREDX, PREDY, XCOL, YCOL
PDIM
Type:
Command
Description: PICT Dimension Command: Replaces PICT with a blank PICT of the specified dimensions.
If the arguments are complex numbers, PDIM changes the size of PICT and makes the
arguments the new values of (xmin, ymin) and (xmax, ymax) in the reserved variable PPAR. Thus, the
scale of a subsequent plot is not changed. If the arguments are binary integers, PPAR remains
unchanged, so the scale of a subsequent plot is changed.
Full Command and Function Reference 3-119
PICT cannot be smaller than 131 pixels wide × 80 pixels high on the hp49g+ (64 pixels on the
hp48gII) nor wider than 2048 pixels (height is unlimited).
Access:
!°PICT PDIM
Input/Output:
See also:
( °is the left-shift of the Nkey).
Level 2/Argument 1
Level 1/Argument 2
(xmin, ymin)
#nwidth
(xmax, ymax)
#mheight
Level 1/Item 1
→
→
PMAX, PMIN
PERM
Type:
Function
Description: Permutations Function: Returns the number of possible permutations of n items taken m at a
time.
The formula used to calculate Pn,m is:
n!
P n, m = -------------------( n – m )!
The arguments n and m must each be less than 1012. If n < m, zero is returned.
Access:
!´LPROBABILITY PERM
Flags:
Numerical Results (–3)
Input/Output:
Level 2/Argument 1
n
'symbn'
n
'symbn'
See also:
( ´ is the left-shift of the Pkey).
Level 1/Argument 2
m
m
'symbm'
'symbm'
Level 1/Item 1
→
→
→
→
Pn,m
'PERM(symbn,m)'
'PERM(n, symbm)'
'PERM(symbn,symbm)'
COMB, FACT, !
PEVAL
Type:
Command
Description: Polynomial Evaluation Command: Evaluates an n-degree polynomial at x.
The arguments must be an array of length n + 1 containing the polynomial's coefficients
listed from highest order to lowest, and the value x at which the polynomial is to be evaluated.
Access:
…µ PEVAL
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
[ array ]coefficients
PCOEF, PROOT
x
Level 1/Item 1
→
p(x)
PGDIR
Type:
Command
Description: Purge Directory Command: Purges the named directory (whether empty or not).
Access:
!°MEMORY DIRECTORY PGDIR
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
→
'global'
CLVAR, CRDIR, HOME, PATH, PURGE, UPDIR
3-120 Full Command and Function Reference
Level 1/Item 1
PICK
Type:
RPL Command
Description: Pick Object Command: Copies the contents of a specified stack level to level 1.
Access:
!°STACK PICK
( °is the left-shift of the Nkey).
Input/Output:
Ln+1...
L2
L1
objn ...
obj1
n
→
Ln+1
L2
L1
objn ...
obj1
obji
L = Level
See also:
DUP, DUPN, DUP2, OVER, ROLL, ROLLD, ROT, SWAP
PICK3
Type:
RPL Command
Description: Duplicates the object on level 3 of the stack.
Access:
!°STACK L PICK3
( °is the left-shift of the Nkey).
Input/Output:
L3
L2
L1
obj1
obj2
obj3
→
L4
L3
L2
L1
obj1
obj2
obj3
obj1
L = Level; A = Argument; I =Item
See also:
PICK, OVER, DUP
PICT
Type:
Command
Description: PICT Command: Puts the name PICT on the stack.
PICT is the name of a storage location in calculator memory containing the current graphics
object. The command PICT enables access to the contents of that memory location as if it were
a variable. Note, however, that PICT is not a variable as defined in the hp49g+/hp48gII: its name
cannot be quoted, and only graphics objects may be stored in it.
If a graphics object smaller than 131 wide × 80 pixels high is stored in PICT, it is enlarged to 131
× 80. (These values are 131 x 64 on the hp48gII). A graphics object of unlimited pixel height and
up to 2048 pixels wide can be stored in PICT.
Access:
!° L[PICT] PICT
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
PICT
GOR, GXOR, NEG, PICTURE, PVIEW, RCL, REPL, SIZE, STO, SUB
PICTURE
Type:
Command
Description: Picture Environment Command: Selects the Picture environment (that is, selects the graphics
display and activates the graphics cursor and Picture menu).
When executed from a program, PICTURE suspends program execution until −is pressed.
Access:
…µ PICTURE
š
Input/Output: None
See also:
PICTURE, PVIEW, TEXT
Full Command and Function Reference 3-121
PINIT
Type:
Command
Description: Port Initialize Command: Initializes all currently active ports. It may affect data already stored in
a port.
Access:
…µ PINIT
Input/Output: None
PIX?
Type:
Command
Description: Pixel On? Command: Tests whether the specified pixel in PICT is on; returns 1 (true) if the pixel
is on, and 0 (false) if the pixel is off.
Access:
!° LPICT L PIX?
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
(x,y)
→
0/1
{ #n #m }
→
0/1
PIXON, PIXOFF
PIXOFF
Type:
Command
Description: Pixel Off Command: Turns off the pixel at the specified coordinate in PICT.
Access:
!°LPICT L PIXOFF
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
(x,y)
→
{ #n #m }
→
PIXON, PIX?
PIXON
Type:
Command
Description: Pixel On Command: Turns on the pixel at the specified coordinate in PICT.
Access:
!°LPICT LPIXON
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
(x,y)
→
{ #n #m }
→
PIXOFF, PIX?
PKT
Type:
Command
Description: Packet Command: Used to send command “packets” (and receive requested data) to a Kermit
server.
To send hp49g+/hp48gII objects, use SEND.
PKT allows additional commands to be sent to a Kermit server.
3-122 Full Command and Function Reference
The packet data, packet type, and the response to the packet transmission are all in string form.
PKT first does an I (initialization) packet exchange with the Kermit server, then sends the server a
packet constructed from the data and packet-type arguments supplied to PKT. The response to
PKT will be either an acknowledging string (possibly blank) or an error packet (see KERRM).
For the type argument, only the first letter is significant.
…µ PKT
I/O Device (-33), I/O Messages (-39). The I/O Data Format flag (-35) can be significant if the
server sends back more than one packet.
Input/Output:
Access:
Flags:
Level 2/Argument 1
See also:
Level 1/Argument 2
“data”
CLOSEIO, KERRM, SERVER
“type”
Level 1/Item 1
→
“response”
PLOT
Type:
Command
Description: Stores its argument in EQ and opens the PLOT SETUP screen.
Access:
P GRAPH PLOT
Input:
An expression.
Output:
The input expression.
Example: Store SIN(X) in EQ and open the PLOT SETUP screen:
Command: PLOT(SIN(X))
Result:
PLOT SETUP screen is open with SIN(X) in EQ. SIN(X) is copied to history (LASTARG in
RPN mode).
See also:
PLOTADD
PLOTADD
Type:
Function
Description: Adds a function to the existing plot function list, and opens the Plot Setup screen.
Access:
P GRAPH PLOTA
Input/Output:
Level 1/Argument 1
(symb)
Level 1/Item 1
→
PMAX
Type:
Command
Description: PICT Maximum Command: Specifies (x, y) as the coordinates at the upper right corner of the
display.
The complex number (x, y) is stored as the second element in the reserved variable PPAR.
Access:
…µ PMAX
Input/Output:
Level 1/Argument 1
See also:
(x,y)
PDIM, PMIN, XRNG, YRNG
PMIN
Type:
Command
Level 1/Item 1
→
Full Command and Function Reference 3-123
Description: PICT Minimum Command: Specifies (x, y) as the coordinates at the lower left corner of the
display. The complex number (x, y) is stored as the first element in the reserved variable PPAR.
Access:
…µ PMIN
Input/Output:
Level 1/Argument 1
See also:
(x,y)
PDIM, PMAX, XRNG, YRNG
PMINI
CAS:
Find the minimal polynomial of a matrix.
Level 1/Item 1
→
POLAR
Type:
Command
Description: Polar Plot Type Command: Sets the plot type to POLAR.
When the plot type is POLAR, the DRAW command plots the current equation in polar
coordinates, where the independent variable is the polar angle and the dependent variable is the
radius. The current equation is specified in the reserved variable EQ.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type POLAR, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a name specifying the independent variable, or a list containing such a name and two
numbers specifying the minimum and maximum values for the independent variable (the
plotting range). The default value of indep is X.
• res is a real number specifying the interval, in user-unit coordinates, between values of the
independent variable. The default value is 0, which specifies an interval of 2 degrees, 2 grads,
or π/90 radians.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command POLAR places
the name POLAR in ptype.
• depend is a name specifying a label for the vertical axis. The default value is Y.
The current equation is plotted as a function of the variable specified in indep. The minimum and
maximum values of the independent variable (the plotting range) can be specified in indep;
otherwise, the default minimum value is 0 and the default maximum value corresponds to one
full circle in the current angle mode (360 degrees, 400 grads, or 2π radians). Lines are drawn
between plotted points unless flag –31 is set.
If flag –28 is set, all equations are plotted simultaneously.
If EQ contains an expression or program, the expression or program is evaluated in Numerical
Results mode for each value of the independent variable to give the values of the dependent
variable. If EQ contains an equation, the plotting action depends on the form of the equation.
3-124 Full Command and Function Reference
Form of Current Equation
Plotting Action
expr = expr
Each expression is plotted separately. The intersection of the two
graphs shows where the expressions are equal
name = expr
Only the expression is plotted
Access:
…µ POLAR
Flags:
Simultaneous Plotting (-28), Curve Filling (-31)
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
POLYNOMIAL
CAS:
Display a menu or list of CAS operations with polynomials.
POP
Type:
Command
Description: Restores the flags and current directory saved by the most recent execution of PUSH. If no
PUSH saves are left, the command has no effect.
Access:
…µ POP
Input:
None
Output:
In Algebraic mode the command returns NOVAL to level 1 of the stack.
See also:
PUSH
POS
Type:
Command
Description: Position Command: Returns the position of a substring within a string or the position of an
object within a list.
If there is no match for obj or substring, POS returns zero.
Access:
!°LCHARS POS
( °is the left-shift of the Nkey).
!°LIST ELEM POS
( °is the left-shift of the Nkey).
@& N POS
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
“string”
“substring”
→
n
obj
→
n
{ list }
CHR, NUM, REPL, SIZE, SUB
Level 1/Item 1
POTENTIAL
CAS:
Find the potential field function describing a field whose vector gradient is input.
POWEXPAND
CAS:
Rewrite an expression raised to a power as a product.
POWMOD
CAS:
Raise number or expression to given power, expresse the result modulo the current modulus.
PR1
Type:
Command
Full Command and Function Reference 3-125
Description: Print Level 1 Command: Prints an object in multiline printer format.
All objects except strings are printed with their identifying delimiters. Strings are printed without
the leading and trailing " delimiters.
Multiline printer format is similar to multiline display format, with the following exceptions:
• Strings and names that are more than 24 characters long are continued on the next printer
line.
• The real and imaginary parts of complex numbers are printed on separate lines if they don't fit
on the same line.
• Grobs are printed graphically.
• Arrays are printed with a numbered heading for each row and with a column number before
each element.
For example, the 2 × 3 array
1 23
4 56
would be printed as follows:
Array (2 3)
Row 1
1] 1
2] 2
3] 3
Row 2
1] 4
2] 5
3] 6
…µ PR1
I/O Device (-33), Printing Device (-34), Double-spaced Printing (-37), Linefeed (-38). If flag -34
is set, flag -33 must be clear.
Input/Output:
Access:
Flags:
Level 1/Argument 1
See also:
Level 1/Item 1
→
object
CR, DELAY, OLDPRT, PRLCD, PRST, PRSTC, PRVAR
object
PREDV
Type:
Command
Description: Predicted y-Value Command: Returns the predicted dependent-variable value ydependent, based on
the independent-variable value xindependent, the currently selected statistical model, and the current
regression coefficients in the reserved variable ΣPAR.
PREDV is the same as PREDY. See PREDY.
Access:
…µ PREDV
Input/Output:
Level 1/Argument 1
xindependent
See also:
PREDY
PREDX
Type:
Command
3-126 Full Command and Function Reference
Level 1/Item 1
→
ydependent
Description: Predicted x-Value Command: Returns the predicted independent-variable value xindependent, based
on the dependent-variable value ydependent, the currently selected statistical model, and the current
regression coefficients in the reserved variable ΣPAR.
The value is predicted using the regression coefficients most recently computed with LR and
stored in the reserved variable ΣPAR. For the linear statistical model, the equation used is this:
ydependent = (mxindependent) + b
where m is the slope (the third element in ΣPAR) and b is the intercept (the fourth element in
ΣPAR).
For the other statistical models, the equations used by PREDX are listed in the LR entry.
If PREDX is executed without having previously generated regression coefficients in ΣPAR, a
default value of zero is used for both regression coefficients, and an error results.
Access:
…µ PREDX
Input/Output:
Level 1/Argument 1
ydependent
See also:
Level 1/Item 1
→
xindependent
COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, LR, PREDY, PWRFIT, XCOL,
YCOL
PREDY
Type:
Command
Description: Predicted y-Value Command: Returns the predicted dependent-variable value ydependent, based on
the independent-variable value xindependent, the currently selected statistical model, and the current
regression coefficients in the reserved variable ΣPAR.
The value is predicted using the regression coefficients most recently computed with LR and
stored in the reserved variable ΣPAR. For the linear statistical model, the equation used is this:
ydependent = (mxindependent) + b
where m is the slope (the third element in ΣPAR) and b is the intercept (the fourth element in
ΣPAR).
For the other statistical models, the equations used by PREDY are listed in the LR entry.
If PREDY is executed without having previously generated regression coefficients in ΣPAR, a
default value of zero is used for both regression coefficients–in this case PREDY will return 0
for statistical models LINFIT and LOGFIT, and error for statistical models EXPFIT and
PWRFIT.
Access:
…µ PREDY
Input/Output:
Level 1/Argument 1
xindependent
See also:
PREVAL
CAS:
Level 1/Item 1
→
ydependent
COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, LR, PREDX, PWRFIT, XCOL,
YCOL
Return difference between values of a function at two specified values of the current variable.
PREVPRIME
CAS:
Given an integer, find the closest prime number smaller than the integer.
Full Command and Function Reference 3-127
PRLCD
Type:
Command
Description: Print LCD Command: Prints a pixel-by-pixel image of the current display (excluding the
annunciators).
The width of the printed image of characters in the display is narrower using PRLCD than using
a print command such as PR1. The difference results from the spacing between characters. On
the display there is a single blank column between characters, and PRLCD prints this spacing.
Print commands such as PR1 print two blank columns between adjacent characters.
Access:
…µ PRLCD
Flags:
I/O Device (-33), Printing Device (-34), Double-spaced Printing (-37), Linefeed (-38). Flag -38
must be clear. If flag -34 is set, flag -33 must be clear.
Input/Output: None
See also:
CR, DELAY, OLDPRT, PRST, PRSTC, PRVAR, PR1
PROMPT
Type:
Command
Description: Prompt Command: Displays the contents of “prompt” in the status area, and halts program
execution.
( °is the left-shift of the Nkey).
Access:
!°LIN LPROMPT
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
“prompt”
CONT, DISP, FREEZE, HALT, INFORM, INPUT, MSGBOX
PROMPTSTO
Type:
Command
Description: Prompt Command: Creates a variable with the name supplied as an argument, prompts for a
value, and stores the value you enter in the variable.
Access:
…µPROMPTSTO
Input/Output:
Level 1/Argument 1
“global”
See also:
Level 1/Item 1
→
PROMPT, STO
PROOT
Type:
Command
Description: Polynomial Roots Command: Returns all roots of an n-degree polynomial having real or complex
coefficients.
For an nth-order polynomial, the argument must be a real or complex array of length n + 1
containing the coefficients listed from highest order to lowest. The result is a real or complex
vector of length n containing the computed roots.
PROOT interprets leading coefficients of zero in a limiting sense. As a leading coefficient
approaches zero, a root of the polynomial approaches infinity: therefore, if flag –22 is clear (the
default), PROOT reports an Infinite Result error if a leading coefficient is zero. If flag –22 is set,
PROOT returns a root of (MAXREAL,0) for each leading zero in an array containing real
coefficients, and a root of (MAXREAL,MAXREAL) for each leading zero in an array containing
complex coefficients.
Access:
!ÞPOLYNOMIAL LLPROOT
(Þis the left-shift of the 1key).
3-128 Full Command and Function Reference
Flags:
Infinite Result Exception (-22)
Input/Output:
Level 1/Argument 1
[ array ]coefficients
See also:
Level 1/Item 1
→
[ array ]roots
PCOEF, PEVAL
PROPFRAC
CAS:
Split an improper fraction, a ratio of integers or expressions, into an integer part and a fraction
part.
PRST
Type:
Command
Description: Print Stack Command: Prints all objects in the stack, starting with the object on the highest level.
Objects are printed in multiline printer format. See the PR1 entry for a description of multiline
printer format.
Access:
…µ PRST
Flags:
I/O Device (-33), Printing Device (-34), Double-spaced Printing (-37), Linefeed (-38). If flag -34
is set, flag -33 must be clear. Generally, flag -38 should be clear.
Input/Output: None
See also:
CR, DELAY, OLDPRT, PRLCD, PRSTC, PRVAR, PR1
PRSTC
Type:
Command
Description: Print Stack (Compact) Command: Prints in compact form all objects in the stack, starting with
the object on the highest level.
Compact printer format is the same as compact display format. Multiline objects are truncated
and appear on one line only.
Access:
…µ PRSTC
Flags:
I/O Device (-33), Printing Device (-34), Double-spaced Printing (-37), Linefeed (-38)
Input/Output: None
See also:
CR, DELAY, OLDPRT, PRLCD, PRST, PRVAR, PR1
PRVAR
Type:
Command
Description: Print Variable Command: Searches the current directory path or port for the specified variables
and prints the name and contents of each variable.
Objects are printed in multiline printer format. See the PR1 entry for a description of multiline
printer format.
Access:
…µ PRVAR
Flags:
I/O Device (-33), Printing Device (-34), Double-spaced Printing (-37), Linefeed (-38). If flag -34
is set, flag -33 must be clear. Generally, flag -38 should be clear.
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'name'
→
{ name1 name2 ... }
→
:nport : 'global'
CR, DELAY, OLDPRT, PR1, PRLCD, PRST, PRSTC
Full Command and Function Reference 3-129
PSDEV
Type:
Command
Description: Population Standard Deviation Command: Calculates the population standard deviation of each
of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT).
PSDEV returns a vector of m real numbers, or a single real number if m = 1. The population
standard deviation is computed using this formula:
n
2
1
--- ∑ ( x k – x )
nk = 1
where xk is the kth coordinate value in a column, x is the mean of the data in this column, and n
is the number of data points.
Access:
…µ PSDEV
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xpsdev
→
[ xpsdev1 xpsdev2 ... xpsdevm }
MEAN, PCOV, PVAR, SDEV, TOT, VAR
PSI
Type:
Function
Description: Calculates the polygamma function, the nth derivative of the digamma function, at a point a.
PSI(a, 0) is equivalent to Psi(a).
Access:
Input:
Output:
Flags:
See also:
!´L SPECIAL
Level 2/Argument 1: A real or complex expression specifying the point a.
Level 1/Argument 2: A non-negative integer, n.
The value of the polygamma function PSI(a, n).
Exact mode must be set (flag –105 clear), and
numeric mode must not be set (flag –3 clear), if symbolic results are wanted.
Complex mode must be set (flag –103 set) if a complex value is used for point a.
Psi
Psi
Type:
Function
Description: Calculates the digamma function at a point a. The digamma function is the derivative of the
natural logarithm (ln) of the gamma function. The function can be represented as follows:
′
Γ (z)
d
Ψ ( z ) = ----- ( ln Γ ( z )) = -----------Γ(z)
dz
Access:
Input:
Output:
Flags:
!´ L SPECIAL
A real or complex expression specifying the point a.
The digamma function at the specified point.
Exact mode must be set (flag –105 clear), and
numeric mode must not be set (flag –3 clear), if symbolic results are wanted. For example, with
these settings, Psi(3) evaluates to the symbolic value Psi(3).
Complex mode must be set (flag –103 set) if a complex value is used for point a.
See also:
PSI
PTAYL
CAS:
Return the Taylor polynomial at x = a for given a and a specified polynomial.
3-130 Full Command and Function Reference
PURGE
Type:
Command
Description: Purge Command: Purges the named variables or empty subdirectories from the current directory.
PURGE executed in a program does not save its argument for recovery by LASTARG.
To empty a named directory before purging it, use PGDIR.
To help prepare a list of variables for purging, use VARS.
Purging PICT replaces the current graphics object with a 0 × 0 graphics object.
If a list of objects (with global names, backup objects, library objects, or PICT) for purging
contains an invalid object, then the objects preceding the invalid object are purged, and the error
Bad Argument Type occurs.
To purge a library or backup object, tag the library number or backup name with the appropriate
port number (:nport), which must be in the range from 0 to 3. For a backup object, the port
number can be replaced with the wildcard character &, in which case the hp49g+/hp48gII will
search ports 0 through 2, and then main memory for the named backup object.
A library object must be detached before it can be purged from the HOME directory.
Neither a library object nor a backup object can be purged if it is currently “referenced”
internally by stack pointers (such as an object on the stack, in a local variable, on the LAST stack,
or on an internal return stack). This produces the error Object in Use. To avoid these
restrictions, use NEWOB before purging. (See NEWOB.)
Access:
!°MEMORY PURGE
( °is the left-shift of the Nkey).
I PURGE
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'global'
→
{ global1 ... globaln }
→
PICT
→
:nport :namebackup
→
:nport :nlibrary
CLEAR, CLVAR, NEWOB, PGDIR
→
PUSH
Type:
Command
Description: Saves the current status of the flags, and the current directory path. This allows the user to
change the flags or the directory path, then restore them all with the command POP. PUSH is
equivalent to saving the results of the commands RCLF and PATH, but it saves them in a stack
from which the most recently saved values are recovered by POP, with no need to use named
variables. The flags and the path are stored in the CASDIR directory, as a list of lists, in the
variable ENVSTACK.
Access:
Input:
Output:
See also:
…µPUSH
None.
Item 1: In Algebraic mode the command returns NOVAL.
POP
PUT
Type:
Command
Full Command and Function Reference 3-131
Description: Put Element Command: Replaces the object at a specified position (second input) in a specified
array or list (first input) with a specifed object (third input). If the array or list is unnamed,
returns the new array or list.
For matrices, nposition counts in row order.
Access:
!°LIST ELEMENTS PUT
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]1
nposition
zput
→
[[ matrix ]]2
[[ matrix ]]1
{ nrow mcol }
zput
→
[[ matrix ]]2
'namematrix'
nposition
zput
→
'namematrix'
{ nrow mcol }
zput
→
[ vector ]1
nposition
zput
→
[ vector ]2
[ vector ]1
{ nposition }
zput
→
[ vector ]2
'namevector'
nposition
zput
→
'namevector'
{ nposition }
zput
→
{ list }1
nposition
objput
→
{ list }2
{ list }1
{ nposition }
objput
→
{ list }2
'namelist'
nposition
objput
→
{ nposition }
objput
→
'namelist'
GET, GETI, PUTI
Level 1/Item 1
PUTI
Type:
Command
Description: Put and Increment Index Command: Replaces the object at a specified position (second input) in
a specified array or list (first input) with a specifed object (third input), returning a new array or
list together with the next position in the array or list.
For matrices, the position is incremented in row order.
Unlike PUT, PUTI returns a named array or list. This enables a subsequent execution of PUTI at
the next position of a named array or list.
Access:
!°LIST ELEMENTS PUTI
( °is the left-shift of the Nkey).
Flags:
Index Wrap Inidicator (-64)
3-132 Full Command and Function Reference
Input/Output:
L3/A1
L2/A2
L1/A3
L2/I1
L1/I2
[[ matrix ]]1
nposition1
zput
→
[[ matrix ]]2
nposition2
[[ matrix ]]1
{ nrow mcol }1
zput
→
[[ matrix ]]2
{ nrow mcol }2
'namematrix'
nposition1
zput
→
'namematrix'
nposition2
'namematrix'
{ nrow mcol }1
zput
→
'namematrix'
{ nrow mcol }2
[ vector ]1
nposition1
zput
→
[ vector ]2
nposition2
[ vector ]1
{ nposition1 }
zput
→
[ vector ]2
{ nposition2 }
'namevector'
nposition1
zput
→
'namevector'
nposition2
'namevector'
{ nposition1 }
zput
→
'namevector'
{ nposition2 }
{ list }1
nposition1
objput
→
{ list }2
nposition2
{ list }1
{ nposition1 }
objput
→
{ list }2
{ nposition2 }
'namelist'
nposition1
objput
→
'namelist'
nposition2
{ nposition1 }
objput
→
'namelist'
{ nposition2 }
'namelist'
L = Level; A = Argument; I = item
See also:
GET, GETI, PUT
PVAR
Type:
Command
Description: Population Variance Command: Calculates the population variance of the coordinate values in
each of the m columns in the current statistics matrix (ΣDAT).
The population variance (equal to the square of the population standard deviation) is returned as
a vector of m real numbers, or as a single real number if m = 1. The population variances are
computed using this formula:
n
2
1
--- ∑ ( x k – x )
nk = 1
where xk is the kth coordinate value in a column, x is the mean of the data in this column, and n
is the number of data points.
Access:
…µ PVAR
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xpvariance
→
[ xpvariance1, ...,xpvariancem ]
MEAN, PCOV, PSDEV, SDEV, VAR
PVARS
Type:
Command
Description: Port-Variables Command: Returns a list of the backup objects (:nport:name) and the library objects
(:nport:nlibrary) in the specified port. Also returns the available memory size (RAM).
The port number, nport, must be in the range from 0 to 2.
If nport = 0, then memory is bytes of available main RAM; otherwise memory is bytes of available
RAM in the specified port.
Access:
…µPVARS
Full Command and Function Reference 3-133
Input/Output:
Level 1/Argument 1
See also:
Level 2/Item 1
Level 1/Item 2
nport
→
{ :nport :namebackup ... }
memory
nport
→
{ :nport :nlibrary ... }
memory
PVARS, VARS
PVIEW
Type:
Command
Description: PICT View Command: Displays PICT with the specified coordinate at the upper left corner of
the graphics display.
PICT must fill the entire display on execution of PVIEW. Thus, if a position other than the
upper left corner of PICT is specified, PICT must be large enough to fill a rectangle that extends
131 pixels to the right and 80 pixes down on the hp49g+ (64 pixels down on the hp48gII).
If PVIEW is executed from a program with a coordinate argument (versus an empty list), the
graphics display persists only until the keyboard is ready for input (for example, until the end of
program execution). However, the FREEZE command freezes the display until a key is pressed.
If PVIEW is executed with an empty list argument, PICT is centred in the graphics display with
scrolling mode activated. In this case, the graphics display persists until −is pressed.
PVIEW does not activate the graphics cursor or the Picture menu. To activate the graphics
cursor and Picture menu, execute PICTURE.
Access:
!°LPICT L PVIEW
( °is the left-shift of the Nkey).
!°LOUT PVIEW
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
(x,y)
→
{ #n, #m }
→
{}
→
FREEZE, PICTURE, TEXT
PWRFIT
Type:
Command
Description: Power Curve Fit Command: Stores PWRFIT as the fifth parameter in the reserved variable
ΣPAR, indicating that subsequent executions of LR are to use the power curve fitting model.
LINFIT is the default specification in ΣPAR.
Access:
…µPWRFIT
Input/Output: None
See also:
BESTFIT, EXPFIT, LINFIT, LOGFIT, LR
PX→C
Type:
Command
Description: Pixel to Complex Command: Converts the specified pixel coordinates to user-unit coordinates.
The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the
reserved variable PPAR. The coordinates correspond to the geometrical center of the pixel.
Access:
!°LPICT LPX→C
( °is the left-shift of the Nkey).
3-134 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
{ #n #m }
See also:
Level 1/Item 1
→
(x,y)
C→PX
→Q
Type:
Command
Description: To Quotient Command: Returns a rational form of the argument.
The rational result is a “best guess”, since there might be more than one rational expression
consistent with the argument. →Q finds a quotient of integers that agrees with the argument to
within the number of decimal places specified by the display format mode.
→Q also acts on numbers that are part of algebraic expressions or equations.
Access:
„Ú REWRITE L→Q
Flags:
Number Display Format (-45 to -50)
Input/Output:
(Ú is the left-shift of the 6key).
Level 1/Argument 1
See also:
→Q π
Type:
Level 1/Item 1
x
→
'a/b'
(x,y)
→
'a/b + c/d*i'
'symb1'
→
'symb2'
→Qπ, /
Command
Description: To Quotient Times π Command: Returns a rational form of the argument, or a rational form of
the argument with π, square roots, natural logs, and exponentials factored out, whichever yields
the smaller denominator.
The rational result is a “best guess”, since there might be more than one rational expression
consistent with the argument. →Qπ finds a quotient of integers that agrees with the argument to
the number of decimal places specified by the display format mode.
→Qπ also acts on numbers that are part of algebraic expressions or equations.
For a complex argument, the real or imaginary part (or both) can have π as a factor.
Access:
„Ú REWRITE L →Qπ
(Ú is the left-shift of the 6key).
Flags:
Number Display Format (-45 to -50)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
'a/b*π'
x
→
'a/b'
'symb1'
→
'symb2'
(x,y)
→
'a/b*π + c/d*π*i'
(x,y)
→
'a/b + c/d*i'
→Q, /, π
qr
Type:
Command
Description: qr Factorization of a square Matrix Command: Returns the qr factorization of an n × n matrix.
Full Command and Function Reference 3-135
qr factors an n × n matrix A into two matrices:
• Q is an n× m orthogonal matrix.
• R is an n × n triangular matrix.
Where A = Q × R.
Access:
!Ø FACTORIZATION qr
(Ø is the left-shift of the 5key).
Input/Output:
Level 1/Argument 1
[[ matrix ]]A
See also:
Level 2/Item 1
Level 1/Item 2
[[ matrix ]]Q
[[ matrix ]]R
→
LQ, LSQ
QR
Type:
Command
Description: QR Factorization of a Matrix Command: Returns the QR factorization of an m × n matrix.
QR factors an m × n matrix A into three matrices:
• Q is an m × m orthogonal matrix.
• R is an m × n upper trapezoidal matrix.
• P is a n × n permutation matrix.
Where A × P = Q × R.
Access:
!Ø FACTORIZATION QR
( Ø is the left-shift of the 5key).
!´ MATRIX FACTORS QR
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
[[ matrix ]]A
See also:
→
Level 3/Item 1
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]Q
[[ matrix ]]R
[[ matrix ]]P
LQ, LSQ
QUAD
Type:
Command
Description: Solve Quadratic Equation Command: This command is identical to the computer algebra
command SOLVE, and is included for backward compatibility with the HP 48G.
Access:
…µ QUAD
Flags:
Principal Solution (-1)
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
→
See also:
'symb1'
'global'
COLCT, EXPAN, ISOL, SHOW, SOLVE
QUOT
CAS:
Return the quotient part of the Euclidean division of two polynomials.
'symb2'
QUOTE
Type:
Function
Description: Quote Argument Function: Returns its argument unevaluated.
When an algebraic expression is evaluated, the arguments to a function in the expression are
evaluated before the function. For example, when SIN(X) is evaluated, the name X is evaluated
first, and the result is placed on the stack as the argument for SIN.
This process creates a problem for functions that require symbolic arguments. For example, the
integration function requires as one of its arguments a name specifying the variable of
3-136 Full Command and Function Reference
integration. If evaluating an integral expression caused the name to be evaluated, the result of
evaluation would be left on the stack for the integral, rather than the name itself. To avoid this
problem, the hp49g+/48gII automatically (and invisibly) quotes such arguments. When the
quoted argument is evaluated, the unquoted argument is returned.
If a user-defined function takes symbolic arguments, quote the arguments using QUOTE.
Access:
…µQUOTE
Input/Output:
Level 1/Argument 1
obj
See also:
APPLY, | (Where)
QXA
CAS:
Express a quadratic form in matrix form.
Level 1/Item 1
→
obj
RAD
Type:
Command
Description: Radians Mode Command: Sets Radians angle mode.
RAD sets flag –17 and clears flag –18, and displays the RAD annunciator.
In Radians angle mode, real-number arguments that represent angles are interpreted as radians,
and real-number results that represent angles are expressed in radians.
Access:
„& H ANGLE RAD
„°L MODES ANGLE RAD
( °is the left-shift of the Nkey).
Input/Output: None
See also:
DEG, GRAD
RAND
Type:
Command
Description: Random Number Command: Returns a pseudo-random number generated using a seed value,
and updates the seed value.
The hp49g+/hp48gII uses a linear congruential method and a seed value to generate a random
number xrandom in the range 0 ≤ x < 1. Each succeeding execution of RAND returns a value
computed from a seed value based upon the previous RAND value. (Use RDZ to change the
seed.)
Access:
!´L PROBABILITY RAND
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
xrandom
COMB, PERM RDZ, !
RANK
Type:
Command
Description: Matrix Rank Command: Returns the rank of a rectangular matrix.
Rank is computed by calculating the singular values of the matrix and counting the number of
non-negligible values. If all computed singular values are zero, RANK returns zero. Otherwise
RANK consults flag –54 as follows:
• If flag –54 is clear (the default), RANK counts all computed singular values that are less than
or equal to 1.E–14 times the largest computed singular value.
• If flag –54 is set, RANK counts all nonzero computed singular values.
Full Command and Function Reference 3-137
Access:
!Ø
OPERATIONS L RANK
( Ø is the left-shift of the 5key).
!´ MATRIX NORMALIZE L RANK
Flags:
Singular Value (-54)
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
[[ matrix ]]
See also:
Level 1/Item 1
→
Nrank
LQ, LSQ, QR
RANM
Type:
Command
Description: Random Matrix Command: Returns a matrix of specified dimensions that contains random
integers in the range –9 through 9.
The probability of a particular nonzero digit occurring is 0.05; the probability of 0 occurring is
0.1.
( Ø is the left-shift of the 5key).
Access:
!Ø CREATE LLRANM
!´MATRIX MAKE RANM
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
{mn}
→
[[ random matrix ]]m×n
[[ matrix ]]m×n
→
[[ random matrix ]]m×n
RAND, RDZ
RATIO
Type:
Function
Description: Prefix Divide Function: Prefix form of / (divide).
RATIO is identical to / (divide), except that, in algebraic syntax, RATIO is a prefix function,
while / is an infix function. For example, RATIO(A,2) is equivalent to A/2.
Access:
…µ RATIO
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
z1
[ array ]
[ array ]
z
'symb'
'symb1'
#n1
n1
#n1
x_unit1
x
x_unit
'symb'
x_unit
z2
{[ matrix ]]
z
'symb'
z
'symb2'
n2
#n2
#n2
y_unit2
y_unit
y
x_unit
'symb'
/
3-138 Full Command and Function Reference
Level 1/Item 1
→
→
→
→
→
→
→
→
→
→
→
→
→
→
z1/z2
[[ array × matrix–1]]
[ array/z ]
'z/symb'
'symb/z'
'symb1/symb2'
#n3
#n3
#n3
(x/y)_unit1/unit2
(x/y)_1/unit
(x/y)_unit
'symb/x_unit'
'x_unit/symb'
RCEQ
Type:
Command
Description: Recall from EQ Command: Returns the unevaluated contents of the reserved variable EQ from
the current directory.
To recall the contents of EQ from a parent directory (when EQ doesn't exist in the current
directory) evaluate the name EQ.
Access:
…µ RCEQ (or …EQ after pressing J)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
objEQ
STEQ
RCI
Type:
Command
Description: Multiply Row by Constant Command: Multiplies row n of a matrix (or element n of a vector) by
a constant xfactor, and returns the modified matrix.
RCI rounds the row number to the nearest integer, and treats vector arguments as column
vectors.
Access:
!Ø CREATE ROW RCI
( Ø is the left-shift of the 5key).
!´ MATRIX ROW RCI
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
[[ matrix ]]1
xfactor
nrow number
→
[[ matrix ]]3
[ vector ]1
xfactor
nelement number
→
[ vector ]2
RCIJ
RCIJ
Type:
Command
Description: Add Multiplied Row Command: Multiplies row i of a matrix by a constant xfactor, adds this
product to row j of the matrix, and returns the modified matrix; or multiplies element i of a
vector by a constant xfactor, adds this product to element j of the vector, and returns the modified
vector. RCIJ rounds the row numbers to the nearest integer, and treats vector arguments as
column vectors.
Access:
!Ø CREATE ROW RCIJ
( Ø is the left-shift of the 5key).
!´ MATRIX ROW RCIJ
( ´ is the left-shift of the Pkey).
Input/Output:
Level 4/Argument 1 Level 3/Argument 2 Level 2/Argument 3 Level 1/Argument 4
See also:
[[ matrix ]]1
xfactor
nrow i
nrow j
[ vector ]1
xfactor
nelement i
nelement j
Level 1/Item 1
→
[[ matrix ]]2
→
[ vector ]2
RCI
RCL
Type:
Command Operation
Description: Recall Command: Returns the unevaluated contents of a specified variable.
RCL searches the entire current path, starting with the current directory. To search a different
path, specify { path name }, where path is the new path to the variable name. The path subdirectory
does not become the current subdirectory (unlike EVAL).
Full Command and Function Reference 3-139
To recall a library or backup object, tag the library number or backup name with the appropriate
port number (nport), which must be an integer in the range 0 to 3. Recalling a backup object
brings a copy of its contents to the stack, not the entire backup object.
To search for a backup object, replace the port number with the wildcard character &, in which
case the hp49g+/hp48gII will search (in order) ports 0 through 3, and the main memory for the
named backup object.
You can specify a port (that is, nport ) in one of two ways:
• H, 0, 1, 2, or 3
• H, R, E, F, or SD
In each case, the ports are home, RAM, extended RAM, flash memory, and the plug-in SD card
slot, respectively.
Access:
!©
Input/Output:
( ©is the left-shift of the Kkey).
Level 1/Argument 1
See also:
Level 1/Item 1
'obj'
→
obj
PICT
→
grob
:nport :nlibrary
→
obj
:nport :namebackup
→
obj
:nport :{ path }
→
obj
STO
RCLALARM
Type:
Command
Description: Recall Alarm Command: Recalls a specified alarm.
objaction is the alarm execution action. If an execution action was not specified, objaction defaults to
an empty string.
xrepeat is the repeat interval in clock ticks, where 1 clock tick equals 1/8192 second. If a repeat
interval was not specified, the default is 0.
Access:
…ÓTools ALRM RCLALARM
( Ó is the right-shift of the 9 key).
…&9ALRM RCLALARM
„°LLTIME ALRM RCLALARM
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
nindex
DELALARM, FINDALARM, STOALARM
Level 1/Item 1
→
{ date time objaction xrepeat }
RCLF
Type:
Command
Description: Recall Flags Command: Returns a list of integers representing the states of the system and user
flags, respectively.
A bit with value 1 indicates that the corresponding flag is set; a bit with value 0 indicates that the
corresponding flag is clear. The rightmost (least significant) bit of #nsystem and #nuser indicate the
states of system flag –1 and user flag +1, respectively.
Used with STOF, RCLF lets a program that alters the state of a flag or flags during program
execution preserve the pre-program-execution flag status.
3-140 Full Command and Function Reference
Access:
„&HFLAG L RCLF
„°LMODES FLAG L RCLF
Flags:
Binary Integer Wordsize (-5 through -10)
Input/Output:
( °is the left-shift of the Nkey).
Level 1/Argument 1
Level 1/Item 1
→
See also:
{ #nsystem #nuser #nsystem2 #nuser2 }
STOF
RCLKEYS
Type:
Command
Description: Recall Key Assignments Command: Returns the current user key assignments. This includes an S
if the standard definitions are active (not suppressed) for those keys without user key
assignments.
The argument xkey is a real number of the form rc.p specifying the key by its row number r, its
column number c, and its plane (shift) p. (For a definition of plane, see the entry for ASN.)
Access:
„&HKEYS RCLKEYS
„°LMODES KEYS RCLKEYS
( °is the left-shift of the Nkey).
Flags:
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
{ obj1, xkey 1, ... ,objn, xkey n }
→
{ S, obj1, xkey 1, ... objn, xkey n }
ASN, DELKEYS, STOKEYS
RCLMENU
Type:
Command
Description: Recall Menu Number Command: Returns the menu number of the currently displayed menu.
xmenu has the form mm.pp, where mm is the menu number and pp is the page of the menu.
Executing RCLMENU when the current menu is a user-defined menu (build by TMENU)
returns 0.01 (in 2 Fix mode), indicating “Last menu”.
Access:
„&HMENU RCLMENU
„°LMODES MENU RCLMENU
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
MENU, TMENU
RCLVX
CAS:
Return the name stored in the current CAS variable.
xmenu
RCLΣ
Type:
Command
Description: Recall Sigma Command: Returns the current statistical matrix (the contents of reserved variable
ΣDAT) from the current directory.
To recall ΣDAT from the parent directory (when ΣDAT doesn't exist in the current directory),
evaluate the name ΣDAT.
Full Command and Function Reference 3-141
Access:
…µ RCLΣ (or …ΣDAT after pressing J)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
obj
CLΣ, STOΣ, Σ+, Σ–
RCWS
Type:
Command
Description: Recall Wordsize Command: Returns the current wordsize in bits (1 through 64).
Access:
…ãL RCWS
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
n
BIN, DEC, HEX, OCT, STWS
RDM
Type:
Command
Description: Redimension Array Command: Rearranges the elements of the argument according to specified
dimensions.
If the list contains a single number nelements, the result is an n-element vector. If the list contains
two numbers nrows and mcols, the result is an n × m matrix.
Elements taken from the argument vector or matrix preserve the same row order in the resulting
vector or matrix. If the result is dimensioned to contain fewer elements than the argument vector
or matrix, excess elements from the argument vector or matrix at the end of the row order are
discarded. If the result is dimensioned to contain more elements than the argument vector or
matrix, the additional elements in the result at the end of the row order are filled with zeros.
If the argument vector or matrix is specified by global, the result replaces the argument as the
contents of the variable.
Access:
!Ø CREATE LLRDM
( Ø is the left-shift of the 5key).
!´MATRIX MAKE RDM
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
[ vector ]1
{ nelements }
→
[ vector ]2
[ vector ]
{ nrows, mcols }
→
[[ matrix ]]
[[ matrix ]]
{ nelements }
→
[ vector ]
[[ matrix ]]1
{ nrows, mcols }
→
[[ matrix ]]2
'global'
{ nelements }
→
'global'
{ nrows, mcols }
→
TRN
RDZ
Type:
Command
Description: Randomize Command: Uses a real number xseed as a seed for the RAND command.
If the argument is 0, a random value based on the system clock is used as the seed.
3-142 Full Command and Function Reference
Access:
!´LPROBABILITY RDZ
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
xseed
See also:
Level 1/Item 1
→
COMB, PERM, RAND, !
RE
Type:
Function
Description: Real Part Function: Returns the real part of the argument.
If the argument is a vector or matrix, RE returns a real array, the elements of which are equal to
the real parts of the corresponding elements of the argument array.
Access:
…ßL RE
(ßis the right-shift of the 1key).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
x
x_unit
→
x
(x,y)
→
x
[ R-array ]
→
[ R-array ]
[ C-array ]
→
[ R-array ]
'symb'
→
'RE(symb')
C→R, IM, R→C
RECN
Type:
Command
Description: Receive Renamed Object Command: Prepares the hp49g+/hp48gII to receive a file from
another Kermit server device, and to store the file in a specified variable.
RECN is identical to RECV except that the name under which the received data is stored is
specified.
Access:
…µ RECN
Flags:
I/O Device flag (-33), I/O Data Format (-35), RECV Overwrite (-36), I/O Messages (-39)
Input/Output:
Level 1/Argument 1
'name'
See also:
Level 1/Item 1
→
→
“name”
BAUD, CKSM, CLOSEIO, FINISH, KERRM, KGET, PARITY, RECV, SEND, SERVER,
TRANSIO
RECT
Type:
Command
Description: Rectangular Mode Command: Sets Rectangular coordinate mode.
RECT clears flags –15 and –16.
In Rectangular mode, vectors are displayed as rectangular components. Therefore, a 3D vector
would appear as [X Y Z].
Full Command and Function Reference 3-143
Access:
„&H ANGLE RECT
„´VECTOR L RECT
( ´is the left-shift of the Pkey).
„°L MODES ANGLE RECT
Input/Output: None
See also:
CYLIN, SPHERE
( °is the left-shift of the Nkey).
RECV
Type:
Command
Description: Receive Object Command: Instructs the hp49g+/hp48gII to look for a named file from another
Kermit server device. The received file is stored in a variable named by the sender.
Since the hp49g+/hp48gII does not normally look for incoming Kermit files, you must use
RECV to tell it to do so.
Access:
…µ RECV
Flags:
I/O Device flag (-33), I/O Data Format (-35), RECV Overwrite (-36), I/O Messages (-39)
Input/Output: None
See also:
BAUD, CKSM, FINISH, KGET, PARITY, RECN, SEND, SERVER, TRANSIO
REF
CAS:
Reduce a matrix to echelon form. This is a subdiagonal reduction (Gauss, not Gauss-Jordan).
REMAINDER
CAS:
Return the remainder of the Euclidean division of two polynomials.
RENAME
Type:
Command
Description: Rename Object Command: Renames an object to the name that you specify.
Access:
…µ RENAME
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
new 'name'
old 'name'
Level 1/Item 1
→
COPY
REORDER
CAS:
Rewrite a polynomial expression in increasing or decreasing order of powers.
REPEAT
Type:
Command
Description: REPEAT Command: Starts loop clause in WHILE … REPEAT … END indefinite loop
structure.
See the WHILE entry for more information.
Access:
!°BRANCH WHILE REPEAT
( °is the left-shift of the Nkey).
Input/Output: None
See also:
END, WHILE
REPL
Type:
Command
Description: Replace Command: Replaces a portion of the target object (first input) with a specified object
(third input), beginning at a specified position (second input).
3-144 Full Command and Function Reference
For arrays, nposition counts in row order. For matrices, nposition specifies the new location of the
upper left-hand element of the replacement matrix.
For graphics objects, the upper left corner of grob1 is positioned at the user-unit or pixel
coordinates (x,y) or { #n #m }. From there, it overwrites a rectangular portion of grobtarget or
PICT. If grob1 extends past grobtarget or PICT in either direction, it is truncated in that direction. If
the specified coordinate is not on the target graphics object, the target graphics object does not
change.
Access:
!°LIST REPL
Input/Output:
See also:
( °is the left-shift of the Nkey).
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
[[ matrix ]]1
nposition
[[ matrix ]]2
→
[[ matrix ]]3
[[ matrix ]]1
{ nrow, ncolumn }
[[ matrix ]]2
→
[[ matrix ]]3
[ vector ]1
nposition
[ vector ]2
→
[ vector ]3
{ listtarget }
nposition
{ list1 }
→
{ listresult }
“stringtarget”
nposition
“string1”
→
“stringresult”
grobtarget
(#n, #m)
grob1
→
grobresult
grobtarget
(x,y)
grob1
→
grobresult
PICT
(#n, #m)
grob1
→
PICT
(x,y)
grob1
CHR, GOR, GXOR, NUM, POS, SIZE, SUB
→
RES
Type:
Command
Description: Resolution Command: Specifies the resolution of mathematical and statistical plots, where the
resolution is the interval between values of the independent variable used to generate the plot.
A real number ninterval specifies the interval in user units. A binary integer #ninterval specifies the
interval in pixels.
The resolution is stored as the fourth item in PPAR, with default value 0. The interpretation of
the default value is summarized in the following table.
Plot Type
Default Interval
BAR
10 pixels (bar width = 10 pixel columns)
DIFFEQ
unlimited: step size is not constrained
FUNCTION
2 pixels (plots a point in every other column of pixels)
CONIC
2 pixels (plots a point in every other column of pixels)
TRUTH
2 pixels (plots a point in every other column of pixels)
GRIDMAP
RES does not apply
HISTOGRAM
10 pixels (bin width = 10 pixel columns)
PARAMETRIC
[independent variable range in user units]/130
PARSURFACE
RES does not apply
Full Command and Function Reference 3-145
Plot Type
Default Interval
PCONTOUR
RES does not apply
POLAR
2°, 2 grads, or π/90 radians
SCATTER
RES does not apply
SLOPEFIELD
RES does not apply
WIREFRAME
RES does not apply
YSLICE
2 pixels (plots a point in every other column of pixels)
Access:
…µ RES
Input/Output:
Level 1/Argument 1
ninterval
See also:
Level 1/Item 1
→
→
#ninterval
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME,
YSLICE
RESTORE
Type:
Command
Description: Restore HOME Command: Replaces the current HOME directory with the specified backup
copy (:nport:namebackup) previously created by ARCHIVE.
The specified port number must be in the range 0 to 3.
To restore a HOME directory that was saved on a remote system using :IO:name ARCHIVE, put
the backup object itself on the stack, execute RESTORE and then execute a warm start.
Access:
„°MEM LRESTORE
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
:nport :namebackup
→
backup
→
ARCHIVE
RESULTANT
CAS:
Return the resultant of two polynomials, that is, the determinant of their Sylvester matrix.
REVLIST
Type:
Command
Description: Reverse List Command: Reverses the order of the elements in a list.
Access:
!°LIST PROCEDURES REVLIST
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
{ objn ... obj1 }
See also:
SORT
3-146 Full Command and Function Reference
Level 1/Item 1
→
{ obj1 ... objn }
REWRITE
CAS:
Display a menu or list of CAS operations that rewrite expressions.
RISCH
CAS:
Perform symbolic integration on a function using the Risch algorithm.
RKF
Type:
Command
Description: Solve for Initial Values (Runge–Kutta–Fehlberg) Command: Computes the solution to an initial
value problem for a differential equation, using the Runge-Kutta-Fehlberg (4,5) method.
RKF solves y'(t) = f(t,y), where y(t0) = y0. The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• xtol sets the absolute error tolerance. If a list is used, the first value is the absolute error
tolerance and the second value is the initial candidate step size.
• xTfinal specifies the final value of the independent variable.
RKF repeatedly calls RKFSTEP as it steps from the initial value to xTfinal.
Access:
…µ RKF
Input/Output:
L3/A1
L2/A2
L1/A3
{ list }
xtol
xT final
{ list }
{ xtol xhstep }
xT final
L2/I1
L1/I2
→
{ list }
xtol
→
{ list }
xtol
L = Level; A = Argument; I = item
See also:
RKFERR, RKFSTEP, RRK, RRKSTEP, RSBERR
RKFERR
Type:
Command
Description: Error Estimate for Runge–Kutta–Fehlberg Method Command: Returns the absolute error
estimate for a given step h when solving an initial value problem for a differential equation.
The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• h is a real number that specifies the step.
• ydelta displays the change in solution for the specified step.
• error displays the absolute error for that step. A zero error indicates that the Runge–Kutta–
Fehlberg method failed and that Euler's method was used instead.
The absolute error is the absolute value of the estimated error for a scalar problem, and the row
(infinity) norm of the estimated error vector for a vector problem. (The latter is a bound on the
maximum error of any component of the solution.)
Access:
…µ RKFE
Input/Output:
L2/A1
L1/A2
{ list }
h
→
L4/I1
L3/I2
L2/I3
L1/I4
{ list }
h
ydelta
error
L = Level; A = Argument; I = item
See also:
RKF, RKFSTEP, RRK, RRKSTEP, RSBERR
Full Command and Function Reference 3-147
RKFSTEP
Type:
Command
Description: Next Solution Step for RKF Command: Computes the next solution step (hnext) to an initial value
problem for a differential equation.
The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• xtol sets the tolerance value.
• h specifies the initial candidate step.
• hnext is the next candidate step.
The independent and solution variables must have values stored in them. RKFSTEP steps these
variables to the next point upon completion.
Note that the actual step used by RKFSTEP will be less than the input value h if the global error
tolerance is not satisfied by that value. If a stringent global error tolerance forces RKFSTEP to
reduce its stepsize to the point that the Runge–Kutta–Fehlberg methods fails, then RKFSTEP
will use the Euler method to compute the next solution step and will consider the error tolerance
satisfied. The Runge-Kutta-Fehlberg method will fail if the current independent variable is zero
and the stepsize ≤ 1.3 × 10-498 or if the variable is nonzero and the stepsize is 1.3 × 10-10 times its
magnitude.
Access:
…µ RKFS
Input/Output:
L3/A1
L2/An
L1/An+1
{ list }
xtol
h
→
L3/I1
L2/I2
L1/I3
{ list }
xtol
hnext
L = Level; A = Argument; I = item
See also:
RKF, RKFERR, RRK, RRKSTEP, RSBERR
RL
Type:
Command
Description: Rotate Left Command: Rotates a binary integer one bit to the left.
The leftmost bit of #n1 becomes the rightmost bit of #n2.
Access:
… ãBIT RL
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
RLB, RR, RRB
RLB
Type:
Command
Description: Rotate Left Byte Command: Rotates a binary integer one byte to the left.
The leftmost byte of #n1 becomes the rightmost byte of #n2. RLB is equivalent to executing RL
eight times.
Access:
… ã L BYTE RLB
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
3-148 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
#n1
See also:
#n2
RL, RR, RRB
RND
Type:
Function
Description: Round Function: Rounds an object to a specified number of decimal places or significant digits,
or to fit the current display format.
nround (or symbround if flag –3 is set) controls how the level 2 argument is rounded, as follows:
nround or symbround
0 through 11
–1 through –11
12
Effect on Level 2 Argument
Rounded to n decimal places.
Rounded to n significant digits.
Rounded to the current display format.
For complex numbers and arrays, each real number element is rounded. For unit objects, the
numerical part of the object is rounded.
Access:
!´ REAL LL RND
Flags:
Numerical Results (-3)
Input/Output:
See also:
( ´ is the left-shift of the Pkey).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
nround
→
z2
z
'symbround'
→
'RND(symbround)'
'symb'
nround
→
'RND(symb,nround)'
'symb1'
'symbround'
→
'RND('symb1, symbround)'
[ array1 ]
nround
→
[ array2 ]
x_unit
nround
→
y_unit
x_unit
'symbround'
→
'RND(x_unit, symbround)'
TRNC
RNRM
Type:
Command
Description: Row Norm Command: Returns the row norm (infinity norm) of its argument array.
The row norm is the maximum (over all rows) of the sums of the absolute values of all elements
in each row. For a vector, the row norm is the largest absolute value of any of its elements.
Access:
!Ø OPERATIONS LRNRM
( Ø is the left-shift of the 5key).
!´ MATRIX NORMALIZE RNRM
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
See also:
[ array ]
CNRM, CROSS, DET, DOT
Level 1/Item 1
→
xrow norm
Full Command and Function Reference 3-149
ROLL
Type:
RPL command
Description: Roll Objects Command: Moves the contents of a specified level to level 1, and rolls upwards the
portion of the stack beneath the specified level.
In RPN mode, 3 ROLL is equivalent to ROT.
Access:
!°STACK LROLL
( °is the left-shift of the Nkey).
Input/Output:
Ln+1... L2
L1
objn ... obj1
n
→
Ln ...
L2
L1
objn–1 ...
obj1
objn
L = Level
See also:
OVER, PICK, ROLLD, ROT, SWAP
ROLLD
Type:
RPL command
Description: Roll Down Command: Moves the contents of level 2 to a specified level, n, and rolls downward
the portion of the stack beneath the specified level.
Access:
!°STACK LROLLD
( °is the left-shift of the Nkey).
Input/Output:
Ln+1... L2
L1
objn ... obj2
n (obj1)
→
Ln
Ln–1 ...
L1
obj1
objn ...
obj2
L = Level
See also:
OVER, PICK, ROLL, ROT, SWAP
ROMUPLOAD
Description: This command remains from earlier HP graphing calculators and should not be used.
ROOT
Type:
Command
Description: Root-Finder Command: Returns a real number xroot that is a value of the specified variable global
for which the specified program or algebraic object most nearly evaluates to zero or a local
extremum.
guess is an initial estimate of the solution. ROOT produces an error if it cannot find a solution,
returning the message Bad Guess(es) if one or more of the guesses lie outside the domain of the
equation, or returns the message Constant? if the equation returns the same value at every
sample point. ROOT does not return interpretive messages when a root is found.
Access:
…µ ROOT
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
«program»
'global'
guess
→
xroot
«program»
'global'
{ guesses }
→
xroot
'symb'
'global'
guess
→
xroot
'symb'
'global'
{ guesses }
→
xroot
3-150 Full Command and Function Reference
Level 1/Item 1
ROT
Type:
RPL Command
Description: Rotate Objects Command: Rotates the first three objects on the stack, moving the object on
level 3 to level 1.
In RPN mode, ROT is equivalent to 3 ROLL.
Access:
!°STACK ROT
( °is the left-shift of the Nkey).
Input/Output:
L3
L2
obj3
obj2
L1
obj1
→
L3
L2
L1
obj2
obj1
obj3
L = Level
See also:
OVER, PICK, ROLL, ROLLD, SWAP, UNROT
ROW–
Type:
Command
Description: Delete Row Command: Deletes row n of a matrix (or element n of a vector), and returns the
modified matrix (or vector) and the deleted row (or element).
nrow or nelement is rounded to the nearest integer.
Access:
!Ø CRREATE ROW ROW–
( Ø is the left-shift of the 5key).
!´ MATRIX ROW ROW–
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
[[ matrix ]]1
nrow
nelement
[ vector ]1
COL–, COL+, ROW+, RSWP
Level 2/Item 1
Level 1/Item 2
→
[[ matrix ]]2
[ vector ]row
→
[ vector ]2
elementn
ROW+
Type:
Command
Description: Insert Row Command: Inserts an array into a matrix (or one or more numbers into a vector) at
the position indicated by nindex, and returns the modified matrix (or vector).
The inserted array must have the same number of columns as the target array.
nindex is rounded to the nearest integer. The original array is redimensioned to include the new
columns or elements, and the elements at and below the insertion point are shifted down.
Access:
!Ø CRREATE ROW ROW+
( Ø is the left-shift of the 5key).
!´ MATRIX ROW ROW+
( ´ is the left-shift of the Pkey).
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]1
[[ matrix ]]2
nindex
→
[[ matrix ]]3
[[ matrix ]]1
[ vector ]row
nindex
→
[[ matrix ]]2
nelement
nindex
→
[ vector ]2
See also:
[ vector ]1
COL–, COL+, ROW–, RSWP
ROW→
Type:
Command
Level 1/Item 1
Full Command and Function Reference 3-151
Description: Rows to Matrix Command: Transforms a series of row vectors and a row count into a matrix
containing those rows, or transforms a sequence of numbers and an element count into a vector
with those numbers as elements.
Access:
!Ø
( Ø is the left-shift of the 5key).
CREATE ROW ROW→
( ´ is the left-shift of the Pkey).
!´ MATRIX ROW ROW→
Input/Output:
Ln+1/A1 …
L2/An
L1/An+1
Level 1/Item 1
[ vector ]row 1 …
[ vector ]row n
nrow count
→
[[ matrix ]]
element1 …
elementn
nelement count
→
[ vector ]column
L = Level; A = Argument; I = item
See also:
→COL, COL→, →ROW
→ROW
Type:
Command
Description: Matrix to Rows Command: Transforms a matrix into a series of row vectors, returning the
vectors and row count, or transforms a vector into its elements, returning the elements and
element count.
( Ø is the left-shift of the 5key).
Access:
!Ø CREATE ROW →ROW
!´ MATRIX ROW →ROW
( ´ is the left-shift of the Pkey).
Input/Output:
L1/Argument1
[[ matrix ]]
[ vector ]
Ln+1/I1 … L2/In
L1/In+1
→
[ vector ]row n … [ vector ]row n
nrowcount
→
element1 … elementn
nelementcount
L =Level; A = Argument; I = Item
See also:
→COL, COL→, ROW→
RPL>
Type:
Command
Description: User RPL program function. This function allows for the entry and execution of User RPL
programs while in algebraic mode. While RPL programs can be written in algebraic mode
without the use of this function, some RPL constructs, such as FOR…NEXT loops, will
produce an error message if not preceded by the RPL> function. As an algebraic function, it will
be placed on the command line with a pair of parentheses attached, which must be removed
before its use.
For example, to enter the user RPL program of << 1 5 + >> in algebraic mode, choose the
RPL> function from the catalog and press `. Remove the parentheses by pressing ™ƒƒ.
Then enter the program by pressing …å1#5#+`. The program object will
now be on the first command line. It can be evaluated by pressing N!î`.
Access:
… µ RPL>
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
RR
Type:
Command
3-152 Full Command and Function Reference
obj
Description: Rotate Right Command: Rotates a binary integer one bit to the right.
The rightmost bit of #n1 becomes the leftmost bit of #n2.
Access:
…ãL BIT RR
(ã is the right-shift of the 3key).
!´ BASE L BIT RR
( ´ is the left-shift of the Pkey).
!Ú BASE L BIT RR
( Ú is the left-shift of the 6key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
RL, RLB, RRB
RRB
Type:
Command
Description: Rotate Right Byte Command: Rotates a binary integer one byte to the right.
The rightmost byte of #n1 becomes the leftmost byte of #n2. RRB is equivalent to doing RR
eight times.
Access:
…ãL BYTE RRB
(ã is the right-shift of the 3key).
!´BASE L BYTE RRB
( ´ is the left-shift of the Pkey).
!Ú BASE L BYTE RRB
( Ú is the left-shift of the 6key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
Level 1/Item 1
→
#n2
See also:
RL, RLB, RR
rref
CAS:
Reduce a matrix to row-reduced echelon form, and provide a list of pivot points.
RREF
CAS:
Reduce a matrix to row-reduced echelon form – the reduction is carried out completely, so a
square matrix is reduced to an identity matrix. Step-by-step mode can be used to show how the
reduction proceeds.
RREFMOD
CAS:
Perform modular row-reduction to echelon form on a matrix, modulo the current modulus.
RRK
Type:
Command
Description: Solve for Initial Values (Rosenbrock, Runge–Kutta) Command: Computes the solution to an
initial value problem for a differential equation with known partial derivatives.
RRK solves y'(t) = f(t,y), where y(t0) = y0. The arguments and results are as follows:
• { list } contains five items in this order:
– The independent variable (t).
– The solution variable (y).
– The right-hand side of the differential equation (or a variable where the expression is
stored).
– The partial derivative of y'(t) with respect to the solution variable (or a variable where the
expression is stored).
Full Command and Function Reference 3-153
– The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• xtol sets the tolerance value. If a list is used, the first value is the tolerance and the second
value is the initial candidate step size.
• xTfinal specifies the final value of the independent variable.
RRK repeatedly calls RKFSTEP as its steps from the initial value to xTfinal.
Access:
…µ RRK
Input/Output:
L3/A1
L2/A2
L1/A3
{ list }
xtol
xT final
{ list }
{ xtol xhstep }
xT final
→
L2/I1
L1/I2
{ list }
xtol
{ list }
xtol
L = Level; A = Argument; I = item
See also:
RKF, RKFERR, RKFSTEP, RRKSTEP, RSBERR
RRKSTEP
Type:
Command
Description: Next Solution Step and Method (RKF or RRK) Command: Computes the next solution step
(hnext) to an initial value problem for a differential equation, and displays the method used to
arrive at that result.
The arguments and results are as follows:
• { list } contains five items in this order:
– The independent variable (t).
– The solution variable (y).
– The right-hand side of the differential equation (or a variable where the expression is
stored).
– The partial derivative of y'(t) with respect to the solution variable (or a variable where the
expression is stored).
– The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• xtol is the tolerance value.
• h specifies the initial candidate step.
• last specifies the last method used (RKF = 1, RRK = 2). If this is the first time you are using
RRKSTEP, enter 0.
• current displays the current method used to arrive at the next step.
• hnext is the next candidate step.
The independent and solution variables must have values stored in them. RRKSTEP steps these
variables to the next point upon completion.
Note that the actual step used by RRKSTEP will be less than the input value h if the global error
tolerance is not satisfied by that value. If a stringent global error tolerance forces RRKSTEP to
reduce its stepsize to the point that the Runge–Kutta–Fehlberg or Rosenbrock methods fails,
then RRKSTEP will use the Euler method to compute the next solution step and will consider
the error tolerance satisfied. The Rosenbrock method will fail if the current independent variable
is zero and the stepsize ≤ 2.5 × 10-499 or if the variable is nonzero and the stepsize is 2.5 × 10-11
times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent
variable is zero and the stepsize ≤ 1.3 × 10-498 or if the variable is nonzero and the stepsize is 1.3
× 10-10 times its magnitude.
Access:
…µ RRKS
3-154 Full Command and Function Reference
Input/Output:
L4/A1
L3/A2
L2/A3
L1/A4
{ list }
xtol
h
last
→
L4/I1
L3/I2
L2/I3
L1/I4
{ list }
xtol
hnext
current
L = Level; A = Argument; I = item
See also:
RKF, RKFERR, RKFSTEP, RRK, RSBERR
RSBERR
Type:
Command
Description: Error Estimate for Rosenbrock Method Command: Returns an error estimate for a given step h
when solving an initial values problem for a differential equation.
The arguments and results are as follows:
• { list } contains five items in this order:
– The independent variable (t).
– The solution variable (y).
– The right-hand side of the differential equation (or a variable where the expression is
stored).
– The partial derivative of y'(t) with respect to the solution variable (or a variable where the
expression is stored).
– The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• h is a real number that specifies the initial step.
• ydelta displays the change in solution.
• error displays the absolute error for that step. The absolute error is the absolute value of the
estimated error for a scalar problem, and the row (infinity) norm of the estimated error vector
for a vector problem. (The latter is a bound on the maximum error of any component of the
solution.) A zero error indicates that the Rosenbrock method failed and Euler's method was
used instead.
Access:
…µ RSBER
Input/Output:
L2/A1
L1/A2
{ list }
h
→
L4/I1
L3/I2
L2/I3
L1/I4
{ list }
h
ydelta
error
L = Level; A = Argument; I = item
See also:
RKF, RKFERR, RKFSTEP, RRK, RRKSTEP
RSD
Type:
Command
Description: Residual Command: Computes the residual B – AZ of the arrays B, A, and Z.
A, B, and Z are restricted as follows:
• A must be a matrix.
• The number of columns of A must equal the number of elements of Z if Z is a vector, or the
number of rows of Z if Z is a matrix.
• The number of rows of A must equal the number of elements of B if B is a vector, or the
number of rows of B if B is a matrix.
• B and Z must both be vectors or both be matrices.
• B and Z must have the same number of columns if they are matrices.
RSD is typically used for computing a correction to Z, where Z has been obtained as an
approximation to the solution X to the system of equations AX = B.
Access:
!Ø OPERATIONS LRSD
( Ø is the left-shift of the 5key).
!´ MATRIX LRSD
( ´ is the left-shift of the Pkey).
Full Command and Function Reference 3-155
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
[ vector ]B
[[ matrix ]]A
[ vector ]Z
→
[ vector ]B–AZ
[[ matrix ]]B
[[ matrix ]]A
[[ matrix ]]Z
→
[[ matrix ]]B–AZ
DET, IDN
RSWP
Type:
Command
Description: Row Swap Command: Swaps rows i and j of a matrix and returns the modified matrix, or swaps
elements i and j of a vector and returns the modified vector.
Row numbers are rounded to the nearest integer. Vector arguments are treated as column
vectors.
Access:
!Ø CREATE ROW LRSWP
( Ø is the left-shift of the 5key).
!´ MATRIX ROW LRSWP
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
[[ matrix ]]1
nrow i
nrow j
→
[[ matrix ]]2
nelement i
nelement j
→
[ vector ]2
[ vector ]1
CSWP, ROW+, ROW–
Level 1/Item 1
RULES
Type:
Command
Description: Displays a list of names of individuals involved with the hp 49g calculator project.
Access:
…µ RULES
Input/Output: None
R→B
Type:
Command
Description: Real to Binary Command: Converts a positive real to its binary integer equivalent.
For any value of n ≤ 0, the result is # 0. For any value of n ≥ 1.84467440738E19 (base 10), the
result is # FFFFFFFFFFFFFFFF (base 16).
Access:
…ãR→B
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
n
See also:
Level 1/Item 1
→
#n
B→R
R→C
Type:
Command
Description: Real to Complex Command: Combines two real numbers or real arrays into a single complex
number or complex array.
The first input represents the real element(s) of the complex result. The second input represents
the imaginary element(s) of the complex result.
Array arguments must have the same dimensions.
3-156 Full Command and Function Reference
Access:
!°TYPE L R→C
Input/Output:
See also:
( °is the left-shift of the Nkey).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
(x,y)
[ R-array1 ]
[ R-array2 ]
→
[ C-array ]
C→R, IM, RE
R→D
Type:
Function
Description: Radians to Degrees Function: Converts a real number expressed in radians to its equivalent in
degrees.
This function operates independently of the angle mode.
Access:
!´REAL LLR→D
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
(180/π)x
'symb'
→
'R→D(symb)'
D→R
R→I
Type:
Function
Description: Converts a real number to an integer.
Access:
Flags:
Input:
Output:
See also:
!Ú REWRITE LL
Numeric mode must not be set (flag –3 clear).
Level 1/Argument 1: An integral real number or an expression that evaluates to an integral real.
Level 1/Item 1: The real value converted to an integer.
I→ R
SAME
Type:
Command
Description: Same Object Command: Compares two objects, and returns a true result (1) if they are identical,
and a false result (0) if they are not.
SAME is identical in effect to == for all object types except algebraics, names, and some units.
(For algebraics and names, == returns an expression that can be evaluated to produce a test
result based on numerical values.
Access:
!° TEST LSAME
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj1
obj2
Level 1/Item 1
→
0/1
TYPE, ==
SBRK
Type:
Command
Description: Serial Break Command: Interrupts serial transmission or reception.
SBRK is typically used when a problem occurs in a serial data transmission.
Access:
…µ SBRK
Full Command and Function Reference 3-157
Flags:
I/O Device (-33)
Input/Output: None
See also:
BUFLEN, SRECV, STIME, XMIT
SCALE
Type:
Command
Description: Scale Plot Command: Adjusts the first two parameters in PPAR, (xmin, ymin) and (xmax, ymax), so
that xscale and yscale are the new plot horizontal and vertical scales, and the center point doesn't
change.
The scale in either direction is the number of user units per tick mark. The default scale in both
directions is 1 user-unit per tick mark.
Access:
…µ SCALE
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
xscale
yscale
AUTO, CENTR, SCALEH, SCALEW
Level 1/Item 1
→
SCALEH
Type:
Command
Description: Multiply Height Command: Multiplies the vertical plot scale by xfactor.
Executing SCALEH changes the y-axis display range—the ymin and ymax components of the first
two complex numbers in the reserved variable PPAR. The plot origin (the user-unit coordinate
of the center pixel) is not changed.
Access:
…µSCALEH
Input/Output:
Level 1/Argument 1
xfactor
See also:
Level 1/Item 1
→
AUTO, SCALEW, YRNG
SCALEW
Type:
Command
Description: Multiply Width Command: Multiplies the horizontal plot scale by xfactor.
Executing SCALEW changes the x-axis display range—the xmin and xmax components of the first
two complex numbers in the reserved variable PPAR. The plot origin (the user-unit coordinate
of the center pixel) is not changed.
Access:
…µSCALEW
Input/Output:
Level 1/Argument 1
xfactor
See also:
Level 1/Item 1
→
AUTO, SCALEH, XRNG
SCATRPLOT
Type:
Command
Description: Draw Scatter Plot Command: Draws a scatterplot of (x, y) data points from the specified
columns of the current statistics matrix (reserved variable ΣDAT ).
The data columns plotted are specified by XCOL and YCOL, and are stored as the first two
parameters in the reserved variable ΣPAR. If no data columns are specified, columns 1
3-158 Full Command and Function Reference
(independent) and 2 (dependent) are selected by default. The y-axis is autoscaled and the plot
type is set to SCATTER.
When SCATRPLOT is executed from a program, the resulting display does not persist unless
PICTURE or PVIEW is subsequently executed.
Access:
…µ SCATRPLOT
Input/Output: None
See also:
BARPLOT, PICTURE, HISTPLOT, PVIEW, SCLΣ, XCOL, YCOL
SCATTER
Type:
Command
Description: Scatter Plot Type Command: Sets the plot type to SCATTER.
When the plot type is SCATTER, the DRAW command plots points by obtaining x and y
coordinates from two columns of the current statistics matrix (reserved variable ΣDAT). The
columns are specified by the first and second parameters in the reserved variable ΣPAR (using
the XCOL and YCOL commands). The plotting parameters are specified in the reserved variable
PPAR, which has this form:
{ (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend }
For plot type SCATTER, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
• ptype is a command name specifying the plot type. Executing the command SCATTER places
the name SCATTER in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µ SCATTER
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
SCHUR
Type:
Command
Description: Schur Decomposition of a Square Matrix Command: Returns the Schur decomposition of a
square matrix. SCHUR decomposes A into two matrices Q and T:
• If A is a complex matrix, Q is a unitary matrix, and T is an upper-triangular matrix.
• If A is a real matrix, Q is an orthogonal matrix, and T is an upper quasi-triangular matrix (T is
upper block triangular with 1 × 1 or 2 × 2 diagonal blocks where the 2 × 2 blocks have
complex conjugate eigenvalues).
In either case, A ≅ Q × T × TRN(Q)
Access:
!Ø FACTORIZATION SCHUR
( Ø is the left-shift of the 5key).
!´ MATRIX FACTORS SCHUR
( ´ is the left-shift of the Pkey).
Full Command and Function Reference 3-159
Input/Output:
Level 1/Argument 1
→
[[ matrix ]]A
See also:
Level 2/Item 1
Level 1/Item 2
[[ matrix ]]Q
[[ matrix ]]T
LQ, LU, QR, SVD, SVL, TRN
SCI
Type:
Command
Description: Scientific Mode Command: Sets the number display format to scientific mode, which displays
one digit to the left of the fraction mark and n significant digits to the right.
Scientific mode is equivalent to scientific notation using n + 1 significant digits, where 0 ≤ n ≤ 11.
(Values for n outside this range are rounded to the nearest integer.) In scientific mode, numbers
are displayed and printed like this:
(sign) mantissa E (sign) exponent
where the mantissa has the form n.(n … ) and has zero to 11 decimal places, and the exponent
has one to three digits.
Access:
„ & H FMT SCI
„°L MODES FMT SCI
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
n
See also:
Level 1/Item 1
→
ENG, FIX, STD
SCLΣ
Type:
Command
Description: Scale Sigma Command: Adjusts (xmin, y min) and (xmax, ymax) in PPAR so that a subsequent scatter
plot exactly fills PICT.
When the plot type is SCATTER, the command AUTO incorporates the functions of SCLΣ. In
addition, the command SCATRPLOT automatically executes AUTO to achieve the same result.
Access:
…µ SCLΣ
Input/Output: None
See also:
AUTO, SCATRPLOT
SCONJ
Type:
Command
Description: Store Conjugate Command: Conjugates the contents of a named object.
The named object must be a number, an array, or an algebraic object. For information on
conjugation, see CONJ.
Access:
!°MEMORY ARITHMETIC LSCONJ
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
'name'
See also:
Level 1/Item 1
→
CONJ, SINV, SNEG
SCROLL
Type:
Command
Description: Displays any object. This is the programmable equivalent of pressing I%VIEW% and is the best
way to view any object larger than the screen, such as complicated algebraic expressions.
Access:
…µ SCROLL
3-160 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
Grob
SDEV
Type:
Command
Description: Standard Deviation Command: Calculates the sample standard deviation of each of the m
columns of coordinate values in the current statistics matrix (reserved variable ΣDAT).
SDEV returns a vector of m real numbers, or a single real number if m = 1. The standard
deviation (the square root of the variances) is computed using this formula:
n
2
1
------------ ∑ ( x i – x )
n – 1i = 1
where xi is the ith coordinate value in a column,
the number of data points.
x
is the mean of the data in this column, and n is
Access:
…µ SDEV
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xsdev
→
[ xsdev 1 xsdev 2 ... xsdev m ]
MAXΣ, MEAN, MINΣ, PSDEV, PVAR, TOT, VAR
SEND
Type:
Command
Description: Send Object Command: Sends a copy of the named objects to a Kermit device.
Data is always sent from a local Kermit, but can be sent either to another local Kermit (which
must execute RECV or RECN) or to a server Kermit.
To rename an object when sending it, include the old and new names in an embedded list.
Access:
…µ SEND
Flags:
I/O Device flag (-33), I/O Data Format (-35), I/O Messages (-39)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
{ name1 ... namen }
→
→
{{ nameold namenew } name ... }
BAUD, CLOSEIO, CKSM, FINISH, KERRM, KGET, PARITY, RECN, RECV, SERVER,
TRANSIO
SEQ
Type:
Command
Description: Sequential Calculation Command: Returns a list of results generated by repeatedly executing
objexec using index over the range xstart to xend, in increments of xincr.
objexec is nominally a program or algebraic object that is a function of index, but can actually be an
object. index must be a global or local name. The remaining objects can be anything that will
evaluate to real numbers.
Full Command and Function Reference 3-161
The action of SEQ for arbitrary inputs can be predicted exactly from this equivalent program.
xstart xend FOR index objexec EVAL xincr STEP n → LIST
where n is the number of new objects left on the stack by the FOR … STEP loop. Notice that
index becomes a local variable regardless of its original type.
Access:
!° LIST PROCEDURES LSEQ
Input/Output:
( °is the left-shift of the Nkey).
L5/A1
L4/A2
L3/A3
L2/A4
L1/A5
objexec
index
xstart
xend
xιncr
Li/I1
→
{ list }
L = Level; A = Argument; I = item
See also:
DOSUBS, STREAM
SERIES
CAS:
Compute Taylor series, asymptotic development and limits of a given function.
SERVER
Type:
Command
Description: Server Mode Command: Selects Kermit Server mode.
A Kermit server (a Kermit device in Server mode) passively processes requests sent to it by the
local Kermit. The server receives data in response to SEND, transmits data in response to
KGET, terminates Server mode in response to FINISH or LOGOUT, and transmits a directory
listing in response to a generic directory request.
Access:
…µ SERVER
Flags:
I/O Device flag (-33), I/O Data Format (-35), RECV Overwrite (-36), I/O Messages (-39)
Input/Output: None
See also:
BAUD, CKSM, FINISH, KERRM, KGET, PARITY, PKT, RECN, RECV, SEND, TRANSIO
SEVAL
CAS:
Simplify a given expression, except at the highest level, and replace variables with their values.
SF
Type:
Command
Description: Set Flag Command: Sets a specified user or system flag.
User flags are numbered 1 through 128. System flags are numbered –1 through –128. See
Appendix C for a listing of system flags and their flag numbers.
Access:
!°TEST LLSF
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
nflagnumber
See also:
Level 1/Item 1
→
CF, FC?, FC?C, FS?, FS?C
SHOW
Type:
Command
Description: Show Variable Command: Returns symb2, which is equivalent to symb1 except that all implicit
references to a variable name are made explicit. If the level 1 argument is a list, SHOW evaluates
all global variables in symb1 not contained in the list.
Access:
…µSHOW
Flags:
Numerical Results (-3)
3-162 Full Command and Function Reference
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
'symb1'
'name'
'symb1'
{ name1 name2 ... }
COLCT, EXPAN, ISOL, QUAD
Level 1/Item 1
→
'symb2'
→
'symb2'
SIDENS
Type:
Function
Description: Silicon Intrinsic Density Command: Calculates the intrinsic density of silicon as a function of
temperature, xT.
If xT is a unit object, it must reduce to a pure temperature, and the density is returned as a unit
object with units of 1/cm3.
If xT is a real number, its units are assumed to be K, and the density is returned as a real number
with implied units of 1/cm3.
xT must be between 0 and 1685 K.
Access:
…µ SIDENS
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
xT
SIGMA
CAS:
Level 1/Item 1
→
xdensity
x_unit
x_1/cm3
'symb'
'SIDENS(symb)'
For given variable y, calculate discrete antiderivative G of given function f : G(y + 1) – G(y) =
f(y).
SIGMAVX
CAS:
For current variable x, calculate discrete antiderivative G of function f : G(x + 1) – G(x) = f(x).
SIGN
Type:
Function
Description: Sign Function: Returns the sign of a real number argument, the sign of the numerical part of a
unit object argument, or the unit vector in the direction of a complex number argument.
For real number and unit object arguments, the sign is defined as +1 for positive arguments, –1
for negative arguments. In exact mode, the sign for argument 0 is undefined (?). In approximate
mode, the sign for argument 0 is 0. SIGN in the !´menu returns the sign of a number,
while SIGN in the …ß menu returns returns the unit vector of a complex number.
For a complex argument:
iy
x
SIGN ( x + iy ) = --------------------- + --------------------2
2
2
2
x +y
x +y
Access:
!´ REAL LSIGN
( ´ is the left-shift of the Pkey).
( ß is the right-shift of the 1key).
Flags:
…ßL SIGN
Numerical Results (-3)
Full Command and Function Reference 3-163
Input/Output:
Level 1/Argument 1
z1
See also:
Level 1/Item 1
→
z2
x_unit
xsign
'symb'
'SIGN(symb)'
ABS, MANT, XPON
SIGNTAB
CAS:
Tabulate the sign of a rational function of the current CAS variable.
SIMP2
CAS:
Simplify two objects by dividing them by their greatest common divisor.
SIMPLIFY
CAS:
Simplify an expression.
SIN
Type:
Analytic function
Description: Sine Analytic Function: Returns the sine of the argument.
For real arguments, the current angle mode determines the number's units, unless angular units
are specified.
For complex arguments, sin(x + iy) = sinx coshy + i cosx sinhy.
If the argument for SIN is a unit object, then the specified angular unit overrides the angle mode
to determine the result. Integration and differentiation, on the other hand, always observe the
angle mode. Therefore, to correctly integrate or differentiate expressions containing SIN with a
unit object, the angle mode must be set to radians (since this is a “neutral” mode).
Access:
S
Flags:
Numerical Results (-3), Angle Mode (-17, -18)
Input/Output:
Level 1/Argument 1
z
See also:
Level 1/Item 1
→
sin z
x_unitangular
sin(x_unitangular)
'symb'
'SIN(symb)'
ASIN, COS, TAN
SINCOS
CAS:
Convert logarithmic and exponential expressions to expressions with trigonometric terms.
SINH
Type:
Analytic function
Description: Hyperbolic Sine Analytic Function: Returns the hyperbolic sine of the argument.
For complex arguments, sinh(x + iy) = sinhx cosy + i coshx siny.
Access:
…Ñ HYPERBOLIC SINH
(Ñ is the right-shift of the 8key).
!´ HYPERBOLIC SINH
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3)
3-164 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
z
'symb'
See also:
sinh z
'SINH(symb)'
ASINH, COSH, TANH
SINV
Type:
Command
Description: Store Inverse Command: Replaces the contents of the named variable with its inverse.
The named object must be a number, a matrix, an algebraic object, or a unit object. For
information on reciprocals, see INV.
Access:
!°MEMORY ARITHMETIC L SINV
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
→
'name'
See also:
Level 1/Item 1
INV, SCONJ, SNEG
SIZE
Type:
Command Operation
Description: Size Command: Returns the number of characters in a string, the number of elements in a list,
the dimensions of an array, the number of objects in a unit object or algebraic object, or the
dimensions of a graphics object.
The size of a unit is computed as follows: the scalar (+1), the underscore (+1), each unit name
(+1), operator or exponent (+1), and each prefix (+2).
Any object type not listed above returns a value of 1.
Access:
!° LCHARS SIZE
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 2/Item 1
Level 1/Item 2
“string”
→
n
{ list }
→
n
[ vector ]
→
{n}
[[ matrix ]]
→
{ n m}
'symb'
→
n
grob
→
#nwidth
#mheight
PICT
→
#nwidth
#mheight
x_unit
CHR, NUM, POS, REPL, SUB
→
n
SL
Type:
Command
Description: Shift Left Command: Shift a binary integer one bit to the left.
The most significant bit is shifted out to the left and lost, while the least significant bit is
regenerated as a zero. SL is equivalent to binary multiplication by 2, truncated to the current
wordsize.
Access:
!´ BASE LBIT SL
( ´ is the left-shift of the Pkey).
…ãL BIT SL
(ã is the right-shift of the 3key).
Full Command and Function Reference 3-165
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
ASR, SLB, SR, SRB
SLB
Type:
Command
Description: Shift Left Byte Command: Shifts a binary integer one byte to the left.
The most significant byte is shifted out to the left and lost, while the least significant byte is
regenerated as zero. SLB is equivalent to binary multiplication by 28 (256) (or executing SL eight
times), truncated to the current wordsize.
Access:
!´ BASE LBYTE SLB
( ´ is the left-shift of the Pkey).
…ãL BYTE SLB
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
ASR, SL, SR, SRB
SLOPEFIELD
Type:
Command
Description: SLOPEFIELD Plot Type Command: Sets the plot type to SLOPEFIELD.
When plot type is set to SLOPEFIELD, the DRAW command plots a slope representation of a
scalar function with two variables. SLOPEFIELD requires values in the reserved variables EQ,
VPAR, and PPAR.
VPAR has the following form:
{ xleft xright ynear yfar zlow zhigh xmin xmax ymin ymax xeye yeye zeye xstep ystep }
For plot type SLOPEFIELD, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
• zlow and zhigh are real numbers that specify the height of the view space.
• xmin and xmax are not used.
• ymin and ymax are not used.
• xeye, yeye, and zeye are real numbers that specify the point in space from which the graph is
viewed.
• xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type SLOPEFIELD, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command SLOPEFIELD
places the command name SLOPEFIELD in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
3-166 Full Command and Function Reference
Access:
…µ SLOPEFIELD
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, TRUTH, WIREFRAME, YSLICE
SNEG
Type:
Command
Description: Store Negate Command: Replaces the contents of a variable with its negative.
The named object must be a number, an array, an algebraic object, a unit object, or a graphics
object. For information on negation, see NEG.
Access:
!°MEMORY ARITHMETIC L SNEG
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
'name'
See also:
NEG, SCONJ, SINV
SNRM
Type:
Command
Description: Spectral Norm Command: Returns the spectral norm of an array.
The spectral norm of a vector is its Euclidean length, and is equal to the largest singular value of
a matrix.
Access:
!Ø OPERATIONS L L SNRM
( Ø is the left-shift of the 5key).
!´ MATRIX NORMALIZE SNRM
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
[ array ]
ABS, CNRM, COND, RNRM, SRAD, TRACE
→
xspectralnorm
SOLVE
CAS:
Find zeros of an expression, or solve an equation with respect to a specified variable.
SOLVEQN
Type:
Command
Description: Starts the appropriate solver for a specified set of equations.
SOLVEQN sets up and starts the appropriate solver for the specified set of equations, bypassing
the Equation Library catalogs. It sets EQ (and Mpar if more than one equation is being solved),
sets the unit options according to flags -60 and -61, and starts the appropriate solver.
SOLVEQN uses subject and title numbers (levels 3 and 2) and a “PICT” option (level 1) and
returns nothing. Subject and title numbers are listed in chapter 5. For example, a 2 in level 3 and
a 9 in level 2 would specify the Electricity category and Capacitive Energy set of equations. If the
“PICT” option is 0, PICT is not affected; otherwise, the equation picture (if any) is copied into
PICT.
Access:
…µ SOLVEQN
Flags:
Unit Type (-60), Units Usage (-61)
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
n
m
0/1
Level 1/Item 1
→
EQNLIB, MSOLVER
Full Command and Function Reference 3-167
SOLVER
Type:
Command
Description: Displays a menu of commands used in solving equations.
Access:
…µ SOLVER
Input/Output: None
SOLVEVX
CAS:
Find zeros of an expression, or solves an equation with respect to the current variable.
SORT
Type:
Command
Description: Ascending Order Sort Command: Sorts the elements in a list in ascending order.
The elements in the list can be real numbers, strings, lists, names, binary integers, or unit objects.
However, all elements in the list must all be of the same type. Strings and names are sorted by
character code number. Lists of lists are sorted by the first element in each list.
To sort in reverse order, use SORT REVLIST.
Access:
!´ LIST SORT
( ´ is the left-shift of the Pkey).
!° LIST PROCEDURES L SORT
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
{ list }1
See also:
Level 1/Item 1
→
{ list }2
REVLIST
SPHERE
Type:
Command
Description: Spherical Mode Command: Sets spherical coordinate mode.
SPHERE sets flags –15 and –16.
In spherical mode, vectors are displayed as polar components.
Access:
„&H ANGLE SPHERE
Input/Output: None
See also:
CYLIN, RECT
SQ
Type:
Analytic function
Description: Square Analytic Function: Returns the square of the argument.
The square of a complex argument (x, y) is the complex number (x2 – y2, 2xy).
Matrix arguments must be square.
Access:
!º
( º is the left-shift of the Rkey).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
z2
x_unit
→
x2_unit2
[[ matrix ]]
→
[[ matrix × matrix ]]
'symb'
→
'SQ(symb)'
√, ^
3-168 Full Command and Function Reference
SR
Type:
Command
Description: Shift Right Command: Shifts a binary integer one bit to the right.
The least significant bit is shifted out to the right and lost, while the most significant bit is
regenerated as a zero. SR is equivalent to binary division by 2.
Access:
!´ BASE L BIT SR
( ´ is the left-shift of the Pkey).
…ã L BIT SR
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
ASR, SL, SLB, SRB
SRAD
Type:
Command
Description: Spectral Radius Command: Returns the spectral radius of a square matrix.
The spectral radius of a matrix is a measure of the size of the matrix, and is equal to the absolute
value of the largest eigenvalue of the matrix.
Access:
!Ø OPERATIONS L L SRAD (Ø is the left-shift of the 5key).
!´ MATRIX NORMALIZE SRAD
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
[[ matrix ]]n×n
See also:
Level 1/Item 1
→
xspectralradius
COND, SNRM, TRACE
SRB
Type:
Command
Description: Shift Right Byte Command: Shifts a binary integer one byte to the right.
The least significant byte is shifted out to the right and lost, while the most significant byte is
regenerated as zero. SRB is equivalent to binary division by 28 (or executing SR eight times).
Access:
!´ BASE L BYTE SRB
( ´ is the left-shift of the Pkey).
…ã L BYTE SRB
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
#n1
See also:
Level 1/Item 1
→
#n2
ASR, SL, SLB, SR
SRECV
Type:
Command
Description: Serial Receive Command: Reads up to n characters from the serial input buffer and returns them
as a string, along with a digit indicating whether errors occurred.
SRECV does not use Kermit protocol.
If n characters are not received within the time specified by STIME (default is 10 seconds),
SRECV “times out”, returning a 0 to level 1 and as many characters as were received to level 2.
Full Command and Function Reference 3-169
If the level 2 output from BUFLEN is used as the input for SRECV, SRECV will not have to
wait for more characters to be received. Instead, it returns the characters already in the input
buffer.
If you want to accumulate bytes in the input buffer before executing SRECV, you must first
open the port using OPENIO (if the port isn't already open).
SRECV can detect three types of error when reading the input buffer:
• Framing errors and UART overruns (both causing "Receive Error" in ERRM).
• Input-buffer overflows (causing "Receive Buffer Overflow" in ERRM).
• Parity errors (causing "Parity Error" in ERRM).
SRECV returns 0 if an error is detected when reading the input buffer, or 1 if no error is
detected.
Parity errors do not stop data flow into the input buffer. However, if a parity error occurs,
SRECV stops reading data after encountering a character with an error.
Framing, overrun, and overflow errors cause all subsequently received characters to be ignored
until the error is cleared. SRECV does not detect and clear any of these types of errors until it
tries to read the byte where the error occurred. Since these three errors cause the byte where the
error occurred and all subsequent bytes to be ignored, the input buffer will be empty after all
previously received good bytes have been read. Therefore, SRECV detects and clears these errors
when it tries to read a byte from an empty input buffer.
Note that BUFLEN also clears the above-mentioned framing, overrun, and overflow errors.
Therefore, SRECV cannot detect an input-buffer overflow after BUFLEN is executed, unless
more characters were received after BUFLEN was executed (causing the input buffer to
overflow again). SRECV also cannot detect framing and UART overrun errors cleared by
BUFLEN. To find where the data error occurred, save the number of characters returned by
BUFLEN (which gives the number of “good” characters received), because as soon as the error
is cleared, new characters can enter the input buffer.
Access:
…µSRECV
Flags:
I/O Device (-33)
Input/Output:
Level 1/Argument 1
See also:
Level 2/Item 1
Level 1/Item 2
→
n
'string'
BUFLEN, CLOSEIO, OPENIO, SBRK, STIME, XMIT
0/1
SREPL
Type:
Command
Description: Find and replace: Finds and replaces a string in a given text object. You supply the following
inputs:
Level 3/argument 1: the string to search.
Level 2/argument 2: the string to find.
Level 1/argument 3: the string to replace it with.
Access:
…&NLSREPL
„°LCHARS LSREPL
( °is the left-shift of the Nkey).
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
'string'
'string'
'string'
See also:
REPL
START
Type:
Command Operation
3-170 Full Command and Function Reference
Level 1/Item 1
→
'string'
Description: START Definite Loop Structure Command: Begins START … NEXT and START … STEP
definite loop structures.
Definite loop structures execute a command or sequence of commands a specified number of times.
• START … NEXT executes a portion of a program a specified number of times.
The RPL syntax is this: xstart xfinish START loop-clause NEXT
The algebraic syntax is this: START(xstart xfinish) loop-clause NEXT
START takes two numbers (xstart and xfinish) from the stack and stores them as the starting
and ending values for a loop counter. Then the loop clause is executed. NEXT increments
the counter by 1 and tests to see if its value is less than or equal to xfinish. If so, the loop
clause is executed again. Notice that the loop clause is always executed at least once.
• START … STEP works just like START … NEXT, except that it can use an increment value
other than 1. The RPL syntax is this: xstart xfinish START loop-clause xincrement STEP
The algebraic syntax is this: START (xstart xfinish ) loop-clause STEP(xincrement)
START takes two numbers (xstart and xfinish) from the stack and stores them as the starting
and ending values for the loop counter. Then the loop clause is executed. STEP takes
xincrement from the stack and increments the counter by that value. If the argument of STEP
is an algebraic or a name, it is automatically evaluated to a number.
The increment value can be positive or negative:
– If positive, the loop is executed again when the counter is less than or equal to xfinish.
– If negative, the loop is executed when the counter is greater than or equal to xfinish.
Access:
!°BRANCH START
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
START xstart
Level 1/Argument 2
xfinish
See also:
STEP
FOR, NEXT, STEP
→
→
NEXT
STEP
Level 1/Item 1
xincrement
→
'symbincrement'
→
STD
Type:
Command
Description: Standard Mode Command: Sets the number display format to standard mode.
Executing STD has the same effect as clearing flags –49 and –50.
Standard format produces the following results when displaying or printing a number.
• Numbers that can be represented exactly as integers with 12 or fewer digits are displayed
without a fraction mark or exponent. Zero is displayed as 0.
• Numbers that can be represented exactly with 12 or fewer digits, but not as integers, are
displayed with a fraction mark but no exponent. Leading zeros to the left of the fraction mark
and trailing zeros to the right of the fraction mark are omitted.
• All other numbers are displayed in scientific notation (see SCI) with both a fraction mark
(with one number to the left) and an exponent (of one or three digits). There are no leading
or trailing zeros.
In algebraic objects, integers less than 103 are always displayed in standard mode.
Access:
…µ STD
Input/Output: None
See also:
ENG, FIX, SCI
Full Command and Function Reference 3-171
STEP
Type:
Command Operation
Description: STEP Command: Defines the increment (step) value, and ends definite loop structure.
See the FOR and START keyword entries for more information.
Access:
!°BRANCH START/FOR STEP
( °is the left-shift of the Nkey).
Input/Output: None
See also:
FOR, NEXT, START
STEQ
Type:
Command
Description: Store in EQ Command: Stores an object into the reserved variable EQ in the current directory.
Access:
…µ STEQ
Input/Output:
Level 1/Argument 1
obj
See also:
Level 1/Item 1
→
RCEQ
STIME
Type:
Command
Description: Serial Time-Out Command: Specifies the period that SRECV (serial reception) and XMIT (serial
transmission) wait before timing out.
The value for x is interpreted as a positive value from 0 to 25.4 seconds. If no value is given, the
default is 10 seconds. If x is 0, there is no time-out; that is, the device waits indefinitely, which
can drain the batteries.
STIME is not used for Kermit time-out.
Access:
…µ STIME
Input/Output:
Level 1/Argument 1
xseconds
See also:
0
BUFLEN, CLOSEIO, SBRK, SRECV, XMIT
Level 1/Item 1
→
→
STO
Type:
Command
Description: Store Command: Stores an object into a specified variable or object.
Storing a graphics object into PICT makes it the current graphics object.
To create a backup object, store the obj into the desired backup location (identified as
:nport:namebackup). STO will not overwrite an existing backup object.
To store backup objects and library objects, specify a port number (0 through 3).
Access:
After storing a library object in a port, it must then be attached to its directory before it can be used.
The easiest way to do this is to execute a warm start (by pressing $& C). This also causes the
calculator to perform a system halt, which clears the stack, the LAST stack, and all local variables.
STO can also replace a single element of an array or list stored in a variable. Specify the variable
in level 1 as name(index), which is a user function with index as the argument. The index can be n
or n,m, where n specifies the row position in a vector or list, and n,m specifies the row-andcolumn position in a matrix.
K
3-172 Full Command and Function Reference
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
obj
'name'
→
grob
PICT
→
obj
:nport :namebackup
→
obj
'name(index)'
→
backup
nport
→
library
nport
→
library
:nport :nlibrary
→
DEFINE, RCL, →, !
STOALARM
Type:
Command
Description: Store Alarm Command: Stores an alarm in the system alarm list and returns its alarm index
number.
If the argument is a real number xtime, the alarm date will be the current system date by default.
If objaction is a string, the alarm is an appointment alarm, and the string is the alarm message. If
objaction is any other object type, the alarm is a control alarm, and the object is executed when the
alarm comes due.
xrepeat is the repeat interval for the alarm in clock ticks, where 8192 ticks equals 1 second.
nindex is a real integer identifying the alarm based on its chronological position in the system alarm
list.
Access:
…ÓTOOLS ALRM STOALARM
(Ó is the right-shift of the 9 key).
Flags:
Date Format (-42), Repeat Alarms Not Rescheduled (-43), Acknowledged Alarms Saved (-44)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
xtime
→
nindex
{ date time }
→
nindex
{ date time objaction }
→
nindex
→
nindex
{ date time objaction xrepeat }
DELALARM, FINDALARM, RCLALARM
STOF
Type:
Command
Description: Store Flags Command: Sets the states of the system flags or the system and user flags.
With argument #nsystem, STOF sets the states of the system flags (–1 through –128) only. With
argument { #nsystem, #nuser, #nsystem2 #nuser2 }, STOF sets the states of both the system and user flags.
A bit with value 1 sets the corresponding flag; a bit with value 0 clears the corresponding flag.
The rightmost (least significant) bit of #nsystem and #nuser correspond to the states of system flag
–1 and user flag +1, respectively.
STOF can preserve the states of flags before a program executes and changes the states. RCLF
can then recall the flag's states after the program is executed.
Access:
…µ STOF
Flags:
Binary Integer Wordsize (-5 through -10)
Full Command and Function Reference 3-173
Input/Output:
Level 1/Argument 1
→
#nsystem
See also:
Level 1/Item 1
{ #nsystem #nuser #nsystem2 #nuser2 }
RCLF, STWS, RCWS
→
STOKEYS
Type:
Command
Description: Store Key Assignments Command: Defines multiple keys on the user keyboard by assigning
objects to specified keys.
xkey is a real number of the form rc.p specifying the key by its row number r, its column number c,
and its plane (shift) p. (For a definition of plane, see the entry for ASN).
The optional initial list parameter or argument S restores all keys without user assignments to
their standard key assignments on the user keyboard. This is meaningful only when all standard
key assignments had been suppressed (for the user keyboard) by the command S DELKEYS.
If the argument obj is the name SKEY, the specified key is restored to its standard key assignment.
Access:
…µ STOKEYS
Flags:
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
Input/Output:
Level 1/Argument 1
Level 1/Item 1
{ obj1, xkey 1, ... objn, xkey n }
→
{ S, obj1, xkey 1, ... objn, xkey n }
→
'S'
→
See also:
ASN, DELKEYS, RCLKEYS
STORE
CAS:
Store a number in a global variable; given an expression evaluate it and store the numerical value.
STOVX
CAS:
Store a name in the current CAS variable.
STO+
Type:
Command
Description: Store Plus Command: Adds a number or other object to the contents of a specified variable.
The object on the stack and the object in the variable must be suitable for addition to each other.
STO+ can add any combination of objects suitable for addition.
Using STO+ to add two arrays (where obj is an array and name is the global name of an array)
requires less memory than using the stack to add them.
Access:
!°MEMORY ARITHMETIC STO+
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
obj
'name'
→
obj
→
See also:
'name'
STO–, STO*, STO/, +
STO–
Type:
Command
3-174 Full Command and Function Reference
Level 1/Item 1
Description: Store Minus Command: Calculates the difference between a number (or other object) and the
contents of a specified variable, and stores the new value in the specified variable.
The object on the stack and the object in the variable must be suitable for subtraction with each
other. STO– can subtract any combination of objects suitable for stack subtraction.
Using STO– to subtract two arrays (where obj is an array and name is the global name of an array)
requires less memory than using the stack to subtract them.
( °is the left-shift of the Nkey).
Access:
!°MEMORY ARITHMETIC STO–
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj
'name'
→
obj
→
'name'
STO+, STO*, STO/, –
Level 1/Item 1
STO*
Type:
Command
Description: Store Times Command: Multiplies the contents of a specified variable by a number or other
object.
The object on the stack and the object in the variable must be suitable for multiplication with
each other. When multiplying two arrays, the result depends on the order of the arguments. The
new object of the named variable is the level 2 array times the level 1 array. The arrays must be
conformable for multiplication.
Using STO* to multiply two arrays or to multiply a number and an array (where obj is an array or
a number and name is the global name of an array) requires less memory than using the stack to
multiply them.
Access:
!°MEMORY ARITHMETIC STO*
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj
'name'
→
obj
→
'name'
STO+, STO–, STO/, *
Level 1/Item 1
STO/
Type:
Command
Description: Store Divide Command: Calculates the quotient of a number (or other object) and the contents
of a specified variable, and stores the new value in the specified variable.
The new object of the specified variable is the level 2 object divided by the level 1 object.
The object on the stack and the object in the variable must be suitable for division with each
other. If both objects are arrays, the divisor (level 1) must be a square matrix, and the dividend
(level 2) must have the same number of columns as the divisor.
Using STO/ to divide one array by another array or to divide an array by a number (where obj is
an array or a number and name is the global name of an array) requires less memory than using
the stack to divide them.
Access:
!°MEMORY ARITHMETIC STO/
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj
'name'
→
obj
→
'name'
STO+, STO–, STO*, /
Level 1/Item 1
Full Command and Function Reference 3-175
STOΣ
Type:
Command
Description: Store Sigma Command: Stores obj in the reserved variable ΣDAT.
STOΣ accepts any object and stores it in ΣDAT. However, if the object is not a matrix or the
name of a variable containing a matrix, an Invalid ΣDATA error occurs upon subsequent
execution of a statistics command.
Access:
…µ STOΣ
Input/Output:
Level 1/Argument 1
obj
See also:
Level 1/Item 1
→
CLΣ, RCLΣ, Σ+, Σ–
STR→
Type:
Command
Description: Evaluate String Command: Evaluates the text of a string as if the text were entered from the
command line.
OBJ→ also includes this function.
Access:
…µ STR→
Input/Output:
Level 1/Argument 1
See also:
“obj”
ARRY→, DTAG, EQ→, LIST→, OBJ→, →STR
Level 1/Item 1
→
evaluated-object
→STR
Type:
Command
Description: Object to String Command: Converts any object to string form.
The full-precision internal form of a number is not necessarily represented in the result string. To
ensure that →STR preserves the full precision of a number, select Standard number display
format or a wordsize of 64 bits (or both) before executing →STR.
The result string includes the entire object, even if the displayed form of the object is too large to
fit in the display.
If the argument object is normally displayed in two or more lines, the result string will contain
newline characters (character 10) at the end of each line. The newlines are displayed as the
character .
If the argument object is already a string, →STR returns the string.
Access:
…µ →STR
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12), Number Display
Format (-49, -50)
Input/Output:
Level 1/Argument 1
obj
See also:
Level 1/Item 1
→
“obj”
→ARRY, →LIST, STR→, →TAG, →UNIT
STREAM
Type:
Command
Description: Stream Execution Command: Moves the first two elements from the list onto the stack, and
executes obj. Then moves the next element (if any) onto the stack, and executes obj again using
3-176 Full Command and Function Reference
the previous result and the new element. Repeats this until the list is exhausted, and returns the
final result.
STREAM is nominally designed for obj to be a program or command that requires two
arguments and returns one result.
Access:
!°LIST PROCEDURES STREAM
( °is the left-shift of the Nkey).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
{ list }
obj
Level 1/Item 1
→
result
See also:
DOSUBS
STURM
CAS:
For a polynomial P, return a list containing Sturm’s sequences of P and their multiplicities.
STURMAB
CAS:
For polynomial P and closed interval [a, b], determine the number of zeros P has in [a, b].
STWS
Type:
Command
Description: Set Wordsize Command: Sets the current binary integer wordsize to n bits, where n is a value
from 1 through 64 (the default is 64).
Values of n less than 1 or greater than 64 are interpreted as 1 or 64, respectively.
If the wordsize is smaller than an integer entered on the command line, then the most significant
bits are not displayed upon entry. The truncated bits are still present internally (unless they
exceed 64), but they are not used for calculations and they are lost when a command uses this
binary integer as an argument.
Results that exceed the given wordsize are also truncated to the wordsize.
Access:
!´ BASE LSTWS
( ´ is the left-shift of the Pkey).
… ã STWS
(ã is the right-shift of the 3key).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
Level 1/Argument 1
n
See also:
#n
BIN, DEC, HEX, OCT, RCWS
Level 1/Item 1
→
→
SUB
Type:
Command Operation
Description: Subset Command: Returns the portion of a string or list defined by specified positions, or
returns the rectangular portion of a graphics object or PICT defined by two corner pixel
coordinates.
If nend position is less than nstart position, SUB returns an empty string or list. Values of n less than 1 are
treated as 1; values of n exceeding the length of the string or list are treated as that length.
For graphics objects, a user-unit coordinate less than the minimum user-unit coordinate of the
graphics object is treated as that minimum. A pixel or user-unit coordinate greater than the
maximum pixel or user-unit coordinate of the graphics object is treated as that maximum.
Access:
!°LIST SUB
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-177
Input/Output:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
[[ matrix ]]1
nstartposition
nendposition
→
[[ matrix ]]2
[[ matrix ]]1
{nrow, ncolumn }
nendposition
→
[[ matrix ]]2
[[ matrix ]]1
nstartposition
{nrow,, ncolumn }
→
[[ matrix ]]2
[[ matrix ]]1
{nrow, ncolumn }
{nrow,, ncolumn }
→
[[ matrix ]]2
“stringtarget”
nstartposition
nendposition
→
“stringresult”
{ listtarget }
nstartposition
nendposition
→
{ listresult }
grobtarget
{ #n1, #m1 }
{ #n2 #m2 }
→
grobresult
grobtarget
( x1, y1 )
( x2, y2 )
→
grobresult
PICT
{ #n1, #m1 }
{ #n2 #m2 }
→
grobresult
PICT
( x1, y1 )
( x2, y2 )
→
grobresult
See also:
CHR, GOR, GXOR, NUM, POS, REPL, SIZE
SUBST
CAS:
Substitute a value for a variable in an expression; the value can be numeric or an expression.
SUBTMOD
CAS:
Perform a subtraction, modulo the current modulus.
SVD
Type:
Command
Description: Singular Value Decomposition Command: Returns the singular value decomposition of an m × n
matrix.
SVD decomposes A into 2 matrices and a vector. U is an m × m orthogonal matrix, V is an n × n
orthogonal matrix, and S is a real vector, such that A = U × diag(S) × V . S has length MIN(m,n)
and contains the singular values of A in nonincreasing order. The matrix diag(S) is an m×n
diagonal matrix containing the singular values S.
The computed results should minimize (within computational precision):
A – U ⋅ diag ( S ) ⋅ V
--------------------------------------------------min ( m, n ) ⋅ A
where diag(S) denotes the m × n diagonal matrix containing the singular values S.
FACTORIZATION SVD
(Ø is the left-shift of the 5key).
!´ MATRIX FACTORS SVD
Input/Output:
( ´ is the left-shift of the Pkey).
Access:
!Ø
Level 1/Argument 1
See also:
[[ matrix ]]A
DIAG→, MIN, SVL
→
Level 3/Item 1
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]U
[[ matrix ]]V
[ vector ]S
SVL
Type:
Command
Description: Singular Values Command: Returns the singular values of an m × n matrix.
SLV returns a real vector that contains the singular values of an m × n matrix in non-increasing
order. The vector has length MIN(m,n).
Access:
!Ø FACTORIZATION LSVL
(Ø is the left-shift of the 5key).
!´ MATRIX FACTORS LSVL
( ´ is the left-shift of the Pkey).
3-178 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
[[ matrix ]]
See also:
[ vector ]
MIN, SVD
SWAP
Type:
RPL Command
Description: Swap Objects Command: Swaps the position of the two inputs.
Access:
!°STACK SWAP
( °is the left-shift of the Nkey).
™ in RPN mode executes SWAP when no command line is present.
Input/Output:
Level 2
See also:
Level 1
→
obj1
obj2
DUP, DUPN, DUP2, OVER, PICK, ROLL, ROLLD, ROT
Level 2
Level 1
obj2
obj1
SYSEVAL
Type:
Command
Description: Evaluate System Object Command: Evaluates unnamed operating system objects specified by
their memory addresses.
WARNING: Use extreme care when executing this function. Using SYSEVAL with
random addresses will almost always cause a memory loss. Do not use this function
unless you know what you are doing.
Access:
…µ SYSEVAL
Input/Output:
Level 1/Argument 1
See also:
#naddress
EVAL, LIBEVAL, FLASHEVAL
Level 1/Item 1
→
SYLVESTER
CAS:
For symmetric matrix A, return D and P where D is diagonal and A = PTDP.
SYST2MAT
CAS:
Convert a system of linear equations in algebraic form to matrix form.
%T
Type:
Function
Description: Percent of Total Function: Returns the percent of the first argument that is represented by the
second argument.
If both arguments are unit objects, the units must be consistent with each other.
The dimensions of a unit object are dropped from the result, but units are part of the calculation.
For more information on using temperature units with arithmetic functions, refer to the entry for
+.
Access:
!´ REAL %T
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3)
Full Command and Function Reference 3-179
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
100y/x
x
'symb'
→
'%T(x,symb)'
'symb'
x
→
'%T(symb,x)'
'symb1'
'symb2'
→
'%T(symb1, symb2)'
x_unit1
y_unit2
→
100y_unit2/x_unit1
x_unit
'symb'
→
'%T(x_unit,symb)'
'symb'
x_unit
→
'%T(symb,x_unit)'
See also:
+, %, %CH
TABVAL
CAS:
Store given expression, and return results of substituting given values in the expression.
TABVAR
CAS:
Compute variation table for a function, of the current variable, with a rational derivative.
→TAG
Type:
Command
Description: Stack to Tag Command: Combines objects in levels 1 and 2 to create tagged (labeled) object.
The “tag” argument is a string of fewer than 256 characters.
Access:
„°TYPE →TAG
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
obj
“tag”
→
:tag:obj
obj
'name'
→
:name:obj
obj
x
→
:x:obj
→ARRY, DTAG, →LIST, OBJ→, →STR, →UNIT
TAIL
Type:
Command
Description: Last Listed Elements Command: Returns all but the first element of a list or string.
Access:
!°LCHARS LTAIL
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
{ obj1 ... objn }
→
{ obj2 ... objn }
“string1”
→
“string2”
HEAD
TAN
Type:
Analytic function
Description: Tangent Analytic Function: Returns the tangent of the argument.
For real arguments, the current angle mode determines the number's interpretation as an angle,
unless the angular units are specified.
3-180 Full Command and Function Reference
For a real argument that is an odd-integer multiple of 90 in Degrees mode, an Infinite Result
exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the
argument.
For complex arguments:
( sin x) ( cos x ) + i ( sinh y ) ( cosh y )
tan ( x + iy ) = ------------------------------------------------------------------------------2
2
sin h y + cos x
If the argument for TAN is a unit object, then the specified angular unit overrides the angle
mode to determine the result. Integration and differentiation, on the other hand, always observe
the angle mode. Therefore, to correctly integrate or differentiate expressions containing TAN
with a unit object, the angle mode must be set to Radians (since this is a “neutral” mode).
Access:
U
Flags:
Numerical Results (-3), Angle Mode (-17, -18), Inifinite Result Exception (-22)
Input/Output:
Level 1/Argument 1
Level 1/Item 1
z
→
tan z
'symb'
→
'TAN(symb)'
x_unitangular
See also:
tan (x_unitangular)
ATAN, COS, SIN
TAN2CS2
CAS:
Replace tan(x) terms in expressions with (1-cos(2x))/sin(2x) terms.
TAN2SC
CAS:
Replace tan(x) terms in expressions with sin(x)/cos(x).
TAN2SC2
CAS:
Replace tan(x) terms in expressions with sin(2x)/1+cos(2x) terms.
TANH
Type:
Analytic function
Description: Hyperbolic Tangent Analytic Function: Returns the hyperbolic tangent of the argument.
For complex arguments,
sinh 2x + i sin 2y
tanh ( x + iy ) = --------------------------------------cosh 2x + cos 2y
Access:
…Ñ HYPERBOLIC TANH
(Ñ is the right-shift of the 8key).
!´ HYPERBOLIC TANH
Flags:
Numerical Results (-3)
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
tanh z
'symb'
→
'TANH(symb)'
ATANH, COSH, SINH
TAYLOR0
CAS:
Perform a fourth-order Taylor expansion of an expression at x = 0.
TAYLR
Type:
Command
Description: Taylor Polynomial Command: Calculates the nth order Taylor polynomial of symb in the variable
global.
Full Command and Function Reference 3-181
The polynomial is calculated at the point global = 0. The expression symb may have a removable
singularity at 0. The order, n, is the relative order of the Taylor polynomial–the difference in order
between the largest and smallest power of global in the polynomial.
TAYLR always returns a symbolic result, regardless of the state of the Numeric Results flag (–3).
Access:
!Ö LIMITS & SERIES TAYLR
( Öis the left-shift of the 4key).
Input/Output:
See also:
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
'symb'
'global'
norder
Level 1/Item 1
→
'symbTaylor'
∂, ∫, Σ
TCHEBYCHEFF
CAS:
Return the nth Tchebycheff polynomial.
TCOLLECT
CAS:
Linearize products in trig expression by collecting and combining sine and cosine terms.
TDELTA
Type:
Function
Description: Temperature Delta Function: Calculates a temperature change.
TDELTA subtracts two points on a temperature scale, yielding a temperature increment (not an
actual temperature). x or x_unit1 is the final temperature, and y or y_unit2 is the initial
temperature. If unit objects are given, the increment is returned as a unit object with the same
units as x_unit1. If real numbers are given, the increment is returned as a real number.
Access:
…µ TDELTA
Flags:
Numerical Results (-3)
Input/Output:
See also:
TESTS
CAS:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
xdelta
x_unit1
x_unit2
→
x_unit1delta
x_unit
'symb'
→
'TDELTA(x_unit, symb)'
'symb'
y_unit
→
'TDELTA(symb, y_unit)'
'symb1'
'symb2'
→
'TDELTA(symb1, symb2)'
TINC
Display menu or list with tests that work in algebraic expressions, and ASSUME and
UNASSUME.
TEVAL
Type:
Function
Description: For the specified operation, performs the same function as EVAL, and returns the time taken to
perform the evaluation as well as the result.
Access:
…µ TEVAL
Input/Output:
Level 1/Argument 1
Object
See also:
EVAL
3-182 Full Command and Function Reference
→
Level 2/Item 2
Level 1/Item 1
result
time taken
TEXPAND
CAS:
Expand transcendental functions in an expression.
TEXT
Type:
Command
Description: Show Stack Display Command: Displays the stack display.
TEXT switches from the graphics display to the stack display. TEXT does not update the stack
display.
Access:
!° LOUT TEXT
( °is the left-shift of the Nkey).
Input/Output: None
See also:
PICTURE, PVIEW
THEN
Type:
Command
Description: THEN Command: Starts the true-clause in conditional or error-trapping structure.
See the IF and IFFER entries for more information.
Access:
!° BRANCH IF/CASE THEN
( °is the left-shift of the Nkey).
Input/Output: None
See also:
CASE, ELSE, END, IF IFERR
TICKS
Type:
Command
Description: Ticks Command: Returns the system time as a binary integer, in units of 1/8192 second.
Access:
…ÓTOOLS TICKS
( Ó is the right-shift of the 9 key).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
Example:
See also:
#ntime
If the result from a previous invocation from TICKS is on level 1 of the stack, then the
command: TICKS SWAP - B→R 8192 /
returns a real number whose value is the elapsed time in seconds between the two invocations.
TIME
TIME
Type:
Command
Description: Time Command: Returns the system time in the form HH.MMSSs.
time has the form HH.MMSSs, where HH is hours, MM is minutes, SS is seconds, and s is zero
or more digits (as many as allowed by the current display mode) representing fractional seconds.
time is always returned in 24-hour format, regardless of the state of the Clock Format flag (–41).
Access:
…Ó TOOLS TIME
(Ó is the right-shift of the 9 key).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
time
DATE, TICKS, TSTR
→TIME
Type:
Command
Description: Set System Time Command: Sets the system time.
time must have the form HH.MMSSs, where HH is hours, MM is minutes, SS is seconds, and s is
zero or more digits (as many as allowed by the current display mode) representing fractional
seconds. time must use 24-hour format.
Full Command and Function Reference 3-183
Access:
…ÓTOOLS →TIME
Input/Output:
(Ó is the right-shift of the 9 key).
Level 1/Argument 1
→
time
See also:
Level 1/Item 1
CLKADJ, →DATE
TINC
Type:
Function
Description: Temperature Increment Command: Calculates a temperature increment.
TINC adds a temperature increment (not an actual temperature) to a point on a temperature scale.
Use a negative increment to subtract the increment from the temperature. xinitial or x_unit1 is the
initial temperature, and ydelta or y_unit2delta is the temperature increment. The returned temperature
is the resulting final temperature. If unit objects are given, the final temperature is returned as a
unit object with the same units as x_unit1. If real numbers are given, the final temperature is
returned as a real number.
Access:
…µ TINC
Flags:
Numerical Results (-3)
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
xinitial
ydelta
→
xfinal
x_unit1
y_unit2delta
→
x_unit1final
x_unit
'symb'
→
'TINC(x_unit, symb)'
'symb'
y_unitdelta
→
'TINC(symb, y_unitdelta)'
'symb1'
'symb2'
→
'TINC(symb1, symb2)'
See also:
TDELTA
TLIN
CAS:
Linearize and simplify trig expression but do not collect sine and cosine terms of the same angle.
TLINE
Type:
Command
Description: Toggle Line Command: For each pixel along the line in PICT defined by the specified
coordinates, TLINE turns off every pixel that is on, and turns on every pixel that is off.
Access:
!°L PICT TLINE
( °is the left-shift of the Nkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
(x1,y1)
(x2,y2)
→
{ #n2 #m2 }
→
{ #n1 #m1 }
ARC, BOX, LINE
Level 1/Item 1
TMENU
Type:
Command
Description: Temporary Menu Command: Displays a built-in menu, library menu, or user-defined menu.
TMENU works just like MENU, except for user-defined menus (specified by a list or by the
name of a variable that contains a list). Such menus are displayed like a custom menu and work
like a custom menu, but are not stored in reserved variable CST. Thus, a menu defined and
displayed by TMENU cannot be redisplayed by evaluating CST.
3-184 Full Command and Function Reference
See Appendix H for a list of the hp49g+/hp48gII built-in menus and the corresponding menu
numbers (xmenu).
Access:
„&H MENU TMENU
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
xmenu
→
{ listdefinition }
→
'namedefinition'
→
MENU, RCLMENU
TOT
Type:
Command
Description: Total Command: Computes the sum of each of the m columns of coordinate values in the
current statistics matrix (reserved variable ΣDAT).
The sums are returned as a vector of m real numbers, or as a single real number if m = 1.
Access:
…µ TOT
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xsum
→
[ xsum 1, xsum 2, ... ,xsum m ]
MAXΣ, MINΣ, MEAN, PSDEV, PVAR, SDEV, VAR
TRACE
Type:
Command
Description: Matrix Trace Command: Returns the trace of a square matrix.
The trace of a square matrix is the sum of its diagonal elements.
Access:
!Ø OPERATIONS LL TRACE
( Ø is the left-shift of the 5key).
!´MATRIX NORMALIZE L TRACE
( ´ is the left-shift of the Pkey).
Input/Output:
Level 1/Argument 1
[[ matrix ]]n×n
See also:
Level 1/Item 1
→
xtrace
CONJ, DET, IDN
TRAN
Type:
Command
Description: Transpose Matrix Command: Returns the transpose of a matrix.
Same as TRN, but without conjugation of complex numbers.
Access:
!Ø OPERATIONS LLTRAN
( Ø is the left-shift of the 5key).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
[[ matrix ]]
→
'name'
→
[[ matrix ]]transpose
CONJ, TRN
TRANSIO
Type:
Command
Full Command and Function Reference 3-185
Description: I/O Translation Command: Specifies the character translation option. These translations affect
only ASCII Kermit transfers and files printed to the serial port.
Legal values for n are as follows:
n
Effect
0
No translation
1
Translate character 10 (line feed only) to /from characters 10 and 13 (line feed with
carriage return, the Kermit protocol) (the default value)
2
Translate characters 128 through 159 (80 through 9F hexadecimal)
3
Translate all characters (128 through 255)
Access:
…µ TRANSIO
Input/Output:
Level 1/Argument 1
noption
Level 1/Item 1
→
See also:
BAUD, CKSM, PARITY
TRIG
CAS:
Convert complex log and exponential terms into equivalent trig terms, also simplify trig terms.
TRIGCOS
CAS:
Simplify trig terms by applying (sinx)2 + (cosx)2 = 1, return only cosine terms if possible.
TRIGO
CAS:
Display menu or list containing the CAS commands for transforming trigonometric expressions.
TRIGSIN
CAS:
Simplify trig terms by applying (sinx)2 + (cosx)2 = 1, return only sine terms if possible.
TRIGTAN
CAS:
Replace sine and cosine terms in a trigonometric expression with tan terms.
TRN
Type:
Command
Description: Transpose Matrix Command: Returns the (conjugate) transpose of a matrix.
TRN replaces an n × m matrix A with an m × n matrix AT, where:
AijT = Aji for real matrices and AijT = CONJ(Aji) for complex matrices
If the matrix is specified by name, AT replaces A in name.
( ´ is the left-shift of the Pkey).
Access:
!´ MATRIX MAKE TRN
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
[[ matrix ]]
→
'name'
→
[[ matrix ]]transpose
CONJ, TRAN
TRNC
Type:
Function
Description: Truncate Function: Truncates an object to a specified number of decimal places or significant
digits, or to fit the current display format.
ntruncate (or symbtruncate if flag –3 is set) controls how the level 2 argument is truncated, as follows:
3-186 Full Command and Function Reference
ntruncate
0 through 11
truncated to n decimal places
–1 through –11
truncated to n significant digits
12
truncated to the current display format
Effect on Level 2 Argument
For complex numbers and arrays, each real number element is truncated. For unit objects, the
number part of the object is truncated.
Access:
!´ REAL LLTRNC
Flags:
Numerical Results (-3)
Input/Output:
( ´ is the left-shift of the Pkey).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
ntruncate
→
z2
z1
'symbtruncate'
→
'TRNC(z1,symbtruncate)'
'symb1'
ntruncate
→
'TRNC(symb1,ntruncate)'
'symb1'
'symbtruncate'
→
'TRNC(symb1,symbtruncate)'
[ array ]1
ntruncate
→
[ array ]2
x_unit
ntruncate
→
y_unit
x_unit
'symbtruncate'
→
'TRNC(x_unit,symbtruncate)'
See also:
RND
TRUNC
CAS:
Truncate a series expansion, performing the expansion, or using a given polynomial.
TRUTH
Type:
Command
Description: Truth Plot Type Command: Sets the plot type to TRUTH.
When the plot type is TRUTH, the DRAW command plots the current equation as a truthvalued function of two real variables. The current equation is specified in the reserved variable
EQ. The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type TRUTH, the elements of PPAR are used as follows:
• (xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9) for the
hp49g+.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0) for the
hp49g+.
• indep is a name specifying the independent variable on the horizontal axis, or a list containing
such a name and two numbers specifying the minimum and maximum values for the
independent variable (the horizontal plotting range). The default value is X.
• res is a real number specifying the interval (in user-unit coordinates) between plotted values of
the independent variable on the horizontal axis, or a binary integer specifying that interval in
pixels. The default value is 0, which specifies an interval of 1 pixel.
• axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. The default
value is (0,0).
Full Command and Function Reference 3-187
• ptype is a command name specifying the plot type. Executing the command TRUTH places
the name TRUTH in ptype.
• depend is a name specifying the independent variable on the vertical axis, or a list containing
such a name and two numbers specifying the minimum and maximum values for the
independent variable on the vertical axis (the vertical plotting range). The default value is Y.
The contents of EQ must be an expression or program, and cannot be an equation. It is
evaluated for each pixel in the plot region. The minimum and maximum values of the
independent variables (the plotting ranges) can be specified in indep and depend; otherwise, the
values in (xmin, ymin) and (xmax, ymax)(the display range) are used. The result of each evaluation
must be a real number. If the result is zero, the state of the pixel is unchanged. If the result is
nonzero, the pixel is turned on (made dark).
Access:
…µ TRUTH
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, WIREFRAME, YSLICE
TSIMP
CAS:
Simplify expressions involving exponentials and logs, convert base 10 logs to natural logs.
TSTR
Type:
Command
Description: Date and Time String Command: Returns a string derived from the date and time.
The string has the form "DOW DATE TIME", where DOW is a three-letter abbreviation of the
day of the week corresponding to the argument date and time, DATE is the argument date in the
current date format, and TIME is the argument time in the current time format.
Access:
…ÓTOOLS LLTSTR
( Ó is the right-shift of the 9 key).
Flags:
Time Format (-41), Date Format (-42)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
date
time
Level 1/Item 1
→
“DOW DATE TIME“
DATE, TICKS, TIME
TVARS
Type:
Command
Description: Typed Variables Command: Lists all global variables in the current directory that contain objects
of the specified types.
If the current directory contains no variables of the specified types, TVARS returns an empty list.
For a table of the object-type numbers, see the entry for TYPE.
Access:
!° MEMORY DIRECTORY LTVARS
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
ntype
→
{ global ... }
{ ntype ...}
→
{ global ... }
PVARS, TYPE, VARS
TVM
Type:
Command
Description: TVM Menu Command: Displays the TVM Solver menu.
Access:
…µ TVM
3-188 Full Command and Function Reference
Input/Output: None
See also:
AMORT, TVMBEG, TVMEND, TVMROOT
TVMBEG
Type:
Command
Description: Payment at Start of Period Command: Specifies that TVM calculations treat payments as being
made at the beginning of the compounding periods.
Access:
…µ TVMBEG
Input/Output: None
See also:
AMORT, TVM, TVMEND, TVMROOT
TVMEND
Type:
Command
Description: Payment at End of Period Command: Specifies that TVM calculations treat payments as being
made at the end of the compounding periods.
Access:
…µ TVMEND
Input/Output: None
See also:
AMORT, TVM, TVMBEG, TVMROOT
TVMROOT
Type:
Command
Description: TVM Root Command: Solves for the specified TVM variable using values from the remaining
TVM variables.
Access:
…µ TVMROOT
Input/Output:
Level 1/Argument 1
'TVM variable'
See also:
Level 1/Item 1
→
xTVM variable
AMORT, TVM, TVMBEG, TVMEND
TYPE
Type:
Command
Description: Type Command: Returns the type number of an object, as shown in the following table:
Full Command and Function Reference 3-189
Object Type:
Number:
User objects:
Real number
Complex number
Character string
Real array
Complex array
List
Global name
Local name
Program
Algebraic object
Binary integer
Graphics object
Tagged object
XLIB name
Library
Backup object
Access:
!°
Input/Output:
Object Type:
28
30
Real integer
Font
Built-in Commands:
Built-in function
Built-in command
System Objects:
System binary
Extended real
Extended complex
Linked array
Character
Code object
Library data
Mini font
Symbolic vector/matrix
Extended object
0
1
2
3
4
5
6
7
8
9
10
11
12
14
16
17
TEST LTYPE
18
19
20
21
22
23
24
25
26
27
29
31
( °is the left-shift of the Nkey).
Level 1/Argument 1
Level 1/Item 1
→
obj
See also:
Number:
ntype
SAME, TVARS, VTYPE, ==
UBASE
Type:
Function
Description: Convert to SI Base Units Function: Converts a unit object to SI base units.
Access:
!Ú UNITS TOOLS UBASE
( Ú is the left-shift of the 6key).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
x_unit
See also:
'symb'
CONVERT, UFACT, →UNIT, UVAL
Level 1/Item 1
→
y_base-units
→
'UBASE(symb)'
UFACT
Type:
Command
Description: Factor Unit Command: Factors the level 1 unit from the unit expression of the level 2 unit
object.
Access:
!Ú UNITS TOOLS UFACT
( Ú is the left-shift of the 6key).
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
x1_unit1
x2_unit2
3-190 Full Command and Function Reference
Level 1/Item 1
→
x3_unit2*unit3
See also:
CONVERT, UBASE, →UNIT, UVAL
UFL1→MINIF
Type:
Command
Description: Converts a UFL1 (universal font library) fontset to an hp49g+/hp48gII minifont.
You specify the fontset and give it an ID (0–255). The font must be a 6-by-4 font.
Access:
…µUFL1→MINIF
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
objfontset
nID
Level 1/Item 1
→
The font converted to minifont.
→MINIFONT, MINIFONT→
UNASSIGN
CAS:
Remove global variables and return their values; an algebraic version of PURGE.
UNASSUME
CAS:
Cancel assumptions on global variables, removing variable names from REALASSUME list.
UNBIND
CAS:
Remove all local variables created by the LOCAL command, and return their values.
→UNIT
Type:
Command
Description: Stack to Unit Object Command: Creates a unit object from a real number and the unit part of a
unit object. →UNIT adds units to a real number, combining the number and the unit part of a
unit object (the numerical part of the unit object is ignored). →UNIT is the reverse of OBJ→
applied to a unit object.
Access:
…µ →UNIT
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
x
y_unit
Level 1/Item 1
→
x_unit
→ARRY, →LIST, →STR, →TAG
UNPICK
Type:
RPL Command
Description: Replaces the object at level n+2 with the object at level 2 and deletes the objects at levels 1 and 2.
Access:
!° STACK L UNPICK
( °is the left-shift of the Nkey).
Input/Output:
Ln+2
See also:
Ln+1
L3
L2
objn
objn-1
obj1
obj
OVER, PICK, ROLL, ROLLD, SWAP, ROT
L1
n
→
Ln
Ln–1
L1
obj
objn-1
obj1
UNROT
Type:
RPL Command
Description: Changes the order of the first three objects on the stack. The order of the change is the opposite
to that of the ROT command.
Access:
!° STACK UNROT
( °is the left-shift of the Nkey).
Full Command and Function Reference 3-191
Input/Output:
L3
See also:
L2
L1
→
obj3
obj2
obj1
OVER, PICK, ROLL, ROLLD, SWAP, ROT
L3
L2
L1
obj1
obj3
obj2
UNTIL
Type:
Command
Description: UNTIL Command: Starts the test clause in a DO … UNTIL … END indefinite loop structure.
See the DO entry for more information.
Access:
!° BRANCH DO UNTIL
( °is the left-shift of the Nkey).
Input/Output: None
See also:
DO, END
UPDIR
Type:
Command
Description: Up Directory Command: Makes the parent of the current directory the new current directory.
UPDIR has no effect if the current directory is HOME.
Access:
!§
( §is the left-shift of the Jkey).
Input/Output: None
See also:
CRDIR, HOME, PATH, PGDIR
UTPC
Type:
Command
Description: Upper Chi-Square Distribution Command: Returns the probability utpc(n, x) that a chi-square
random variable is greater than x, where n is the number of degrees of freedom of the
distribution.
The defining equations are these:
• For x ≥ 0:
1
utpc ( n, x ) = --------------n
--n
2
2 Γ ( --2- )
∞
∫t
n
--- – 1
2
– 2--t-
⋅ e dt
x
• For x < 0:
utpc ( n, x ) ) = 1
For any value z, Γ ⎛⎝ --z-⎞⎠ = ⎛⎝ --z- – 1⎞⎠ ! , where ! is the factorial command.
2
2
The value n is rounded to the nearest integer and, when rounded, must be positive.
Access:
!´ L PROBABILITY L UTPC
Input/Output:
Level 2/Argument 1
See also:
n
UTPF, UTPN, UTPT
UTPF
Type:
Command
( ´ is the left-shift of the Pkey).
Level 1/Argument 2
3-192 Full Command and Function Reference
x
Level 1/Item 1
→
utpc(n,x)
Description: Upper Snedecor's F Distribution Command: Returns the probability utpf(n1, n2, x) that a
Snedecor's F random variable is greater than x, where n1 and n2 are the numerator and
denominator degrees of freedom of the F distribution.
The defining equations for utpf(n1, n2, x) are these:
• For x ≥ 0:
n 1 + n 2⎞
n1
----- Γ ⎛ ---------------2
n
⎝
1
2 ⎠
⎛ -----⎞
-----------------------------⎝n ⎠
n2
n1
2
Γ ⎛⎝ -----⎞⎠ Γ ⎛⎝ -----⎞⎠
2
2
∞
∫x t
n1 – 2
-------------2
( n1 + n2 )
n1
1 + ⎛⎝ ----- ⎞⎠ t
n2
– ---------------------2
dt
• For x < 0:
utp f ( n 1, n 2, x ) = 1
For any value z,
z
z
Γ ⎛⎝ ---⎞⎠ = ⎛⎝ --- – 1⎞⎠ ! , where ! is the hp49g+/hp48gII factorial command.
2
2
The values n1 and n2 are rounded to the nearest integers and, when rounded, must be positive.
Access:
!´ L PROBABILITY L UTPF
Input/Output:
Level 3/Argument 1
See also:
( ´ is the left-shift of the Pkey).
Level 2/Argument 2
Level 1/Argument 3
n2
x
n1
UTPC, UTPN, UTPT
Level 1/Item 1
→
utpf(n1,n2,x)
UTPN
Type:
Command
Description: Upper Normal Distribution Command: Returns the probability utpn(m, v, x) that a normal
random variable is greater than x, where m and v are the mean and variance, respectively, of the
normal distribution.
For all x and m, and for v > 0, the defining equation is this:
2
1
utpn ( m, v, x ) = ------------2πv
(t – m)
∞ – -----------------2v
∫x e
dt
For v = 0, UTPN returns 0 for x ≥ m, and 1 for x < m.
Access:
!´ L PROBABILITY L UTPN
Input/Output:
Level 3/Argument 1
See also:
m
UTPC, UTPF, UTPT
( ´ is the left-shift of the Pkey).
Level 2/Argument 2
Level 1/Argument 3
v
x
Level 1/Item 1
→
utpn(m,v,x)
UTPT
Type:
Command
Description: Upper Student's t Distribution Command: Returns the probability utpt(n, x) that a Student's t
random variable is greater than x, where n is the number of degrees of freedom of the
distribution.
The following is the defining equation for all x:
Full Command and Function Reference 3-193
n+1
n+1
– -----------Γ ⎛⎝ ------------⎞⎠ ∞
2
2
t
2
utpt ( n, x ) = ----------------------- ∫ ⎛ 1 + ---- ⎞
dt
⎝
n⎠
n⎞
x
⎛
Γ ⎝ ---⎠ nπ
2
For any value z,
z
z
Γ ⎛⎝ ---⎞⎠ = ⎛⎝ --- – 1⎞⎠ ! , where ! is the factorial command.
2
2
The value n is rounded to the nearest integer and, when rounded, must be positive.
Access:
!´ L PROBABILITY L UTPT
Input/Output:
Level 2/Argument 1
See also:
( ´ is the left-shift of the Pkey).
Level 1/Argument 2
n
UTPC, UTPF, UTPN
Level 1/Item 1
→
x
utpt(n,x)
UVAL
Type:
Function
Description: Unit Value Function: Returns the numerical part of a unit object.
Access:
…Û TOOLS UVAL
(Û is the right-shift of the 6key).
Flags:
Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
→
x_unit
'symb'
CONVERT, UBASE, UFACT, →UNIT
x
'UVAL(symb)'
V→
Type:
Command
Description: Vector/Complex Number to Stack Command: Separates a vector or complex number into its
component elements.
For vectors with four or more elements, V→ executes independently of the coordinate system
mode, and always returns the elements of the vector to the stack as they are stored internally (in
rectangular form). Thus, V→ is equivalent to OBJ→ for vectors with four or more elements.
Access:
!´ VECTOR V→
( ´ is the left-shift of the Pkey).
Flags:
Coordinate System (-15 and -16)
Input/Output:
L1/A1
[xy]
[ xr, ytheta ]
[ x 1, x 2, x 3 ]
[ x1, xtheta, xz ]
[ x1, xtheta, xphi ]
[ x1, x2, ..., xn ]
(x, y)
(xr, ytheta)
→
→
→
→
→
→
→
→
Ln/I1 ... L3/In–2
L2/In–1
L1/In
x1
x1
x1
x1 ... xn–2
x
xr
x2
xtheta
xtheta
xn–1
x
xr
y
ytheta
x3
xz
xphi
xn
y
ytheta
L = Level; A = Argument; I = item
See also:
→V2, →V3
3-194 Full Command and Function Reference
→V2
Type:
Command
Description: Stack to Vector/Complex Number Command: Converts two specified numbers into a 2-element
vector or a complex number.
The result returned depends on the setting of flags –16 and –19, as shown in the following table:
Flag –19 clear
Flag –19 set
Flag –16 clear (Rectangular mode)
[xy]
(x, y)
Flag –16 set (Polar mode)
[xy]
(x,  y)
Access:
!´ VECTOR →V2
( ´ is the left-shift of the Pkey).
Flags:
Coordinate System (-16), Complex Mode (-19)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
[xy]
x
y
→
[xy]
x
y
→
(x, y)
x
y
→
(x,  y)
V→, →V3
→V3
Type:
Command
Description: Stack to 3-Element Vector Command: Converts three numbers into a 3-element vector.
The result returned depends on the coordinate mode used, as shown in the following table:
Mode
Result
Rectangular (flag –16 clear)
[ x1 x2 x3 ]
Polar/Cylindrical (flag –15 clear and –16 set)
[ x1 xtheta xz ]
Polar/Spherical (flag –15 and –16 set)
[ x1 xtheta xphi ]
Access:
!´ VECTOR →V3
Flags:
Coordinate System (-15 and -16)
Input/Output:
See also:
( ´ is the left-shift of the Pkey).
Level 3/Argument 1
Level 2/Argument 2
Level 1/Argument 3
Level 1/Item 1
x1
x2
x3
→
[ x1 x2 x3 ]
x1
xtheta
xz
→
[ x1 xtheta xz ]
x1
xtheta
xphi
→
[ x1 xtheta xphi ]
V→, →V2
VANDERMONDE
CAS:
Build Vandermonde matrix, or alternant matrix, from a list of objects.
Full Command and Function Reference 3-195
VAR
Type:
Command
Description: Variance Command: Calculates the sample variance of the coordinate values in each of the m
columns in the current statistics matrix (ΣDAT).
The variance (equal to the square of the standard deviation) is returned as a vector of m real
numbers, or as a single real number if m = 1. The variances are computed using this formula:
1
------------ ⋅
n–1
n
∑
i=1
(xi – x)
2
where xi is the ith coordinate value in a column, x is the mean of the data in this column, and
n is the number of data points.
Access:
…µ VAR
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
xvariance
→
[ xvariance1, ..., xvariancem ]
MAXΣ, MEAN, MINΣ, PSDEV, PVAR, SDEV, TOT
VARS
Type:
Command
Description: Variables Command: Returns a list of the names of all variables in the VAR menu for the current
directory.
Access:
!° MEMORY DIRECTORY L VARS
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
{ global1 ... globaln }
See also:
ORDER, PVARS, TVARS
VER
CAS:
Return the Computer Algebra System version number and date of release.
VERSION
Type:
Command
Description: Software Version Command: Displays the software version and copyright message.
Access:
…µ VERSION
Input/Output:
Level 1/Argument 1
→
Level 2/Item 1
Level 1/Item 2
“version number”
“copyright message”
VISIT
Type:
Command
Description: For a specified variable, opens the contents in the command-line editor.
Access:
…µ VISIT or „˜
3-196 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
A variable name
See also:
Level 1/Item 1
→
The contents opened in the command line editor.
VISITB, EDIT, EDITB
VISITB
Type:
Command
Description: For a specified variable, opens the contents in the most suitable editor for the object type. For
example, if the specified variable holds an equation, the equation is opened in Equation Writer.
Access:
…µ VISITB
Input/Output:
Level 1/Argument 1
A variable name
See also:
Level 1/Item 1
→
The contents opened in the most suitable editor.
VISIT, EDIT, EDITB
VPOTENTIAL
CAS:
Find a vector potential function describing a field whose curl (or “rot”) is the input.
VTYPE
Type:
Command
Description: Variable Type Command: Returns the type number of the object contained in the named
variable.
If the named variable does not exist, VTYPE returns –1.
For a table of the objects' type numbers, see the entry for TYPE.
Access:
!° TYPE L L VTYPE
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
'name'
→
ntype
:nport : namebackup
→
ntype
:nport : nlibrary
→
ntype
TYPE
WAIT
Type:
Command
Description: Wait Command: Suspends program execution for specified time, or until a key is pressed.
The function of WAIT depends on the argument, as follows:
• Argument x interrupts program execution for x seconds.
• Argument 0 suspends program execution until a valid key is pressed (see below). WAIT then
returns xkey, which defines where the pressed key is on the keyboard, and resumes program
execution.
xkey is a three-digit number that identifies a key's location on the keyboard. See the entry for
ASN for a description of the format of xkey.
Full Command and Function Reference 3-197
• Argument –1 works as with argument 0, except that the currently specified menu is also
displayed.
!, …, ~, ~!, and ~… are not by themselves valid keys.
Arguments 0 and –1 do not affect the display, so that messages persist even though the keyboard
is ready for input (FREEZE is not required).
Normally, the MENU command does not update the menu keys until a program halts or ends.
WAIT with argument –1 enables a previous execution of MENU to display that menu while the
program is suspended for a key press.
Access:
!° L
Input/Output:
( °is the left-shift of the Nkey).
IN WAIT
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
0
→
xkey
–1
→
xkey
KEY
WHILE
Type:
Command Operation
Description: WHILE Indefinite Loop Structure Command: Starts the WHILE … REPEAT … END
indefinite loop structure.
WHILE … REPEAT … END repeatedly evaluates a test and executes a loop clause if the test is
true. Since the test clause occurs before the loop-clause, the loop clause is never executed if the
test is initially false. The syntax is this:
WHILE test-clause REPEAT loop-clause END
The test clause is executed and must return a test result to the stack. REPEAT takes the value
from the stack. If the value is not zero, execution continues with the loop clause; otherwise,
execution resumes following END.
Access:
!° BRANCH WHILE
( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
WHILE
REPEAT
END
See also:
T/F
→
→
DO, END, REPEAT
WIREFRAME
Type:
Command
Description: WIREFRAME Plot Type Command: Sets the plot type to WIREFRAME.
When the plot type is set to WIREFRAME, the DRAW command plots a perspective view of
the graph of a scalar function of two variables. WIREFRAME requires values in the reserved
variables EQ, VPAR, and PPAR.
VPAR has the following form:
{ xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep }
For plot type WIREFRAME, the elements of VPAR are used as follows:
3-198 Full Command and Function Reference
xleft and xright are real numbers that specify the width of the view space.
ynear and yfar are real numbers that specify the depth of the view space.
zlow and zhigh are real numbers that specify the height of the view space.
xmin and xmax are not used.
ymin and ymax are not used.
xeye, yeye, and zeye are real numbers that specify the point in space from which the graph is
viewed.
• xstep and ystep are real numbers that set the number of x-coordinates versus the number of ycoordinates plotted.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
For plot type WIREFRAME, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is not used.
• axes is not used.
• ptype is a name specifying the plot type. Executing the command WIREFRAME places the
command name WIREFRAME in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
•
•
•
•
•
•
Access:
…µ WIREFRAME
Input/Output: None
See also:
BAR, CONIC DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, YSLICE
WSLOG
Type:
Command
Description: Warmstart Log Command: Returns four strings recording the date, time, and cause of the four
most recent warmstart events.
Each string "logn" has the form "code–date time". The following table summarizes the legal values
of code and their meanings.
Code
Description
0
The warmstart log was cleared by pressing $†.
1
The interrupt system detected a very low battery condition at the battery contacts
(not the same as a low system voltage), and put the calculator in “Deep Sleep
mode” (with the system clock running). When $ is pressed after the battery voltage
is restored, the system warmstarts and puts a 1 in the log.
2
Hardware failed during transmission (timeout).
3
Run through address 0.
4
System time is corrupt
5
A Deep Sleep wakeup (for example, $, Alarm).
6
Not used
Full Command and Function Reference 3-199
Code
Description
7
A 5-nibble word (CMOS test word) in RAM was corrupt. (This word is checked
on every interrupt, but it is used only as an indicator of potentially corrupt RAM.)
8
Not used
9
The alarm list is corrupt.
A
System RPL jump to #0.
B
The card module was removed (or card bounce).
C
Hardware reset occurred (for example, an electrostatic discharge or user reset)
D
An expected System (RPL) error handler was not found in runstream
The date and time stamp (date time) part of the log may be displayed as 00…0000 for one of three
reasons:
• The system time was corrupt when the stamp was recorded.
• The date and time stamp itself is corrupt (bad checksum).
• Fewer than four warmstarts have occurred since the log was last cleared.
Access:
…µ WSLOG
Flags:
Date Format (-42)
Input/Output:
Level 1/Argument 1
Level 4/Item 1 ... Level 1/Item 4
→
“log4” ... “log1”
ΣX
Type:
Command
Description: Sum of x-Values Command: Sums the values in the independent-variable column of the current
statistical matrix (reserved variable ΣDAT).
The independent-variable column is specified by XCOL and is stored as the first parameter in
the reserved variable ΣPAR. The default independent-variable column number is 1.
Access:
…µΣX
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
xsum
NΣ, XCOL, ΣXY, ΣX2, ΣY, ΣY2
ΣX2
Type:
Command
Description: Sum of Squares of x-Values Command: Sums the squares of the values in the independentvariable column of the current statistical matrix (reserved variable ΣDAT).
The independent-variable column is specified by XCOL and is stored as the first parameter in
the reserved variable ΣPAR. The default independent-variable column number is 1.
Access:
…µΣX2
3-200 Full Command and Function Reference
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Sum of X2
NΣ, ΣX, XCOL, ΣXY, ΣY, ΣY2
XCOL
Type:
Command
Description: Independent Column Command: Specifies the independent-variable column of the current
statistics matrix (reserved variable ΣDAT).
The independent-variable column number is stored as the first parameter in the reserved variable
ΣPAR. The default independent-variable column number is 1.
XCOL will accept a noninteger real number and store it in ΣPAR, but subsequent commands
that utilize the XCOL specification in ΣPAR will cause an error.
Access:
…µXCOL
Input/Output:
Level 1/Argument 1
ncol
See also:
Level 1/Item 1
→
BARPLOT, BESTFIT, COLΣ, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR,
PREDX, PREDY, PWRFIT, SCATRPLOT, YCOL
XGET
Type:
Command
Description: XModem Get Command: Retrieves a specified filename via XMODEM from another calculator.
The other calculator needs to be in server mode for the operation to work (G I/O FUNCTIONS
START SERVER).
Access:
…µ XGET
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'name'
BAUD, RECN, RECV, SEND XRECV, XSERV, XPUT
XMIT
Type:
Command
Description: Serial Transmit Command: Sends a string serially without using Kermit protocol, and returns a
single digit that indicates whether the transmission was successful.
XMIT is useful for communicating with non-Kermit devices such as RS-232 printers.
If the transmission is successful, XMIT returns a 1. If the transmission is not successful, XMIT
returns the unsent portion of the string and a 0. Use ERRM to get the error message.
After receiving an XOFF command (with transmit pacing in the reserved variable IOPAR set),
XMIT stops transmitting and waits for an XON command. XMIT resumes transmitting if an
XON is received before the time-out set by STIME elapses; otherwise, XMIT terminates, returns
a 0, and stores "Timeout" in ERRM.
Access:
…µ XMIT
Flags:
I/O Device (-33)
Full Command and Function Reference 3-201
Input/Output:
Level 1/Argument 1
Level 2/Item 1
Level 1/Item 2
→
“string”
1
→
See also:
“string”
BUFLEN, SBRK, SRECV, STIME
“substringunsent”
XNUM
CAS:
Convert objects to 12-digit decimal numeric values.
0
XOR
Type:
Function
Description: Exclusive OR Function: Returns the logical exclusive OR of two arguments.
When the arguments are binary integers or strings, XOR does a bit-by-bit (base 2) logical
comparison:
• Binary integer arguments are treated as sequences of bits with length equal to the current
wordsize. Each bit in the result is determined by comparing the corresponding bits (bit1 and
bit2) in the two arguments, as shown in the following table:
bit1
bit1 XOR bit2
bit2
0
0
0
0
1
1
1
0
1
1
1
0
• String arguments are treated as sequences of bits, using 8 bits per character (that is, using the
binary version of the character code). The two string arguments must be the same length.
When the arguments are real numbers or symbolics, XOR simply does a true/false test. The
result is 1 (true) if either, but not both, arguments are nonzero; it is 0 (false) if both arguments
are nonzero or zero. This test is usually done to compare two test results.
If either or both of the arguments are algebraic objects, then the result is an algebraic of the form
symb1 XOR symb2. Execute →NUM (or set flag –3 before executing XOR) to produce a numeric
result from the algebraic result.
Access:
…ã L LOGIC XOR
(ã is the right-shift of the 3key).
!´ BASE L LOGIC XOR
( ´ is the left-shift of the Pkey).
Flags:
Binary Integer Wordsize (-5 through -10), Binary Integer Base (-11, -12)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
#n1
#n2
→
#n3
“string1”
“string2”
→
“string3”
T/F1
T/F2
→
0/1
T/F
'symb'
→
'T/F XOR symb'
'symb'
T/F
→
'symb XOR T/F'
'symb1'
'symb2'
→
'symb1 XOR symb2'
AND, NOT, OR
XPON
Type:
Function
Description: Exponent Function: Returns the exponent of the argument.
3-202 Full Command and Function Reference
Access:
!´ REAL L XPON
Flags:
Numerical Results (-3)
Input/Output:
( ´ is the left-shift of the Pkey).
Level 1/Argument 1
See also:
Level 1/Item 1
x
→
nexpon
'symb'
→
'XPON(symb)'
MANT, SIGN
XPUT
Type:
Command
Description: XModem Send Command: Sends a specified filename via XMODEM to a calculator. The
receiving calculator needs to be in Server mode (G I/O FUNCTIONS START SERVER).
Access:
…µ XPUT
Input/Output:
Level 1/Argument 1
Level 1/Item 1
See also:
→
'name'
BAUD, RECN, RECV, SEND XRECV, XSERV, XGET
XQ
CAS:
Convert a number, or a list of numbers, in decimal format, to quotient (rational) format.
XRECV
Type:
Command
Description: XModem Receive Command: Prepares the hp49g+/hp48gII to receive an object via XModem.
The received object is stored in the given variable name.
The transfer will start more quickly if you start the XModem sender before executing XRECV.
Invalid object names cause an error. If flag –36 is clear, object names that are already in use also
cause an error.
If you are transferring data between two hp49g+/hp48gII calculators, executing {AAA BBB
CCC} XRECV receives AAA, BBB, and CCC. You also need to use a list on the sending end
({AAA BBB CCC} XSEND, for example).
Access:
…µ XRECV
Flags:
I/O Device (-33), RECV Overwrite (-36)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'name'
BAUD, RECV, RECN, SEND, XSEND
XRNG
Type:
Command
Description: x-Axis Display Range Command: Specifies the x-axis display range.
The x-axis display range is stored in the reserved variable PPAR as xmin and xmax in the complex
numbers (xmin, ymin) and (xmax, ymax). These complex numbers are the first two elements of PPAR
and specify the coordinates of the lower left and upper right corners of the display ranges.
The default values of xmin and xmax are –6.5 and 6.5, respectively.
Access:
…µ XRNG
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
xmin
xmax
AUTO, PDIM, PMAX, PMIN, YRNG
Level 1/Item 1
→
Full Command and Function Reference 3-203
XROOT
Type:
Analytic function
Description: xth Root of y Command: Computes the xth root of a real number.
XROOT is equivalent to y1/x, but with greater accuracy.
If y < 0, x must be an integer.
Access:
…»
(» is the right-shift of the Rkey).
Flags:
Numerical Results (-3)
Input/Output(RPN):
Level 2
Level 1
Level 1
y
x
→
xy
'symb1'
'symb2'
→
'XROOT(symb2,symb1)'
'symb'
x
→
'XROOT(x,symb)'
y
'symb'
→
'XROOT(symb,y)'
y_unit
x
→
y_unit
'symb'
→
Argument 1
Argument 2
y
x
→
yx
'symb1'
'symb2'
→
'XROOT(symb1,symb2)'
'symb'
x
→
'XROOT(symb,x)'
y
'symb'
→
'XROOT(y,symb)'
x
y_unit
→
'symb'
y_unit
→
xy
_unit1/x
'XROOT(symb,y_unit)'
Input/Output(ALG):
Level 1
xy
_unit1/x
'XROOT(symb,y_unit)'
XSEND
Type:
Command
Description: XModem Send Command: Sends a copy of the named object via XModem.
A receiving hp49g+/hp48gII must execute XRECV to receive an object via XModem.
The transfer occurs more quickly if you start the receiving XModem after executing XSEND.
Also, configuring the receiving modem not to do CRC checksums (if possible) will avoid a 30 to
60-second delay when starting the transfer.
If you are transferring data between two hp49g+/hp48gIIs, executing {AAA BBB CCC}
XSEND sends AAA, BBB, and CCC. You also need to use a list on the receiving end ( {AAA
BBB CCC} XRECV, for example).
Access:
…µ XSEND
Flags:
I/O Device (-33)
Input/Output:
Level 1/Argument 1
See also:
'name'
BAUD, RECN, RECV, SEND XRECV
3-204 Full Command and Function Reference
Level 1/Item 1
→
XSERV
Type:
Command
Description: XModem Server Command: Puts the calculator in Xmodem server mode. When in server mode,
the following commands are available:
P: Put a file in the calculator
G: Get a file from the calculator
E: Execute a command line
M Get the calculator memory
L: List the files in the current directory
Access:
…µ XSERV
See also:
BAUD, RECN, RECV, SEND XRECV, XGET, XPUT
XVOL
Type:
Command
Description: X Volume Coordinates Command: Sets the width of the view volume in the reserved variable
VPAR.
xleft and xright set the x-coordinates for the view volume used in 3D plots. These values are stored
in the reserved variable VPAR.
Access:
…µ XVOL
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
xleft
xright
EYEPT, XXRNG, YVOL, YYRNG, ZVOL
Level 1/Item 1
→
XXRNG
Type:
Command
Description: X Range of an Input Plane (Domain) Command: Specifies the x range of an input plane
(domain) for GRIDMAP and PARSURFACE plots.
xmin and xmax are real numbers that set the x-coordinates for the input plane. These values are
stored in the reserved variable VPAR.
Access:
…µ XXRNG
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
Level 1/Item 1
→
xmin
xmax
EYEPT, NUMX, NUMY, XVOL, YVOL, YYRNG, ZVOL
ΣXY
Type:
Command
Description: Sum of X times Y command: Sums the products of each of the corresponding values in the
independent- and dependent-variable columns of the current statistical matrix (reserved variable
ΣDAT). The independent column is the column designated as XCOL and the dependent column
is the column designated as YCOL.
Access:
…µΣXY
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Sum of X*Y
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL, ΣY2
Full Command and Function Reference 3-205
ΣY
Type:
Command
Description: Sum of y-Values Command: Sums the values in the dependent variable column of the current
statistical matrix (reserved variable ΣDAT).
The dependent variable column is specified by YCOL, and is stored as the second parameter in
the reserved variable ΣPAR. The default dependent variable column number is 2.
Access:
…µΣY
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Sum of Y
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL, ΣY2
ΣY2
Type:
Command
Description: Sum of squares of Y-value command: Sums the squares of the values in the dependent-variable
columns of the current statistical matrix (reserved variable ΣDAT). The dependent column is the
column designated as YCOL
Access:
…µΣY2
Input/Output:
Level 1/Argument 1
Level 1/Item 1
→
See also:
Sum of Y2
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL
YCOL
Type:
Command
Description: Dependent Column Command: Specifies the dependent variable column of the current statistics
matrix (reserved variable ΣDAT).
The dependent variable column number is stored as the second parameter in the reserved
variable ΣPAR. The default dependent variable column number is 2.
YCOL will accept a noninteger real number and store it in ΣPAR, but subsequent commands
that utilize the YCOL specification in ΣPAR will cause an error.
Access:
…µ YCOL
Input/Output:
Level 1/Argument 1
ncol
See also:
Level 1/Item 1
→
BARPLOT, BESTFIT, COLΣ, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR,
PREDX, PREDY, PWRFIT, SCATRPLOT, XCOL
YRNG
Type:
Command
Description: y-Axis Display Range Command: Specifies the y-axis display range.
The y-axis display range is stored in the reserved variable PPAR as ymin and ymax in the complex
numbers (xmin, ymin) and (xmax, ymax). These complex numbers are the first two elements of PPAR
and specify the coordinates of the lower left and upper right corners of the display ranges. The
3-206 Full Command and Function Reference
default values of ymin and ymax are –3.1 and 3.2, respectively for the hp48gII and -3.9 and 4.0,
respectively for the hp49g+.
Access:
…µ YRNG
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
ymin
ymax
AUTO, PDIM, PMAX, PMIN, XRNG
Level 1/Item 1
→
YSLICE
Type:
Command
Description: Y-Slice Plot Command: Sets the plot type to YSLICE.
When plot type is set YSLICE, the DRAW command plots a slicing view of a scalar function of
two variables. YSLICE requires values in the reserved variables EQ, VPAR, and PPAR.
VPAR has the following form:
{ xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep }
For plot type YSLICE, the elements of VPAR are used as follows:
• xleft and xright are real numbers that specify the width of the view space.
• ynear and yfar are real numbers that specify the depth of the view space.
• zlow and zhigh are real numbers that specify the height of the view space.
• xmin and xmax are not used.
• ymin and ymax are not used.
• xeye, yeye, and zeye are real numbers that specify the point in space from which the graph is
viewed.
• xstep determines the interval between plotted x-values within each “slice”.
• ystep determines the number of slices to draw.
The plotting parameters are specified in the reserved variable PPAR, which has this form:
{ (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend }
For plot type YSLICE, the elements of PPAR are used as follows:
• (xmin, ymin) is not used.
• (xmax, ymax) is not used.
• indep is a name specifying the independent variable. The default value of indep is X.
• res is a real number specifying the interval, in user-unit coordinates, between plotted values of
the independent variable; or a binary integer specifying the interval in pixels. The default value
is 0, which specifies an interval of 1 pixel.
• axes is not used.
• ptype is a command name specifying the plot type. Executing the command YSLICE places
YSLICE in ptype.
• depend is a name specifying the dependent variable. The default value is Y.
Access:
…µ YSLICE
Input/Output: None
See also:
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC,
PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME
YVOL
Type:
Command
Description: Y Volume Coordinates Command: Sets the depth of the view volume in the reserved variable
VPAR.
Full Command and Function Reference 3-207
The variables ynear and yfar are real numbers that set the y-coordinates for the view volume used in
3D plots. ynear must be less than yfar. These values are stored in the reserved variable VPAR.
Access:
…µ YVOL
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
ynear
yfar
EYEPT, XVOL, XXRNG, YYRNG, ZVOL
Level 1/Item 1
→
YYRNG
Type:
Command
Description: Y Range of an Input Plane (Domain) Command: Specifies the y range of an input plane
(domain) for GRIDMAP and PARSURFACE plots.
The variables yy near and yy far are real numbers that set the y-coordinates for the input plane. These
values are stored in the reserved variable VPAR.
Access:
…µ YYRNG
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
→
See also:
ynear
yfar
EYEPT, XVOL, XXRNG, YVOL, ZVOL
ZEROS
CAS:
Return the zeros of a function of one variable, without giving their multiplicity.
ZFACTOR
Type:
Function
Description: Gas Compressibility Z Factor Function: Calculates the gas compressibility correction factor for
non-ideal behavior of a hydrocarbon gas.
xTr is the reduced temperature: the ratio of the actual temperature (T) to the pseudocritical
temperature (Tc). (Calculate the ratio using absolute temperatures.) xTr must be between 1.05 and
3.0.
yPr is the reduced pressure: the ratio of the actual pressure (P) to the pseudocritical pressure (Pc).
yPr must be between 0 and 30.
xTr and yPr must be real numbers or unit objects that reduce to dimensionless numbers.
Access:
…µ ZFACTOR
Flags:
Numerical Results (-3)
Input/Output:
ZVOL
Type:
Level 2/Argument 1
Level 1/Argument 2
xTr
yPr
→
xZfactor
xTr
'symb'
→
'ZFACTOR(xTr,symb)'
'symb'
yPr
→
'ZFACTOR(symb,yPr)'
'symb1'
'symb2'
→
'ZFACTOR(symb1,symb2)'
Command
3-208 Full Command and Function Reference
Level 1/Item 1
Description: Z Volume Coordinates Command: Sets the height of the view volume in the reserved variable
VPAR.
xlow and xhigh are real numbers that set the z-coordinates for the view volume used in 3D plots.
These values are stored in the reserved variable VPAR.
Access:
…µ ZVOL
Input/Output:
Level 2/Argument 1
See also:
Level 1/Argument 2
xlow
xhigh
EYEPT, XVOL, XXRNG, YVOL, YYRNG
Level 1/Item 1
→
^ (Power)
Type:
Function
Description: Power Analytic Function: Returns the value of the level 2 object raised to the power of the level
1 object. This can also apply to a square matrix raised to a whole-number power.
If either argument is complex, the result is complex.
The branch cuts and inverse relations for wz are determined by this relationship:
wz = exp(z(ln w))
Access:
Q
Flags:
Principal Solution (-1), Numerical Results (-3)
Input/Output:
Level 2/Argument 1
See also:
w
z
'symb'
'symb1'
x_unit
x_unit
EXP, ISOL, LN, XROOT
Level 1/Argument 2
z
'symb'
z
'symb2'
y
'symb'
Level 1/Item 1
→
→
→
→
→
→
wz
'z^(symb)'
'(symb)^z'
'symb1^('symb2)'
xy_unity
'(x_unit)^(symb)'
|
(Where)
Type:
Function
Description: Where Function: Substitutes values for names in an expression.
| is used primarily in algebraic objects, where its syntax is:
'symbold | (name1 = symb1, name2 = symb2 …)'
It enables algebraics to include variable-like substitution information about names. Symbolic
functions that delay name evaluation (such as ∫ and ∂) can then extract substitution information
from local variables and include that information in the expression, avoiding the problem that
would occur if the local variables no longer existed when the local names were finally evaluated.
Access:
@¦
(¦is the right-shift of the Ikey).
Flags:
Numerical Results (-3)
Input/Output:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
'symbold'
{ name1, 'symb1', name2, 'symb2' … }
→
'symbnew'
x
{ name1, 'symb1', name2, 'symb2' … }
→
x
(x,y)
{ name1, 'symb1', name2, 'symb2' … }
→
(x,y)
Full Command and Function Reference 3-209
See also:
APPLY, QUOTE
√
(Square Root)
Type:
Function
Description: Square Root Analytic Function: Returns the (positive) square root of the argument.
For a complex number (x1, y1), the square root is this complex number:
θ
θ
( x 2, y 2 ) = ⎛⎝ r cos ---, r sin ---⎞⎠
2
2
where r = ABS (x1, y1), and θ = ARG (x1, y1).
If (x1, y1) = (0,0), then the square root is (0, 0).
The inverse of SQ is a relation, not a function, since SQ sends more than one argument to the same
result. The inverse relation for SQ is expressed by ISOL as this general solution:
's1*√Z'
The function √ is the inverse of a part of SQ, a part defined by restricting the domain of SQ such that:
1. each argument is sent to a distinct result, and
2. each possible result is achieved. The points in this restricted domain of SQ are called the principal
values of the inverse relation. The √ function in its entirety is called the principal branch of the inverse
relation, and the points sent by √ to the boundary of the restricted domain of SQ form the branch
cuts of √.
The principal branch used by the hp49g+/hp48gII for √ was chosen because it is analytic in the
regions where the arguments of the real-valued inverse function are defined. The branch cut for the
complex-valued square root function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of √. The graph of the domain shows where the
branch cut occurs: the heavy solid line marks one side of the cut, while the feathered lines mark the
other side of the cut. The graph of the range shows where each side of the cut is mapped under the
function.
3-210 Full Command and Function Reference
These graphs show the inverse relation 's1*√Z' for the case s1=1. For the other value of s1, the
half-plane in the lower graph is rotated. Taken together, the half-planes cover the whole complex
plane, which is the domain of SQ.
View these graphs with domain and range reversed to see how the domain of SQ is restricted to
make an inverse function possible. Consider the half-plane in the lower graph as the restricted
domain Z = (x, y). SQ sends this domain onto the whole complex plane in the range W = (u, v)
= SQ(x, y) in the upper graph.
Access:
R
Flags:
Principal Solution (-1), Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
z
→
x_unit
→
'symb'
→
z
x unit
1⁄2
' ( symb ) '
SQ, ^, ISOL
∫
(Integrate)
Type:
Function
Description: Integral Function: Integrates an integrand from lower limit to upper limit with respect to a specified
variable of integration.
The algebraic syntax for ∫ parallels its stack syntax:
∫ (lower limit, upper limit, integrand, name)
where lower limit, upper limit, and integrand can be real or complex numbers, unit objects, names, or
algebraic expressions.
Evaluating ∫ in Symbolic Results mode (flag –3 clear) returns a symbolic result. Some functions
that the hp49g+/hp48gII can integrate include the following:
• All built-in functions whose antiderivatives can be expressed in terms of other built-in
functions—for example, SIN can be integrated since its antiderivative, COS, is a built-in
function. The arguments for these functions must be linear.
• Sums, differences, and negations of built-in functions whose antiderivatives can be expressed
in terms of other built-in functions—for example, 'SIN(X)–COS(X)'.
• Derivatives of all built-in functions—for example, 'INV(1+X^2)' can be integrated because it
is the derivative of the built-in function ATAN.
• Polynomials whose base term is linear—for example, 'X^3+X^2–2*X+6' can be integrated
since X is a linear term. '(X^2–6)^3+(X^2–6)^2' cannot be integrated since X^2–6 is not
linear.
• Selected patterns composed of functions whose antiderivatives can be expressed in terms of
other built-in functions—for example, '1/(COS(X)*SIN(X))' returns 'LN(TAN(X))'.
If the result of the integration is an expression with no integral sign in the result, the symbolic
integration was successful. If, however, the result still contains an integral sign, try rearranging
the expression and evaluating again, or estimate the answer using numerical integration.
Evaluating ∫ in Numerical Results mode (flag –3 set) returns a numerical approximation, and
stores the error of integration in variable IERR. ∫ consults the number format setting to
determine how accurately to compute the result.
Access:
…Á
(Á is the right-shift of the Ukey).
Flags:
Numerical Result (-3), Number Format (-45 to -50)
Full Command and Function Reference 3-211
Input/Output:
L4/A1
L3/A2
L2/A3
L1/A4
lower limit
upper limit
integrand
'name'
L1/I1
→
'symbintegral'
L = Level; A = Argument; I = Item
See also:
TAYLR, ∂, Σ
?
(Undefined)
CAS:
The “undefined” symbol for numeric results that are not defined by the rules of arithmetic.
∞
(Infinity)
CAS:
Symbol signifies infinite numeric result, such as division of a non-zero number by zero.
Σ
(Summation)
Type:
Function
Description: Summation Function: Calculates the value of a finite series.
The summand argument smnd can be a real number, a complex number, a unit object, a local or global
name, or an algebraic object. The algebraic syntax for Σ differs from the stack syntax. The algebraic
syntax is: 'Σ(index=initial,final,summand)'
Access:
…½
(½ is the right-shift of the Skey).
Flags:
Symbolic Constants (-2), Numerical Results (-3)
Input/Output:
L4/A1
L3/A2
L2/A3
L1/A4
L1/I1
'indx'
xinit
xfinal
smnd
→
xsum
'indx'
'init'
xfinal
smnd
→
'Σ(indx = init, xfinal, smnd)'
'indx'
xinit
'final'
smnd
→
'Σ(indx = xinit, final, smnd)'
'indx'
'init'
'final'
smnd
→
'Σ(indx = init, final, smnd)'
L = Level; A = Argument; I = Item
See also:
TAYLR, ∫, ∂
Σ+
(Sigma Plus)
Type:
Command
Description: Sigma Plus Command: Adds one or more data points to the current statistics matrix (reserved
variable ΣDAT).
For a statistics matrix with m columns, arguments for Σ+ can be entered several ways:
• To enter one data point with a single coordinate value, the argument for Σ+ must be a real
number.
• To enter one data point with multiple coordinate values, the argument for Σ+ must be a
vector with m real coordinate values.
• To enter several data points, the argument for Σ+ must be a matrix of n rows of m real
coordinate values.
In each case, the coordinate values of the data point(s) are added as new rows to the current
statistics matrix (reserved variable ΣDAT). If ΣDAT does not exist, Σ+ creates an n x m matrix
and stores the matrix in ΣDAT. If ΣDAT does exist, an error occurs if it does not contain a real
matrix, or if the number of coordinate values in each data point entered with Σ+ does not match
the number of columns in the current statistics matrix.
Once ΣDAT exists, individual data points of m coordinates can be entered as m separate real
numbers or an m-element vector. LASTARG returns the m-element vector in either case.
Access:
…µΣ+
3-212 Full Command and Function Reference
Input/Output:
Lm/A1 … L2/Am–1
L1/Am
L1/I1
x
→
[ x1, x2, …, xm ]
→
[[ x1 1, …, x1 m ] [ xn 1, … ,xn m ]]
→
xm
→
x1 … xm–1
L = Level; A = Argument; I = Item
See also:
CLΣ, RCLΣ, STOΣ, Σ–
Σ–
(Sigma Minus)
Type:
Command
Description: Sigma Minus Command: Returns a vector of m real numbers (or one number x if m = 1)
corresponding to the coordinate values of the last data point entered by Σ+ into the current
statistics matrix (reserved variable ΣDAT).
The last row of the statistics matrix is deleted.
The vector returned by Σ– can be edited or replaced, then restored to the statistics matrix by Σ+.
Access:
…µΣ–
Input/Output:
Level 1/Argument 1
See also:
π
Level 1/Item 1
→
x
→
[ x1 x2 … xm ]
CLΣ, RCLΣ, STOΣ, Σ+
(Pi)
Type:
Function
Description: π Function: Returns the symbolic constant 'π' or its numerical representation, 3.14159265359.
The number returned for π is the closest approximation of the constant π to 12-digit accuracy.
In Radians mode with flag –2 and –3 clear (to return symbolic results), trigonometric functions
of π and π/2 are automatically simplified. For example, evaluating 'SIN(π)' returns zero.
However, if flag –2 or flag –3 is set (to return numerical results), then evaluating 'SIN(π)' returns
the numerical approximation –2.06761537357E–13.
Access:
!ì
( ìis the left-shift of the #key).
Flags:
Symbolic Constants (-2), Numerical Results (-3)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
→
'π'
→
3.14159265359…
e, i, MAXR, MINR, →Qπ
∂
(Derivative)
Type:
Function
Description: Derivative Function: Takes the derivative of an expression, number, or unit object with respect
to a specified variable of differentiation.
Full Command and Function Reference 3-213
When executed in stack syntax, ∂ executes a complete differentiation: the expression 'symb1' is
evaluated repeatedly until it contains no derivatives. As part of this process, if the variable of
differentiation name has a value, the final form of the expression substitutes that value substituted
for all occurrences of the variable.
The algebraic syntax for ∂ is '∂name(symb1'). When executed in algebraic syntax, ∂ executes a
stepwise differentiation of symb1, invoking the chain rule of differentiation— the result of one
evaluation of the expression is the derivative of the argument expression symb1, multiplied by a
new subexpression representing the derivative of symb1's argument.
If ∂ is applied to a function for which thehp49g+/hp48gII does not provide a derivative, ∂
returns a new function whose name is der followed by the original function name.
Access:
…¿
(¿is the right-shift of the Tkey).
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
'symb1'
'name'
→
'symb2'
z
'name'
→
0
x_unit
'name'
→
0
TAYLOR, ∫, Σ
!
(Factorial)
Type:
Function
Description: Factorial (Gamma) Function: Returns the factorial n! of a positive integer argument n, or the
gamma function Γ(x+1) of a non-integer argument x.
For x ≥ 253.1190554375 or n < 0, ! causes an overflow exception (if flag –21 is set, the exception
is treated as an error). For non-integer x ≤ –254.1082426465, ! causes an underflow exception (if
flag –20 is set, the exception is treated as an error).
In algebraic syntax, ! follows its argument. Thus the algebraic syntax for the factorial of 7 is 7!.
For non-integer arguments x, x! = Γ(x + 1), defined for x > –1 as:
∞
Γ( x + 1 ) =
∫e
–t x
t dt
0
and defined for other values of x by analytic continuation: Γ(x + 1) = n Γ(x)
Access:
!´ L PROBABILITY !
( ´ is the left-shift of the Pkey).
Flags:
Numerical Results (-3), Underflow Exception (-20), Overflow Exception (-21)
Input/Output:
Level 1/Argument 1
See also:
Level 1/Item 1
n
→
n!
x
→
Γ(x + 1)
'symb'
→
'(symb!)'
COMB, PERM
%
(Percent)
Type:
Function
Description: Percent Function: Returns x percent of y.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a
thermometer reading, then the temperature is a unit with an additive constant: 0 ºC=273.15 K,
3-214 Full Command and Function Reference
and 0 ºF=459.67 ºR. But when ºC or ºF represents a difference in thermometer readings, then the
temperature is a unit with no additive constant: 1 ºC=1 K and 1 ºF=1 ºR.
The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any
additive constant. However, +, –, %CH, and %T require both arguments to be either absolute
(K and ºR), both ºC, or both ºF. No other combinations are allowed.
For more information on using temperature units with arithmetic functions, see the entry for +.
Access:
!´ REAL %
( ´ is the left-shift of the Pkey).
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
xy/100
x
'symb'
→
'%(x,symb)'
'symb'
x
→
'%(symb,x)'
'symb1'
'symb2'
→
'%(symb1, symb2)'
x
y_unit
→
(xy/100)_unit
x_unit
y
→
(xy/100)_unit
'symb'
x_unit
→
'%(symb,x_unit)'
x_unit
'symb'
→
'%(x_unit,symb)'
+, %CH, %T
_
(Unit attachment)
Type:
Unit attachment
Description: Unit attachment symbol: Attaches a unit type to a numeric value.
The hp49g+/hp48gII handles units by attaching the unit to a numeric value using the
underscore symbol. For example, the value of 3 kilometers is shown as 3_km, and is created by
entering 3 and then the underscore character, followed by attaching the kilometer unit.
Access:
…Ý
(Ý is the right-shift of the -key).
Input:
Numeric value
Output:
Numeric value ready for a unit attachment
« » (Program delimeters)
Type:
Object
Description: Program delimeter object: Enters a pair of program delimeter objects.
A program is a set of instructions enclosed by an open program object delimeter and a close
program object delimeter. These can be nested to have a program procedure enclosed within an
outer program object.
Access:
…å
(å is the right-shift of the +key).
Input:
None
Output:
A pair of program delimeters
<
(Less than)
Type:
Function
Description: Less Than Function: Tests whether one object is less than another object.
The function < returns a true test result (1) if the first argument is less than the second
argument, or a false test result (0) otherwise.
Full Command and Function Reference 3-215
If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or
unit object, < returns a symbolic comparison expression that can be evaluated to return a test
result.
For real numbers and binary integers, “less than” means numerically smaller (1 is less than 2).
For real numbers, “less than” also means more negative (–2 is less than –1).
For strings, “less than” means alphabetically previous (“ABC” is less than “DEF”; “AAA” is less
than “AAB”; “A” is less than “AA”). In general, characters are ordered according to their
character codes. This means, for example, that “B” is less than “a”, since “B” is character code
66, and “a” is character code 97.
For unit objects, the two objects must be dimensionally consistent, and are converted to
common units for comparison. If you use simple temperature units, the calculator assumes the
values represent temperatures and not differences in temperatures. For compound temperature
units, the calculator assumes temperature units represent temperature differences. For more
information on using temperature units with arithmetic functions, refer to the entry for +.
Access:
…Ç
Flags:
Numerical Results (-3)
Input/Output:
See also:
(Ç is the right-shift of the Xkey above the 8).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
#n1
#n2
→
0/1
0/1
“string1”
“string2”
→
0/1
x
'symb'
→
'x < symb'
'symb'
x
→
'symb < x'
'symb1'
'symb2'
→
'symb1 < symb2'
x_unit1
y_unit2
→
0/1
x_unit
'symb'
→
'x_unit < symb'
'symb'
x_unit
→
'symb < x_unit'
≤, >, ≥, ==, ≠
≤
(Less than or Equal)
Type:
Function
Description: Less Than or Equal Function: Tests whether one object is less than or equal to another object.
The function ≤ returns a true test result (1) if the first argument is less than or equal to the
second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a
name), and the other is a number or symbolic or unit object, ≤ returns a symbolic comparison
expression that can be evaluated to return a test result.
For real numbers and binary integers, “less than or equal” means numerically equal or smaller (1
is less than 2). For real numbers, “less than or equal” also means equally or more negative (–2 is
less than –1). For strings, “less than or equal” means alphabetically equal or previous (“ABC” is
less than or equal to “DEF”; “AAA” is less than or equal to “AAB”; “A” is less than or equal to
“AA”). In general, characters are ordered according to their character codes. This means, for
example, that “B” is less than “a”, since “B” is character code 66, and “a” is character code 97.
For unit objects, the two objects must be dimensionally consistent and are converted to common
units for comparison. If you use simple temperature units, the calculator assumes the values
represent temperature and not differences in temperatures. For compound temperature units, the
calculator assumes temperature units represent temperature differences. For more information
on using temperature units with arithmetic functions, refer to the entry for +.
Access:
!Æ
( Æis the left-shift of the Xkey above the 8).
3-216 Full Command and Function Reference
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
#n1
y
#n2
→
→
0/1
0/1
“string1”
“string2”
→
0/1
x
'symb'
→
'x ≤ symb'
'symb'
x
→
'symb ≤ x'
'symb1'
'symb2'
→
x_unit1
y_unit2
→
'symb1 ≤ symb2'
0/1
x_unit
'symb'
→
'x_unit ≤ symb'
'symb'
x_unit
→
'symb ≤ x_unit'
<, >, ≥, ==, ≠
>
(Greater than)
Type:
Function
Description: Greater Than Function: Tests whether one object is greater than another object.
The function > returns a true test result (1) if the first argument is greater than the second
argument, or a false test result (0) otherwise.
If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or
unit object, > returns a symbolic comparison expression that can be evaluated to return a test
result.
For real numbers and binary integers, “greater than” means numerically greater (2 is greater than
1). For real numbers, “greater than” also means less negative (–1 is greater than –2).
For strings, “greater than” means alphabetically subsequent (“DEF” is greater than “ABC”;
“AAB” is greater than “AAA”; “AA” is greater than “A”). In general, characters are ordered
according to their character codes. This means, for example, that “a” is greater than “B”, since
“B” is character code 66, and “a” is character code 97.
For unit objects, the two objects must be dimensionally consistent and are converted to common
units for comparison. If you use simple temperature units, the calculator assumes the values
represent temperatures and not differences in temperatures. For compound temperature units,
the calculator assumes temperature units represent temperature differences. For more
information on using temperature units with arithmetic functions, refer to the entry for +.
Access:
…É
(É is the right-shift of the Ykey).
Flags:
Numerical Results (-3)
Full Command and Function Reference 3-217
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
x
#n1
“string1”
x
'symb'
'symb1'
x_unit1
x_unit
'symb'
y
#n2
“string2”
'symb'
x
'symb2'
y_unit2
'symb'
x_unit
Level 1/Item 1
→
→
→
→
→
→
→
→
→
0/1
0/1
0/1
'x > symb'
'symb > x'
'symb1 > symb2'
0/1
'x_unit > symb'
'symb > x_unit'
<, ≤, ≥, ==, ≠
≥
(Greater than or Equal)
Type:
Function
Description: Greater Than or Equal Function: Tests whether one object is greater than or equal to another
object.
The function ≥ returns a true test result (1) if the first argument is greater than or equal to the
second argument, or a false test result (0) otherwise.
If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or
unit object, ≥ returns a symbolic comparison expression that can be evaluated to return a test
result.
For real numbers and binary integers, “greater than or equal to” means numerically equal or
greater (2 is greater than or equal to 1). For real numbers, “greater than or equal to” also means
equally or less negative (–1 is greater than or equal to –2).
For strings, “greater than or equal to” means alphabetically equal or subsequent (“DEF” is
greater than or equal to “ABC”; “AAB” is greater than or equal to “AAA”; “AA” is greater than
or equal to “A”). In general, characters are ordered according to their character codes. This
means, for example, that “a” is greater than or equal to “B”, since “B” is character code 66, and
“a” is character code 97.
For unit objects, the two objects must be dimensionally consistent and are converted to common
units for comparison. If you use simple temperature units, the calculator assumes the values
represent temperatures and not differences in temperatures. For compound temperature units,
the calculator assumes temperature units represent temperature differences. For more
information on using temperature units with arithmetic functions, refer to the entry for +.
Access:
!È
( Èis the left-shift of the Ykey).
Flags:
Numerical Results (-3)
3-218 Full Command and Function Reference
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
x
y
→
0/1
#n1
#n2
→
0/1
“string1”
“string2”
→
0/1
x
'symb'
→
'x ≥ symb'
'symb'
x
→
'symb ≥ x'
'symb1'
'symb2'
→
'symb1 ≥ symb2'
x_unit1
y_unit2
→
0/1
x_unit
'symb'
→
'x_unit ≥ symb'
'symb'
x_unit
→
'symb ≥ x_unit'
<, ≤, >, ==, ≠
≠
(Not equal)
Type:
Function
Description: Not Equal Function: Tests if two objects are not equal.
The function ≠ returns a true result (1) if the two objects have different values, or a false result
(0) otherwise. (Lists and programs are considered to have the same values if the objects they
contain are identical.)
If one object is algebraic or a name, and the other is a number, a name, or algebraic, ≠ returns a
symbolic comparison expression that can be evaluated to return a test result.
If the imaginary part of a complex number is 0, it is ignored when the complex number is
compared to a real number, so, for example, 6 and (6,0) and considered to be equal.
For unit objects, the two objects must be dimensionally consistent and are converted to common
units for comparison. If you use simple temperature units, the calculator assumes the values
represent temperatures and not differences in temperatures. For compound temperature units,
the calculator assumes temperature units represent temperature differences. For more
information on using temperature units with arithmetic functions, refer to the entry for +.
Access:
!Ä
( Äis the left-shift of the Wkey).
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
obj1
obj2
→
0/1
(x,0)
x
→
0/1
x
(x,0)
→
0/1
z
'symb'
→
'z ≠ symb'
'symb'
z
'symb1'
'symb2'
'symb ≠ z'
→
'symb1 ≠ symb2'
SAME, TYPE, <, ≤, >,≥, ==, ≠
*
(Multiply)
Type:
Function
Full Command and Function Reference 3-219
Description: Multiply Analytic Function: Returns the product of the arguments.
The product of a real number a and a complex number (x, y) is the complex number (xa, ya).
The product of two complex numbers (x1, y1) and (x2, y2) is the complex number (x1 x2 – y1 y2, x1
y2 + x2 y1).
The product of a real array and a complex array or number is a complex array. Each element x of
the real array is treated as a complex element (x, 0).
Multiplying a matrix by an array returns a matrix product. The matrix must have the same
number of columns as the array has rows (or elements, if it is a vector).
Although a vector is entered and displayed as a row of numbers, the hp49g+/hp48gII treats a
vector as an n × 1 matrix when multiplying matrices or computing matrix norms.
Multiplying a binary integer by a real number returns a binary integer that is the product of the
two arguments, truncated to the current wordsize. (The real number is converted to a binary
integer before the multiplication.)
The product of two binary integers is truncated to the current binary integer wordsize.
When multiplying two unit objects, the scalar parts and the unit parts are multiplied separately.
Access:
*
Flags:
Numerical Results (-3), Binary Integer Wordsize (-5 through -10)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
z2
→
z1 z2
[[ matrix ]]
[ array ]
→
[[ matrix × array ]]
z
[ array ]
→
[ z × array ]
[ array ]
z
→
[ array × z ]
z
'symb'
→
'z * symb'
'symb'
z
→
'symb * z'
'symb1'
'symb2'
→
'symb1 *symb2'
#n1
n2
→
#n3
n1
#n2
→
#n3
#n1
#n2
→
#n3
x_unit
y_unit
→
xy_unitx × unity
x
y_unit
→
xy_unit
x_unit
y
→
xy_unit
'symb'
x_unit
→
'symb * x_unit'
x_unit
'symb'
→
'x_unit * symb'
+, –, /, =
+
(Add)
Type:
Function
Description: Add Analytic Function: Returns the sum of the arguments.
The sum of a real number a and a complex number (x, y) is the complex number (x+a, y).
The sum of two complex numbers (x1, y1) and (x2, y2) is the complex number (x1+x2, y1+y2).
The sum of a real array and a complex array is a complex array, where each element x of the real
array is treated as a complex element (x, 0). The arrays must have the same dimensions.
3-220 Full Command and Function Reference
The sum of a binary integer and a real number is a binary integer that is the sum of the two
arguments, truncated to the current wordsize. (The real number is converted to a binary integer
before the addition.)
The sum of two binary integers is truncated to the current binary integer wordsize.
The sum of two unit objects is a unit object with the same dimensions as the second argument.
The units of the two arguments must be consistent.
The sum of two graphics objects is the same as the result of performing a logical OR, except that
the two graphics objects must have the same dimensions.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a
thermometer reading, then the temperature is a unit with an additive constant: 0 ºC = 273.15 K,
and 0ºF = 459.67ºR. But when ºC or ºF represents a difference in thermometer readings, then the
temperature is a unit with no additive constant: 1 ºC=1 K and 1 ºF =1 ºR.
The calculator assumes that the simple temperature units x_ºC and x_ºF represent thermometer
temperatures when used as arguments to the functions <, >, ≤, ≥, ==, and ≠. This means that, in
order to do the calculation, the calculator will first convert any Celsius temperature to Kelvins
and any Fahrenheit temperature to Rankines. (For other functions or compound temperature units,
such as x_ºC/min, the calculator assumes temperature units represent temperature differences,
so there is no additive constant involved, and hence no conversion.) The arithmetic operators +,
–, %CH, and %T treat temperatures as differences, without any additive constant, but require
both arguments to be either absolute (K and ºR), both ºC, or both ºF. No other combinations
are allowed.
Access:
+
Flags:
Numerical Results (-3), Binary Integer Wordsize (-5 through -10)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
z2
→
z1 + z2
[ array ]1
[ array ]2
→
[ array ]3
z
'symb'
→
'z +symb'
'symb'
z
→
'symb +z'
'symb1'
'symb2'
→
'symb1 + symb2'
{ list1 }
{ list2
→
{ list1 list2 }
objA
{ obj1 … objn }
→
{ objA obj1 … objn }
{ obj1 … objn }
objA
→
{obj1 … objn objA }
“string1”
“string2”
→
“string1 string2”
obj
“string”
→
“obj string”
“string”
obj
→
“string obj”
#n1
n2
→
#n3
n1
#n2
→
#n3
#n1
#n2
→
#n3
x1_unit1
y_unit2
→
(x2 + y)_unit2
'symb'
x_unit
→
'symb + x_unit'
x_unit
'symb'
→
'x_unit + symb'
grob1
grob2
→
grob3
–, *, /, =, ADD
Full Command and Function Reference 3-221
–
(Subtract)
Type:
Function
Description: Subtract Analytic Function: Returns the difference of the arguments.
The difference of a real number a and a complex number (x, y) is (x–a, y) or (a–x, –y). The
difference of two complex numbers (x1, y1) and (x2, y2) is (x1 – x2, y1 – y2).
The difference of a real array and a complex array is a complex array, where each element x of
the real array is treated as a complex element (x, 0). The two array arguments must have the same
dimensions.
The difference of a binary integer and a real number is a binary integer that is the sum of the first
argument and the two's complement of the second argument. (The real number is converted to a
binary integer before the subtraction.)
The difference of two binary integers is a binary integer that is the sum of the first argument and
the two's complement of the second argument.
The difference of two unit objects is a unit object with the same dimensions as the second
argument. The units of the two arguments must be consistent.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a
thermometer reading, then the temperature is a unit with an additive constant: 0 ºC = 273.15
K, and 0 ºF = 459.67 ºR. But when ºC or ºF represents a difference in thermometer readings,
then the temperature is a unit with no additive constant: 1 ºC = 1 K and 1 ºF = 1 ºR.
The calculator assumes that the simple temperature units x_ºC and x_ºF represent thermometer
temperatures when used as arguments to the functions <, >, ≤, ≥, ==, and ≠. This means that, in
order to do the calculation, the calculator will first convert any Celsius temperature to Kelvins
and any Fahrenheit temperature to Rankines. (For other functions or compound temperature units,
such as x_ºC/min, the calculator assumes temperature units represent temperature differences,
so there is no additive constant involved, and hence no conversion.)
The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any
additive constant, but require both arguments to be either absolute (K and ºR), both ºC, or both
ºF. No other combinations are allowed.
Access:
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
z1
z2
→
z1 – z2
[ array ]1
[ array ]2
→
[ array ]1–2
z
'symb'
→
'z – symb'
'symb'
z
→
'symb – z'
'symb1'
'symb2'
→
'symb1 – symb2'
#n1
n2
→
#n3
n1
#n2
→
#n3
#n1
#n2
→
#n3
x1_unit1
y_unit2
→
(x2 – y)_unit2
'symb'
x_unit
→
'symb – x_unit'
x_unit
'symb'
→
'x_unit – symb'
+, *, /, =
3-222 Full Command and Function Reference
Level 1/Item 1
/
(Divide)
Type:
Function
Description: Divide Analytic Function: Returns the quotient of the arguments: the first argument is divided by
the second argument.
A real number a divided by a complex number (x, y) returns:
ax
ay
⎛ ---------------, ----------------⎞
⎝ 2
2 2
2⎠
x +y x +y
A complex number (x, y) divided by a real number a returns the complex number (x/a, y/a).
A complex number (x1, y1) divided by another complex number (x2, y2) returns this complex
quotient:
⎛ x 1 x 2 + y 1 y 2 y 1 x 2 – x 1 y 2⎞
- , ---------------------------⎟
⎜ --------------------------2
2
⎝ x2 + y2
x +y ⎠
2
2
2
2
An array B divided by a matrix A solves the system of equations AX=B for X; that is, X = A–1 B.
This operation uses 15-digit internal precision, providing a more precise result than the
calculation INV(A)*B. The matrix must be square, and must have the same number of columns
as the array has rows (or elements, if the array is a vector).
A binary integer divided by a real or binary number returns a binary integer that is the integral
part of the quotient. (The real number is converted to a binary integer before the division.) A
divisor of zero returns # 0.
When dividing two unit objects, the scalar parts and the unit parts are divided separately.
Access:
/
Flags:
Numerical Results (-3)
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
z2
→
z1 / z2
[ array ]
[[ matrix ]]
→
[[ matrix–1 ×array ]]
z
'symb'
→
'z /symb'
'symb'
z
→
'symb /z'
'symb1'
'symb2'
→
'symb1 / symb2'
#n1
n2
→
#n3
n1
#n2
→
#n3
#n1
#n2
→
#n3
x_unit1
y_unit2
→
(x / y)_unit1/unit2
x
y_unit
→
(x / y)_1/unit
x_unit
y
→
(x / y)_unit
'symb'
x_unit
→
'symb / x_unit'
x_unit
'symb'
→
'x_unit / symb'
+, –, *, =
=
(Equal)
Type:
Function
Full Command and Function Reference 3-223
Description: Equals Analytic Function: Returns an equation formed from the two arguments.
The equals sign equates two expressions such that the difference between them is zero.
In Symbolic Results mode, the result is an algebraic equation. In Numerical Results mode, the
result is the difference of the two arguments because = acts equivalent to –. This allows
expressions and equations to be used interchangeably as arguments for symbolic and numerical
rootfinders.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a
thermometer reading, then the temperature is a unit with an additive constant: 0 ºC = 273.15 K,
and 0ºF = 459.67ºR. But when ºC or ºF represents a difference in thermometer readings, then the
temperature is a unit with no additive constant: 1ºC=1 K and 1ºF = 1ºR.
The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any
additive constant. However, +, –, %CH, and %T require both arguments to be either absolute
(K and ºR), both ºC, or both ºF. No other combinations are allowed.
Access:
…Å
Flags:
Numerical Results (-3)
Input/Output:
See also:
(Å is the right-shift of the Wkey).
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
z1
z2
→
z1 = z2
z
'symb'
→
'z = symb'
'symb'
z
→
'symb = z'
'symb1'
'symb2'
→
'symb1 = symb2'
y_unit
x
→
y_unit1 = x
y_unit
x_unit
→
y_unit1 = x_unit
'symb'
x_unit
→
'symb = x_unit'
x_unit
DEFINE, EVAL, –
'symb'
→
'x_unit = symb'
==
(Logical Equality)
Type:
Function
Description: Logical Equality Function: Tests if two objects are equal.
The function == returns a true result (1) if the two objects are the same type and have the same
value, or a false result (0) otherwise. Lists and programs are considered to have the same values if
the objects they contain are identical. If one object is algebraic (or a name), and the other is a
number (real or complex) or an algebraic, == returns a symbolic comparison expression that can
be evaluated to return a test result. Note that == is used for comparisons, while = separates two
sides of an equation. If the imaginary part of a complex number is 0, it is ignored when the
complex number is compared to a real number.
For unit objects, the two objects must be dimensionally consistent and are converted to common
units for comparison. If you use simple temperature units, the calculator assumes the values
represent temperatures and not differences in temperatures. For compound temperature units,
the calculator assumes temperature units represent temperature differences. For more
information on using temperature units with arithmetic functions, refer to the entry for +.
Access:
!°TEST ==
( °is the left-shift of the Nkey).
Flags:
Numerical Results (-3)
3-224 Full Command and Function Reference
Input/Output:
See also:
!
Level 2/Argument 1
Level 1/Argument 2
Level 1/Item 1
obj1
obj2
→
0/1
(x,0)
x
→
0/1
x
(x,0)
→
0/1
z
'symb'
→
'z == symb'
'symb'
z
→
'symb == z'
'symb1'
'symb2'
→
'symb1 == symb2'
SAME, TYPE, <, ≤, >, ≥, ≠
(Store)
Type:
Command
Description: Store Command: Stores an object into a specified variable. To create a backup object, store the
obj into the desired backup location (identified as :nport:namebackup). ! will not overwrite an existing
backup object. To replace an element of an array or list, use STO. Also use STO to store a
graphic object into PICT or a library or backup object into a port.
Access:
K
Input/Output:
See also:
Level 2/Argument 1
Level 1/Argument 2
obj
'name'
→
obj
:nport :namebackup
→
obj
obj
DEFINE, RCL, →, STO
Level 1/Item 1
→
(Create Local)
Type:
Command
Description: Create Local Variables Command: Creates local variables.
Local variable structures specify one or more local variables and a defining procedure.
A local variable structure consists of the → command, followed by one or more names, followed
by a defining procedure—either a program or an algebraic. The → command stores objects into
local variables with the specified names. The resultant local variables exist only while the defining
procedure is being executed. The syntax of a local variable structure is one of the following:
• → name1 name2 … namen « program »
• → name1 name2 … namen 'algebraic expression'
Access:
…é
(é is the right-shift of the 0key).
Input/Output:
Leveln/Argument1 … Level1/Argumentn
obj1 … objn
See also:
Level 1/Item 1
→
DEFINE, LOCAL, STO
Full Command and Function Reference 3-225
4
4.Computer Algebra Commands
Introduction
The Computer Algebra System, or CAS, is a collection of operations that can be applied to algebraic
expressions.
The hp49g+/hp48gII operations can be used with numbers to produce numeric results, or with symbols to
produce algebraic expressions. Algebraic expressions and equations can be written using the Equation Writer
too. Algebraic expressions and symbolic operations on them, called computer algebra operations, are
introduced in Chapter 5 of the User’s Manual.
Further explanations of computer algebra operations, are given in the User’s Guide, whereas this part of the
Advanced User’s Guide lists the computer algebra operations that can be applied to symbolic expressions, with
a description of each one listed.
These operations perform tasks such as rearrangement of trigonometric and logarithmic functions, or
manipulation of polynomials, series and matrices. They are referred to as the “Computer Algebra System” or
the CAS. Many of the CAS operations are of particular use in Linear Algebra applications and in Vector
Algebra. The CAS on the hp48gII and the hp49g+ allows these calculators to provide many of the features of
the Computer Algebra Systems used on laptop and desktop computers.
Note: The Computer Algebra System should not be confused with Algebraic mode, which is one of the
calculator’s operating modes. The CAS works with algebraic (or symbolic) expressions, which can be entered
and used in Algebraic mode or in RPN mode.
CAS Operations
This volume of the Command Reference lists CAS operations, first according to the menus they appear in,
then in detail, in alphabetic order. A few CAS operations appear in more than one menu. Some menus contain
CAS operations and also operations that are not part of the CAS. Operations that are not part of the CAS are
described in the full Command Reference in the previous chapter.
For each CAS operation in the alphabetical list, some or all of the following details are provided:
Type:
Function or command. Functions, for example LCM, can be part of an algebraic expression.
Commands, for example SOLVE, cannot. When working with functions or commands within
the Equation Writer:
• When you apply a function to an expression, the function becomes part of the expression.
You need to ensure that the expression is selected, then press Nto apply the function
to the selection.
• When you apply a command to an expression in Equation Writer, it is evaluated
immediately.
Description:
A description of the operation.
Access:
The menu or choose-list on which an operation can be found, and the keys that you press to
access it. If the operation is on a sub-menu, the sub-menu name is in SMALL CAPITALS after
the keys.
CAS commands that are not in any of the other menus on the keyboard can be accessed from
the …µ menu. Most CAS commands can also be accessed from the CASCMD chooselist, from CAS soft menus and from menus created by the MENUXY command.
Computer Algebra Commands 4-1
Input:
The input argument or arguments that the operation needs. If the operation uses more than
one input argument, details of the arguments and the order in which to supply them are
provided: in argument order for algebraic mode and in stack order for RPN mode.
Output:
The output that the operation produces.
• In RPN mode, the outputs are placed on the stack.
• In algebraic mode, the outputs are displayed; if there is more than one output, they are
written to a list.
As with the input arguments, the outputs for both algebraic and RPN mode are described.
Flags:
Details of how flag settings affect the operation of the function or command. See also the
section below on CAS Settings.
Example:
An example of the function or command. Examples are also available in the built-in CAS help
on the calculator. The examples given here are shown in Algebraic mode, but can be
transferred to RPN mode according to the descriptions given in “Input” and “Output”.
See also:
Related functions or commands.
CAS Settings
Selecting CAS Settings
CAS settings are selected using the CAS MODES input form, described in Chapter 1 of the User’s Manual.
Selecting a mode is equivalent to setting or clearing one of the system flags, the flag numbers are given in the
“Flags” part of the operation descriptions.
Pressing the L key in the CAS MODES input form displays a menu that allows the user to calculate settings.
For example, if the Modulo field is selected in the CAS MODES form, and L is pressed, the following menu
keys are available.
!TYPES lists the types of object that can be chosen for this setting. For the modulo, this can be a real number or
an integer. For checked mode settings, this can only be a real number; if it is zero the mode is unchecked, if it
is anything else the mode is checked.
!CALC lets the user calculate a value for the setting, for example a new value for the modulo setting can be
calculated. The !STS! menu key allows the user to switch the heading lines between the “CAS MODES” heading
and the normal heading lines, so that the user can see what the current settings are while carrying out a
calculation.
!RESET allows the setting to be reset to its default value, or all CAS settings to be reset to their default values.
See Appendix C in the User’s Guide for further details of the CAS settings, and for other information about
the CAS. Information on the Help system of the CAS is provided in Appendix C and also in Appendix H of
the User’s Guide.
The CAS directory, CASDIR
CAS settings are stored as flag settings, and as variables in the CASDIR directory, which is automatically
created as a subdirectory of the HOME directory. Variables in this directory include:
VX:
A name or list of names of the current CAS variable or variables. Default value is X
MODULO:
The current modulus used for CAS modulo operations. Default value is 13, but is reset to 3
by the !RESET key in the CAS menu.
PERIOD:
The period for CAS periodic operations, 2π by default.
EPS:
The value chosen such that coefficients in a polynomial smaller than this value are replaced
with 0 by the EPSX0 command. 1E-10 by default.
REALASSUME: A list of the names of variables that some CAS operations treat as real numbers when
complex mode is set. If additional assumptions are made on any variables, these are
included here. By default the list is {X, Y, t, S1, S2}.
4-2 Computer Algebra Commands
PRIMIT:
Temporary storage of anti-derivative expressions used during CAS operations.
MATRIX:
Temporary storage of a matrix used during CAS operations.
CASINFO:
Temporary storage of graphic display during step-by-step operations.
PPAR:
Plot parameters.
Points to note when choosing settings
The CAS is a powerful tool, and part of that power lies in the many modes and settings available. This means
that if a setting is wrong then the CAS can give unexpected results or error messages. The following points
should be observed. If an unexpected error occurs, or an unexpected message is seen, check this list.
• Many CAS commands will give numeric results instead of symbolic results if numeric mode is set
instead of being cleared. Though these results may be correct, they will not be what the user wants if a
symbolic result is needed. For this reason, the Flags section of most operation descriptions says that
numeric mode should not be set.
• If approximate mode is set instead of exact mode, CAS commands will often give reasonable results,
but unexpected results can be obtained, because, for example, powers are real numbers, not integers,
for instance a cube will be treated as x3.0 instead of x3. For this reason, the Flags section of most
operation descriptions says that exact mode should be set. Some commands, like the numeric solvers,
will only find approximate solutions if approximate mode is set.
• CAS operations are designed to work with integers if possible, and some CAS operations round their
inputs before using them. FIX 0 mode will round to whole numbers, losing accuracy. STD mode will
retain full accuracy, so it is the best display mode to use with the CAS and is used in most of the
examples in this chapter.
• For the same reasons, the general solutions, symbolic constants and symbolic arguments flags (flags –1,
–2 and –3) should normally be clear when working with the CAS.
• Where possible, integer numbers should be used as input, not real numbers. The functions RND,
CEIL and FLOOR can round a real number to a whole real number, and R$I will convert a whole
real number to an integer.
• If complex inputs are given, approximate mode may need to be set to find solutions, and complex
mode must be set (flag –103 set).
• Not only the trigonometry rewriting operations, but some other CAS operations require the angle
mode to be set to radians (flag –17 clear), even if it is not immediately obvious that this is so. For this
reason, the Flags section of many operation descriptions says that radians mode should be set.
• Some CAS operations will work one step at a time if step-by-step mode is set (flag –100 set). If a result
is wanted immediately, and the calculator instead displays one step of the operation, cancel the
operation, clear flag –100, then repeat the operation.
• If a mode needs to be changed for an operation to work, the calculator will by default ask if the mode
can be changed. If the Silent mode switch flag (flag –120) is set, the calculator changes the mode
without asking. If the mode switch disallowed flag (flag –123) is set, the mode will not be changed and
an error will occur.
• All the system flags from –99 to –128 are intended for use by the CAS. It is worth reading Appendix C
in the User’s Guide to learn the detailed effects of these flags on CAS operations and displays.
• Remember that in RPN mode, symbolic expressions typed on the command line should be enclosed in
single quote marks ′x + y′. For clarity, it can be helpful to type expressions in single quote marks in
Algebraic mode too.
• It is important to write symbolic expressions using the current variable. Some CAS operations will
work with this variable, but treat other variables simply as unknown numbers. If an expression has
been entered using a variable other than the current variable, it may be simpler to change the current
variable in the CAS MODES form, rather than rewrite the whole expression.
• In algebraic mode (flag –95 set), some CAS commands will replace variables with their numeric values
before returning a result, even if “argument to symbolic” mode is set (flag –3 clear). In RPN mode,
Computer Algebra Commands 4-3
•
•
they will be returned as variables. Some other CAS commands will always replace variables with their
numeric results.
Because of the above, variables used in symbolic operations should not have the same names as
variables stored in the current directory/folder (or in directories above this directory). If, for example,
x is the current variable, and a variable called ′x′ exists in the current directory or in the HOME
directory, then the value stored in ′x′ might be used instead of the symbolic variable x.
The modulo value used in modulus calculations is 13 after the calculator is reset. If the CAS modes are
reset with CASCFG, the modulo is also 13, but if the modes are reset using !RESET as above, the
modulo is 3, otherwise it is the value most recently set. It is important to change this to the required
value before carrying out any modulus operations.
Using the CAS
Examples and Help
In addition to the examples in this Command Reference, the built-in CAS help provides examples of CAS
operations.
• If an operation is selected from the operations catalog, …µ, and if help is available, then pressing the
!HELP key shows help information. Pressing the %OK% menu key copies the operation to the command line,
ready for use.
• If an operation is selected from the CASCMD list, IL CASCMD, the same help information is available,
but instead of %OK%, there is an !ECHO key to copy the name and example to the command line. Evaluating
the example and comparing it with the result shown in the help text is a quick way to check if the CAS
settings are correct.
Compatibility with Other Calculators
Some CAS operations replace similar operations that were available on older HP calculators. The older
operation names have been kept on the hp48gII and the hp49g+ so that programs written for the older
calculators will work on the new models without being rewritten. This means that some commands and
functions have more than one name; the CAS names are in this part of the Command Reference, the older
names are listed in Chapter 3. In other cases, operations that would naturally belong with the Computer
Algebra System were already available on the older models; these operations too are described in Chapter 3.
The older models whose programs can be run on the hp48gII and the hp49g+ are the HP 28C and HP 28S,
the HP 48S and the HP 48SX, and the HP 48G, HP 48GX and HP 48G+. These models only had the RPL
programming language, so programs written for them should be used in RPN mode. The HP 49G is a more
recent model which does have the CAS, and Algebraic mode, so programs written for it in either RPL or in
Algebraic mode can be used on the hp48gII and the hp49g+. The CAS of the hp48gII and the hp49g+ is also
very similar to the CAS of the HP40 models, so programs and books written for them may be helpful.
Extending the CAS
Users can extend the CAS by writing their own functions or commands. Functions can be written as UDFs
(User Defined Functions); see the descriptions of DEFINE in Chapter 3 of the calculator User’s Guide and in
Part A of this Command Reference, and also DEF in this part. The pattern matching commands ↑MATCH
and ↓MATCH allow the user to write programs to edit algebraic expressions. Here is an example of an RPL
program using ↑MATCH to replace the square root of a square of a symbol with the symbol itself. The
wildcard &A means that any symbol or expression squared can be replaced. The conditional expression &A≥0
means that the replacement is only carried out if the square root is not of a negative value.
« { '√(&A^2)' &A '&A≥0' } ↑MATCH »
Dealing with unexpected CAS results or messages
If a CAS operation gives an unexpected result or message, check the list of points given in the section on CAS
settings. Some problems can be caused by unexpected settings, so it can be helpful to reset all CAS settings to
their default values, with the CASCFG command, or with the !RESET key in the CAS settings menu.
4-4 Computer Algebra Commands
Computer algebra command categories listed by menu
CAS operations are listed here in order of the keyboard menus they appear in. These menus can be selected
from the CAS menu in G, or directly from the keyboard. Many CAS commands are also available from the
P menu, or from the „´ menu; these menus are not listed here, to avoid duplication. The CAS has
its own menu commands too, they are included in the alphabetical list of commands. Operations that do not
appear in any menu can be spelled out or selected from …µ.
Algebra commands, …×
COLLECT .......................... 4-19
EXPAND
.......................... 4-29
FACTOR
.......................... 4-30
LIN
.......................... 4-48
LNCOLLECT ......................... 4-49
PARTFRAC .......................... 4-56
SOLVE
.......................... 4-67
SUBST
.......................... 4-69
TEXPAND .......................... 4-74
Arithmetic commands
Arithmetic Integer commands, !ÞINTEGER
EULER
.......................... 4-28
IABCUV
.......................... 4-38
IBERNOULLI ......................... 4-39
ICHINREM .......................... 4-40
IDIV2
.......................... 4-40
IEGCD
.......................... 4-40
IQUOT
.......................... 4-43
IREMAINDER........................ 4-43
ISPRIME?
.......................... 4-44
NEXTPRIME .......................... 4-55
PA2B2
.......................... 4-55
PREVPRIME .......................... 4-59
Arithmetic Polynomial commands, !ÞPOLYNOMIAL
ABCUV
.......................... 4-12
CHINREM .......................... 4-17
CYCLOTOMIC ....................... 4-20
DIV2
.......................... 4-23
EGCD
.......................... 4-27
FACTOR
.......................... 4-30
FCOEF
.......................... 4-31
FROOTS
.......................... 4-33
GCD
.......................... 4-34
HERMITE .......................... 4-37
Computer Algebra Commands 4-5
HORNER
.......................... 4-38
LAGRANGE .......................... 4-45
LCM
.......................... 4-46
LEGENDRE .......................... 4-47
PARTFRAC .......................... 4-56
PTAYL
.......................... 4-59
QUOT
.......................... 4-60
REMAINDER ......................... 4-61
RESULTANT .......................... 4-62
STURM
.......................... 4-69
STURMAB .......................... 4-69
Other POLYNOMIAL operations are described in Chapter 3.
Arithmetic Modulo commands, !ÞMODULO
ADDTMOD .......................... 4-12
DIV2MOD .......................... 4-24
DIVMOD
.......................... 4-25
EXPANDMOD....................... 4-30
FACTORMOD........................ 4-31
GCDMOD .......................... 4-35
INVMOD
.......................... 4-42
MODSTO
.......................... 4-53
MULTMOD .......................... 4-54
POWMOD .......................... 4-58
SUBTMOD .......................... 4-70
Other MODULO operations are described in Chapter 3.
Arithmetic Permutation commands, !ÞPERMUTATION
C2P
.......................... 4-17
CIRC
.......................... 4-18
P2C
.......................... 4-55
Other Arithmetic commands, !Þ
DIVIS
.......................... 4-24
FACTORS
.......................... 4-31
LGCD
.......................... 4-48
PROPFRAC .......................... 4-59
SIMP2
.......................... 4-66
Calculus commands
Derivation and integration commands, !ÖDERIV. & INTEG.
CURL
.......................... 4-19
DERIV
.......................... 4-21
DERVX
.......................... 4-21
DIV
.......................... 4-23
FOURIER
.......................... 4-32
HESS
.......................... 4-37
4-6 Computer Algebra Commands
IBP
INTVX
LAPL
PREVAL
RISCH
SIGMA
SIGMAVX
.......................... 4-39
.......................... 4-42
.......................... 4-46
.......................... 4-58
.......................... 4-62
.......................... 4-65
.......................... 4-65
Limits and series commands, !ÖLIMITS & SERIES
DIVPC
.......................... 4-25
lim
.......................... 4-48
SERIES
.......................... 4-64
TAYLOR0
.......................... 4-73
Other LIMITS & SERIES operations are described in Chapter 3.
Differential equations commands, !ÖDIFFERENTIAL EQNS
DESOLVE .......................... 4-22
ILAP
.......................... 4-41
LAP
.......................... 4-45
LDEC
.......................... 4-47
Graphing commands, !ÖGRAPH
SIGNTAB
.......................... 4-65
TABVAL
.......................... 4-71
TABVAR
.......................... 4-71
Other GRAPH operations are described in Chapter 3.
Other Calculus commands, !Ö
DERVX
.......................... 4-21
INTVX
.......................... 4-42
These two operations are available directly from the CALC menu as well as being in the Derivation and
Integration commands menu.
Exp and Lin commands, !Ð
EXPLN
.......................... 4-30
LIN
.......................... 4-48
LNCOLLECT .......................... 4-49
TEXPAND .......................... 4-74
TSIMP
.......................... 4-77
Other EXP & LN operations are described in Chapter 3.
Matrix-related commands
Create, !Ø CREATE
AUGMENT .......................... 4-15
HILBERT
.......................... 4-37
VANDERMONDE ................ 4-78
Computer Algebra Commands 4-7
Other CREATE operations are described in Chapter 3.
Operations, !Ø OPERATIONS
AXL
.......................... 4-15
AXM
.......................... 4-16
HADAMARD .......................... 4-36
MAD
.......................... 4-51
Other operations in the OPERATIONS submenu are described Chapter 3.
All operations in the FACTORIZATION submenu are described Chapter 3.
Quadratic form, !Ø QUADRATIC FORM
AXQ
.......................... 4-16
CHOLESKY .......................... 4-18
GAUSS
.......................... 4-33
QXA
.......................... 4-60
SYLVESTER .......................... 4-70
Linear Systems, !Ø LINEAR SYSTEMS
LINSOLVE .......................... 4-49
REF
.......................... 4-60
RREF
.......................... 4-62
rref
.......................... 4-63
SYST2MAT .......................... 4-71
Linear Applications, !Ø LINEAR APPL
IMAGE
.......................... 4-41
ISOM
.......................... 4-43
KER
.......................... 4-45
MKISOM
.......................... 4-53
Eigenvectors, !Ø EIGENVECTORS
DIAGMAP .......................... 4-22
JORDAN
.......................... 4-44
PCAR
.......................... 4-56
PMINI
.......................... 4-56
Other operations in the EIGENVECTORS submenu are described in Chapter 3.
Vector, !Ø VECTOR
BASIS
.......................... 4-16
GRAMSCHMIDT................... 4-35
IBASIS
.......................... 4-38
Other operations in the VECTOR submenu are described in Chapter 3.
Symbolic solve commands, !Î
DESOLVE
LDEC
LINSOLVE
SOLVEVX
.......................... 4-22
.......................... 4-47
.......................... 4-49
.......................... 4-68
4-8 Computer Algebra Commands
SOLVE
.......................... 4-67
ZEROS
.......................... 4-80
Other S.SLV operations are described in Chapter 3.
Trigonometry commands, …Ñ
All operations in the HYPERBOLIC submenu are described in Chapter 3.
ACOS2S
.......................... 4-12
ASIN2C
.......................... 4-14
ASIN2T
.......................... 4-14
ATAN2S
.......................... 4-15
HALFTAN .......................... 4-36
SINCOS
.......................... 4-67
TAN2SC
.......................... 4-72
TAN2SC2
.......................... 4-73
TCOLLECT .......................... 4-74
TEXPAND .......................... 4-74
TLIN
.......................... 4-74
TRIG
.......................... 4-75
TRIGCOS
.......................... 4-75
TRIGSIN
.......................... 4-76
TRIGTAN
.......................... 4-76
TSIMP ....................................... 4-77
Convert commands, !Ú
All operations in the UNITS and BASE submenus are described in Chapter 3.
Trigonometric conversions, !Ú TRIG CONV
ACOS2S
.......................... 4-12
ASIN2C
.......................... 4-14
ASIN2T
.......................... 4-14
ATAN2S
.......................... 4-15
HALFTAN .......................... 4-36
SINCOS
.......................... 4-67
TAN2SC
.......................... 4-72
TAN2SC2
.......................... 4-73
TLIN
.......................... 4-74
TRIG
.......................... 4-75
TRIGCOS
.......................... 4-75
TRIGSIN
.......................... 4-76
TSIMP
.......................... 4-77
Rewrite expression, !Ú REWRITE
DISTRIB
.......................... 4-23
EXP2POW .......................... 4-29
Computer Algebra Commands 4-9
EXPLN
.......................... 4-30
FDISTRIB
.......................... 4-32
LIN
.......................... 4-48
LNCOLLECT .......................... 4-49
POWEXPAND ....................... 4-57
SIMPLIFY
.......................... 4-66
Other operations in the REWRITE submenu are described in Chapter 3.
Matrix convert, !Ú MATRIX CONVERT
AXL
.......................... 4-15
AXQ
.......................... 4-16
QXA
.......................... 4-60
SYST2MAT .......................... 4-71
Other CAS operations, …µ
These operations are in other menus, as described in Access for each one, or can be accessed with
…µ.
Other mathematics operations
DEGREE
.......................... 4-21
DOMAIN
.......................... 4-25
DROITE
.......................... 4-26
dn
.......................... 4-26
EPSX0
.......................... 4-27
EXLR
.......................... 4-28
EXP2HYP
.......................... 4-28
FXND
.......................... 4-33
GBASIS
.......................... 4-34
GREDUCE .......................... 4-35
LCXM
.......................... 4-46
LIMIT
.......................... 4-48
LNAME
.......................... 4-49
LVAR
.......................... 4-50
MSLV
.......................... 4-54
P2C
.......................... 4-55
POTENTIAL .......................... 4-57
REORDER .......................... 4-61
RREFMOD .......................... 4-63
SEVAL
.......................... 4-64
TAN2CS2
.......................... 4-72
TCHEBYCHEFF ................... 4-73
TRUNC
.......................... 4-77
VPOTENTIAL........................ 4-79
XNUM
.......................... 4-80
4-10 Computer Algebra Commands
XQ
?
∞
.......................... 4-80
.......................... 4-81
.......................... 4-81
CAS menu commands, …µ
These commands display menus or lists of CAS operations.
ALGB
.......................... 4-13
ARIT
.......................... 4-13
CONSTANTS .......................... 4-19
DIFF
.......................... 4-23
EXP&LN
.......................... 4-28
INTEGER
.......................... 4-42
MAIN
.......................... 4-51
MATHS
.......................... 4-51
MATR
.......................... 4-52
MENUXY
.......................... 4-52
MODULAR .......................... 4-53
POLYNOMIAL....................... 4-57
REWRITE
.......................... 4-62
TESTS
.......................... 4-74
TRIGO
.......................... 4-76
CAS utility operations
ADDTOREAL......................... 4-13
ASSUME
.......................... 4-14
CASCFG
.......................... 4-17
CASCMD
.......................... 4-17
DEDICACE .......................... 4-20
DEF
.......................... 4-20
HELP
.......................... 4-36
LOCAL
.......................... 4-50
RCLVX
.......................... 4-60
STORE
.......................... 4-68
STOVX
.......................... 4-68
UNASSIGN .......................... 4-77
UNASSUME .......................... 4-78
UNBIND
.......................... 4-78
VER
.......................... 4-79
Computer Algebra Commands 4-11
Alphabetical command list
The following pages contain the commands in alphabetical order. See "Computer algebra command
categories" on page 4-5 to view the commands in the order that they appear on the menus. Chapters 11 to 16
in the User’s Guide provide examples using many of these commands.
ABCUV
Type:
Command
Description:
Returns a solution in polynomials u and v of au+bv =c where a and b are polynomials in the
current CAS independent variable, and c is a value.
Access:
Arithmetic, !Þ
Input:
Level 3/Argument 1: The polynomial corresponding to a.
Level 2/Argument 2: The polynomial corresponding to b.
Level 1/Argument 3: The value corresponding to c.
Output:
Level 2/Item 1: The solution corresponding to u.
Level 1/Item 2: The solution corresponding to v.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Find a solution in polynomials u and v for the following equation:
2
POLYNOMIAL
2
( x + x + 1 )u + ( x + 4 ) V = 13
Command: ABCUV(X^2+X+1,X^2+4,13)
Result:
{-(X+3),X+4}
See also:
IABCUV, EGCD
ACOS2S
Type:
Command
Description:
Transforms an expression by replacing acos(x) in subexpressions with π/2–asin(x).
Access:
Trigonometry, …Ñ
Input:
The expression to transform.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Simplify the following expression:
2
arc cos ⎛ ---⎞ + arc cos ( x )
⎝ 3⎠
Command:
Result:
ACOS2S(ACOS(2/3)+ACOS(X))
See also:
ASIN2C, ASIN2T, ATAN2S
ADDTMOD
Type:
Description:
Function
π/2-ASIN(2/3)+π/2-ASIN(X)
Adds two expressions or values, modulo the current modulus.
4-12 Computer Algebra Commands
Access:
Arithmetic, !Þ
Input:
Level 2/Argument 1: The first expression.
Level 1/Argument 2: The second expression.
Output:
The sum of the two expressions, modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Express the result of the following addition in modulo 7.
(x2+3x+6)+(9x+3)
Note: Before trying this example, use the CAS modes input form to set the modulo to 7.
MODULO
Command: ADDTMOD(X^2+3*X+6,9*X+3)
Result:
X^2-2*X+2
ADDTOREAL
Type:
Command
Description: Adds specified global names to the reserved variable REALASSUME. This is a list of the
global variables that will be treated by some CAS operations as real numbers when Complex
mode is set.
If a variable is already in the REALASSSUME list, this command removes any additional
assumptions made on it by ASSUME.
Access:
Catalog, …µ
Input:
Level 1/Item 1: The name of the global variable to be added to the REALASSUME list, or a
list of names.
Output:
No output in RPN mode, NOVAL in Algebraic mode.
Flags:
If the “all variables are real” flag is set (flag –128 set), ADDTOREAL will not add anything to
the REALASSUME list, as all variables are assumed real anyway. In this case it will only
remove further assumptions made by ASSUME.
See also:
ASSUME, DEF, STORE, UNASSUME, UNBIND
ALGB
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
Displays a menu or list of CAS algebraic operations.
ARIT
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the submenus as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
Displays a menu or list showing the three CAS submenus for arithmetical operations,
INTEGER, MODULAR and POLYNOMIAL.
Computer Algebra Commands 4-13
See also:
ASIN2C
Type:
ALGB, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Command
Description:
Transforms an expression by replacing asin(x) subexpressions with π/2–acos(x)
subexpressions.
Access:
Trigonometry, …Ñ
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
See also:
ACOS2S, ASIN2T, ATAN2S
ASIN2T
Type:
Description:
Command
Transforms an expression by replacing asin(x) subexpressions with the following:
⎛ x ⎞
atan ⎜ ------------------⎟
⎝ 1 – x 2⎠
Access:
Trigonometry, …Ñ
Input:
An expression.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
See also:
ASIN2C, ACOS2S, ATAN2S
ASSUME
Type:
Description:
Function
Adds global names to the reserved variable REALASSUME, with specific assumptions.
REALASSUME is a list of the global variables that will be considered by some CAS
operations to represent real numbers when complex mode is set. ASSUME adds further
assumptions, for example that a variable is greater than or equal to zero. Assumptions must
be of the form v≤expression, or v≥expression, where v is the variable name. Several
assumptions can be combined.
These assumptions are used by the solve commands; for example if a variable is assumed to
be greater than zero then the solvers will not look for solutions where that variable is negative.
Some of the solvers will give complex solutions for variables even if they are in
REALASSUME.
Access:
Catalog, …µ
Input:
Level 1/Item 1: An expression giving the name of the global variable to be added to the
REALASSUME list, and the assumption to be placed on it, or a list of such assumptions.
Output:
Level 1/Item 1: The input expression or list of expressions.
4-14 Computer Algebra Commands
Example:
Add the CAS assumption that the global variable Z is real and positive. Note that ASSUME
will replace Z>0 with Z≥0, which does not guarantee that Z is positive, so Z≥MINR is used
instead, which guarantees that Z is greater than or equal to the smallest positive number the
calculator recognizes.
Command: ASSUME(Z≥MINR)
Result:
Z≥MINR
See also:
ADDTOREAL, UNASSUME
ATAN2S
Type:
Description:
Command
Transforms an expression by replacing atan(x) subexpressions with the following:
⎛ x ⎞
asin ⎜ ------------------⎟
⎝ x 2 + 1⎠
Access:
Trigonometry, …Ñ
Input:
An expression.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
See also:
ASIN2C, ACOS2S, ASIN2T
AUGMENT
Type:
Description:
Command
Concatenate two lists, a list and an element, or a vector and an element. Also creates a matrix
from component row vectors.
Access:
Input:
Matrices, !Ø CREATE
Level 2/Argument 1: A vector, a list, a matrix, or a string.
Level 1/Argument 2: A vector, a list, a matrix, or an element.
Output:
The matrix, list or string formed by combining the arguments. In the case of a string in level
2, AUGMENT acts exactly like “+” or “ADD”.
Append 3 to the list {1,2}:
Example 1:
Command:
Result:
Example 2:
Command:
Result:
AUGMENT({1,2},3)
{1,2,3}
Combine the rows [1,2,3] and [4,5,6] into a matrix:
AUGMENT([1,2,3],[4,5,6])
123
456
AXL
Type:
Description:
Command
Access:
Convert, !Ú
Input:
A list or an array.
Converts a list to an array, or an array to a list.
MATRIX CONVERT,
or matrices !Ø
OPERATIONS
Computer Algebra Commands 4-15
Output:
If the input is a list, returns the corresponding array. If the input is an array, returns the
corresponding list.
Example:
Convert the following matrix to a list:
01
10
Command: AXL([[0,1][1,0]])
Result:
{{0,1},{1,0}}
See also:
AXM, AXQ
AXM
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A numeric array or a symbolic matrix.
Output:
The corresponding symbolic matrix or numeric array.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
See also:
AXL, AXQ
AXQ
Type:
Description:
Command
Access:
Convert, !Ú
Input:
Level 2/Argument 1: An n×n matrix.
Level 1/Argument 2: A vector containing n variables.
Output:
Level 2/Item 1: The corresponding quadratic form.
Level 1/Item 2: The vector containing the variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the quadratic form, expressed in terms of x, y, and z, associated with the following
matrix:
Converts a numeric array (object type 3) to a symbolic matrix (object type 29), or a symbolic
matrix to a numeric array.
OPERATIONS
Converts a square matrix into the associated quadratic form.
MATRIX CONVERT, or
matrices !Ø
360
241
111
Command: AXQ([[3,6,0][2,4,1][1,1,1]],[X,Y,Z])
Result:
{3*X^2+(8*Y+Z)*X+(4*Y^2+2*Z*Y+Z^2),[X,Y,Z]}
See also:
AXL, AXM, GAUSS, QXA
BASIS
Type:
Description:
Command
Access:
Matrices, !Ø LVECTOR
Determines the basis of a sub-space of the n-space Rn.
4-16 Computer Algebra Commands
QUADRATIC FORM
Input:
Output:
Flags:
A list of vectors defining a vector sub-space of Rn.
A list containing the vectors of a basis of the vector sub-space.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Command:
Result:
See also:
Find the vectors that form a basis of the sub-space defined by [1,2,3], [1,1,1], and [2,3,4]
C2P
Type:
Description:
BASIS({[1,2,3],[1,1,1],[2,3,4]})
{[1,0,-1],[0,1,2]}
IBASIS
Command
Takes a list of cycles as an argument, and returns the equivalent permutation. In other words,
finds a permutation from its cyclical decomposition.
Output:
Example:
Command:
Result:
Arithmetic, !ÞPERMUTATION
A list of cycles equivalent to a permutation. For example, the list {1,3,5} defines a cycle C,
such that C(1)=3, C(3)=5 and C(5)=1, while items 2 and 4 are not changed. This could be
followed by {2,4} which defines a cycle C, such that C(2)=4, and C(4)=2.
A list representing the permutation equivalent to the cycles.
Convert the cycles given by {{1,3,5},{2,4}} into a permutation:
C2P( {{1,3,5},{2,4}})
{3,4,5,2,1}
See also:
P2C, CIRC
CASCFG
Type:
Command
Access:
Input:
Description:
Restores the default CAS mode settings. This command is almost equivalent to pressing L
!RESET, then selecting “Reset all” and pressing !!OK!, when the CAS Modes input form is
displayed. The difference is that CASCFG sets the modulus value to 13, whereas “Reset all”
sets the modulus to 3.
Access:
Catalog, …µ
CASCMD
Type:
Description:
Command
Access:
See also:
Catalog, …µ, or tools IL
HELP
CHINREM
Type:
Description:
Command
Access:
Arithmetic, !Þ POLYNOMIAL
Displays a list of CAS operations. Selecting one with OK displays a description, related
operations, an example of the operation, and the option to copy the example to the command
line. More details are given in Appendix C and Appendix H of the User’s Guide. If level 1 of
the stack contains a string, the list of CAS operations will be displayed beginning at this point.
Chinese Remainder function. Solves a system of simultaneous polynomial congruences in the
ring Z[x].
Computer Algebra Commands 4-17
Input:
Level 2/Argument 1: A vector of the first congruence (expression and modulus).
Level 1/Argument 2: A vector of the second congruence (expression and modulus).
Output:
A vector of the solution congruence (expression and modulus).
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Solve the following simultaneous congruences for the polynomial u:
2
u≡x +1
(mod x+2)
u ≡ x – 1 (mod x+3)
Command: CHINREM([X^2+1,X+2],[X-1,X+3])
Result:
[X^3+2*X^2+5,-(X^2+5*X+6)]
See also:
EGCD, ICHINREM
CHOLESKY
Type:
Command
Description: Returns the Cholesky factorization of a square matrix.
Access:
Input:
Output:
Flags:
Example:
Matrices, !Ø QUADRATIC FORM
A positive square matrix, M
An upper triangular matrix, P, such that tP*P=M. (tP is the transpose of P.)
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Find the Cholesky factorization of:
11
15
Command:
Result:
CIRC
Type:
Description:
Access:
Input:
⎛
⎞
CHOLESKY⎜ 1 1 ⎟
⎝ 15⎠
1 1
0 2
Command
Composes two permutations.
Arithmetic, !ÞPERMUTATION
Two lists, L1 and L2, representing two permutations. The composition L1○L2 is the
permutation equivalent to performing permutation L2 first and L1 second.
Level 2/Argument 1: L1
Level 1/Argument 2: L2
Output:
A list representing the single equivalent permutation, L = L1○L2
Example:
Compose the permutations given by {3,4,5,2,1} and {2,1,4,3,5}
Command: CIRC({3,4,5,2,1},{2,1,4,3,5})
Result:
{4,3,2,5,1}
See also:
C2P, P2C
4-18 Computer Algebra Commands
COLLECT
Type:
Description:
Command
Access:
Algebra, …×
Input:
An expression or an integer
Output:
The factorized expression, or the integer expressed as the product of prime numbers.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
If complex inputs are given, complex mode must be set (flag –103 set).
Example:
Factorize the following:
Factorizes a polynomial or an integer. This command is identical to the COLCT command
and similar to the FACTOR command. Unlike FACTOR it does not factorize symbolically
into square roots. It is included to ensure backward-compatibility with earlier calculators.
2
x + 5x + 6
Command: COLLECT(X^2+5*X+6)
Result:
(X+2)(X+3)
See also:
COLCT, EXPAND, FACTOR
CONSTANTS
Type:
Command
Description: Displays a menu or list of CAS symbolic constants.
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
CURL
Type:
Description:
Function
Access:
Calculus, !ÖDERIV. & INTEG.
Input:
Level 2/Argument 1: A three-dimensional vector function of three variables.
Level 1/Argument 2: An array comprising the three variables.
Output:
The curl of the vector function with respect to the specified variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Find the curl of the following vector function:
Returns the curl of a three-dimensional vector function.
2
2
2
v = x yi + x yj + y zk
˜
˜
˜
Command: CURL([X^2*Y, X^2*Y, Y^2*Z],[X,Y,Z])
Result:
[Z*2*Y,0,Y*2*X-X^2]
See Also:
DIV, HESS, VPOTENTIAL
Computer Algebra Commands 4-19
CYCLOTOMIC
Type:
Function
Description: Returns the cyclotomic polynomial of order n. This is the polynomial whose roots are all the
nth roots of 1, except those that are also roots of 1 for smaller values of n. For example, if n is
4, the 4th roots of 1 are {1, i, -1, -i}, but 1 is the 1st root of 1 and –1 is a 2nd root of 1, so only i
and -i are left, giving the polynomial (x-i)(x+i) = x2+1.
Access:
Input:
Output:
Flags:
Arithmetic, !ÞPOLYNOMIAL
A non-negative integer n
The cyclotomic polynomial of order n.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Find the 20th cyclotomic polynomial.
Example:
Command: CYCLOTOMIC(20)
Result:
X^8-X^6+X^4-X^2+1
DEDICACE
Type:
Description:
Function
Access:
Catalog, …µ
Example:
In algebraic mode, the message can be extended. Try: DEDICACE(Salutations)
DEF
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 1/Argument 1: An expression of the form
name=expression or
name(name1, … namen)=expression(name1,… name n)
In the first case, name is the name of a variable, and expression is an expression or a number to
be stored in the variable. If the variable does not exist, it is created in the current directory. In
the second case, name is the name of a variable that will be treated as a function, name1 to namen
are formal variables used to define inputs the function will take.
Output:
Level 1/Item 1: Unlike DEFINE, which returns NOVAL in Algebraic mode, and no result in
RPN mode, DEF returns the expression used as the input.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example 1:
Define a new function that calculates:
(a-b)/(a+b)
Displays a greeting from the CAS team and dedication to all HP calculator users.
Defines a variable or a function. Works like the DEFINE command, except that it returns a
result and can be included in an algebraic expression. Given an expression as input, DEF
stores the expression, unlike STORE which evaluates the expression and stores the numerical
value.
Command: DEF(NEW(A,B)=(A-B)/(A+B))
Result:
NEW(A,B)=(A-B)/(A+B)
Example 2:
Check that the newly defined function works:
Command: NEW(2,1)
4-20 Computer Algebra Commands
Result:
1/3
See also:
DEFINE, STORE
DEGREE
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 1/Argument 1: A polynomial expression or equation; all powers must be integers or real
numbers with no fractional part.
Output:
Level 1/Item 1: An integer representing the highest power in the polynomial. If the input
contains powers of more than one variable, including the current variable, returns the highest
power of the current variable. If the input contains powers of more than one variable, not
including the current variable, returns the highest power of the first symbolic variable (one
that is not stored in the current directory path). If the input contains powers of more than one
variable, and all the variables are stored in the current directory path, returns the highest
power of any of the variables.
Flags:
If exact mode is set (flag –105 clear), the result is returned as an integer, otherwise it is
returned as a real number.
Example 1:
Find the degree of the polynomial represented by:
x2-17=x3+2x
Returns the degree of a polynomial expression. Returns 0 for a constant expression, but –1 if
the expression is zero.
Command: DEGREE(x^2-17=x^3+2*X)
Result:
3
DERIV
Type:
Description:
Function
Access:
Calculus, P CALCULUS or !ÖDERIV. & INTEG.
Input:
Level 2/Argument 1: A function or a list of functions.
Level 1/Argument 2: A variable, or a vector of variables. The variable or variables must not
exist as variables stored in the current directory nor directories above it.
Output:
The derivative, or a vector of the derivatives, of the function or functions.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Find the gradient of the following function of the spatial variables x, y, and z:
Returns the partial derivatives of a function, with respect to the specified variables.
2
2
2x y + 3y z + zx
Command: DERIV(2*X^2*Y+3*Y^2*Z+Z*X, [X,Y,Z])
Result:
EXPAND(ANS(1))
[4*Y*X+Z,2*X^2+6*Z*Y,X+3*Y^2]
See also:
DERVX, dn, ∂, POTENTIAL
DERVX
Type:
Description:
Function
Access:
Calculus, !Ö or P CALCULUS or !ÖDERIV. & INTEG.
Returns the derivative of a function with respect to the current variable. This variable must
not exist as a variable stored in the current directory path.
Computer Algebra Commands 4-21
Input:
The function or list of functions to be differentiated.
Output:
The derivative, or a vector of the derivatives, of the function or functions.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
See also:
DERIV, dn, ∂
DESOLVE
Type:
Description:
Command
Access:
Symbolic solve, !Î or calculus, !ÖDIFFERENTIAL EQNS.
Input:
Level 2/Argument 1: A first-order differential equation.
Level 1/Argument 2: The function to solve for.
Output:
The solution to the equation, either y as a function of x or x as a function of y, or x and y as
functions of a parameter.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Solve the following differential equation:
Solves certain first-order ordinary differential equations with respect to the current variable.
y′ ( x ) + 2y ( x ) = e
3x
Command: DESOLVE(d1Y(X)+2*Y(X)=EXP(3*X),Y(X))
(See the description of dn and Chapter 16 of the User’s Guide for an explanation of the use of
“d1” for a derivative.)
Result:
See also:
DIAGMAP
Type:
Description:
Access:
Input:
Output:
Flags:
Example:
Command:
{Y(X)=(1/5*EXP(5*X)+cC0)*(1/EXP(X)^2)}
dn, LDEC
Command
Applies an holomorphic operator to a diagonalizable matrix.
Matrices, !Ø L EIGENVECTORS.
Level 2/Argument 1: A diagonalizable matrix.
Level 1/Argument 2: An operator, expressed as a function. The function can be stored in a
variable with DEF, or can be a program, or a single expression.
The matrix that results from applying the operator to the matrix.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Apply the operator ex to the matrix
11
02
⎛
⎞
DIAGMAP ⎜ 1 1 , << → X<<EXP(X)>> >>⎟
⎝ 0 2
⎠
or DIAGMAP([[1,1],[0,2]],exp(X))
Result:
EXP ( 1 ) – EXP ( 1 ) + EXP ( 2 )
EXP ( 2 )
0
4-22 Computer Algebra Commands
DIFF
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
DISTRIB
Type:
Description:
Access:
Input:
Output:
Flags:
Displays a menu or list containing the CAS commands for differential calculus, including
commands for working with series.
Command
Applies one step of the distributive property of multiplication and division with respect to
addition and subtraction. Used for single-stepping through a multi-step distribution.
!Ú REWRITE
An expression.
An equivalent expression that results from applying the distributive property of multiplication
over addition one time.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Expand (X+1)( X-1)( X+2).
Command: DISTRIB((X+1)*(X-1)*(X+2))
Result:
X*(X-1)*(X+2)+1*(X-1)*(X+2)
See also:
FDISTRIB
DIV
Type:
Description:
Command
Access:
Calculus, !ÖDERIV. & INTEG.
Input:
Level 2/Argument 1: An array representing a vector function.
Level 1/Argument 2: An array containing the variables.
Output:
The divergence of the vector function with respect to the specified variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Find the divergence of the following vector function:
Returns the divergence of a vector function.
2
2
2
v = x y i + x yj + y zk
˜
˜
˜
DIV([X^2*Y, X^2*Y, Y^2*Z],[X,Y,Z])
Command:
Result:
Y*(2*X)+(X^2+Y^2)
See also:
CURL, HESS
DIV2
Type:
Description:
Command
Performs euclidean division on two expressions. Step-by-step mode is available with this
command.
Computer Algebra Commands 4-23
Access:
Arithmetic, !ÞPOLYNOMIAL
Input:
Level 2/Argument 1: The dividend.
Level 1/Argument 2: The divisor.
Output:
Level 2/Item 1: The quotient.
Level 1/Item 2: The remainder.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Step-by-step mode can be set (flag –100 set).
Radians mode must be set (flag –17 set).
Example:
Perform the following division:
2
x +x+1
----------------------2x + 4
Command: DIV2(X^2+X+1,2*X+4)
Result:
{1/2(X-1),3}
DIV2MOD
Type:
Description:
Command
Access:
Arithmetic, !Þ MODULO
Input:
Level 2/Argument 1: The dividend.
Level 1/Argument 2: The divisor.
Output:
Level 2/Item 1: The quotient.
Level 1/Item 2: The remainder.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Performs euclidean division on two expressions modulo the current modulus.
3
x +4
------------2
Find the result of x – 1 , modulo 3.
Example:
Command: DIV2MOD(X^3+4,X^2-1)
Result:
{X X+1}
DIVIS
Type:
Description:
Command
Access:
Arithmetic, !Þor PARITH
Input:
A polynomial or an integer.
Output:
A list containing the expressions or integers that exactly divide into the input.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Find the divisors of the following polynomial:
Returns a list of divisors of a polynomial or an integer.
2
x + 3x + 2
Command: DIVIS(X^2+3*X+2)
Result:
{1,X+1,X+2,X^2+3*X+2}
See also:
DIV2
4-24 Computer Algebra Commands
DIVMOD
Type:
Description:
Function
Access:
Arithmetic, !Þ MODULO
Input:
Level 2/Argument 1: The dividend.
Level 1/Argument 2: The divisor.
Output:
The quotient of the terms modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Divides two expressions modulo the current modulus.
Example:
Modulo 3, divide 5x2+4x+2 by x2+1.
Command: DIVMOD(5*X^2+4*X+2,X^2+1)
Result:
-((X^2-X+1)/X^2+1))
DIVPC
Type:
Description:
Command
Access:
Calculus, !Ö LIMITS & SERIES
Input:
Level 3/Argument 1: The numerator expression.
Level 2/Argument 2: The denominator expression.
Level 1/Argument 3: The degree of the Taylor polynomial.
Output:
The Taylor polynomial at x = 0 of the quotient of the two expressions, to the specified
degree.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Incremental power mode must be set (flag –114 set).
Example:
Find the fourth degree Taylor polynomial for the following:
Returns a Taylor polynomial for the quotient of two polynomial expressions.
3
x + 4x + 12
----------------------------11
11x + 1
Command: DIVPC(X^3+4*X+12,11*X^11+1,4)
Result:
12+4*X+X^3
See also:
TAYLOR0, TAYLR, SERIES
DOMAIN
Type:
Description:
Command
Access:
Catalog, …µ
Input:
Level 1/Item 1: A function, or an expression, in terms of the current variable.
Output:
Level 1/Item 1: A list with regions where the function is undefined marked by '?' and
regions where the function is defined marked by +. Rational singularities, such as 0 in 1/x,
are not listed.
For a function of the current variable, lists the domains of real numbers for which the
function is defined and for which it is undefined. DOMAIN works for functions of more
than one argument, for example DOMAIN (X*X), and for user defined functions, as in the
example below. For functions which it does not recognize, DOMAIN returns the message
“Unknown operator”.
Computer Algebra Commands 4-25
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Define a function f =√(a+1) by typing DEF(F(A)=√(A+1)). Then tabulate the domain over
which it is defined and undefined.
Command: DOMAIN(F(X))
Result:
{'-∞' '?' –1 + '+∞'}, showing that the function f is undefined for values from –∞ to –1 and is
defined from –1 to +∞.
See also:
SIGNTAB, TABVAR
DROITE
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 2/Argument 1: The first point, in the form a+b *i, or (a,b), where a and b must be
numbers, or variables or expressions that evaluate to numbers.
Level 1/Argument 2: The second point, in the form c+d *i, or (c,d), where c and d must be
numbers, or variables or expressions that evaluate to numbers.
Output:
Level 1/Item 1: An equation for the straight line through the two points. The general form is
Y=(d-b)/(c-a)*(X-a)+b.
Flags:
Numeric mode must not be set (flag –3 clear).
Complex mode must be set (flag –103 set).
In algebraic mode, if any of a, b, c, d are variables, they will be converted to their numeric
values, even if “argument to symbolic” mode is set (flag –3 clear). In RPN mode, they will be
returned as variables. If ALG mode is set and “constants to numeric” mode is selected (flag –
2 set) π and e used in inputs will be converted to their real number approximations, otherwise
they will be returned in symbolic form.
Returns an equation for the line through two given points in a plane. For more than two
points, LAGRANGE will fit a polynomial.
Example 1:
Find an equation for the straight line through the points (1, 2), (3, 4).
Command: DROITE((1, 2), (3, 4))
Result:
Y=X-1.+2.
Example 2:
Find a symbolic equation for the straight line through the points (π, e), (e, π).
Command: With “constants to symbolic ” mode selected and exact mode set, type:
DROITE(π+e*i, e+π*i)
Result:
Y=(π-e)/(e-π)*(X-π)+e
See also:
LAGRANGE
dn
Type:
Description:
Function
Differential of a function with respect to its argument n. For example d1f(x,y) is the
differential of f(x,y) with respect to x and d3g(y,z,t) is the differential of g(y,z,t) with respect to
t. The second-order derivative of f(x,y) with respect to x is written d1d1f(x,y). The dn function
is an alternative to the ∂ function; d1f(x,y) is the same as ∂x(f(x,y)). dn does not require
brackets after it, it must be followed immediately by the function name, with no spaces. dn
differentiates with respect to the whole of argument n, see the example. dn is mainly used for
formal arguments, see the example in DESOLVE, but can be used to differentiate
expressions, as in the example.
4-26 Computer Algebra Commands
Access:
Access is by typing the letter “d” from the alpha keyboard, followed by the number n, before
the function whose differential is required.
Output:
dn does not change its argument, it works like the negative sign placed before a number or an
expression. If the argument can be differentiated, N will carry out the differentiation.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Differentiate the function sin(2x) with respect to its argument:
Command: EVAL(d1SIN(2*X))
Result:
COS(2*X)
(Note that the function was differentiated with respect to its argument 2x, not with respect to
the variable x.)
See also:
DERIV, DERVX, DESOLVE, ∂
EGCD
Type:
Description:
Command
Access:
Arithmetic, !ÞPOLYNOMIAL
Input:
Level 2/Argument 1: The expression corresponding to a in the equation.
Level 1/Argument 2: The expression corresponding to b in the equation.
Output:
Level 3/Item 1: The result corresponding to c in the equation.
Level 2/Item 2: The result corresponding to u in the equation.
Level 1/Item 3: The result corresponding to v in the equation.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the polynomials for u, v, and c, where c is the greatest common divisor of a and b such
that:
Given two polynomials, a and b, returns polynomials u, v, and c where: au+bv=c
In the equation, c is the greatest common divisor of a and b.
2
u(x + 1 ) + v (x – 1 ) = c
Command: EGCD(X^2+1,X-1)
Result:
{2,1,-(X+1)}
See also:
IEGCD, ABCUV
EPSX0
Type:
Description:
Function
Access:
Catalog, …µ
Input:
A polynomial.
Output:
The polynomial with conforming coefficients replaced with 0.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example:
Replace with zero the terms smaller than EPS in the expression: 10-13x + 10-2
Replaces all coefficients in a polynomial that have an absolute value less than that held in the
CASDIR variable EPS, with 0. The default value of EPS is 1E-10, which can be changed by
storing a new number in the variable EPS in the CASDIR directory; this must be less than 1.
Computer Algebra Commands 4-27
Command: EPSX0(1E-13*X+.01)
Result:
0*X+.01
EULER
Type:
Description:
Function
Access:
!ÞINTEGER
Input:
A non-negative integer, or an expression that evaluates to a non-negative integer.
Output:
The number of positive integers, less than, and co-prime with, the integer.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
For a given integer, returns the number of integers less than the integer that are co-prime with
the integer. (Euler’s Φ function.)
EXLR
Type:
Description:
Command
Access:
Catalog, …µ
Input:
An equation.
Output:
Level 2/Item 1: The expression to the left of the “=” sign in the original equation, or, if the
input is an expression and not an equation, the independent variable.
Level 1/Item 2: The expression to the right of the “=” sign in the original equation, or, if the
input is an expression, the expression.
Flags:
Numeric mode must not be set (flag -3 clear).
In Algebraic mode (flag –95 set), the output expressions are evaluated (variables are replaced
by numeric values) before the result is returned.
Returns the left- and right-hand sides of an equation as discrete expressions.
Example:
Split the following equation into its two component expressions: sin(x)=5x+y
Command: EXLR(SIN(X)=5*X+Y)
Result:
{SIN(X), 5*X+Y}
See also:
FXND
EXP&LN
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, INTEGER, MAIN, MATHS, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
Displays a menu or list of the CAS exponential and logarithmic operations.
EXP2HYP
Type:
Description:
Function
Access:
Catalog, …µ
Input:
An expression
Converts expressions involving the exponential function into expressions with hyperbolic
functions.
4-28 Computer Algebra Commands
Output:
The rewritten expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Rewrite in terms of hyperbolic functions the expression e
Command: EXP2HYP(EXP(5*LN(X)))
Result:
SINH(5*LN(X))+COSH(5*LN(X))
EXP2POW
Type:
Description:
Function
Access:
!Ú
Input:
An expression
Output:
The simplified expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
5 ⋅ ln ( x )
Simplifies expressions involving the composition of the exponential and logarithmic
functions. Compare this to LNCOLLECT which combines logarithmic terms; the difference
is shown in the results of the second example used here and for LNCOLLECT.
REWRITE
Example 1:
Simplify the expression e 5·ln(x)
Command: EXP2POW(EXP(5*LN(X)))
Result:
5
X
Example 2:
Simplify the expression e n·ln(x)
Command: EXP2POW(EXP(N*LN(X)))
Result:
N
X
See also:
LNCOLLECT
EXPAND
Type:
Description:
Command
Access:
Algebra, …×or PALG
Input:
An expression, or an array of expressions.
Output:
The expanded and simplified expression or array of expressions.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Simplify the following expression:
Expands and simplifies an algebraic expression. This command is similar to the EXPAN
command (which is included to ensure backward-compatibility with the HP 48-series
calculators), except that EXPAND does more a more in-depth analysis and often does a
better job at simplifying an expression than EXPAN.
2
(x + 2x + 1)
------------------------------x+1
Command: EXPAND((X^2+2*X+1)/(X+1))
Result:
X+1
See also:
EXPAN
Computer Algebra Commands 4-29
EXPANDMOD
Type:
Function
Description: Expands and simplifies an algebraic expression, or an array of expressions, modulo the
current modulus.
Access:
!ÞMODULO
Input:
An expression, or an array of expressions.
Output:
The expanded and simplified expression, or array of expressions, modulo the current
modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Expand the following expression and give the result modulo 3:
( x + 3 )( x + 4 )
Command: EXPANDMOD((X+3)*(X+4))
Result:
X^2+X
EXPLN
Type:
Description:
Command
Access:
!Ð or Convert, !Ú
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Complex mode must be set (flag –103 set).
Example:
Transform the following expression and simplify the result using the EXPAND command:
Transforms the trigonometric terms in an expression to exponential and logarithmic terms.
REWRITE
or PLEXP & LN
2
2 cos ( x )
Command: EXPLN(2*COS(X^2))
EXPAND(ANS(1))
Result:
(EXP(i*X^2)^2+1)/EXP(i*X^2)
See also:
SINCOS
FACTOR
Type:
Description:
Command
Access:
Algebra, …×or PALG or !ÞPOLY
Input:
An expression or an integer.
Output:
The factorized expression, or the integer expressed as the product of prime numbers.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Results including complex terms are returned if complex mode is set (flag –103 set).
Factorizes a polynomial or an integer:
• The function expresses a polynomial as the product of irreducible polynomials.
• The function expresses an integer as the product of prime numbers.
4-30 Computer Algebra Commands
Example:
Factorize the following:
2
x + 5x + 6
Command: FACTOR(X^2+5*X+6)
Result:
(X+2)(X+3)
See also:
EXPAN, EXPAND
FACTORMOD
Type:
Function
Description: Factorizes a polynomial modulo the current modulus. The modulus must be less than 100,
and a prime number, it can be changed by MODSTO.
Access:
Arithmetic, !Þ MODULO
Input:
The expression to be factorized.
Output:
The factorized expression modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Factorize the following expression modulo 3.
x2+2
Command: FACTORMOD(X^2+2)
Result:
(X+1)*(X-1)
See also:
MODSTO
FACTORS
Type:
Description:
Command
Access:
Arithmetic, !Þ
Input:
A value or expression.
Output:
A list of prime factors of the value or expression, with each factor followed by its multiplicity
expressed as a real number.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
For a value or expression, returns a list of prime factors and their multiplicities.
Example 1:
Find the prime factors of 100.
Command: FACTORS(100)
Result:
{5 2. 2 2.}
2
Example 2:
Find the irreducible factors of: x + 4x + 4
Command: FACTORS(X^2+4*X+4)
Result:
{X+2,2.}
FCOEF
Type:
Description:
Command
Access:
Arithmetic, !ÞPOLY L
From an array of roots and multiplicities/poles, returns a rational polynomial with a leading
coefficient of 1, with the specified set of roots or poles, and with the specified multiplicities.
Computer Algebra Commands 4-31
Input:
An array of the form [Root 1, multiplicity/pole 1, Root 2, multiplicity/pole 2, . . .] The
multiplicity/pole must be an integer. A positive number signifies a multiplicity. A negative
number signifies a pole.
Output:
The rational polynomial with the specified roots and multiplicities/poles. The polynomial is
written using the current independent variable.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the rational polynomial corresponding to the following set of roots and poles:
1, 2, 3, –1
Command: FCOEF([1,2,3,-1])
Result:
(X-1)^2/(X-3)
See also:
FROOTS
FDISTRIB
Type:
Command
Description:
Performs a full distribution of multiplication and division with respect to addition and
subtraction in a single step.
Access:
!Ú
Input:
An expression.
Output:
An equivalent expression that results from fully applying the distributive property of
multiplication and division over addition and subtraction.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
REWRITE
Example:
Expand (X+1)(X-1)(X+2):
Command: FDISTRIB((X+1)*(X-1)*(X+2))
Result:
X*(X*X)+2*(X*X)+(-(X*(1*X))+-(2*(1*X)))+ (X*(X*1)+2*(X*1)+
(-(X*(1*1))+-(2*(1*1))))
See also:
DISTRIB
FOURIER
Type:
Description:
Function
Returns the nth coefficient of a complex Fourier series expansion. The PERIOD variable must
be in the CAS directory, CASDIR, or in current path, and set to hold L, the period of the
input function. The expression is expanded in terms of the current CAS variable.
Access:
Calculus !ÖDERIV. & INTEG.
Input:
Level 1/Argument 2: An expression in terms of the current variable
Level 2/Argument 1: The number, n, of the coefficient to return.
Output:
The nth Fourier coefficient of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Complex mode must be set, that is, flag –103 must be set.
Example:
Obtain the Fourier coefficient as below, with the default value of 2π in the PERIOD variable in
CASDIR, and simplify it with EXPAND:
4-32 Computer Algebra Commands
Command: FOURIER(X^2,0)
Result:
EXPAND(ANS(1))
4/3* π^2
FROOTS
Type:
Description:
Command
Access:
Arithmetic, !ÞPOLY L
Input:
A rational polynomial.
Output:
An array of the form [Root 1, Multiplicity 1, Root 2, Multiplicity 2, . . .]
A negative multiplicity indicates a pole.
Flags:
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
If complex mode is set (flag –103 set), FROOTS looks for complex solutions as well as real
solutions.
For a rational polynomial, returns an array of its roots and poles, with their corresponding
multiplicities. This is the inverse of FCOEF and uses the same notation for roots and poles.
If approximate mode is set (flag –105 set) FROOTS searches for numeric roots.
See also:
FCOEF
FXND
Type:
Description:
Command
Access:
Catalog, …µ
Input:
A fraction, or an object that evaluates to a fraction.
Output:
The object split into numerator and denominator.
Level 2/Item 1: The numerator.
Level 1/Item 2: The denominator.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Return the numerator and the denominator of the following expression:
Splits an object into a numerator and a denominator.
2
(x – 3)
------------------z+4
Command: FXND((X-3)^2/(Z+4))
Result:
{(X-3)^2, Z+4}
See also:
EXLR
GAUSS
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
Level 2/Argument 1: The quadratic form.
Level 1/Argument 2: A vector containing the independent variables.
Output:
Level 4/Item 1: An array of the coefficients of the diagonal.
Level 3/Item 2: A matrix, P, such that the quadratic form is represented as PTDP, where the
diagonal matrix D contains the coefficients of the diagonal representation.
Returns the diagonal representation of a quadratic form.
QUADRATIC FORM
Computer Algebra Commands 4-33
Level 2/Item 3: The diagonal representation of the quadratic form.
Level 1/Item 4: The vector of the variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the Gaussian symbolic quadratic form of the following:
2
x + 2axy
Command: GAUSS(X^2+2*A*X*Y,[X,Y])
Result:
{[1,-A^2], [[1,A][0,1]], -(A^2*Y^2)+(A*Y+X)^2,[X,Y]}
See also:
AXQ, QXA
GBASIS
Type:
Description:
Command
Access:
Catalog, …µ
Input:
Level 2/Argument 1: A vector F of polynomials in several variables.
Level 1/Argument 2: A vector giving the names of the variables.
Output:
Level 1/Item 1: A vector containing the resulting set G of polynomials. The command
attempts to order the polynomials as given in the vector of variable names.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find a Grœbner basis of the ideal polynomial generated by the polynomials:
x2 + 2xy2, xy + 2y3 – 1
Returns a set of polynomials that are a Grœbner basis G of the ideal I generated from an
input set of polynomials F.
Command: GBASIS([X^2 + 2*X*Y^2, X*Y + 2*Y^3 – 1], [X,Y])
Result:
[X, 2*Y^3-1]
Note this is not the minimal Grœbner basis, as the leading coefficient of the second term is not
1; the algorithm used avoids giving results with fractions.
See also:
GREDUCE
GCD
Type:
Description:
Function
Access:
Arithmetic, !ÞPOLY L
Input:
Level 2/Argument 1: An expression, or an object that evaluates to a number.
Level 1/Argument 2: An expression, or an object that evaluates to a number.
Output:
The greatest common divisor of the two objects.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Returns the greatest common divisor of two objects.
Example:
Find the greatest common divisor of 2805 and 99.
Command: GCD(2805,99)
Result:
33
See also:
GCDMOD, EGCD, IEGCD, LCM
4-34 Computer Algebra Commands
GCDMOD
Type:
Description:
Function
Access:
Arithmetic, !ÞMODULO
Input:
Level 2/Argument 1: A polynomial expression.
Level 1/Argument 2: A polynomial expression.
Output:
The greatest common divisor of the two expressions modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Finds the greatest common divisor of two polynomials modulo the current modulus.
Example:
Find the greatest common divisor of 2x^2+5 and 4x^2-5x, modulo 13.
Command: GCDMOD(2X^2+5,4X^2-5X)
Result:
-(4X-5)
See also:
GCD
GRAMSCHMIDT
Type:
Command
Description: Finds an orthonormal base of a vector space with respect to a given scalar product.
Access:
Matrices, !Ø LVECTOR
Input:
Level 2/Argument 1: A vector representing a basis of a vector space.
Level 1/Argument 2: A function that defines a scalar product in that space. This can be given
as a program, or as the name of a variable containing the definition of the function.
Output:
An orthonormal base of the vector space with respect to the given scalar product.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find an orthonormal base for the vector space with base [1, 1+X] with respect to the scalar
product defined by :
P⋅Q =
1
∫ – 1 P ( x ) ⋅ Q ( x ) dx
Command: GRAMSCHMIDT([1,1+X], « → P Q « PREVAL(INTVX(P*Q),-1,1) » »)
Result:
1
X
------- -------------2 1
--- ⋅ 6
3
GREDUCE
Type:
Description:
Command
Access:
Catalog, …µ
Input:
Level 3/Argument 1: A vector of polynomials in several variables.
Level 2/Argument 2: A vector of polynomials that is a Grœbner basis in the same variables.
Level 1/Argument 3: A vector giving the names of the variables.
Output:
Level 1/Item 1: A vector containing the input polynomial reduced with respect to the
Grœbner basis, up to a constant; as with GBASIS, fractions in the result are avoided.
Reduces a polynomial with respect to a Grœbner basis.
Computer Algebra Commands 4-35
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Reduce the polynomial:
x2y – xy – 1
with respect to the Grœbner basis (obtained in the example for GBASIS):
x, 2y3 – 1
Command: GREDUCE(X^2*Y–X*Y–1, [X,2*Y^3–1], [X,Y])
Result:
-1
See also:
Note this is the remainder of the input polynomial modulo the term x in the Grœbner basis
GBASIS
HADAMARD
Type:
Command
Description: Performs an element by element multiplication of two matrices (Hadamard product).
Access:
Matrices, !Ø
Input:
Level 2/Argument 1: Matrix 1.
Level 1/Argument 2: Matrix 2.
The matrices must have the same order.
Output:
The matrix representing the result of the multiplication.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the Hadamard product of the following two matrices:
3 –1 2
0 1 4
and
OPERATIONS L
230
152
Command: HADAMARD([[3,-1,2][0,1,4]],[2,3,0][1,5,2]])
Result:
[[6,-3,0][0,5,8]]
HALFTAN
Type:
Description:
Command
Access:
Trigonometry, …Ñor P TRIG
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
See also:
TAN2CS2, TAN2SC2
HELP
Type:
Description:
Command
Transforms an expression by replacing sin(x), cos(x) and tan(x) subexpressions with tan(x/2)
terms.
Similar to CASCMD, displays a list of CAS operations. Selecting one with OK displays help
for it, an example of the operation, and the option to copy the example to the command line.
More details are given in Appendix C and Appendix H of the User’s Guide.
4-36 Computer Algebra Commands
Access:
See also:
Catalog, …µ, or tools IL
CASCMD
HERMITE
Type:
Description:
Function
Access:
Arithmetic, !ÞPOLY L
Input:
A non-negative integer.
Output:
The corresponding polynomial expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Command:
Result:
See also:
Find the Hermite polynomial with degree 4.
Returns the nth Hermite polynomial.
HERMITE(4)
16*X^4-48*X^2+12
LEGENDRE, TCHEBYCHEFF
HESS
Type:
Description:
Command
Access:
Calculus !ÖDERIV & INTEG
Input:
Level 2/Argument 1: An expression.
Level 1/Argument 2: A vector of the variables.
Output:
Level 3/Item 1: The Hessian matrix with respect to the specified variables.
Level 2/Item 2: The gradient with respect to the variables.
Level 1/Item 3: The vector of the variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the Hessian matrix, and the gradient with respect to each variable, of the expression:
Returns the Hessian matrix and the gradient of an expression with respect to the specified
variables.
t2 + 2tu2.
Command: HESS(T^2+2*T*U^2, [T, U])
Result:
{[[2, 2*(2*U)], [2*(2*U), 2*(2*T)]], [2*T+2*U^2, 2*T*(2*U)], [T, U]}
See also:
CURL, DIV
HILBERT
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A positive integer, representing the order.
Output:
The Hilbert matrix of the specified order.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the order 3 Hilbert matrix.
Command:
HILBERT(3)
Returns a square Hilbert matrix of the specified order.
CREATE Lor
!´ MATRX
MAKE
LL
Computer Algebra Commands 4-37
Result:
1
1 --2
1 1
--- --2 3
1 1
--- --3 4
1
--3
1
--4
1
--5
See also:
CON, IDN, RANM, VANDERMONDE
HORNER
Type:
Description:
Command
Access:
Arithmetic, !ÞPOLY L
Input:
Level 2/Argument 1: A polynomial, P.
Level 1/Argument 2: A number, r.
Output:
Level 3/Item 1: QUOT(P/(x–r))
Level 2/Item 2: r
Level 1/Item 3: P(r), the remainder of the division process.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
For r = 3, find the result of executing a Horner scheme on the following polynomial:
Executes a Horner scheme on a polynomial. That is, for a given polynomial P, and a number
r, HORNER returns QUOT(P/(x–r)), r and also P(r)
2
x +x+1
Command: HORNER(X^2+X+1,3)
Results:
(X+4,3,13)
IABCUV
Type:
Description:
Command
Access:
Arithmetic, !ÞINTEGER
Input:
Level 3/Argument 1: the value of a.
Level 2/Argument 2: the value of b.
Level 1/Argument 3: the value of c.
Output:
Level 2/Item 1: The value for u.
Level 1/Item 2: The value for v.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find a solution in integers of the equation:
6a + 11b = 3
Returns a solution in integers u and v of au + bv = c, where a, b, and c are integers.
Command: IABCUV(6,11,3)
Result:
{6,-3}
See also:
ABCUV, IEGCD
IBASIS
Type:
Command
4-38 Computer Algebra Commands
Description:
Determines the basis of the intersection between two vector spaces.
Access:
Matrices, !Ø L VECTOR
Input:
Two lists of vectors
Output:
A list of vectors.
Flags:
Exact mode must be set (flag –105 clear).
Example:
Command:
Result:
See also:
Find a vector of a basis of the intersection of the vector sub-spaces defined by [1, 2] and [2, 4]
IBASIS({[1,2]}, {[2,4]})
{[1,2]}
BASIS
IBERNOULLI
Type:
Function
Description: Returns the nth Bernoulli number for a given integer n.
Access:
Arithmetic, !ÞINTEGER
Input:
Level 1/Argument 1: an integer.
Output:
Level 1/Item 1: The corresponding nth Bernoulli number for the integer. For numbers greater
than about 40 the calculation can take a long time.
Flags:
Numeric mode must not be set (flag -3 clear).
IBP
Type:
Description:
Command
Performs integration by parts on a function. The function must be able to be represented as a
product of two functions, where the antiderivative of one of the functions is known:
f(x) = u(x).v’(x)
Note that the command is designed for use in RPN mode only.
Access:
PCALC or Calculus, !ÖDERIV & INTEG L
Input:
Level 2: The integrand expressed as a product of two functions, u(x).v’(x)
Level 1: The antiderivative of one of the component functions, v(x).
Output:
Level 2: u(x)v(x)
Level 1: -u'(x)v(x)
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Use integration by parts to calculate the following:
∫ x cos ( x ) dx
Command 1: Apply the IBP command in RPN mode:
Level 2: X*COS(X)
Level 1: SIN(X)
Result:
Level 2: SIN(X)*X
Level 1: -SIN(X)
Command 2: Apply the INTVX command to level 1, -SIN(X)
Result:
Level 2: SIN(X)*X
Level 1: COS(X)
Command 3: Press + to add the result to the value at level 2 to obtain the final result.
Computer Algebra Commands 4-39
Result:
SIN(X)*(X)+COS(X)
See also:
INTVX, INT, PREVAL, RISCH
ICHINREM
Type:
Description:
Command
Access:
Arithmetic, !ÞINTEGER
Input:
Level 2/Argument 1: A vector of the first value and the modulus.
Level 1/Argument 2: A vector of the second value and the modulus.
Output:
A vector of the solution.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Solve the following system of congruences:
x ≡ 2 Modulo 3
x ≡ 1 Modulo 5
Solves a system of two congruences in integers using the Chinese Remainder theorem.
Command: ICHINREM([2,3],[1,5])
Results:
[-4, 15]
See also:
CHINREM
IDIV2
Type:
Description:
Command
Access:
Arithmetic, !ÞINTEGER
Input:
Level 2/Argument 1: a.
Level 1/Argument 2: b.
Output:
Level 2/Item 1: The integer part of a/b.
Level 1/Item 2: The remainder.
Flags:
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Command:
Result:
See also:
Return the integer part and the remainder of 11632/864.
For two integers, a and b, returns the integer part of a/b, and the remainder, r.
IDIV2(11632,864)
{13,400}
DIV2, IQUOT
IEGCD
Type:
Description:
Command
Access:
PARITH or Arithmetic, !ÞINTEGER
Input:
Level 2/Argument 1: x.
Level 1/Argument 2: y.
Output:
Level 3/Item 1: c.
Level 2/Item 2: a.
Given two integers x and y, returns three integers, a, b, and c, such that:
ax+by=c
where c is the GCD of x and y.
4-40 Computer Algebra Commands
Level 1/Item 3: b.
Note the order, c is first.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Command:
Result:
See also:
Find a, b and c such that a18 + b24 = c, where c is the GCD of 18 and 24.
IEGCD(18,24)
{6,-1,1}
ABCUV, EGCD, IABCUV
ILAP
Type:
Description:
Function
Access:
Calculus, !ÖDIFFERENTIAL EQNS
Input:
A rational expression.
Output:
The inverse Laplace transformation of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Command:
Result:
See also:
Returns the inverse Laplace transform of an expression. The expression must evaluate to a
rational fraction.
1
Find the inverse Laplace transform of: ------------------2(x – 5)
ILAP(1/(X-5)^2)
X*EXP(5*X)
LAP, LAPL
IMAGE
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A matrix representing a linear application f in terms of the standard basis.
Output:
A list of vectors representing a basis of the image of f.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Computes the basis of the image (also called the range) of a linear application f.
LINEAR APPL
112
213
314
Example:
Find the image of
Command: IMAGE([1,1,2] [2,1,3] [3,1,4])
Result:
{[1,0,-1] [0,1,2]}
See also:
BASIS, KER
INT
Type:
Description:
Function
Access:
Catalog, …µ
Calculates the antiderivative of a function for a given variable, at a given point.
Computer Algebra Commands 4-41
Input:
Level 3/Argument 1: A function.
Level 2/Argument 2: The variable to obtain the derivative with respect to.
Level 1/Argument 3: The point at which to calculate the antiderivative. This point can be a
variable or an expression.
Output:
The antiderivative of the function for the given variable, at the point you specified.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the integral of sin(x) with respect to x, at the point where x=y.
Command: INT(SIN(X),X,Y)
Result:
-COS(Y)
See also:
INTVX, RISCH
INTEGER
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, MAIN, MATHS, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
Displays a menu or list of CAS integer operations.
INTVX
Type:
Description:
Function
Access:
Calculus, !Öor P CALC or !Ö DERIV. & INTEG L
Input:
An expression.
Output:
The antiderivative of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the antiderivative of the following:
Finds the antiderivative of a function symbolically, with respect to the current default variable.
2
x ln x
Command: INTVX(X^2*LN(X))
Result:
1/3*X^3*LN(X)+(-1/9)*X^3
See also:
IBP, RISCH, PREVAL
INVMOD
Type:
Description:
Function
Access:
Arithmetic, !ÞMODULO L
Input:
An object.
Output:
The modular inverse of the object.
Performs modular inversion on an object modulo the current modulus.
4-42 Computer Algebra Commands
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Solve the following for x, modulo the default modulus, 13.
( 2x ≡ 1 )
Command: INVMOD(2)
Result:
-6
IQUOT
Type:
Description:
Function
Access:
PARITH or Arithmetic, !ÞINTEGER L
Input:
Level 2/Argument 1: The dividend.
Level 1/Argument 2: The divisor.
Output:
The integer quotient.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
See also:
QUOT, IDIV2
Returns the integer quotient (or Euclidean quotient) of two integers. That is, given two
integers, a and b, returns the integer q, such that:
a = qb + r, and 0 ≤ r < b
IREMAINDER
Type:
Function
Description: Returns the remainder of an integer division.
Access:
PARITH or Arithmetic, !ÞINTEGER L
Input:
Level 2/Argument 1: The numerator.
Level 1/Argument 2: The denominator.
Output:
The remainder.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
IDIV2
See also:
ISOM
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A square matrix representing a linear isometry.
Output:
A vector and/or an angle that represent the symmetry of the matrix, and 1 (for a direct
isometry) or -1 (for an indirect isometry).
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Determine the characteristics of a 2-d or 3-d linear isometry.
LINEAR APPL
Computer Algebra Commands 4-43
Example 1:
Analyze the isometry given by the matrix
0 –1
–1 0
Command: ISOM([[0,-1] [-1,0]])
Result:
{ [1, 1] –1}, meaning the matrix represents a symmetry in the line y = –x, and this is an indirect
isometry.
1 – 3
--- ---------2 2
Example 2:
Analyze the isometry given by the matrix
Command: ISOM([[1/2, -√3/2][√3/2, 1/2]])
3
------2
1
--2
Result:
{ π/3, 1 }, meaning the matrix represents a rotation of π/3 radians, and this is a direct isometry.
See also:
MKISOM
ISPRIME?
Type:
Description:
Function
Tests if a number is prime. For numbers of the order of 1014 or greater (to be exact, greater
than 341550071728321), tests if the number is a pseudoprime; this has a chance of less than 1
in 1012 of wrongly identifying a number as a prime.
Access:
PARITH or Arithmetic, !ÞINTEGER L
Input:
An object that evaluates to an integer or a whole real number.
Output:
1 (True) if the number is prime, 0 (False) if it is not.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
See also:
NEXTPRIME, PREVPRIME
JORDAN
Type:
Description:
Command
Access:
Matrices, !Ø LEIGENVECTORS
Input:
An n × n matrix.
Output:
Level 4/Item 1: The minimum polynomial.
Level 3/Item 2: The characteristic polynomial.
Level 2/Item 3: A list of characteristic spaces tagged by the corresponding eigenvalue (either a
vector or a list of Jordan chains, each of them ending with an "Eigen:"-tagged eigenvector).
Level 1/Item 4: An array of the eigenvalues, with multiplicities
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Diagonalization, or Jordan cycle decomposition, of a matrix. Computes the eigenvalues,
eigenvectors, minimum polynomial, and characteristic polynomial of a matrix.
Example:
Perform the following diagonalization:
Command: JORDAN([1,1][1,1])
Result:
{X^2-2*X,
X^2-2*X,
4-44 Computer Algebra Commands
{0: [1,-1]}, 2: [1,1]}
[0,2]}
KER
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A matrix representing a linear application f in terms of the standard basis.
Output:
A list of vectors representing a basis of the kernel (also called the nullspace) of f.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Computes the basis of the kernel of a linear application f.
LINEAR APPL
112
213
314
Example:
Find the kernel of
Command: KER([1,1,2][2,1,3][3,1,4])
Result:
{[1,1,-1]}
See also:
BASIS, IMAGE
LAGRANGE
Type:
Command
Description: Returns the interpolating polynomial of minimum degree for a set of pairs of values. For two
pairs, DROITE will fit a straight line.
Access:
Arithmetic, !ÞPOLY L
Input:
A two × n matrix of the n pairs of values.
Output:
The polynomial that results from the Lagrange interpolation of the data.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find an interpolating polynomial for the data (1,6), (3,7), (4,8), (2,9)
Command: LAGRANGE([[1,3,4,2][6,7,8,9]])
3
Result:
2
8x – 63x + 151x – 60
-------------------------------------------------------6
See also:
DROITE
LAP
Type:
Description:
Function
Access:
Calculus, !Ö
Input:
An expression.
Output:
The Laplace transform of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Performs a Laplace transform on an expression with respect to the current default variable.
DIFFERENTIAL EQNS
Computer Algebra Commands 4-45
Example:
Find the Laplace transform of ex.
Command: LAP(EXP(X))
Result:
1/(X-1)
See also:
ILAP, LAPL
LAPL
Type:
Description:
Command
Access:
!Ö DERIV & INTEG L
Input:
Level 2/Argument 1:An expression.
Level 1/Argument 2: A vector of variables.
Output:
The Laplacian of the expression with respect to the variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find, and simplify, the Laplacian of the following expression:
Returns the Laplacian of a function with respect to a list of variables.
x
e cos ( zy )
Command: LAPL(EXP(X)*COS(Z*Y),[X,Y,Z])
Result:
EXPAND(ANS(1))
-((Y^2+Z^2-1)*EXP(X)*COS(Z*Y))
See also:
LAP, ILAP
LCM
Type:
Description:
Function
Access:
Arithmetic, !ÞPOLYNOMIAL LL
Input:
Level 2/Argument 1: An expression, a number, or object that evaluates to a number.
Level 1/Argument 2: An expression, a number, or object that evaluates to a number.
Output:
The least common multiple of the objects.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the least common multiple of the following two expressions:
Returns the least common multiple of two objects.
2
x –1
x–1
Command: LCM(X^2-1,X-1)
Results:
X^2-1
See also:
GCD
LCXM
Type:
Description:
Command
Access:
Catalog, …µ
From a program with two arguments, builds a matrix with the specified number of rows and
columns, with aij = f(i,j).
4-46 Computer Algebra Commands
Input:
Level 3/Argument 1: The number of rows you want in the resulting matrix.
Level 2/Argument 2: The number of columns you want in the resulting matrix.
Level 1/Argument 3: A program that uses two arguments. An expression with the two
variables I, J can be used instead.
Output:
The resulting matrix.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Build a 2 × 3 matrix with aij=i+2j.
Command: LCXM(2,3,« →I J 'I+2*J'»)
Result:
357
468
LDEC
Type:
Description:
Command
Access:
Symbolic solve, !Îor PSOLVER or !ÖDIFF
Input:
Level 2/Argument 1: For a single equation, the function forming the right hand side of the
equation. For a system of equations, an array comprising the terms not containing the
dependent variables.
Level 1/Argument 2: For one equation, the auxiliary polynomial. For a system of equations,
the matrix of coefficients of the dependent variables.
Output:
The solution.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Solves a linear differential equation with constant coefficients, or a system of first order linear
differential equations with constant coefficients.
Example:
Solve 2sin(x), with the auxiliary polynomial x2+1:
Command: LDEC(2*SIN(X),X^2+1)
Result:
COS(X)*(cC0 -X)+(cC1 — -1)*SIN(X)
See also:
DESOLVE
LEGENDRE
Type:
Function
Description: Returns the nth degree Legendre polynomial.
Access:
Arithmetic, !Þ POLYNOMIAL LL
Input:
An integer, n.
Output:
The nth Legendre polynomial.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the Legendre polynomial with degree 4.
Command: LEGENDRE(4)
Result:
(35*X^4-30*X^2+3)/8
See also:
HERMITE, TCHEBYCHEFF
Computer Algebra Commands 4-47
LGCD
Type:
Description:
Function
Access:
Arithmetic, !Þ L
Input:
A list of expressions or values.
Output:
Level 2/Item 1: The list of elements.
Level 1/Item 2: The greatest common divisor of the elements.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
See also:
GCD
LIMIT
Type:
Description:
Function
Access:
Catalog, …µ
lim
Type:
Description:
Function
Access:
Calculus, !Ö LIMITS&SERIES
Input:
Level 2/Argument 1: An expression.
Returns the greatest common divisor of a list of expressions or values.
Returns the limit of a function as its argument approaches a specified value. This function is
identical to the lim function, described below, and is included to ensure backwardcompatibility with the HP49G calculator.
Returns the limit of a function as its argument approaches a specified value. Expands and
simplifies an algebraic expression.
Level 1/Argument 2: An expression of the form x = y, where x is the variable and y is the
value at which the limit is to be evaluated. If the variable approaching a value is the current
CAS variable, it is sufficient to give its value alone. The ∞ symbol provided by the calculator
can be used to set the limiting value at plus or minus infinity.
Output:
The limit of the expression at the limit point.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the following limit:
n
n
–y
⎛ lim ⎞ x--------------⎝ x → y⎠ x – y -
Command: lim((X^N-Y^N)/(X-Y), X=Y)
Result:
N*EXP(N*LN(Y))/Y
See also:
SERIES
LIN
Type:
Description:
Command
Access:
Linearizes expressions involving exponential terms.
…× or Exponential and logarithm, !Ð or PALG, or !Ú
or PLEXPLN.
4-48 Computer Algebra Commands
REWRITE,
Input:
An expression.
Output:
The linearized expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Linearize the following expression:
x y 4
x(e e )
Command: LIN(X*(EXP(X)*EXP(Y))^4)
Result:
X*EXP(4X+4Y)
See also:
TEXPAND
LINSOLVE
Type:
Description:
Command
Access:
Symbolic solve, !Î, PSOLVE, !Ø
Input:
Level 2/Argument 1: An array of equations.
Level1/Argument 2: A vector of the variables to solve for.
Output:
Level 3/Item 1: The system of equations, as a list containing the inputs as above.
Level 2/Item 2: A list of the pivot points.
Level 1/Item 3: The solution.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
See also:
DESOLVE, SOLVE, MSLV
LNAME
Type:
Description:
Access:
Input:
Output:
Flags:
Solves a system of linear equations.
LIN-S
Command
Returns the variable names contained in a symbolic expression.
Catalog, …µ
A symbolic expression.
Level 2/Argument 1: The original expression.
Level 1/Argument 2: A vector containing the variable names. The variable names are sorted
by length, longest first, and ones of equal length are sorted alphabetically.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
List the variables in the expression COS(B)/2*A + MYFUNC(PQ) + 1/T.
Example:
Command: LNAME(COS(B)/2*A + MYFUNC(PQ) + INV(T))
Result:
{COS(B)/2*A + MYFUNC(PQ) + 1/T, [MYFUNC,PQ,A,B,T]}
See also:
LVAR
LNCOLLECT
Type:
Command
Description: Simplifies an expression by collecting logarithmic terms. For symbolic powers does not
perform the same simplification as EXP2POW; compare example 2 here with example 2 for
EXP2POW.
Access:
Algebra, …×, !Ð, or PLEXP & LN, or !Ú REWRITE L
Input:
An expression.
Output:
The simplified expression.
Computer Algebra Commands 4-49
Flags:
Example 1:
Command:
Result:
Example 2:
Command:
Result:
See also:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Simplify the following expression:
2(ln(x)+ln(y))
LNCOLLECT(2(LN(X)+LN(Y))
LN(X^2*Y)
Compare the effect of LNCOLLECT with the effect of EXP2POW on the expression e n·ln(x)
LNCOLLECT(EXP(N*LN(X))
EXP(N*LN(X))
EXP2POW, TEXPAND
LOCAL
Type:
Description:
Command
Access:
Catalog, …µ
Input:
Level 1/Argument 1: A list of one or more local variable names (names beginning with the
local variable identifier ←), each one followed by an equals sign and the value to be stored in
it. Any variable not followed by an equal sign and a value is set equal to zero.
Output:
Level 1/Item 1: The input list.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Creates one or more local variables. This command is intended mainly for use in Algebraic
mode; it can not be single stepped when a program containing it is being debugged in
Algebraic mode.
Example:
Create local variables ←A and ←B and store the values 0 in the first and 2 in the second.
Command: LOCAL({←A,←B=2})
Result:
{←A,←B=2}
See also:
DEF, STORE, UNBIND
LVAR
Type:
Description:
Command
Access:
Catalog, …µ
Input:
An algebraic object.
Output:
Level 2/Item 1: The algebraic object.
Level 1/Item 2: A list which includes both the original expression and a vector containing the
variable names. Variable names include functions of variables, as described above. The names
are sorted by length, longest first, and ones of equal length are sorted alphabetically.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
List the variables and function names in the expression COS(B)/2*A + MYFUNC(PQ) +
1/T.
Returns a list of variables in an algebraic object. Differs from LNAME above in that
functions of variables, such as COS(X) or LN(AB) are returned, instead of the variable names,
X or AB. INV() and SQ() are not treated as functions. Compare the example here with the
same example in LNAME.
Command: LVAR(COS(B)/2*A + MYFUNC(PQ) + INV(T))
4-50 Computer Algebra Commands
Result:
{COS(B)/2*A + MYFUNC(PQ) + 1/T, [MYFUNC(PQ),COS(B),A,T]}
See also:
LNAME
MAD
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A square matrix
Output:
Level 4/Item 1: The determinant.
Level 3/Item 2: The formal inverse.
Level 2/Item 3: The matrix coefficients of the polynomial, p, defined by
(xi–a)p(x)=m(x)i, where a is the matrix, and m is the characteristic polynomial of a.
Level 1/Item 4: The characteristic polynomial.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Obtain the adjoint matrix of:
Returns details of a square matrix, including the information needed to obtain the adjoint
matrix. The adjoint matrix is obtained by multiplying the inverse matrix by the determinant.
OPERATIONS L
0 –1
1 0
Command: MAD([[0, -1][1, 0]])
Result:
{1,[[0, 1][-1, 0]],{[[1, 0][0, 1]], [[0, -1][1, 0]]}, X^2+1}
The determinant is 1, so the adjoint is the second item[[0, 1][-1, 0]].
See also:
LNAME
MAIN
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a list. If the
flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MATHS, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
Displays the main menu (or list) of CAS operations. This displays the CASCFG command,
the ALGB, ARIT, DIFF, EXP&LN, MATHS MATR, REWRITE and TRIGO menu
commands described in this part of the Command Reference, and the CMPLX and SOLVER
menu commands described in the Full Command and Function Reference (Chapter 3). Other
menus are not shown because they are within the submenus given by MAIN. More details are
given in Appendix K of the User’s Guide.
MATHS
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the submenus as a list. If the flag
is set, displays the submenus as a menu of function keys.
Displays a menu or list of CAS mathematics submenus. Details are given in Appendix J of the
User’s Guide.
Computer Algebra Commands 4-51
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATR, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
MATR
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MODULAR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
MENUXY
Type:
Description:
Access:
Input:
Output:
Displays a menu or list containing the CAS commands for matrix operations.
Command
Displays a function key menu of computer algebra commands in a specified range.
Catalog, …µ
Level 2/Argument 1: The number of the first command in the range to be displayed.
Level 1/Argument 2: The number of the last command in the range to be displayed.
Arguments below 0 are treated as 0, arguments above 140 are treated as 140.
On the function key menu, the computer algebra commands in the range specified. NOVAL
is returned in Algebraic mode.
This list gives the number of each operation that can be displayed by the command. The
complete menu below can be generated by MENUXY(0,140). Items 127 through to 135 allow
access from the top row of keys to CAS menus.
Number
0-5
6-11
12-17
18-23
24-29
30-35
36-41
42-47
48-53
54-59
60-65
66-71
72-77
78-83
84-89
90-95
96-101
102-107
108-113
114-119
120-125
126-131
132-137
138-140
EXPAND
TAYLOR0
PREVAL
LDEC
SINCOS
TRIGTAN
ASIN2C
REMAINDER
ABCUV
PTAYL
ISPRIME?
FROOTS
REF
SYLVESTER
HILBERT
LEGENDRE
TABVAR
MAP
EXLR
DIV2MOD
RREFMOD
CASCFG
DIFF
∞
FACTOR
SERIES
RISCH
TEXPAND
TLIN
TAN2SC
ACOS2S
IREMAINDER
IABCUV
HORNER
NEXTPRIME
FACTORS
AXM
PCAR
LCXM
TCHEBYCHEFF
TABVAL
XNUM
LNAME
POWMOD
MODSTO
MAIN
ARIT
PROMPTSTO
Operation
SUBST
SOLVEVX
DERIV
LIN
TCOLLECT
HALFTAN
DIV2
GCD
LGCD
EULER
PREVPRIME
DIVIS
AXL
JORDAN
DIV
HERMITE
DIVPC
XQ
ADDTMOD
INVMOD
MENUXY
ALGB
SOLVER
VER
DERVX
PLOT
DESOLVE
TSIMP
TRIG
TAN2SC2
IDIV2
LCM
SIMP2
PA2B2
SOLVE
TRAN
QXA
MAD
CURL
LAGRANGE
TRUNC
REORDER
SUBTMOD
GCDMOD
KEYEVAL
CMPLX
EXP&LN
INTVX
PLOTADD
LAP
LNCOLLECT
TRIGCOS
ATAN2S
QUOT
EGCD
PARTFRAC
CHINREM
ZEROS
HADAMARD
AXQ
LINSOLVE
LAPL
FOURIER
SEVAL
LVAR
MULTMOD
EXPANDMOD
GROBADD
TRIGO
EPSX0
Example:
Display a menu containing ATAN2S, ASIN2T, ASIN2C and ACOS2S.
Command: MENUXY(34,37)
4-52 Computer Algebra Commands
lim
IBP
ILAP
EXPLN
TRIGSIN
ASIN2T
IQUOT
IEGCD
PROPFRAC
ICHINREM
FCOEF
rref
GAUSS
VANDERMONDE
HESS
SIGNTAB
TEVAL
FXND
DIVMOD
FACTORMOD
SCROLL
MATR
?
Result:
The four functions are displayed above the A to D keys. In Algebraic mode, NOVAL is
returned as item 1.
See also:
MENU, TMENU
MKISOM
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
Level 2/Argument 1: For a 3-d isometry, a list of the characteristic elements of the isometry.
For a 2-d isometry, the characteristic element of the isometry (either an angle or a vector).
Level 1/Argument 2: +1 for a direct isometry or -1 for an indirect isometry.
Output:
The matrix that represents the given isometry.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example 1:
Find the matrix for a rotation of π/2 radians in two dimensions
Returns the matrix representation for a given isometry.
LINEAR APPL
Command: MKISOM(π/2, 1)
Result:
0 –1
1 0
Example 2:
Find the matrix for a rotation with axis [1 1 1] and angle π/3 radians combined with a
reflection in the plane x + y + z = 0
Command:
MKISOM({ [1, 1, 1],π/3}, -1) then simplify with EXPAND(ANS(1))
Result:
0 –1 0
0 0 –1
–1 0 0
See also:
ISOM
MODSTO
Type:
Description:
Command
Access:
Arithmetic, !Þ MODULO L
Input:
The modulo value that you want to set, an integer or an expression that evaluates to an
integer.
Output:
The modulo setting is changed to the specified number. In Algebraic mode, NOVAL is
returned as argument 1.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Changes the modulo setting to the specified number. The number that you set is reflected in
the CAS Modes input form. Negative numbers are replaced by their positive value, 0 and 1 are
replaced by 2.
MODULAR
Type:
Description:
Command
Access:
Catalog, …µ
Displays a menu or list of the CAS modulo operations.
Computer Algebra Commands 4-53
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
POLYNOMIAL, REWRITE, TESTS, TRIGO
MSLV
Type:
Description:
Command
Access:
Numeric solve, …Ï or catalog, …µ
Input:
Level 3/Argument 1: A vector containing the equations or expressions (assumed equal to
zero) to solve.
Level 2/Argument 2: A vector containing the variables to solve for
Level 1/Argument 3: A vector containing initial guesses
Output:
Level 3/Item 1: The vector containing the equations to solve.
Level 2/Item 2: The vector containing the variables to solve for
Level 1/Item 3: A vector representing an approximate solution to the system of equations.
Flags:
Exact mode must be set (flag –105 clear), The calculator will set approximate mode and will
look for approximate results if exact results are not found.
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Complex mode must be set (flag –103 set) if complex results are wanted.
Step-by-step mode can be set (flag –100 set).
Example:
Find x and y values, allowing for complex solutions, that solve the following two equations.
The first equation is an expression equal to zero, so only the expression needs to be given.
Setting the second expression equal to a complex number forces the solver to look for
complex solutions:
sin(x)+y=0, x+sin(y)=1:
Numerically approximates a solution to a system of equations. Searches for a solution
accurate to 12 digits, regardless of the display setting. Underdetermined and overdetermined
systems are rejected. Complex solutions will be looked for if any of the inputs contain
complex values. If a single expression or equation is to be solved, use SOLVE instead, or for
linear equations, use LINSOLVE. This command is similar to MSOLVR, but is more
appropriate for use with the CAS as it automates the solution instead of working through a
menu. Step-by-step mode is available with this command.
Command: MSLV('[SIN(X)+Y, X+SIN(Y)=(1,0)]', '[X,Y]', [0,0])
Results:
('[SIN(X)+Y, X+SIN(Y)=(1,0)]', '[X,Y]', [(1.82384112611,0.),
(-.968154636174,0.)])
See also:
DESOLVE, LINSOLVE, MSOLVR, SOLVE
MULTMOD
Type:
Description:
Function
Access:
Arithmetic, !Þ
Input:
Level 2/Argument 1: A number or an expression.
Level 1/Argument 2: A number or an expression.
Output:
The result of modular multiplication of the two objects, modulo the current modulus.
Performs modular multiplication of two objects, modulo the current modulus.
MODULO L
4-54 Computer Algebra Commands
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the product of 2x and 38x2, modulo the default modulus, 3.
Command: MULTMOD(2*X,38*X^2)
Result:
X^3
NEXTPRIME
Type:
Function
Description: Given an integer, returns the next prime number larger than the integer. Like ISPRIME?, it
uses a pseudoprime check for large numbers.
Access:
Arithmetic, !Þ INTEGER L
Input:
An integer or an expression that evaluates to an integer.
Output:
The next prime number larger than the integer.
Example:
Find the closest, larger prime number to 145.
Command: NEXTPRIME(145)
Result:
149
See also:
ISPRIME?, PREVPRIME
P2C
Type:
Description:
Command
Access:
!Þ PERM
Input:
A list representing a permutation. For example, the list {3,1,2,5,4} defines a permutation P,
such that P(1)=3, P(2)=1, P(3)=2, P(4)=5, and P(5)=4
Output:
Level 2/Item 1:A list of cycles equivalent to the permutation. For example, the list {3,1,2,5,4}
defines a cycle C, such that C(3)=1, C(1)=2, C(2)=5, C(5)=4, and C(4)=3
Level 1, Item 2: The signature of the permutation, 1 or -1.
Takes a list representing a permutation as an argument, and returns the permutation
decomposed into lists that represent cycles.
Example:
Convert the permutation given by {3,4,5,2,1} into cycles:
Command: P2C({3,4,5,2,1})
Result:
{{{1,3,5},{2,4}},-1}
See also:
C2P, CIRC
PA2B2
Type:
Description:
Function
Access:
Arithmetic, !Þ INTEGER L
Input:
A prime number, p, such that p=2 or p ≡ 1 modulo 4
Output:
A Gaussian integer a+ib such that p=a2+b2
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Complex mode must be set (flag –103 set).
Takes a prime number, p, such that p=2 or p ≡ 1 modulo 4, and returns a Gaussian integer a +
ib such that p = a2 + b2. This function is useful for factorizing Gaussian integers.
Computer Algebra Commands 4-55
See also:
GAUSS
PARTFRAC
Type:
Command
Description: Performs partial fraction decomposition on a partial fraction.
Access:
Algebra …× or Arithmetic, !Þ
Input:
An algebraic expression.
Output:
The partial fraction decomposition of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Perform a partial fraction decomposition of the following expression:
POLYNOMIAL LL
1
------------2
x –1
Command: PARTFRAC(1/(X^2-1))
Result:
1/2/(X-1)+-1/2/(X+1)
See also:
PROPFRAC
PCAR
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A square matrix.
Output:
The characteristic polynomial of the matrix.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the characteristic polynomial of the following matrix:
Returns the characteristic polynomial of an n × n matrix.
L EIGENVECTORS
5 8 16
4 1 8
– 4 – 4 – 11
Command: PCAR([[5,8,16][4,1,8][-4,-4,-11]])
Result:
X^3+5*X^2+3*X-9
See also:
JORDAN, PMINI
PMINI
Type:
Description:
Command
Access:
Matrices, ! Ø
Input:
An nxn matrix A.
Output:
A matrix whose first zero-row contains the minimal polynomial of A. In step-by-step mode,
PMINI shows the row-reduction steps.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Step-by-step mode can be set (flag –100 set).
Finds the minimal polynomial of a matrix.
LEIGENVECTORS
4-56 Computer Algebra Commands
Example:
Find the minimal polynomial of
Command: PMINI([[0,1][1,0]])
1 0 0 1
0 1 1 0
01
10
:
1
X
2
Result:
See also:
0 0 0 0 X –1
So, the minimal polynomial is X2-1, as it is in the first row to contain entirely
zeros, except for the result.
JORDAN, PCAR
POLYNOMIAL
Type:
Command
Description: Displays a menu or list of CAS operations with polynomials.
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, REWRITE, TESTS, TRIGO
POTENTIAL
Type:
Command
Description: Find the potential field function describing a field whose vector gradient is input. This
command is the opposite of DERIV. Given a vector V it attempts to return a function U
such that grad U is equal to V; ∇U = V . For this to be possible, CURL(V) must be zero,
otherwise the command reports a “Bad Argument Value” error. Step-by-step mode is
available with this command.
Access:
Catalog, …µ
Input:
Level 2/Argument 1: A vector V of expressions.
Level 1/Argument 2: A vector of the names of the variables.
Output:
Level 1/Item 1: A function U of the variables that is the potential from which V is derived.
An arbitrary constant can be added, the command does not do this.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Step-by-step mode can be set (flag –100 set).
Example:
To confirm that this command is the opposite of DERIV, use the output of the example in
DERIV, and show that the result is the same as the input given in the DERIV example. Find
the function of the spatial variables x, y, and z whose gradient is:
(4xy+z)i + (2x2 + 6yz)j + (x+3y2)k
Command: POTENTIAL([4*X*Y+Z, 2*X^2+6*Y*Z, X+3*Y^2], [X,Y,Z])
Result:
See also:
EXPAND(ANS(1))
2*Y*X^2+Z*X+3*Z*Y^2
DERIV, VPOTENTIAL
POWEXPAND
Type:
Function
Computer Algebra Commands 4-57
Description:
Rewrites an expression raised to a power as a product. If followed by repeated execution of
DISTRIB allows an expression to be expanded fully, step by step.
Access:
!Ú
Input:
An expression raised to a power.
Output:
The result from applying the distributive property of exponentiation over multiplication.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
REWRITE L
Example:
Expand (X+1)3.
Command: POWEXPAND((X+1)^3)
Result:
(X+1)⋅(X+1)⋅(X+1)
POWMOD
Type:
Description:
Function
Access:
Arithmetic, !Þ MODULO L
Input:
Level 2/Argument 1: The object.
Level 1/Argument 2: The exponent.
Output:
The result of the object raised to the exponent, modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
PREVAL
Type:
Description:
Raises an object (number or expression) to the specified power, and expresses the result
modulo the current modulus.
Function
With respect to the current default variable, returns the difference between the values of a
function at two specified values of the variable.
PREVAL can be used in conjunction with INTVX to evaluate definite integrals. See the
example below.
Access:
Calculus, !Ö
Input:
Level 3/Argument 1: A function.
Level 2/Argument 2: The lower bound.
Level 3/Argument 1: The upper bound.
The bounds can be expressions.
Output:
The result of the evaluation.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Evaluate the following:
3
∫0 ( x
3
DERIV. & INTEG
+ 3x ) dx
Command: PREVAL(INTVX(X^3+3*X),0,3)
Result:
135/4
PREVPRIME
Type:
Function
4-58 Computer Algebra Commands
L.
Description:
Given an integer, finds the closest prime number smaller than the integer. Like ISPRIME?, it
uses a pseudoprime check for large numbers.
Access:
Arithmetic, !Þ INTEGER L
Input:
An integer or an expression that evaluates to an integer.
Output:
The closest prime number smaller than the integer.
Example:
Find the closest, smaller prime number to 145.
Command: PREVPRIME(145)
Result:
139
See also:
ISPRIME?, NEXTPRIME
PROPFRAC
Type:
Command
Description: Toggles between an improper fraction and its corresponding integer and fractional part.
Access:
PARITH or Arithmetic, !ÞL
Input:
An improper fraction, or an object that evaluates to an improper fraction. It must not contain
real numbers. Alternately, the input may be an integer part plus a proper fraction.
Output:
An integer part plus a proper fraction; or alternately, if the input was an integer part plus a
proper fraction, an improper fraction.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Express the following as a proper fraction:
3
x +4
------------2
x
Command: PROPFRAC((X^3+4)/X^2))
Result:
X+(4/X^2)
PTAYL
Type:
Description:
Function
Access:
Arithmetic, !Þ
Input:
Level 2/Argument 1: A polynomial, P.
Level 1/Argument 2: A number, a.
Output:
A polynomial, Q such that Q(x – a)=P(x).
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the polynomial Q(x) such that
Q(x-2)=x2+3x+2.
Returns the Taylor polynomial at x = a for a specified polynomial.
POLYNOMIAL LL
Command: PTAYL(X^2+3*X+2, 2)
Result:
X^2+7*X+12
QUOT
Type:
Function
Computer Algebra Commands 4-59
Description:
Returns the quotient part of the Euclidean division of two polynomials.
Access:
Arithmetic, !Þ
Input:
Level 2/Argument 1: The numerator polynomial.
Level 1/Argument 2: The denominator polynomial.
Output:
The quotient of the Euclidean division.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
POLYNOMIAL !«
Example:
Find the quotient of the division of x 3 + 6 x 2 + 11 x + 6 by
Command: QUOT(X^3+6*X^2+11*X+6, X^2+5*X+6)
Result:
X+1
2
x + 5x + 6
See also:
REMAINDER, DIV2, IQUOT
QXA
Type:
Description:
Command
Access:
!Ø
Input:
Level 2/Argument 1: A quadratic form.
Level 1/Argument 2: A vector containing the variables.
Output:
Level 2/Item 1: The quadratic form expressed in matrix form.
Level 1/Item 2: The vector containing the variables.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Express the following quadratic form in matrix form:
.
Expresses a quadratic form in matrix form.
2
x + xy + y
QUADF,
!Ú
MATRX
2
Command: QXA(X^2+X*Y+Y^2, [X,Y])
Result:
{[[1,1/2][1/2,1]],[X,Y]}
See also:
AXQ, GAUSS, SYLVESTER
RCLVX
Type:
Description:
Command
Access:
Catalog, …µ
Input:
None.
Output:
Level 1/Item 1: The name of the current CAS variable.
See also:
STOVX
REF
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A real or complex matrix.
Returns the name or list of names stored in the current CAS variable. This is the same action
as recalling the contents of the variable VX in the CASDIR directory.
Reduces a matrix to echelon form. This is a subdiagonal reduction (Gauss, not Gauss-Jordan).
LINEAR SYSTEMS
4-60 Computer Algebra Commands
Output:
The equivalent matrix in echelon form.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Complex mode must be set (flag –103 set) if the input is complex.
See also:
rref, RREFMOD
REMAINDER
Type:
Function
Description: Returns the remainder of the Euclidean division of two polynomials.
Access:
Arithmetic, !ÞPOLYNOMIAL !«
Input:
Level 2/Argument 1: The numerator polynomial.
Level 1/Argument 2: The denominator polynomial.
Output:
The remainder resulting from the Euclidean division.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Complex mode must be set (flag –103 set) if either input is complex.
3
2
2
Example:
Find the remainder of the division of x + 6x + 11 x + 6 by x + 5x + 6 .
Command: REMAINDER(X^3+6*X^2+11*X+6, X^2+5*X+6)
Result:
0
See also:
QUOT
REORDER
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 2/Argument 1: The polynomial expression.
Level 1/Argument 2: The variable with respect to which the reordering is performed.
Output:
The reordered expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Complex mode must be set (flag –103 set) if the polynomial contains complex terms.
The polynomial terms order flag (flag –114) must be set for increasing power order, or clear
(the default) for decreasing power order.
Example:
Reorder the polynomial x2 + 2y2 +2x +3y in order of powers of y. Assume that increasing
power mode has been set in the CAS modes.
Given a polynomial expression and a variable, reorders the variables in the expression in the
order of powers set on the CAS Modes screen, that is, either in increasing or decreasing order.
Command: REORDER(X^2+2*Y^2+2*X+6+3*Y, Y)
Result:
2*Y^2+3*Y+(X^2+2*X)
RESULTANT
Type:
Function
Description: Returns the resultant of two polynomials of the current variable. That is, it returns the
determinant of the Sylvester matrix of the two polynomials.
Computer Algebra Commands 4-61
Access:
!ÞPOLY !«
Input:
Level 2/Argument 1: The first polynomial.
Level 1/Argument 2: The second polynomial.
Output:
The determinant of the two matrices that correspond to the polynomials.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Complex mode must be set (flag –103 set) if either input contains complex terms.
Example:
Obtain the resultant of the two polynomials
x3-px+q and 3x2-p.
Command: RESULTANT(X^3-P*X+Q, 3*X^2-P)
Result:
27*Q^2-4*P^3
REWRITE
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, POLYNOMIAL, TESTS, TRIGO
RISCH
Type:
Description:
Access:
Input:
Output:
Flags:
Example:
Displays a menu or list of CAS operations that rewrite expressions.
Function
Performs symbolic integration on a function using the Risch algorithm. RISCH is similar to
the INTVX command, except that it allows you to specify the variable of integration.
Calculus !Ö DERIV. & INTEG L.
Level 2/Argument 1: The function to integrate.
Level 1/Argument 2: The variable of integration.
The antiderivative of the function with respect to the variable.
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Find the antiderivative of the following function, with respect to y:
2
y + 3y + 2
Command: RISCH(Y^2-3*Y+2,Y)
Result:
1/3*Y^3-3*(1/2*Y^2)+2*Y
See also:
IBP, INT, INTVX
RREF
Type:
Description:
Command
Access:
Matrices, !Ø
Input:
A matrix.
Reduces a matrix to row-reduced echelon form. The reduction is carried out completely, so a
square matrix is reduced to an identity matrix. Step-by-step mode can be used to show how
the reduction proceeds.
LINEAR SYSTEMS,
4-62 Computer Algebra Commands
!´ MATRX
FACTR
Output:
An equivalent matrix in row reduced echelon form.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Step-by-step mode can be set (flag –100 set).
Example:
Solve the system of linear equations:
3x + 4y = 5
5x + 6y = 7
by reducing the augmented matrix that represents this system.
Command: RREF([[3, 4, 5] [ 5, 6, 7]])
Result:
[[1, 0, -1] [0, 1, 2]]
This reduced matrix represents the system:
1x + 0y = –1
0x + 1y = 2
so that the solution is x = –1, y = 2 .
See also:
rref, RREFMOD
rref
Type:
Description:
Command
Access:
PSOLVE, Matrices, !Ø
Input:
A matrix.
Output:
Level 2/Item 1: The pivot points.
Reduces a matrix to row-reduced echelon form, and provides a list of pivot points.
LINEAR SYSTEMS
Level 1/Item 2: An equivalent matrix in row reduced echelon form.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear)
If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set,
row reduction is done without reducing the last column, but the last column will be modified
by the reduction of the rest of the matrix.
Example:
Reduce to row-reduced echelon form, and find the pivot points, for the matrix:
2 1
3 4
Command: rref([[2,1][3,4]])
Result:
{Pivots: {5,1.,2,1.},[[10,0][0,5]]}
See also:
RREFMOD
RREFMOD
Type:
Description:
Command
Access:
Catalog, …µ
Input:
A matrix.
Output:
The modular row-reduced matrix. The modulo value is set using the Modes CAS input form.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set,
Performs modular row-reduction to echelon form on a matrix, modulo the current modulus.
Computer Algebra Commands 4-63
row reduction is done without reducing the last column, but the last column will be modified
by the reduction of the rest of the matrix.
Example:
Reduce to row-reduced echelon form, modulo 3, the matrix:
2 1
3 4
Command: rref[[2,1][3,4]]
Result:
[[-1,0][0,1]]
See also:
rref
SERIES
Type:
Description:
Command
Access:
Calculus, PCALC, or Limits and series, !Ö
Input:
Level 3/Argument 1: The function f(x)
Level 2/Argument 2: The variable if the limit point is 0, or an equation x = a if the limit point
is a. If the function is in terms of the current variable, this can be given as just the value a.
Level 1/Argument 3: The order for the series expansion. The minimum value is 2, and the
maximum value is 20.
Output:
Level 2/Item 1: A list containing the limit as a value and as the equivalent expression, an
expression approximating the function near the limit point, and the order of the remainder.
These are expressed in terms of a small parameter h.
Level 1/Item 2: An expression for h in terms of the original variable.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
For a given function, computes Taylor series, asymptotic development and limit at finite or
infinite points.
LIMITS & SERIES
Example:
Obtain the second order Taylor series expansion of ln(x) at x=1.
Command: SERIES(LN(X),1,2)
Result:
{{Limit: 0, Equiv: h, Expans: -1/2*h^2+h, Remain: h^3}, h=X- 1}
See also:
TAYLOR0
SEVAL
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 1/Argument 1: An algebraic expression.
Output:
The expression simplified and with existing variables evaluated.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
With π stored in the variable Y, and the variables X and Z not in the current path, simplify the
following expression. Note that the top-level simplification is not carried out.
Sin(3x – y + 2z – (2x – z)) – Sin(x – 2y + (y + 3z))
Simplifies the given expression. Simplifies the expression except at the highest level, and also
evaluates any existing variables that the expression contains and substitutes these back into
the expression.
4-64 Computer Algebra Commands
Command: SEVAL(SIN(3*X-Y+2*Z-(2*X-Z)) - SIN(X-2*Y+(Y+3*Z))
Result:
-SIN(π –(X+3*Z)) -SIN(π –(X+3*Z))
See also:
EXPAND, SIMPLIFY
SIGMA
Type:
Description:
Function
Calculates the discrete antiderivative of a function f with respect to a specified variable. This is
a function G such that:
G(x + 1) – G(x) = f(x)
where x is the specified variable.
Access:
!ÖDERIV L
Input:
Level 2/Argument 1: A function
Level 1/Argument 2: The variable to calculate the antiderivative with respect to.
Output:
The discrete antiderivative of the function.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Obtain the discrete antiderivative with respect to the variable y of the expression:
2x-2y
Command: SIGMA(2*X-2*Y,Y)
Result:
-(Y^2 –(2*X+1)*Y)
See also:
SIGMAVX, RISCH
SIGMAVX
Type:
Description:
Function
Calculates the discrete antiderivative of a function f with respect to the current variable. This
is a function G such that:
G(x + 1) – G(x) = f(x)
where x is the current variable.
Access:
!ÖDERIV LL
Input:
Level 1/Argument 1: A function.
Output:
The discrete antiderivative of the function.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Obtain the discrete antiderivative with respect to the current variable x of the expression:
2x-2y
Command: SIGMAVX(2*X-2*Y)
Result:
X^2 –(2*Y+1)*X
See also:
SIGMA, RISCH
SIGNTAB
Type:
Description:
Command
Access:
PGRAPH, !ÖGRAPH
Tabulates the sign of a rational function of the current CAS variable.
Computer Algebra Commands 4-65
Input:
An algebraic expression.
Output:
A list containing, the points where the expression changes sign, and between each pair of
points, the sign of the expression between those points.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Show the ranges of values of x for which the expression 2-x2 is positive and negative.
Command: SIGNTAB(2 – X^2)
Result:
{ '-∞' – '-√2' + '√2' – '+∞' }
See also:
TABVAR
SIMP2
Type:
Description:
Command
Access:
Arithmetic, !Þ L
Input:
Level 2/Argument 1: The first object.
Level 1/Argument 2: The second object.
Output:
Level 2/Item 1: The first object divided by the greatest common divisor.
Level 1/Item 2: The second object divided by the greatest common divisor.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Divide the following expressions by their greatest common divisor:
Simplifies two objects by dividing them by their greatest common divisor.
3
2
x + 6x + 11 x + 6
3
x – 7x – 6
Command: SIMP2(X^3+6*X^2+11*X+6, X^3-7*X-6)
Result:
{X+3,X-3}
See also:
EGCD
SIMPLIFY
Type:
Description:
Command
Access:
!Ú
Input:
An expression
Output:
An equivalent simplified expression. SIMPLIFY follows an extensive built-in set of rules, but
these might not give exactly the simplification the user expects.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Simplify
Simplifies an expression.
REWRITE L
SIN ( 3 ⋅ X ) + SIN ( 7 ⋅ X )
---------------------------------------------------------SIN ( 5 ⋅ X )
Command: SIMPLIFY((SIN(3*X)+SIN(7*X))/SIN(5*X))
Result:
4*COS(X)^2 - 2
See also:
COLLECT, EXPAND
4-66 Computer Algebra Commands
SINCOS
Type:
Description:
Command
Access:
Trigonometry, …ÑL, PLEXPLN
Input:
An expression with complex linear and exponential terms.
Output:
The expression with logarithmic and exponential subexpressions converted to trigonometric
and inverse trigonometric expressions.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Must be in complex mode (flag –103 set).
Converts complex logarithmic and exponential expressions to expressions with trigonometric
terms.
Example:
Express eix in trigonometric terms.
Command: SINCOS(EXP(i*X))
Result:
COS(X)+iSIN(X)
See also:
EXPLN
SOLVE
Type:
Description:
Command
Access:
Symbolic solve, !Î, P SOLVE, …×L
Input:
Level 2/Argument 1: The expression or equation. A list of equations and expressions can be
given too, each will be solved for the same variable.
Level 1/Argument 2: The variable to solve for.
Output:
A zero or solution, or a list of zeros or solutions.
Flags:
Radians mode must be set (flag –17 set).
If exact mode is set (flag –105 clear) and there are no exact solutions, the command returns a
null list even when there are approximate solutions.
Radians mode must be set (flag –17 set).
If complex mode is set (flag –103 set) then SOLVE will search for complex roots as well as
real ones. Complex roots are displayed according to the coordinate system selected.
Example 1:
Find the zeros of the following expression:
Finds zeros of an expression equated to 0, or solves an equation.
3
x –x–9
Command: SOLVE(X^3-X-9,X)
Result:
X=2.24004098747
Example 2:
Find the real and complex roots of the two equations:
4
2
x – 1=3 ,
x – A= 0
Command: Clear numeric mode, clear approximate mode, set complex mode, set rectangular mode, enter:
SOLVE({X^4-1=3,X^2-A=0},X)
Result:
{{X=√2×i,X=√2×-1,X=-(√2×i),X=√2},
{X=√A×-1,X=√A}} Note that in this case, imaginary solutions for X are returned, even if X is in
REALASSUME.
See also:
DESOLVE, LDEC, LINSOLVE, MSLV, QUAD, SOLVEVX
Computer Algebra Commands 4-67
SOLVEVX
Type:
Description:
Command
Access:
Symbolic solve, !Î, P SOLVE
Input:
An expression or equation in the current variable. A list of equations and expressions can be
given too, each will be solved for the current variable.
Output:
A zero or solution, or a list of zeros or solutions.
Flags:
Radians mode must be set (flag –17 set).
For a symbolic result, clear the CAS modes numeric option (flag -3 clear).
If Exact mode is set (flag –105 clear) and there are no exact solutions, the command returns a
null list even when there are approximate solutions.
If complex mode is set (flag –103 set) then SOLVE will search for complex roots as well as
real ones. Complex roots are displayed according to the coordinate system selected.
Example:
Solve the following expression for 0, where X is the default variable on the calculator:
Finds zeros of an expression with respect to the current variable, or solves an equation with
respect to the current variable. (You use the CAS modes input form to set the current
variable.)
3
x –x–9
Command: SOLVEVX(X^3-X-9)
Result:
X=2.24004098747
Note that if exact mode is set, this example returns a null list as there are no exact solutions to
the equation.
See also:
LINSOLVE, SOLVE
STORE
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 2/Argument 1: A number or an expression that evaluates to a numeric value.
Level 1/Argument 2: The name of the variable in which the number is to be stored. If this
variable does not already exist in the current directory path then it is created.
Output:
Level 1/Item 1: The number to which the first argument is evaluated, and which is stored in
the variable.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Store in variable Z the result of calculating 17*Y. Assume that Y contains the integer number
2.
Stores a number in a global variable. Given an expression as input, STORE evaluates the
expression and stores the numerical value, unlike DEF which stores the expression.
Command: STORE(17*Y, Z)
Result:
34
See also:
DEF, DEFINE, UNASSIGN
STOVX
Type:
Command
4-68 Computer Algebra Commands
Description:
Stores a name or list of names in the current CAS variable. This is the same as storing into the
VX variable in the CASDIR directory. By default, the CAS variable is called X; this command
allows a program to change that name.
Access:
Catalog, …µ
Input:
Level 1/Argument 1: A name or list of names.
Output:
None in RPN mode, NOVAL in Algebraic mode.
See also:
RCLVX
STURM
Type:
Description:
Command
For a polynomial P, STURM returns a list containing Sturm’s sequences of P and their
multiplicities
Access:
Arithmetic, !Þ POLYNOMIAL !«
Input:
A polynomial P
Output:
A list containing the Sturm’s sequences for P, and the multiplicity for each (as a real number).
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the Sturm sequences and their multiplicities for the polynomial:
3
x +1
Command: STURM(X^3+1)
Result:
{[1],-1.,[1],1.,[X^3+1,-(3*X^2),-1],1.}
See also:
STURMAB
STURMAB
Type:
Description:
Command
For a polynomial P and a closed interval [a, b], STURMAB determines the number of zeroes
P has in [a, b]
Access:
Arithmetic, !ÞPOLYNOMIAL !«
Input:
A polynomial P
Output:
A list containing a number that is the same sign as P(a) and the number of zeroes P has in [a,
b].
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
For the polynomial:
3
x +2
in the interval [-2,0] find the sign at the lower bound, and the number of zeroes
Command: STURMAB(X^3+2, -2, 0)
Result:
{-6,1}
See also:
STURM, ZEROS
SUBST
Type:
Function
Computer Algebra Commands 4-69
Description:
Substitutes a value for a variable in an expression. The value can be numeric or an expression.
This is similar to the Where function, denoted by the symbol |, but SUBST substitutes
without evaluating the resulting expression.
Access:
Algebra, …×L, PALG
Input:
Level 2/Argument 1: An expression.
Level 1/Argument 2: The value or expression to be substituted.
Output:
The expression with the substitution made.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Substitute x = z+1 for x in the following expression, and apply the EXPAND command to
simplify the result:
2
x + 3x + 7
Command: SUBST(X^2+3*X+7,X=Z+1)
Result:
EXPAND(ANS(1))
Z^2+5*Z+11
See also:
| (where command)
SUBTMOD
Type:
Description:
Function
Access:
Arithmetic, !Þ
Input:
Level 2/Argument 1: The object or number to be subtracted from.
Level 1/Argument 2: The object or number to subtract.
Output:
The result of the subtraction, modulo the current modulus.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Performs a subtraction, modulo the current modulus.
MODULO L
SYLVESTER
Type:
Command
Description: For a symmetric matrix A, returns D and P where D is a diagonal matrix and
A = PTDP
Access:
!Ø
Input:
A symmetric matrix.
Output:
Level 2/Item 1: the diagonal matrix, D.
Level 1/Item 2: The matrix P.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Rewrite in PTDP form the matrix:
QUADF
12
24
Command: SYLVESTER([1, 2][2, 4])
4-70 Computer Algebra Commands
Result:
{[1, 0], [[1, 2][0, 1]]}
SYST2MAT
Type:
Description:
Command
Access:
!Ú
Input:
Level 2/Argument 1: A vector containing a system of linear equations. An expression with no
equal sign is treated as an equation setting the expression equal to zero.
Level 1/Argument 2: A vector whose elements are the system’s variables. The variables must
not exist in the current path.
Output:
A matrix that represents the system of linear equations.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Converts a system of linear equations in algebraic form to matrix form.
MATRX, Matrices,
!Ø
LINEAR SYSTEMS
Convert this system to a matrix:
X–Y=0
2X + Y = 5
Command: SYST2MAT([X-Y, 2*X+Y=5],[X, Y])
Result:
TABVAL
Type:
Description:
1 –1 0
2 1 –5
Command
For an expression and a list of values, stores the expression in EQ, and returns the results of
substituting the values for the current variable in the expression.
Access:
PGRAPH L, !ÖGRAPHL
Input:
Level 2/Argument 1: An algebraic expression in terms of the current variable.
Level 1/Argument 2: A list of values for which the expression is to be evaluated.
Output:
Level 2/Item 1: The algebraic expression.
Level 1/Item 2: A list containing two lists: a list of the values and a list of the corresponding
results.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Substitute 1, 2, and 3 into x 2 + 1 .
Command: TABVAL(X^2+1,{1, 2, 3})
Result:
{ X^2+1,{{1, 2, 3},{2, 5, 10}}}
TABVAR
Type:
Description:
Command
Access:
PGRAPH L, !ÖGRAPH L
Input:
An expression in terms of the current variable, which has a rational derivative.
Output:
Level 3/Item 1: The original rational function.
Level 2/Item 2: A list of two lists. The first list indicates the variation of the function (where
it is increasing or decreasing) in terms of the independent variable. The second list indicates
For a function of the current variable, with a rational derivative, computes the variation table,
that is the turning points of the function and where the function is increasing or decreasing.
Computer Algebra Commands 4-71
the variation in terms of the dependent variable, the function value.
Level 1/Item 3: A graphic object that shows how the variation table was computed.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Tabulate the variation of the function:
2
x –1
Command: TABVAR(X^2-1)
Result:
{'X^2-1' {{ '-∞' – 0 + '∞' }{ '+∞' ↓ '-1' ↑ '+∞' }} Graphic 96 × 55 }
Viewing the graphic, one sees the original function F and its derivative, as functions of X, and
the variation table for X and F, shown as a matrix
See also:
SIGNTAB
TAN2CS2
Type:
Description:
Command
Access:
Catalog, …µ
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Replace tan(x) terms in the function:
Replaces tan(x) terms in an expression with (1-cos(2x))/sin(2x) terms.
( tan ( x ) )
2
Command: TAN2CS2(TAN(X)^2)
Result:
((1-COS(2*X))/SIN(2*X))^2
See also:
TAN2SC, TAN2SC2
TAN2SC
Type:
Description:
Command
Access:
PTRIG, Trigonometry, …ÑL
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Replace tan(x) terms in the function:
Replaces tan(x) sub-expressions with sin(x)/cos(x).
( tan ( x ) )
2
Command: TAN2SC(TAN(X)^2)
Result:
(SIN(X)/COS(X))^2
See also:
HALFTAN, TAN2CS2, TAN2SC2
4-72 Computer Algebra Commands
TAN2SC2
Type:
Description:
Command
Access:
PTRIG, Trigonometry, …ÑL
Input:
An expression
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
In previous versions of the CAS, if flag –116 was set (Prefer sin()), then TAN2SC2 replaced tan(x)
terms with: 1 – Cos(2x)/Sin(2x). This action is now performed by the TAN2CS2 command.
Example:
Replace tan(x) terms in the function:
Replaces tan(x) terms in an expression with sin(2x)/1+cos(2x) terms.
( tan ( x ) )
2
Command: TAN2SC2(TAN(X)^2)
Result:
(SIN(2*X)/(1+COS(2*X)))^2
See also:
HALFTAN, TAN2CS2, TAN2SC
TAYLOR0
Type:
Description:
Function
Access:
Calculus, !Ö LIMITS & SERIES, PCALC L
Input:
An expression
Output:
The Taylor expansion of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Performs a fourth-order Taylor expansion of an expression at x = 0.
Example:
Obtain the fourth-order Taylor series expansion of cos(x) at x=0.
Command: TAYLOR0(COS(X))
Result:
1/24*X^4+-1/2*X^2+1
See also:
DIVPC, lim, TAYLR, SERIES
TCHEBYCHEFF
Type:
Function
Description: Returns the nth Tchebycheff polynomial.
Access:
Catalog, …µ
Input:
A non-negative integer, n.
Output:
The nth Tchebycheff polynomial.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Obtain the fourth Tchebycheff polynomial.
Command: TCHEBYCHEFF(4)
Result:
8*X^4-8*X^2+1
See also:
HERMITE, LEGENDRE
Computer Algebra Commands 4-73
TCOLLECT
Type:
Description:
Command
Access:
Trigonometry, …ÑL
Input:
An expression with trigonometric terms.
Output:
The simplified expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Collect terms in the expression:
Linearizes products in a trigonometric expression by collecting sine and cosine terms, and by
combining sine and cosine terms of the same argument.
sin 2x + cos 2x
Command: TCOLLECT(SIN(2*X)+COS(2*X))
Result:
√2*COS(2*X-π/4)
See also:
TEXPAND, TLIN
TESTS
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, POLYNOMIAL, REWRITE, TRIGO
Displays a menu or list containing the ASSUME and UNASSUME commands, and tests that
can be included in algebraic expressions.
TEXPAND
Type:
Description:
Command
Access:
!Ð, PALG, PTRIG, …×L, …ÑL, PLEXPLN
Input:
An expression.
Output:
The transformation of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Expand the following expression:
ln(sin(x+y))
Expands transcendental functions.
Command: TEXPAND(LN(SIN(X+Y)))
Result:
LN(COS(Y)*SIN(X)+SIN(Y)* COS(X))
See also:
TCOLLECT, TLIN
TLIN
Type:
Command
4-74 Computer Algebra Commands
Description:
Linearizes and simplifies trigonometric expressions. Note that this function does not collect
sin and cos terms of the same angle.
Access:
PTRIG, Trigonometry, …ÑL
Input:
An expression.
Output:
The transformation of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Linearize and simplify the following:
( cos ( x ) )
4
Command: TLIN(COS(X)^4)
Result:
(1/8)*COS(4X)+(1/2)*COS(2X)+(3/8)
See also:
SIMPLIFY, TCOLLECT, TEXPAND
TRIG
Type:
Description:
Command
Converts complex logarithmic and exponential subexpressions into their equivalent
trigonometric expressions. It also simplifies trigonometric expressions by using:
2
2
( sin x ) + ( cos x ) = 1
Access:
PTRIG, Trigonometry, …ÑLL
Input:
A complex expression with logarithmic and/or exponential terms, or a trigonometric
expression.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Prefers cosine terms if “prefer cos” is selected (flag –116 clear), prefers sine terms if flag –116
is set.
Must be in Complex mode (flag –103 set) if a complex expression is being simplified.
Example:
Express the following in trigonometric terms:
ln ( x + i )
Command: TRIG(LN(X+i))
Result:
2
1
L N ( X + 1 ) + 2 × i × A T AN ⎛⎝ ---⎞⎠
x
-----------------------------------------------------------------------------2
See also:
TRIGCOS, TRIGSIN, TRIGTAN
TRIGCOS
Type:
Description:
Command
Simplifies a trigonometric expression by applying the identity:
2
2
( sin x ) + ( cos x ) = 1
Returns only cosine terms if possible.
Access:
Trigonometry, …ÑLL
Input:
An expression with trigonometric terms.
Computer Algebra Commands 4-75
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
See also:
TRIG, TRIGSIN, TRIGTAN
TRIGO
Type:
Description:
Command
Access:
Catalog, …µ
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
See also:
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, POLYNOMIAL, REWRITE, TESTS
TRIGSIN
Type:
Description:
Displays a menu or list containing the CAS commands for transforming trigonometric
expressions.
Command
Simplifies a trigonometric expression by applying the identity:
2
2
( sin x ) + ( cos x ) = 1
Returns only sine terms if possible.
Access:
Trigonometry, …ÑLL
Input:
An expression with trigonometric terms.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
See also:
TRIG, TRIGCOS, TRIGTAN
TRIGTAN
Type:
Description:
Command
Access:
Trigonometry, …ÑLL
Input:
An expression with trigonometric terms.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Express the following in tan terms:
2
( sinx)
Replaces sine and cosine terms in a trigonometric expression with tangent terms.
Command: TRIGTAN(SIN(X)^2)
Result:
TAN(X)^2/(TAN(X)^2+1)
See also:
TRIG, TRIGCOS, TRIGSIN
4-76 Computer Algebra Commands
TRUNC
Type:
Description:
Function
Access:
Catalog, …µ
Input:
Level 2/Argument 1: The expression that you want to truncate.
Level 1/Argument 2: The expression to truncate with respect to.
Output:
The expression from Level 2/Argument 1, with terms of order greater than or equal to the
order of the expression in Level 1/Argument 2 removed.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Truncates a series expansion.
Example:
Expand the expression (x+1)7, and remove all terms in x4 and higher powers of x
Command: TRUNC((X+1)^7,X^4)
Result:
35*X^3+21*X^2+7*X+1
See also:
DIVPC, EXPAND, SERIES
TSIMP
Type:
Description:
Command
Access:
Exponential and logarithms, !Ð L, or …ÑLL
Input:
An expression
Output:
The simplified expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Performs simplifications on expressions involving exponentials and logarithms. Converts base
10 logarithms to natural logarithms
Example:
Simplify log(x+x)
Command: TSIMP(LOG(X+X))
Result:
(LN(2)+LN(X))/(LN(5)+LN(2))
See also:
TEXPAND, TLIN
UNASSIGN
Type:
Description:
Command
Access:
Catalog, …µ
Input:
Level 1/Item 1: The name of a global variable, or a list of global names, to be purged.
Output:
Level 1/Item 1: The value or list of values that were stored in the now purged variables. If a
variable does not exist, or is not in the current directory path, it is not removed, and its name
is returned.
Flags:
The status of the purge confirm flag (flag –76) is ignored, variables are purged with no request
for confirmation.
Example:
Try to remove the global variable U, which contains 17.5, and the global variable V, which is
not on the current directory path.
Removes global variables and returns their values. This is an algebraic version of the PURGE
command.
Computer Algebra Commands 4-77
Command: UNASSIGN({U, V})
Result:
{17.5, V}
See also:
ADDTOREAL, ASSUME, DEF, LOCAL, PURGE, STO, STORE, UNASSUME,
UNBIND
UNASSUME
Type:
Command
Description: Removes all assumptions on specified global variables, whether created by default, by
ADDTOREAL or by ASSUME. Does this by removing the variable names from the list
REALASSUME. Returns the variable names. To remove assumptions on a variable but leave
it in REALASSUME, use ADDTOREAL instead of UNASSUME.
Access:
Catalog, …µ
Input:
Level 1/Item 1: The name of a global variable, or a list of global names, to be removed from
the REALASSUME list.
Output:
Level 1/Item 1: The same name or list of names as was input, even if any of the named
variables were not in REALASSUME.
Example:
Remove the variables S1 and S2 which are include in the REALASSUME list by default.
Command: UNASSUME({S1, S2})
Result:
{S1, S2}
See also:
ADDTOREAL, ASSUME, DEF, LOCAL, UNASSIGN, UNBIND
UNBIND
Type:
Description:
Command
Access:
Catalog, …µ
Input:
None
Output:
Level 1/Item 1: A list of the local variables that have been removed, with their values.
Removes all local variables created by the LOCAL command, and returns their values. This is
useful only if a program needs to remove local variables created earlier in the same program.
Example:
Remove the local variables ←A and ←B created by the example for LOCAL.
Command: UNBIND
Result:
{←B=2, ←A=0}
See also:
DEF, LOCAL, STORE, UNASSIGN, UNASSUME
VANDERMONDE
Type:
Command
Description: Builds the Vandermonde matrix (also called the alternant matrix) from a list of objects. That
is, for a list of n objects, the command creates an n × n matrix. The ith column in the matrix
consists of the list items raised to the power of (i–1). Sometimes the Vandermonde matrix is
defined with the ith row containing the items raised to the power of (i–1); to obtain this,
transpose the result with the command TRAN.
Access:
Matrices, !Ø
Input:
A list of objects. A vector is allowed too.
Output:
The corresponding Vandermonde matrix.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
CREATELL,
4-78 Computer Algebra Commands
!´ MATRX MAKE LL
Example:
Build the row version of the Vandermonde matrix from the following list of objects:
{x, y, z}
Command: TRAN(VANDERMONDE({x,y,z}))
1 1 1
x y z
2
Result:
2
x y z
2
See also:
CON, HILBERT, IDN, RANM
VER
Type:
Description:
Command
Access:
Catalog, …µ
Input:
No input required.
Output:
A real number giving the version and release date of the Computer Algebra System software.
Flags:
The version and release date are given as a number of the form V.YYYYMMDD, so a display
mode showing at least 8 digits after the fraction mark is needed to display the result in full.
Returns the Computer Algebra System version number, and date of release.
VPOTENTIAL
Type:
Command
Description: Find a vector potential function describing a field whose curl (or “rot”) is the input. This
command is the opposite of CURL. Given a vector V it attempts to return a function U such
that curl U is equal to V; ∇ × U = V . For this to be possible, DIV(V) must be zero,
otherwise the command reports a “Bad Argument Value” error. Step-by-step mode is
available with this command.
Access:
Catalog, …µ
Input:
Level 2/Argument 1: A vector V of expressions.
Level 1/Argument 2: A vector of the names of the variables.
Output:
Level 1/Item 1: A vector U of the variables that is the potential from which V is obtained. An
arbitrary constant can be added, the command does not do this.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Step-by-step mode can be set (flag –100 set).
Example:
To see if this command is the opposite of CURL, use the output of the example in CURL as
input to VPOTENTIAL. Find a vector in the spatial variables x, y, and z whose curl is:
(2yz)i + (0)j + (2xy – x2)k
Command: VPOTENTIAL([2*Y*Z, 0, 2*X*Y-X^2], [X,Y,Z])
Result:
EXPAND(ANS(1))
[0, -((X^3-3*Y*X^2)/3), Z*Y^2]
This shows that the reversal is not unique – more than one vector can have the same curl.
However, obtaining the curl of the above result, and then applying VPOTENTIAL to it again
will give the same result.
See al