Texas Instruments TI-Nspire CAS Reference Manual

TI-Nspire™ CAS
Reference Guide
This guidebook applies to TI-Nspire™ software version 4.3. To obtain the latest version
of the documentation, go to education.ti.com/guides.
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© 2006 - 2016 Texas Instruments Incorporated
2
Contents
Important Information
2
Expression Templates
5
Alphabetical Listing
12
A
B
C
D
E
F
G
I
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z
12
21
24
49
60
70
79
86
93
109
117
126
128
137
140
153
178
193
194
195
197
198
Symbols
206
Empty (Void) Elements
232
Shortcuts for Entering Math Expressions
234
EOS™ (Equation Operating System) Hierarchy
236
Error Codes and Messages
238
Warning Codes and Messages
246
Support and Service
249
Texas Instruments Support and Service
249
3
Service and Warranty Information
Index
4
249
251
Expression Templates
Expression templates give you an easy way to enter math expressions in standard
mathematical notation. When you insert a template, it appears on the entry line with
small blocks at positions where you can enter elements. A cursor shows which element
you can enter.
Position the cursor on each element, and type a value or expression for the element.
/p keys
Fraction template
Example:
Note: See also / (divide) , page 208.
l key
Exponent template
Example:
Note: Type the first value, press l, and
then type the exponent. To return the cursor
to the baseline, press right arrow ( ¢).
Note: See also ^ (power) , page 209.
/q keys
Square root template
Example:
Note: See also √() (square root) , page
219.
/l keys
Nth root template
Example:
Note: See also root() , page 150.
Expression Templates
5
/l keys
Nth root template
u keys
e exponent template
Example:
Natural exponential e raised to a power
Note: See also e^() , page 60.
/s key
Log template
Example:
Calculates log to a specified base. For a
default of base 10, omit the base.
Note: See also log() , page 105.
Piecewise template (2-piece)
Catalog >
Example:
Lets you create expressions and conditions
for a two-piece piecewise function. To add
a piece, click in the template and repeat the
template.
Note: See also piecewise() , page 130.
6
Expression Templates
Piecewise template (N-piece)
Lets you create expressions and conditions
for an N-piece piecewise function. Prompts
for N.
Catalog >
Example:
See the example for Piecewise template (2piece).
Note: See also piecewise() , page 130.
System of 2 equations template
Catalog >
Example:
Creates a system of two equations. To add
a row to an existing system, click in the
template and repeat the template.
Note: See also system() , page 177.
System of N equations template
Lets you create a system of N equations.
Prompts for N.
Catalog >
Example:
See the example for System of equations
template (2-equation).
Note: See also system() , page 177.
Absolute value template
Note: See also abs() , page 12.
Catalog >
Example:
Expression Templates
7
Absolute value template
Catalog >
dd° mm’ss.ss’’ template
Catalog >
Example:
Lets you enter angles in dd°mm’ss.ss ’’
format, where dd is the number of decimal
degrees, mm is the number of minutes, and
ss.ss is the number of seconds.
Matrix template (2 x 2)
Catalog >
Example:
Creates a 2 x 2 matrix.
Matrix template (1 x 2)
.
Catalog >
Example:
Matrix template (2 x 1)
Catalog >
Example:
Matrix template (m x n)
The template appears after you are
prompted to specify the number of rows
and columns.
8
Expression Templates
Catalog >
Example:
Matrix template (m x n)
Catalog >
Note: If you create a matrix with a large
number of rows and columns, it may take a
few moments to appear.
Sum template (Σ)
Catalog >
Example:
Note: See also Σ() ( sumSeq), page 220.
Product template (Π)
Catalog >
Example:
Note: See also Π() ( prodSeq), page 219.
First derivative template
Catalog >
Example:
The first derivative template can also be
used to calculate first derivative at a point.
Note: See also d() (derivative) , page 217.
Expression Templates
9
Second derivative template
Catalog >
Example:
The second derivative template can also be
used to calculate second derivative at a
point.
Note: See also d() (derivative) , page 217.
Nth derivative template
Catalog >
Example:
The nth derivative template can be used to
calculate the nth derivative.
Note: See also d() (derivative) , page 217.
Definite integral template
Catalog >
Example:
Note: See also∫() integral() , page 217.
Indefinite integral template
Catalog >
Example:
Note: See also ∫() integral() , page 217.
Limit template
Catalog >
Example:
10
Expression Templates
Limit template
Use − or ( −) for left hand limit. Use + for
Catalog >
right hand limit.
Note: See also limit() , page 10.
Expression Templates
11
Alphabetical Listing
Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this
section, page 206. Unless otherwise specified, all examples in this section were
performed in the default reset mode, and all variables are assumed to be undefined.
A
abs()
abs(Expr1) ⇒ expression
Catalog >
abs(List1) ⇒ list
abs(Matrix1) ⇒ matrix
Returns the absolute value of the
argument.
Note: See also Absolute value template,
page 7.
If the argument is a complex number,
returns the number’s modulus.
Note: All undefined variables are treated as
real variables.
amortTbl()
amortTbl(NPmt ,N,I,PV, [Pmt ], [FV],
[PpY], [CpY], [PmtAt ], [roundValue ]) ⇒
matrix
Amortization function that returns a matrix
as an amortization table for a set of TVM
arguments.
NPmt is the number of payments to be
included in the table. The table starts with
the first payment.
N, I, PV, Pmt , FV, PpY, CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
•
•
•
12
If you omit Pmt , it defaults to
Pmt =tvmPmt
( N,I,PV,FV,PpY,CpY,PmtAt ).
If you omit FV, it defaults to FV=0.
The defaults for PpY, CpY, and PmtAt
are the same as for the TVM functions.
Alphabetical Listing
Catalog >
Catalog >
amortTbl()
roundValue specifies the number of
decimal places for rounding. Default=2.
The columns in the result matrix are in this
order: Payment number, amount paid to
interest, amount paid to principal, and
balance.
The balance displayed in row n is the
balance after payment n.
You can use the output matrix as input for
the other amortization functions ΣInt() and
ΣPrn() , page 221, and bal() , page 21.
Catalog >
and
BooleanExpr1 and BooleanExpr2 ⇒
Boolean expression
BooleanList1 and BooleanList2 ⇒
Boolean list
BooleanMatrix1 and BooleanMatrix2 ⇒
Boolean matrix
Returns true or false or a simplified form of
the original entry.
Integer1 andInteger2 ⇒ integer
Compares two real integers bit-by-bit using
an and operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if both bits are 1;
otherwise, the result is 0. The returned
value represents the bit results, and is
displayed according to the Base mode.
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base 10).
In Hex base mode:
Important: Zero, not the letter O.
In Bin base mode:
In Dec base mode:
Note: A binary entry can have up to 64 digits
(not counting the 0b prefix). A hexadecimal
entry can have up to 16 digits.
Alphabetical Listing
13
angle()
angle(Expr1) ⇒ expression
Catalog >
In Degree angle mode:
Returns the angle of the argument,
interpreting the argument as a complex
number.
Note: All undefined variables are treated as
In Gradian angle mode:
real variables.
In Radian angle mode:
angle(List1) ⇒ list
angle(Matrix1) ⇒ matrix
Returns a list or matrix of angles of the
elements in List1 or Matrix1, interpreting
each element as a complex number that
represents a two-dimensional rectangular
coordinate point.
ANOVA
ANOVA List1,List2[,List3,...,List20][,Flag]
Catalog >
Performs a one-way analysis of variance for
comparing the means of two to 20
populations. A summary of results is stored
in the stat.results variable. (page 172)
Flag=0 for Data, Flag=1 for Stats
Output variable
Description
stat. F
Value of the F statistic
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom of the groups
stat.SS
Sum of squares of the groups
stat.MS
Mean squares for the groups
14
Alphabetical Listing
Output variable
Description
stat.dfError
Degrees of freedom of the errors
stat.SSError
Sum of squares of the errors
stat.MSError
Mean square for the errors
stat.sp
Pooled standard deviation
stat.xbarlist
Mean of the input of the lists
stat.CLowerList
95% confidence intervals for the mean of each input list
stat.CUpperList
95% confidence intervals for the mean of each input list
Catalog >
ANOVA2way
ANOVA2way List1,List2[,List3,…,List10]
[,levRow]
Computes a two-way analysis of variance for
comparing the means of two to 10
populations. A summary of results is stored
in the stat.results variable. (See page 172.)
LevRow=0 for Block
LevRow=2,3,...,Len-1, for Two Factor,
where Len=length( List1)=length( List2) = …
= length( List10) and Len / LevRow Î
{2,3,…}
Outputs: Block Design
Output variable
Description
stat. F
F statistic of the column factor
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom of the column factor
stat.SS
Sum of squares of the column factor
stat.MS
Mean squares for column factor
stat. FBlock
F statistic for factor
stat.PValBlock
Least probability at which the null hypothesis can be rejected
stat.dfBlock
Degrees of freedom for factor
stat.SSBlock
Sum of squares for factor
Alphabetical Listing
15
Output variable
Description
stat.MSBlock
Mean squares for factor
stat.dfError
Degrees of freedom of the errors
stat.SSError
Sum of squares of the errors
stat.MSError
Mean squares for the errors
stat.s
Standard deviation of the error
COLUMN FACTOR Outputs
Output variable
Description
stat. Fcol
F statistic of the column factor
stat.PValCol
Probability value of the column factor
stat.dfCol
Degrees of freedom of the column factor
stat.SSCol
Sum of squares of the column factor
stat.MSCol
Mean squares for column factor
ROW FACTOR Outputs
Output variable
Description
stat. FRow
F statistic of the row factor
stat.PValRow
Probability value of the row factor
stat.dfRow
Degrees of freedom of the row factor
stat.SSRow
Sum of squares of the row factor
stat.MSRow
Mean squares for row factor
INTERACTION Outputs
Output variable
Description
stat. FInteract
F statistic of the interaction
stat.PValInteract
Probability value of the interaction
stat.dfInteract
Degrees of freedom of the interaction
stat.SSInteract
Sum of squares of the interaction
stat.MSInteract
Mean squares for interaction
ERROR Outputs
16
Alphabetical Listing
Output variable
Description
stat.dfError
Degrees of freedom of the errors
stat.SSError
Sum of squares of the errors
stat.MSError
Mean squares for the errors
s
Standard deviation of the error
Ans
/v keys
Ans ⇒ value
Returns the result of the most recently
evaluated expression.
approx()
approx(Expr1) ⇒ expression
Catalog >
Returns the evaluation of the argument as
an expression containing decimal values,
when possible, regardless of the current
Auto or Approximate mode.
This is equivalent to entering the argument
and pressing /·.
approx(List1) ⇒ list
approx(Matrix1) ⇒ matrix
Returns a list or matrix where each
element has been evaluated to a decimal
value, when possible.
►approxFraction()
Catalog >
Expr►approxFraction([Tol]) ⇒
expression
List►approxFraction([Tol ]) ⇒ list
Matrix►approxFraction([Tol ]) ⇒ matrix
Returns the input as a fraction, using a
tolerance of Tol . If Tol is omitted, a
tolerance of 5.E-14 is used.
Alphabetical Listing
17
►approxFraction()
Catalog >
Note: You can insert this function from the
computer keyboard by typing
@>approxFraction(...).
approxRational()
approxRational(Expr[, Tol ]) ⇒ expression
Catalog >
approxRational(List [, Tol ]) ⇒ list
approxRational(Matrix [, Tol ]) ⇒ matrix
Returns the argument as a fraction using a
tolerance of Tol . If Tol is omitted, a
tolerance of 5.E-14 is used.
arccos()
See cos⁻¹(), page 35.
arccosh()
See cosh⁻¹(), page 36.
arccot()
See cot ⁻¹(), page 37.
arccoth()
See coth⁻¹(), page 38.
arccsc()
See csc ⁻¹(), page 41.
arccsch()
See csch⁻¹(), page 41.
18
Alphabetical Listing
arcLen()
arcLen(Expr1,Var,Start ,End) ⇒
expression
Catalog >
Returns the arc length of Expr1 from
Start to End with respect to variable Var.
Arc length is calculated as an integral
assuming a function mode definition.
arcLen(List1,Var,Start ,End) ⇒ list
Returns a list of the arc lengths of each
element of List1 from Start to End with
respect to Var.
arcsec()
See sec ⁻¹(), page 154.
arcsech()
See sech⁻¹(), page 154.
arcsin()
See sin⁻¹(), page 164.
arcsinh()
See sinh⁻¹(), page 165.
arctan()
See tan⁻¹(), page 179.
arctanh()
See tanh⁻¹(), page 180.
augment()
augment(List1, List2) ⇒ list
Catalog >
Alphabetical Listing
19
augment()
Catalog >
Returns a new list that is List2 appended to
the end of List1.
augment(Matrix1, Matrix2) ⇒ matrix
Returns a new matrix that is Matrix2
appended to Matrix1. When the “,”
character is used, the matrices must have
equal row dimensions, and Matrix2 is
appended to Matrix1 as new columns.
Does not alter Matrix1 or Matrix2.
avgRC()
avgRC(Expr1, Var [=Value ] [, Step]) ⇒
expression
avgRC(Expr1, Var [=Value ] [, List1]) ⇒
list
avgRC(List1, Var [=Value ] [, Step]) ⇒
list
avgRC(Matrix1, Var [=Value ] [, Step]) ⇒
matrix
Returns the forward-difference quotient
(average rate of change).
Expr1 can be a user-defined function name
(see Func).
When Value is specified, it overrides any
prior variable assignment or any current “|”
substitution for the variable.
Step is the step value. If Step is omitted, it
defaults to 0.001.
Note that the similar function centralDiff()
uses the central-difference quotient.
20
Alphabetical Listing
Catalog >
B
bal()
bal(NPmt ,N,I,PV ,[Pmt ], [FV], [PpY],
[CpY], [PmtAt ], [roundValue ]) ⇒ value
Catalog >
bal(NPmt ,amortTable ) ⇒ value
Amortization function that calculates
schedule balance after a specified payment.
N, I, PV, Pmt , FV, PpY, CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
NPmt specifies the payment number after
which you want the data calculated.
N, I, PV, Pmt , FV, PpY, CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
•
•
•
If you omit Pmt , it defaults to
Pmt =tvmPmt
( N,I,PV,FV,PpY,CpY,PmtAt ).
If you omit FV, it defaults to FV=0.
The defaults for PpY, CpY, and PmtAt
are the same as for the TVM functions.
roundValue specifies the number of
decimal places for rounding. Default=2.
bal( NPmt ,amortTable ) calculates the
balance after payment number NPmt ,
based on amortization table amortTable .
The amortTable argument must be a
matrix in the form described under
amortTbl() , page 12.
Note: See also ΣInt() and ΣPrn() , page 221.
►Base2
Catalog >
Integer1 ►Base2 ⇒ integer
Note: You can insert this operator from the
computer keyboard by typing @>Base2.
Alphabetical Listing
21
►Base2
Catalog >
Converts Integer1 to a binary number.
Binary or hexadecimal numbers always
have a 0b or 0h prefix, respectively. Use a
zero, not the letter O, followed by b or h.
0b binaryNumber
0h hexadecimalNumber
A binary number can have up to 64 digits. A
hexadecimal number can have up to 16.
Without a prefix, Integer1 is treated as
decimal (base 10). The result is displayed in
binary, regardless of the Base mode.
Negative numbers are displayed in “two's
complement” form. For example,
⁻1 is displayed as
0hFFFFFFFFFFFFFFFF in Hex base mode
0b111...111 (64 1’s) in Binary base mode
⁻263 is displayed as
0h8000000000000000 in Hex base mode
0b100...000 (63 zeros) in Binary base mode
If you enter a decimal integer that is
outside the range of a signed, 64-bit binary
form, a symmetric modulo operation is
used to bring the value into the appropriate
range. Consider the following examples of
values outside the range.
263 becomes ⁻263 and is displayed as
0h8000000000000000 in Hex base mode
0b100...000 (63 zeros) in Binary base mode
264 becomes 0 and is displayed as
0h0 in Hex base mode
0b0 in Binary base mode
⁻263 − 1 becomes 263 − 1 and is displayed
as
0h7FFFFFFFFFFFFFFF in Hex base mode
0b111...111 (64 1’s) in Binary base mode
►Base10
Integer1 ►Base10 ⇒ integer
22
Alphabetical Listing
Catalog >
►Base10
Catalog >
Note: You can insert this operator from the
computer keyboard by typing @>Base10.
Converts Integer1 to a decimal (base 10)
number. A binary or hexadecimal entry
must always have a 0b or 0h prefix,
respectively.
0b binaryNumber
0h hexadecimalNumber
Zero, not the letter O, followed by b or h.
A binary number can have up to 64 digits. A
hexadecimal number can have up to 16.
Without a prefix, Integer1 is treated as
decimal. The result is displayed in decimal,
regardless of the Base mode.
►Base16
Catalog >
Integer1 ►Base16 ⇒ integer
Note: You can insert this operator from the
computer keyboard by typing @>Base16.
Converts Integer1 to a hexadecimal
number. Binary or hexadecimal numbers
always have a 0b or 0h prefix, respectively.
0b binaryNumber
0h hexadecimalNumber
Zero, not the letter O, followed by b or h.
A binary number can have up to 64 digits. A
hexadecimal number can have up to 16.
Without a prefix, Integer1 is treated as
decimal (base 10). The result is displayed in
hexadecimal, regardless of the Base mode.
If you enter a decimal integer that is too
large for a signed, 64-bit binary form, a
symmetric modulo operation is used to
bring the value into the appropriate range.
For more information, see ►Base2, page
21.
Alphabetical Listing
23
binomCdf()
binomCdf(n,p) ⇒ list
Catalog >
binomCdf(n,p,lowBound,upBound) ⇒
number if lowBound and upBound are
numbers, list if lowBound and upBound are
lists
binomCdf(n,p,upBound)for P(0≤X≤upBound)
⇒ number if upBound is a number, list if
upBound is a list
Computes a cumulative probability for the
discrete binomial distribution with n number
of trials and probability p of success on each
trial.
For P(X ≤ upBound), set lowBound=0
binomPdf()
binomPdf(n,p) ⇒ list
Catalog >
binomPdf(n,p,XVal ) ⇒ number if XVal is a
number, list if XVal is a list
Computes a probability for the discrete
binomial distribution with n number of trials
and probability p of success on each trial.
C
Catalog >
ceiling(Expr1) ⇒ integer
Returns the nearest integer that is ≥ the
argument.
The argument can be a real or a complex
number.
Note: See also floor() .
ceiling(List1) ⇒ list
ceiling(Matrix1) ⇒ matrix
Returns a list or matrix of the ceiling of
each element.
24
Alphabetical Listing
centralDiff()
centralDiff(Expr1,Var [=Value ][,Step]) ⇒
expression
Catalog >
centralDiff(Expr1,Var [,Step])|Var=Value
⇒ expression
centralDiff(Expr1,Var [=Value ][,List ]) ⇒
list
centralDiff(List1,Var [=Value ][,Step]) ⇒
list
centralDiff(Matrix1,Var [=Value ][,Step])
⇒ matrix
Returns the numerical derivative using the
central difference quotient formula.
When Value is specified, it overrides any
prior variable assignment or any current “|”
substitution for the variable.
Step is the step value. If Step is omitted, it
defaults to 0.001.
When using List1 or Matrix1, the operation
gets mapped across the values in the list or
across the matrix elements.
Note: See also avgRC() and d() .
cFactor()
cFactor(Expr1[,Var]) ⇒ expression
cFactor(List1[,Var]) ⇒ list
cFactor(Matrix1[,Var]) ⇒ matrix
Catalog >
cFactor( Expr1) returns Expr1 factored with
respect to all of its variables over a
common denominator.
Expr1 is factored as much as possible
toward linear rational factors even if this
introduces new non-real numbers. This
alternative is appropriate if you want
factorization with respect to more than one
variable.
Alphabetical Listing
25
cFactor()
cFactor( Expr1,Var) returns Expr1 factored
with respect to variable Var.
Catalog >
Expr1 is factored as much as possible
toward factors that are linear in Var, with
perhaps non-real constants, even if it
introduces irrational constants or
subexpressions that are irrational in other
variables.
The factors and their terms are sorted with
Var as the main variable. Similar powers of
Var are collected in each factor. Include
Var if factorization is needed with respect
to only that variable and you are willing to
accept irrational expressions in any other
variables to increase factorization with
respect to Var. There might be some
incidental factoring with respect to other
variables.
For the Auto setting of the Auto or
Approximate mode, including Var also
permits approximation with floating-point
coefficients where irrational coefficients
cannot be explicitly expressed concisely in
terms of the built-in functions. Even when
there is only one variable, including Var
might yield more complete factorization.
Note: See also factor() .
char()
char(Integer) ⇒ character
Returns a character string containing the
character numbered Integer from the
handheld character set. The valid range for
Integer is 0–65535.
26
Alphabetical Listing
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Catalog >
charPoly()
charPoly(squareMatrix,Var) ⇒
polynomial expression
Catalog >
charPoly(squareMatrix,Expr) ⇒
polynomial expression
charPoly(squareMatrix1,Matrix2) ⇒
polynomial expression
Returns the characteristic polynomial of
squareMatrix . The characteristic
polynomial of n×n matrix A, denoted by pA
( λ), is the polynomial defined by
pA(λ) = det(λ•I−A)
where I denotes the n×n identity matrix.
squareMatrix1 and squareMatrix2 must
have the equal dimensions.
χ22way
χ 22way
Catalog >
obsMatrix
chi22way obsMatrix
Computes a χ 2 test for association on the
two-way table of counts in the observed
matrix obsMatrix . A summary of results is
stored in the stat.results variable. (page
172)
For information on the effect of empty
elements in a matrix, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat. χ2
Chi square stat: sum (observed - expected)2/expected
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom for the chi square statistics
stat.ExpMat
Matrix of expected elemental count table, assuming null hypothesis
stat.CompMat
Matrix of elemental chi square statistic contributions
Alphabetical Listing
27
χ2Cdf()
Catalog >
⇒ number if
lowBound and upBound are numbers, list if
lowBound and upBound are lists
χ 2Cdf(lowBound,upBound,df )
chi2Cdf(lowBound,upBound,df ) ⇒ number
if lowBound and upBound are numbers, list
if lowBound and upBound are lists
Computes the χ 2 distribution probability
between lowBound and upBound for the
specified degrees of freedom df .
For P( X ≤ upBound), set lowBound = 0.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
χ2GOF
Catalog >
χ 2GOF obsList ,expList ,df
chi2GOF obsList ,expList ,df
Performs a test to confirm that sample data
is from a population that conforms to a
specified distribution. obsList is a list of
counts and must contain integers. A
summary of results is stored in the
stat.results variable. (See page 172.)
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat. χ2
Chi square stat: sum((observed - expected)2/expected
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom for the chi square statistics
stat.CompList
Elemental chi square statistic contributions
χ2Pdf()
χ 2Pdf(XVal ,df )
28
Catalog >
⇒ number if XVal is a
Alphabetical Listing
χ2Pdf()
Catalog >
number, list if XVal is a list
chi2Pdf(XVal ,df ) ⇒ number if XVal is a
number, list if XVal is a list
Computes the probability density function
(pdf) for the χ 2 distribution at a specified
XVal value for the specified degrees of
freedom df .
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
ClearAZ
Catalog >
ClearAZ
Clears all single-character variables in the
current problem space.
If one or more of the variables are locked,
this command displays an error message
and deletes only the unlocked variables. See
unLock, page 193.
ClrErr
ClrErr
Clears the error status and sets system
variable errCode to zero.
Catalog >
For an example of ClrErr , See Example 2
under the Try command, page 187.
The Else clause of the Try...Else...EndTry
block should use ClrErr or PassErr. If the
error is to be processed or ignored, use
ClrErr. If what to do with the error is not
known, use PassErr to send it to the next
error handler. If there are no more pending
Try...Else...EndTry error handlers, the error
dialog box will be displayed as normal.
Note: See also PassErr, page 129, and Try,
page 187.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product guidebook.
Alphabetical Listing
29
colAugment()
colAugment(Matrix1, Matrix2) ⇒ matrix
Catalog >
Returns a new matrix that is Matrix2
appended to Matrix1. The matrices must
have equal column dimensions, and
Matrix2 is appended to Matrix1 as new
rows. Does not alter Matrix1 or Matrix2.
colDim()
colDim(Matrix ) ⇒ expression
Catalog >
Returns the number of columns contained
in Matrix .
Note: See also rowDim() .
colNorm()
colNorm(Matrix ) ⇒ expression
Catalog >
Returns the maximum of the sums of the
absolute values of the elements in the
columns in Matrix .
Note: Undefined matrix elements are not
allowed. See also rowNorm() .
comDenom()
comDenom(Expr1[,Var]) ⇒ expression
comDenom(List1[,Var]) ⇒ list
comDenom(Matrix1[,Var]) ⇒ matrix
comDenom( Expr1) returns a reduced ratio
of a fully expanded numerator over a fully
expanded denominator.
30
Alphabetical Listing
Catalog >
comDenom()
comDenom( Expr1,Var) returns a reduced
Catalog >
ratio of numerator and denominator
expanded with respect to Var. The terms
and their factors are sorted with Var as the
main variable. Similar powers of Var are
collected. There might be some incidental
factoring of the collected coefficients.
Compared to omitting Var, this often saves
time, memory, and screen space, while
making the expression more
comprehensible. It also makes subsequent
operations on the result faster and less
likely to exhaust memory.
If Var does not occur in Expr1, comDenom
( Expr1,Var) returns a reduced ratio of an
unexpanded numerator over an unexpanded
denominator. Such results usually save even
more time, memory, and screen space.
Such partially factored results also make
subsequent operations on the result much
faster and much less likely to exhaust
memory.
Even when there is no denominator, the
comden function is often a fast way to
achieve partial factorization if factor() is
too slow or if it exhausts memory.
Hint: Enter this comden() function definition
and routinely try it as an alternative to
comDenom() and factor() .
completeSquare ()
completeSquare(ExprOrEqn, Var) ⇒
expression or equation
Catalog >
completeSquare(ExprOrEqn, Var^Power)
⇒ expression or equation
completeSquare(ExprOrEqn, Var1, Var2
[,...]) ⇒ expression or equation
completeSquare(ExprOrEqn, {Var1, Var2
[,...]}) ⇒ expression or equation
Converts a quadratic polynomial expression
of the form a•x2+b•x+c into the form a•(xh) 2+k
Alphabetical Listing
31
completeSquare ()
Catalog >
- or Converts a quadratic equation of the form
a•x2+b•x+c=d into the form a•(x-h) 2=k
The first argument must be a quadratic
expression or equation in standard form
with respect to the second argument.
The Second argument must be a single
univariate term or a single univariate term
raised to a rational power, for example
x, y2, or z(1/3).
The third and fourth syntax attempt to
complete the square with respect to
variables Var1, Var2 [,… ]).
conj()
conj(Expr1) ⇒ expression
Catalog >
conj(List1) ⇒ list
conj(Matrix1) ⇒ matrix
Returns the complex conjugate of the
argument.
Note: All undefined variables are treated as
real variables.
constructMat()
constructMat
(Expr,Var1,Var2,numRows,numCols) ⇒
matrix
Returns a matrix based on the arguments.
Expr is an expression in variables Var1 and
Var2. Elements in the resulting matrix are
formed by evaluating Expr for each
incremented value of Var1 and Var2.
Var1 is automatically incremented from 1
through numRows. Within each row, Var2
is incremented from 1 through numCols.
32
Alphabetical Listing
Catalog >
CopyVar
CopyVar Var1, Var2
Catalog >
CopyVar Var1., Var2.
CopyVar Var1, Var2 copies the value of
variable Var1 to variable Var2, creating
Var2 if necessary. Variable Var1 must have
a value.
If Var1 is the name of an existing userdefined function, copies the definition of
that function to function Var2. Function
Var1 must be defined.
Var1 must meet the variable-naming
requirements or must be an indirection
expression that simplifies to a variable
name meeting the requirements.
CopyVar Var1., Var2. copies all members
of the Var1. variable group to the Var2.
group, creating Var2. if necessary.
Var1. must be the name of an existing
variable group, such as the statistics stat .nn
results, or variables created using the
LibShortcut() function. If Var2. already
exists, this command replaces all members
that are common to both groups and adds
the members that do not already exist. If
one or more members of Var2. are locked,
all members of Var2. are left unchanged.
corrMat()
corrMat(List1,List2[,…[,List20]])
Catalog >
Computes the correlation matrix for the
augmented matrix [List1, List2, ..., List20].
►cos
Catalog >
Expr ►cos
Note: You can insert this operator from the
computer keyboard by typing @>cos.
Represents Expr in terms of cosine. This is
a display conversion operator. It can be
used only at the end of the entry line.
Alphabetical Listing
33
Catalog >
►cos
►cos reduces all powers of
sin(...) modulo 1−cos(...)^2
so that any remaining powers of cos(...)
have exponents in the range (0, 2). Thus,
the result will be free of sin(...) if and only
if sin(...) occurs in the given expression only
to even powers.
Note: This conversion operator is not
supported in Degree or Gradian Angle
modes. Before using it, make sure that the
Angle mode is set to Radians and that Expr
does not contain explicit references to
degree or gradian angles.
cos()
cos(Expr1) ⇒ expression
µ key
In Degree angle mode:
cos(List1) ⇒ list
cos( Expr1) returns the cosine of the
argument as an expression.
cos( List1) returns a list of the cosines of all
elements in List1.
Note: The argument is interpreted as a
degree, gradian or radian angle, according
to the current angle mode setting. You can
use °, G, or r to override the angle mode
temporarily.
In Gradian angle mode:
In Radian angle mode:
cos(squareMatrix1) ⇒ squareMatrix
Returns the matrix cosine of
squareMatrix1. This is not the same as
calculating the cosine of each element.
34
Alphabetical Listing
In Radian angle mode:
µ key
cos()
When a scalar function f(A) operates on
squareMatrix1 (A), the result is calculated
by the algorithm:
Compute the eigenvalues ( λi) and
eigenvectors (Vi) of A.
squareMatrix1 must be diagonalizable.
Also, it cannot have symbolic variables that
have not been assigned a value.
Form the matrices:
Then A = X B X⁻¹ and f(A) = X f(B) X⁻¹. For
example, cos(A) = X cos(B) X⁻¹ where:
cos(B) =
All computations are performed using
floating-point arithmetic.
cos⁻¹()
cos⁻¹(Expr1) ⇒ expression
µ key
In Degree angle mode:
cos⁻¹(List1) ⇒ list
cos ⁻¹( Expr1) returns the angle whose
cosine is Expr1 as an expression.
In Gradian angle mode:
cos ⁻¹( List1) returns a list of the inverse
cosines of each element of List1.
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arccos(...).
Alphabetical Listing
35
cos⁻¹()
cos⁻¹(squareMatrix1) ⇒ squareMatrix
Returns the matrix inverse cosine of
squareMatrix1. This is not the same as
calculating the inverse cosine of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
µ key
In Radian angle mode and Rectangular
Complex Format:
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
cosh()
cosh(Expr1) ⇒ expression
Catalog >
In Degree angle mode:
cosh(List1) ⇒ list
cosh( Expr1) returns the hyperbolic cosine
of the argument as an expression.
cosh( List1) returns a list of the hyperbolic
cosines of each element of List1.
cosh(squareMatrix1) ⇒ squareMatrix
In Radian angle mode:
Returns the matrix hyperbolic cosine of
squareMatrix1. This is not the same as
calculating the hyperbolic cosine of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
cosh⁻¹()
cosh⁻¹(Expr1) ⇒ expression
cosh⁻¹(List1) ⇒ list
cosh⁻¹( Expr1) returns the inverse
hyperbolic cosine of the argument as an
expression.
36
Alphabetical Listing
Catalog >
cosh⁻¹()
cosh⁻¹( List1) returns a list of the inverse
Catalog >
hyperbolic cosines of each element of
List1.
Note: You can insert this function from the
keyboard by typing arccosh(...).
cosh⁻¹(squareMatrix1) ⇒ squareMatrix
Returns the matrix inverse hyperbolic
cosine of squareMatrix1. This is not the
same as calculating the inverse hyperbolic
cosine of each element. For information
about the calculation method, refer to cos
() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
cot()
cot(Expr1) ⇒ expression
In Radian angle mode and In Rectangular
Complex Format:
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
µ key
In Degree angle mode:
cot(List1) ⇒ list
Returns the cotangent of Expr1 or returns a
list of the cotangents of all elements in
List1.
In Gradian angle mode:
Note: The argument is interpreted as a
degree, gradian or radian angle, according
to the current angle mode setting. You can
use °, G, or r to override the angle mode
temporarily.
cot⁻¹()
cot⁻¹(Expr1) ⇒ expression
In Radian angle mode:
µ key
In Degree angle mode:
cot⁻¹(List1) ⇒ list
Returns the angle whose cotangent is
Expr1 or returns a list containing the
inverse cotangents of each element of
List1.
In Gradian angle mode:
Alphabetical Listing
37
µ key
cot⁻¹()
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arccot(...).
coth()
coth(Expr1) ⇒ expression
Catalog >
coth(List1) ⇒ list
Returns the hyperbolic cotangent of Expr1
or returns a list of the hyperbolic
cotangents of all elements of List1.
coth⁻¹()
coth⁻¹(Expr1) ⇒ expression
Catalog >
coth⁻¹(List1) ⇒ list
Returns the inverse hyperbolic cotangent of
Expr1 or returns a list containing the
inverse hyperbolic cotangents of each
element of List1.
Note: You can insert this function from the
keyboard by typing arccoth(...).
count()
count(Value1orList1 [,Value2orList2
[,...]]) ⇒ value
Catalog >
Returns the accumulated count of all
elements in the arguments that evaluate to
numeric values.
Each argument can be an expression, value,
list, or matrix. You can mix data types and
use arguments of various dimensions.
For a list, matrix, or range of cells, each
element is evaluated to determine if it
should be included in the count.
38
Alphabetical Listing
In the last example, only 1/2 and 3+4*i are
counted. The remaining arguments,
assuming x is undefined, do not evaluate to
numeric values.
Catalog >
count()
Within the Lists & Spreadsheet application,
you can use a range of cells in place of any
argument.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
Catalog >
countif()
countif(List ,Criteria) ⇒ value
Returns the accumulated count of all
elements in List that meet the specified
Criteria.
Counts the number of elements equal to 3.
Criteria can be:
•
•
A value, expression, or string. For
example, 3 counts only those elements in
List that simplify to the value 3.
A Boolean expression containing the
symbol ? as a placeholder for each
element. For example, ?<5 counts only
those elements in List that are less than
5.
Within the Lists & Spreadsheet application,
you can use a range of cells in place of List .
Empty (void) elements in the list are
ignored. For more information on empty
elements, see page 232.
Counts the number of elements equal to
“def.”
Counts the number of elements equal to x;
this example assumes the variable x is
undefined.
Counts 1 and 3.
Note: See also sumIf() , page 176, and
frequency() , page 77.
Counts 3, 5, and 7.
Counts 1, 3, 7, and 9.
Alphabetical Listing
39
Catalog >
cPolyRoots()
cPolyRoots(Poly ,Var) ⇒ list
cPolyRoots(ListOfCoeffs) ⇒ list
The first syntax, cPolyRoots( Poly ,Var) ,
returns a list of complex roots of
polynomial Poly with respect to variable
Var.
Poly must be a polynomial in one variable.
The second syntax, cPolyRoots
( ListOfCoeffs) , returns a list of complex
roots for the coefficients in ListOfCoeffs.
Note: See also polyRoots() , page 134.
Catalog >
crossP()
crossP(List1, List2) ⇒ list
Returns the cross product of List1 and
List2 as a list.
List1 and List2 must have equal
dimension, and the dimension must be
either 2 or 3.
crossP(Vector1, Vector2) ⇒ vector
Returns a row or column vector (depending
on the arguments) that is the cross product
of Vector1 and Vector2.
Both Vector1 and Vector2 must be row
vectors, or both must be column vectors.
Both vectors must have equal dimension,
and the dimension must be either 2 or 3.
csc()
csc(Expr1) ⇒ expression
µ key
In Degree angle mode:
csc(List1) ⇒ list
Returns the cosecant of Expr1 or returns a
list containing the cosecants of all elements
in List1.
40
Alphabetical Listing
In Gradian angle mode:
µ key
csc()
In Radian angle mode:
csc ⁻¹()
csc⁻¹(Expr1) ⇒ expression
µ key
In Degree angle mode:
csc⁻¹(List1) ⇒ list
Returns the angle whose cosecant is Expr1
or returns a list containing the inverse
cosecants of each element of List1.
In Gradian angle mode:
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arccsc(...).
csch()
csch(Expr1) ⇒ expression
Catalog >
csch(List1) ⇒ list
Returns the hyperbolic cosecant of Expr1 or
returns a list of the hyperbolic cosecants of
all elements of List1.
csch⁻¹()
csch⁻¹(Expr1) ⇒ expression
Catalog >
csch⁻¹(List1) ⇒ list
Returns the inverse hyperbolic cosecant of
Expr1 or returns a list containing the
inverse hyperbolic cosecants of each
element of List1.
Note: You can insert this function from the
keyboard by typing arccsch(...).
Alphabetical Listing
41
cSolve()
cSolve(Equation, Var) ⇒ Boolean
expression
Catalog >
cSolve(Equation, Var=Guess) ⇒ Boolean
expression
cSolve(Inequality , Var) ⇒ Boolean
expression
Returns candidate complex solutions of an
equation or inequality for Var. The goal is
to produce candidates for all real and nonreal solutions. Even if Equation is real,
cSolve() allows non-real results in Real
result Complex Format.
Although all undefined variables that do not
end with an underscore (_) are processed
as if they were real, cSolve() can solve
polynomial equations for complex solutions.
cSolve() temporarily sets the domain to
complex during the solution even if the
current domain is real. In the complex
domain, fractional powers having odd
denominators use the principal rather than
the real branch. Consequently, solutions
from solve() to equations involving such
fractional powers are not necessarily a
subset of those from cSolve() .
cSolve() starts with exact symbolic
methods. cSolve() also uses iterative
In Display Digits mode of Fix 2:
approximate complex polynomial factoring,
if necessary.
Note: See also cZeros() , solve() , and zeros() .
Note: If Equation is non-polynomial with
functions such as abs() , angle() , conj() , real
() , or imag() , you should place an
underscore (press /_) at the end of
Var. By default, a variable is treated as a
real value.
If you use var_ , the variable is treated as
complex.
42
Alphabetical Listing
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
cSolve()
Catalog >
You should also use var_ for any other
variables in Equation that might have
unreal values. Otherwise, you may receive
unexpected results.
cSolve(Eqn1andEqn2 [and…],
VarOrGuess1, VarOrGuess2 [, … ]) ⇒
Boolean expression
cSolve(SystemOfEqns, VarOrGuess1,
VarOrGuess2 [, …]) ⇒
Boolean expression
Returns candidate complex solutions to the
simultaneous algebraic equations, where
each varOrGuess specifies a variable that
you want to solve for.
Optionally, you can specify an initial guess
for a variable. Each varOrGuess must have
the form:
variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3+i .
If all of the equations are polynomials and
if you do NOT specify any initial guesses,
cSolve() uses the lexical
Gröbner/Buchberger elimination method to
attempt to determine all complex solutions.
Note: The following examples use an
underscore (press /_ ) so that the
variables will be treated as complex.
Complex solutions can include both real and
non-real solutions, as in the example to the
right.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Simultaneous polynomial equations can
have extra variables that have no values,
but represent given numeric values that
could be substituted later.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Alphabetical Listing
43
cSolve()
You can also include solution variables that
do not appear in the equations. These
solutions show how families of solutions
might contain arbitrary constants of the
form ck , where k is an integer suffix from 1
through 255.
For polynomial systems, computation time
or memory exhaustion may depend strongly
on the order in which you list solution
variables. If your initial choice exhausts
memory or your patience, try rearranging
the variables in the equations and/or
varOrGuess list.
Catalog >
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
If you do not include any guesses and if any
equation is non-polynomial in any variable
but all equations are linear in all solution
variables, cSolve() uses Gaussian
elimination to attempt to determine all
solutions.
If a system is neither polynomial in all of its
variables nor linear in its solution variables,
cSolve() determines at most one solution
using an approximate iterative method. To
do so, the number of solution variables
must equal the number of equations, and
all other variables in the equations must
simplify to numbers.
A non-real guess is often necessary to
determine a non-real solution. For
convergence, a guess might have to be
rather close to a solution.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
CubicReg
CubicReg X, Y[, [Freq] [, Category ,
Include ]]
Computes the cubic polynomial regression
y=a•x3+b•x2+c•x+d on lists X and Y with
frequency Freq. A summary of results is
stored in the stat.results variable. (See page
172.)
44
Alphabetical Listing
Catalog >
Catalog >
CubicReg
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: a•x 3+b•x 2+c•x+d
stat.a, stat.b,
stat.c, stat.d
Regression coefficients
stat.R 2
Coefficient of determination
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
cumulativeSum()
cumulativeSum(List1) ⇒ list
Catalog >
Returns a list of the cumulative sums of the
elements in List1, starting at element 1.
Alphabetical Listing
45
cumulativeSum()
cumulativeSum(Matrix1) ⇒ matrix
Catalog >
Returns a matrix of the cumulative sums of
the elements in Matrix1. Each element is
the cumulative sum of the column from top
to bottom.
An empty (void) element in List1 or
Matrix1 produces a void element in the
resulting list or matrix. For more
information on empty elements, see page
232.
Cycle
Cycle
Transfers control immediately to the next
iteration of the current loop ( For, While, or
Loop).
Catalog >
Function listing that sums the integers from 1
to 100 skipping 50.
Cycle is not allowed outside the three
looping structures ( For, While, or Loop).
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
►Cylind
Catalog >
Vector ►Cylind
Note: You can insert this operator from the
computer keyboard by typing @>Cylind.
Displays the row or column vector in
cylindrical form [r,∠ θ, z].
Vector must have exactly three elements.
It can be either a row or a column.
cZeros()
cZeros(Expr, Var) ⇒ list
46
Alphabetical Listing
Catalog >
In Display Digits mode of Fix 3:
cZeros()
Returns a list of candidate real and non-real
values of Var that make Expr=0. cZeros()
does this by computing
exp►list(cSolve( Expr=0,Var) ,Var) .
Otherwise, cZeros() is similar to zeros() .
Note: See also cSolve() , solve() , and zeros() .
Catalog >
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Note: If Expr is non-polynomial with
functions such as abs() , angle() , conj() , real
() , or imag() , you should place an
underscore (press /_) at the end of
Var. By default, a variable is treated as a
real value. If you use var_ , the variable is
treated as complex.
You should also use var_ for any other
variables in Expr that might have unreal
values. Otherwise, you may receive
unexpected results.
cZeros({Expr1, Expr2 [, … ] },
{VarOrGuess1,VarOrGuess2 [, … ] }) ⇒
matrix
Returns candidate positions where the
expressions are zero simultaneously. Each
VarOrGuess specifies an unknown whose
value you seek.
Optionally, you can specify an initial guess
for a variable. Each VarOrGuess must have
the form:
variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3+i .
If all of the expressions are polynomials and
you do NOT specify any initial guesses,
cZeros() uses the lexical
Gröbner/Buchberger elimination method to
attempt to determine all complex zeros.
Note: The following examples use an
underscore _ (press /_ ) so that the
variables will be treated as complex.
Alphabetical Listing
47
Catalog >
cZeros()
Complex zeros can include both real and
non-real zeros, as in the example to the
right.
Each row of the resulting matrix represents
an alternate zero, with the components
ordered the same as the VarOrGuess list.
To extract a row, index the matrix by [row].
Extract row 2:
Simultaneous polynomials can have extra
variables that have no values, but represent
given numeric values that could be
substituted later.
You can also include unknown variables that
do not appear in the expressions. These
zeros show how families of zeros might
contain arbitrary constants of the form ck ,
where k is an integer suffix from 1 through
255.
For polynomial systems, computation time
or memory exhaustion may depend strongly
on the order in which you list unknowns. If
your initial choice exhausts memory or your
patience, try rearranging the variables in
the expressions and/or VarOrGuess list.
If you do not include any guesses and if any
expression is non-polynomial in any variable
but all expressions are linear in all
unknowns, cZeros() uses Gaussian
elimination to attempt to determine all
zeros.
48
Alphabetical Listing
Catalog >
cZeros()
If a system is neither polynomial in all of its
variables nor linear in its unknowns, cZeros
() determines at most one zero using an
approximate iterative method. To do so, the
number of unknowns must equal the
number of expressions, and all other
variables in the expressions must simplify
to numbers.
A non-real guess is often necessary to
determine a non-real zero. For
convergence, a guess might have to be
rather close to a zero.
D
Catalog >
dbd()
dbd(date1,date2) ⇒ value
Returns the number of days between date1
and date2 using the actual-day-count
method.
date1 and date2 can be numbers or lists of
numbers within the range of the dates on
the standard calendar. If both date1 and
date2 are lists, they must be the same
length.
date1 and date2 must be between the
years 1950 through 2049.
You can enter the dates in either of two
formats. The decimal placement
differentiates between the date formats.
MM.DDYY (format used commonly in the
United States)
DDMM.YY (format use commonly in
Europe)
Catalog >
►DD
Expr1 ►DD ⇒ valueList1
►DD ⇒ listMatrix1
►DD ⇒ matrix
In Degree angle mode:
Alphabetical Listing
49
Catalog >
►DD
Note: You can insert this operator from the
computer keyboard by typing @>DD.
Returns the decimal equivalent of the
argument expressed in degrees. The
argument is a number, list, or matrix that is
interpreted by the Angle mode setting in
gradians, radians or degrees.
In Gradian angle mode:
In Radian angle mode:
►Decimal
Catalog >
Expression1 ►Decimal ⇒ expression
List1 ►Decimal ⇒ expression
Matrix1 ►Decimal ⇒ expression
Note: You can insert this operator from the
computer keyboard by typing @>Decimal.
Displays the argument in decimal form.
This operator can be used only at the end of
the entry line.
Define
Define Var = Expression
Define Function(Param1, Param2, ...) =
Expression
Defines the variable Var or the userdefined function Function.
Parameters, such as Param1, provide
placeholders for passing arguments to the
function. When calling a user-defined
function, you must supply arguments (for
example, values or variables) that
correspond to the parameters. When called,
the function evaluates Expression using
the supplied arguments.
50
Alphabetical Listing
Catalog >
Define
Var and Function cannot be the name of a
Catalog >
system variable or built-in function or
command.
Note: This form of Define is equivalent to
executing the expression: expression →
Function(Param1,Param2).
Define Function(Param1, Param2, ...) =
Func
Block
EndFunc
Define Program(Param1, Param2, ...) =
Prgm
Block
EndPrgm
In this form, the user-defined function or
program can execute a block of multiple
statements.
Block can be either a single statement or a
series of statements on separate lines.
Block also can include expressions and
instructions (such as If , Then, Else, and For).
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Note: See also Define LibPriv, page 51, and
Define LibPub, page 52.
Define LibPriv
Define LibPriv Var = Expression
Define LibPriv Function(Param1, Param2,
...) = Expression
Catalog >
Define LibPriv Function(Param1, Param2,
...) = Func
Block
EndFunc
Define LibPriv Program(Param1, Param2,
Alphabetical Listing
51
Define LibPriv
Catalog >
...) = Prgm
Block
EndPrgm
Operates the same as Define, except defines
a private library variable, function, or
program. Private functions and programs do
not appear in the Catalog.
Note: See also Define, page 50, and Define
LibPub, page 52.
Define LibPub
Define LibPub Var = Expression
Define LibPub Function(Param1, Param2,
...) = Expression
Catalog >
Define LibPub Function(Param1, Param2,
...) = Func
Block
EndFunc
Define LibPub Program(Param1, Param2,
...) = Prgm
Block
EndPrgm
Operates the same as Define, except defines
a public library variable, function, or
program. Public functions and programs
appear in the Catalog after the library has
been saved and refreshed.
Note: See also Define, page 50, and Define
LibPriv, page 51.
deltaList()
deltaTmpCnv()
52
Alphabetical Listing
See ΔList(), page 101.
See ΔtmpCnv(), page 185.
DelVar
DelVar Var1[, Var2] [, Var3] ...
Catalog >
DelVar Var.
Deletes the specified variable or variable
group from memory.
If one or more of the variables are locked,
this command displays an error message
and deletes only the unlocked variables. See
unLock, page 193.
DelVar Var. deletes all members of the
Var. variable group (such as the statistics
stat .nn results or variables created using
the LibShortcut() function) . The dot ( .) in
this form of the DelVar command limits it
to deleting a variable group; the simple
variable Var is not affected.
delVoid()
delVoid(List1) ⇒ list
Catalog >
Returns a list that has the contents of List1
with all empty (void) elements removed.
For more information on empty elements,
see page 232.
derivative()
deSolve()
deSolve(1stOr2ndOrderODE, Var,
depVar) ⇒ a general solution
See d(), page 217.
Catalog >
Returns an equation that explicitly or
implicitly specifies a general solution to the
1st- or 2nd-order ordinary differential
equation (ODE). In the ODE:
•
Use a prime symbol (press º) to denote
Alphabetical Listing
53
deSolve()
•
the 1st derivative of the dependent
variable with respect to the independent
variable.
Use two prime symbols to denote the
corresponding second derivative.
The prime symbol is used for derivatives
within deSolve() only. In other cases, use d
() .
The general solution of a 1st-order equation
contains an arbitrary constant of the form
ck , where k is an integer suffix from 1
through 255. The solution of a 2nd-order
equation contains two such constants.
Apply solve() to an implicit solution if you
want to try to convert it to one or more
equivalent explicit solutions.
When comparing your results with textbook
or manual solutions, be aware that different
methods introduce arbitrary constants at
different points in the calculation, which
may produce different general solutions.
deSolve(1stOrderODE and initCond, Var,
depVar) ⇒ a particular solution
Returns a particular solution that satisfies
1stOrderODE and initCond. This is usually
easier than determining a general solution,
substituting initial values, solving for the
arbitrary constant, and then substituting
that value into the general solution.
initCond is an equation of the form:
depVar (initialIndependentValue ) =
initialDependentValue
The initialIndependentValue and
initialDependentValue can be variables
such as x0 and y0 that have no stored
values. Implicit differentiation can help
verify implicit solutions.
54
Alphabetical Listing
Catalog >
deSolve()
deSolve(2ndOrderODE and initCond1 and
initCond2, Var, depVar)
⇒ particular solution
Catalog >
Returns a particular solution that satisfies
2nd Order ODE and has a specified value
of the dependent variable and its first
derivative at one point.
For initCond1, use the form:
depVar (initialIndependentValue ) =
initialDependentValue
For initCond2, use the form:
depVar (initialIndependentValue ) =
initial1stDerivativeValue
deSolve(2ndOrderODE and bndCond1 and
bndCond2, Var, depVar)
⇒ a particular solution
Returns a particular solution that satisfies
2ndOrderODE and has specified values at
two different points.
det()
det(squareMatrix [, Tolerance ]) ⇒
expression
Catalog >
Returns the determinant of squareMatrix .
Optionally, any matrix element is treated as
zero if its absolute value is less than
Tolerance . This tolerance is used only if the
matrix has floating-point entries and does
not contain any symbolic variables that
have not been assigned a value. Otherwise,
Tolerance is ignored.
•
If you use /· or set the Auto or
Approximate mode to Approximate,
Alphabetical Listing
55
det()
•
Catalog >
computations are done using floatingpoint arithmetic.
If Tolerance is omitted or not used, the
default tolerance is calculated as:
5E ⁻14 •max(dim
( squareMatrix )) •rowNorm
( squareMatrix )
diag()
diag(List ) ⇒ matrix
diag(rowMatrix ) ⇒ matrix
diag(columnMatrix ) ⇒ matrix
Catalog >
Returns a matrix with the values in the
argument list or matrix in its main
diagonal.
diag(squareMatrix ) ⇒ rowMatrix
Returns a row matrix containing the
elements from the main diagonal of
squareMatrix .
squareMatrix must be square.
dim()
dim(List ) ⇒ integer
Returns the dimension of List .
dim(Matrix ) ⇒ list
Returns the dimensions of matrix as a twoelement list {rows, columns}.
dim(String) ⇒ integer
Returns the number of characters contained
in character string String.
56
Alphabetical Listing
Catalog >
Catalog >
Disp
Disp exprOrString1 [, exprOrString2] ...
Displays the arguments in the Calculator
history. The arguments are displayed in
succession, with thin spaces as separators.
Useful mainly in programs and functions to
ensure the display of intermediate
calculations.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Catalog >
►DMS
Expr ►DMS
In Degree angle mode:
List ►DMS
Matrix ►DMS
Note: You can insert this operator from the
computer keyboard by typing @>DMS.
Interprets the argument as an angle and
displays the equivalent DMS
(DDDDDD°MM'SS.ss'') number. See °, ', ''
on page 224 for DMS (degree, minutes,
seconds) format.
Note: ►DMS will convert from radians to
degrees when used in radian mode. If the
input is followed by a degree symbol ° , no
conversion will occur. You can use ►DMS
only at the end of an entry line.
Alphabetical Listing
57
domain()
domain(Expr1, Var) ⇒ expression
Catalog >
Returns the domain of Expr1 with respect
to Var.
domain() can be used to examine domains
of functions. It is restricted to real and
finite domain.
This functionality has limitations due to
shortcomings of computer algebra
simplification and solver algorithms.
Certain functions cannot be used as
arguments for domain() , regardless of
whether they appear explicitly or within
user-defined variables and functions. In the
following example, the expression cannot
be simplified because ∫() is a disallowed
function.
dominantTerm()
dominantTerm(Expr1, Var [, Point ]) ⇒
expression
dominantTerm(Expr1, Var [, Point ]) |
Var>Point ⇒ expression
dominantTerm(Expr1, Var [, Point ]) |
Var<Point ⇒ expression
58
Alphabetical Listing
Catalog >
dominantTerm()
Catalog >
Returns the dominant term of a power
series representation of Expr1 expanded
about Point . The dominant term is the one
whose magnitude grows most rapidly near
Var = Point . The resulting power of (Var −
Point ) can have a negative and/or
fractional exponent. The coefficient of this
power can include logarithms of ( Var −
Point ) and other functions of Var that are
dominated by all powers of ( Var − Point )
having the same exponent sign.
Point defaults to 0. Point can be ∞ or −∞,
in which cases the dominant term will be
the term having the largest exponent of
Var rather than the smallest exponent of
Var.
dominantTerm(…) returns “dominantTerm
(…) ” if it is unable to determine such a
representation, such as for essential
singularities such as sin(1/ z) at z=0, e−1/z
at z=0, or ez at z = ∞ or −∞.
If the series or one of its derivatives has a
jump discontinuity at Point , the result is
likely to contain sub-expressions of the
form sign(…) or abs(…) for a real expansion
variable or (-1) floor(…angle(…)…) for a complex
expansion variable, which is one ending
with “_”. If you intend to use the dominant
term only for values on one side of Point ,
then append to dominantTerm( ...) the
appropriate one of “| Var > Point ”, “| Var
< Point ”, “| “Var ≥ Point ”, or “Var ≤
Point ” to obtain a simpler result.
dominantTerm() distributes over 1st-
argument lists and matrices.
dominantTerm() is useful when you want to
know the simplest possible expression that
is asymptotic to another expression as
Var→Point . dominantTerm() is also useful
when it isn’t obvious what the degree of
the first non-zero term of a series will be,
and you don’t want to iteratively guess
either interactively or by a program loop.
Alphabetical Listing
59
dominantTerm()
Catalog >
Note: See also series() , page 157.
dotP()
dotP(List1, List2) ⇒ expression
Catalog >
Returns the “dot” product of two lists.
dotP(Vector1, Vector2) ⇒ expression
Returns the “dot” product of two vectors.
Both must be row vectors, or both must be
column vectors.
E
e^()
e ^(Expr1) ⇒ expression
Returns e raised to the Expr1 power.
Note: See also e exponent template, page
6.
Note: Pressing u to display e^( is different
from pressing the character E on the
keyboard.
You can enter a complex number in reiθ
polar form. However, use this form in
Radian angle mode only; it causes a
Domain error in Degree or Gradian angle
mode.
e ^(List1) ⇒ list
Returns e raised to the power of each
element in List1.
e ^(squareMatrix1) ⇒ squareMatrix
Returns the matrix exponential of
squareMatrix1. This is not the same as
calculating e raised to the power of each
element. For information about the
calculation method, refer to cos() .
60
Alphabetical Listing
u key
u key
e^()
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
eff()
eff(nominalRate,CpY) ⇒ value
Catalog >
Financial function that converts the nominal
interest rate nominalRate to an annual
effective rate, given CpY as the number of
compounding periods per year.
nominalRate must be a real number, and
CpY must be a real number > 0.
Note: See also nom() , page 121.
eigVc()
eigVc(squareMatrix ) ⇒ matrix
Catalog >
In Rectangular Complex Format:
Returns a matrix containing the
eigenvectors for a real or complex
squareMatrix , where each column in the
result corresponds to an eigenvalue. Note
that an eigenvector is not unique; it may be
scaled by any constant factor. The
eigenvectors are normalized, meaning that:
if V = [x1 , x2 , … , xn ]
then x1 2 + x2 2 + … + xn 2 = 1
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
squareMatrix is first balanced with
similarity transformations until the row and
column norms are as close to the same
value as possible. The squareMatrix is then
reduced to upper Hessenberg form and the
eigenvectors are computed via a Schur
factorization.
eigVl()
eigVl(squareMatrix ) ⇒ list
Catalog >
In Rectangular complex format mode:
Alphabetical Listing
61
eigVl()
Catalog >
Returns a list of the eigenvalues of a real or
complex squareMatrix .
squareMatrix is first balanced with
similarity transformations until the row and
column norms are as close to the same
value as possible. The squareMatrix is then
reduced to upper Hessenberg form and the
eigenvalues are computed from the upper
Hessenberg matrix.
Else
ElseIf
If BooleanExpr1 Then
Block1
ElseIf BooleanExpr2 Then
Block2
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
See If, page 86.
Catalog >
⋮
ElseIf BooleanExprN Then
BlockN
EndIf
⋮
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
EndFor
EndFunc
EndIf
62
Alphabetical Listing
See For, page 75.
See Func, page 78.
See If, page 86.
EndLoop
See Loop, page 108.
EndPrgm
See Prgm, page 135.
EndTry
EndWhile
euler ()
euler(Expr, Var, depVar, {Var0, VarMax },
depVar0, VarStep [, eulerStep]) ⇒ matrix
See Try, page 187.
See While, page 197.
Catalog >
Differential equation:
y'=0.001*y*(100-y) and y(0)=10
euler(SystemOfExpr, Var, ListOfDepVars,
{Var0, VarMax },
ListOfDepVars0,
VarStep [, eulerStep]) ⇒ matrix
euler(ListOfExpr, Var, ListOfDepVars,
{Var0, VarMax }, ListOfDepVars0,
VarStep [, eulerStep]) ⇒ matrix
To see the entire result, press £ and then
Uses the Euler method to solve the system
Compare above result with CAS exact
solution obtained using deSolve() and
seqGen():
use ¡ and ¢ to move the cursor.
with depVar( Var0)=depVar0 on the
interval [Var0,VarMax ]. Returns a matrix
whose first row defines the Var output
values and whose second row defines the
value of the first solution component at the
corresponding Var values, and so on.
Expr is the right-hand side that defines the
ordinary differential equation (ODE).
SystemOfExpr is the system of right-hand
sides that define the system of ODEs
(corresponds to order of dependent
variables in ListOfDepVars).
Alphabetical Listing
63
euler ()
ListOfExpr is a list of right-hand sides that
Catalog >
System of equations:
define the system of ODEs (corresponds to
the order of dependent variables in
ListOfDepVars).
Var is the independent variable.
with y1 (0)=2 and y2 (0)=5
ListOfDepVars is a list of dependent
variables.
{Var0, VarMax } is a two-element list that
tells the function to integrate from Var0 to
VarMax .
ListOfDepVars0 is a list of initial values
for dependent variables.
VarStep is a nonzero number such that sign
( VarStep) = sign( VarMax -Var0) and
solutions are returned at Var0+i•VarStep
for all i =0,1,2,… such that Var0+i•VarStep
is in [var0,VarMax ] (there may not be a
solution value at VarMax ).
eulerStep is a positive integer (defaults to
1) that defines the number of euler steps
between output values. The actual step size
used by the euler method is
VarStep ⁄ eulerStep.
eval ()
eval(Expr) ⇒ string
eval() is valid only in the TI-Innovator™ Hub
Command argument of programming
commands Get, GetStr, and Send. The
software evaluates expression Expr and
replaces the eval() statement with the
result as a character string.
Hub Menu
Set the blue element of the RGB LED to half
intensity.
Reset the blue element to OFF.
The argument Expr must simplify to a real
number.
eval() argument must simplify to a real
number.
64
Alphabetical Listing
eval ()
Hub Menu
Program to fade-in the red element
Execute the program.
Although eval() does not display its result,
you can view the resulting Hub command
string after executing the command by
inspecting any of the following special
variables.
iostr.SendAns
iostr.GetAns
iostr.GetStrAns
Note: See also Get (page 80), GetStr (page
83), and Send (page 155).
Catalog >
exact()
exact(Expr1 [, Tolerance ]) ⇒ expression
exact(List1 [, Tolerance ]) ⇒ list
exact(Matrix1 [, Tolerance ]) ⇒ matrix
Uses Exact mode arithmetic to return,
when possible, the rational-number
equivalent of the argument.
Tolerance specifies the tolerance for the
conversion; the default is 0 (zero).
Catalog >
Exit
Exit
Function listing:
Exits the current For, While, or Loop block.
Alphabetical Listing
65
Exit
Catalog >
Exit is not allowed outside the three looping
structures ( For, While, or Loop).
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
►exp
Catalog >
Expr►exp
Represents Expr in terms of the natural
exponential e . This is a display conversion
operator. It can be used only at the end of
the entry line.
Note: You can insert this operator from the
computer keyboard by typing @>exp.
exp()
exp(Expr1) ⇒ expression
Returns e raised to the Expr1 power.
Note: See also e exponent template, page
6.
You can enter a complex number in reiθ
polar form. However, use this form in
Radian angle mode only; it causes a
Domain error in Degree or Gradian angle
mode.
exp(List1) ⇒ list
Returns e raised to the power of each
element in List1.
exp(squareMatrix1) ⇒ squareMatrix
66
Alphabetical Listing
u key
exp()
u key
Returns the matrix exponential of
squareMatrix1. This is not the same as
calculating e raised to the power of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
exp►list()
exp►list(Expr,Var) ⇒ list
Catalog >
Examines Expr for equations that are
separated by the word “or,” and returns a
list containing the right-hand sides of the
equations of the form Var=Expr. This
gives you an easy way to extract some
solution values embedded in the results of
the solve() , cSolve() , fMin() , and fMax()
functions.
Note: exp►list() is not necessary with the
zeros() and cZeros() functions because they
return a list of solution values directly.
You can insert this function from the
keyboard by typing exp@>list(...).
expand()
expand(Expr1 [, Var]) ⇒ expression
expand(List1 [,Var]) ⇒ list
expand(Matrix1 [,Var]) ⇒ matrix
Catalog >
expand( Expr1) returns Expr1 expanded
with respect to all its variables. The
expansion is polynomial expansion for
polynomials and partial fraction expansion
for rational expressions.
The goal of expand() is to transform Expr1
into a sum and/or difference of simple
terms. In contrast, the goal of factor() is to
transform Expr1 into a product and/or
quotient of simple factors.
Alphabetical Listing
67
expand()
expand( Expr1,Var) returns Expr1
expanded with respect to Var. Similar
powers of Var are collected. The terms and
their factors are sorted with Var as the
Catalog >
main variable. There might be some
incidental factoring or expansion of the
collected coefficients. Compared to
omitting Var, this often saves time,
memory, and screen space, while making
the expression more comprehensible.
Even when there is only one variable, using
Var might make the denominator
factorization used for partial fraction
expansion more complete.
Hint: For rational expressions, propFrac() is
a faster but less extreme alternative to
expand() .
Note: See also comDenom() for an
expanded numerator over an expanded
denominator.
expand( Expr1,[Var]) also distributes
logarithms and fractional powers
regardless of Var. For increased
distribution of logarithms and fractional
powers, inequality constraints might be
necessary to guarantee that some factors
are nonnegative.
expand( Expr1, [Var]) also distributes
absolute values, sign() , and exponentials,
regardless of Var.
Note: See also tExpand() for trigonometric
angle-sum and multiple-angle expansion.
expr()
expr(String) ⇒ expression
Returns the character string contained in
String as an expression and immediately
executes it.
68
Alphabetical Listing
Catalog >
Catalog >
ExpReg
ExpReg X, Y [, [Freq] [, Category,
Include ]]
Computes the exponential regression y = a•
(b) x on lists X and Y with frequency Freq. A
summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: a•(b)x
stat.a, stat.b
Regression coefficients
stat.r 2
Coefficient of linear determination for transformed data
stat.r
Correlation coefficient for transformed data (x, ln(y))
stat.Resid
Residuals associated with the exponential model
stat.ResidTrans
Residuals associated with linear fit of transformed data
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
Alphabetical Listing
69
Output
variable
Description
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
F
factor()
factor(Expr1[, Var]) ⇒ expression
factor(List1[,Var]) ⇒ list
factor(Matrix1[,Var]) ⇒ matrix
factor( Expr1) returns Expr1 factored with
respect to all of its variables over a
common denominator.
Expr1 is factored as much as possible
toward linear rational factors without
introducing new non-real subexpressions.
This alternative is appropriate if you want
factorization with respect to more than one
variable.
factor( Expr1,Var) returns Expr1 factored
with respect to variable Var.
Expr1 is factored as much as possible
toward real factors that are linear in Var,
even if it introduces irrational constants or
subexpressions that are irrational in other
variables.
The factors and their terms are sorted with
Var as the main variable. Similar powers of
Var are collected in each factor. Include
Var if factorization is needed with respect
to only that variable and you are willing to
accept irrational expressions in any other
variables to increase factorization with
respect to Var. There might be some
incidental factoring with respect to other
variables.
70
Alphabetical Listing
Catalog >
factor()
Catalog >
For the Auto setting of the Auto or
Approximate mode, including Var permits
approximation with floating-point
coefficients where irrational coefficients
cannot be explicitly expressed concisely in
terms of the built-in functions. Even when
there is only one variable, including Var
might yield more complete factorization.
Note: See also comDenom() for a fast way
to achieve partial factoring when factor() is
not fast enough or if it exhausts memory.
Note: See also cFactor() for factoring all the
way to complex coefficients in pursuit of
linear factors.
factor( rationalNumber) returns the rational
number factored into primes. For
composite numbers, the computing time
grows exponentially with the number of
digits in the second-largest factor. For
example, factoring a 30-digit integer could
take more than a day, and factoring a 100digit number could take more than a
century.
To stop a calculation manually,
•
Handheld: Hold down the c key and
press · repeatedly.
•
Windows®: Hold down the F12 key and
press Enter repeatedly.
Macintosh®: Hold down the F5 key and
press Enter repeatedly.
iPad®: The app displays a prompt. You
can continue waiting or cancel.
•
•
If you merely want to determine if a
number is prime, use isPrime() instead. It is
much faster, particularly if rationalNumber
is not prime and if the second-largest factor
has more than five digits.
FCdf()
Catalog >
FCdf
(lowBound,upBound,dfNumer,dfDenom) ⇒
Alphabetical Listing
71
FCdf()
Catalog >
number if lowBound and upBound are
numbers, list if lowBound and upBound are
lists
FCdf
(lowBound,upBound,dfNumer,dfDenom) ⇒
number if lowBound and upBound are
numbers, list if lowBound and upBound are
lists
Computes the F distribution probability
between lowBound and upBound for the
specified dfNumer (degrees of freedom) and
dfDenom.
For P( X ≤ upBound), set lowBound = 0.
Fill
Catalog >
Fill Expr, matrixVar ⇒ matrix
Replaces each element in variable
matrixVar with Expr.
matrixVar must already exist.
Fill Expr, listVar ⇒ list
Replaces each element in variable listVar
with Expr.
listVar must already exist.
FiveNumSummary
FiveNumSummary X[,[Freq]
[,Category ,Include ]]
Provides an abbreviated version of the 1variable statistics on list X. A summary of
results is stored in the stat.results variable.
(See page 172.)
X represents a list containing the data.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1.
72
Alphabetical Listing
Catalog >
FiveNumSummary
Category is a list of numeric category codes
for the corresponding X data.
Catalog >
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
An empty (void) element in any of the lists
X, Freq, or Category results in a void for
the corresponding element of all those lists.
For more information on empty elements,
see page 232.
Output variable
Description
stat.MinX
Minimum of x values.
stat.Q1X
1st Quartile of x.
stat.MedianX
Median of x.
stat.Q3X
3rd Quartile of x.
stat.MaxX
Maximum of x values.
floor()
floor(Expr1) ⇒ integer
Catalog >
Returns the greatest integer that is ≤ the
argument. This function is identical to int() .
The argument can be a real or a complex
number.
floor(List1) ⇒ list
floor(Matrix1) ⇒ matrix
Returns a list or matrix of the floor of each
element.
Note: See also ceiling() and int() .
fMax()
fMax(Expr, Var) ⇒ Boolean expression
fMax(Expr, Var,lowBound)
Catalog >
fMax(Expr, Var,lowBound,upBound)
Alphabetical Listing
73
fMax()
fMax(Expr, Var) |
lowBound≤Var≤upBound
Catalog >
Returns a Boolean expression specifying
candidate values of Var that maximize
Expr or locate its least upper bound.
You can use the constraint (“|”) operator to
restrict the solution interval and/or specify
other constraints.
For the Approximate setting of the Auto or
Approximate mode, fMax() iteratively
searches for one approximate local
maximum. This is often faster, particularly
if you use the “|” operator to constrain the
search to a relatively small interval that
contains exactly one local maximum.
Note: See also fMin() and max() .
fMin()
fMin(Expr, Var) ⇒ Boolean expression
fMin(Expr, Var,lowBound)
fMin(Expr, Var,lowBound,upBound)
fMin(Expr, Var) |
lowBound≤Var≤upBound
Returns a Boolean expression specifying
candidate values of Var that minimize
Expr or locate its greatest lower bound.
You can use the constraint (“|”) operator to
restrict the solution interval and/or specify
other constraints.
For the Approximate setting of the Auto or
Approximate mode, fMin() iteratively
searches for one approximate local
minimum. This is often faster, particularly
if you use the “|” operator to constrain the
search to a relatively small interval that
contains exactly one local minimum.
Note: See also fMax() and min() .
74
Alphabetical Listing
Catalog >
For
Catalog >
For Var, Low, High [, Step]
Block
EndFor
Executes the statements in Block
iteratively for each value of Var, from Low
to High, in increments of Step.
Var must not be a system variable.
Step can be positive or negative. The
default value is 1.
Block can be either a single statement or a
series of statements separated with the “:”
character.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
format()
format(Expr[, formatString]) ⇒ string
Catalog >
Returns Expr as a character string based on
the format template.
Expr must simplify to a number.
formatString is a string and must be in the
form: “F[n]”, “S[n]”, “E[n]”, “G[n][c]”,
where [ ] indicate optional portions.
F[n]: Fixed format. n is the number of digits
to display after the decimal point.
S[n]: Scientific format. n is the number of
digits to display after the decimal point.
E[n]: Engineering format. n is the number
of digits after the first significant digit. The
exponent is adjusted to a multiple of three,
and the decimal point is moved to the right
by zero, one, or two digits.
Alphabetical Listing
75
format()
Catalog >
G[n][c]: Same as fixed format but also
separates digits to the left of the radix into
groups of three. c specifies the group
separator character and defaults to a
comma. If c is a period, the radix will be
shown as a comma.
[Rc]: Any of the above specifiers may be
suffixed with the Rc radix flag, where c is a
single character that specifies what to
substitute for the radix point.
fPart()
fPart(Expr1) ⇒ expression
fPart(List1) ⇒ list
fPart(Matrix1) ⇒ matrix
Catalog >
Returns the fractional part of the argument.
For a list or matrix, returns the fractional
parts of the elements.
The argument can be a real or a complex
number.
FPdf()
Catalog >
FPdf(XVal ,dfNumer,dfDenom) ⇒ number
if XVal is a number, list if XVal is a list
Computes the F distribution probability at
XVal for the specified dfNumer (degrees of
freedom) and dfDenom.
freqTable►list()
freqTable►list(List1,freqIntegerList ) ⇒
list
Returns a list containing the elements from
List1 expanded according to the
frequencies in freqIntegerList . This
function can be used for building a
frequency table for the Data & Statistics
application.
List1 can be any valid list.
76
Alphabetical Listing
Catalog >
Catalog >
freqTable►list()
freqIntegerList must have the same
dimension as List1 and must contain nonnegative integer elements only. Each
element specifies the number of times the
corresponding List1 element will be
repeated in the result list. A value of zero
excludes the corresponding List1 element.
Note: You can insert this function from the
computer keyboard by typing
freqTable@>list(...).
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
Catalog >
frequency()
frequency(List1,binsList ) ⇒ list
Returns a list containing counts of the
elements in List1. The counts are based on
ranges (bins) that you define in binsList .
If binsList is {b(1), b(2), …, b(n)}, the
specified ranges are {?≤b(1), b(1)<?≤b
(2),…,b(n-1)<?≤b(n), b(n)>?}. The resulting
list is one element longer than binsList .
Each element of the result corresponds to
the number of elements from List1 that
are in the range of that bin. Expressed in
terms of the countIf() function, the result is
{ countIf(list, ?≤b(1)), countIf(list, b(1)<?≤b
(2)), …, countIf(list, b(n-1)<?≤b(n)), countIf
(list, b(n)>?)}.
Explanation of result:
2 elements from Datalist are ≤2.5
4 elements from Datalist are >2.5 and ≤4.5
3 elements from Datalist are >4.5
The element “hello” is a string and cannot be
placed in any of the defined bins.
Elements of List1 that cannot be “placed in
a bin” are ignored. Empty (void) elements
are also ignored. For more information on
empty elements, see page 232.
Within the Lists & Spreadsheet application,
you can use a range of cells in place of both
arguments.
Note: See also countIf() , page 39.
Alphabetical Listing
77
Catalog >
FTest_2Samp
FTest_2Samp List1,List2[,Freq1[,Freq2
[,Hypoth]]]
FTest_2Samp List1,List2[,Freq1[,Freq2
[,Hypoth]]]
(Data list input)
FTest_2Samp sx1,n1,sx2,n2[,Hypoth]
FTest_2Samp sx1,n1,sx2,n2[,Hypoth]
(Summary stats input)
Performs a two-sample F test. A summary
of results is stored in the stat.results
variable. (See page 172.)
For Ha: σ1 > σ2, set Hypoth>0
For Ha: σ1 ≠ σ2 (default), set Hypoth =0
For Ha: σ1 < σ2, set Hypoth<0
For information on the effect of empty
elements in a list, see Empty (Void)
Elements, page 232.
Output variable
Description
stat. F
Calculated F statistic for the data sequence
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.dfNumer
numerator degrees of freedom = n1-1
stat.dfDenom
denominator degrees of freedom = n2-1
stat.sx1, stat.sx2
Sample standard deviations of the data sequences in List 1 and List 2
stat.x1_bar
stat.x2_bar
Sample means of the data sequences in List 1 and List 2
stat.n1, stat.n2
Size of the samples
Catalog >
Func
Func
Block
EndFunc
Template for creating a user-defined
function.
78
Alphabetical Listing
Define a piecewise function:
Catalog >
Func
Block can be a single statement, a series
of statements separated with the “:”
character, or a series of statements on
separate lines. The function can use the
Return instruction to return a specific result.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Result of graphing g(x)
G
gcd()
gcd(Number1, Number2) ⇒ expression
Catalog >
Returns the greatest common divisor of the
two arguments. The gcd of two fractions is
the gcd of their numerators divided by the
lcm of their denominators.
In Auto or Approximate mode, the gcd of
fractional floating-point numbers is 1.0.
gcd(List1, List2) ⇒ list
Returns the greatest common divisors of
the corresponding elements in List1 and
List2.
gcd(Matrix1, Matrix2) ⇒ matrix
Returns the greatest common divisors of
the corresponding elements in Matrix1 and
Matrix2.
geomCdf()
geomCdf(p,lowBound,upBound) ⇒ number
Catalog >
Alphabetical Listing
79
geomCdf()
if lowBound and upBound are numbers, list
if lowBound and upBound are lists
Catalog >
geomCdf(p,upBound)for P(1≤X≤upBound)
⇒ number if upBound is a number, list if
upBound is a list
Computes a cumulative geometric
probability from lowBound to upBound with
the specified probability of success p.
For P(X ≤ upBound), set lowBound = 1.
geomPdf()
geomPdf(p,XVal ) ⇒ number if XVal is a
number, list if XVal is a list
Catalog >
Computes a probability at XVal , the number
of the trial on which the first success occurs,
for the discrete geometric distribution with
the specified probability of success p.
Get
Get [promptString,] var[, statusVar]
Get [promptString,] func (arg1, ...argn)
[, statusVar]
Hub Menu
Example: Request the current value of the
hub's built-in light-level sensor. Use Get to
retrieve the value and assign it to variable
lightval.
Programming command: Retrieves a value
from a connected TI-Innovator™ Hub and
assigns the value to variable var.
The value must be requested:
•
In advance, through a Send "READ ..."
command.
— or —
•
80
By embedding a "READ ..." request as
the optional promptString argument.
This method lets you use a single
command to request the value and
retrieve it.
Alphabetical Listing
Embed the READ request within the Get
command.
Get
Hub Menu
Implicit simplification takes place. For
example, a received string of "123" is
interpreted as a numeric value. To preserve
the string, use GetStr instead of Get.
If you include the optional argument
statusVar, it is assigned a value based on
the success of the operation. A value of
zero means that no data was received.
In the second syntax, the func () argument
allows a program to store the received
string as a function definition. This syntax
operates as if the program executed the
command:
Define func ( arg1, ...argn) = received
string
The program can then use the defined
function func ().
Note: You can use the Get command within
a user-defined program but not within a
function.
Note: See also GetStr, page 83 and Send,
page 155.
getDenom()
getDenom(Expr1) ⇒ expression
Catalog >
Transforms the argument into an
expression having a reduced common
denominator, and then returns its
denominator.
getLangInfo()
getLangInfo() ⇒ string
Catalog >
Returns a string that corresponds to the
short name of the currently active
language. You can, for example, use it in a
program or function to determine the
current language.
Alphabetical Listing
81
getLangInfo()
Catalog >
English = “en”
Danish = “da”
German = “de”
Finnish = “fi”
French = “fr”
Italian = “it”
Dutch = “nl”
Belgian Dutch = “nl_BE”
Norwegian = “no”
Portuguese = “pt”
Spanish = “es”
Swedish = “sv”
getLockInfo()
getLockInfo( Var) ⇒ value
Catalog >
Returns the current locked/unlocked state
of variable Var.
value =0: Var is unlocked or does not exist.
value =1: Var is locked and cannot be
modified or deleted.
See Lock, page 104, and unLock, page 193.
getMode()
getMode(ModeNameInteger) ⇒ value
getMode(0) ⇒ list
getMode( ModeNameInteger) returns a
value representing the current setting of
the ModeNameInteger mode.
getMode(0) returns a list containing
number pairs. Each pair consists of a mode
integer and a setting integer.
For a listing of the modes and their
settings, refer to the table below.
82
Alphabetical Listing
Catalog >
Catalog >
getMode()
If you save the settings with getMode(0) →
var, you can use setMode( var) in a function
or program to temporarily restore the
settings within the execution of the
function or program only. See setMode() ,
page 158.
Mode
Name
Mode
Integer
Display
Digits
1
1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5,
7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10,
12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2,
17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8,
23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12
Angle
2
1=Radian, 2=Degree, 3=Gradian
Exponential
Format
3
1=Normal, 2=Scientific, 3=Engineering
Real or
Complex
4
1=Real, 2=Rectangular, 3=Polar
Auto or
Approx.
5
1=Auto, 2=Approximate, 3=Exact
Vector
Format
6
1=Rectangular, 2=Cylindrical, 3=Spherical
Base
7
1=Decimal, 2=Hex, 3=Binary
Unit
system
8
1=SI, 2=Eng/US
Setting Integers
Catalog >
getNum()
getNum(Expr1) ⇒ expression
Transforms the argument into an
expression having a reduced common
denominator, and then returns its
numerator.
GetStr
GetStr [promptString,] var[, statusVar]
Hub Menu
For examples, see Get .
GetStr [promptString,] func (arg1, ...argn)
Alphabetical Listing
83
GetStr
[, statusVar]
Hub Menu
Programming command: Operates
identically to the Get command, except that
the retrieved value is always interpreted as
a string. By contrast, the Get command
interprets the response as an expression
unless it is enclosed in quotation marks ("").
Note: See also Get, page 80 and Send, page
155.
getType()
getType(var) ⇒ string
Catalog >
Returns a string that indicates the data type
of variable var.
If var has not been defined, returns the
string "NONE".
getVarInfo()
getVarInfo() ⇒ matrix or string
getVarInfo(LibNameString) ⇒ matrix or
string
getVarInfo() returns a matrix of information
(variable name, type, library accessibility,
and locked/unlocked state) for all variables
and library objects defined in the current
problem.
If no variables are defined, getVarInfo()
returns the string "NONE".
getVarInfo( LibNameString) returns a matrix
of information for all library objects defined
in library LibNameString. LibNameString
must be a string (text enclosed in quotation
marks) or a string variable.
If the library LibNameString does not exist,
an error occurs.
84
Alphabetical Listing
Catalog >
Catalog >
getVarInfo()
Note the example, in which the result of
getVarInfo() is assigned to variable vs.
Attempting to display row 2 or row 3 of vs
returns an “Invalid list or matrix” error
because at least one of elements in those
rows (variable b, for example) revaluates to
a matrix.
This error could also occur when using Ans
to reevaluate a getVarInfo() result.
The system gives the above error because
the current version of the software does not
support a generalized matrix structure
where an element of a matrix can be either
a matrix or a list.
Catalog >
Goto
Goto labelName
Transfers control to the label labelName .
labelName must be defined in the same
function using a Lbl instruction.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Catalog >
►Grad
Expr1►Grad ⇒ expression
In Degree angle mode:
Converts Expr1 to gradian angle measure.
Note: You can insert this operator from the
computer keyboard by typing @>Grad.
In Radian angle mode:
Alphabetical Listing
85
I
identity()
identity(Integer) ⇒ matrix
Catalog >
Returns the identity matrix with a
dimension of Integer.
Integer must be a positive integer.
Catalog >
If
If BooleanExpr
Statement
If BooleanExpr Then
Block
EndIf
If BooleanExpr evaluates to true, executes
the single statement Statement or the block
of statements Block before continuing
execution.
If BooleanExpr evaluates to false,
continues execution without executing the
statement or block of statements.
Block can be either a single statement or a
sequence of statements separated with the
“:” character.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
If BooleanExpr Then
Block1
Else
Block2
EndIf
If BooleanExpr evaluates to true, executes
Block1 and then skips Block2.
If BooleanExpr evaluates to false, skips
Block1 but executes Block2.
86
Alphabetical Listing
Catalog >
If
Block1 and Block2 can be a single
statement.
If BooleanExpr1 Then
Block1
ElseIf BooleanExpr2 Then
Block2
⋮
ElseIf BooleanExprN Then
BlockN
EndIf
Allows for branching. If BooleanExpr1
evaluates to true, executes Block1. If
BooleanExpr1 evaluates to false, evaluates
BooleanExpr2, and so on.
Catalog >
ifFn()
ifFn(BooleanExpr,Value_If_true [,Value_
If_false [,Value_If_unknown]]) ⇒
expression, list, or matrix
Evaluates the boolean expression
BooleanExpr (or each element from
BooleanExpr ) and produces a result based
on the following rules:
•
•
•
•
•
Test value of 1 is less than 2.5, so its
corresponding
Value_If_True element of 5 is copied to
the result list.
BooleanExpr can test a single value, a
list, or a matrix.
If an element of BooleanExpr evaluates
to true, returns the corresponding
element from Value_If_true .
If an element of BooleanExpr evaluates
to false, returns the corresponding
element from Value_If_false . If you
omit Value_If_false , returns undef.
If an element of BooleanExpr is neither
true nor false, returns the corresponding
element Value_If_unknown. If you omit
Value_If_unknown, returns undef.
If the second, third, or fourth argument
of the ifFn() function is a single
expression, the Boolean test is applied to
every position in BooleanExpr.
Test value of 2 is less than 2.5, so its
corresponding
Value_If_True element of 6 is copied to
the result list.
Test value of 3 is not less than 2.5, so its
corresponding Value_If_False element of
10 is copied to the result list.
Value_If_true is a single value and
corresponds to any selected position.
Alphabetical Listing
87
Catalog >
ifFn()
Note: If the simplified BooleanExpr
statement involves a list or matrix, all other
list or matrix arguments must have the
same dimension(s), and the result will have
the same dimension(s).
Value_If_false is not specified. Undef is
used.
One element selected from Value_If_true.
One element selected from Value_If_
unknown .
imag()
imag(Expr1) ⇒ expression
Catalog >
Returns the imaginary part of the
argument.
Note: All undefined variables are treated as
real variables. See also real(), page 144
imag(List1) ⇒ list
Returns a list of the imaginary parts of the
elements.
imag(Matrix1) ⇒ matrix
Returns a matrix of the imaginary parts of
the elements.
impDif()
impDif(Equation, Var, dependVar[,Ord])
⇒ expression
Catalog >
where the order Ord defaults to 1.
Computes the implicit derivative for
equations in which one variable is defined
implicitly in terms of another.
Indirection
88
Alphabetical Listing
See #(), page 222.
inString()
inString(srcString, subString[, Start ]) ⇒
integer
Catalog >
Returns the character position in string
srcString at which the first occurrence of
string subString begins.
Start , if included, specifies the character
position within srcString where the search
begins. Default = 1 (the first character of
srcString).
If srcString does not contain subString or
Start is > the length of srcString, returns
zero.
int()
int(Expr) ⇒ integer
Catalog >
int(List1) ⇒ list
int(Matrix1) ⇒ matrix
Returns the greatest integer that is less
than or equal to the argument. This
function is identical to floor() .
The argument can be a real or a complex
number.
For a list or matrix, returns the greatest
integer of each of the elements.
intDiv()
intDiv(Number1, Number2) ⇒ integer
intDiv(List1, List2) ⇒ list
intDiv(Matrix1, Matrix2) ⇒ matrix
Catalog >
Returns the signed integer part of
( Number1 ÷ Number2).
For lists and matrices, returns the signed
integer part of (argument 1 ÷ argument 2)
for each element pair.
Alphabetical Listing
89
integral
interpolate ()
interpolate(xValue , xList , yList ,
yPrimeList ) ⇒ list
See ∫(), page 217.
Catalog >
Differential equation:
y'=-3•y+6•t+5 and y(0)=5
This function does the following:
Given xList , yList =f( xList ) , and
yPrimeList =f'( xList ) for some unknown
function f , a cubic interpolant is used to
approximate the function f at xValue . It is
assumed that xList is a list of
monotonically increasing or decreasing
numbers, but this function may return a
value even when it is not. This function
walks through xList looking for an interval
[xList [i], xList [i+1]] that contains xValue .
If it finds such an interval, it returns an
interpolated value for f( xValue ) ; otherwise,
it returns undef.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Use the interpolate() function to calculate the
function values for the xvaluelist:
xList , yList , and yPrimeList must be of
equal dimension ≥ 2 and contain
expressions that simplify to numbers.
xValue can be an undefined variable, a
number, or a list of numbers.
invχ2 ()
Catalog >
invχ 2(Area,df )
invChi2(Area,df )
Computes the Inverse cumulative χ 2 (chisquare) probability function specified by
degree of freedom, df for a given Area
under the curve.
invF()
invF(Area,dfNumer,dfDenom)
invF(Area,dfNumer,dfDenom)
90
Alphabetical Listing
Catalog >
invF()
Catalog >
computes the Inverse cumulative F
distribution function specified by dfNumer
and dfDenom for a given Area under the
curve.
invNorm()
invNorm(Area[,μ[,σ]])
Catalog >
Computes the inverse cumulative normal
distribution function for a given Area under
the normal distribution curve specified by μ
and σ.
invt()
invt(Area,df )
Catalog >
Computes the inverse cumulative student-t
probability function specified by degree of
freedom, df for a given Area under the
curve.
iPart()
iPart(Number) ⇒ integer
iPart(List1) ⇒ list
iPart(Matrix1) ⇒ matrix
Catalog >
Returns the integer part of the argument.
For lists and matrices, returns the integer
part of each element.
The argument can be a real or a complex
number.
irr()
irr(CF0,CFList [,CFFreq]) ⇒ value
Catalog >
Financial function that calculates internal
rate of return of an investment.
CF0 is the initial cash flow at time 0; it
must be a real number.
Alphabetical Listing
91
irr()
CFList is a list of cash flow amounts after
Catalog >
the initial cash flow CF0.
CFFreq is an optional list in which each
element specifies the frequency of
occurrence for a grouped (consecutive) cash
flow amount, which is the corresponding
element of CFList . The default is 1; if you
enter values, they must be positive integers
< 10,000.
Note: See also mirr() , page 113.
isPrime()
isPrime(Number) ⇒ Boolean constant
expression
Returns true or false to indicate if number
is a whole number ≥ 2 that is evenly
divisible only by itself and 1.
Catalog >
Function to find the next prime after a
specified number:
If Number exceeds about 306 digits and has
no factors ≤1021, isPrime( Number) displays
an error message.
If you merely want to determine if Number
is prime, use isPrime() instead of factor() . It
is much faster, particularly if Number is not
prime and has a second-largest factor that
exceeds about five digits.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
isVoid()
isVoid(Var) ⇒ Boolean constant
expression
isVoid(Expr) ⇒ Boolean constant
expression
isVoid(List ) ⇒ list of Boolean constant
expressions
Returns true or false to indicate if the
argument is a void data type.
92
Alphabetical Listing
Catalog >
isVoid()
Catalog >
For more information on void elements, see
page 232.
L
Lbl
Catalog >
Lbl labelName
Defines a label with the name labelName
within a function.
You can use a Goto labelName instruction
to transfer control to the instruction
immediately following the label.
labelName must meet the same naming
requirements as a variable name.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
lcm()
lcm(Number1, Number2) ⇒ expression
lcm(List1, List2) ⇒ list
lcm(Matrix1, Matrix2) ⇒ matrix
Catalog >
Returns the least common multiple of the
two arguments. The lcm of two fractions is
the lcm of their numerators divided by the
gcd of their denominators. The lcm of
fractional floating-point numbers is their
product.
For two lists or matrices, returns the least
common multiples of the corresponding
elements.
left()
left(sourceString[, Num]) ⇒ string
Catalog >
Returns the leftmost Num characters
contained in character string sourceString.
Alphabetical Listing
93
left()
Catalog >
If you omit Num, returns all of
sourceString.
left(List1[, Num]) ⇒ list
Returns the leftmost Num elements
contained in List1.
If you omit Num, returns all of List1.
left(Comparison) ⇒ expression
Returns the left-hand side of an equation or
inequality.
libShortcut()
libShortcut(LibNameString,
ShortcutNameString
[, LibPrivFlag]) ⇒ list of variables
Creates a variable group in the current
problem that contains references to all the
objects in the specified library document
libNameString. Also adds the group
members to the Variables menu. You can
then refer to each object using its
ShortcutNameString.
Set LibPrivFlag=0 to exclude private
library objects (default)
Set LibPrivFlag=1 to include private
library objects
To copy a variable group, see CopyVar on
page 33.
To delete a variable group, see DelVar on
page 53.
94
Alphabetical Listing
Catalog >
This example assumes a properly stored and
refreshed library document named linalg2
that contains objects defined as clearmat,
gauss1 , and gauss2 .
limit() or lim()
limit(Expr1, Var, Point [,Direction]) ⇒
expression
limit(List1, Var, Point [, Direction]) ⇒
list
limit(Matrix1, Var, Point [, Direction]) ⇒
matrix
Catalog >
Returns the limit requested.
Note: See also Limit template, page 10.
Direction: negative=from left,
positive=from right, otherwise=both. (If
omitted, Direction defaults to both.)
Limits at positive ∞ and at negative ∞ are
always converted to one-sided limits from
the finite side.
Depending on the circumstances, limit()
returns itself or undef when it cannot
determine a unique limit. This does not
necessarily mean that a unique limit does
not exist. undef means that the result is
either an unknown number with finite or
infinite magnitude, or it is the entire set of
such numbers.
limit() uses methods such as L’Hopital’s
rule, so there are unique limits that it
cannot determine. If Expr1 contains
undefined variables other than Var, you
might have to constrain them to obtain a
more concise result.
Limits can be very sensitive to rounding
error. When possible, avoid the
Approximate setting of the Auto or
Approximate mode and approximate
numbers when computing limits.
Otherwise, limits that should be zero or
have infinite magnitude probably will not,
and limits that should have finite non-zero
magnitude might not.
LinRegBx
LinRegBx X,Y[,[Freq][,Category ,Include ]]
Catalog >
Alphabetical Listing
95
Catalog >
LinRegBx
Computes the linear regression y = a+b•x on
lists X and Y with frequency Freq. A
summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression Equation: a+b•x
stat.a, stat.b
Regression coefficients
stat.r 2
Coefficient of determination
stat.r
Correlation coefficient
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
96
Alphabetical Listing
LinRegMx
LinRegMx X,Y[,[Freq][,Category ,Include ]]
Catalog >
Computes the linear regression y = m •x+b on
lists X and Y with frequency Freq. A
summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression Equation: y = m•x+b
stat.m,
stat.b
Regression coefficients
stat.r 2
Coefficient of determination
stat.r
Correlation coefficient
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
Alphabetical Listing
97
Catalog >
LinRegtIntervals
LinRegtIntervals X,Y[,F[,0[,CLev ]]]
For Slope. Computes a level C confidence
interval for the slope.
LinRegtIntervals X,Y[,F[,1,Xval [,CLev ]]]
For Response. Computes a predicted y-value,
a level C prediction interval for a single
observation, and a level C confidence
interval for the mean response.
A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension.
X and Y are lists of independent and
dependent variables.
F is an optional list of frequency values.
Each element in F specifies the frequency of
occurrence for each corresponding X and Y
data point. The default value is 1. All
elements must be integers ≥ 0.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.RegEqn
Regression Equation: a+b•x
stat.a, stat.b
Regression coefficients
stat.df
Degrees of freedom
stat.r 2
Coefficient of determination
stat.r
Correlation coefficient
stat.Resid
Residuals from the regression
For Slope type only
Output variable
Description
[stat.CLower, stat.CUpper]
Confidence interval for the slope
stat.ME
Confidence interval margin of error
stat.SESlope
Standard error of slope
98
Alphabetical Listing
Output variable
Description
stat.s
Standard error about the line
For Response type only
Output variable
Description
[stat.CLower, stat.CUpper]
Confidence interval for the mean response
stat.ME
Confidence interval margin of error
stat.SE
Standard error of mean response
[stat.LowerPred,
stat.UpperPred]
Prediction interval for a single observation
stat.MEPred
Prediction interval margin of error
stat.SEPred
Standard error for prediction
stat. y
a + b•XVal
LinRegtTest
LinRegtTest X,Y[,Freq[,Hypoth]]
Catalog >
Computes a linear regression on the X and Y
lists and a t test on the value of slope β and
the correlation coefficient ρ for the equation
y =α +βx. It tests the null hypothesis H0:β=0
(equivalently, ρ=0) against one of three
alternative hypotheses.
All the lists must have equal dimension.
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Hypoth is an optional value specifying one
of three alternative hypotheses against
which the null hypothesis (H0:β=ρ=0) will be
tested.
Alphabetical Listing
99
LinRegtTest
For Ha: β≠0 and ρ≠0 (default), set Hypoth=0
For Ha: β<0 and ρ<0, set Hypoth<0
For Ha: β>0 and ρ>0, set Hypoth>0
Catalog >
A summary of results is stored in the
stat.results variable. (See page 172.)
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.RegEqn
Regression equation: a + b•x
stat.t
t-Statistic for significance test
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom
stat.a, stat.b
Regression coefficients
stat.s
Standard error about the line
stat.SESlope
Standard error of slope
stat.r 2
Coefficient of determination
stat.r
Correlation coefficient
stat.Resid
Residuals from the regression
linSolve()
linSolve( SystemOfLinearEqns, Var1,
Var2, ...) ⇒ list
linSolve(LinearEqn1 and LinearEqn2 and
..., Var1, Var2, ...) ⇒ list
linSolve({LinearEqn1, LinearEqn2, ...},
Var1, Var2, ...) ⇒ list
linSolve(SystemOfLinearEqns, {Var1,
Var2, ...}) ⇒ list
linSolve(LinearEqn1 and LinearEqn2 and
..., {Var1, Var2, ...}) ⇒ list
linSolve({LinearEqn1, LinearEgn2, ...},
{Var1, Var2, ...}) ⇒ list
100
Alphabetical Listing
Catalog >
linSolve()
Catalog >
Returns a list of solutions for the variables
Var1, Var2, ...
The first argument must evaluate to a
system of linear equations or a single linear
equation. Otherwise, an argument error
occurs.
For example, evaluating linSolve(x=1
and x=2,x) produces an “Argument
Error” result.
ΔList()
Catalog >
ΔList(List1) ⇒ list
Note: You can insert this function from the
keyboard by typing deltaList(...).
Returns a list containing the differences
between consecutive elements in List1.
Each element of List1 is subtracted from
the next element of List1. The resulting list
is always one element shorter than the
original List1.
list ►mat()
list►mat(List [, elementsPerRow]) ⇒
matrix
Catalog >
Returns a matrix filled row-by-row with the
elements from List .
elementsPerRow, if included, specifies the
number of elements per row. Default is the
number of elements in List (one row).
If List does not fill the resulting matrix,
zeros are added.
Note: You can insert this function from the
computer keyboard by typing list@>mat
(...).
Alphabetical Listing
101
►ln
Catalog >
Expr►ln ⇒ expression
Causes the input Expr to be converted to an
expression containing only natural logs (ln).
Note: You can insert this operator from the
computer keyboard by typing @>ln.
ln()
ln(Expr1) ⇒ expression
/u keys
ln(List1) ⇒ list
Returns the natural logarithm of the
argument.
If complex format mode is Real:
For a list, returns the natural logarithms of
the elements.
If complex format mode is Rectangular:
ln(squareMatrix1) ⇒ squareMatrix
Returns the matrix natural logarithm of
squareMatrix1. This is not the same as
calculating the natural logarithm of each
element. For information about the
calculation method, refer to cos() on.
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
In Radian angle mode and Rectangular
complex format:
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
LnReg
LnReg X, Y[, [Freq] [, Category , Include ]]
Computes the logarithmic regression y =
a+b•ln(x) on lists X and Y with frequency
Freq. A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
102
Alphabetical Listing
Catalog >
Catalog >
LnReg
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: a+b•ln(x)
stat.a, stat.b
Regression coefficients
stat.r 2
Coefficient of linear determination for transformed data
stat.r
Correlation coefficient for transformed data (ln(x), y)
stat.Resid
Residuals associated with the logarithmic model
stat.ResidTrans
Residuals associated with linear fit of transformed data
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
Alphabetical Listing
103
Local
Local Var1[, Var2] [, Var3] ...
Catalog >
Declares the specified vars as local
variables. Those variables exist only during
evaluation of a function and are deleted
when the function finishes execution.
Note: Local variables save memory because
they only exist temporarily. Also, they do
not disturb any existing global variable
values. Local variables must be used for For
loops and for temporarily saving values in a
multi-line function since modifications on
global variables are not allowed in a
function.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Lock
LockVar1[, Var2] [, Var3] ...
LockVar.
Locks the specified variables or variable
group. Locked variables cannot be modified
or deleted.
You cannot lock or unlock the system
variable Ans, and you cannot lock the
system variable groups stat . or tvm.
Note: The Lock command clears the
Undo/Redo history when applied to
unlocked variables.
See unLock, page 193, and getLockInfo() ,
page 82.
104
Alphabetical Listing
Catalog >
log()
log( Expr1[,Expr2]) ⇒ expression
/s keys
log( List1[,Expr2]) ⇒ list
Returns the base-Expr2 logarithm of the
first argument.
Note: See also Log template, page 6.
If complex format mode is Real:
For a list, returns the base-Expr2 logarithm
of the elements.
If the second argument is omitted, 10 is
used as the base.
log( squareMatrix1[,Expr]) ⇒
squareMatrix
If complex format mode is Rectangular:
In Radian angle mode and Rectangular
complex format:
Returns the matrix base-Expr logarithm of
squareMatrix1. This is not the same as
calculating the base-Expr logarithm of
each element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
If the base argument is omitted, 10 is used
as base.
►logbase
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Catalog >
Expr►logbase(Expr1) ⇒ expression
Causes the input Expression to be simplified
to an expression using base Expr1.
Note: You can insert this operator from the
computer keyboard by typing @>logbase
(...).
Alphabetical Listing
105
Logistic
Logistic X, Y[, [Freq] [, Category , Include ]]
Catalog >
Computes the logistic regression y = (c/
(1+a•e-bx)) on lists X and Y with frequency
Freq. A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: c/(1+a•e-bx)
stat.a,
stat.b, stat.c
Regression coefficients
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
106
Alphabetical Listing
Catalog >
LogisticD
LogisticD X, Y [, [Iterations] , [Freq] [,
Category , Include ] ]
Computes the logistic regression y = (c/
(1+a•e-bx)+d) on lists X and Y with frequency
Freq, using a specified number of
Iterations. A summary of results is stored in
the stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: c/(1+a•e-bx)+d)
stat.a, stat.b,
stat.c, stat.d
Regression coefficients
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
Alphabetical Listing
107
Loop
Catalog >
Loop
Block
EndLoop
Repeatedly executes the statements in
Block . Note that the loop will be executed
endlessly, unless a Goto or Exit instruction
is executed within Block .
Block is a sequence of statements
separated with the “:” character.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Catalog >
LU
LU Matrix , lMatrix , uMatrix , pMatrix
[,Tol]
Calculates the Doolittle LU (lower-upper)
decomposition of a real or complex matrix.
The lower triangular matrix is stored in
lMatrix , the upper triangular matrix in
uMatrix , and the permutation matrix
(which describes the row swaps done
during the calculation) in pMatrix .
lMatrix•uMatrix = pMatrix•matrix
Optionally, any matrix element is treated as
zero if its absolute value is less than Tol .
This tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise, Tol is ignored.
•
•
108
If you use /· or set the Auto or
Approximate mode to Approximate,
computations are done using floatingpoint arithmetic.
If Tol is omitted or not used, the default
tolerance is calculated as:
5E ⁻14•max(dim(Matrix ))•rowNorm
(Matrix )
Alphabetical Listing
LU
Catalog >
The LU factorization algorithm uses partial
pivoting with row interchanges.
M
mat ►list()
mat►list(Matrix ) ⇒ list
Catalog >
Returns a list filled with the elements in
Matrix . The elements are copied from
Matrix row by row.
Note: You can insert this function from the
computer keyboard by typing mat@>list
(...).
max()
max(Expr1, Expr2) ⇒ expression
Catalog >
max(List1, List2) ⇒ list
max(Matrix1, Matrix2) ⇒ matrix
Returns the maximum of the two
arguments. If the arguments are two lists
or matrices, returns a list or matrix
containing the maximum value of each pair
of corresponding elements.
max(List ) ⇒ expression
Returns the maximum element in list .
max(Matrix1) ⇒ matrix
Returns a row vector containing the
maximum element of each column in
Matrix1.
Alphabetical Listing
109
max()
Catalog >
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
Note: See also fMax() and min().
mean()
mean(List [, freqList ]) ⇒ expression
Catalog >
Returns the mean of the elements in List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
mean(Matrix1[, freqMatrix ]) ⇒ matrix
In Rectangular vector format:
Returns a row vector of the means of all
the columns in Matrix1.
Each freqMatrix element counts the
number of consecutive occurrences of the
corresponding element in Matrix1.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
median()
median(List [, freqList ]) ⇒ expression
Returns the median of the elements in List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
median(Matrix1[, freqMatrix ]) ⇒ matrix
Returns a row vector containing the
medians of the columns in Matrix1.
Each freqMatrix element counts the
number of consecutive occurrences of the
corresponding element in Matrix1.
110
Alphabetical Listing
Catalog >
Catalog >
median()
Notes:
•
•
All entries in the list or matrix must
simplify to numbers.
Empty (void) elements in the list or
matrix are ignored. For more information
on empty elements, see page 232.
MedMed
MedMed X,Y [, Freq] [, Category , Include ]]
Catalog >
Computes the median-median line y =
(m •x+b) on lists X and Y with frequency
Freq. A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Median-median line equation: m•x+b
stat.m,
stat.b
Model coefficients
Alphabetical Listing
111
Output
variable
Description
stat.Resid
Residuals from the median-median line
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
mid()
mid(sourceString, Start [, Count ]) ⇒
string
Returns Count characters from character
string sourceString, beginning with
character number Start .
If Count is omitted or is greater than the
dimension of sourceString, returns all
characters from sourceString, beginning
with character number Start .
Count must be ≥ 0. If Count = 0, returns an
empty string.
mid(sourceList , Start [, Count ]) ⇒ list
Returns Count elements from sourceList ,
beginning with element number Start .
If Count is omitted or is greater than the
dimension of sourceList , returns all
elements from sourceList , beginning with
element number Start .
Count must be ≥ 0. If Count = 0, returns an
empty list.
mid(sourceStringList , Start [, Count ]) ⇒
list
Returns Count strings from the list of
strings sourceStringList , beginning with
element number Start .
112
Alphabetical Listing
Catalog >
min()
min(Expr1, Expr2) ⇒ expression
Catalog >
min(List1, List2) ⇒ list
min(Matrix1, Matrix2) ⇒ matrix
Returns the minimum of the two
arguments. If the arguments are two lists
or matrices, returns a list or matrix
containing the minimum value of each pair
of corresponding elements.
min(List ) ⇒ expression
Returns the minimum element of List .
min(Matrix1) ⇒ matrix
Returns a row vector containing the
minimum element of each column in
Matrix1.
Note: See also fMin() and max().
mirr()
Catalog >
mirr
(financeRate ,reinvestRate ,CF0,CFList
[,CFFreq])
Financial function that returns the modified
internal rate of return of an investment.
financeRate is the interest rate that you
pay on the cash flow amounts.
reinvestRate is the interest rate at which
the cash flows are reinvested.
CF0 is the initial cash flow at time 0; it
must be a real number.
CFList is a list of cash flow amounts after
the initial cash flow CF0.
CFFreq is an optional list in which each
element specifies the frequency of
occurrence for a grouped (consecutive) cash
flow amount, which is the corresponding
element of CFList . The default is 1; if you
enter values, they must be positive integers
< 10,000.
Alphabetical Listing
113
mirr()
Catalog >
Note: See also irr() , page 91.
mod()
mod(Expr1, Expr2) ⇒ expression
Catalog >
mod(List1, List2) ⇒ list
mod(Matrix1, Matrix2) ⇒ matrix
Returns the first argument modulo the
second argument as defined by the
identities:
mod(x,0) = x
mod(x,y) = x − y floor(x/y)
When the second argument is non-zero, the
result is periodic in that argument. The
result is either zero or has the same sign as
the second argument.
If the arguments are two lists or two
matrices, returns a list or matrix containing
the modulo of each pair of corresponding
elements.
Note: See also remain() , page 146
mRow()
mRow(Expr, Matrix1, Index ) ⇒ matrix
Catalog >
Returns a copy of Matrix1 with each
element in row Index of Matrix1 multiplied
by Expr.
mRowAdd()
mRowAdd(Expr, Matrix1, Index1, Index2)
⇒ matrix
Returns a copy of Matrix1 with each
element in row Index2 of Matrix1 replaced
with:
Expr • row Index1 + row Index2
114
Alphabetical Listing
Catalog >
Catalog >
MultReg
MultReg Y, X1[,X2[,X3,…[,X10]]]
Calculates multiple linear regression of list Y
on lists X1, X2, …, X10. A summary of
results is stored in the stat.results variable.
(See page 172.)
All the lists must have equal dimension.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.RegEqn
Regression Equation: b0+b1•x1+b2•x2+ ...
stat.b0, stat.b1, ...
Regression coefficients
stat.R 2
Coefficient of multiple determination
stat. y List
yList = b0+b1•x1+ ...
stat.Resid
Residuals from the regression
Catalog >
MultRegIntervals
MultRegIntervals Y, X1[, X2[, X3,…[,
X10]]], XValList [, CLevel ]
Computes a predicted y-value, a level C
prediction interval for a single observation,
and a level C confidence interval for the
mean response.
A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.RegEqn
Regression Equation: b0+b1•x1+b2•x2+ ...
stat. y
A point estimate: y = b0 + b1 • xl + ... for XValList
stat.dfError
Error degrees of freedom
Alphabetical Listing
115
Output variable
Description
stat.CLower, stat.CUpper
Confidence interval for a mean response
stat.ME
Confidence interval margin of error
stat.SE
Standard error of mean response
stat.LowerPred,
stat.UpperrPred
Prediction interval for a single observation
stat.MEPred
Prediction interval margin of error
stat.SEPred
Standard error for prediction
stat.bList
List of regression coefficients, {b0,b1,b2,...}
stat.Resid
Residuals from the regression
MultRegTests
MultRegTests Y, X1[, X2[, X3,…[, X10]]]
Catalog >
Multiple linear regression test computes a
multiple linear regression on the given data
and provides the global F test statistic and t
test statistics for the coefficients.
A summary of results is stored in the
stat.results variable. (See page 172.)
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Outputs
Output
variable
Description
stat.RegEqn
Regression Equation: b0+b1•x1+b2•x2+ ...
stat.F
Global F test statistic
stat.PVal
P-value associated with global F statistic
stat.R 2
Coefficient of multiple determination
stat.AdjR 2
Adjusted coefficient of multiple determination
stat.s
Standard deviation of the error
stat.DW
Durbin-Watson statistic; used to determine whether first-order auto correlation is
present in the model
116
Alphabetical Listing
Output
variable
Description
stat.dfReg
Regression degrees of freedom
stat.SSReg
Regression sum of squares
stat.MSReg
Regression mean square
stat.dfError
Error degrees of freedom
stat.SSError
Error sum of squares
stat.MSError
Error mean square
stat.bList
{b0,b1,...} List of coefficients
stat.tList
List of t statistics, one for each coefficient in the bList
stat.PList
List P-values for each t statistic
stat.SEList
List of standard errors for coefficients in bList
stat. y List
yList = b0+b1•x1+ . . .
stat.Resid
Residuals from the regression
stat.sResid
Standardized residuals; obtained by dividing a residual by its standard deviation
stat.CookDist
Cook’s distance; measure of the influence of an observation based on the residual
and leverage
stat.Leverage
Measure of how far the values of the independent variable are from their mean
values
N
nand
BooleanExpr1 nand BooleanExpr2 returns
Boolean expression
BooleanList1 nand BooleanList2 returns
Boolean list
BooleanMatrix1 nand BooleanMatrix2
returns Boolean matrix
/= keys
Returns the negation of a logical and
operation on the two arguments. Returns
true, false, or a simplified form of the
equation.
For lists and matrices, returns comparisons
element by element.
Alphabetical Listing
117
nand
Integer1 nand Integer2 ⇒ integer
/= keys
Compares two real integers bit-by-bit using
a nand operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if both bits are 1;
otherwise, the result is 0. The returned
value represents the bit results, and is
displayed according to the Base mode.
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base 10).
nCr()
nCr(Expr1, Expr2) ⇒ expression
For integer Expr1 and Expr2 with Expr1 ≥
Expr2 ≥ 0, nCr() is the number of
combinations of Expr1 things taken Expr2
at a time. (This is also known as a binomial
coefficient.) Both arguments can be
integers or symbolic expressions.
nCr(Expr, 0) ⇒ 1
nCr(Expr, negInteger) ⇒ 0
nCr(Expr, posInteger) ⇒ Expr•(Expr−1) ...
(Expr−posInteger+1) / posInteger!
nCr(Expr, nonInteger) ⇒ expression! /
((Expr−nonInteger)!•nonInteger!)
nCr(List1, List2) ⇒ list
Returns a list of combinations based on the
corresponding element pairs in the two
lists. The arguments must be the same size
list.
nCr(Matrix1, Matrix2) ⇒ matrix
118
Alphabetical Listing
Catalog >
nCr()
Catalog >
Returns a matrix of combinations based on
the corresponding element pairs in the two
matrices. The arguments must be the same
size matrix.
nDerivative()
nDerivative(Expr1,Var=Value [,Order])
⇒ value
Catalog >
nDerivative(Expr1,Var[,Order])
|Var=Value ⇒ value
Returns the numerical derivative calculated
using auto differentiation methods.
When Value is specified, it overrides any
prior variable assignment or any current “|”
substitution for the variable.
Order of the derivative must be 1 or 2.
newList()
newList(numElements) ⇒ list
Catalog >
Returns a list with a dimension of
numElements. Each element is zero.
newMat()
newMat(numRows, numColumns) ⇒
matrix
Catalog >
Returns a matrix of zeros with the
dimension numRows by numColumns.
nfMax()
nfMax(Expr, Var) ⇒ value
nfMax(Expr, Var, lowBound) ⇒ value
nfMax(Expr, Var, lowBound, upBound) ⇒
value
nfMax(Expr, Var) |
lowBound≤Var≤upBound ⇒ value
Catalog >
Alphabetical Listing
119
nfMax()
Catalog >
Returns a candidate numerical value of
variable Var where the local maximum of
Expr occurs.
If you supply lowBound and upBound, the
function looks in the closed interval
[lowBound,upBound] for the local
maximum.
Note: See also fMax() and d() .
nfMin()
nfMin(Expr, Var) ⇒ value
nfMin(Expr, Var, lowBound) ⇒ value
nfMin(Expr, Var, lowBound, upBound) ⇒
value
nfMin(Expr, Var) |
lowBound≤Var≤upBound ⇒ value
Catalog >
Returns a candidate numerical value of
variable Var where the local minimum of
Expr occurs.
If you supply lowBound and upBound, the
function looks in the closed interval
[lowBound,upBound] for the local
minimum.
Note: See also fMin() and d() .
nInt()
nInt(Expr1, Var, Lower, Upper) ⇒
expression
If the integrand Expr1 contains no variable
other than Var, and if Lower and Upper
are constants, positive ∞, or negative ∞,
then nInt() returns an approximation of ∫
( Expr1, Var, Lower, Upper) . This
approximation is a weighted average of
some sample values of the integrand in the
interval Lower<Var<Upper.
120
Alphabetical Listing
Catalog >
nInt()
Catalog >
The goal is six significant digits. The
adaptive algorithm terminates when it
seems likely that the goal has been
achieved, or when it seems unlikely that
additional samples will yield a worthwhile
improvement.
A warning is displayed (“Questionable
accuracy”) when it seems that the goal has
not been achieved.
Nest nInt() to do multiple numeric
integration. Integration limits can depend
on integration variables outside them.
Note: See also ∫() , page 217.
nom()
nom(effectiveRate,CpY) ⇒ value
Catalog >
Financial function that converts the annual
effective interest rate effectiveRate to a
nominal rate, given CpY as the number of
compounding periods per year.
effectiveRate must be a real number, and
CpY must be a real number > 0.
Note: See also eff() , page 61.
nor
BooleanExpr1 nor BooleanExpr2 returns
Boolean expression
BooleanList1 nor BooleanList2 returns
Boolean list
BooleanMatrix1 nor BooleanMatrix2
returns Boolean matrix
/= keys
Returns the negation of a logical or
operation on the two arguments. Returns
true, false, or a simplified form of the
equation.
For lists and matrices, returns comparisons
element by element.
Alphabetical Listing
121
nor
Integer1 nor Integer2 ⇒ integer
/= keys
Compares two real integers bit-by-bit using
a nor operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if both bits are 1;
otherwise, the result is 0. The returned
value represents the bit results, and is
displayed according to the Base mode.
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base 10).
norm()
norm(Matrix ) ⇒ expression
Catalog >
norm(Vector) ⇒ expression
Returns the Frobenius norm.
normalLine()
normalLine(Expr1,Var,Point ) ⇒
expression
normalLine(Expr1,Var=Point ) ⇒
expression
Returns the normal line to the curve
represented by Expr1 at the point specified
in Var=Point .
Make sure that the independent variable is
not defined. For example, If f1(x):=5 and
x:=3, then normalLine( f1(x),x,2) returns
“false.”
122
Alphabetical Listing
Catalog >
Catalog >
normCdf()
normCdf(lowBound,upBound[,μ[,σ]]) ⇒
number if lowBound and upBound are
numbers, list if lowBound and upBound are
lists
Computes the normal distribution probability
between lowBound and upBound for the
specified μ (default=0) and σ (default=1).
For P(X ≤ upBound), set lowBound = ⁻∞.
Catalog >
normPdf()
normPdf(XVal [,μ[,σ]]) ⇒ number if XVal is
a number, list if XVal is a list
Computes the probability density function
for the normal distribution at a specified
XVal value for the specified μ and σ.
Catalog >
not
not BooleanExpr ⇒ Boolean expression
Returns true, false, or a simplified form of
the argument.
not Integer1 ⇒ integer
In Hex base mode:
Returns the one’s complement of a real
integer. Internally, Integer1 is converted to
a signed, 64-bit binary number. The value of
each bit is flipped (0 becomes 1, and vice
versa) for the one’s complement. Results
are displayed according to the Base mode.
Important: Zero, not the letter O.
In Bin base mode:
You can enter the integer in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, the integer is treated as
decimal (base 10).
If you enter a decimal integer that is too
large for a signed, 64-bit binary form, a
symmetric modulo operation is used to
bring the value into the appropriate range.
For more information, see ►Base2, page
21.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Note: A binary entry can have up to 64 digits
(not counting the 0b prefix). A hexadecimal
entry can have up to 16 digits.
Alphabetical Listing
123
nPr()
nPr(Expr1, Expr2) ⇒ expression
Catalog >
For integer Expr1 and Expr2 with Expr1 ≥
Expr2 ≥ 0, nPr() is the number of
permutations of Expr1 things taken Expr2
at a time. Both arguments can be integers
or symbolic expressions.
nPr(Expr, 0 ⇒ 1
nPr(Expr, negInteger) ⇒ 1 / ((Expr+1)•
(Expr+2) ... (expression−negInteger))
nPr(Expr, posInteger) ⇒ Expr•(Expr−1) ...
(Expr−posInteger+1)
nPr(Expr, nonInteger) ⇒ Expr! /
(Expr−nonInteger)!
nPr(List1, List2) ⇒ list
Returns a list of permutations based on the
corresponding element pairs in the two
lists. The arguments must be the same size
list.
nPr(Matrix1, Matrix2) ⇒ matrix
Returns a matrix of permutations based on
the corresponding element pairs in the two
matrices. The arguments must be the same
size matrix.
npv()
npv(InterestRate ,CFO,CFList [,CFFreq])
Financial function that calculates net
present value; the sum of the present
values for the cash inflows and outflows. A
positive result for npv indicates a profitable
investment.
InterestRate is the rate by which to
discount the cash flows (the cost of money)
over one period.
CF0 is the initial cash flow at time 0; it
must be a real number.
CFList is a list of cash flow amounts after
the initial cash flow CF0.
124
Alphabetical Listing
Catalog >
npv()
CFFreq is a list in which each element
Catalog >
specifies the frequency of occurrence for a
grouped (consecutive) cash flow amount,
which is the corresponding element of
CFList . The default is 1; if you enter
values, they must be positive integers <
10,000.
nSolve()
nSolve(Equation,Var[=Guess]) ⇒ number
or error_string
Catalog >
nSolve(Equation,Var[=Guess],lowBound)
⇒ number or error_string
nSolve(Equation,Var
[=Guess],lowBound,upBound) ⇒ number
or error_string
Note: If there are multiple solutions, you can
use a guess to help find a particular solution.
nSolve(Equation,Var[=Guess]) |
lowBound≤Var≤upBound ⇒ number or
error_string
Iteratively searches for one approximate
real numeric solution to Equation for its
one variable. Specify the variable as:
variable
– or –
variable = real number
For example, x is valid and so is x=3.
nSolve() is often much faster than solve() or
zeros() , particularly if the “|” operator is
used to constrain the search to a small
interval containing exactly one simple
solution.
nSolve() attempts to determine either one
point where the residual is zero or two
relatively close points where the residual
has opposite signs and the magnitude of
the residual is not excessive. If it cannot
achieve this using a modest number of
sample points, it returns the string “no
solution found.”
Alphabetical Listing
125
Catalog >
nSolve()
Note: See also cSolve() , cZeros() , solve() ,
and zeros() .
O
Catalog >
OneVar
OneVar [1,]X[,[Freq][,Category ,Include ]]
OneVar [n,]X1,X2[X3[,…[,X20]]]
Calculates 1-variable statistics on up to 20
lists. A summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of numeric category codes
for the corresponding X values.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
An empty (void) element in any of the lists
X, Freq, or Category results in a void for
the corresponding element of all those lists.
An empty element in any of the lists X1
through X20 results in a void for the
corresponding element of all those lists. For
more information on empty elements, see
page 232.
Output variable
Description
stat. v
Mean of x values
stat. Σ x
Sum of x values
stat. Σ x 2
Sum of x 2 values
126
Alphabetical Listing
Output variable
Description
stat.sx
Sample standard deviation of x
stat. σx
Population standard deviation of x
stat.n
Number of data points
stat.MinX
Minimum of x values
stat.Q1X
1st Quartile of x
stat.MedianX
Median of x
stat.Q3X
3rd Quartile of x
stat.MaxX
Maximum of x values
stat.SSX
Sum of squares of deviations from the mean of x
Catalog >
or
BooleanExpr1 or BooleanExpr2 returns
Boolean expression
BooleanList1 or BooleanList2 returns
Boolean list
BooleanMatrix1 or BooleanMatrix2
returns Boolean matrix
Returns true or false or a simplified form of
the original entry.
Returns true if either or both expressions
simplify to true. Returns false only if both
expressions evaluate to false.
Note: See xor.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Integer1 or Integer2 ⇒ integer
In Hex base mode:
Important: Zero, not the letter O.
In Bin base mode:
Alphabetical Listing
127
Catalog >
or
Compares two real integers bit-by-bit using
an or operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if either bit is 1;
the result is 0 only if both bits are 0. The
returned value represents the bit results,
and is displayed according to the Base
mode.
Note: A binary entry can have up to 64 digits
(not counting the 0b prefix). A hexadecimal
entry can have up to 16 digits.
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base 10).
If you enter a decimal integer that is too
large for a signed, 64-bit binary form, a
symmetric modulo operation is used to
bring the value into the appropriate range.
For more information, see ►Base2, page
21.
Note: See xor.
Catalog >
ord()
ord(String) ⇒ integer
ord(List1) ⇒ list
Returns the numeric code of the first
character in character string String, or a list
of the first characters of each list element.
P
P►Rx()
P►Rx(rExpr, θExpr) ⇒ expression
P►Rx(rList , θList ) ⇒ list
P►Rx(rMatrix , θMatrix ) ⇒ matrix
Returns the equivalent x-coordinate of the
(r, θ) pair.
128
Alphabetical Listing
Catalog >
In Radian angle mode:
Catalog >
P►Rx()
Note: The θ argument is interpreted as
either a degree, gradian or radian angle,
according to the current angle mode. If the
argument is an expression, you can use °, G,
or r to override the angle mode setting
temporarily.
Note: You can insert this function from the
computer keyboard by typing P@>Rx(...).
P►Ry()
P►Ry(rExpr, θExpr) ⇒ expression
Catalog >
In Radian angle mode:
P►Ry(rList , θList ) ⇒ list
P►Ry(rMatrix , θMatrix ) ⇒ matrix
Returns the equivalent y-coordinate of the
(r, θ) pair.
Note: The θ argument is interpreted as
either a degree, radian or gradian angle,
according to the current angle mode. If the
argument is an expression, you can use °, G,
or r to override the angle mode setting
temporarily.
Note: You can insert this function from the
computer keyboard by typing P@>Ry(...).
PassErr
PassErr
Passes an error to the next level.
Catalog >
For an example of PassErr , See Example 2
under the Try command, page 187.
If system variable errCode is zero, PassErr
does not do anything.
The Else clause of the Try...Else...EndTry
block should use ClrErr or PassErr. If the
error is to be processed or ignored, use
ClrErr. If what to do with the error is not
known, use PassErr to send it to the next
error handler. If there are no more pending
Try...Else...EndTry error handlers, the error
dialog box will be displayed as normal.
Alphabetical Listing
129
PassErr
Catalog >
Note: See also ClrErr, page 29, and Try, page
187.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product guidebook.
piecewise()
piecewise(Expr1[, Cond1[, Expr2 [, Cond2
Catalog >
[, … ]]]])
Returns definitions for a piecewise function
in the form of a list. You can also create
piecewise definitions by using a template.
Note: See also Piecewise template, page 7.
poissCdf()
poissCdf(λ,lowBound,upBound) ⇒ number
if lowBound and upBound are numbers, list
if lowBound and upBound are lists
Catalog >
poissCdf(λ,upBound)for P(0≤X≤upBound) ⇒
number if upBound is a number, list if
upBound is a list
Computes a cumulative probability for the
discrete Poisson distribution with specified
mean λ.
For P(X ≤ upBound), set lowBound=0
poissPdf()
poissPdf(λ,XVal ) ⇒ number if XVal is a
number, list if XVal is a list
Computes a probability for the discrete
Poisson distribution with the specified mean
λ.
130
Alphabetical Listing
Catalog >
Catalog >
►Polar
Vector ►Polar
Note: You can insert this operator from the
computer keyboard by typing @>Polar.
Displays vector in polar form [r∠ θ]. The
vector must be of dimension 2 and can be a
row or a column.
Note: ►Polar is a display-format
instruction, not a conversion function. You
can use it only at the end of an entry line,
and it does not update ans.
Note: See also ►Rect, page 144.
complexValue ►Polar
In Radian angle mode:
Displays complexVector in polar form.
•
•
Degree angle mode returns (r∠ θ).
Radian angle mode returns reiθ.
complexValue can have any complex form.
However, an reiθ entry causes an error in
Degree angle mode.
In Gradian angle mode:
Note: You must use the parentheses for an
(r∠ θ) polar entry.
In Degree angle mode:
polyCoeffs()
polyCoeffs(Poly [,Var]) ⇒ list
Catalog >
Returns a list of the coefficients of
polynomial Poly with respect to variable
Var.
Poly must be a polynomial expression in
Var. We recommend that you do not omit
Var unless Poly is an expression in a single
variable.
Expands the polynomial and selects x for the
omitted Var.
Alphabetical Listing
131
polyCoeffs()
Catalog >
polyDegree()
polyDegree(Poly [,Var]) ⇒ value
Catalog >
Returns the degree of polynomial
expression Poly with respect to variable
Var. If you omit Var, the polyDegree()
function selects a default from the
variables contained in the polynomial Poly .
Constant polynomials
Poly must be a polynomial expression in
Var. We recommend that you do not omit
Var unless Poly is an expression in a single
variable.
The degree can be extracted even though
the coefficients cannot. This is because the
degree can be extracted without expanding
the polynomial.
polyEval()
polyEval(List1, Expr1) ⇒ expression
polyEval(List1, List2) ⇒ expression
Interprets the first argument as the
coefficient of a descending-degree
polynomial, and returns the polynomial
evaluated for the value of the second
argument.
132
Alphabetical Listing
Catalog >
polyGcd()
polyGcd(Expr1,Expr2) ⇒ expression
Catalog >
Returns greatest common divisor of the
two arguments.
Expr1 and Expr2 must be polynomial
expressions.
List, matrix, and Boolean arguments are not
allowed.
polyQuotient()
polyQuotient(Poly1,Poly2 [,Var]) ⇒
expression
Catalog >
Returns the quotient of polynomial Poly1
divided by polynomial Poly2 with respect to
the specified variable Var.
Poly1 and Poly2 must be polynomial
expressions in Var. We recommend that
you do not omit Var unless Poly1 and
Poly2 are expressions in the same single
variable.
polyRemainder()
polyRemainder(Poly1,Poly2 [,Var]) ⇒
expression
Catalog >
Returns the remainder of polynomial Poly1
divided by polynomial Poly2 with respect to
the specified variable Var.
Poly1 and Poly2 must be polynomial
expressions in Var. We recommend that
you do not omit Var unless Poly1 and
Poly2 are expressions in the same single
variable.
Alphabetical Listing
133
polyRemainder()
Catalog >
polyRoots()
polyRoots(Poly ,Var) ⇒ list
Catalog >
polyRoots(ListOfCoeffs) ⇒ list
The first syntax, polyRoots( Poly ,Var) ,
returns a list of real roots of polynomial
Poly with respect to variable Var. If no real
roots exist, returns an empty list: { }.
Poly must be a polynomial in one variable.
The second syntax, polyRoots
( ListOfCoeffs) , returns a list of real roots
for the coefficients in ListOfCoeffs.
Note: See also cPolyRoots() , page 40.
PowerReg
PowerReg X,Y[, Freq][, Category , Include ]]
Computes the power regressiony = (a•
(x) b)on lists X and Y with frequency Freq. A
summary of results is stored in the
stat.results variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
134
Alphabetical Listing
Catalog >
Catalog >
PowerReg
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: a•(x)b
stat.a, stat.b
Regression coefficients
stat.r 2
Coefficient of linear determination for transformed data
stat.r
Correlation coefficient for transformed data (ln(x), ln(y))
stat.Resid
Residuals associated with the power model
stat.ResidTrans
Residuals associated with linear fit of transformed data
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
Prgm
Prgm
Block
EndPrgm
Catalog >
Calculate GCD and display intermediate
results.
Template for creating a user-defined
program. Must be used with the Define,
Define LibPub, or Define LibPriv command.
Block can be a single statement, a series
of statements separated with the “:”
character, or a series of statements on
separate lines.
Alphabetical Listing
135
Prgm
Catalog >
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
prodSeq()
See Π (), page 219.
Product (PI)
See Π (), page 219.
product()
product(List [, Start [, End]]) ⇒ expression
Catalog >
Returns the product of the elements
contained in List . Start and End are
optional. They specify a range of elements.
product(Matrix1[, Start [, End]]) ⇒ matrix
Returns a row vector containing the
products of the elements in the columns of
Matrix1. Start and end are optional. They
specify a range of rows.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
propFrac()
propFrac(Expr1[, Var]) ⇒ expression
propFrac( rational_number) returns
rational_number as the sum of an integer
and a fraction having the same sign and a
greater denominator magnitude than
numerator magnitude.
136
Alphabetical Listing
Catalog >
propFrac()
propFrac( rational_expression,Var) returns
Catalog >
the sum of proper ratios and a polynomial
with respect to Var. The degree of Var in
the denominator exceeds the degree of Var
in the numerator in each proper ratio.
Similar powers of Var are collected. The
terms and their factors are sorted with Var
as the main variable.
If Var is omitted, a proper fraction
expansion is done with respect to the most
main variable. The coefficients of the
polynomial part are then made proper with
respect to their most main variable first
and so on.
For rational expressions, propFrac() is a
faster but less extreme alternative to
expand() .
You can use the propFrac() function to
represent mixed fractions and demonstrate
addition and subtraction of mixed fractions.
Q
Catalog >
QR
QR Matrix , qMatrix , rMatrix [, Tol ]
Calculates the Householder QR factorization
of a real or complex matrix. The resulting Q
and R matrices are stored to the specified
Matrix . The Q matrix is unitary. The R
matrix is upper triangular.
The floating-point number (9.) in m1 causes
results to be calculated in floating-point
form.
Optionally, any matrix element is treated as
zero if its absolute value is less than Tol .
This tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise, Tol is ignored.
•
If you use /· or set the Auto or
Approximate mode to Approximate,
Alphabetical Listing
137
Catalog >
QR
•
computations are done using floatingpoint arithmetic.
If Tol is omitted or not used, the default
tolerance is calculated as:
5E −14 •max(dim(Matrix )) •rowNorm
(Matrix )
The QR factorization is computed
numerically using Householder
transformations. The symbolic solution is
computed using Gram-Schmidt. The
columns in qMatName are the orthonormal
basis vectors that span the space defined by
matrix .
QuadReg
QuadReg X,Y[, Freq][, Category , Include ]]
Computes the quadratic polynomial
regression y=a•x 2 +b•x+c on lists X and Y
with frequency Freq. A summary of results
is stored in the stat.results variable. (See
page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of category codes for the
corresponding X and Y data.
138
Alphabetical Listing
Catalog >
QuadReg
Include is a list of one or more of the
Catalog >
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression equation: a•x 2+b•x+c
stat.a,
stat.b, stat.c
Regression coefficients
stat.R 2
Coefficient of determination
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
QuartReg
QuartReg X,Y[, Freq][, Category , Include ]]
Catalog >
Computes the quartic polynomial regression
y = a•x4+b•x3+c• x2+d•x+e on lists X and Y
with frequency Freq. A summary of results
is stored in the stat.results variable. (See
page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Alphabetical Listing
139
Catalog >
QuartReg
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.RegEqn
Regression equation: a•x 4+b•x 3+c• x 2+d•x+e
stat.a, stat.b,
stat.c, stat.d,
stat.e
Regression coefficients
stat.R 2
Coefficient of determination
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
R
R►Pθ()
R►Pθ (xExpr, yExpr) ⇒ expression
Catalog >
In Degree angle mode:
R►Pθ (xList , yList ) ⇒ list
R►Pθ (xMatrix , yMatrix ) ⇒ matrix
Returns the equivalent θ-coordinate of the
( x,y ) pair arguments.
In Gradian angle mode:
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
Note: You can insert this function from the
computer keyboard by typing R@>Ptheta
(...).
140
Alphabetical Listing
In Radian angle mode:
Catalog >
R►Pθ()
R►Pr()
R►Pr (xExpr, yExpr) ⇒ expression
Catalog >
In Radian angle mode:
R►Pr (xList , yList ) ⇒ list
R►Pr (xMatrix , yMatrix ) ⇒ matrix
Returns the equivalent r-coordinate of the
( x,y ) pair arguments.
Note: You can insert this function from the
computer keyboard by typing R@>Pr(...).
Catalog >
►Rad
Expr1►Rad ⇒ expression
In Degree angle mode:
Converts the argument to radian angle
measure.
Note: You can insert this operator from the
computer keyboard by typing @>Rad.
rand()
rand() ⇒ expression
rand(#Trials) ⇒ list
In Gradian angle mode:
Catalog >
Set the random-number seed.
rand() returns a random value between 0
and 1.
rand( #Trials) returns a list containing
#Trials random values between 0 and 1.
Alphabetical Listing
141
randBin()
randBin(n, p) ⇒ expression
randBin(n, p, #Trials) ⇒ list
Catalog >
randBin( n, p) returns a random real number
from a specified Binomial distribution.
randBin( n, p, #Trials) returns a list
containing #Trials random real numbers
from a specified Binomial distribution.
randInt()
Catalog >
randInt
(lowBound,upBound)
⇒ expression
randInt
(lowBound,upBound
,#Trials) ⇒ list
randInt
( lowBound,upBound)
returns a random
integer within the
range specified by
lowBound and
upBound integer
bounds.
randInt
( lowBound,upBound
,#Trials) returns a
list containing
#Trials random
integers within the
specified range.
randMat()
randMat(numRows, numColumns) ⇒
matrix
Catalog >
Returns a matrix of integers between -9
and 9 of the specified dimension.
Both arguments must simplify to integers.
142
Alphabetical Listing
Note: The values in this matrix will change
each time you press ·.
randNorm()
randNorm(μ, σ) ⇒ expression
randNorm(μ, σ, #Trials) ⇒ list
Catalog >
randNorm( μ, σ) returns a decimal number
from the specified normal distribution. It
could be any real number but will be heavily
concentrated in the interval [μ−3•σ, μ+3•σ].
randNorm( μ, σ, #Trials) returns a list
containing #Trials decimal numbers from
the specified normal distribution.
randPoly()
randPoly(Var, Order) ⇒ expression
Catalog >
Returns a polynomial in Var of the
specified Order. The coefficients are
random integers in the range −9 through 9.
The leading coefficient will not be zero.
Order must be 0–99.
randSamp()
randSamp(List ,#Trials[,noRepl ]) ⇒ list
Catalog >
Returns a list containing a random sample
of #Trials trials from List with an option
for sample replacement ( noRepl =0), or no
sample replacement ( noRepl =1). The
default is with sample replacement.
RandSeed
RandSeed Number
Catalog >
If Number = 0, sets the seeds to the factory
defaults for the random-number generator.
If Number ≠ 0, it is used to generate two
seeds, which are stored in system variables
seed1 and seed2.
Alphabetical Listing
143
Catalog >
real()
real(Expr1) ⇒ expression
Returns the real part of the argument.
Note: All undefined variables are treated as
real variables. See also imag() , page 88.
real(List1) ⇒ list
Returns the real parts of all elements.
real(Matrix1) ⇒ matrix
Returns the real parts of all elements.
Catalog >
►Rect
Vector ►Rect
Note: You can insert this operator from the
computer keyboard by typing @>Rect.
Displays Vector in rectangular form [x, y,
z]. The vector must be of dimension 2 or 3
and can be a row or a column.
Note: ►Rect is a display-format instruction,
not a conversion function. You can use it
only at the end of an entry line, and it does
not update ans.
Note: See also ►Polar, page 131.
complexValue ►Rect
In Radian angle mode:
Displays complexValue in rectangular form
a+bi. The complexValue can have any
complex form. However, an reiθ entry
causes an error in Degree angle mode.
Note: You must use parentheses for an
(r∠ θ) polar entry.
In Gradian angle mode:
In Degree angle mode:
Note: To type ∠ , select it from the symbol
list in the Catalog.
144
Alphabetical Listing
ref()
ref(Matrix1[, Tol ]) ⇒ matrix
Catalog >
Returns the row echelon form of Matrix1.
Optionally, any matrix element is treated as
zero if its absolute value is less than Tol .
This tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise, Tol is ignored.
•
•
If you use /· or set the Auto or
Approximate mode to Approximate,
computations are done using floatingpoint arithmetic.
If Tol is omitted or not used, the default
tolerance is calculated as:
5E −14 •max(dim(Matrix1)) •rowNorm
(Matrix1)
Avoid undefined elements in Matrix1. They
can lead to unexpected results.
For example, if a is undefined in the
following expression, a warning message
appears and the result is shown as:
The warning appears because the
generalized element 1/ a would not be valid
for a=0.
You can avoid this by storing a value to a
beforehand or by using the constraint (“|”)
operator to substitute a value, as shown in
the following example.
Note: See also rref() , page 153.
Alphabetical Listing
145
Catalog >
remain()
remain(Expr1, Expr2) ⇒ expression
remain(List1, List2) ⇒ list
remain(Matrix1, Matrix2) ⇒ matrix
Returns the remainder of the first
argument with respect to the second
argument as defined by the identities:
remain(x,0) x
remain(x,y) x−y•iPart(x/y)
As a consequence, note that remain( −x,y) −
remain( x,y) . The result is either zero or it
has the same sign as the first argument.
Note: See also mod() , page 114.
Request
Request promptString, var[, DispFlag
[, statusVar]]
Request promptString, func (arg1, ...argn)
[, DispFlag [, statusVar]]
Programming command: Pauses the
program and displays a dialog box
containing the message promptString and
an input box for the user’s response.
Catalog >
Define a program:
Define request_demo()=Prgm
Request “Radius: ”,r
Disp “Area = “,pi*r2
EndPrgm
Run the program and type a response:
request_demo()
When the user types a response and clicks
OK, the contents of the input box are
assigned to variable var.
If the user clicks Cancel, the program
proceeds without accepting any input. The
program uses the previous value of var if
var was already defined.
Result after selecting OK :
The optional DispFlag argument can be
any expression.
Radius: 6/2
Area= 28.2743
•
•
146
If DispFlag is omitted or evaluates to 1,
the prompt message and user’s response
are displayed in the Calculator history.
If DispFlag evaluates to 0, the prompt
and response are not displayed in the
history.
Alphabetical Listing
Catalog >
Request
The optional statusVar argument gives the
program a way to determine how the user
dismissed the dialog box. Note that
statusVar requires the DispFlag argument.
•
•
If the user clicked OK or pressed Enter or
Ctrl+Enter, variable statusVar is set to a
value of 1.
Otherwise, variable statusVar is set to a
value of 0.
Define a program:
Define polynomial()=Prgm
Request "Enter a polynomial in
x:",p(x)
Disp "Real roots are:",polyRoots
(p(x),x)
EndPrgm
Run the program and type a response:
polynomial()
The func () argument allows a program to
store the user’s response as a function
definition. This syntax operates as if the
user executed the command:
Define func ( arg1, ...argn) = user’s
response
The program can then use the defined
function func (). The promptString should
guide the user to enter an appropriate
user’s response that completes the
function definition.
Result after entering x^3+3x+1 and selecting
OK :
Real roots are: {-0.322185}
Note: You can use the Request command
within a user-defined program but not
within a function.
To stop a program that contains a Request
command inside an infinite loop:
•
Handheld: Hold down the c key and
press · repeatedly.
•
Windows®: Hold down the F12 key and
press Enter repeatedly.
Macintosh®: Hold down the F5 key and
press Enter repeatedly.
iPad®: The app displays a prompt. You
can continue waiting or cancel.
•
•
Note: See also RequestStr, page 147.
RequestStr
RequestStr promptString, var[, DispFlag]
Catalog >
Define a program:
Alphabetical Listing
147
Catalog >
RequestStr
Programming command: Operates
identically to the first syntax of the Request
command, except that the user’s response
is always interpreted as a string. By
contrast, the Request command interprets
the response as an expression unless the
user encloses it in quotation marks (““).
Define requestStr_demo()=Prgm
RequestStr “Your name:”,name,0
Disp “Response has “,dim(name),”
characters.”
EndPrgm
Note: You can use the RequestStr command
within a user-defined program but not
within a function.
requestStr_demo()
Run the program and type a response:
To stop a program that contains a
RequestStr command inside an infinite loop:
•
Handheld: Hold down the c key and
press · repeatedly.
•
Windows®: Hold down the F12 key and
press Enter repeatedly.
Macintosh®: Hold down the F5 key and
press Enter repeatedly.
iPad®: The app displays a prompt. You
can continue waiting or cancel.
•
•
Note: See also Request, page 146.
Return
Result after selecting OK (Note that the
DispFlag argument of 0 omits the prompt
and response from the history):
requestStr_demo()
Response has 5 characters.
Catalog >
Return [Expr]
Returns Expr as the result of the function.
Use within a Func...EndFunc block.
Note: Use Return without an argument
within a Prgm...EndPrgm block to exit a
program.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
right()
right(List1[, Num]) ⇒ list
148
Alphabetical Listing
Catalog >
Catalog >
right()
Returns the rightmost Num elements
contained in List1.
If you omit Num, returns all of List1.
right(sourceString[, Num]) ⇒ string
Returns the rightmost Num characters
contained in character string sourceString.
If you omit Num, returns all of
sourceString.
right(Comparison) ⇒ expression
Returns the right side of an equation or
inequality.
rk23 ()
rk23(Expr, Var, depVar, {Var0, VarMax },
depVar0, VarStep [, diftol ]) ⇒ matrix
Catalog >
Differential equation:
y'=0.001*y*(100-y) and y(0)=10
rk23(SystemOfExpr, Var, ListOfDepVars,
{Var0, VarMax }, ListOfDepVars0,
VarStep[, diftol ]) ⇒ matrix
rk23(ListOfExpr, Var, ListOfDepVars,
{Var0, VarMax }, ListOfDepVars0,
VarStep[, diftol ]) ⇒ matrix
To see the entire result, press £ and then
Uses the Runge-Kutta method to solve the
system
Same equation with diftol set to 1. E−6
with depVar( Var0)=depVar0 on the
interval [Var0,VarMax ]. Returns a matrix
whose first row defines the Var output
values as defined by VarStep. The second
row defines the value of the first solution
component at the corresponding Var
values, and so on.
Compare above result with CAS exact
solution obtained using deSolve() and
seqGen():
use ¡ and ¢ to move the cursor.
Expr is the right hand side that defines the
ordinary differential equation (ODE).
SystemOfExpr is a system of right-hand
sides that define the system of ODEs
(corresponds to order of dependent
variables in ListOfDepVars).
System of equations:
Alphabetical Listing
149
Catalog >
rk23 ()
ListOfExpr is a list of right-hand sides that
define the system of ODEs (corresponds to
order of dependent variables in
ListOfDepVars).
with y1(0)=2 and y2(0)=5
Var is the independent variable.
ListOfDepVars is a list of dependent
variables.
{Var0, VarMax } is a two-element list that
tells the function to integrate from Var0 to
VarMax .
ListOfDepVars0 is a list of initial values
for dependent variables.
If VarStep evaluates to a nonzero number:
sign( VarStep) = sign( VarMax -Var0) and
solutions are returned at Var0+i*VarStep
for all i=0,1,2,… such that Var0+i*VarStep
is in [var0,VarMax ] (may not get a solution
value at VarMax ).
if VarStep evaluates to zero, solutions are
returned at the "Runge-Kutta" Var values.
diftol is the error tolerance (defaults to
0.001).
Catalog >
root()
root(Expr) ⇒ root
root(Expr1, Expr2) ⇒ root
root( Expr) returns the square root of Expr.
root( Expr1, Expr2) returns the Expr2 root
of Expr1. Expr1 can be a real or complex
floating point constant, an integer or
complex rational constant, or a general
symbolic expression.
Note: See also Nth root template, page 5.
rotate()
rotate(Integer1[,#ofRotations]) ⇒ integer
150
Alphabetical Listing
Catalog >
In Bin base mode:
Catalog >
rotate()
Rotates the bits in a binary integer. You can
enter Integer1 in any number base; it is
converted automatically to a signed, 64-bit
binary form. If the magnitude of Integer1 is
too large for this form, a symmetric modulo
operation brings it within the range. For
more information, see ►Base2, page 21.
If #ofRotations is positive, the rotation is to
the left. If #ofRotations is negative, the
rotation is to the right. The default is −1
(rotate right one bit).
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
In Hex base mode:
For example, in a right rotation:
Each bit rotates right.
0b00000000000001111010110000110101
Important: To enter a binary or
hexadecimal number, always use the 0b or
0h prefix (zero, not the letter O).
Rightmost bit rotates to leftmost.
produces:
0b10000000000000111101011000011010
The result is displayed according to the
Base mode.
rotate(List1[,#ofRotations]) ⇒ list
In Dec base mode:
Returns a copy of List1 rotated right or left
by #of Rotations elements. Does not alter
List1.
If #ofRotations is positive, the rotation is to
the left. If #of Rotations is negative, the
rotation is to the right. The default is −1
(rotate right one element).
rotate(String1[,#ofRotations]) ⇒ string
Returns a copy of String1 rotated right or
left by #ofRotations characters. Does not
alter String1.
If #ofRotations is positive, the rotation is to
the left. If #ofRotations is negative, the
rotation is to the right. The default is −1
(rotate right one character).
Alphabetical Listing
151
round()
round(Expr1[, digits]) ⇒ expression
Catalog >
Returns the argument rounded to the
specified number of digits after the decimal
point.
digits must be an integer in the range 0–
12. If digits is not included, returns the
argument rounded to 12 significant digits.
Note: Display digits mode may affect how
this is displayed.
round(List1[, digits]) ⇒ list
Returns a list of the elements rounded to
the specified number of digits.
round(Matrix1[, digits]) ⇒ matrix
Returns a matrix of the elements rounded
to the specified number of digits.
rowAdd()
rowAdd(Matrix1, rIndex1, rIndex2) ⇒
matrix
Catalog >
Returns a copy of Matrix1 with row
rIndex2 replaced by the sum of rows
rIndex1 and rIndex2.
rowDim()
rowDim(Matrix ) ⇒ expression
Catalog >
Returns the number of rows in Matrix .
Note: See also colDim() , page 30.
rowNorm()
rowNorm(Matrix ) ⇒ expression
Returns the maximum of the sums of the
absolute values of the elements in the rows
in Matrix .
Note: All matrix elements must simplify to
numbers. See also colNorm() , page 30.
152
Alphabetical Listing
Catalog >
Catalog >
rowSwap()
rowSwap(Matrix1, rIndex1, rIndex2) ⇒
matrix
Returns Matrix1 with rows rIndex1 and
rIndex2 exchanged.
Catalog >
rref()
rref(Matrix1[, Tol ]) ⇒ matrix
Returns the reduced row echelon form of
Matrix1.
Optionally, any matrix element is treated as
zero if its absolute value is less than Tol .
This tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise, Tol is ignored.
•
•
If you use /· or set the Auto or
Approximate mode to Approximate,
computations are done using floatingpoint arithmetic.
If Tol is omitted or not used, the default
tolerance is calculated as:
5E −14 •max(dim(Matrix1)) •rowNorm
(Matrix1)
Note: See also ref() , page 145.
S
sec()
sec(Expr1) ⇒ expression
µ key
In Degree angle mode:
sec(List1) ⇒ list
Returns the secant of Expr1 or returns a
list containing the secants of all elements
in List1.
Alphabetical Listing
153
µ key
sec()
Note: The argument is interpreted as a
degree, gradian or radian angle, according
to the current angle mode setting. You can
use °, G, or r to override the angle mode
temporarily.
sec ⁻¹()
sec⁻¹(Expr1) ⇒ expression
µ key
In Degree angle mode:
sec⁻¹(List1) ⇒ list
Returns the angle whose secant is Expr1 or
returns a list containing the inverse secants
of each element of List1.
In Gradian angle mode:
Note: The result is returned as a degree,
gradian, or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arcsec(...).
sech()
sech(Expr1) ⇒ expression
Catalog >
sech(List1) ⇒ list
Returns the hyperbolic secant of Expr1 or
returns a list containing the hyperbolic
secants of the List1 elements.
sech⁻¹()
sech⁻¹(Expr1) ⇒ expression
sech⁻¹(List1) ⇒ list
Returns the inverse hyperbolic secant of
Expr1 or returns a list containing the
inverse hyperbolic secants of each element
of List1.
Note: You can insert this function from the
keyboard by typing arcsech(...).
154
Alphabetical Listing
Catalog >
In Radian angle and Rectangular complex
mode:
Send
Send exprOrString1 [, exprOrString2] ...
Programming command: Sends one or
more TI-Innovator™ Hub commands to a
connected hub.
exprOrString must be a valid TI-Innovator™
Hub Command. Typically, exprOrString
contains a "SET ..." command to control a
device or a "READ ..." command to request
data.
Hub Menu
Example: Turn on the blue element of the
built-in RGB LED for 0.5 seconds.
Example: Request the current value of the
hub's built-in light-level sensor. A Get
command retrieves the value and assigns it
to variable lightval.
The arguments are sent to the hub in
succession.
Note: You can use the Send command
within a user-defined program but not
within a function.
Note: See also Get (page 80), GetStr (page
83), and eval() (page 64).
seq()
seq(Expr, Var, Low, High[, Step]) ⇒ list
Example: Send a calculated frequency to the
hub's built-in speaker. Use special variable
iostr.SendAns to show the hub command
with the expression evaluated.
Catalog >
Increments Var from Low through High by
an increment of Step, evaluates Expr, and
returns the results as a list. The original
contents of Var are still there after seq() is
completed.
The default value for Step = 1.
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
.
Alphabetical Listing
155
seqGen()
seqGen(Expr, Var, depVar, {Var0,
VarMax }[, ListOfInitTerms
[, VarStep[, CeilingValue ]]]) ⇒ list
Generates a list of terms for sequence
depVar(Var)=Expr as follows: Increments
independent variable Var from Var0
through VarMax by VarStep, evaluates
depVar(Var) for corresponding values of
Var using the Expr formula and
ListOfInitTerms, and returns the results as
a list.
Catalog >
Generate the first 5 terms of the sequence u
(n ) = u (n -1)2/2, with u (1)=2 and VarStep =1.
Example in which Var0=2:
seqGen(ListOrSystemOfExpr, Var,
ListOfDepVars, {Var0, VarMax } [
, MatrixOfInitTerms[, VarStep[,
CeilingValue ]]]) ⇒ matrix
Generates a matrix of terms for a system
(or list) of sequences ListOfDepVars
( Var)=ListOrSystemOfExpr as follows:
Increments independent variable Var from
Var0 through VarMax by VarStep,
evaluates ListOfDepVars( Var) for
corresponding values of Var using
ListOrSystemOfExpr formula and
MatrixOfInitTerms, and returns the results
as a matrix.
Example in which initial term is symbolic:
System of two sequences:
The original contents of Var are unchanged
after seqGen() is completed.
The default value for VarStep = 1.
Note: The Void (_) in the initial term matrix
above is used to indicate that the initial term
for u1(n) is calculated using the explicit
sequence formula u1(n)=1/n.
seqn()
seqn(Expr(u, n[, ListOfInitTerms[, nMax [,
CeilingValue ]]]) ⇒ list
156
Alphabetical Listing
Catalog >
Generate the first 6 terms of the sequence u
(n ) = u (n -1)/2, with u (1)=2.
seqn()
Catalog >
Generates a list of terms for a sequence u
( n)=Expr( u, n) as follows: Increments n
from 1 through nMax by 1, evaluates u( n)
for corresponding values of n using the
Expr(u, n) formula and ListOfInitTerms,
and returns the results as a list.
seqn(Expr(n[, nMax [, CeilingValue ]]) ⇒
list
Generates a list of terms for a nonrecursive sequence u( n)=Expr( n) as
follows: Increments n from 1 through nMax
by 1, evaluates u( n) for corresponding
values of n using the Expr( n) formula, and
returns the results as a list.
If nMax is missing, nMax is set to 2500
If nMax =0, nMax is set to 2500
Note: seqn() calls seqGen( ) with n0=1 and
nstep =1
series()
series(Expr1, Var, Order[, Point ]) ⇒
expression
Catalog >
series(Expr1, Var, Order[, Point ]) |
Var>Point ⇒ expression
series(Expr1, Var, Order[, Point ]) |
Var<Point ⇒ expression
Returns a generalized truncated power
series representation of Expr1 expanded
about Point through degree Order. Order
can be any rational number. The resulting
powers of ( Var − Point ) can include
negative and/or fractional exponents. The
coefficients of these powers can include
logarithms of ( Var − Point ) and other
functions of Var that are dominated by all
powers of ( Var − Point ) having the same
exponent sign.
Alphabetical Listing
157
series()
Point defaults to 0. Point can be ∞ or −∞,
Catalog >
in which cases the expansion is through
degree Order in 1/( Var − Point ).
series(...) returns “series(...) ” if it is unable
to determine such a representation, such as
for essential singularities such as sin(1/z)
at z=0, e−1/z at z=0, or ez at z = ∞ or −∞.
If the series or one of its derivatives has a
jump discontinuity at Point , the result is
likely to contain sub-expressions of the
form sign(…) or abs(…) for a real expansion
variable or (-1) floor(…angle(…)…) for a complex
expansion variable, which is one ending
with “_”. If you intend to use the series only
for values on one side of Point , then
append the appropriate one of “| Var >
Point ”, “| Var < Point ”, “| “Var ≥ Point ”,
or “Var ≤ Point ” to obtain a simpler result.
series() can provide symbolic
approximations to indefinite integrals and
definite integrals for which symbolic
solutions otherwise can't be obtained.
series() distributes over 1st-argument lists
and matrices.
series() is a generalized version of taylor() .
As illustrated by the last example to the
right, the display routines downstream of
the result produced by series(...) might
rearrange terms so that the dominant term
is not the leftmost one.
Note: See also dominantTerm() , page 58.
setMode()
setMode(modeNameInteger,
settingInteger) ⇒ integer
setMode(list ) ⇒ integer list
Valid only within a function or program.
158
Alphabetical Listing
Catalog >
Display approximate value of π using the
default setting for Display Digits, and then
display π with a setting of Fix2. Check to see
that the default is restored after the
program executes.
setMode()
setMode( modeNameInteger,
settingInteger) temporarily sets mode
modeNameInteger to the new setting
settingInteger, and returns an integer
Catalog >
corresponding to the original setting of that
mode. The change is limited to the duration
of the program/function’s execution.
modeNameInteger specifies which mode
you want to set. It must be one of the mode
integers from the table below.
settingInteger specifies the new setting for
the mode. It must be one of the setting
integers listed below for the specific mode
you are setting.
setMode( list ) lets you change multiple
settings. list contains pairs of mode
integers and setting integers. setMode( list )
returns a similar list whose integer pairs
represent the original modes and settings.
If you have saved all mode settings with
getMode(0) →var, you can use setMode
( var) to restore those settings until the
function or program exits. See getMode() ,
page 82.
Note: The current mode settings are passed
to called subroutines. If any subroutine
changes a mode setting, the mode change
will be lost when control returns to the
calling routine.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Mode
Name
Mode
Integer
Display
Digits
1
Setting Integers
1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5,
7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10,
12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2,
17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8,
23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12
Alphabetical Listing
159
Mode
Name
Mode
Integer
Setting Integers
Angle
2
1=Radian, 2=Degree, 3=Gradian
Exponential
Format
3
1=Normal, 2=Scientific, 3=Engineering
Real or
Complex
4
1=Real, 2=Rectangular, 3=Polar
Auto or
Approx.
5
1=Auto, 2=Approximate, 3=Exact
Vector
Format
6
1=Rectangular, 2=Cylindrical, 3=Spherical
Base
7
1=Decimal, 2=Hex, 3=Binary
Unit
system
8
1=SI, 2=Eng/US
shift()
shift(Integer1[,#ofShifts]) ⇒ integer
Shifts the bits in a binary integer. You can
enter Integer1 in any number base; it is
converted automatically to a signed, 64-bit
binary form. If the magnitude of Integer1 is
too large for this form, a symmetric modulo
operation brings it within the range. For
more information, see ►Base2, page 21.
If #ofShifts is positive, the shift is to the
left. If #ofShifts is negative, the shift is to
the right. The default is −1 (shift right one
bit).
In a right shift, the rightmost bit is dropped
and 0 or 1 is inserted to match the leftmost
bit. In a left shift, the leftmost bit is
dropped and 0 is inserted as the rightmost
bit.
For example, in a right shift:
Each bit shifts right.
0b0000000000000111101011000011010
Inserts 0 if leftmost bit is 0,
or 1 if leftmost bit is 1.
produces:
160
Alphabetical Listing
Catalog >
In Bin base mode:
In Hex base mode:
Important: To enter a binary or
hexadecimal number, always use the 0b or
0h prefix (zero, not the letter O).
Catalog >
shift()
0b00000000000000111101011000011010
The result is displayed according to the
Base mode. Leading zeros are not shown.
shift(List1[,#ofShifts]) ⇒ list
In Dec base mode:
Returns a copy of List1 shifted right or left
by #ofShifts elements. Does not alter List1.
If #ofShifts is positive, the shift is to the
left. If #ofShifts is negative, the shift is to
the right. The default is −1 (shift right one
element).
Elements introduced at the beginning or
end of list by the shift are set to the symbol
“undef”.
shift(String1[,#ofShifts]) ⇒ string
Returns a copy of String1 shifted right or
left by #ofShifts characters. Does not alter
String1.
If #ofShifts is positive, the shift is to the
left. If #ofShifts is negative, the shift is to
the right. The default is −1 (shift right one
character).
Characters introduced at the beginning or
end of string by the shift are set to a space.
sign()
sign(Expr1) ⇒ expression
Catalog >
sign(List1) ⇒ list
sign(Matrix1) ⇒ matrix
For real and complex Expr1, returns
Expr1/abs( Expr1) when Expr1≠ 0.
If complex format mode is Real:
Returns 1 if Expr1 is positive. Returns −1 if
Expr1is negative.
sign(0) represents the unit circle in the
complex domain.
For a list or matrix, returns the signs of all
the elements.
Alphabetical Listing
161
simult()
simult(coeffMatrix , constVector[, Tol ]) ⇒
matrix
Returns a column vector that contains the
solutions to a system of linear equations.
Catalog >
Solve for x and y:
x + 2y = 1
3x + 4y = −1
Note: See also linSolve() , page 100.
coeffMatrix must be a square matrix that
contains the coefficients of the equations.
The solution is x=−3 and y=2.
constVector must have the same number
of rows (same dimension) as coeffMatrix
and contain the constants.
Solve:
ax + by = 1
cx + dy = 2
Optionally, any matrix element is treated as
zero if its absolute value is less than Tol .
This tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise, Tol is ignored.
•
•
If you set the Auto or Approximate mode
to Approximate, computations are done
using floating-point arithmetic.
If Tol is omitted or not used, the default
tolerance is calculated as:
5E −14 •max(dim(coeffMatrix ))
•rowNorm(coeffMatrix )
simult(coeffMatrix , constMatrix [, Tol ]) ⇒
matrix
Solves multiple systems of linear equations,
where each system has the same equation
coefficients but different constants.
Each column in constMatrix must contain
the constants for a system of equations.
Each column in the resulting matrix
contains the solution for the corresponding
system.
►sin
Expr►sin
Note: You can insert this operator from the
computer keyboard by typing @>sin.
162
Alphabetical Listing
Solve:
x + 2y = 1
3x + 4y = −1
x + 2y = 2
3x + 4y = −3
For the first system, x=−3 and y=2. For the
second system, x=−7 and y=9/2.
Catalog >
Catalog >
►sin
Represents Expr in terms of sine. This is a
display conversion operator. It can be used
only at the end of the entry line.
►sin reduces all powers of
cos(...) modulo 1−sin(...)^2
so that any remaining powers of sin(...)
have exponents in the range (0, 2). Thus,
the result will be free of cos(...) if and only
if cos(...) occurs in the given expression only
to even powers.
Note: This conversion operator is not
supported in Degree or Gradian Angle
modes. Before using it, make sure that the
Angle mode is set to Radians and that Expr
does not contain explicit references to
degree or gradian angles.
sin()
sin(Expr1) ⇒ expression
µ key
In Degree angle mode:
sin(List1) ⇒ list
sin( Expr1) returns the sine of the argument
as an expression.
sin( List1) returns a list of the sines of all
elements in List1.
Note: The argument is interpreted as a
degree, gradian or radian angle, according
to the current angle mode. You can use °, g,
or r to override the angle mode setting
temporarily.
In Gradian angle mode:
In Radian angle mode:
sin(squareMatrix1) ⇒ squareMatrix
In Radian angle mode:
Alphabetical Listing
163
µ key
sin()
Returns the matrix sine of squareMatrix1.
This is not the same as calculating the sine
of each element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
sin⁻¹()
sin⁻¹(Expr1) ⇒ expression
µ key
In Degree angle mode:
sin⁻¹(List1) ⇒ list
sin⁻¹( Expr1) returns the angle whose sine
is Expr1 as an expression.
In Gradian angle mode:
sin⁻¹( List1) returns a list of the inverse
sines of each element of List1.
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arcsin(...).
sin⁻¹(squareMatrix1) ⇒ squareMatrix
Returns the matrix inverse sine of
squareMatrix1. This is not the same as
calculating the inverse sine of each
element. For information about the
calculation method, refer to cos() .
In Radian angle mode and Rectangular
complex format mode:
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
sinh()
sinh(Expr1) ⇒ expression
sinh(List1) ⇒ list
sinh ( Expr1) returns the hyperbolic sine of
the argument as an expression.
164
Alphabetical Listing
Catalog >
sinh()
sinh ( List1) returns a list of the hyperbolic
sines of each element of List1.
sinh(squareMatrix1) ⇒ squareMatrix
Catalog >
In Radian angle mode:
Returns the matrix hyperbolic sine of
squareMatrix1. This is not the same as
calculating the hyperbolic sine of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
sinh⁻¹()
sinh⁻¹(Expr1) ⇒ expression
Catalog >
sinh⁻¹(List1) ⇒ list
sinh⁻¹( Expr1) returns the inverse hyperbolic
sine of the argument as an expression.
sinh⁻¹( List1) returns a list of the inverse
hyperbolic sines of each element of List1.
Note: You can insert this function from the
keyboard by typing arcsinh(...).
sinh⁻¹(squareMatrix1) ⇒ squareMatrix
In Radian angle mode:
Returns the matrix inverse hyperbolic sine
of squareMatrix1. This is not the same as
calculating the inverse hyperbolic sine of
each element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
SinReg
Catalog >
SinReg X, Y[, [Iterations],[Period][,
Category , Include ]]
Computes the sinusoidal regression on lists
X and Y. A summary of results is stored in
the stat.results variable. (See page 172.)
Alphabetical Listing
165
Catalog >
SinReg
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Iterations is a value that specifies the
maximum number of times (1 through 16) a
solution will be attempted. If omitted, 8 is
used. Typically, larger values result in better
accuracy but longer execution times, and
vice versa.
Period specifies an estimated period. If
omitted, the difference between values in X
should be equal and in sequential order. If
you specify Period, the differences between
x values can be unequal.
Category is a list of category codes for the
corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
The output of SinReg is always in radians,
regardless of the angle mode setting.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output
variable
Description
stat.RegEqn
Regression Equation: a•sin(bx+c)+d
stat.a, stat.b,
stat.c, stat.d
Regression coefficients
stat.Resid
Residuals from the regression
stat.XReg
List of data points in the modified X List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.YReg
List of data points in the modified Y List actually used in the regression based on
restrictions of Freq , Category List, and Include Categories
stat.FreqReg
List of frequencies corresponding to stat.XReg and stat.YReg
166
Alphabetical Listing
Catalog >
solve()
solve(Equation, Var) ⇒ Boolean
expression
solve(Equation, Var=Guess) ⇒ Boolean
expression
solve(Inequality , Var) ⇒ Boolean
expression
Returns candidate real solutions of an
equation or an inequality for Var. The goal
is to return candidates for all solutions.
However, there might be equations or
inequalities for which the number of
solutions is infinite.
Solution candidates might not be real finite
solutions for some combinations of values
for undefined variables.
For the Auto setting of the Auto or
Approximate mode, the goal is to produce
exact solutions when they are concise, and
supplemented by iterative searches with
approximate arithmetic when exact
solutions are impractical.
Due to default cancellation of the greatest
common divisor from the numerator and
denominator of ratios, solutions might be
solutions only in the limit from one or both
sides.
For inequalities of types ≥, ≤, <, or >,
explicit solutions are unlikely unless the
inequality is linear and contains only Var.
For the Exact mode, portions that cannot be
solved are returned as an implicit equation
or inequality.
Use the constraint (“|”) operator to restrict
the solution interval and/or other variables
that occur in the equation or inequality.
When you find a solution in one interval,
you can use the inequality operators to
exclude that interval from subsequent
searches.
In Radian angle mode:
Alphabetical Listing
167
Catalog >
solve()
false is returned when no real solutions are
found. true is returned if solve() can
determine that any finite real value of Var
satisfies the equation or inequality.
Since solve() always returns a Boolean
result, you can use “and,” “or,” and “not” to
combine results from solve() with each
other or with other Boolean expressions.
Solutions might contain a unique new
undefined constant of the form nj with j
being an integer in the interval 1–255. Such
variables designate an arbitrary integer.
In Real mode, fractional powers having odd
denominators denote only the real branch.
Otherwise, multiple branched expressions
such as fractional powers, logarithms, and
inverse trigonometric functions denote only
the principal branch. Consequently, solve()
produces only solutions corresponding to
that one real or principal branch.
Note: See also cSolve() , cZeros() , nSolve() ,
and zeros() .
solve(Eqn1 and Eqn2[and …],
VarOrGuess1, VarOrGuess2[, …])
⇒ Boolean expression
solve(SystemOfEqns, VarOrGuess1,
VarOrGuess2[, …])
⇒ Boolean expression
solve({Eqn1, Eqn2 [,...]}
{VarOrGuess1,VarOrGuess2 [, … ]})
⇒ Boolean expression
Returns candidate real solutions to the
simultaneous algebraic equations, where
each VarOrGuess specifies a variable that
you want to solve for.
168
Alphabetical Listing
In Radian angle mode:
solve()
Catalog >
You can separate the equations with the
and operator, or you can enter a
SystemOfEqns using a template from the
Catalog. The number of VarOrGuess
arguments must match the number of
equations. Optionally, you can specify an
initial guess for a variable. Each
VarOrGuess must have the form:
variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3.
If all of the equations are polynomials and
if you do NOT specify any initial guesses,
solve() uses the lexical Gröbner/Buchberger
elimination method to attempt to
determine all real solutions.
For example, suppose you have a circle of
radius r at the origin and another circle of
radius r centered where the first circle
crosses the positive x-axis. Use solve() to
find the intersections.
As illustrated by r in the example to the
right, simultaneous polynomial equations
can have extra variables that have no
values, but represent given numeric values
that could be substituted later.
You can also (or instead) include solution
variables that do not appear in the
equations. For example, you can include z
as a solution variable to extend the previous
example to two parallel intersecting
cylinders of radius r.
The cylinder solutions illustrate how
families of solutions might contain arbitrary
constants of the form ck , where k is an
integer suffix from 1 through 255.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Alphabetical Listing
169
solve()
Catalog >
For polynomial systems, computation time
or memory exhaustion may depend strongly
on the order in which you list solution
variables. If your initial choice exhausts
memory or your patience, try rearranging
the variables in the equations and/or
varOrGuess list.
If you do not include any guesses and if any
equation is non-polynomial in any variable
but all equations are linear in the solution
variables, solve() uses Gaussian elimination
to attempt to determine all real solutions.
If a system is neither polynomial in all of its
variables nor linear in its solution variables,
solve() determines at most one solution
using an approximate iterative method. To
do so, the number of solution variables
must equal the number of equations, and
all other variables in the equations must
simplify to numbers.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Each solution variable starts at its guessed
value if there is one; otherwise, it starts at
0.0.
Use guesses to seek additional solutions
one by one. For convergence, a guess may
have to be rather close to a solution.
SortA
SortA List1[, List2] [, List3]...
SortA Vector1[, Vector2] [, Vector3]...
Sorts the elements of the first argument in
ascending order.
If you include additional arguments, sorts
the elements of each so that their new
positions match the new positions of the
elements in the first argument.
All arguments must be names of lists or
vectors. All arguments must have equal
dimensions.
170
Alphabetical Listing
Catalog >
Catalog >
SortA
Empty (void) elements within the first
argument move to the bottom. For more
information on empty elements, see page
232.
Catalog >
SortD
SortD List1[, List2][, List3]...
SortD Vector1[,Vector2][,Vector3]...
Identical to SortA, except SortD sorts the
elements in descending order.
Empty (void) elements within the first
argument move to the bottom. For more
information on empty elements, see page
232.
Catalog >
►Sphere
Vector►Sphere
Note: To force an approximate result,
Note: You can insert this operator from the
computer keyboard by typing @>Sphere.
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
Displays the row or column vector in
spherical form [ρ∠ θ∠ φ].
.
Vector must be of dimension 3 and can be
either a row or a column vector.
Note: ►Sphere is a display-format
instruction, not a conversion function. You
can use it only at the end of an entry line.
Press
·
Alphabetical Listing
171
►Sphere
Catalog >
sqrt()
sqrt(Expr1) ⇒ expression
Catalog >
sqrt(List1) ⇒ list
Returns the square root of the argument.
For a list, returns the square roots of all the
elements in List1.
Note: See also Square root template, page
5.
stat.results
stat.results
Displays results from a statistics
calculation.
The results are displayed as a set of namevalue pairs. The specific names shown are
dependent on the most recently evaluated
statistics function or command.
You can copy a name or value and paste it
into other locations.
Note: Avoid defining variables that use the
same names as those used for statistical
analysis. In some cases, an error condition
could occur. Variable names used for
statistical analysis are listed in the table
below.
172
Alphabetical Listing
Catalog >
stat.a
stat.AdjR²
stat.b
stat.b0
stat.b1
stat.b2
stat.b3
stat.b4
stat.b5
stat.b6
stat.b7
stat.b8
stat.b9
stat.b10
stat.bList
stat.χ²
stat.c
stat.CLower
stat.CLowerList
stat.CompList
stat.CompMatrix
stat.CookDist
stat.CUpper
stat.CUpperList
stat.d
stat.dfDenom
stat.dfBlock
stat.dfCol
stat.dfError
stat.dfInteract
stat.dfReg
stat.dfNumer
stat.dfRow
stat.DW
stat.e
stat.ExpMatrix
stat.F
stat.FBlock
stat.Fcol
stat.FInteract
stat.FreqReg
stat.Frow
stat.Leverage
stat.LowerPred
stat.LowerVal
stat.m
stat.MaxX
stat.MaxY
stat.ME
stat.MedianX
stat.MedianY
stat.MEPred
stat.MinX
stat.MinY
stat.MS
stat.MSBlock
stat.MSCol
stat.MSError
stat.MSInteract
stat.MSReg
stat.MSRow
stat.n
Stat.Ç
stat.Ç1
stat.Ç2
stat.ÇDiff
stat.PList
stat.PVal
stat.PValBlock
stat.PValCol
stat.PValInteract
stat.PValRow
stat.Q1X
stat.Q1Y
stat.Q3X
stat.Q3Y
stat.r
stat.r²
stat.RegEqn
stat.Resid
stat.ResidTrans
stat.σx
stat.σy
stat.σx1
stat.σx2
stat.Σx
stat.Σx²
stat.Σxy
stat.Σy
stat.Σy²
stat.s
stat.SE
stat.SEList
stat.SEPred
stat.sResid
stat.SEslope
stat.sp
stat.SS
stat.SSBlock
stat.SSCol
stat.SSX
stat.SSY
stat.SSError
stat.SSInteract
stat.SSReg
stat.SSRow
stat.tList
stat.UpperPred
stat.UpperVal
stat.v
stat.v 1
stat.v 2
stat.v Diff
stat.v List
stat.XReg
stat.XVal
stat.XValList
stat.w
stat.y
stat.yList
stat.YReg
Note: Each time the Lists & Spreadsheet application calculates statistical results, it
copies the “stat.” group variables to a “stat#.” group, where # is a number that is
incremented automatically. This lets you maintain previous results while
performing multiple calculations.
stat.values
stat.values
Catalog >
See the stat.results example.
Displays a matrix of the values calculated for
the most recently evaluated statistics
function or command.
Unlike stat.results , stat.values omits the
names associated with the values.
You can copy a value and paste it into other
locations.
Alphabetical Listing
173
stDevPop()
stDevPop(List [, freqList ]) ⇒ expression
Catalog >
In Radian angle and auto modes:
Returns the population standard deviation
of the elements in List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
Note:List must have at least two elements.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
stDevPop(Matrix1[, freqMatrix ]) ⇒
matrix
Returns a row vector of the population
standard deviations of the columns in
Matrix1.
Each freqMatrix element counts the
number of consecutive occurrences of the
corresponding element in Matrix1.
Note:Matrix1must have at least two rows.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
stDevSamp()
stDevSamp(List [, freqList ]) ⇒ expression
Returns the sample standard deviation of
the elements in List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
Note:List must have at least two elements.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
174
Alphabetical Listing
Catalog >
stDevSamp()
stDevSamp(Matrix1[, freqMatrix ]) ⇒
matrix
Catalog >
Returns a row vector of the sample
standard deviations of the columns in
Matrix1.
Each freqMatrix element counts the
number of consecutive occurrences of the
corresponding element in Matrix1.
Note:Matrix1must have at least two rows.
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
Stop
Catalog >
Stop
Programming command: Terminates the
program.
Stop is not allowed in functions.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
Store
string()
string(Expr) ⇒ string
See →(store), page 229.
Catalog >
Simplifies Expr and returns the result as a
character string.
Alphabetical Listing
175
subMat()
subMat(Matrix1[, startRow][, startCol ][,
endRow][, endCol ]) ⇒ matrix
Catalog >
Returns the specified submatrix of Matrix1.
Defaults: startRow=1, startCol =1,
endRow=last row, endCol =last column.
Sum (Sigma)
sum()
sum(List [, Start [, End]]) ⇒ expression
See Σ(), page 220.
Catalog >
Returns the sum of all elements in List .
Start and End are optional. They specify a
range of elements.
Any void argument produces a void result.
Empty (void) elements in List are ignored.
For more information on empty elements,
see page 232.
sum(Matrix1[, Start [, End]]) ⇒ matrix
Returns a row vector containing the sums
of all elements in the columns in Matrix1.
Start and End are optional. They specify a
range of rows.
Any void argument produces a void result.
Empty (void) elements in Matrix1 are
ignored. For more information on empty
elements, see page 232.
sumIf()
sumIf(List ,Criteria[, SumList ]) ⇒ value
Returns the accumulated sum of all
elements in List that meet the specified
Criteria. Optionally, you can specify an
alternate list, sumList , to supply the
elements to accumulate.
176
Alphabetical Listing
Catalog >
sumIf()
List can be an expression, list, or matrix.
SumList , if specified, must have the same
dimension(s) as List .
Catalog >
Criteria can be:
•
•
A value, expression, or string. For
example, 34 accumulates only those
elements in List that simplify to the
value 34.
A Boolean expression containing the
symbol ? as a placeholder for each
element. For example, ?<10 accumulates
only those elements in List that are less
than 10.
When a List element meets the Criteria,
the element is added to the accumulating
sum. If you include sumList , the
corresponding element from sumList is
added to the sum instead.
Within the Lists & Spreadsheet application,
you can use a range of cells in place of List
and sumList .
Empty (void) elements are ignored. For
more information on empty elements, see
page 232.
Note: See also countIf() , page 39.
sumSeq()
system()
system(Eqn1[, Eqn2[, Eqn3[, ...]]])
See Σ(), page 220.
Catalog >
system(Expr1[, Expr2[, Expr3[, ...]]])
Returns a system of equations, formatted
as a list. You can also create a system by
using a template.
Note: See also System of equations , page 7.
Alphabetical Listing
177
T
Catalog >
T (transpose)
Matrix1T ⇒ matrix
Returns the complex conjugate transpose of
Matrix1.
Note: You can insert this operator from the
computer keyboard by typing @t.
tan()
tan(Expr1) ⇒ expression
µ key
In Degree angle mode:
tan(List1) ⇒ list
tan( Expr1) returns the tangent of the
argument as an expression.
tan( List1) returns a list of the tangents of
all elements in List1.
Note: The argument is interpreted as a
In Gradian angle mode:
degree, gradian or radian angle, according
to the current angle mode. You can use °, g
or r to override the angle mode setting
temporarily.
In Radian angle mode:
tan(squareMatrix1) ⇒ squareMatrix
Returns the matrix tangent of
squareMatrix1. This is not the same as
calculating the tangent of each element.
For information about the calculation
method, refer to cos() .
178
Alphabetical Listing
In Radian angle mode:
µ key
tan()
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
tan⁻¹()
tan⁻¹(Expr1) ⇒ expression
µ key
In Degree angle mode:
tan⁻¹(List1) ⇒ list
tan⁻¹( Expr1) returns the angle whose
tangent is Expr1 as an expression.
In Gradian angle mode:
tan⁻¹( List1) returns a list of the inverse
tangents of each element of List1.
Note: The result is returned as a degree,
gradian or radian angle, according to the
current angle mode setting.
In Radian angle mode:
Note: You can insert this function from the
keyboard by typing arctan(...).
tan⁻¹(squareMatrix1) ⇒ squareMatrix
In Radian angle mode:
Returns the matrix inverse tangent of
squareMatrix1. This is not the same as
calculating the inverse tangent of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
tangentLine()
tangentLine(Expr1,Var,Point ) ⇒
expression
Catalog >
tangentLine(Expr1,Var=Point ) ⇒
expression
Returns the tangent line to the curve
represented by Expr1 at the point specified
in Var=Point .
Alphabetical Listing
179
Catalog >
tangentLine()
Make sure that the independent variable is
not defined. For example, If f1(x):=5 and
x:=3, then tangentLine( f1(x),x,2) returns
“false.”
Catalog >
tanh()
tanh(Expr1) ⇒ expression
tanh(List1) ⇒ list
tanh( Expr1) returns the hyperbolic tangent
of the argument as an expression.
tanh( List1) returns a list of the hyperbolic
tangents of each element of List1.
tanh(squareMatrix1) ⇒ squareMatrix
In Radian angle mode:
Returns the matrix hyperbolic tangent of
squareMatrix1. This is not the same as
calculating the hyperbolic tangent of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
tanh⁻¹()
tanh⁻¹(Expr1) ⇒ expression
Catalog >
In Rectangular complex format:
tanh⁻¹(List1) ⇒ list
tanh⁻¹( Expr1) returns the inverse
hyperbolic tangent of the argument as an
expression.
tanh⁻¹( List1) returns a list of the inverse
hyperbolic tangents of each element of
List1.
Note: You can insert this function from the
keyboard by typing arctanh(...).
tanh⁻¹(squareMatrix1) ⇒ squareMatrix
180
Alphabetical Listing
In Radian angle mode and Rectangular
complex format:
tanh⁻¹()
Catalog >
Returns the matrix inverse hyperbolic
tangent of squareMatrix1. This is not the
same as calculating the inverse hyperbolic
tangent of each element. For information
about the calculation method, refer to cos
() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
taylor()
taylor(Expr1, Var, Order[, Point ]) ⇒
expression
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
Catalog >
Returns the requested Taylor polynomial.
The polynomial includes non-zero terms of
integer degrees from zero through Order in
( Var minus Point ). taylor() returns itself if
there is no truncated power series of this
order, or if it would require negative or
fractional exponents. Use substitution
and/or temporary multiplication by a power
of ( Var minus Point ) to determine more
general power series.
Point defaults to zero and is the expansion
point.
tCdf()
tCdf(lowBound,upBound,df ) ⇒ number if
lowBound and upBound are numbers, list if
lowBound and upBound are lists
Catalog >
Computes the Student-t distribution
probability between lowBound and upBound
for the specified degrees of freedom df .
For P(X ≤ upBound), set lowBound = ⁻∞.
Alphabetical Listing
181
tCollect()
tCollect(Expr1) ⇒ expression
Catalog >
Returns an expression in which products
and integer powers of sines and cosines are
converted to a linear combination of sines
and cosines of multiple angles, angle sums,
and angle differences. The transformation
converts trigonometric polynomials into a
linear combination of their harmonics.
Sometimes tCollect() will accomplish your
goals when the default trigonometric
simplification does not. tCollect() tends to
reverse transformations done by tExpand() .
Sometimes applying tExpand() to a result
from tCollect() , or vice versa, in two
separate steps simplifies an expression.
tExpand()
tExpand(Expr1) ⇒ expression
Returns an expression in which sines and
cosines of integer-multiple angles, angle
sums, and angle differences are expanded.
Because of the identity (sin(x))2+(cos
(x))2=1, there are many possible equivalent
results. Consequently, a result might differ
from a result shown in other publications.
Sometimes tExpand() will accomplish your
goals when the default trigonometric
simplification does not. tExpand() tends to
reverse transformations done by tCollect() .
Sometimes applying tCollect() to a result
from tExpand() , or vice versa, in two
separate steps simplifies an expression.
Note: Degree-mode scaling by π/180
interferes with the ability of tExpand() to
recognize expandable forms. For best
results, tExpand() should be used in Radian
mode.
182
Alphabetical Listing
Catalog >
Text
TextpromptString[, DispFlag]
Programming command: Pauses the
program and displays the character string
promptString in a dialog box.
When the user selects OK, program
execution continues.
Catalog >
Define a program that pauses to display
each of five random numbers in a dialog
box.
Within the Prgm...EndPrgm template,
complete each line by pressing @ instead
of ·. On the computer keyboard, hold
down Alt and press Enter .
The optional flag argument can be any
expression.
•
•
If DispFlag is omitted or evaluates to 1,
the text message is added to the
Calculator history.
If DispFlag evaluates to 0, the text
message is not added to the history.
If the program needs a typed response from
the user, refer to Request, page 146, or
RequestStr, page 147.
Define text_demo()=Prgm
For i,1,5
strinfo:=”Random number “ &
string(rand(i))
Text strinfo
EndFor
EndPrgm
Run the program:
text_demo()
Note: You can use this command within a
user-defined program but not within a
function.
Then
tInterval
tInterval List [, Freq[, CLevel ]]
Sample of one dialog box:
See If, page 86.
Catalog >
(Data list input)
tInterval v, sx , n[, CLevel ]
(Summary stats input)
Computes a t confidence interval. A
summary of results is stored in the
stat.results variable. (See page 172.)
Alphabetical Listing
183
Catalog >
tInterval
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower, stat.CUpper
Confidence interval for an unknown population mean
stat. v
Sample mean of the data sequence from the normal random distribution
stat.ME
Margin of error
stat.df
Degrees of freedom
stat. σx
Sample standard deviation
stat.n
Length of the data sequence with sample mean
tInterval_2Samp
tInterval_2Samp List1,List2[,Freq1[,Freq2
[,CLevel [,Pooled]]]]
Catalog >
(Data list input)
tInterval_2Samp v 1,sx1,n1,v 2,sx2,n2
[,CLevel [,Pooled]]
(Summary stats input)
Computes a two-sample t confidence
interval. A summary of results is stored in
the stat.results variable. (See page 172.)
Pooled=1 pools variances; Pooled=0 does
not pool variances.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower,
stat.CUpper
Confidence interval containing confidence level probability of distribution
stat. v1-v2
Sample means of the data sequences from the normal random
distribution
stat.ME
Margin of error
stat.df
Degrees of freedom
184
Alphabetical Listing
Output variable
Description
stat. v1, stat. v2
Sample means of the data sequences from the normal random
distribution
stat. σx1, stat. σx2
Sample standard deviations for List 1 and List 2
stat.n1, stat.n2
Number of samples in data sequences
stat.sp
The pooled standard deviation. Calculated when Pooled = YES
tmpCnv()
tmpCnv(Expr_°tempUnit , _°tempUnit2)
⇒ expression _°tempUnit2
Catalog >
Converts a temperature value specified by
Expr from one unit to another. Valid
temperature units are:
_°C Celsius
_°F Fahrenheit
_°K Kelvin
_°R Rankine
Note: You can use the Catalog to select
temperature units.
To type °, select it from the Catalog
symbols.
to type _ , press /_.
For example, 100_°C converts to 212_°F.
To convert a temperature range, use
ΔtmpCnv() instead.
ΔtmpCnv()
Catalog >
ΔtmpCnv(Expr_°tempUnit , _°tempUnit2)
⇒ expression _°tempUnit2
Note: You can insert this function from the
keyboard by typing deltaTmpCnv(...).
Converts a temperature range (the
difference between two temperature
values) specified by Expr from one unit to
another. Valid temperature units are:
Note: You can use the Catalog to select
temperature units.
_°C Celsius
_°F Fahrenheit
_°K Kelvin
_°R Rankine
Alphabetical Listing
185
ΔtmpCnv()
Catalog >
To enter °, select it from the Symbol
Palette or type @d.
To type _ , press /_.
1_°C and 1_°K have the same magnitude,
as do 1_°F and 1_°R. However, 1_°C is 9/5
as large as 1_°F.
For example, a 100_°C range (from 0_°C to
100_°C) is equivalent to a 180_°F range.
To convert a particular temperature value
instead of a range, use tmpCnv() .
tPdf()
tPdf(XVal ,df ) ⇒ number if XVal is a
number, list if XVal is a list
Catalog >
Computes the probability density function
(pdf) for the Student-t distribution at a
specified x value with specified degrees of
freedom df .
trace()
trace(squareMatrix ) ⇒ expression
Returns the trace (sum of all the elements
on the main diagonal) of squareMatrix .
186
Alphabetical Listing
Catalog >
Catalog >
Try
Try
block1
Else
block2
EndTry
Executes block1 unless an error occurs.
Program execution transfers to block2 if an
error occurs in block1. System variable
errCode contains the error code to allow
the program to perform error recovery. For
a list of error codes, see “Error codes and
messages,” page 246.
block1 and block2 can be either a single
statement or a series of statements
separated with the “:” character.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
To see the commands Try, ClrErr, and
PassErr in operation, enter the eigenvals()
program shown at the right. Run the
program by executing each of the following
expressions.
Define eigenvals(a,b)=Prgm
© Program eigenvals(A,B) displays
eigenvalues of A•B
Try
Disp "A= ",a
Disp "B= ",b
Disp " "
Disp "Eigenvalues of A•B are:",eigVl(a*b)
Note: See also ClrErr, page 29, and PassErr,
page 129.
Else
If errCode=230 Then
Disp "Error: Product of A•B must be a
square matrix"
ClrErr
Else
PassErr
EndIf
EndTry
EndPrgm
Alphabetical Listing
187
tTest
tTest μ0,List [,Freq[,Hypoth]]
Catalog >
(Data list input)
tTest μ0,v,sx ,n,[Hypoth]
(Summary stats input)
Performs a hypothesis test for a single
unknown population mean μ when the
population standard deviation σ is unknown.
A summary of results is stored in the
stat.results variable. (See page 172.)
Test H0: μ = μ0, against one of the
following:
For Ha: μ < μ0, set Hypoth<0
For Ha: μ ≠ μ0 (default), set Hypoth=0
For Ha: μ > μ0, set Hypoth>0
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.t
(v − μ0) / (stdev / sqrt(n))
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom
stat. v
Sample mean of the data sequence in List
stat.sx
Sample standard deviation of the data sequence
stat.n
Size of the sample
tTest_2Samp
tTest_2Samp List1,List2[,Freq1[,Freq2
[,Hypoth[,Pooled]]]]
(Data list input)
tTest_2Samp v 1,sx1,n1,v 2,sx2,n2[,Hypoth
[,Pooled]]
(Summary stats input)
188
Alphabetical Listing
Catalog >
Catalog >
tTest_2Samp
Computes a two-sample t test. A summary
of results is stored in the stat.results
variable. (See page 172.)
Test H0: μ1 = μ2, against one of the
following:
For Ha: μ1< μ2, set Hypoth<0
For Ha: μ1≠ μ2 (default), set Hypoth=0
For Ha: μ1> μ2, set Hypoth>0
Pooled=1 pools variances
Pooled=0 does not pool variances
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.t
Standard normal value computed for the difference of means
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat.df
Degrees of freedom for the t-statistic
stat. v1, stat. v2
Sample means of the data sequences in List 1 and List 2
stat.sx1, stat.sx2
Sample standard deviations of the data sequences in List 1 and List 2
stat.n1, stat.n2
Size of the samples
stat.sp
The pooled standard deviation. Calculated when Pooled =1.
tvmFV()
tvmFV(N,I,PV,Pmt ,[PpY],[CpY],[PmtAt ])
⇒ value
Catalog >
Financial function that calculates the future
value of money.
Note: Arguments used in the TVM functions
are described in the table of TVM
arguments, page 191. See also amortTbl() ,
page 12.
tvmI()
tvmI(N,PV,Pmt ,FV,[PpY],[CpY],[PmtAt ])
⇒ value
Catalog >
Alphabetical Listing
189
tvmI()
Catalog >
Financial function that calculates the
interest rate per year.
Note: Arguments used in the TVM functions
are described in the table of TVM
arguments, page 191. See also amortTbl() ,
page 12.
tvmN()
tvmN(I,PV,Pmt ,FV,[PpY],[CpY],[PmtAt ])
⇒ value
Catalog >
Financial function that calculates the
number of payment periods.
Note: Arguments used in the TVM functions
are described in the table of TVM
arguments, page 191. See also amortTbl() ,
page 12.
tvmPmt()
tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt ])
⇒ value
Catalog >
Financial function that calculates the
amount of each payment.
Note: Arguments used in the TVM functions
are described in the table of TVM
arguments, page 191. See also amortTbl() ,
page 12.
tvmPV()
tvmPV(N,I,Pmt ,FV,[PpY],[CpY],[PmtAt ])
⇒ value
Financial function that calculates the
present value.
Note: Arguments used in the TVM functions
are described in the table of TVM
arguments, page 191. See also amortTbl() ,
page 12.
190
Alphabetical Listing
Catalog >
TVM
argument*
Description
Data type
N
Number of payment periods
real number
I
Annual interest rate
real number
PV
Present value
real number
Pmt
Payment amount
real number
FV
Future value
real number
PpY
Payments per year, default=1
integer > 0
CpY
Compounding periods per year, default=1
integer > 0
PmtAt
Payment due at the end or beginning of each period,
default=end
integer (0=end,
1=beginning)
* These time-value-of-money argument names are similar to the TVM variable names
(such as tvm.pv and tvm.pmt) that are used by the Calculator application’s finance
solver. Financial functions, however, do not store their argument values or results to
the TVM variables.
TwoVar
TwoVar X, Y[, [Freq][, Category , Include ]]
Catalog >
Calculates the TwoVar statistics. A summary
of results is stored in the stat.results
variable. (See page 172.)
All the lists must have equal dimension
except for Include .
X and Y are lists of independent and
dependent variables.
Freq is an optional list of frequency values.
Each element in Freq specifies the
frequency of occurrence for each
corresponding X and Y data point. The
default value is 1. All elements must be
integers ≥ 0.
Category is a list of numeric category codes
for the corresponding X and Y data.
Include is a list of one or more of the
category codes. Only those data items
whose category code is included in this list
are included in the calculation.
Alphabetical Listing
191
Catalog >
TwoVar
An empty (void) element in any of the lists
X, Freq, or Category results in a void for
the corresponding element of all those lists.
An empty element in any of the lists X1
through X20 results in a void for the
corresponding element of all those lists. For
more information on empty elements, see
page 232.
Output variable
Description
stat. v
Mean of x values
stat. Σ x
Sum of x values
stat. Σ x2
Sum of x2 values
stat.sx
Sample standard deviation of x
stat. σx
Population standard deviation of x
stat.n
Number of data points
stat. w
Mean of y values
stat. Σ y
Sum of y values
stat. Σ y2
Sum of y2 values
stat.sy
Sample standard deviation of y
stat. σy
Population standard deviation of y
stat. Σ xy
Sum of x •y values
stat.r
Correlation coefficient
stat.MinX
Minimum of x values
stat.Q1X
1st Quartile of x
stat.MedianX
Median of x
stat.Q3X
3rd Quartile of x
stat.MaxX
Maximum of x values
stat.MinY
Minimum of y values
stat.Q1Y
1st Quartile of y
stat.MedY
Median of y
stat.Q3Y
3rd Quartile of y
192
Alphabetical Listing
Output variable
Description
stat.MaxY
Maximum of y values
stat. Σ (x-v)2
Sum of squares of deviations from the mean of x
stat. Σ (y-w)2
Sum of squares of deviations from the mean of y
U
unitV()
unitV(Vector1) ⇒ vector
Catalog >
Returns either a row- or column-unit vector,
depending on the form of Vector1.
Vector1 must be either a single-row matrix
or a single-column matrix.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
unLock
unLock Var1[, Var2] [, Var3] ...
unLock Var.
Catalog >
Unlocks the specified variables or variable
group. Locked variables cannot be modified
or deleted.
See Lock, page 104, and getLockInfo() , page
82.
Alphabetical Listing
193
V
varPop()
varPop(List [, freqList ]) ⇒ expression
Catalog >
Returns the population variance of List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
Note: List must contain at least two
elements.
If an element in either list is empty (void),
that element is ignored, and the
corresponding element in the other list is
also ignored. For more information on
empty elements, see page 232.
varSamp()
varSamp(List [, freqList ]) ⇒ expression
Returns the sample variance of List .
Each freqList element counts the number
of consecutive occurrences of the
corresponding element in List .
Note: List must contain at least two
elements.
If an element in either list is empty (void),
that element is ignored, and the
corresponding element in the other list is
also ignored. For more information on
empty elements, see page 232.
varSamp(Matrix1[, freqMatrix ]) ⇒
matrix
Returns a row vector containing the sample
variance of each column in Matrix1.
Each freqMatrix element counts the
number of consecutive occurrences of the
corresponding element in Matrix1.
194
Alphabetical Listing
Catalog >
Catalog >
varSamp()
If an element in either matrix is empty
(void), that element is ignored, and the
corresponding element in the other matrix
is also ignored. For more information on
empty elements, see page 232.
Note: Matrix1 must contain at least two
rows.
W
Catalog >
Wait
Wait timeInSeconds
To wait 4 seconds:
Suspends execution for a period of
timeInSeconds seconds.
Wait 4
Wait is particularly useful in a program that
To wait 1/2 second:
needs a brief delay to allow requested data
to become available.
Wait 0.5
The argument timeInSeconds must be an
expression that simplifies to a decimal value
in the range 0 through 100. The command
rounds this value up to the nearest 0.1
seconds.
To wait 1.3 seconds using the variable
seccount:
To cancel a Wait that is in progress,
This example switches a green LED on for
0.5 seconds and then switches it off.
•
Handheld: Hold down the c key and
press · repeatedly.
•
Windows®: Hold down the F12 key and
press Enter repeatedly.
Macintosh®: Hold down the F5 key and
press Enter repeatedly.
iPad®: The app displays a prompt. You can
continue waiting or cancel.
•
•
seccount:=1.3
Wait seccount
Send "SET GREEN 1 ON"
Wait 0.5
Send "SET GREEN 1 OFF"
Note: You can use the Wait command within
a user-defined program but not within a
function.
Alphabetical Listing
195
warnCodes ()
warnCodes(Expr1, StatusVar) ⇒
expression
Evaluates expression Expr1, returns the
result, and stores the codes of any
generated warnings in the StatusVar list
variable. If no warnings are generated, this
function assigns StatusVar an empty list.
Expr1 can be any valid TI-Nspire™ or
TI-Nspire™ CAS math expression. You
cannot use a command or assignment as
Expr1.
Catalog >
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
StatusVar must be a valid variable name.
For a list of warning codes and associated
messages, see page 246.
when()
when(Condition, trueResult [, falseResult ]
[, unknownResult ]) ⇒ expression
Returns trueResult , falseResult , or
unknownResult , depending on whether
Condition is true, false, or unknown.
Returns the input if there are too few
arguments to specify the appropriate result.
Omit both falseResult and unknownResult
to make an expression defined only in the
region where Condition is true.
Use an undef falseResult to define an
expression that graphs only on an interval.
when() is helpful for defining recursive
functions.
196
Alphabetical Listing
Catalog >
Catalog >
While
While Condition
Block
EndWhile
Executes the statements in Block as long
as Condition is true.
Block can be either a single statement or a
sequence of statements separated with the
“:” character.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
X
Catalog >
xor
BooleanExpr1 xor BooleanExpr2 returns
Boolean expressionBooleanList1
xor BooleanList2 returns Boolean
listBooleanMatrix1
xor BooleanMatrix2 returns Boolean
matrix
Returns true if BooleanExpr1 is true and
BooleanExpr2 is false, or vice versa.
Returns false if both arguments are true or
if both are false. Returns a simplified
Boolean expression if either of the
arguments cannot be resolved to true or
false.
Note: See or, page 127.
Integer1 xor Integer2⇒ integer
In Hex base mode:
Compares two real integers bit-by-bit using
an xor operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if either bit (but
not both) is 1; the result is 0 if both bits are
0 or both bits are 1. The returned value
represents the bit results, and is displayed
according to the Base mode.
Important: Zero, not the letter O.
In Bin base mode:
Alphabetical Listing
197
Catalog >
xor
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base 10).
Note: A binary entry can have up to 64 digits
(not counting the 0b prefix). A hexadecimal
entry can have up to 16 digits.
If you enter a decimal integer that is too
large for a signed, 64-bit binary form, a
symmetric modulo operation is used to
bring the value into the appropriate range.
For more information, see ►Base2, page
21.
Note: See or, page 127.
Z
zeros()
zeros(Expr, Var) ⇒ list
zeros(Expr, Var=Guess) ⇒ list
Returns a list of candidate real values of
Var that make Expr=0. zeros() does this by
computing exp►list(solve
( Expr=0,Var) ,Var) .
For some purposes, the result form for
zeros() is more convenient than that of
solve() . However, the result form of zeros()
cannot express implicit solutions, solutions
that require inequalities, or solutions that
do not involve Var.
Note: See also cSolve() , cZeros() , and solve
() .
zeros({Expr1, Expr2},
{VarOrGuess1, VarOrGuess2 [, … ]}) ⇒
matrix
Returns candidate real zeros of the
simultaneous algebraic expressions, where
each VarOrGuess specifies an unknown
whose value you seek.
Optionally, you can specify an initial guess
for a variable. Each VarOrGuess must have
the form:
198
Alphabetical Listing
Catalog >
Catalog >
zeros()
variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3.
If all of the expressions are polynomials and
if you do NOT specify any initial guesses,
zeros() uses the lexical Gröbner/Buchberger
elimination method to attempt to
determine all real zeros.
For example, suppose you have a circle of
radius r at the origin and another circle of
radius r centered where the first circle
crosses the positive x-axis. Use zeros() to
find the intersections.
As illustrated by r in the example to the
right, simultaneous polynomial expressions
can have extra variables that have no
values, but represent given numeric values
that could be substituted later.
Each row of the resulting matrix represents
an alternate zero, with the components
ordered the same as the varOrGuess list.
To extract a row, index the matrix by [row].
Extract row 2:
You can also (or instead) include unknowns
that do not appear in the expressions. For
example, you can include z as an unknown
to extend the previous example to two
parallel intersecting cylinders of radius r.
The cylinder zeros illustrate how families of
zeros might contain arbitrary constants in
the form ck, where k is an integer suffix
from 1 through 255.
For polynomial systems, computation time
or memory exhaustion may depend strongly
on the order in which you list unknowns. If
your initial choice exhausts memory or your
patience, try rearranging the variables in
the expressions and/or varOrGuess list.
Alphabetical Listing
199
Catalog >
zeros()
If you do not include any guesses and if any
expression is non-polynomial in any variable
but all expressions are linear in the
unknowns, zeros() uses Gaussian
elimination to attempt to determine all real
zeros.
If a system is neither polynomial in all of its
variables nor linear in its unknowns, zeros()
determines at most one zero using an
approximate iterative method. To do so, the
number of unknowns must equal the
number of expressions, and all other
variables in the expressions must simplify
to numbers.
Each unknown starts at its guessed value if
there is one; otherwise, it starts at 0.0.
Use guesses to seek additional zeros one by
one. For convergence, a guess may have to
be rather close to a zero.
zInterval
zInterval σ,List [,Freq[,CLevel ]]
Catalog >
(Data list input)
zInterval σ,v,n [,CLevel ]
(Summary stats input)
Computes a z confidence interval. A
summary of results is stored in the
stat.results variable. (See page 172.)
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower, stat.CUpper
Confidence interval for an unknown population mean
stat. x
Sample mean of the data sequence from the normal random distribution
stat.ME
Margin of error
stat.sx
Sample standard deviation
200
Alphabetical Listing
Output variable
Description
stat.n
Length of the data sequence with sample mean
stat. σ
Known population standard deviation for data sequence List
zInterval_1Prop
zInterval_1Prop x ,n [,CLevel ]
Catalog >
Computes a one-proportion z confidence
interval. A summary of results is stored in
the stat.results variable. (See page 172.)
x is a non-negative integer.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower, stat.CUpper
Confidence interval containing confidence level probability of distribution
stat. Ç
The calculated proportion of successes
stat.ME
Margin of error
stat.n
Number of samples in data sequence
zInterval_2Prop
zInterval_2Prop x1,n1,x2,n2[,CLevel ]
Catalog >
Computes a two-proportion z confidence
interval. A summary of results is stored in
the stat.results variable. (See page 172.)
x1 and x2 are non-negative integers.
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower, stat.CUpper
Confidence interval containing confidence level probability of distribution
stat. Ç Diff
The calculated difference between proportions
stat.ME
Margin of error
Alphabetical Listing
201
Output variable
Description
stat. Ç 1
First sample proportion estimate
stat. Ç 2
Second sample proportion estimate
stat.n1
Sample size in data sequence one
stat.n2
Sample size in data sequence two
zInterval_2Samp
zInterval_2Samp σ1 ,σ2 ,List1,List2[,Freq1
[,Freq2,[CLevel ]]]
Catalog >
(Data list input)
zInterval_2Samp σ1 ,σ2 ,v 1,n1,v 2,n2
[,CLevel ]
(Summary stats input)
Computes a two-sample z confidence
interval. A summary of results is stored in
the stat.results variable. (See page 172.)
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.CLower,
stat.CUpper
Confidence interval containing confidence level probability of distribution
stat. x1-x2
Sample means of the data sequences from the normal random
distribution
stat.ME
Margin of error
stat. x1, stat. x2
Sample means of the data sequences from the normal random
distribution
stat. σx1, stat. σx2
Sample standard deviations for List 1 and List 2
stat.n1, stat.n2
Number of samples in data sequences
stat.r1, stat.r2
Known population standard deviations for data sequence List 1 and List
2
zTest
zTest μ0,σ,List ,[Freq[,Hypoth]]
202
Alphabetical Listing
Catalog >
Catalog >
zTest
(Data list input)
zTest μ0,σ,v,n[,Hypoth]
(Summary stats input)
Performs a z test with frequency freqlist . A
summary of results is stored in the
stat.results variable. (See page 172.)
Test H0: μ = μ0, against one of the
following:
For Ha: μ < μ0, set Hypoth<0
For Ha: μ ≠ μ0 (default), set Hypoth=0
For Ha: μ > μ0, set Hypoth>0
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.z
(x − μ0) / (σ / sqrt(n))
stat.P Value
Least probability at which the null hypothesis can be rejected
stat. x
Sample mean of the data sequence in List
stat.sx
Sample standard deviation of the data sequence. Only returned for Data input.
stat.n
Size of the sample
Catalog >
zTest_1Prop
Output variable
Description
stat.p0
Hypothesized population proportion
stat.z
Standard normal value computed for the proportion
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat. Ç
Estimated sample proportion
stat.n
Size of the sample
zTest_2Prop
zTest_2Prop x1,n1,x2,n2[,Hypoth]
Catalog >
Alphabetical Listing
203
Catalog >
zTest_2Prop
Computes a two-proportion z test. A
summary of results is stored in the
stat.results variable. (See page 172.)
x1 and x2 are non-negative integers.
Test H0: p1 = p2, against one of the
following:
For Ha: p1 > p2, set Hypoth>0
For Ha: p1 ≠ p2 (default), set Hypoth=0
For Ha: p < p0, set Hypoth<0
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.z
Standard normal value computed for the difference of proportions
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat. Ç 1
First sample proportion estimate
stat. Ç 2
Second sample proportion estimate
stat. Ç
Pooled sample proportion estimate
stat.n1, stat.n2
Number of samples taken in trials 1 and 2
zTest_2Samp
zTest_2Samp σ1 ,σ2 ,List1,List2[,Freq1
[,Freq2[,Hypoth]]]
(Data list input)
zTest_2Samp σ1 ,σ2 ,v 1,n1,v 2,n2[,Hypoth]
(Summary stats input)
Computes a two-sample z test. A summary
of results is stored in the stat.results
variable. (See page 172.)
Test H0: μ1 = μ2, against one of the
following:
For Ha: μ1 < μ2, set Hypoth<0
For Ha: μ1 ≠ μ2 (default), set Hypoth=0
For Ha: μ1 > μ2, Hypoth>0
204
Alphabetical Listing
Catalog >
Catalog >
zTest_2Samp
For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 232.
Output variable
Description
stat.z
Standard normal value computed for the difference of means
stat.PVal
Smallest level of significance at which the null hypothesis can be rejected
stat. x1, stat. x2
Sample means of the data sequences in List1 and List2
stat.sx1, stat.sx2
Sample standard deviations of the data sequences in List1 and List2
stat.n1, stat.n2
Size of the samples
Alphabetical Listing
205
Symbols
+ (add)
Expr1 + Expr2 ⇒ expression
+ key
Returns the sum of the two arguments.
List1 + List2 ⇒ list
Matrix1 + Matrix2 ⇒ matrix
Returns a list (or matrix) containing the
sums of corresponding elements in List1
and List2 (or Matrix1 and Matrix2).
Dimensions of the arguments must be
equal.
Expr + List1 ⇒ list
List1 + Expr ⇒ list
Returns a list containing the sums of Expr
and each element in List1.
Expr + Matrix1 ⇒ matrix
Matrix1 + Expr ⇒ matrix
Returns a matrix with Expr added to each
element on the diagonal of Matrix1.
Matrix1 must be square.
Note: Use .+ (dot plus) to add an expression
to each element.
− (subtract)
Expr1 − Expr2 ⇒ expression
Returns Expr1 minus Expr2.
List1 −List2⇒ list
Matrix1 −Matrix2 ⇒ matrix
206
Symbols
- key
− (subtract)
- key
Subtracts each element in List2 (or
Matrix2) from the corresponding element
in List1 (or Matrix1), and returns the
results.
Dimensions of the arguments must be
equal.
Expr − List1 ⇒ list
List1 − Expr ⇒ list
Subtracts each List1 element from Expr or
subtracts Expr from each List1 element,
and returns a list of the results.
Expr − Matrix1 ⇒ matrix
Matrix1 − Expr ⇒ matrix
Expr − Matrix1 returns a matrix of Expr
times the identity matrix minus
Matrix1. Matrix1 must be square.
Matrix1 − Expr returns a matrix of Expr
times the identity matrix subtracted from
Matrix1. Matrix1 must be square.
Note: Use .− (dot minus) to subtract an
expression from each element.
• (multiply)
r key
Expr1•Expr2 ⇒ expression
Returns the product of the two arguments.
List1•List2 ⇒ list
Returns a list containing the products of the
corresponding elements in List1 and List2.
Dimensions of the lists must be equal.
Matrix1•Matrix2 ⇒ matrix
Returns the matrix product of Matrix1 and
Matrix2.
The number of columns in Matrix1 must
equal the number of rows in Matrix2.
Symbols
207
• (multiply)
r key
Expr •List1 ⇒ list
List1•Expr ⇒ list
Returns a list containing the products of
Expr and each element in List1.
Expr •Matrix1 ⇒ matrix
Matrix1•Expr ⇒ matrix
Returns a matrix containing the products of
Expr and each element in Matrix1.
Note: Use .•(dot multiply) to multiply an
expression by each element.
⁄ (divide)
Expr1 ⁄ Expr2 ⇒ expression
Returns the quotient of Expr1 divided by
Expr2.
Note: See also Fraction template, page 5.
List1 ⁄ List2 ⇒ list
Returns a list containing the quotients of
List1 divided by List2.
Dimensions of the lists must be equal.
Expr ⁄ List1 ⇒ list
List1 ⁄ Expr ⇒ list
Returns a list containing the quotients of
Expr divided by List1 orList1 divided by
Expr.
Matrix1 ⁄ Expr ⇒ matrix
Returns a matrix containing the quotients
of Matrix1 ⁄ Expr.
Matrix1 ⁄ Value ⇒ matrix
208
Symbols
p key
⁄ (divide)
p key
Note: Use . ⁄ (dot divide) to divide an
expression by each element.
^ (power)
Expr1 ^ Expr2⇒ expression
l key
List1 ^ List2 ⇒ list
Returns the first argument raised to the
power of the second argument.
Note: See also Exponent template, page 5.
For a list, returns the elements in List1
raised to the power of the corresponding
elements in List2.
In the real domain, fractional powers that
have reduced exponents with odd
denominators use the real branch versus
the principal branch for complex mode.
Expr ^ List1 ⇒ list
Returns Expr raised to the power of the
elements in List1.
List1 ^ Expr ⇒ list
Returns the elements in List1 raised to the
power of Expr.
squareMatrix1 ^ integer ⇒ matrix
Returns squareMatrix1 raised to the
integer power.
squareMatrix1 must be a square matrix.
If integer = −1, computes the inverse
matrix.
If integer < −1, computes the inverse
matrix to an appropriate positive power.
Symbols
209
x2 (square)
Expr12⇒
q key
expression
Returns the square of the argument.
List12 ⇒ list
Returns a list containing the squares of the
elements in List1.
squareMatrix12 ⇒ matrix
Returns the matrix square of
squareMatrix1. This is not the same as
calculating the square of each element. Use
.^2 to calculate the square of each element.
.+ (dot add)
Matrix1 .+ Matrix2 ⇒ matrix
^+ keys
Expr .+ Matrix1⇒ matrix
Matrix1.+Matrix2 returns a matrix that is
the sum of each pair of corresponding
elements in Matrix1 and Matrix2.
Expr .+ Matrix1 returns a matrix that is
the sum of Expr and each element in
Matrix1.
. ⁻(dot subt.)
Matrix1 .− Matrix2⇒ matrix
Expr .− Matrix1 ⇒ matrix
Matrix1.− Matrix2 returns a matrix that is
the difference between each pair of
corresponding elements in Matrix1 and
Matrix2.
Expr .− Matrix1 returns a matrix that is
the difference of Expr and each element in
Matrix1.
.
210
Symbols
^- keys
. •(dot mult.)
Matrix1 .• Matrix2⇒ matrix
^r keys
Expr .• Matrix1 ⇒ matrix
Matrix1.• Matrix2 returns a matrix that is
the product of each pair of corresponding
elements in Matrix1 and Matrix2.
Expr .• Matrix1 returns a matrix
containing the products of Expr and each
element in Matrix1.
. ⁄ (dot divide)
Matrix1. ⁄ Matrix2 ⇒ matrix
^p keys
Expr . ⁄ Matrix1⇒ matrix
Matrix1 . ⁄ Matrix2 returns a matrix that is
the quotient of each pair of corresponding
elements in Matrix1 and Matrix2.
Expr . ⁄ Matrix1 returns a matrix that is
the quotient of Expr and each element in
Matrix1.
.^ (dot power)
Matrix1 .^ Matrix2 ⇒ matrix
^l keys
Expr . ^ Matrix1⇒ matrix
Matrix1.^ Matrix2 returns a matrix where
each element in Matrix2 is the exponent
for the corresponding element in Matrix1.
Expr .^ Matrix1 returns a matrix where
each element in Matrix1 is the exponent
for Expr.
− (negate)
v key
−Expr1 ⇒ expression
−List1 ⇒ list
−Matrix1 ⇒ matrix
Symbols
211
v key
− (negate)
Returns the negation of the argument.
For a list or matrix, returns all the elements
negated.
In Bin base mode:
Important: Zero, not the letter O.
If the argument is a binary or hexadecimal
integer, the negation gives the two’s
complement.
To see the entire result, press £ and then
use ¡ and ¢ to move the cursor.
% (percent)
Expr1% ⇒ expression
List1% ⇒ list
Matrix1% ⇒ matrix
/k keys
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
.
Returns
For a list or matrix, returns a list or matrix
with each element divided by 100.
= (equal)
Expr1=Expr2 ⇒ Boolean expression
List1=List2 ⇒ Boolean list
= key
Example function that uses math test
symbols: =, ≠, <, ≤, >, ≥
Matrix1=Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
equal to Expr2.
Returns false if Expr1 is determined to not
be equal to Expr2.
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
Result of graphing g(x)
212
Symbols
= key
= (equal)
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
/= keys
≠ (not equal)
Expr1≠Expr2 ⇒ Boolean expression
See “=” (equal) example.
List1≠List2 ⇒ Boolean list
Matrix1≠Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
not equal to Expr2.
Returns false if Expr1 is determined to be
equal to Expr2.
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
Note: You can insert this operator from the
keyboard by typing /=
< (less than)
Expr1<Expr2 ⇒ Boolean expression
/= keys
See “=” (equal) example.
List1<List2 ⇒ Boolean list
Matrix1<Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
less than Expr2.
Returns false if Expr1 is determined to be
greater than or equal to Expr2.
Symbols
213
/= keys
< (less than)
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
/= keys
≤ (less or equal)
Expr1≤Expr2 ⇒ Boolean expression
See “=” (equal) example.
List1≤List2 ⇒ Boolean list
Matrix1 ≤Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
less than or equal to Expr2.
Returns false if Expr1 is determined to be
greater than Expr2.
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
Note: You can insert this operator from the
keyboard by typing <=
> (greater than)
Expr1>Expr2 ⇒ Boolean expression
List1>List2 ⇒ Boolean list
Matrix1>Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
greater than Expr2.
Returns false if Expr1 is determined to be
less than or equal to Expr2.
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
214
Symbols
/= keys
See “=” (equal) example.
/= keys
≥ (greater or equal)
Expr1≥Expr2 ⇒ Boolean expression
See “=” (equal) example.
List1≥List2 ⇒ Boolean list
Matrix1 ≥Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be
greater than or equal to Expr2.
Returns false if Expr1 is determined to be
less than Expr2.
Anything else returns a simplified form of
the equation.
For lists and matrices, returns comparisons
element by element.
Note: You can insert this operator from the
keyboard by typing >=
⇒ (logical implication)
/= keys
BooleanExpr1 ⇒ BooleanExpr2 returns
Boolean expression
BooleanList1 ⇒ BooleanList2 returns
Boolean list
BooleanMatrix1 ⇒ BooleanMatrix2
returns Boolean matrix
Integer1 ⇒ Integer2 returns Integer
Evaluates the expression not <argument1>
or <argument2> and returns true, false, or a
simplified form of the equation.
For lists and matrices, returns comparisons
element by element.
Note: You can insert this operator from the
keyboard by typing =>
Symbols
215
⇔ (logical double implication, XNOR)
/= keys
BooleanExpr1 ⇔ BooleanExpr2 returns
Boolean expression
BooleanList1 ⇔ BooleanList2 returns
Boolean list
BooleanMatrix1 ⇔ BooleanMatrix2
returns Boolean matrix
Integer1 ⇔ Integer2 returns Integer
Returns the negation of an XOR Boolean
operation on the two arguments. Returns
true, false, or a simplified form of the
equation.
For lists and matrices, returns comparisons
element by element.
Note: You can insert this operator from the
keyboard by typing <=>
! (factorial)
Expr1! ⇒ expression
º key
List1! ⇒ list
Matrix1! ⇒ matrix
Returns the factorial of the argument.
For a list or matrix, returns a list or matrix
of factorials of the elements.
& (append)
String1 & String2 ⇒ string
Returns a text string that is String2
appended to String1.
216
Symbols
/k keys
d() (derivative)
Catalog >
d(Expr1, Var[, Order]) ⇒ expression
d(List1, Var[, Order]) ⇒ list
d(Matrix1,Var[, Order]) ⇒ matrix
Returns the first derivative of the first
argument with respect to variable Var.
Order, if included, must be an integer. If
the order is less than zero, the result will be
an anti-derivative.
Note: You can insert this function from the
keyboard by typing derivative(...).
d() does not follow the normal evaluation
mechanism of fully simplifying its
arguments and then applying the function
definition to these fully simplified
arguments. Instead, d() performs the
following steps:
1. Simplify the second argument only to
the extent that it does not lead to a
non-variable.
2. Simplify the first argument only to the
extent that it does recall any stored
value for the variable determined by
step 1.
3. Determine the symbolic derivative of
the result of step 2 with respect to the
variable from step 1.
If the variable from step 1 has a stored
value or a value specified by the constraint
(“|”) operator, substitute that value into
the result from step 3.
Note: See also First derivative, page 9;
Second derivative, page 10; or
Nth derivative, page 10.
∫() (integral)
Catalog >
∫(Expr1, Var[,Lower,Upper]) ⇒
expression
∫(Expr1,Var[,Constant ]) ⇒ expression
Symbols
217
∫() (integral)
Catalog >
Returns the integral of Expr1 with respect
to the variable Var from Lower to Upper.
Note: See also Definite or Indefinite integral
template, page 10.
Note: You can insert this function from the
keyboard by typing integral(...).
If Lower and Upper are omitted, returns an
anti-derivative. A symbolic constant of
integration is omitted unless you provide
the Constant argument.
Equally valid anti-derivatives might differ by
a numeric constant. Such a constant might
be disguised—particularly when an antiderivative contains logarithms or inverse
trigonometric functions. Moreover,
piecewise constant expressions are
sometimes added to make an antiderivative valid over a larger interval than
the usual formula.
∫() returns itself for pieces of Expr1 that it
cannot determine as an explicit finite
combination of its built-in functions and
operators.
When you provide Lower and Upper, an
attempt is made to locate any
discontinuities or discontinuous derivatives
in the interval Lower < Var < Upper and to
subdivide the interval at those places.
For the Auto setting of the Auto or
Approximate mode, numerical integration is
used where applicable when an antiderivative or a limit cannot be determined.
For the Approximate setting, numerical
integration is tried first, if applicable. Antiderivatives are sought only where such
numerical integration is inapplicable or
fails.
218
Symbols
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
.
∫() (integral)
Catalog >
∫() can be nested to do multiple integrals.
Integration limits can depend on integration
variables outside them.
Note: See also nInt() , page 120.
√() (square root)
/q keys
√(Expr1) ⇒ expression
√(List1) ⇒ list
Returns the square root of the argument.
For a list, returns the square roots of all the
elements in List1.
Note: You can insert this function from the
keyboard by typing sqrt(...)
Note: See also Square root template, page
5.
Π() (prodSeq)
Catalog >
Π(Expr1, Var, Low, High) ⇒ expression
Note: You can insert this function from the
keyboard by typing prodSeq(...).
Evaluates Expr1 for each value of Var from
Low to High, and returns the product of the
results.
Note: See also Product template ( Π) , page
9.
Symbols
219
Π() (prodSeq)
Catalog >
Π(Expr1, Var, Low, Low−1) ⇒ 1
Π(Expr1, Var, Low, High) ⇒ 1/Π(Expr1,
Var, High+1, Low−1) if High < Low−1
The product formulas used are derived from
the following reference:
Ronald L. Graham, Donald E. Knuth, and
Oren Patashnik. Concrete Mathematics: A
Foundation for Computer Science .
Reading, Massachusetts: Addison-Wesley,
1994.
Σ() (sumSeq)
Σ(Expr1, Var, Low, High) ⇒ expression
Note: You can insert this function from the
keyboard by typing sumSeq(...).
Evaluates Expr1 for each value of Var from
Low to High, and returns the sum of the
results.
Note: See also Sum template, page 9.
Σ(Expr1, Var, Low, Low−1) ⇒ 0
Σ(Expr1, Var, Low, High) ⇒ μ
Σ(Expr1, Var, High+1, Low−1) if High <
Low−1
The summation formulas used are derived
from the following reference:
Ronald L. Graham, Donald E. Knuth, and
Oren Patashnik. Concrete Mathematics: A
Foundation for Computer Science .
Reading, Massachusetts: Addison-Wesley,
1994.
220
Symbols
Catalog >
ΣInt()
Catalog >
ΣInt(NPmt1, NPmt2, N, I, PV ,[Pmt ], [FV],
[PpY], [CpY], [PmtAt ], [roundValue ])
⇒ value
ΣInt(NPmt1,NPmt2,amortTable ) ⇒ value
Amortization function that calculates the
sum of the interest during a specified range
of payments.
NPmt1 and NPmt2 define the start and end
boundaries of the payment range.
N, I, PV, Pmt , FV, PpY, CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
•
•
•
If you omit Pmt , it defaults to
Pmt =tvmPmt
( N,I,PV,FV,PpY,CpY,PmtAt ).
If you omit FV, it defaults to FV=0.
The defaults for PpY, CpY, and PmtAt
are the same as for the TVM functions.
roundValue specifies the number of
decimal places for rounding. Default=2.
ΣInt( NPmt1,NPmt2,amortTable ) calculates
the sum of the interest based on
amortization table amortTable . The
amortTable argument must be a matrix in
the form described under amortTbl() , page
12.
Note: See also ΣPrn(), below, and Bal() ,
page 21.
ΣPrn()
Catalog >
ΣPrn(NPmt1, NPmt2, N, I, PV, [Pmt ],
[FV], [PpY], [CpY], [PmtAt ],
[roundValue ]) ⇒ value
ΣPrn(NPmt1, NPmt2, amortTable ) ⇒
value
Amortization function that calculates the
sum of the principal during a specified
range of payments.
Symbols
221
ΣPrn()
Catalog >
NPmt1 and NPmt2 define the start and end
boundaries of the payment range.
N, I, PV, Pmt , FV, PpY, CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
•
•
•
If you omit Pmt , it defaults to
Pmt =tvmPmt
( N,I,PV,FV,PpY,CpY,PmtAt ).
If you omit FV, it defaults to FV=0.
The defaults for PpY, CpY, and PmtAt
are the same as for the TVM functions.
roundValue specifies the number of
decimal places for rounding. Default=2.
ΣPrn( NPmt1,NPmt2,amortTable )
calculates the sum of the principal paid
based on amortization table amortTable .
The amortTable argument must be a
matrix in the form described under
amortTbl() , page 12.
Note: See also ΣInt(), above, and Bal() ,
page 21.
# (indirection)
# varNameString
Refers to the variable whose name is
varNameString. This lets you use strings to
create variable names from within a
function.
/k keys
Creates or refers to the variable xyz .
Returns the value of the variable (r) whose
name is stored in variable s1.
222
Symbols
E (scientific notation)
i key
mantissaEexponent
Enters a number in scientific notation. The
number is interpreted as
mantissa × 10exponent.
Hint: If you want to enter a power of 10
without causing a decimal value result, use
10^integer.
Note: You can insert this operator from the
computer keyboard by typing @E. for
example, type 2.3@E4 to enter 2.3E 4.
g (gradian)
Expr1g ⇒ expression
¹ key
In Degree, Gradian or Radian mode:
List1g ⇒ list
Matrix1g ⇒ matrix
This function gives you a way to specify a
gradian angle while in the Degree or Radian
mode.
In Radian angle mode, multiplies Expr1 by
π/200.
In Degree angle mode, multiplies Expr1 by
g/100.
In Gradian mode, returns Expr1 unchanged.
Note: You can insert this symbol from the
computer keyboard by typing @g.
r(radian)
Expr1r ⇒ expression
¹ key
In Degree, Gradian or Radian angle mode:
List1r ⇒ list
Matrix1r ⇒ matrix
Symbols
223
r(radian)
¹ key
This function gives you a way to specify a
radian angle while in Degree or Gradian
mode.
In Degree angle mode, multiplies the
argument by 180/ π.
In Radian angle mode, returns the
argument unchanged.
In Gradian mode, multiplies the argument
by 200/ π.
Hint: Use r if you want to force radians in a
function definition regardless of the mode
that prevails when the function is used.
Note: You can insert this symbol from the
computer keyboard by typing @r.
¹ key
° (degree)
Expr1° ⇒ expression
In Degree, Gradian or Radian angle mode:
List1° ⇒ list
Matrix1° ⇒ matrix
This function gives you a way to specify a
degree angle while in Gradian or Radian
mode.
In Radian angle mode, multiplies the
argument by π/180.
In Degree angle mode, returns the
argument unchanged.
In Radian angle mode:
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
.
In Gradian angle mode, multiplies the
argument by 10/9.
Note: You can insert this symbol from the
computer keyboard by typing @d.
/k keys
°, ', '' (degree/minute/second)
dd°mm'ss.ss'' ⇒ expression
224
Symbols
In Degree angle mode:
/k keys
°, ', '' (degree/minute/second)
dd A positive or negative number
mm A non-negative number
ss.ss A non-negative number
Returns dd+( mm/60)+( ss.ss/3600).
This base-60 entry format lets you:
•
•
Enter an angle in
degrees/minutes/seconds without regard
to the current angle mode.
Enter time as hours/minutes/seconds.
Note: Follow ss.ss with two apostrophes
(''), not a quote symbol (").
/k keys
∠ (angle)
[Radius,∠ θ_Angle ] ⇒ vector
(polar input)
In Radian mode and vector format set to:
rectangular
[Radius,∠ θ_Angle ,Z_Coordinate ] ⇒
vector
(cylindrical input)
[Radius,∠ θ_Angle ,∠ θ_Angle ] ⇒ vector
(spherical input)
cylindrical
Returns coordinates as a vector depending
on the Vector Format mode setting:
rectangular, cylindrical, or spherical.
Note: You can insert this symbol from the
computer keyboard by typing @<.
spherical
( Magnitude∠ Angle ) ⇒ complexValue
(polar input)
In Radian angle mode and Rectangular
complex format:
Enters a complex value in (r∠ θ) polar
form. The Angle is interpreted according to
the current Angle mode setting.
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter .
Macintosh®: Press “+Enter .
iPad®: Hold enter , and select
.
Symbols
225
/k keys
∠ (angle)
º key
' (prime)
variable '
variable ' '
Enters a prime symbol in a differential
equation. A single prime symbol denotes a
1st-order differential equation, two prime
symbols denote a 2nd-order, and so on.
_ (underscore as an empty element)
See “Empty (Void) Elements,”
page 232.
/_ keys
_ (underscore as unit designator)
Expr_Unit
Designates the units for an Expr. All unit
names must begin with an underscore.
You can use pre-defined units or create your
own units. For a list of pre-defined units,
open the Catalog and display the Unit
Conversions tab. You can select unit names
from the Catalog or type the unit names
directly.
Variable _
When Variable has no value, it is treated
as though it represents a complex number.
By default, without the _ , the variable is
treated as real.
If Variable has a value, the _ is ignored and
Variable retains its original data type.
Note: You can store a complex number to a
variable without
using _ . However, for best results in
calculations such as cSolve() and cZeros() ,
the _ is recommended.
226
Symbols
Note: You can find the conversion symbol,
►, in the Catalog. Click
Math Operators.
Assuming z is undefined:
, and then click
► (convert)
/k keys
Expr_Unit1►_Unit2 ⇒ Expr_Unit2
Converts an expression from one unit to
another.
The _ underscore character designates the
units. The units must be in the same
category, such as Length or Area.
For a list of pre-defined units, open the
Catalog and display the Unit Conversions
tab:
•
•
You can select a unit name from the list.
You can select the conversion operator,
►, from the top of the list.
You can also type unit names manually. To
type “_” when typing unit names on the
handheld, press /_.
Note: To convert temperature units, use
tmpCnv() and ΔtmpCnv() . The ► conversion
operator does not handle temperature
units.
10^()
10^ (Expr1) ⇒ expression
Catalog >
10^ (List1) ⇒ list
Returns 10 raised to the power of the
argument.
For a list, returns 10 raised to the power of
the elements in List1.
10^(squareMatrix1) ⇒ squareMatrix
Returns 10 raised to the power of
squareMatrix1. This is not the same as
calculating 10 raised to the power of each
element. For information about the
calculation method, refer to cos() .
squareMatrix1 must be diagonalizable. The
result always contains floating-point
numbers.
Symbols
227
^ ⁻¹ (reciprocal)
Expr1 ^⁻¹ ⇒ expression
Catalog >
List1 ^⁻¹ ⇒ list
Returns the reciprocal of the argument.
For a list, returns the reciprocals of the
elements in List1.
squareMatrix1 ^⁻¹ ⇒ squareMatrix
Returns the inverse of squareMatrix1.
squareMatrix1 must be a non-singular
square matrix.
| (constraint operator)
Expr | BooleanExpr1[and
BooleanExpr2]...
Expr | BooleanExpr1[ orBooleanExpr2]...
The constraint (“|”) symbol serves as a
binary operator. The operand to the left of |
is an expression. The operand to the right of
| specifies one or more relations that are
intended to affect the simplification of the
expression. Multiple relations after | must
be joined by logical “and” or “or” operators.
The constraint operator provides three basic
types of functionality:
•
•
•
Substitutions
Interval constraints
Exclusions
Substitutions are in the form of an equality,
such as x=3 or y=sin(x). To be most
effective, the left side should be a simple
variable. Expr | Variable = value will
substitute value for every occurrence of
Variable in Expr.
228
Symbols
/k keys
| (constraint operator)
/k keys
Interval constraints take the form of one or
more inequalities joined by logical “and” or
“or” operators. Interval constraints also
permit simplification that otherwise might
be invalid or not computable.
Exclusions use the “not equals” (/= or ≠)
relational operator to exclude a specific
value from consideration. They are used
primarily to exclude an exact solution when
using cSolve() , cZeros() , fMax() , fMin() ,
solve() , zeros() , and so on.
→ (store)
/h key
Expr → Var
List → Var
Matrix → Var
Expr → Function(Param1,...)
List → Function(Param1,...)
Matrix → Function(Param1,...)
If the variable Var does not exist, creates it
and initializes it to Expr, List , or Matrix .
If the variable Var already exists and is not
locked or protected, replaces its contents
with Expr, List , or Matrix .
Symbols
229
→ (store)
/h key
Hint: If you plan to do symbolic
computations using undefined variables,
avoid storing anything into commonly used,
one-letter variables such as a, b, c, x, y, z,
and so on.
Note: You can insert this operator from the
keyboard by typing =: as a shortcut. For
example, type pi/4 =: myvar.
:= (assign)
Var := Expr
Var := List
Var := Matrix
Function(Param1,...) := Expr
Function(Param1,...) := List
Function(Param1,...) := Matrix
If variable Var does not exist, creates Var
and initializes it to Expr, List , or Matrix .
If Var already exists and is not locked or
protected, replaces its contents with Expr,
List , or Matrix .
Hint: If you plan to do symbolic
computations using undefined variables,
avoid storing anything into commonly used,
one-letter variables such as a, b, c, x, y, z,
and so on.
230
Symbols
/t keys
/k keys
© (comment)
© [text ]
© processes text as a comment line,
allowing you to annotate functions and
programs that you create.
© can be at the beginning or anywhere in
the line. Everything to the right of © , to the
end of the line, is the comment.
Note for entering the example: For
instructions on entering multi-line program
and function definitions, refer to the
Calculator section of your product
guidebook.
0b, 0h
0b binaryNumber
0h hexadecimalNumber
Denotes a binary or hexadecimal number,
respectively. To enter a binary or hex
number, you must enter the 0b or 0h prefix
regardless of the Base mode. Without a
prefix, a number is treated as decimal
(base 10).
Results are displayed according to the Base
mode.
0B keys, 0H keys
In Dec base mode:
In Bin base mode:
In Hex base mode:
Symbols
231
Empty (Void) Elements
When analyzing real-world data, you might not always have a complete data set.
TI-Nspire™ CAS Software allows empty, or void, data elements so you can proceed
with the nearly complete data rather than having to start over or discard the
incomplete cases.
You can find an example of data involving empty elements in the Lists & Spreadsheet
chapter, under “Graphing spreadsheet data.”
The delVoid() function lets you remove empty elements from a list. The isVoid()
function lets you test for an empty element. For details, see delVoid() , page 53, and
isVoid() , page 92.
Note: To enter an empty element manually in a math expression, type “_” or the
keyword void. The keyword void is automatically converted to a “_” symbol when
the expression is evaluated. To type “_” on the handheld, press / _.
Calculations involving void elements
The majority of calculations involving a void
input will produce a void result. See special
cases below.
List arguments containing void elements
The following functions and commands
ignore (skip) void elements found in list
arguments.
count, countIf , cumulativeSum,
freqTable►list, frequency, max, mean,
median, product, stDevPop, stDevSamp,
sum, sumIf , varPop, and varSamp, as well as
regression calculations, OneVar, TwoVar,
and FiveNumSummary statistics, confidence
intervals, and stat tests
SortA and SortD move all void elements
within the first argument to the bottom.
232
Empty (Void) Elements
List arguments containing void elements
In regressions, a void in an X or Y list
introduces a void for the corresponding
element of the residual.
An omitted category in regressions
introduces a void for the corresponding
element of the residual.
A frequency of 0 in regressions introduces a
void for the corresponding element of the
residual.
Empty (Void) Elements
233
Shortcuts for Entering Math Expressions
Shortcuts let you enter elements of math expressions by typing instead of using the
Catalog or Symbol Palette. For example, to enter the expression √6, you can type sqrt
(6) on the entry line. When you press ·, the expression sqrt(6) is changed to
√6. Some shortrcuts are useful from both the handheld and the computer keyboard.
Others are useful primarily from the computer keyboard.
From the Handheld or Computer Keyboard
To enter this:
Type this shortcut:
π
pi
θ
theta
∞
infinity
≤
<=
≥
>=
≠
/=
⇒ (logical implication)
=>
⇔ (logical double implication, XNOR)
<=>
→ (store operator)
=:
| | (absolute value)
abs(...)
√()
sqrt(...)
d()
derivative(...)
∫()
integral(...)
Σ() (Sum template)
sumSeq(...)
Π() (Product template)
prodSeq(...)
sin⁻¹() , cos ⁻¹() , ...
arcsin(...), arccos(...), ...
ΔList()
deltaList(...)
ΔtmpCnv()
deltaTmpCnv(...)
From the Computer Keyboard
To enter this:
Type this shortcut:
c1, c2, ... (constants)
@c1, @c2, ...
234
Shortcuts for Entering Math Expressions
To enter this:
Type this shortcut:
n1, n2, ... (integer constants)
@n1, @n2, ...
i (imaginary constant)
@i
e (natural log base e)
@e
E
(scientific notation)
@E
T
(transpose)
@t
r
(radians)
@r
° (degrees)
@d
g
@g
(gradians)
∠ (angle)
@<
► (conversion)
@>
►Decimal, ►approxFraction() , and
so on.
@>Decimal, @>approxFraction(), and
so on.
Shortcuts for Entering Math Expressions
235
EOS™ (Equation Operating System) Hierarchy
This section describes the Equation Operating System (EOS™) that is used by the
TI-Nspire™ CAS math and science learning technology. Numbers, variables, and
functions are entered in a simple, straightforward sequence. EOS™ software evaluates
expressions and equations using parenthetical grouping and according to the priorities
described below.
Order of Evaluation
Level
Operator
1
Parentheses ( ), brackets [ ], braces { }
2
Indirection (#)
3
Function calls
4
Post operators: degrees-minutes-seconds ( °,',"), factorial (!), percentage
(%), radian ( r), subscript ([ ]), transpose ( T)
5
Exponentiation, power operator (^)
6
Negation ( ⁻)
7
String concatenation (&)
8
Multiplication ( •), division (/)
9
Addition (+), subtraction (-)
10
Equality relations: equal (=), not equal ( ≠ or /=),
less than (<), less than or equal ( ≤ or <=), greater than (>), greater than or
equal ( ≥ or >=)
11
Logical not
12
Logical and
13
Logical or
14
xor, nor, nand
15
Logical implication ( ⇒ )
16
Logical double implication, XNOR ( ⇔ )
17
Constraint operator (“|”)
18
Store ( → )
Parentheses, Brackets, and Braces
All calculations inside a pair of parentheses, brackets, or braces are evaluated first. For
example, in the expression 4(1+2), EOS™ software first evaluates the portion of the
expression inside the parentheses, 1+2, and then multiplies the result, 3, by 4.
236
EOS™ (Equation Operating System) Hierarchy
The number of opening and closing parentheses, brackets, and braces must be the
same within an expression or equation. If not, an error message is displayed that
indicates the missing element. For example, (1+2)/(3+4 will display the error message
“Missing ).”
Note: Because the TI-Nspire™ CAS software allows you to define your own functions, a
variable name followed by an expression in parentheses is considered a “function call”
instead of implied multiplication. For example a(b+c) is the function a evaluated by
b+c. To multiply the expression b+c by the variable a, use explicit multiplication: a•
(b+c).
Indirection
The indirection operator (#) converts a string to a variable or function name. For
example, #(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows the
creation and modification of variables from inside a program. For example, if 10→ r
and “r”→ s1, then #s1=10.
Post Operators
Post operators are operators that come directly after an argument, such as 5!, 25%, or
60°15' 45". Arguments followed by a post operator are evaluated at the fourth priority
level. For example, in the expression 4^3!, 3! is evaluated first. The result, 6, then
becomes the exponent of 4 to yield 4096.
Exponentiation
Exponentiation (^) and element-by-element exponentiation (.^) are evaluated from
right to left. For example, the expression 2^3^2 is evaluated the same as 2^(3^2) to
produce 512. This is different from (2^3)^2, which is 64.
Negation
To enter a negative number, press v followed by the number. Post operations and
exponentiation are performed before negation. For example, the result of −x2 is a
negative number, and −92 = −81. Use parentheses to square a negative number such
as ( −9) 2 to produce 81.
Constraint (“|”)
The argument following the constraint (“|”) operator provides a set of constraints that
affect the evaluation of the argument preceding the operator.
EOS™ (Equation Operating System) Hierarchy
237
Error Codes and Messages
When an error occurs, its code is assigned to variable errCode . User-defined programs
and functions can examine errCode to determine the cause of an error. For an
example of using errCode , See Example 2 under the Try command, page 187.
Note: Some error conditions apply only to TI-Nspire™ CAS products, and some apply
only to TI-Nspire™ products.
Error
code
Description
10
A function did not return a value
20
A test did not resolve to TRUE or FALSE.
Generally, undefined variables cannot be compared. For example, the test If a<b will cause
this error if either a or b is undefined when the If statement is executed.
30
Argument cannot be a folder name.
40
Argument error
50
Argument mismatch
Two or more arguments must be of the same type.
60
Argument must be a Boolean expression or integer
70
Argument must be a decimal number
90
Argument must be a list
100
Argument must be a matrix
130
Argument must be a string
140
Argument must be a variable name.
Make sure that the name:
•
•
•
•
does not begin with a digit
does not contain spaces or special characters
does not use underscore or period in invalid manner
does not exceed the length limitations
See the Calculator section in the documentation for more details.
160
Argument must be an expression
165
Batteries too low for sending or receiving
Install new batteries before sending or receiving.
170
Bound
The lower bound must be less than the upper bound to define the search interval.
238
Error Codes and Messages
Error
code
Description
180
Break
The d or c key was pressed during a long calculation or during program execution.
190
Circular definition
This message is displayed to avoid running out of memory during infinite replacement of
variable values during simplification. For example, a+1->a, where a is an undefined variable,
will cause this error.
200
Constraint expression invalid
For example, solve(3x^2-4=0,x) | x<0 or x>5 would produce this error message because the
constraint is separated by “or” instead of “and.”
210
Invalid Data type
An argument is of the wrong data type.
220
Dependent limit
230
Dimension
A list or matrix index is not valid. For example, if the list {1,2,3,4} is stored in L1, then L1[5] is a
dimension error because L1 only contains four elements.
235
Dimension Error. Not enough elements in the lists.
240
Dimension mismatch
Two or more arguments must be of the same dimension. For example, [1,2]+[1,2,3] is a
dimension mismatch because the matrices contain a different number of elements.
250
Divide by zero
260
Domain error
An argument must be in a specified domain. For example, rand(0) is not valid.
270
Duplicate variable name
280
Else and ElseIf invalid outside of If...EndIf block
290
EndTry is missing the matching Else statement
295
Excessive iteration
300
Expected 2 or 3-element list or matrix
310
The first argument of nSolve must be an equation in a single variable. It cannot contain a nonvalued variable other than the variable of interest.
320
First argument of solve or cSolve must be an equation or inequality
For example, solve(3x^2-4,x) is invalid because the first argument is not an equation.
Error Codes and Messages
239
Error
code
Description
345
Inconsistent units
350
Index out of range
360
Indirection string is not a valid variable name
380
Undefined Ans
Either the previous calculation did not create Ans, or no previous calculation was entered.
390
Invalid assignment
400
Invalid assignment value
410
Invalid command
430
Invalid for the current mode settings
435
Invalid guess
440
Invalid implied multiply
For example, x(x+1) is invalid; whereas, x*(x+1) is the correct syntax. This is to avoid
confusion between implied multiplication and function calls.
450
Invalid in a function or current expression
Only certain commands are valid in a user-defined function.
490
Invalid in Try..EndTry block
510
Invalid list or matrix
550
Invalid outside function or program
A number of commands are not valid outside a function or program. For example, Local
cannot be used unless it is in a function or program.
560
Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks
For example, the Exit command is valid only inside these loop blocks.
565
Invalid outside program
570
Invalid pathname
For example, \var is invalid.
575
Invalid polar complex
580
Invalid program reference
Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a
program.
240
Error Codes and Messages
Error
code
Description
600
Invalid table
605
Invalid use of units
610
Invalid variable name in a Local statement
620
Invalid variable or function name
630
Invalid variable reference
640
Invalid vector syntax
650
Link transmission
A transmission between two units was not completed. Verify that the connecting cable is
connected firmly to both ends.
665
Matrix not diagonalizable
670
Low Memory
1. Delete some data in this document
2. Save and close this document
If 1 and 2 fail, pull out and re-insert batteries
672
Resource exhaustion
673
Resource exhaustion
680
Missing (
690
Missing )
700
Missing “
710
Missing ]
720
Missing }
730
Missing start or end of block syntax
740
Missing Then in the If..EndIf block
750
Name is not a function or program
765
No functions selected
780
No solution found
800
Non-real result
For example, if the software is in the Real setting, √(-1) is invalid.
Error Codes and Messages
241
Error
code
Description
To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or
POLAR.
830
Overflow
850
Program not found
A program reference inside another program could not be found in the provided path during
execution.
855
Rand type functions not allowed in graphing
860
Recursion too deep
870
Reserved name or system variable
900
Argument error
Median-median model could not be applied to data set.
910
Syntax error
920
Text not found
930
Too few arguments
The function or command is missing one or more arguments.
940
Too many arguments
The expression or equation contains an excessive number of arguments and cannot be
evaluated.
950
Too many subscripts
955
Too many undefined variables
960
Variable is not defined
No value is assigned to variable. Use one of the following commands:
•
•
•
sto →
:=
Define
to assign values to variables.
965
Unlicensed OS
970
Variable in use so references or changes are not allowed
980
Variable is protected
990
Invalid variable name
Make sure that the name does not exceed the length limitations
242
Error Codes and Messages
Error
code
Description
1000
Window variables domain
1010
Zoom
1020
Internal error
1030
Protected memory violation
1040
Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™
CAS.
1045
Unsupported operator. This operator requires Computer Algebra System. Try TI-Nspire™
CAS.
1050
Unsupported feature. This operator requires Computer Algebra System. Try TI-Nspire™
CAS.
1060
Input argument must be numeric. Only inputs containing numeric values are allowed.
1070
Trig function argument too big for accurate reduction
1080
Unsupported use of Ans.This application does not support Ans.
1090
Function is not defined. Use one of the following commands:
•
•
•
Define
:=
sto →
to define a function.
1100
Non-real calculation
For example, if the software is in the Real setting, √(-1) is invalid.
To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or
POLAR.
1110
Invalid bounds
1120
No sign change
1130
Argument cannot be a list or matrix
1140
Argument error
The first argument must be a polynomial expression in the second argument. If the second
argument is omitted, the software attempts to select a default.
1150
Argument error
The first two arguments must be polynomial expressions in the third argument. If the third
argument is omitted, the software attempts to select a default.
1160
Invalid library pathname
Error Codes and Messages
243
Error
code
Description
A pathname must be in the form xxx\yyy, where:
•
•
The xxx part can have 1 to 16 characters.
The yyy part can have 1 to 15 characters.
See the Library section in the documentation for more details.
1170
Invalid use of library pathname
•
•
1180
A value cannot be assigned to a pathname using Define, :=, or sto → .
A pathname cannot be declared as a Local variable or be used as a
parameter in a function or program definition.
Invalid library variable name.
Make sure that the name:
•
•
•
Does not contain a period
Does not begin with an underscore
Does not exceed 15 characters
See the Library section in the documentation for more details.
1190
Library document not found:
•
•
Verify library is in the MyLib folder.
Refresh Libraries.
See the Library section in the documentation for more details.
1200
Library variable not found:
•
•
•
Verify library variable exists in the first problem in the library.
Make sure library variable has been defined as LibPub or LibPriv.
Refresh Libraries.
See the Library section in the documentation for more details.
1210
Invalid library shortcut name.
Make sure that the name:
•
•
•
•
Does not contain a period
Does not begin with an underscore
Does not exceed 16 characters
Is not a reserved name
See the Library section in the documentation for more details.
1220
Domain error:
The tangentLine and normalLine functions support real-valued functions only.
1230
244
Domain error.
Error Codes and Messages
Error
code
Description
Trigonometric conversion operators are not supported in Degree or Gradian angle modes.
1250
Argument Error
Use a system of linear equations.
Example of a system of two linear equations with variables x and y:
3x+7y=5
2y-5x=-1
1260
Argument Error:
The first argument of nfMin or nfMax must be an expression in a single variable. It cannot
contain a non-valued variable other than the variable of interest.
1270
Argument Error
Order of the derivative must be equal to 1 or 2.
1280
Argument Error
Use a polynomial in expanded form in one variable.
1290
Argument Error
Use a polynomial in one variable.
1300
Argument Error
The coefficients of the polynomial must evaluate to numeric values.
1310
Argument error:
A function could not be evaluated for one or more of its arguments.
1380
Argument error:
Nested calls to domain() function are not allowed.
Error Codes and Messages
245
Warning Codes and Messages
You can use the warnCodes() function to store the codes of warnings generated by
evaluating an expression. This table lists each numeric warning code and its associated
message. For an example of storing warning codes, see warnCodes() , page 196.
Warning
code
Message
10000
Operation might introduce false solutions.
10001
Differentiating an equation may produce a false equation.
10002
Questionable solution
10003
Questionable accuracy
10004
Operation might lose solutions.
10005
cSolve might specify more zeros.
10006
Solve may specify more zeros.
10007
More solutions may exist. Try specifying appropriate lower and upper bounds and/or a
guess.
Examples using solve():
•
•
•
solve(Equation, Var=Guess)|lowBound<Var<upBound
solve(Equation, Var)|lowBound<Var<upBound
solve(Equation, Var=Guess)
10008
Domain of the result might be smaller than the domain of the input.
10009
Domain of the result might be larger than the domain of the input.
10012
Non-real calculation
10013
∞^0 or undef^0 replaced by 1
10014
undef^0 replaced by 1
10015
1^∞ or 1^undef replaced by 1
10016
1^undef replaced by 1
10017
Overflow replaced by ∞ or −∞
10018
Operation requires and returns 64 bit value.
10019
Resource exhaustion, simplification might be incomplete.
10020
Trig function argument too big for accurate reduction.
10021
Input contains an undefined parameter.
Result might not be valid for all possible parameter values.
246
Warning Codes and Messages
Warning
code
Message
10022
Specifying appropriate lower and upper bounds might produce a solution.
10023
Scalar has been multiplied by the identity matrix.
10024
Result obtained using approximate arithmetic.
10025
Equivalence cannot be verified in EXACT mode.
10026
Constraint might be ignored. Specify constraint in the form "\" 'Variable MathTestSymbol
Constant' or a conjunct of these forms, for example 'x<3 and x>-12'
Warning Codes and Messages
247
248
Support and Service
Texas Instruments Support and Service
General Information: North and South America
Home Page:
KnowledgeBase and e-mail inquiries:
education.ti.com
education.ti.com/support
Phone:
(800) TI-CARES / (800) 842-2737
For North and South America and U.S.
Territories
International contact information:
http://education.ti.com/en/us/customersupport/support_worldwide
For Technical Support
Knowledge Base and support by e-mail:
education.ti.com/support or [email protected]
Phone (not toll-free):
(972) 917-8324
For Product (Hardware) Service
Customers in the U.S., Canada, Mexico, and U.S. territories: Always contact Texas
Instruments Customer Support before returning a product for service.
For All Other Countries:
For general information
For more information about TI products and services, contact TI by e-mail or visit the
TI Internet address.
E-mail inquiries:
Home Page:
[email protected]
education.ti.com
Service and Warranty Information
For information about the length and terms of the warranty or about product service,
refer to the warranty statement enclosed with this product or contact your local Texas
Instruments retailer/distributor.
Support and Service
249
250
Index
-, subtract
206
!
!, factorial
216
"
", second notation
224
#
#, indirection
#, indirection operator
222
237
%
%, percent
212
&
&, append
216
*
*, multiply
207
.
.-, dot subtraction
.*, dot multiplication
./, dot division
.^, dot power
.+, dot addition
210
211
211
211
210
/
/, divide
208
:
:=, assign
230
^
^⁻¹, reciprocal
228
Index
251
^, power
209
_
_, unit designation
226
|
|, constraint operator
228
′
′ minute notation
′, prime
224
226
+
+, add
206
=
≠, not equal
≤, less than or equal
≥, greater than or equal
>, greater than
=, equal
213
214
215
214
212
∏
∏, product
219
∑
∑( ), sum
∑Int( )
∑Prn( )
220
221
221
√
√, square root
219
∠
∠ (angle)
225
∫
∫, integral
252
Index
217
►
►, convert units
►approxFraction( )
►Base10, display as decimal integer
►Base16, display as hexadecimal
►Base2, display as binary
►cos, display in terms of cosine
►Cylind, display as cylindrical vector
►DD, display as decimal angle
►Decimal, display result as decimal
►DMS, display as degree/minute/second
►exp, display in terms of e
►Grad, convert to gradian angle
►Polar, display as polar vector
►Rad, convert to radian angle
►Rect, display as rectangular vector
►sin, display in terms of sine
►Sphere, display as spherical vector
227
17
22
23
21
33
46
49
50
57
66
85
131
141
144
162
171
⇒
⇒ , logical implication
215, 234
→
→, store variable
229
⇔
⇔ , logical double implication
216, 234
©
©, comment
231
°
°, degree notation
°, degrees/minutes/seconds
224
224
0
0b, binary indicator
0h, hexadecimal indicator
231
231
Index
253
1
10^( ), power of ten
227
2
2-sample F Test
78
A
abs( ), absolute value
absolute value
template for
add, +
amortization table, amortTbl( )
amortTbl( ), amortization table
and, Boolean operator
angle( ), angle
angle, angle( )
ANOVA, one-way variance analysis
ANOVA2way, two-way variance analysis
Ans, last answer
answer (last), Ans
append, &
approx( ), approximate
approximate, approx( )
approxRational( )
arc length, arcLen( )
arccos(), cos⁻¹()
arccosh(), cosh⁻¹()
arccot(), cot⁻¹()
arccoth(), coth⁻¹()
arccsc(), csc⁻¹()
arccsch(), csch⁻¹()
arcLen( ), arc length
arcsec(), sec⁻¹()
arcsech(), csech⁻¹()
arcsin(), sin⁻¹()
arcsinh(), sinh⁻¹()
arctan(), tan⁻¹()
arctanh(), tanh⁻¹()
arguments in TVM functions
augment( ), augment/concatenate
augment/concatenate, augment( )
254
Index
12
7-8
206
12, 21
12, 21
13
14
14
14
15
17
17
216
17-18
17-18
18
19
18
18
18
18
18
18
19
19
19
19
19
19
19
191
19
19
average rate of change, avgRC( )
avgRC( ), average rate of change
20
20
B
binary
display, ►Base2
indicator, 0b
binomCdf( )
binomPdf( )
Boolean operators
⇒
⇔
and
nand
nor
not
or
xor
21
231
24
24
215, 234
216
13
117
121
123
127
197
C
Cdf( )
ceiling( ), ceiling
ceiling, ceiling( )
centralDiff( )
cFactor( ), complex factor
char( ), character string
character string, char( )
characters
numeric code, ord( )
string, char( )
charPoly( )
χ²2way
clear
error, ClrErr
ClearAZ
ClrErr, clear error
colAugment
colDim( ), matrix column dimension
colNorm( ), matrix column norm
combinations, nCr( )
comDenom( ), common denominator
comment, ©
71
24
24-25, 40
25
25
26
26
128
26
27
27
29
29
29
30
30
30
118
30
231
Index
255
common denominator, comDenom( )
completeSquare( ), complete square
complex
conjugate, conj( )
factor, cFactor( )
solve, cSolve( )
zeros, cZeros( )
conj( ), complex conjugate
constant
in solve( )
constants
in cSolve( )
in cZeros( )
in deSolve( )
in solve( )
in zeros( )
shortcuts for
constraint operator "|"
constraint operator, order of evaluation
construct matrix, constructMat( )
constructMat( ), construct matrix
convert
►Grad
►Rad
units
copy variable or function, CopyVar
correlation matrix, corrMat( )
corrMat( ), correlation matrix
cos⁻¹, arccosine
cos( ), cosine
cosh⁻¹( ), hyperbolic arccosine
cosh( ), hyperbolic cosine
cosine
display expression in terms of
cosine, cos( )
cot⁻¹( ), arccotangent
cot( ), cotangent
cotangent, cot( )
coth⁻¹( ), hyperbolic arccotangent
coth( ), hyperbolic cotangent
count days between dates, dbd( )
count items in a list conditionally , countif( )
count items in a list, count( )
256
Index
30
31
32
25
42
46
32
168
44
48
54
169
199
234
228
236
32
32
85
141
227
33
33
33
35
34
36
36
33
34
37
37
37
38
38
49
39
38
count( ), count items in a list
countif( ), conditionally count items in a list
cPolyRoots()
cross product, crossP( )
crossP( ), cross product
csc⁻¹( ), inverse cosecant
csc( ), cosecant
csch⁻¹( ), inverse hyperbolic cosecant
csch( ), hyperbolic cosecant
cSolve( ), complex solve
cubic regression, CubicReg
CubicReg, cubic regression
cumulative sum, cumulativeSum( )
cumulativeSum( ), cumulative sum
cycle, Cycle
Cycle, cycle
cylindrical vector display, ►Cylind
cZeros( ), complex zeros
38
39
40
40
40
41
40
41
41
42
44
44
45
45
46
46
46
46
D
d( ), first derivative
days between dates, dbd( )
dbd( ), days between dates
decimal
angle display, ►DD
integer display, ►Base10
Define
Define LibPriv
Define LibPub
define, Define
Define, define
defining
private function or program
public function or program
definite integral
template for
degree notation, °
degree/minute/second display, ►DMS
degree/minute/second notation
delete
void elements from list
deleting
variable, DelVar
217
49
49
49
22
50
51
52
50
50
51
52
10
224
57
224
53
53
Index
257
deltaList()
deltaTmpCnv()
DelVar, delete variable
delVoid( ), remove void elements
denominator
derivative or nth derivative
template for
derivative()
derivatives
first derivative, d( )
numeric derivative, nDeriv( )
numeric derivative, nDerivative( )
deSolve( ), solution
det( ), matrix determinant
diag( ), matrix diagonal
dim( ), dimension
dimension, dim( )
Disp, display data
display as
binary, ►Base2
cylindrical vector, ►Cylind
decimal angle, ►DD
decimal integer, ►Base10
degree/minute/second, ►DMS
hexadecimal, ►Base16
polar vector, ►Polar
rectangular vector, ►Rect
spherical vector, ►Sphere
display data, Disp
distribution functions
binomCdf( )
binomPdf( )
invNorm( )
invt( )
Invχ²( )
normCdf( )
normPdf( )
poissCdf( )
poissPdf( )
tCdf( )
tPdf( )
χ²2way( )
χ²Cdf( )
258
Index
52
52
53
53
30
10
53
217
119-120
119
53
55
56
56
56
57, 155
21
46
49
22
57
23
131
144
171
57, 155
24
24
91
91
90
123
123
130
130
181
186
27
28
χ²GOF( )
χ²Pdf( )
divide, /
domain function, domain( )
domain( ), domain function
dominant term, dominantTerm( )
dominantTerm( ), dominant term
dot
addition, .+
division, ./
multiplication, .*
power, .^
product, dotP( )
subtraction, .dotP( ), dot product
28
28
208
58
58
58
58
210
211
211
211
60
210
60
E
e exponent
template for
e to a power, e^( )
e, display expression in terms of
E, exponent
e^( ), e to a power
eff( ), convert nominal to effective rate
effective rate, eff( )
eigenvalue, eigVl( )
eigenvector, eigVc( )
eigVc( ), eigenvector
eigVl( ), eigenvalue
else if, ElseIf
else, Else
ElseIf, else if
empty (void) elements
end
for, EndFor
function, EndFunc
if, EndIf
loop, EndLoop
program, EndPrgm
try, EndTry
while, EndWhile
end function, EndFunc
end if, EndIf
6
60, 66
66
223
60
61
61
61
61
61
61
62
86
62
232
75
78
86
108
135
187
197
78
86
Index
259
end loop, EndLoop
end while, EndWhile
EndTry, end try
EndWhile, end while
EOS (Equation Operating System)
equal, =
Equation Operating System (EOS)
error codes and messages
errors and troubleshooting
clear error, ClrErr
pass error, PassErr
euler( ), Euler function
evaluate polynomial, polyEval( )
evaluation, order of
exact( ), exact
exact, exact( )
exclusion with "|" operator
exit, Exit
Exit, exit
exp( ), e to a power
exp►list( ), expression to list
expand( ), expand
expand, expand( )
exponent, E
exponential regession, ExpReg
exponents
template for
expr( ), string to expression
ExpReg, exponential regession
expressions
expression to list, exp►list( )
string to expression, expr( )
108
197
187
197
236
212
236
238, 246
29
129
63
132
236
65
65
228
65
65
66
67
67
67
223
69
5
68, 105
69
67
68, 105
F
factor( ), factor
factor, factor( )
factorial, !
Fill, matrix fill
financial functions, tvmFV( )
financial functions, tvmI( )
financial functions, tvmN( )
financial functions, tvmPmt( )
financial functions, tvmPV( )
260
Index
70
70
216
72
189
189
190
190
190
first derivative
template for
FiveNumSummary
floor( ), floor
floor, floor( )
fMax( ), function maximum
fMin( ), function minimum
For
for, For
For, for
format string, format( )
format( ), format string
fpart( ), function part
fractions
propFrac
template for
freqTable( )
frequency( )
Frobenius norm, norm( )
Func, function
Func, program function
functions
maximum, fMax( )
minimum, fMin( )
part, fpart( )
program function, Func
user-defined
functions and variables
copying
9
72
73
73
73
74
75
75
75
75
75
76
136
5
76
77
122
78
78
73
74
76
78
50
33
G
g, gradians
gcd( ), greatest common divisor
geomCdf( )
geomPdf( )
Get
get/return
denominator, getDenom( )
number, getNum( )
variables injformation, getVarInfo( )
getDenom( ), get/return denominator
getLangInfo( ), get/return language information
getLockInfo( ), tests lock status of variable or variable group
223
79
79
80
80
81
83
81, 84
81
81
82
Index
261
getMode( ), get mode settings
getNum( ), get/return number
GetStr
getType( ), get type of variable
getVarInfo( ), get/return variables information
go to, Goto
Goto, go to
gradian notation, g
greater than or equal, ≥
greater than, >
greatest common divisor, gcd( )
groups, locking and unlocking
groups, testing lock status
82
83
83
84
84
85
85
223
215
214
79
104, 193
82
H
hexadecimal
display, ►Base16
indicator, 0h
hyperbolic
arccosine, cosh⁻¹( )
arcsine, sinh⁻¹( )
arctangent, tanh⁻¹( )
cosine, cosh( )
sine, sinh( )
tangent, tanh( )
23
231
36
165
180
36
164
180
I
identity matrix, identity( )
identity( ), identity matrix
if, If
If, if
ifFn( )
imag( ), imaginary part
imaginary part, imag( )
ImpDif( ), implicit derivative
implicit derivative, Impdif( )
indefinite integral
template for
indirection operator (#)
indirection, #
input, Input
Input, input
262
Index
86
86
86
86
87
88
88
88
88
10
237
222
88
88
inString( ), within string
int( ), integer
intDiv( ), integer divide
integer divide, intDiv( )
integer part, iPart( )
integer, int( )
integral, ∫
interpolate( ), interpolate
inverse cumulative normal distribution (invNorm( )
inverse, ^⁻¹
invF( )
invNorm( ), inverse cumulative normal distribution)
invt( )
Invχ²( )
iPart( ), integer part
irr( ), internal rate of return
internal rate of return, irr( )
isPrime( ), prime test
isVoid( ), test for void
89
89
89
89
91
89
217
90
91
228
90
91
91
90
91
91
92
92
L
label, Lbl
language
get language information
Lbl, label
lcm, least common multiple
least common multiple, lcm
left( ), left
left, left( )
length of string
less than or equal, ≤
LibPriv
LibPub
library
create shortcuts to objects
libShortcut( ), create shortcuts to library objects
limit
lim( )
limit( )
template for
limit( ) or lim( ), limit
linear regression, LinRegAx
linear regression, LinRegBx
93
81
93
93
93
93
93
56
214
51
52
94
94
95
95
10
95
97
95, 98
Index
263
LinRegBx, linear regression
LinRegMx, linear regression
LinRegtIntervals, linear regression
LinRegtTest
linSolve()
Δlist( ), list difference
list to matrix, list►mat( )
list, conditionally count items in
list, count items in
list►mat( ), list to matrix
lists
augment/concatenate, augment( )
cross product, crossP( )
cumulative sum, cumulativeSum( )
differences in a list, Δlist( )
dot product, dotP( )
empty elements in
expression to list, exp►list( )
list to matrix, list►mat( )
matrix to list, mat►list( )
maximum, max( )
mid-string, mid( )
minimum, min( )
new, newList( )
product, product( )
sort ascending, SortA
sort descending, SortD
summation, sum( )
ln( ), natural logarithm
LnReg, logarithmic regression
local variable, Local
local, Local
Local, local variable
Lock, lock variable or variable group
locking variables and variable groups
Log
template for
logarithmic regression, LnReg
logarithms
logical double implication, ⇔
logical implication, ⇒
logistic regression, Logistic
logistic regression, LogisticD
264
Index
95
97
98
99
100
101
101
39
38
101
19
40
45
101
60
232
67
101
109
109
112
113
119
136
170
171
176
102
102
104
104
104
104
104
6
102
102
216
215, 234
106
107
Logistic, logistic regression
LogisticD, logistic regression
loop, Loop
Loop, loop
LU, matrix lower-upper decomposition
106
107
108
108
108
M
mat►list( ), matrix to list
matrices
augment/concatenate, augment( )
column dimension, colDim( )
column norm, colNorm( )
cumulative sum, cumulativeSum( )
determinant, det( )
diagonal, diag( )
dimension, dim( )
dot addition, .+
dot division, ./
dot multiplication, .*
dot power, .^
dot subtraction, .eigenvalue, eigVl( )
eigenvector, eigVc( )
filling, Fill
identity, identity( )
list to matrix, list►mat( )
lower-upper decomposition, LU
matrix to list, mat►list( )
maximum, max( )
minimum, min( )
new, newMat( )
product, product( )
QR factorization, QR
random, randMat( )
reduced row echelon form, rref( )
row addition, rowAdd( )
row dimension, rowDim( )
row echelon form, ref( )
row multiplication and addition, mRowAdd( )
row norm, rowNorm( )
row operation, mRow( )
row swap, rowSwap( )
109
19
30
30
45
55
56
56
210
211
211
211
210
61
61
72
86
101
108
109
109
113
119
136
137
142
153
152
152
145
114
152
114
153
Index
265
submatrix, subMat( )
summation, sum( )
transpose, T
matrix (1 × 2)
template for
matrix (2 × 1)
template for
matrix (2 × 2)
template for
matrix (m × n)
template for
matrix to list, mat►list( )
max( ), maximum
maximum, max( )
mean( ), mean
mean, mean( )
median( ), median
median, median( )
medium-medium line regression, MedMed
MedMed, medium-medium line regression
mid-string, mid( )
mid( ), mid-string
min( ), minimum
minimum, min( )
minute notation, ′
mirr( ), modified internal rate of return
mixed fractions, using propFrac(› with
mod( ), modulo
mode settings, getMode( )
modes
setting, setMode( )
modified internal rate of return, mirr( )
modulo, mod( )
mRow( ), matrix row operation
mRowAdd( ), matrix row multiplication and addition
Multiple linear regression t test
multiply, *
MultReg
MultRegIntervals( )
MultRegTests( )
176-177
176
178
8
8
8
8
109
109
109
110
110
110
110
111
111
112
112
113
113
224
113
136
114
82
158
113
114
114
114
116
207
115
115
116
N
nand, Boolean operator
266
Index
117
natural logarithm, ln( )
nCr( ), combinations
nDerivative( ), numeric derivative
negation, entering negative numbers
net present value, npv( )
new
list, newList( )
matrix, newMat( )
newList( ), new list
newMat( ), new matrix
nfMax( ), numeric function maximum
nfMin( ), numeric function minimum
nInt( ), numeric integral
nom ), convert effective to nominal rate
nominal rate, nom( )
nor, Boolean operator
norm( ), Frobenius norm
normal distribution probability, normCdf( )
normal line, normalLine( )
normalLine( )
normCdf( )
normPdf( )
not equal, ≠
not, Boolean operator
nPr( ), permutations
npv( ), net present value
nSolve( ), numeric solution
nth root
template for
numeric
derivative, nDeriv( )
derivative, nDerivative( )
integral, nInt( )
solution, nSolve( )
102
118
119
237
124
119
119
119
119
119
120
120
121
121
121
122
123
122
122
123
123
213
123
124
124
125
5
119-120
119
120
125
O
objects
create shortcuts to library
one-variable statistics, OneVar
OneVar, one-variable statistics
operators
order of evaluation
or (Boolean), or
94
126
126
236
127
Index
267
or, Boolean operator
ord( ), numeric character code
127
128
P
P►Rx( ), rectangular x coordinate
P►Ry( ), rectangular y coordinate
pass error, PassErr
PassErr, pass error
Pdf( )
percent, %
permutations, nPr( )
piecewise function (2-piece)
template for
piecewise function (N-piece)
template for
piecewise( )
poissCdf( )
poissPdf( )
polar
coordinate, R►Pr( )
coordinate, R►Pθ( )
vector display, ►Polar
polyCoef( )
polyDegree( )
polyEval( ), evaluate polynomial
polyGcd( )
polynomials
evaluate, polyEval( )
random, randPoly( )
PolyRoots()
power of ten, 10^( )
power regression, PowerReg
power, ^
PowerReg, power regression
Prgm, define program
prime number test, isPrime( )
prime, ′
probability densiy, normPdf( )
prodSeq()
product( ), product
product, ∏( )
template for
product, product( )
268
Index
128
129
129
129
76
212
124
6
7
130
130
130
141
140
131
131
132
132
133
132
143
134
227
134, 146-147, 183
209
134
135
92
226
123
136
136
219
9
136
programming
define program, Prgm
display data, Disp
pass error, PassErr
programs
defining private library
defining public library
programs and programming
clear error, ClrErr
display I/O screen, Disp
end program, EndPrgm
end try, EndTry
try, Try
proper fraction, propFrac
propFrac, proper fraction
135
57, 155
129
51
52
29
57, 155
135
187
187
136
136
Q
QR factorization, QR
QR, QR factorization
quadratic regression, QuadReg
QuadReg, quadratic regression
quartic regression, QuartReg
QuartReg, quartic regression
137
137
138
138
139
139
R
R, radian
R►Pr( ), polar coordinate
R►Pθ( ), polar coordinate
radian, R
rand( ), random number
randBin, random number
randInt( ), random integer
randMat( ), random matrix
randNorm( ), random norm
random
matrix, randMat( )
norm, randNorm( )
number seed, RandSeed
polynomial, randPoly( )
random sample
randPoly( ), random polynomial
randSamp( )
223
141
140
223
141
142
142
142
143
142
143
143
143
143
143
143
Index
269
RandSeed, random number seed
real( ), real
real, real( )
reciprocal, ^⁻¹
rectangular-vector display, ►Rect
rectangular x coordinate, P►Rx( )
rectangular y coordinate, P►Ry( )
reduced row echelon form, rref( )
ref( ), row echelon form
regressions
cubic, CubicReg
exponential, ExpReg
linear regression, LinRegAx
linear regression, LinRegBx
logarithmic, LnReg
Logistic
logistic, Logistic
medium-medium line, MedMed
MultReg
power regression, PowerReg
quadratic, QuadReg
quartic, QuartReg
sinusoidal, SinReg
remain( ), remainder
remainder, remain( )
remove
void elements from list
Request
RequestStr
result
display in terms of cosine
display in terms of e
display in terms of sine
result values, statistics
results, statistics
return, Return
Return, return
right( ), right
right, right( )
rk23( ), Runge Kutta function
rotate( ), rotate
rotate, rotate( )
round( ), round
270
Index
143
144
144
228
144
128
129
153
145
44
69
97
95, 98
102
106
107
111
115
134, 146-147, 183
138
139
165
146
146
53
146
147
33
66
162
173
172
148
148
148
31, 63, 90, 148-149
149
150
150
152
round, round( )
row echelon form, ref( )
rowAdd( ), matrix row addition
rowDim( ), matrix row dimension
rowNorm( ), matrix row norm
rowSwap( ), matrix row swap
rref( ), reduced row echelon form
152
145
152
152
152
153
153
S
sec⁻¹( ), inverse secant
sec( ), secant
sech⁻¹( ), inverse hyperbolic secant
sech( ), hyperbolic secant
second derivative
template for
second notation, "
seq( ), sequence
seqGen( )
seqn( )
sequence, seq( )
series( ), series
series, series( )
set
mode, setMode( )
setMode( ), set mode
settings, get current
shift( ), shift
shift, shift( )
sign( ), sign
sign, sign( )
simult( ), simultaneous equations
simultaneous equations, simult( )
sin⁻¹( ), arcsine
sin( ), sine
sine
display expression in terms of
sine, sin( )
sinh⁻¹( ), hyperbolic arcsine
sinh( ), hyperbolic sine
SinReg, sinusoidal regression
sinusoidal regression, SinReg
solution, deSolve( )
solve( ), solve
154
153
154
154
10
224
155
156
156
155-156
157
157
158
158
82
160
160
161
161
162
162
164
163
162
163
165
164
165
165
53
167
Index
271
solve, solve( )
SortA, sort ascending
SortD, sort descending
sorting
ascending, SortA
descending, SortD
spherical vector display, ►Sphere
sqrt( ), square root
square root
template for
square root, √( )
standard deviation, stdDev( )
stat.results
stat.values
statistics
combinations, nCr( )
factorial, !
mean, mean( )
median, median( )
one-variable statistics, OneVar
permutations, nPr( )
random norm, randNorm( )
random number seed, RandSeed
standard deviation, stdDev( )
two-variable results, TwoVar
variance, variance( )
stdDevPop( ), population standard deviation
stdDevSamp( ), sample standard deviation
Stop command
store variable (→)
storing
symbol, &
string
dimension, dim( )
length
string( ), expression to string
strings
append, &
character code, ord( )
character string, char( )
expression to string, string( )
format, format( )
formatting
272
Index
167
170
171
170
171
171
172
5
172, 219
174, 194
172
173
118
216
110
110
126
124
143
143
174, 194
191
194
174
174
175
229
230
56
56
175
216
128
26
175
75
75
indirection, #
left, left( )
mid-string, mid( )
right, right( )
rotate, rotate( )
shift, shift( )
string to expression, expr( )
using to create variable names
within, InString
student-t distribution probability, tCdf( )
student-t probability density, tPdf( )
subMat( ), submatrix
submatrix, subMat( )
substitution with "|" operator
subtract, sum of interest payments
sum of principal payments
sum( ), summation
sum, ∑( )
template for
sumIf( )
summation, sum( )
sumSeq()
system of equations (2-equation)
template for
system of equations (N-equation)
template for
222
93
112
31, 63, 90, 148-149
150
160
68, 105
237
89
181
186
176-177
176-177
228
206
221
221
176
220
9
176
176
177
7
7
T
t test, tTest
T, transpose
tan⁻¹( ), arctangent
tan( ), tangent
tangent line, tangentLine( )
tangent, tan( )
tangentLine( )
tanh⁻¹( ), hyperbolic arctangent
tanh( ), hyperbolic tangent
Taylor polynomial, taylor( )
taylor( ), Taylor polynomial
tCdf( ), studentt distribution probability
tCollect( ), trigonometric collection
188
178
179
178
179
178
179
180
180
181
181
181
182
Index
273
templates
absolute value
definite integral
derivative or nth derivative
e exponent
exponent
first derivative
fraction
indefinite integral
limit
Log
matrix (1 × 2)
matrix (2 × 1)
matrix (2 × 2)
matrix (m × n)
nth root
piecewise function (2-piece)
piecewise function (N-piece)
product, ∏( )
second derivative
square root
sum, ∑( )
system of equations (2-equation)
system of equations (N-equation)
test for void, isVoid( )
Test_2S, 2-sample F test
tExpand( ), trigonometric expansion
Text command
time value of money, Future Value
time value of money, Interest
time value of money, number of payments
time value of money, payment amount
time value of money, present value
tInterval, t confidence interval
tInterval_2Samp, twosample t confidence interval
ΔtmpCnv()
tmpCnv()
tPdf( ), student probability density
trace( )
transpose, T
trigonometric collection, tCollect( )
trigonometric expansion, tExpand( )
Try, error handling command
274
Index
7-8
10
10
6
5
9
5
10
10
6
8
8
8
8
5
6
7
9
10
5
9
7
7
92
78
182
183
189
189
190
190
190
183
184
185
185
186
186
178
182
182
187
tTest, t test
tTest_2Samp, two-sample t test
TVM arguments
tvmFV( )
tvmI( )
tvmN( )
tvmPmt( )
tvmPV( )
two-variable results, TwoVar
TwoVar, two-variable results
188
188
191
189
189
190
190
190
191
191
U
underscore, _
unit vector, unitV( )
units
convert
unitV( ), unit vector
unLock, unlock variable or variable group
unlocking variables and variable groups
user-defined functions
user-defined functions and programs
226
193
227
193
193
193
50
51-52
V
variable
creating name from a character string
variable and functions
copying
variables
clear all single-letter
delete, DelVar
local, Local
variables, locking and unlocking
variance, variance( )
varPop( )
varSamp( ), sample variance
vectors
cross product, crossP( )
cylindrical vector display, ►Cylind
dot product, dotP( )
unit, unitV( )
void elements
void elements, remove
void, test for
237
33
29
53
104
82, 104, 193
194
194
194
40
46
60
193
232
53
92
Index
275
W
Wait command
warnCodes( ), Warning codes
warning codes and messages
when( ), when
when, when( )
while, While
While, while
with, |
within string, inString( )
195
196
246
196
196
197
197
228
89
X
x², square
XNOR
xor, Boolean exclusive or
210
216
197
Z
zeroes( ), zeroes
zeroes, zeroes( )
zInterval, z confidence interval
zInterval_1Prop, one-proportion z confidence interval
zInterval_2Prop, two-proportion z confidence interval
zInterval_2Samp, two-sample z confidence interval
zTest
zTest_1Prop, one-proportion z test
zTest_2Prop, two-proportion z test
zTest_2Samp, two-sample z test
198
198
200
201
201
202
202
203
203
204
Χ
χ²Cdf( )
χ²GOF
χ²Pdf( )
276
Index
28
28
28
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