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TI-Nspire Calculator Manual (User Guide)

TI-Nspire™ CX CAS

Reference Guide

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ii

Contents

Expression Templates

1

Alphabetical Listing

8

A

8

B 17

C 20

D 44

E 57

F 67

G 76

I 86

L 95

M 111

N 119

O 128

P 130

Q 139

R 142

S 157

T 182

U 197

V 198

W 199

X 201

Z 202

Symbols 210

TI-Nspire™ CX II - Draw Commands 236

Graphics Programming 236

Graphics Screen 236

Default View and Settings 237

Graphics Screen Errors Messages 238

Invalid Commands While in Graphics Mode 238

C 239

D 240

F 243

G 245

P 246

S 248

U 250

iii

Empty (Void) Elements 251

Shortcuts for Entering Math Expressions 253

EOS™ (Equation Operating System) Hierarchy 255

TI-Nspire CX II - TI-Basic Programming Features 257

Auto-indentation in Programming Editor 257

Improved Error Messages for TI-Basic 257

Constants and Values 260

Error Codes and Messages 261

Warning Codes and Messages 269

General Information 271

Online Help 271

Contact TI Support 271

Service and Warranty Information 271

Index 272

iv

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.

Fraction template /p keys

Example:

Note: See also / (divide), page 212.

Exponent template l key

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 213.

Square root template /q keys

Example:

Note: See also () (square root), page

223.

Nth root template /l keys

Example:

Note: See also root(), page 154.


Expression Templates 1

Nth root template /l keys

e exponent template u keys

Example:

Natural exponential e raised to a power

Note: See also e^(), page 57.

Log template /s key

Example:

Calculates log to a specified base. For a default of base 10, omit the base.

Note: See also log(), page 107.

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 132.

2 Expression Templates

Piecewise template (N-piece) Catalog >


Lets you create expressions and conditions for an N-piece piecewise function. Prompts for N.

Note: See also piecewise(), page 132.

Example:

See the example for Piecewise template (2- piece).

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 181.

System of N equations template Catalog >

Lets you create a system of N equations. Prompts for N.

Note: See also system(), page 181.

Example:

See the example for System of equations template (2-equation).

Absolute value template Catalog >

Example:

Note: See also abs(), page 8.

Expression Templates 3

Absolute value template Catalog >

dd°mm’ss.ss’’ template Catalog >

Example:



Lets you enter angles in dd°mmss.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) Catalog >


The template appears after you are prompted to specify the number of rows and columns.

4 Expression Templates

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 224.

Product template (Π) Catalog >

Example:

Note: See also Π() (prodSeq), page 223.

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 221.

Expression Templates 5

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 221.

Nth derivative template Catalog >

Example:

The nth derivative template can be used to calculate the nth derivative.

Note: See also d() (derivative), page 221.

Definite integral template Catalog >

Example:

Note: See also() integral(), page 221.

Indefinite integral template Catalog >

Example:

Note: See also () integral(), page 221.

Limit template Catalog >

Example:

6 Expression Templates

Limit template Catalog >


Use or () for left hand limit. Use + for right hand limit.

Note: See also limit(), page 6.

Expression Templates 7

Alphabetical Listing

Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, page 210. 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() Catalog >

abs(Expr1) expression

abs(List1) list

abs(Matrix1) matrix

Returns the absolute value of the argument.

Note: See also Absolute value template, page 3.

If the argument is a complex number, returns the number’s modulus.

Note: All undefined variables are treated as real variables.

amortTbl() Catalog >

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 195.

• 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.

8 Alphabetical Listing

amortTbl() Catalog >

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 225, and bal(), page 17.

and Catalog >

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 9

angle() Catalog >

angle(Expr1) expression

Returns the angle of the argument, interpreting the argument as a complex number.

Note: All undefined variables are treated as real variables.

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.



In Degree angle mode: In Gradian angle mode: In Radian angle mode:

ANOVA Catalog >

ANOVA List1,List2[,List3,...,List20][,Flag]

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 176)

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

10 Alphabetical Listing

Output variable

Description

stat.df

Degrees of freedom of the groups

stat.SS

Sum of squares of the groups

stat.MS

Mean squares for the groups

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

ANOVA2way Catalog >

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 176.)

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

Alphabetical Listing 11

Output variable

Description

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

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

12 Alphabetical Listing

Output variable

Description

stat.SSInteract

Sum of squares of the interaction

stat.MSInteract

Mean squares for interaction

ERROR Outputs

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() Catalog >

approx(Expr1) expression

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.

Alphabetical Listing 13

approxFraction() Catalog >

ExprapproxFraction([Tol])

expression

ListapproxFraction([Tol]) list

MatrixapproxFraction([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.

Note: You can insert this function from the computer keyboard by typing

@>approxFraction(...).

approxRational() Catalog >

approxRational(Expr[, Tol]) expression 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 31.

arccosh() See cosh-1(), page 32.

arccot() See cot-1(), page 33.

arccoth() See coth-1(), page 34.

14 Alphabetical Listing

arccsc() See csc-1(), page 37.

arccsch() See csch-1(), page 37.

arcLen() Catalog >

arcLen(Expr1,Var,Start,End)

expression

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 157.

arcsech() See sech-1(), page 158.

arcsin() See sin-1(), page 167.

arcsinh() See sinh-1(), page 168.

arctan() See tan-1(), page 183.

Alphabetical Listing 15

arctanh() See tanh-1(), page 184.

augment() Catalog >

augment(List1, List2) list

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() Catalog >

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.

16 Alphabetical Listing

B

bal() Catalog >

bal(NPmt,N,I,PV ,[Pmt], [FV], [PpY],

[CpY], [PmtAt], [roundValue]) value

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 195.

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 195.

• 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 8.

Note: See also ΣInt() and ΣPrn(), page 225.

Base2 Catalog >

Integer1 Base2 integer

Note: You can insert this operator from the computer keyboard by typing @>Base2.

Alphabetical Listing 17

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 Catalog >

Integer1 Base10 integer

18 Alphabetical Listing

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
17.

Alphabetical Listing 19

binomCdf() Catalog >

binomCdf(n,p) list

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(0XupBound)

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() Catalog >

binomPdf(n,p) list

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

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.

Catalog >


20 Alphabetical Listing

centralDiff() Catalog >

centralDiff(Expr1,Var [=Value][,Step])

expression

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() Catalog >

cFactor(Expr1[,Var]) expression cFactor(List1[,Var]) list cFactor(Matrix1[,Var]) matrix

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 21

cFactor() Catalog >

cFactor(Expr1,Var) returns Expr1 factored with respect to variable Var.

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().

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

char() Catalog >

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.

22 Alphabetical Listing

charPoly() Catalog >

charPoly(squareMatrix,Var)

polynomial expression

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•IA)

where I denotes the n×n identity matrix.

squareMatrix1 and squareMatrix2 must have the equal dimensions.

χ22way Catalog >

χ22way obsMatrix

chi22way obsMatrix

Computes a χ2 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
176)
For information on the effect of empty elements in a matrix, see “Empty (Void) Elements,” page 251.

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 23

χ2Cdf() Catalog >

χ2Cdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists

chi2Cdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists

Computes the χ2 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 251.

χ2GOF Catalog >

χ2GOF 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 176.)
For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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() Catalog >

χ2Pdf(XVal,df) number if XVal is a

24 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 χ2 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 251.

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 197.

ClrErr Catalog >

ClrErr

Clears the error status and sets system variable errCode to zero.
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 131, and Try, page 191.

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.

For an example of ClrErr, See Example 2 under the Try command, page 191.

Alphabetical Listing 25

colAugment() Catalog >

colAugment(Matrix1, Matrix2) matrix

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() Catalog >

colDim(Matrix) expression

Returns the number of columns contained in Matrix.

Note: See also rowDim().

colNorm() Catalog >

colNorm(Matrix) expression

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() Catalog >

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.

26 Alphabetical Listing

comDenom() Catalog >

comDenom(Expr1,Var) returns a reduced 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 () Catalog >

completeSquare(ExprOrEqn, Var)

expression or equation

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 ax2+bx+c into the form a(x- h)2+k

Alphabetical Listing 27

completeSquare () Catalog >

- or -
Converts a quadratic equation of the form ax2+bx+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() Catalog >

conj(Expr1) expression conj(List1) list conj(Matrix1) matrix

Returns the complex conjugate of the argument.

Note: All undefined variables are treated as real variables.

constructMat() Catalog >

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.

28 Alphabetical Listing

CopyVar Catalog >

CopyVar Var1, Var2

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 user- defined 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() Catalog >

corrMat(List1,List2[,…[,List20]])

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 29

cos Catalog >

cos reduces all powers of sin(...) modulo 1cos(...)^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() µ key

cos(Expr1) expression

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 Degree angle mode:


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.

In Radian angle mode:

30 Alphabetical Listing

cos() µ key

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() µ key

cos-1(Expr1) expression

cos-1(List1) list

cos-1(Expr1) returns the angle whose cosine is Expr1 as an expression.

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.

Note: You can insert this function from the keyboard by typing arccos(...).

In Degree angle mode:

In Gradian angle mode:


In Radian angle mode:

Alphabetical Listing 31

cos-1() µ key

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.

In Radian angle mode and Rectangular

Complex Format:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

cosh() Catalog >

cosh(Expr1) expression

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

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.

In Degree angle mode:


In Radian angle mode:

cosh-1() Catalog >

cosh-1(Expr1) expression

cosh-1(List1) list

cosh-1(Expr1) returns the inverse

new screenshots format (see Z_ WriterNotes)

hyperbolic cosine of the argument as an
expression.

32 Alphabetical Listing

cosh-1() Catalog >

cosh-1(List1) returns a list of the inverse 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.

In Radian angle mode and In Rectangular

Complex Format:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

cot() µ key

cot(Expr1) expression

cot(List1) list

Returns the cotangent of Expr1 or returns a list of the cotangents 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 Degree angle mode:

In Gradian angle mode:


In Radian angle mode:

cot⁻¹() µ key

cot⁻¹(Expr1) expression

cot-1(List1) list

Returns the angle whose cotangent is

Expr1 or returns a list containing the

In Degree angle mode:

In Gradian angle mode:

inverse cotangents of each element of

List1.

Alphabetical Listing 33

cot⁻¹() µ key

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 keyboard by typing arccot(...).

In Radian angle mode:

coth() Catalog >

coth(Expr1) expression

coth(List1) list

Returns the hyperbolic cotangent of Expr1 or returns a list of the hyperbolic cotangents of all elements of List1.

coth-1() Catalog >

coth-1(Expr1) expression

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() Catalog >

count(Value1orList1 [,Value2orList2

[,...]]) value
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.

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.

34 Alphabetical Listing

count() Catalog >

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 251.

countif() Catalog >

countif(List,Criteria) value

Returns the accumulated count of all
elements in List that meet the specified

Criteria.

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 251.

Note: See also sumIf(), page 180, and

frequency(), page 74.

Counts the number of elements equal to 3.

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. Counts 3, 5, and 7. Counts 1, 3, 7, and 9.

Alphabetical Listing 35

cPolyRoots() Catalog >

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 136.

crossP() Catalog >

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() µ key

csc(Expr1) expression

csc(List1) list

Returns the cosecant of Expr1 or returns a list containing the cosecants of all elements in List1.

36 Alphabetical Listing

In Degree angle mode:


In Gradian angle mode:

csc() µ key

In Radian angle mode:


csc-1() µ key

csc-1(Expr1) expression

csc-1(List1) list

Returns the angle whose cosecant is Expr1
or returns a list containing the inverse

In Degree angle mode:

In Gradian angle mode:


cosecants of each element of List1.

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 keyboard by typing arccsc(...).

In Radian angle mode:

csch() Catalog >

csch(Expr1) expression

csch(List1) list

Returns the hyperbolic cosecant of Expr1 or returns a list of the hyperbolic cosecants of all elements of List1.

csch-1() Catalog >

csch-1(Expr1) expression

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 37

cSolve() Catalog >

cSolve(Equation, Var) Boolean expression

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 non- real 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 approximate complex polynomial factoring, if necessary.

Note: See also cZeros(), solve(), and zeros().

In Display Digits mode of Fix 2:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

cSolve(Eqn1andEqn2 [and…], VarOrGuess1, VarOrGuess2 [, … ]) Boolean expression

38 Alphabetical Listing

cSolve() Catalog >

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.

Complex solutions can include both real and non-real solutions, as 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 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.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

Alphabetical Listing 39

cSolve() 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 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 5 and then use 7 and 8 to move the cursor.



To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

CubicReg Catalog >

CubicReg X, Y[, [Freq] [, Category,

Include]]

Computes the cubic polynomial regression y=ax3+bx2+cx+d on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page
176.)
All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

40 Alphabetical Listing

CubicReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: ax3+bx2+cx+d

stat.a, stat.b, stat.c, stat.d

Regression coefficients

stat.R2

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() Catalog >

cumulativeSum(List1) list

Returns a list of the cumulative sums of the elements in List1, starting at element 1.

Alphabetical Listing 41

cumulativeSum() Catalog >

cumulativeSum(Matrix1) matrix

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
251.

Cycle Catalog >

Cycle

Transfers control immediately to the next iteration of the current loop (For, While, or Loop).

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.

Function listing that sums the integers from 1 to 100 skipping 50.

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.

42 Alphabetical Listing

cZeros() Catalog >

cZeros(Expr, Var) list

Returns a list of candidate real and non-real values of Var that make Expr=0. cZeros() does this by computing explist(cSolve(Expr=0,Var),Var). Otherwise, cZeros() is similar to zeros().

Note: See also cSolve(), solve(), and zeros().

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.
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].

In Display Digits mode of Fix 3:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

Extract row 2:


Alphabetical Listing 43

cZeros() Catalog >

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.

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

dbd() Catalog >

dbd(date1,date2) value

Returns the number of days between date1 and date2 using the actual-day-count method.

44 Alphabetical Listing

dbd() Catalog >

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)

DD Catalog >

Expr1 DD valueList1

DD listMatrix1

DD matrix

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 Degree angle mode:

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.

Alphabetical Listing 45

Decimal Catalog >

Displays the argument in decimal form.
This operator can be used only at the end of
the entry line.

Define Catalog >

Define Var = Expression

Define Function(Param1, Param2, ...) =

Expression

Defines the variable Var or the user- defined 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.

Var and Function cannot be the name of a 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).

46 Alphabetical Listing

Define 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.

Note: See also Define LibPriv, page 47, and

Define LibPub, page 47.

Define LibPriv Catalog >

Define LibPriv Var = Expression

Define LibPriv Function(Param1, Param2,

...) = Expression

Define LibPriv Function(Param1, Param2,

...) = Func

Block

EndFunc

Define LibPriv Program(Param1, Param2,

...) = 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 46, and Define

LibPub, page 47.

Define LibPub Catalog >

Define LibPub Var = Expression

Define LibPub Function(Param1, Param2,

...) = Expression

Define LibPub Function(Param1, Param2,

...) = Func

Block

EndFunc

Alphabetical Listing 47

Define LibPub Catalog >

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 46, and Define

LibPriv, page 47.

deltaList() See ΔList(), page 103.

deltaTmpCnv() See ΔtmpCnv(), page 189.

DelVar Catalog >

DelVar Var1[, Var2] [, Var3] ...

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 197.

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.

48 Alphabetical Listing

delVoid() Catalog >

delVoid(List1) list

Returns a list that has the contents of List1
with all empty (void) elements removed.
For more information on empty elements, see page 251.

derivative() See d(), page 221.

deSolve() Catalog >

deSolve(1stOr2ndOrderODE, Var,

depVar) a general solution

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 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.

Alphabetical Listing 49

deSolve() Catalog >

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.

deSolve(2ndOrderODE and initCond1 and

initCond2, Var, depVar)

particular solution

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.

50 Alphabetical Listing

deSolve() Catalog >

det() Catalog >

det(squareMatrix[, Tolerance])

expression

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, computations are done using floating- point arithmetic.

• If Tolerance is omitted or not used, the default tolerance is calculated as:

5E-14 max(dim

(squareMatrix))rowNorm

(squareMatrix)

diag() Catalog >

diag(List) matrix diag(rowMatrix) matrix diag(columnMatrix) matrix

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.

Alphabetical Listing 51

diag() Catalog >

squareMatrix must be square.

dim() Catalog >

dim(List) integer

Returns the dimension of List.

dim(Matrix) list

Returns the dimensions of matrix as a two- element list {rows, columns}.

dim(String) integer

Returns the number of characters contained in character string String.

Disp Catalog >

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.

DispAt Catalog >

DispAt int,expr1 [,expr2 ...] ...

DispAt allows you to specify the line where the specified expression or string will be displayed on the screen.

The line number can be specified as an expression.

Example

52 Alphabetical Listing

DispAt Catalog >

Please note that the line number is not for the entire screen but for the area immediately following the command/program.
This command allows dashboard-like output from programs where the value of an expression or from a sensor reading is updated on the same line.

DispAt and Disp can be used within the same program.

Note: The maximum number is set to 8 since that matches a screen-full of lines on the handheld screen - as long as the lines don't have 2D math expressions. The exact number of lines depends on the content of the displayed information.

Illustrative examples:

Define z()= Prgm

For n,1,3

DispAt 1,"N: ",n Disp "Hello" EndFor

EndPrgm

Output z()

Iteration 1:

Line 1: N:1

Line 2: Hello

Iteration 2:

Line 1: N:2

Line 2: Hello

Line 3: Hello

Iteration 3:

Line 1: N:3

Line 2: Hello

Line 3: Hello

Alphabetical Listing 53

DispAt Catalog >

Line 4: Hello

Define z1()= Prgm

For n,1,3

DispAt 1,"N: ",n

EndFor

For n,1,4

Disp "Hello" EndFor EndPrgm

z1()

Line 1: N:3

Line 2: Hello Line 3: Hello Line 4: Hello Line 5: Hello

Error conditions:

Error Message

DispAt line number must be between 1 and 8

Description

Expression evaluates the line number outside the range 1-8 (inclusive)

Too few arguments

The function or command is missing one or more arguments.

No arguments

Same as current 'syntax error' dialog

Too many arguments

Limit argument. Same error as Disp.

Invalid data type

First argument must be a number.

Void: DispAt void

"Hello World" Datatype error is thrown for the void (if the callback is defined)

Conversion operator: DispAt 2_ft @> _m, "Hello World"

CAS: Datatype Error is thrown (if the callback is defined)

Numeric: Conversion will be evaluated and if the result is a valid argument, DispAt print the string at the result line.

DMS Catalog >

Expr DMS

List DMS

Matrix DMS

In Degree angle mode:

54 Alphabetical Listing

DMS Catalog >

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 228 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.

domain() Catalog >

domain(Expr1, Var) expression

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.

Alphabetical Listing 55

dominantTerm() Catalog >

dominantTerm(Expr1, Var [, Point])

expression

dominantTerm(Expr1, Var [, Point]) |

Var>Point expression

dominantTerm(Expr1, Var [, Point]) |

Var<Point expression

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, e1/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.

56 Alphabetical Listing

dominantTerm() Catalog >

dominantTerm() is useful when you want to know the simplest possible expression that is asymptotic to another expression as VarPoint. 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.

Note: See also series(), page 161.

dotP() Catalog >

dotP(List1, List2) expression 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.

See Also: TI-Nspire™ CX II - Draw Commands

E

e^() u key

e^(Expr1) expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page


2.
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.

Alphabetical Listing 57

e^() u key

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().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

eff() Catalog >

eff(nominalRate,CpY) value

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 123.

eigVc() Catalog >

eigVc(squareMatrix) matrix

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 x12 + x22 + … + xn2 = 1

In Rectangular Complex Format:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

58 Alphabetical Listing

eigVc() Catalog >

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() Catalog >

eigVl(squareMatrix) list

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.

In Rectangular complex format mode:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

Else See If, page 86.

ElseIf Catalog >

If BooleanExpr1 Then

Block1

ElseIf BooleanExpr2 Then

Block2

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.

Alphabetical Listing 59

EndFor See For, page 72.

EndFunc See Func, page 76.

EndIf See If, page 86.

EndLoop See Loop, page 110.

EndPrgm See Prgm, page 137.

EndTry See Try, page 191.

EndWhile See While, page 201.

euler () Catalog >

euler(Expr, Var, depVar, {Var0, VarMax},

depVar0, VarStep [, eulerStep]) matrix

euler(SystemOfExpr, Var, ListOfDepVars,

{Var0, VarMax}, ListOfDepVars0,

VarStep [, eulerStep]) matrix

euler(ListOfExpr, Var, ListOfDepVars,

{Var0, VarMax}, ListOfDepVars0,

VarStep [, eulerStep]) matrix

Differential equation:

y'=0.001*y*(100-y) and y(0)=10

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

Compare above result with CAS exact solution obtained using deSolve() and seqGen():

60 Alphabetical Listing

euler () Catalog >

Uses the Euler method to solve the system
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).

ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to the order of dependent variables in ListOfDepVars).

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.

VarStep is a nonzero number such that sign (VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+iVarStep for all i=0,1,2,… such that Var0+iVarStep

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.

System of equations:


with y1(0)=2 and y2(0)=5

Alphabetical Listing 61

eval () Hub Menu

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.
The argument Expr must simplify to a real number.

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 77), GetStr (page

84), and Send (page 158).

Set the blue element of the RGB LED to half intensity.

Reset the blue element to OFF.

eval() argument must simplify to a real number.

Program to fade-in the red element


Execute the program.

62 Alphabetical Listing

exact() Catalog >

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).

Exit Catalog >

Exit

Exits the current For, While, or Loop block.

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.

Function listing:

exp Catalog >

Exprexp

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.

Alphabetical Listing 63

exp() u key

exp(Expr1) expression

Returns e raised to the Expr1 power.
Note: See also e exponent template, page

2.
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

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.

explist() Catalog >

explist(Expr,Var) list

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: explist() 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 [email protected]>list(...).

64 Alphabetical Listing

expand() Catalog >

expand(Expr1 [, Var]) expression expand(List1 [,Var]) list expand(Matrix1 [,Var]) matrix

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.

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 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.

Alphabetical Listing 65

expand() Catalog >

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() Catalog >

expr(String) expression

Returns the character string contained in String as an expression and immediately executes it.

ExpReg Catalog >

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 176.)
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.

66 Alphabetical Listing

ExpReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: a(b)x

stat.a, stat.b

Regression coefficients

stat.r2

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

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() Catalog >

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.

Alphabetical Listing 67

factor() Catalog >

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.


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.

68 Alphabetical Listing

factor() Catalog >

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 100- digit 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)

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.

Alphabetical Listing 69

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 Catalog >

FiveNumSummary X[,[Freq] [,Category,Include]]

Provides an abbreviated version of the 1- variable statistics on list X. A summary of results is stored in the stat.results variable. (See page 176.)

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.

Category is a list of numeric category codes for the corresponding X 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.

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 251.

Output variable

Description

stat.MinX

Minimum of x values.

stat.Q1X

1st Quartile of x.

70 Alphabetical Listing

Output variable

Description

stat.MedianX

Median of x.

stat.Q3X

3rd Quartile of x.

stat.MaxX

Maximum of x values.

floor() Catalog >

floor(Expr1) integer

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() Catalog >

fMax(Expr, Var) Boolean expression

fMax(Expr, Var,lowBound)

fMax(Expr, Var,lowBound,upBound)

fMax(Expr, Var) |

lowBoundVarupBound

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().

Alphabetical Listing 71

fMin() Catalog >

fMin(Expr, Var) Boolean expression

fMin(Expr, Var,lowBound) fMin(Expr, Var,lowBound,upBound) fMin(Expr, Var) |

lowBoundVarupBound

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().

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.

72 Alphabetical Listing

format() Catalog >

format(Expr[, formatString]) string

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.
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() Catalog >

fPart(Expr1) expression fPart(List1) list fPart(Matrix1) matrix

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.

Alphabetical Listing 73

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.

freqTablelist() Catalog >

freqTablelist(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.

freqIntegerList must have the same dimension as List1 and must contain non- negative 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 [email protected]>list(...).
Empty (void) elements are ignored. For more information on empty elements, see page 251.

frequency() Catalog >

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.

Explanation of result:

2 elements from Datalist are 2.5

74 Alphabetical Listing

frequency() Catalog >

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)>?)}.
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 251.
Within the Lists & Spreadsheet application, you can use a range of cells in place of both arguments.

Note: See also countIf(), page 35.

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.

FTest_2Samp Catalog >

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 176.)
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 251.

Output variable

Description

stat.F

Calculated F statistic for the data sequence

Alphabetical Listing 75

Output variable

Description

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

Func Catalog >

Func

Block

EndFunc

Template for creating a user-defined function.
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.

G

Define a piecewise function:


Result of graphing g(x)

gcd() Catalog >

gcd(Number1, Number2) expression

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.

76 Alphabetical Listing

gcd() Catalog >

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() Catalog >

geomCdf(p,lowBound,upBound) number if lowBound and upBound are numbers, list if lowBound and upBound are lists

geomCdf(p,upBound)for P(1XupBound)

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() Catalog >

geomPdf(p,XVal) number if XVal is a number, list if XVal is a list

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 Hub Menu

Get [promptString,] var[, statusVar]

Get [promptString,] func(arg1, ...argn)

[, statusVar]

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.

Alphabetical Listing 77

Get Hub Menu

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 —
• 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.
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 84 and Send, page 158.

Embed the READ request within the Get

command.

78 Alphabetical Listing

getDenom() Catalog >

getDenom(Expr1) expression

Transforms the argument into an expression having a reduced common denominator, and then returns its denominator.

getKey() Catalog >

getKey([0|1]) returnString

Description:getKey() - allows a TI-Basic program to get keyboard input - handheld, desktop and emulator on desktop.

Example:

• keypressed := getKey() will return a key or an empty string if no key has been pressed. This call will return immediately.

• keypressed := getKey(1) will wait till a key is pressed. This call will pause execution of the program till a key is pressed.

Example:

Handling of key presses:

Handheld Device/Emulator

Key

Esc

Desktop

Esc

Return Value

"esc"

Touchpad - Top click

n/a

"up"

On

n/a

"home"

Scratchapps

n/a

"scratchpad"

Touchpad - Left click

n/a

"left"

Touchpad - Center click

n/a

"center"

Touchpad - Right click

n/a

"right"

Doc

n/a

"doc"

Alphabetical Listing 79

Handheld Device/Emulator

Key

Desktop

Return Value

Tab

Tab

"tab"

Touchpad - Bottom click

Down Arrow

"down"

Menu

n/a

"menu"

Ctrl

Ctrl

no return

Shift

Shift

no return

Var

n/a

"var"

Del

n/a

"del"

=

=

"="

trig

n/a

"trig"

0 through 9

0-9

"0" ... "9"

Templates

n/a

"template"

Catalog

n/a

"cat"

^

^

"^"

X^2

n/a

"square"

/ (division key)

/

"/"

* (multiply key)

*

"*"

e^x

n/a

"exp"

10^x

n/a

"10power"

+

+

"+"

-

-

"-"

(

(

"("

)

)

")"

.

.

"."

(-)

n/a

"-" (negate sign)

Enter

Enter

"enter"

ee

n/a

"E" (scientific notation E)

a - z

a-z

alpha = letter pressed (lower

80 Alphabetical Listing

Handheld Device/Emulator

Key

Desktop

Return Value

case)

("a" - "z")

shift a-z

shift a-z

alpha = letter pressed

"A" - "Z"

Note: ctrl-shift works to lock caps

?!

n/a

"?!"

pi

n/a

"pi"

Flag

n/a

no return

,

,

","

Return

n/a

"return"

Space

Space

" " (space)

Inaccessible

Special Character Keys like

@,!,^, etc.

The character is returned

n/a

Function Keys

No returned character

n/a

Special desktop control keys

No returned character

Inaccessible

Other desktop keys that are not available on the calculator while getkey() is waiting for a keystroke. ({,

},;, :, ...)

Same character you get in

Notes (not in a math box)

Note: It is important to note that the presence of getKey() in a program changes how certain events are handled by the system. Some of these are described below.

Terminate program and Handle event - Exactly as if the user were to break out of program by pressing the ON key

"Support" below means - System works as expected - program continues to run.


Event Device Desktop - TI-Nspire™ Student Software

Quick Poll Terminate program, handle event

Remote file mgmt Terminate program, handle event

Same as the handheld (TI- Nspire™ Student Software, TI-Nspire™ Navigator™ NC Teacher Software-only)

Same as the handheld. (TI-Nspire™ Student


Alphabetical Listing 81


Event Device Desktop - TI-Nspire™ Student Software

(Incl. sending 'Exit Press 2

Test' file from another

handheld or desktop-

handheld)

End Class Terminate program, handle event

Software, TI-Nspire™ Navigator™ NC Teacher Software-only)

Support

(TI-Nspire™ Student Software, TI-Nspire™ Navigator™ NC Teacher Software-only)


Event Device Desktop - TI-Nspire™ All

Versions

TI-Innovator™ Hub connect/disconnect

Support - Can successfully issue commands to the TI- Innovator™ Hub. After you exit the program the TI- Innovator™ Hub is still working with the

handheld.

Same as the handheld


getLangInfo() Catalog >

getLangInfo() string

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.
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”

82 Alphabetical Listing

getLockInfo() Catalog >

getLockInfo(Var) value
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 106, and unLock, page 197.

getMode() Catalog >

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.

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 162.

Mode

Name


Display
Digits

Mode

Integer Setting Integers

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


Alphabetical Listing 83

Mode

Name


Real or
Complex

Auto or
Approx.

Vector

Format

Mode

Integer Setting Integers

4 1=Real, 2=Rectangular, 3=Polar

5 1=Auto, 2=Approximate, 3=Exact

6 1=Rectangular, 2=Cylindrical, 3=Spherical


Base 7 1=Decimal, 2=Hex, 3=Binary
Unit system

8 1=SI, 2=Eng/US


getNum() Catalog >

getNum(Expr1) expression

Transforms the argument into an expression having a reduced common denominator, and then returns its numerator.

GetStr Hub Menu

GetStr [promptString,] var[, statusVar]

GetStr [promptString,] func(arg1, ...argn)

[, statusVar]
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 77 and Send, page

158.

For examples, see Get.

84 Alphabetical Listing

getType() Catalog >

getType(var) string

Returns a string that indicates the data type of variable var.
If var has not been defined, returns the string "NONE".

getVarInfo() Catalog >

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.

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.

Alphabetical Listing 85

Goto Catalog >

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.

Grad Catalog >

Expr1Grad expression

Converts Expr1 to gradian angle measure.
Note: You can insert this operator from the computer keyboard by typing @>Grad.

I

In Degree angle mode:


In Radian angle mode:

identity() Catalog >

identity(Integer) matrix

Returns the identity matrix with a dimension of Integer.

Integer must be a positive integer.

If Catalog >

If BooleanExpr

Statement

If BooleanExpr Then

Block

EndIf

86 Alphabetical Listing

If Catalog >

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

EndIf

Block2

If BooleanExpr evaluates to true, executes

Block1 and then skips Block2.

If BooleanExpr evaluates to false, skips

Block1 but executes Block2.

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.

Alphabetical Listing 87

ifFn() Catalog >

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:

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.

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).

Test value of 1 is less than 2.5, so its corresponding

Value_If_True element of 5 is copied to the result list.

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.

Value_If_false is not specified. Undef is used.


One element selected from Value_If_true. One element selected from Value_If_ unknown.

imag() Catalog >

imag(Expr1) expression

Returns the imaginary part of the argument.

88 Alphabetical Listing

imag() Catalog >

Note: All undefined variables are treated as real variables. See also real(), page 146

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() Catalog >

impDif(Equation, Var, dependVar[,Ord])

expression

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 See #(), page 226.

inString() Catalog >

inString(srcString, subString[, Start])

integer

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.

Alphabetical Listing 89

int() Catalog >

int(Expr) integer

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() Catalog >

intDiv(Number1, Number2) integer intDiv(List1, List2) list intDiv(Matrix1, Matrix2) matrix

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.

integral See (), page 221.

interpolate () Catalog >

interpolate(xValue, xList, yList,

yPrimeList) list

This function does the following:

Differential equation:

y'=-3y+6t+5 and y(0)=5

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

90 Alphabetical Listing

interpolate () Catalog >

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.

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.

Use the interpolate() function to calculate the function values for the xvaluelist:

invχ2() Catalog >

invχ2(Area,df)

invChi2(Area,df)

Computes the Inverse cumulative χ2 (chi- square) probability function specified by degree of freedom, df for a given Area under the curve.

invF() Catalog >

invF(Area,dfNumer,dfDenom)

invF(Area,dfNumer,dfDenom)

computes the Inverse cumulative F distribution function specified by dfNumer and dfDenom for a given Area under the curve.

Alphabetical Listing 91

invBinom() Catalog >

invBinom (CumulativeProb,NumTrials,Prob, OutputForm)scalar or matrix

Inverse binomial. Given the number of trials (NumTrials) and the probability of success of each trial (Prob), this function returns
the minimum number of successes, k, such that the value, k, is greater than or equal to the given cumulative probability (CumulativeProb).
OutputForm=0, displays result as a scalar
(default).
OutputForm=1, displays result as a matrix.

Example: Mary and Kevin are playing a dice game. Mary has to guess the maximum number of times 6 shows up in 30 rolls. If the number 6 shows up that many times or less, Mary wins. Furthermore, the smaller the number that she guesses, the greater her winnings. What is the smallest number Mary can guess if she wants the probability of winning to be greater than 77%?

invBinomN() Catalog >

invBinomN(CumulativeProb,Prob,

NumSuccess,OutputForm)scalar or

matrix

Inverse binomial with respect to N. Given the probability of success of each trial (Prob), and the number of successes (NumSuccess), this function returns the minimum number of trials, N, such that the value, N, is less than or equal to the given cumulative probability (CumulativeProb).
OutputForm=0, displays result as a scalar
(default).
OutputForm=1, displays result as a matrix.

Example: Monique is practicing goal shots for netball. She knows from experience that her chance of making any one shot is 70%. She plans to practice until she scores 50 goals. How many shots must she attempt to ensure that the probability of making at least

50 goals is more than 0.99?

invNorm() Catalog >

invNorm(Area[,μ[,σ]])

Computes the inverse cumulative normal distribution function for a given Area under the normal distribution curve specified by μ and σ.

invt() Catalog >

invt(Area,df)

92 Alphabetical Listing

invt() Catalog >

Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the curve.

iPart() Catalog >

iPart(Number) integer iPart(List1) list iPart(Matrix1) matrix

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() Catalog >

irr(CF0,CFList [,CFFreq]) value

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.

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.

Note: See also mirr(), page 115.

isPrime() Catalog >

isPrime(Number) Boolean constant expression

Alphabetical Listing 93

isPrime() Catalog >

Returns true or false to indicate if number
is a whole number 2 that is evenly
divisible only by itself and 1.
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.

Function to find the next prime after a specified number:

isVoid() Catalog >

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.
For more information on void elements, see page 251.

94 Alphabetical Listing

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() Catalog >

lcm(Number1, Number2) expression

lcm(List1, List2) list

lcm(Matrix1, Matrix2) matrix

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() Catalog >

left(sourceString[, Num]) string

Returns the leftmost Num characters contained in character string sourceString.
If you omit Num, returns all of

sourceString.

left(List1[, Num]) list

Alphabetical Listing 95

left() Catalog >

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() Catalog >

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 29.
To delete a variable group, see DelVar on page 48.

This example assumes a properly stored and refreshed library document named linalg2 that contains objects defined as clearmat, gauss1, and gauss2.

limit() or lim() Catalog >

limit(Expr1, Var, Point [,Direction])

expression

limit(List1, Var, Point [, Direction])

list

limit(Matrix1, Var, Point [, Direction])

matrix

Returns the limit requested.

Note: See also Limit template, page 6.

Direction: negative=from left, positive=from right, otherwise=both. (If omitted, Direction defaults to both.)

96 Alphabetical Listing

limit() or lim() Catalog >

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 Catalog >

LinRegBx X,Y[,[Freq][,Category,Include]]

Computes the linear regression y = a+bx on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

Alphabetical Listing 97

LinRegBx Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression Equation: a+bx

stat.a, stat.b

Regression coefficients

stat.r2

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

LinRegMx Catalog >

LinRegMx X,Y[,[Freq][,Category,Include]]

Computes the linear regression y = mx+b on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.

98 Alphabetical Listing

LinRegMx Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression Equation: y = mx+b

stat.m, stat.b

Regression coefficients

stat.r2

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

LinRegtIntervals Catalog >

LinRegtIntervals X,Y[,F[,0[,CLev]]]

For Slope. Computes a level C confidence interval for the slope.

LinRegtIntervals X,Y[,F[,1,Xval[,CLev]]]

Alphabetical Listing 99

LinRegtIntervals Catalog >

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 176.)

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 251.

Output variable

Description

stat.RegEqn

Regression Equation: a+bx

stat.a, stat.b

Regression coefficients

stat.df

Degrees of freedom

stat.r2

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

stat.s

Standard error about the line

For Response type only

100 Alphabetical Listing

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 + bXVal

LinRegtTest Catalog >

LinRegtTest X,Y[,Freq[,Hypoth]]

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.
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
A summary of results is stored in the

stat.results variable. (See page 176.)

Alphabetical Listing 101

LinRegtTest Catalog >

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

Output variable

Description

stat.RegEqn

Regression equation: a + bx

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.r2

Coefficient of determination

stat.r

Correlation coefficient

stat.Resid

Residuals from the regression

linSolve() Catalog >

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

Returns a list of solutions for the variables

Var1, Var2, ...

102 Alphabetical Listing

linSolve() Catalog >

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.

listmat() Catalog >

listmat(List [, elementsPerRow])

matrix

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 [email protected]>mat (...).

ln Catalog >

Exprln expression

Causes the input Expr to be converted to an expression containing only natural logs (ln).

Alphabetical Listing 103

ln Catalog >

Note: You can insert this operator from the computer keyboard by typing @>ln.

ln() /u keys

ln(Expr1) expression

ln(List1) list

Returns the natural logarithm of the argument.
For a list, returns the natural logarithms of the elements.

If complex format mode is Real:

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 5 and then use 7 and 8 to move the cursor.

LnReg Catalog >

LnReg X, Y[, [Freq] [, Category, Include]]

Computes the logarithmic regression y = a+bln(x) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

104 Alphabetical Listing

LnReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: a+bln(x)

stat.a, stat.b

Regression coefficients

stat.r2

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 105

Local Catalog >

Local Var1[, Var2] [, Var3] ...

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 Catalog >

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 197, and getLockInfo(), page 83.

106 Alphabetical Listing

log() /s keys

log(Expr1[,Expr2]) expression

log(List1[,Expr2]) list

Returns the base-Expr2 logarithm of the first argument.

Note: See also Log template, page 2.

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

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.

If complex format mode is Real:

If complex format mode is Rectangular:

In Radian angle mode and Rectangular complex format:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

logbase Catalog >

Exprlogbase(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 107

Logistic Catalog >

Logistic X, Y[, [Freq] [, Category, Include]]

Computes the logistic regression y = (c/ (1+ae-bx)) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
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 251.

Output variable

Description

stat.RegEqn

Regression equation: c/(1+ae-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

108 Alphabetical Listing

LogisticD Catalog >

LogisticD X, Y [, [Iterations] , [Freq] [,

Category, Include] ]

Computes the logistic regression y = (c/ (1+ae-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 176.)

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 251.

Output variable

Description

stat.RegEqn

Regression equation: c/(1+ae-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 109

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.

LU Catalog >

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.

lMatrixuMatrix = pMatrixmatrix

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 floating- point arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E-14max(dim(Matrix))rowNorm

(Matrix)

110 Alphabetical Listing

LU Catalog >

The LU factorization algorithm uses partial pivoting with row interchanges.

M

matlist() Catalog >

matlist(Matrix) list

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 [email protected]>list (...).

max() Catalog >

max(Expr1, Expr2) expression

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 111

max() Catalog >

Empty (void) elements are ignored. For more information on empty elements, see page 251.

Note: See also fMax() and min().

mean() Catalog >

mean(List[, freqList]) expression

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

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 251.

In Rectangular vector format:

median() Catalog >

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.

112 Alphabetical Listing

median() Catalog >

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 251.

MedMed Catalog >

MedMed X,Y [, Freq] [, Category, Include]]

Computes the median-median line y = (mx+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
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 251.

Output variable

Description

stat.RegEqn

Median-median line equation: mx+b

stat.m, stat.b

Model coefficients

Alphabetical Listing 113

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() Catalog >

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.

114 Alphabetical Listing

min() Catalog >

min(Expr1, Expr2) expression

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 115

mirr() Catalog >

Note: See also irr(), page 93.

mod() Catalog >

mod(Expr1, Expr2) expression

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 149

mRow() Catalog >

mRow(Expr, Matrix1, Index) matrix

Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Expr.

mRowAdd() Catalog >

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

116 Alphabetical Listing

MultReg Catalog >

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 176.)
All the lists must have equal dimension. For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 251.

Output variable

Description

stat.RegEqn

Regression Equation: b0+b1x1+b2x2+ ...

stat.b0, stat.b1, ...

Regression coefficients

stat.R2

Coefficient of multiple determination

stat.y List

y List = b0+b1x1+ ...

stat.Resid

Residuals from the regression

MultRegIntervals Catalog >

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 176.)

All the lists must have equal dimension. For information on the effect of empty
elements in a list, see “Empty (Void)
Elements,” page 251.

Output variable

Description

stat.RegEqn

Regression Equation: b0+b1x1+b2x2+ ...

stat.y

A point estimate: y = b0 + b1 xl + ... for XValList

stat.dfError

Error degrees of freedom

Alphabetical Listing 117

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 Catalog >

MultRegTests Y, X1[, X2[, X3,…[, X10]]]

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 176.)

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

Outputs

Output variable

Description

stat.RegEqn

Regression Equation: b0+b1x1+b2x2+ ...

stat.F

Global F test statistic

stat.PVal

P-value associated with global F statistic

stat.R2

Coefficient of multiple determination

stat.AdjR2

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

118 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

y List = b0+b1x1+ . . .

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 /= keys

BooleanExpr1 nand BooleanExpr2 returns

Boolean expression

BooleanList1 nand BooleanList2 returns

Boolean list

BooleanMatrix1 nand BooleanMatrix2

returns Boolean matrix
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 119

nand /= keys

Integer1 nand Integer2 integer


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 0 if both bits are 1; otherwise, the result is 1. 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() Catalog >

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(Expr1) ... (ExprposInteger+1) / posInteger!

nCr(Expr, nonInteger) expression! / ((ExprnonInteger)!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

120 Alphabetical Listing

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() Catalog >

nDerivative(Expr1,Var=Value[,Order])

value

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() Catalog >

newList(numElements) list

Returns a list with a dimension of

numElements. Each element is zero.

newMat() Catalog >

newMat(numRows, numColumns)

matrix

Returns a matrix of zeros with the dimension numRows by numColumns.

nfMax() Catalog >

nfMax(Expr, Var) value nfMax(Expr, Var, lowBound) value nfMax(Expr, Var, lowBound, upBound)

value

nfMax(Expr, Var) |

lowBoundVarupBound value

Alphabetical Listing 121

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() Catalog >

nfMin(Expr, Var) value nfMin(Expr, Var, lowBound) value nfMin(Expr, Var, lowBound, upBound)

value

nfMin(Expr, Var) |

lowBoundVarupBound value

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() Catalog >

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.

122 Alphabetical Listing

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 221.

nom() Catalog >

nom(effectiveRate,CpY) value

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 58.

nor /= keys

BooleanExpr1 nor BooleanExpr2 returns

Boolean expression

BooleanList1 nor BooleanList2 returns

Boolean list

BooleanMatrix1 nor BooleanMatrix2

returns Boolean matrix
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 123

nor /= keys

Integer1 nor Integer2 integer

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() Catalog >

norm(Matrix) expression

norm(Vector) expression

Returns the Frobenius norm.

normalLine() Catalog >

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.”

124 Alphabetical Listing

normCdf() Catalog >

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 = -∞.

normPdf() Catalog >

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.

not Catalog >

not BooleanExpr Boolean expression

Returns true, false, or a simplified form of the argument.

not Integer1 integer

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.
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
17.

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

To see the entire result,

press 5 and then use 7 and 8 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 125

nPr() Catalog >

nPr(Expr1, Expr2) expression

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) ... (expressionnegInteger))

nPr(Expr, posInteger) Expr(Expr1) ... (ExprposInteger+1)

nPr(Expr, nonInteger) Expr! / (ExprnonInteger)!

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() Catalog >

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.

126 Alphabetical Listing

npv() Catalog >

CFFreq is a 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.

nSolve() Catalog >

nSolve(Equation,Var[=Guess]) number or error_string

nSolve(Equation,Var[=Guess],lowBound)

number or error_string

nSolve(Equation,Var [=Guess],lowBound,upBound) number or error_string

nSolve(Equation,Var[=Guess]) |

lowBoundVarupBound 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.”

Note: If there are multiple solutions, you can use a guess to help find a particular solution.

Alphabetical Listing 127

nSolve() Catalog >

Note: See also cSolve(), cZeros(), solve(), and zeros().

O

OneVar Catalog >

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 176.)

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 251.

Output variable

Description

stat.v

Mean of x values

stat.Σx

Sum of x values

stat.Σx2

Sum of x2 values

128 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

or Catalog >

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 129

or Catalog >

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.
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
17.

Note: See xor.

Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits.

ord() Catalog >

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

PRx() Catalog >

PRx(rExpr, θExpr) expression PRx(rList, θList) list PRx(rMatrix, θMatrix) matrix

Returns the equivalent x-coordinate of the
(r, θ) pair.

130 Alphabetical Listing

In Radian angle mode:

PRx() Catalog >

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 [email protected]>Rx(...).

PRy() Catalog >

PRy(rExpr, θExpr) expression

PRy(rList, θList) list

PRy(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 [email protected]>Ry(...).

In Radian angle mode:

PassErr Catalog >

PassErr

Passes an error to the next level.
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.

For an example of PassErr, See Example 2 under the Try command, page 191.

Alphabetical Listing 131

PassErr Catalog >

Note: See also ClrErr, page 25, and Try, page

191.

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() Catalog >

piecewise(Expr1[, Cond1[, Expr2 [, Cond2

[, … ]]]])
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 3.

poissCdf() Catalog >

poissCdf(λ,lowBound,upBound) number if lowBound and upBound are numbers, list if lowBound and upBound are lists

poissCdf(λ,upBound)for P(0XupBound) 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() Catalog >

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.

132 Alphabetical Listing

Polar Catalog >

Vector Polar

Note: You can insert this operator from the computer keyboard by typing @>Polar.
Displays vector in polar form [rθ]. 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 146.

complexValue Polar

Displays complexVector in polar form.

• Degree angle mode returns (rθ).

• Radian angle mode returns reiθ.

complexValue can

In Radian angle mode:

In Gradian angle mode:


have any complex
form. However, an reiθ
entry causes an error in
Degree angle mode.

Note: You must use the parentheses for an


(rθ) polar entry.

In Degree angle mode:

polyCoeffs() Catalog >

polyCoeffs(Poly [,Var]) list

Alphabetical Listing 133

polyCoeffs() 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.


polyDegree() Catalog >

polyDegree(Poly [,Var]) value

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.

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.

Constant polynomials



The degree can be extracted even though the coefficients cannot. This is because the degree can be extracted without expanding the polynomial.

134 Alphabetical Listing

polyEval() Catalog >

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.

polyGcd() Catalog >

polyGcd(Expr1,Expr2) expression

Returns greatest common divisor of the two arguments.

Expr1 and Expr2 must be polynomial expressions.

List, matrix, and Boolean arguments are not allowed.

polyQuotient() Catalog >

polyQuotient(Poly1,Poly2 [,Var])

expression

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.


Alphabetical Listing 135

polyRemainder() Catalog >

polyRemainder(Poly1,Poly2 [,Var])

expression

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.

polyRoots() Catalog >

polyRoots(Poly,Var) list

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 36.

PowerReg Catalog >

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 176.)
All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

136 Alphabetical Listing

PowerReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: a(x)b

stat.a, stat.b

Regression coefficients

stat.r2

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 Catalog >

Prgm

Block

EndPrgm

Template for creating a user-defined program. Must be used with the Define, Define LibPub, or Define LibPriv command.

Calculate GCD and display intermediate results.

Alphabetical Listing 137

Prgm Catalog >

Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines.

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 223.

Product (PI) See Π (), page 223.

product() Catalog >

product(List[, Start[, End]]) expression

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 251.

138 Alphabetical Listing

propFrac() Catalog >

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.

propFrac(rational_expression,Var) returns 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

QR Catalog >

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.

Alphabetical Listing 139

QR Catalog >

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 floating- point arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E14 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 Catalog >

QuadReg X,Y[, Freq][, Category, Include]]

Computes the quadratic polynomial regression y=ax2+bx+c on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

140 Alphabetical Listing

QuadReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: ax2+bx+c

stat.a,

stat.b, stat.c

Regression coefficients

stat.R2

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 Catalog >

QuartReg X,Y[, Freq][, Category, Include]]

Computes the quartic polynomial regression y = ax4+bx3+cx2+dx+e on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.

Alphabetical Listing 141

QuartReg Catalog >

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 251.

Output variable

Description

stat.RegEqn

Regression equation: ax4+bx3+cx2+dx+e

stat.a, stat.b, stat.c, stat.d, stat.e

Regression coefficients

stat.R2

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

RPθ() Catalog >

RPθ (xExpr, yExpr) expression

RPθ (xList, yList) list

RPθ (xMatrix, yMatrix) matrix

In Degree angle mode:

142 Alphabetical Listing

RPθ() Catalog >

Returns the equivalent θ-coordinate of the
(x,y) pair arguments.

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 [email protected]>Ptheta (...).

In Gradian angle mode:


In Radian angle mode:

RPr() Catalog >

RPr (xExpr, yExpr) expression

RPr (xList, yList) list

RPr (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 [email protected]>Pr(...).

In Radian angle mode:

Rad Catalog >

Expr1Rad expression

Converts the argument to radian angle measure.
Note: You can insert this operator from the computer keyboard by typing @>Rad.

In Degree angle mode:

In Gradian angle mode:

rand() Catalog >

rand() expression

rand(#Trials) list

Set the random-number seed.

Alphabetical Listing 143

rand() Catalog >

rand() returns a random value between 0 and 1.

rand(#Trials) returns a list containing

#Trials random values between 0 and 1.

randBin() Catalog >

randBin(n, p) expression

randBin(n, p, #Trials) list

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.

144 Alphabetical Listing

randMat() Catalog >

randMat(numRows, numColumns)

matrix

Returns a matrix of integers between -9 and 9 of the specified dimension.

Both arguments must simplify to integers. Note: The values in this matrix will change each time you press ·.

randNorm() Catalog >

randNorm(μ, σ) expression

randNorm(μ, σ, #Trials) list

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() Catalog >

randPoly(Var, Order) expression

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() Catalog >

randSamp(List,#Trials[,noRepl]) list

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.

Alphabetical Listing 145

RandSeed Catalog >

RandSeed Number

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.

real() Catalog >

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.

Rect Catalog >

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 133.

complexValue Rect

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

(rθ) polar entry.

In Radian angle mode:

146 Alphabetical Listing

Rect Catalog >

In Gradian angle mode:

In Degree angle mode:

Note: To type , select it from the symbol list in the Catalog.

ref() Catalog >

ref(Matrix1[, Tol]) matrix

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 floating- point arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E14 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:

Alphabetical Listing 147

ref() Catalog >

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 156.

RefreshProbeVars Catalog >

RefreshProbeVars

Allows you to access sensor data from all connected sensor probes in your TI-Basic program.

StatusVar

Value Status

statusVar Normal (continue with the

=0 program)

The Vernier DataQuest™ application is in data collection mode.

statusVar Note: The Vernier DataQuest™

=1 application must be in meter

mode for this command to work.

Example

Define temp()= Prgm

© Check if system is ready

RefreshProbeVars status

If status=0 Then

Disp "ready" For n,1,50

RefreshProbeVars status temperature:=meter.temperature

Disp "Temperature: ",temperature

statusVar The Vernier DataQuest™

=2 application is not launched.

statusVar The Vernier DataQuest™

=3 application is launched, but you

have not connected any probes.

If temperature>30 Then

Disp "Too hot" EndIf

© Wait for 1 second between samples

Wait 1

EndFor

148 Alphabetical Listing

RefreshProbeVars Catalog >

Else

Disp "Not ready. Try again later"

EndIf

EndPrgm

Note: This can also be used with TI- Innovator™ Hub.

remain() Catalog >

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) xyiPart(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 116.

Request Catalog >

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.
When the user types a response and clicks OK, the contents of the input box are assigned to variable var.

Define a program:

Define request_demo()=Prgm Request “Radius: ”,r Disp “Area = “,pi*r2

EndPrgm

Run the program and type a response:

request_demo()

Alphabetical Listing 149

Request Catalog >

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.
The optional DispFlag argument can be any expression.

• 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.

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.

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.

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.

Result after selecting OK:

Radius: 6/2

Area= 28.2743

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()

Result after entering x^3+3x+1 and selecting

OK:

Real roots are: {-0.322185}

150 Alphabetical Listing

Request Catalog >

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 151.

RequestStr Catalog >

RequestStr promptString, var[, DispFlag]

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 (““).
Note: You can use the RequestStr command within a user-defined program but not within a function.
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 149.

Define a program:

Define requestStr_demo()=Prgm

RequestStr “Your name:”,name,0

Disp “Response has “,dim(name),”

characters.”

EndPrgm

Run the program and type a response:

requestStr_demo()

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.

Alphabetical Listing 151

Return 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() Catalog >

right(List1[, Num]) list

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 () Catalog >

rk23(Expr, Var, depVar, {Var0, VarMax},

depVar0, VarStep [, diftol]) matrix

rk23(SystemOfExpr, Var, ListOfDepVars,

{Var0, VarMax}, ListOfDepVars0,

VarStep[, diftol]) matrix

rk23(ListOfExpr, Var, ListOfDepVars,

{Var0, VarMax}, ListOfDepVars0,

VarStep[, diftol]) matrix

Differential equation:

y'=0.001*y*(100-y) and y(0)=10

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

152 Alphabetical Listing

rk23 () Catalog >

Uses the Runge-Kutta method to solve the system

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.

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).

ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars).

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).

Same equation with diftol set to 1.E6

Compare above result with CAS exact solution obtained using deSolve() and seqGen():


System of equations:


with y1(0)=2 and y2(0)=5

Alphabetical Listing 153

root() Catalog >

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 1.

rotate() Catalog >

rotate(Integer1[,#ofRotations]) integer

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 17.
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).
For example, in a right rotation: Each bit rotates right.
0b00000000000001111010110000110101
Rightmost bit rotates to leftmost. produces:
0b10000000000000111101011000011010
The result is displayed according to the Base mode. rotate(List1[,#ofRotations]) list
Returns a copy of List1 rotated right or left by #of Rotations elements. Does not alter List1.

154 Alphabetical Listing

In Bin base mode:

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

In Hex base mode:

Important: To enter a binary or hexadecimal number, always use the 0b or

0h prefix (zero, not the letter O).

In Dec base mode:

rotate() Catalog >

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).

round() Catalog >

round(Expr1[, digits]) expression

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() Catalog >

rowAdd(Matrix1, rIndex1, rIndex2)

matrix

Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2.

Alphabetical Listing 155

rowDim() Catalog >

rowDim(Matrix) expression

Returns the number of rows in Matrix.

Note: See also colDim(), page 26.

rowNorm() Catalog >

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 26.

rowSwap() Catalog >

rowSwap(Matrix1, rIndex1, rIndex2)

matrix

Returns Matrix1 with rows rIndex1 and

rIndex2 exchanged.

rref() Catalog >

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 floating- point arithmetic.

156 Alphabetical Listing

rref() Catalog >

• If Tol is omitted or not used, the default tolerance is calculated as:

5E14 max(dim(Matrix1)) rowNorm

(Matrix1)

Note: See also ref(), page 147.

S

sec() µ key

sec(Expr1) expression

sec(List1) list

Returns the secant of Expr1 or returns a list containing the secants 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 Degree angle mode:

sec-1() µ key

sec-1(Expr1) expression

sec-1(List1) list

Returns the angle whose secant is Expr1 or returns a list containing the inverse secants of each element of List1.

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 keyboard by typing arcsec(...).



In Degree angle mode: In Gradian angle mode: In Radian angle mode:

Alphabetical Listing 157

sech() Catalog >

sech(Expr1) expression

sech(List1) list

Returns the hyperbolic secant of Expr1 or returns a list containing the hyperbolic secants of the List1 elements.

sech-1() Catalog >

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(...).

In Radian angle and Rectangular complex mode:

Send Hub Menu

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.
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 77), GetStr (page

84), and eval() (page 62).

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.

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.

158 Alphabetical Listing

Send Hub Menu

seq() Catalog >

seq(Expr, Var, Low, High[, Step]) list

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 .


seqGen() Catalog >

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.

seqGen(ListOrSystemOfExpr, Var,

ListOfDepVars, {Var0, VarMax} [

, MatrixOfInitTerms[, VarStep[,

CeilingValue]]]) matrix

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:


Alphabetical Listing 159

seqGen() Catalog >

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.
The original contents of Var are unchanged after seqGen() is completed.
The default value for VarStep = 1.

Example in which initial term is symbolic:


System of two sequences:

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() Catalog >

seqn(Expr(u, n[, ListOfInitTerms[, nMax[,

CeilingValue]]]) list


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 non- recursive 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

Generate the first 6 terms of the sequence u

(n) = u(n-1)/2, with u(1)=2.

160 Alphabetical Listing

series() Catalog >

series(Expr1, Var, Order[, Point])

expression

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.

Point defaults to 0. Point can be or −∞, 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, e1/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.

Alphabetical Listing 161

series() Catalog >

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 56.

setMode() Catalog >

setMode(modeNameInteger, settingInteger) integer setMode(list) integer list

Valid only within a function or program.

setMode(modeNameInteger, settingInteger) temporarily sets mode modeNameInteger to the new setting settingInteger, and returns an integer 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 83.

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.

162 Alphabetical Listing

setMode() Catalog >

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


Display
Digits

Mode

Integer Setting Integers

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

Real or
Complex

Auto or
Approx.

Vector

Format

3 1=Normal, 2=Scientific, 3=Engineering

4 1=Real, 2=Rectangular, 3=Polar

5 1=Auto, 2=Approximate, 3=Exact

6 1=Rectangular, 2=Cylindrical, 3=Spherical


Base 7 1=Decimal, 2=Hex, 3=Binary
Unit system

8 1=SI, 2=Eng/US


shift() Catalog >

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 17.

In Bin base mode:

In Hex base mode:

Alphabetical Listing 163

shift() Catalog >

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:
0b00000000000000111101011000011010
The result is displayed according to the Base mode. Leading zeros are not shown. shift(List1[,#ofShifts]) list
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).

Important: To enter a binary or hexadecimal number, always use the 0b or

0h prefix (zero, not the letter O).

In Dec base mode:

164 Alphabetical Listing

shift() Catalog >

Characters introduced at the beginning or end of string by the shift are set to a space.

sign() Catalog >

sign(Expr1) expression

sign(List1) list

sign(Matrix1) matrix

For real and complex Expr1, returns

Expr1/abs(Expr1) when Expr10.

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.

If complex format mode is Real:

simult() Catalog >

simult(coeffMatrix, constVector[, Tol])

matrix

Returns a column vector that contains the solutions to a system of linear equations.
Note: See also linSolve(), page 102.

coeffMatrix must be a square matrix that contains the coefficients of the equations.

constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants.

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.

Solve for x and y:

x + 2y = 1

3x + 4y = 1

The solution is x=3 and y=2. Solve:

ax + by = 1 cx + dy = 2

Alphabetical Listing 165

simult() Catalog >

• If Tol is omitted or not used, the default tolerance is calculated as:

5E14 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.

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.

sin Catalog >

Exprsin

Note: You can insert this operator from the computer keyboard by typing @>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 1sin(...)^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() µ key

sin(Expr1) expression In Degree angle mode:

166 Alphabetical Listing

sin() µ key

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.

sin(squareMatrix1) squareMatrix

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.

In Gradian angle mode:

In Radian angle mode:


In Radian angle mode:

sin-1() µ key

sin-1(Expr1) expression

sin-1(List1) list

sin-1(Expr1) returns the angle whose sine is Expr1 as an expression.

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 Degree angle mode: In Gradian angle mode: In Radian angle mode:

Alphabetical Listing 167

sin-1() µ key


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().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format mode:

sinh() Catalog >

sinh(Expr1) expression

sinh(List1) list

sinh (Expr1) returns the hyperbolic sine of the argument as an expression.

sinh (List1) returns a list of the hyperbolic sines of each element of List1.

sinh(squareMatrix1) squareMatrix

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.

In Radian angle mode:

sinh-1() Catalog >

sinh-1(Expr1) expression

sinh-1(List1) list

sinh-1(Expr1) returns the inverse hyperbolic sine of the argument as an expression.

168 Alphabetical Listing

sinh-1() Catalog >

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

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.

In Radian angle mode:

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 176.)
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.

Alphabetical Listing 169

SinReg 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.

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 251.

Output variable

Description

stat.RegEqn

Regression Equation: asin(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

solve() Catalog >

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.

170 Alphabetical Listing

solve() Catalog >

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.
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 Radian angle mode:




In Radian angle mode:

Alphabetical Listing 171

solve() Catalog >

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.
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.

172 Alphabetical Listing

solve() Catalog >

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.
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.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

Alphabetical Listing 173

solve() Catalog >

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.

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.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

SortA Catalog >

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.
Empty (void) elements within the first argument move to the bottom. For more information on empty elements, see page
251.

174 Alphabetical Listing

SortD Catalog >

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
251.

Sphere Catalog >

VectorSphere

Note: You can insert this operator from the computer keyboard by typing @>Sphere.

Displays the row or column vector in spherical form [ρθφ].

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.

Note: To force an approximate result,

Handheld: Press / ·. Windows®: Press Ctrl+Enter. Macintosh®: Press +Enter. iPad®: Hold enter, and select .


Press ·


Alphabetical Listing 175

Sphere Catalog >

sqrt() Catalog >

sqrt(Expr1) expression

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

1.

stat.results Catalog >

stat.results

Displays results from a statistics calculation.
The results are displayed as a set of name- value 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.

176 Alphabetical Listing

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.v1

stat.v2 stat.vDiff stat.vList 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 Catalog >

stat.values

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.

See the stat.results example.

Alphabetical Listing 177

stDevPop() Catalog >

stDevPop(List [, freqList]) expression

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 251.

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 251.

In Radian angle and auto modes:

stDevSamp() Catalog >

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 251.

178 Alphabetical Listing

stDevSamp() Catalog >

stDevSamp(Matrix1[, freqMatrix])

matrix

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 251.

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 See (store), page 233.

string() Catalog >

string(Expr) string

Simplifies Expr and returns the result as a character string.

Alphabetical Listing 179

subMat() Catalog >

subMat(Matrix1[, startRow][, startCol][,

endRow][, endCol]) matrix

Returns the specified submatrix of Matrix1. Defaults: startRow=1, startCol=1,

endRow=last row, endCol=last column.

Sum (Sigma) See Σ(), page 224.

sum() Catalog >

sum(List[, Start[, End]]) expression

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 251.

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 251.

sumIf() Catalog >

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.

180 Alphabetical Listing

sumIf() Catalog >

List can be an expression, list, or matrix. SumList, if specified, must have the same dimension(s) as List.

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 251.

Note: See also countIf(), page 35.

sumSeq() See Σ(), page 224.

system() Catalog >

system(Eqn1[, Eqn2[, Eqn3[, ...]]])

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 3.

Alphabetical Listing 181

T

T (transpose) Catalog >

Matrix1T matrix

Returns the complex conjugate transpose of

Matrix1.

Note: You can insert this operator from the computer keyboard by typing @t.

tan() µ key

tan(Expr1) expression

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 degree, gradian or radian angle, according to the current angle mode. You can use °, g or r to override the angle mode setting temporarily.

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().

182 Alphabetical Listing




In Degree angle mode: In Gradian angle mode: In Radian angle mode:

In Radian angle mode:

tan() µ key

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

tan-1() µ key

tan-1(Expr1) expression

tan-1(List1) list

tan-1(Expr1) returns the angle whose tangent is Expr1 as an expression.

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.

Note: You can insert this function from the keyboard by typing arctan(...).

tan-1(squareMatrix1) squareMatrix

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.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:


In Radian angle mode:

tangentLine() Catalog >

tangentLine(Expr1,Var,Point)

expression

tangentLine(Expr1,Var=Point)

expression

Returns the tangent line to the curve represented by Expr1 at the point specified in Var=Point.

Alphabetical Listing 183

tangentLine() Catalog >

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.”

tanh() Catalog >

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

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.

In Radian angle mode:

tanh-1() Catalog >

tanh-1(Expr1) expression

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(...).

In Rectangular complex format:

tanh-1(squareMatrix1) squareMatrix In Radian angle mode and Rectangular complex format:

184 Alphabetical Listing

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.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

taylor() Catalog >

taylor(Expr1, Var, Order[, Point])

expression

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() Catalog >

tCdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists

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 185

tCollect() Catalog >

tCollect(Expr1) expression

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() Catalog >

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.

186 Alphabetical Listing

Text Catalog >

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.
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 149, or RequestStr, page 151.

Note: You can use this command within a user-defined program but not within a function.

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.

Define text_demo()=Prgm

For i,1,5

strinfo:=”Random number “ &

string(rand(i))

Text strinfo

EndFor

EndPrgm

Run the program:

text_demo()

Sample of one dialog box:


Then See If, page 86.

tInterval Catalog >

tInterval List[, Freq[, CLevel]] (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 176.)

Alphabetical Listing 187

tInterval Catalog >

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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 Catalog >

tInterval_2Samp List1,List2[,Freq1[,Freq2

[,CLevel[,Pooled]]]]
(Data list input)

tInterval_2Samp v1,sx1,n1,v2,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 176.)
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 251.

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

188 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() Catalog >

tmpCnv(Expr_°tempUnit, _°tempUnit2)

expression _°tempUnit2

Converts a temperature value specified by Expr from one unit to another. Valid temperature units are:
_°C Celsius
_°F Fahrenheit
_°K Kelvin
_°R Rankine
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.

Note: You can use the Catalog to select temperature units.

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:
_°C Celsius
_°F Fahrenheit
_°K Kelvin
_°R Rankine

Note: You can use the Catalog to select

temperature units.

Alphabetical Listing 189

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() Catalog >

tPdf(XVal,df) number if XVal is a number, list if XVal is a list

Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df.

trace() Catalog >

trace(squareMatrix) expression

Returns the trace (sum of all the elements on the main diagonal) of squareMatrix.

190 Alphabetical Listing

Try Catalog >

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 261.

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.

Note: See also ClrErr, page 25, and PassErr, page 131.

Define eigenvals(a,b)=Prgm

© Program eigenvals(A,B) displays eigenvalues of AB

Try

Disp "A= ",a Disp "B= ",b Disp " "

Disp "Eigenvalues of AB are:",eigVl(a*b) Else

If errCode=230 Then

Disp "Error: Product of AB must be a

square matrix" ClrErr

Else

PassErr

EndIf

EndTry

EndPrgm

Alphabetical Listing 191

tTest Catalog >

tTest μ0,List[,Freq[,Hypoth]] (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 176.)
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 251.

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 Catalog >

tTest_2Samp List1,List2[,Freq1[,Freq2

[,Hypoth[,Pooled]]]]
(Data list input)

tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth

[,Pooled]]
(Summary stats input)

192 Alphabetical Listing

tTest_2Samp Catalog >

Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See page 176.)
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 251.

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() Catalog >

tvmFV(N,I,PV,Pmt,[PpY],[CpY],[PmtAt])

value

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 195. See also amortTbl(), page 8.

tvmI() Catalog >

tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt])

value

Alphabetical Listing 193

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 195. See also amortTbl(), page 8.

tvmN() Catalog >

tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt])

value

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 195. See also amortTbl(), page 8.

tvmPmt() Catalog >

tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt])

value

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 195. See also amortTbl(), page 8.

tvmPV() Catalog >

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 195. See also amortTbl(), page 8.

194 Alphabetical Listing

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 Catalog >

TwoVar X, Y[, [Freq][, Category, Include]]

Calculates the TwoVar statistics. A summary of results is stored in the stat.results variable. (See page 176.)
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 195

TwoVar Catalog >

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 251.

Output variable

Description

stat.v

Mean of x values

stat.Σx

Sum of x values

stat.Σx2

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.Σy

Sum of y values

stat.Σy2

Sum of y2 values

stat.sy

Sample standard deviation of y

stat.σy

Population standard deviation of y

stat.Σxy

Sum of xy 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

196 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() Catalog >

unitV(Vector1) vector

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 5 and then use 7 and 8 to move the cursor.

unLock Catalog >

unLock Var1[, Var2] [, Var3] ...

unLock Var.

Unlocks the specified variables or variable group. Locked variables cannot be modified or deleted.
See Lock, page 106, and getLockInfo(), page
83.

Alphabetical Listing 197

V

varPop() Catalog >

varPop(List[, freqList]) expression

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 251.

varSamp() Catalog >

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 251.

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.

198 Alphabetical Listing

varSamp() Catalog >

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 251.

Note: Matrix1 must contain at least two rows.

W

Wait Catalog >

Wait timeInSeconds

Suspends execution for a period of

timeInSeconds seconds.

Wait is particularly useful in a program that needs a brief delay to allow requested data to become available.

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 cancel a Wait that is in progress,

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: You can use the Wait command within a user-defined program but not within a function.

To wait 4 seconds:

Wait 4

To wait 1/2 second:

Wait 0.5

To wait 1.3 seconds using the variable

seccount:

seccount:=1.3

Wait seccount

This example switches a green LED on for

0.5 seconds and then switches it off.

Send "SET GREEN 1 ON" Wait 0.5

Send "SET GREEN 1 OFF"

Alphabetical Listing 199

warnCodes () Catalog >

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.

StatusVar must be a valid variable name. For a list of warning codes and associated

messages, see page 269.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

when() Catalog >

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.

200 Alphabetical Listing

While Catalog >

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

xor Catalog >

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 129.

Integer1 xor Integer2integer

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.

In Hex base mode:

Important: Zero, not the letter O.


In Bin base mode:

Alphabetical Listing 201

xor Catalog >

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
17.

Note: See or, page 129.

Z

Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits.

zeros() Catalog >

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 explist(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:

202 Alphabetical Listing

zeros() Catalog >

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].

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.

Extract row 2:

Alphabetical Listing 203

zeros() Catalog >

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 Catalog >

zInterval σ,List[,Freq[,CLevel]] (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 176.)
For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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

204 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 Catalog >

zInterval_1Prop x,n [,CLevel]

Computes a one-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 176.)

x is a non-negative integer.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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 Catalog >

zInterval_2Prop x1,n1,x2,n2[,CLevel]

Computes a two-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 176.)

x1 and x2 are non-negative integers. For information on the effect of empty

elements in a list, see “Empty (Void)
Elements,” page 251.

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 205

Output variable

Description

stat.Ç1

First sample proportion estimate

stat.Ç2

Second sample proportion estimate

stat.n1

Sample size in data sequence one

stat.n2

Sample size in data sequence two

zInterval_2Samp Catalog >

zInterval_2Samp σ1,σ2 ,List1,List2[,Freq1

[,Freq2,[CLevel]]]
(Data list input)

zInterval_2Samp σ1,σ2,v1,n1,v2,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 176.)
For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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 Catalog >

zTest μ0,σ,List,[Freq[,Hypoth]]

206 Alphabetical Listing

zTest Catalog >

(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 176.)
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 251.

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

zTest_1Prop Catalog >

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 Catalog >

zTest_2Prop x1,n1,x2,n2[,Hypoth]

Alphabetical Listing 207

zTest_2Prop Catalog >

Computes a two-proportion z test. A summary of results is stored in the stat.results variable. (See page 176.)
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 251.

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.Ç1

First sample proportion estimate

stat.Ç2

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 Catalog >

zTest_2Samp σ1,σ2 ,List1,List2[,Freq1

[,Freq2[,Hypoth]]]
(Data list input)

zTest_2Samp σ1,σ2,v1,n1,v2,n2[,Hypoth] (Summary stats input)

Computes a two-sample z test. A summary of results is stored in the stat.results variable. (See page 176.)
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

208 Alphabetical Listing

zTest_2Samp Catalog >

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 251.

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 209

Symbols

+ (add) + key

Expr1 + Expr2 expression

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) - key

Expr1 Expr2 expression

Returns Expr1 minus Expr2.

List1 List2list

Matrix1 Matrix2 matrix

210 Symbols

(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

Expr1Expr2 expression

Returns the product of the two arguments.

List1List2 list

Returns a list containing the products of the corresponding elements in List1 and List2.
Dimensions of the lists must be equal.

Matrix1Matrix2 matrix

Returns the matrix product of Matrix1 and

Matrix2.

The number of columns in Matrix1 must equal the number of rows in Matrix2.

Symbols 211

(multiply) r key

Expr List1 list

List1Expr list

Returns a list containing the products of

Expr and each element in List1.

Expr Matrix1 matrix

Matrix1Expr 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) p key

Expr1 Expr2 expression

Returns the quotient of Expr1 divided by

Expr2.

Note: See also Fraction template, page 1.

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

212 Symbols

(divide) p key

Note: Use . (dot divide) to divide an expression by each element.

^ (power) l key

Expr1 ^ Expr2expression

List1 ^ List2 list


Returns the first argument raised to the power of the second argument.

Note: See also Exponent template, page 1. 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 213

x2 (square) q key

Expr12expression

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) ^+ keys

Matrix1 .+ Matrix2 matrix

Expr .+ Matrix1matrix

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.) ^- keys

Matrix1 .Matrix2matrix

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.

.

214 Symbols

.(dot mult.) ^r keys

Matrix1 .Matrix2matrix

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) ^p keys

Matrix1. Matrix2 matrix

Expr . Matrix1matrix

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) ^l keys

Matrix1 .^ Matrix2 matrix

Expr . ^ Matrix1matrix

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 215

(negate) v key


Returns the negation of the argument.
For a list or matrix, returns all the elements negated.
If the argument is a binary or hexadecimal integer, the negation gives the two’s complement.

In Bin base mode:

Important: Zero, not the letter O.

To see the entire result,

press 5 and then use 7 and 8 to move the cursor.

% (percent) /k keys

Expr1% expression List1% list Matrix1% matrix


Returns

For a list or matrix, returns a list or matrix with each element divided by 100.

Note: To force an approximate result,


Handheld: Press / ·. Windows®: Press Ctrl+Enter. Macintosh®: Press +Enter. iPad®: Hold enter, and select .

= (equal) = key

Expr1=Expr2 Boolean expression List1=List2 Boolean list 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.

Example function that uses math test symbols: =, , <, , >,

216 Symbols

= (equal) = key

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)

(not equal) /= keys

Expr1Expr2 Boolean expression List1List2 Boolean list Matrix1Matrix2 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 /=

See “=” (equal) example.

< (less than) /= keys

Expr1<Expr2 Boolean expression List1<List2 Boolean list Matrix1<Matrix2 Boolean matrix

Returns true if Expr1 is determined to be less than Expr2.

See “=” (equal) example.

Symbols 217

< (less than) /= keys


Returns false if Expr1 is determined to be greater than or equal to Expr2.
Anything else returns a simplified form of the equation.
For lists and matrices, returns comparisons element by element.

(less or equal) /= keys

Expr1Expr2 Boolean expression

List1List2 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 <=

See “=” (equal) example.

> (greater than) /= keys

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.

See “=” (equal) example.

218 Symbols

> (greater than) /= keys


For lists and matrices, returns comparisons element by element.

(greater or equal) /= keys

Expr1Expr2 Boolean expression

List1List2 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 >=

See “=” (equal) example.

(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 219

(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) º key

Expr1! expression

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) /k keys

String1 & String2 string


Returns a text string that is String2
appended to String1.

220 Symbols

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 5;

Second derivative, page 6; or

Nth derivative, page 6.

() (integral) Catalog >

(Expr1, Var[,Lower,Upper])

expression

(Expr1,Var[,Constant]) expression

Symbols 221

() (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 6.

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 anti- derivative contains logarithms or inverse trigonometric functions. Moreover, piecewise constant expressions are sometimes added to make an anti- derivative 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 anti- derivative or a limit cannot be determined.
For the Approximate setting, numerical integration is tried first, if applicable. Anti- derivatives are sought only where such numerical integration is inapplicable or fails.

222 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 122.

() (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

1.

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

5.

Symbols 223

Π() (prodSeq) Catalog >

Π(Expr1, Var, Low, Low1) 1

Π(Expr1, Var, Low, High) 1/Π(Expr1,

Var, High+1, Low1) if High < Low1


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) Catalog >

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 5.

Σ(Expr1, Var, Low, Low1) 0

Σ(Expr1, Var, Low, High) μ

Σ(Expr1, Var, High+1, Low1) if High <

Low1

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.

224 Symbols

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 195.

• 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
8.
Note: See also ΣPrn(), below, and Bal(), page 17.

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 225

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 195.

• 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 8.
Note: See also ΣInt(), above, and Bal(), page 17.

# (indirection) /k keys

# varNameString


Refers to the variable whose name is

varNameString. This lets you use strings to create variable names from within a function.

Creates or refers to the variable xyz .

Returns the value of the variable (r) whose name is stored in variable s1.

226 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 [email protected] to enter 2.3E4.

g (gradian) 1 key

Expr1g expression

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.

In Degree, Gradian or Radian mode:

r(radian) 1 key

Expr1r expression

List1r list

Matrix1r matrix

In Degree, Gradian or Radian angle mode:


Symbols 227

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.

° (degree) 1 key

Expr1° expression 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 Gradian angle mode, multiplies the argument by 10/9.
Note: You can insert this symbol from the computer keyboard by typing @d.

In Degree, Gradian or Radian angle mode:

In Radian angle mode:

Note: To force an approximate result,


Handheld: Press / ·. Windows®: Press Ctrl+Enter. Macintosh®: Press +Enter. iPad®: Hold enter, and select .

°, ', '' (degree/minute/second) /k keys

dd°mm'ss.ss'' expression In Degree angle mode:

228 Symbols

°, ', '' (degree/minute/second) /k keys

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 (").

(angle) /k keys

[Radius,θ_Angle] vector
(polar input)
[Radius,θ_Angle,Z_Coordinate]

vector

(cylindrical input)
[Radius,θ_Angle,θ_Angle] vector
(spherical input)
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 @<.

(MagnitudeAngle) complexValue

(polar input)
Enters a complex value in (rθ) polar
form. The Angle is interpreted according to
the current Angle mode setting.

In Radian mode and vector format set to:

rectangular

cylindrical

spherical

In Radian angle mode and Rectangular complex format:

Note: To force an approximate result,

Handheld: Press / ·. Windows®: Press Ctrl+Enter. Macintosh®: Press +Enter. iPad®: Hold enter, and select .

Symbols 229

(angle) /k keys

' (prime) º key

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 251.

_ (underscore as unit designator) /_ keys

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.

Note: You can find the conversion symbol,

, in the Catalog. Click , and then click

Math Operators.

Assuming z is undefined:

230 Symbols

(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^() Catalog >

10^ (Expr1) expression

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 231

^-1 (reciprocal) Catalog >

Expr1 ^-1 expression

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) /k keys

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.

232 Symbols

| (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 233

(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) /t keys

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.

234 Symbols

© (comment) /k keys

© [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 keys, 0H keys

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.



In Dec base mode: In Bin base mode: In Hex base mode:

Symbols 235

TI-Nspire™ CX II - Draw Commands

This is a supplemental document for the TI-Nspire™ Reference Guide and the TI- Nspire™ CAS Reference Guide. All TI-Nspire™ CX II commands will be incorporated and published in version 5.1 of the TI-Nspire™ Reference Guide and the TI-Nspire™ CAS Reference Guide.

Graphics Programming

New commands have been added on TI-Nspire™ CX II Handhelds and TI-Nspire™
desktop applications for graphics programming.
The TI-Nspire™ CX II Handhelds will switch into this graphics mode while executing graphics commands and switch back to the context in which the program was executed after completion of the program.
The screen will display “Running…” in the top bar while the program is being executed. It will show “Finished” when the program completes. Any key-press will transition the system out of the graphics mode.
• The transition to graphics mode is triggered automatically when one of the Draw
(graphics) commands is encountered during execution of the TI-Basic program.
• This transition will only happen when executing a program from calculator; in a document or calculator in scratchpad.
• The transition out of graphics mode happens upon termination of the program.
• The graphics mode is only available on the TI-Nspire™ CX II Handhelds and the desktop TI-Nspire™ CX II Handhelds view. This means it is not available in the computer document view or PublishView (.tnsp) on the desktop nor on iOS.
- If a graphics command is encountered while executing a TI-Basic program from the incorrect context, an error message is displayed and the TI-Basic program
is terminated.

Graphics Screen

The graphics screen will contain a header at the top of the screen that cannot be written to by graphics commands.
The graphics screen drawing area will be cleared (color = 255,255,255) when the graphics screen is initialized.

Graphics

Default

Screen

Height 212

Width 318

Color white: 255,255,255


236 TI-Nspire™ CX II - Draw Commands

Default View and Settings

• The status icons in the top bar (battery status, press-to-test status, network indicator etc.) will not be visible while a graphics program is running.
• Default drawing color: Black (0,0,0)
• Default pen style - normal, smooth
- Thickness: 1 (thin), 2 (normal), 3 (thickest)
- Style: 1 (smooth), 2 (dotted), 3 (dashed)
• All drawing commands will use the current color and pen settings; either default values or those which were set via TI-Basic commands.
• Text font is fixed and cannot be changed.
• Any output to the graphics screen will be drawn within a clipping window which is the size of the graphics screen drawing area. Any drawn output that extends outside of this clipped graphics screen drawing area will not be drawn. No error message will be displayed.
• All x,y coordinates specified for drawing commands are defined such that 0,0 is at the top left corner of the graphics screen drawing area.
- Exceptions:
- DrawText uses the coordinates as the bottom left corner of the bounding box for the text.
- SetWindow uses the bottom left corner of the screen
• All parameters for the commands can be provided as expressions that evaluate to a number which is then rounded to the nearest integer.

TI-Nspire™ CX II - Draw Commands 237

Graphics Screen Errors Messages

If the validation fails, an error message will display.

Error Message

Description

View

Error

Syntax

If the syntax checker finds any syntax errors, it displays an error message and tries to position the cursor near the first error so you can correct it.

Error

Too few arguments

The function or command is missing one or more arguments

Error

Too many

arguments

The function or command contains and excessive number of arguments and cannot be evaluated.

Error

Invalid data type

An argument is of the wrong data type.

Invalid Commands While in Graphics Mode

Some commands are not allowed once the program switches to graphics mode. If these commands are encountered while in graphics mode and error will be displayed and the program will be terminated.

Disallowed

Command

Error Message



Request Request cannot be executed in graphics mode RequestStr RequestStr cannot be executed in graphics mode Text Text cannot be executed in graphics mode

The commands that print text to the calculator - disp and dispAt - will be supported commands in the graphics context. The text from these commands will be sent to the Calculator screen (not on Graphics) and will be visible after the program exits and the system switches back to the Calculator app

238 TI-Nspire™ CX II - Draw Commands

C

Clear Catalog > CXII

Clear x, y, width, height

Clears entire screen if no parameters are specified.
If x, y, width and height are specified, the rectangle defined by the parameters will be cleared.

Clear

Clears entire screen

Clear 10,10,100,50

Clears a rectangle area with top left corner on (10, 10) and with width 100, height 50


TI-Nspire™ CX II - Draw Commands 239

D

DrawArc Catalog > CXII

DrawArc x, y, width, height, startAngle, arcAngle

Draw an arc within the defined bounding rectangle with the provided start and arc angles.

x, y: upper left coordinate of bounding rectangle

width, height: dimensions of bounding rectangle

The "arc angle" defines the sweep of the arc.
These parameters can be provided as expressions that evaluate to a number which is then rounded to the nearest integer.

See Also: FillArc

DrawArc 20,20,100,100,0,90


DrawArc 50,50,100,100,0,180

DrawCircle Catalog > CXII

DrawCircle x, y, radius

x, y: coordinate of center

radius: radius of the circle

See Also: FillCircle

DrawCircle 150,150,40

240 TI-Nspire™ CX II - Draw Commands

DrawLine Catalog > CXII

DrawLine x1, y1, x2, y2

Draw a line from x1, y1, x2, y2.
Expressions that evaluate to a number which is then rounded to the nearest integer.

Screen bounds: If the specified coordinates causes any part of the line to be drawn outside of the graphics screen, that part of the line will be clipped and no error message will be displayed.

DrawLine 10,10,150,200

DrawPoly Catalog > CXII

The commands have two variants:

DrawPoly xlist, ylist

or

DrawPoly x1, y1, x2, y2, x3, y3...xn, yn

Note: DrawPoly xlist, ylist

Shape will connect x1, y1 to x2, y2, x2, y2 to

x3, y3 and so on.

Note: DrawPoly x1, y1, x2, y2, x3, y3...xn, yn

xn, yn will NOT be automatically connected to x1, y1.
Expressions that evaluate to a list of real floats

xlist, ylist

Expressions that evaluate to a single real float

x1, y1...xn, yn = coordinates for vertices of

polygon

xlist:={0,200,150,0} ylist:={10,20,150,10} DrawPoly xlist,ylist


DrawPoly 0,10,200,20,150,150,0,10

TI-Nspire™ CX II - Draw Commands 241

DrawPoly Catalog > CXII

Note: DrawPoly: Input size dimensions (width/height) relative to drawn lines. The lines are drawn in a bounding box around the specified coordinate and

dimensions such that the actual size of the drawn polygon will be larger than the width and height.

See Also: FillPoly

DrawRect Catalog > CXII

DrawRect x, y, width, height

x, y: upper left coordinate of rectangle

width, height: width and height of rectangle (rectangle drawn down and right from starting coordinate).

Note: The lines are drawn in a bounding box around the specified coordinate and dimensions such that the actual size of the drawn rectangle will be larger than the width and height indicate.

See Also: FillRect

DrawRect 25,25,100,50

DrawText Catalog > CXII

DrawText x, y, exprOrString1 [,exprOrString2]...

x, y: coordinate of text output

Draws the text in exprOrString at the specified x, y coordinate location.
The rules for exprOrString are the same as for Disp DrawText can take multiple arguments.

DrawText 50,50,"Hello World"


242 TI-Nspire™ CX II - Draw Commands

F

FillArc Catalog > CXII

FillArc x, y, width, height startAngle, arcAngle

x, y: upper left coordinate of bounding rectangle

Draw and fill an arc within the defined bounding rectangle with the provided start and arc angles.

Default fill color is black. The fill color can be set by the SetColor command

The "arc angle" defines the sweep of the arc

FillArc 50,50,100,100,0,180

FillCircle Catalog > CXII

FillCircle x, y, radius

x, y: coordinate of center

Draw and fill a circle at the specified center with the specified radius.

Default fill color is black. The fill color can be set by the SetColor command.

FillCircle 150,150,40

Here!

FillPoly Catalog > CXII

FillPoly xlist, ylist

or

FillPoly x1, y1, x2, y2, x3, y3...xn, yn

Note: The line and color are specified by

SetColor and SetPen

xlist:={0,200,150,0} ylist:={10,20,150,10} FillPoly xlist,ylist


TI-Nspire™ CX II - Draw Commands 243

FillPoly Catalog > CXII

FillPoly 0,10,200,20,150,150,0,10


FillRect Catalog > CXII

FillRect x, y, width, height

x, y: upper left coordinate of rectangle width, height: width and height of rectangle Draw and fill a rectangle with the top left

corner at the coordinate specified by (x,y)

Default fill color is black. The fill color can be set by the SetColor command

Note: The line and color are specified by

SetColor and SetPen

FillRect 25,25,100,50


244 TI-Nspire™ CX II - Draw Commands

G

getPlatform() Catalog > CXII

getPlatform()

Returns:
“dt” on desktop software applications
“hh” on TI-Nspire™ CX handhelds
“ios” on TI-Nspire™ CX iPad® app

TI-Nspire™ CX II - Draw Commands 245

P

PaintBuffer Catalog > CXII

PaintBuffer

Paint graphics buffer to screen
This command is used in conjunction with UseBuffer to increase the speed of display on the screen when the program generates multiple graphical objects.

UseBuffer For n,1,10 x:=randInt(0,300) y:=randInt(0,200) radius:=randInt(10,50) Wait 0.5

DrawCircle x,y,radius

EndFor

PaintBuffer

This program will display all the

10 circles at once.

If the “UseBuffer” command is removed, each circle will be displayed as it is drawn.

See Also: UseBuffer

246 TI-Nspire™ CX II - Draw Commands

PlotXY Catalog > CXII

PlotXY x, y, shape

x, y: coordinate to plot shape

shape : a number between 1 and 13 specifying the shape

1 - Filled circle
2 - Empty circle
3 - Filled square
4 - Empty square
5 - Cross
6 - Plus
7 - Thin
8 - medium point, solid
9 - medium point, empty
10 - larger point, solid
11 - larger point, empty
12 - largest point, solid
13 - largest point, empty

PlotXY 100,100,1

For n,1,13

DrawText 1+22*n,40,n PlotXY 5+22*n,50,n EndFor


TI-Nspire™ CX II - Draw Commands 247

S

SetColor Catalog > CXII

SetColor

Red-value, Green-value, Blue-value
Valid values for red, green and blue are between 0 and 255
Sets the color for subsequent Draw commands

SetColor 255,0,0

DrawCircle 150,150,100

SetPen Catalog > CXII

SetPen

thickness, style
thickness: 1 <= thickness <= 3|1 is thinnest,
3 is thickest
style: 1 = Smooth, 2 = Dotted, 3 = Dashed
Sets the pen style for subsequent Draw commands

SetPen 3,3

DrawCircle 150,150,50

SetWindow Catalog > CXII

SetWindow

xMin, xMax, yMin, yMax
Establishes a logical window that maps to the graphics drawing area. All parameters are required.
If the part of drawn object is outside the window, the output will be clipped (not shown) and no error message is displayed.

SetWindow 0,160,0,120

will set the output window to have

0,0 in the bottom left corner with

a width of 160 and a height of 120

DrawLine 0,0,100,100

SetWindow 0,160,0,120

SetPen 3,3

DrawLine 0,0,100,100

248 TI-Nspire™ CX II - Draw Commands

SetWindow Catalog > CXII

If xmin is greater than or equal to xmax or ymin is greater than or equal to ymax, an error message is shown.
Any objects drawn before a SetWindow command will not be re-drawn in the new configuration.
To reset the window parameters to the default, use:
SetWindow 0,0,0,0

TI-Nspire™ CX II - Draw Commands 249

U

UseBuffer Catalog > CXII

UseBuffer

Draw to an off screen graphics buffer instead of screen (to increase performance)
This command is used in conjunction with PaintBuffer to increase the speed of display on the screen when the program generates multiple graphical objects.
With UseBuffer, all the graphics are displayed only after the next PaintBuffer command is executed.
UseBuffer only needs to be called once in the program i.e. every use of PaintBuffer does not need a corresponding UseBuffer

UseBuffer For n,1,10 x:=randInt(0,300) y:=randInt(0,200) radius:=randInt(10,50) Wait 0.5

DrawCircle x,y,radius

EndFor

PaintBuffer

This program will display all the 10 circles at once.

If the “UseBuffer” command is removed, each circle will be displayed as it is drawn.

See Also: PaintBuffer


250 TI-Nspire™ CX II - Draw Commands

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 49, and isVoid(), page 94.
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, freqTablelist, 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.


Empty (Void) Elements 251

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.

252 Empty (Void) Elements

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 shortcuts 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, ...

Shortcuts for Entering Math Expressions 253

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 (gradians) @g

(angle) @<


(conversion) @>

Decimal, approxFraction(), and so on.

@>Decimal, @>approxFraction(), and so on.


254 Shortcuts for Entering Math Expressions

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.

EOS™ (Equation Operating System) Hierarchy 255

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 10r 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.

256 EOS™ (Equation Operating System) Hierarchy

TI-Nspire CX II - TI-Basic Programming Features

Auto-indentation in Programming Editor

The TI-Nspire™ program editor now auto-indents statements inside a block command. Block commands are If/EndIf, For/EndFor, While/EndWhile, Loop/EndLoop, Try/EndTry The editor will automatically prepend spaces to program commands inside a block
command. The closing command of the block will be aligned with the opening
command.
The example below shows auto-indentation in nested block commands.

Code fragments that are copied and pasted will retain the original indentation.
Opening a program created in an earlier version of the software will retain the original indentation.

Improved Error Messages for TI-Basic

Errors

Error Condition

New message

Error in condition statement (If/While)

A conditional statement did not resolve to TRUE

or FALSE

NOTE: With the change to place the cursor on the line with the error, we no longer need to specify if the error is in an "If" statement or a "While" statement.

Missing EndIf

Expected EndIf but found a different end statement

Missing EndFor

Expected EndFor but found a different end statement

Missing EndWhile

Expected EndWhile but found a different end statement

Missing EndLoop

Expected EndLoop but found a different end statement

TI-Nspire CX II - TI-Basic Programming Features 257

Error Condition

New message

Missing EndTry

Expected EndTry but found a different end statement

Then” omitted after If <condition>

Missing If..Then

Then” omitted after ElseIf <condition>

Then missing in block: ElseIf.

When “Then”, “Else” and “ElseIf” were encountered outside of control blocks

Else invalid outside of blocks: If..Then..EndIf or

Try..EndTry

ElseIf” appears outside of “If..Then..EndIf

block

ElseIf invalid outside of block: If..Then..EndIf

"Then” appears outside of “If....EndIf” block

Then invalid outside of block: If..EndIf

Syntax Errors

In case commands that expect one or more arguments are called with an incomplete list of arguments, a “Too few argument error” will be issued instead of “syntax” error

Current behavior

New CX II behavior

258 TI-Nspire CX II - TI-Basic Programming Features

Current behavior

New CX II behavior

Note: When an incomplete list of arguments is not followed by a comma, the error message is: “too few arguments”. This is the same as previous releases.


TI-Nspire CX II - TI-Basic Programming Features 259

Constants and Values

The following table lists the constants and their values that are available when performing unit conversions. They can be typed in manually or selected from the Constants list in Utilities > Unit Conversions (Handheld: Press k 3).

Constant Name Value

_c Speed of light 299792458 _m/_s

_Cc Coulomb constant 8987551787.3682 _m/_F

_Fc Faraday constant 96485.33289 _coul/_mol

_g Acceleration of gravity 9.80665 _m/_s2

_Gc Gravitational constant 6.67408E-11 _m3/_kg/_s2

_h Planck's constant 6.626070040E-34 _J _s

_k Boltzmann's constant 1.38064852E-23 _J/_¡K

_m0 Permeability of a vacuum 1.2566370614359E-6 _N/_A2

_mb Bohr magneton 9.274009994E-24 _J _m2/_Wb

_Me Electron rest mass 9.10938356E-31 _kg

_Mm Muon mass 1.883531594E-28 _kg

_Mn Neutron rest mass 1.674927471E-27 _kg

_Mp Proton rest mass 1.672621898E-27 _kg

_Na Avogadro's number 6.022140857E23 /_mol

_q Electron charge 1.6021766208E-19 _coul

_Rb Bohr radius 5.2917721067E-11 _m

_Rc Molar gas constant 8.3144598 _J/_mol/_¡K

_Rdb Rydberg constant 10973731.568508/_m

_Re Electron radius 2.8179403227E-15 _m

_u Atomic mass 1.660539040E-27 _kg

_Vm Molar volume 2.2413962E-2 _m3/_mol

_H0 Permittivity of a vacuum 8.8541878176204E-12 _F/_m

_s Stefan-Boltzmann constant 5.670367E-8 _W/_m2/_¡K4


_f0 Magnetic flux quantum 2.067833831E-15 _Wb

260 Constants and Values

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 191.

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.

Error Codes and Messages 261

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 non- valued 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.

262 Error Codes and Messages

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.

Error Codes and Messages 263

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.

264 Error Codes and Messages

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

Error Codes and Messages 265

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

266 Error Codes and Messages

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

• 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.

1180

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

Domain error.

Error Codes and Messages 267

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.

268 Error Codes and Messages

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 200.

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.

Warning Codes and Messages 269

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'

270 Warning Codes and Messages

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General Information 271

Index

-

-, subtract 210

!

!, factorial 220

"

", second notation 228

#

#, indirection 226

#, indirection operator 256

%

%, percent 216

&

^, power 213

_

_, unit designation 230

|

|, constraint operator 232

′ minute notation 228

′, prime 230

+

+, add 210

=

≠, not equal 217

≤, less than or equal 218

≥, greater than or equal 219

>, greater than 218

&, append 220

*

*, multiply 211

.

.-, dot subtraction 214

=, equal

∏, product

∑( ), sum

216
223
224

.*, dot multiplication 215

./, dot division 215

.^, dot power 215

.+, dot addition 214

∑Int( )

∑Prn( )

225
225

/

/, divide 212

:

:=, assign 234

^

^⁻¹, reciprocal 232

√, square root 223

(angle) 229

∫, integral 221

272 Index

, convert units 231

approxFraction( ) 14

Base10, display as decimal integer 18

Base16, display as hexadecimal 19

Base2, display as binary 17

cos, display in terms of cosine 29

Cylind, display as cylindrical vector 42

DD, display as decimal angle 45

Decimal, display result as decimal 45

DMS, display as

1

10^( ), power of ten 231

2

2-sample F Test 75

A

abs( ), absolute value 8

absolute value

template for 3-4

degree/minute/second 54

exp, display in terms of e 63

Grad, convert to gradian angle 86

add, +

amortization table, amortTbl( )

amortTbl( ), amortization table

210
8, 17
8, 17

Polar, display as polar vector 133

Rad, convert to radian angle 143

and, Boolean operator 9

angle( ), angle 10

Rect, display as rectangular vector 146

sin, display in terms of sine 166

Sphere, display as spherical vector 175

, logical implication 219, 253

→, store variable 233

, logical double implication 220

©

©, comment

°

°, degree notation 228

°, degrees/minutes/seconds 228

0

0b, binary indicator 235

0h, hexadecimal indicator 235

angle, angle( ) 10

ANOVA, one-way variance analysis 10

ANOVA2way, two-way variance

analysis 11

Ans, last answer 13

answer (last), Ans 13

append, & 220

approx( ), approximate 13, 15

approximate, approx( ) 13, 15

approxRational( ) 14

arc length, arcLen( ) 15

arcsech(), csech⁻¹() 15 arcsin(), sin⁻¹() 15 arcsinh(), sinh⁻¹() 15 arctan(), tan⁻¹() 15

arctanh(), tanh⁻¹()

16

arguments in TVM functions

195

augment( ), augment/concatenate

16

augment/concatenate, augment( )

16


Index 273

average rate of change, avgRC( ) 16

avgRC( ), average rate of change 16

B

binary

display, Base2 17

indicator, 0b 235

binomCdf( ) 20, 92

binomPdf( ) 20

Boolean operators

219, 253

220

and

9

nand

119

nor

123

not

125

or

129

xor

201

C

Cdf( ) 69 ceiling( ), ceiling 20 ceiling, ceiling( ) 20-21, 36 centralDiff( ) 21

comment, © 235

common denominator, comDenom

( ) 26 completeSquare( ), complete square 27 complex

conjugate, conj( ) 28 factor, cFactor( ) 21 solve, cSolve( ) 38 zeros, cZeros( ) 43 conj( ), complex conjugate 28

constant

in solve( ) 171

constants

in cSolve( ) 39 in cZeros( ) 44 in deSolve( ) 49 in solve( ) 173 in zeros( ) 203 shortcuts for 253

constraint operator "|" 232

constraint operator, order of


evaluation 255 construct matrix, constructMat( ) 28 constructMat( ), construct matrix 28 convert

cFactor( ), complex factor 21 char( ), character string 22 character string, char( ) 22

Grad

Rad

units

86
143
231

characters

numeric code, ord( ) 130 string, char( ) 22 charPoly( ) 23 χ²2way 23

clear

error, ClrErr 25

Clear 239

ClearAZ 25

ClrErr, clear error 25

colAugment 26

colDim( ), matrix column dimension 26

colNorm( ), matrix column norm 26

combinations, nCr( ) 120

comDenom( ), common

denominator 26

copy variable or function, CopyVar 29

correlation matrix, corrMat( ) 29

corrMat( ), correlation matrix 29

cos⁻¹, arccosine 31

cos( ), cosine 30

cosh⁻¹( ), hyperbolic arccosine 32

cosh( ), hyperbolic cosine 32

cosine

display expression in terms of 29 cosine, cos( ) 30 cot⁻¹( ), arccotangent 33 cot( ), cotangent 33 cotangent, cot( ) 33 coth⁻¹( ), hyperbolic arccotangent 34 coth( ), hyperbolic cotangent 34 count days between dates, dbd( ) 44

274 Index

count items in a list conditionally ,

countif( ) 35 count items in a list, count( ) 34 count( ), count items in a list 34 countif( ), conditionally count items

in a list 35

degree/minute/second notation 228

delete

void elements from list 49

deleting

variable, DelVar 48 deltaList() 48 deltaTmpCnv() 48

DelVar, delete variable 48 delVoid( ), remove void elements 49 denominator 26 derivative or nth derivative

template for 6 derivative() 49 derivatives

first derivative, d( ) 221 numeric derivative, nDeriv( ) 121-122 numeric derivative, nDerivative(

) 121


deSolve( ), solution 49

det( ), matrix determinant 51

diag( ), matrix diagonal 51

dim( ), dimension 52

D

d( ), first derivative 221 days between dates, dbd( ) 44 dbd( ), days between dates 44 decimal

angle display, DD 45

integer display, Base10 18

Define 46

Define LibPriv 47

Define LibPub 47

define, Define 46

Define, define 46

defining

private function or program 47

public function or program 47

definite integral

template for 6 degree notation, ° 228 degree/minute/second display,

dimension, dim( ) 52

Disp, display data 52, 158

DispAt 52

display as

binary, Base2 17

cylindrical vector, Cylind 42

decimal angle, DD 45

decimal integer, Base10 18

degree/minute/second, DMS 54

hexadecimal, Base16 19

polar vector, Polar 133

rectangular vector, Rect 146

spherical vector, Sphere 175

display data, Disp 52, 158

distribution functions

binomCdf( ) 20, 92 binomPdf( ) 20 invNorm( ) 92 invt( ) 92

Invχ²( ) 91

DMS 54

normCdf( )

125

normPdf( ) 125

Index 275

poissCdf( )

132

function, EndFunc

76

poissPdf( )

132

if, EndIf

86

tCdf( )

185

loop, EndLoop

110

tPdf( )

190

program, EndPrgm

137

χ²2way( )

23

try, EndTry

191

χ²Cdf( )

24

while, EndWhile

201

χ²GOF( )

24

end function, EndFunc

76

χ²Pdf( )

24

end if, EndIf

86

divide, /

212

end loop, EndLoop

110

domain function, domain( )

55

end while, EndWhile

201

domain( ), domain function

55

EndTry, end try

191

dominant term, dominantTerm( )

56

EndWhile, end while

201

dominantTerm( ), dominant term

56

EOS (Equation Operating System)

255

dot

addition, .+ 214 division, ./ 215 multiplication, .* 215 power, .^ 215 product, dotP( ) 57 subtraction, .- 214

equal, = 216

Equation Operating System (EOS) 255

error codes and messages 261, 269

errors and troubleshooting

clear error, ClrErr 25 pass error, PassErr 131 euler( ), Euler function 60

dotP( ), dot product 57

draw 240-242

E

e exponent

template for 2 e to a power, e^( ) 57, 64 e, display expression in terms of 63

E, exponent 227 e^( ), e to a power 57 eff( ), convert nominal to effective

rate 58 effective rate, eff( ) 58 eigenvalue, eigVl( ) 59

evaluate polynomial, polyEval( ) 135 evaluation, order of 255 exact( ), exact 63 exact, exact( ) 63 exclusion with "|" operator 232 exit, Exit 63

Exit, exit 63 exp( ), e to a power 64 explist( ), expression to list 64 expand( ), expand 65

expand, expand( ) 65 exponent, E 227 exponential regession, ExpReg 66 exponents

ElseIf, else if 59 empty (void) elements 251 end

string to expression, expr( ) 66, 107

F

for, EndFor 72

factor( ), factor 67

276 Index

factor, factor( ) 67 factorial, ! 220 fill 243-244

Fill, matrix fill 70 financial functions, tvmFV( ) 193 financial functions, tvmI( ) 193 financial functions, tvmN( ) 194 financial functions, tvmPmt( ) 194 financial functions, tvmPV( ) 194

geomPdf( ) 77

Get 77, 245

get/return

denominator, getDenom( ) 79 number, getNum( ) 84 variables injformation,

getVarInfo( ) 82, 85

getDenom( ), get/return

denominator 79

first derivative

template for 5

FiveNumSummary 70

floor( ), floor 71

floor, floor( ) 71

fMax( ), function maximum 71

fMin( ), function minimum 72

For 72

for, For 72

For, for 72

format string, format( ) 73

format( ), format string 73

fpart( ), function part 73

fractions

propFrac 139 template for 1 freqTable( ) 74 frequency( ) 74

Frobenius norm, norm( ) 124

Func, function 76

Func, program function 76

functions

maximum, fMax( ) 71 minimum, fMin( ) 72 part, fpart( ) 73 program function, Func 76 user-defined 46

functions and variables

copying 29

G

getKey() 79

getLangInfo( ), get/return language

information 82

getLockInfo( ), tests lock status of

variable or variable group 83 getMode( ), get mode settings 83 getNum( ), get/return number 84

GetStr 84 getType( ), get type of variable 85 getVarInfo( ), get/return variables

information 85

go to, Goto 86

Goto, go to 86

gradian notation, g 227

greater than or equal, ≥ 219

greater than, > 218

greatest common divisor, gcd( ) 76

groups, locking and unlocking 106, 197

groups, testing lock status 83

H

hexadecimal

display, Base16 19

indicator, 0h 235

hyperbolic

arccosine, cosh⁻¹( ) 32 arcsine, sinh⁻¹( ) 168 arctangent, tanh⁻¹( ) 184 cosine, cosh( ) 32 sine, sinh( ) 168 tangent, tanh( ) 184

I

identity matrix, identity( ) 86

Index 277

identity( ), identity matrix 86

if, If 86

If, if 86

ifFn( ) 88

imag( ), imaginary part 88

imaginary part, imag( ) 88

ImpDif( ), implicit derivative 89

implicit derivative, Impdif( ) 89

indefinite integral

template for 6 indirection operator (#) 256 indirection, # 226 input, Input 89

Input, input 89

left( ), left 95 left, left( ) 95 length of string 52 less than or equal, ≤ 218

LibPriv 47

LibPub 47

library

create shortcuts to objects 96

libShortcut( ), create shortcuts to

library objects 96

limit

lim( ) 96 limit( ) 96 template for 6

inString( ), within string 89

limit( ) or lim( ), limit 96

int( ), integer 90 intDiv( ), integer divide 90 integer divide, intDiv( ) 90 integer part, iPart( ) 93

linear regression, LinRegAx

linear regression, LinRegBx LinRegBx, linear regression LinRegMx, linear regression

98
97, 99
97
98

integer, int( ) 90

LinRegtIntervals, linear regression 99

integral, ∫ 221

interpolate( ), interpolate 90

LinRegtTest

linSolve()

101
102

inverse cumulative normal

Δlist( ), list difference 103

distribution (invNorm( ) 92

list to matrix, listmat( )

103

inverse, ^⁻¹ 232 invF( ) 91 invNorm( ), inverse cumulative

normal distribution) 92

invt( ) 92

Invχ²( ) 91

list, conditionally count items in 35

list, count items in 34 listmat( ), list to matrix 103 lists

augment/concatenate,

augment( ) 16

iPart( ), integer part 93

irr( ), internal rate of return

cross product, crossP( ) 36

cumulative sum,

cumulativeSum( ) 41

differences in a list, Δlist( )

dot product, dotP( )

103
57

L

label, Lbl 95

language

get language information 82

Lbl, label 95

lcm, least common multiple 95

least common multiple, lcm 95

empty elements in 251 expression to list, explist( ) 64 list to matrix, listmat( ) 103 matrix to list, matlist( ) 111 maximum, max( ) 111 mid-string, mid( ) 114 minimum, min( ) 115 new, newList( ) 121 product, product( ) 138

278 Index

sort ascending, SortA

174

eigenvector, eigVc( )

58

sort descending, SortD

175

filling, Fill

70

summation, sum( )

180

identity, identity( )

86

ln( ), natural logarithm

104

list to matrix, listmat( )

103

LnReg, logarithmic regression

104

lower-upper decomposition, LU

110

local variable, Local

106

matrix to list, matlist( )

111

local, Local

106

maximum, max( )

111

Local, local variable

106

minimum, min( )

115

Lock, lock variable or variable group

106

new, newMat( )

121

locking variables and variable groups

106

product, product( )

138

Log QR factorization, QR 139

template for

2

random, randMat( ) 145

logarithmic regression, LnReg

104

reduced row echelon form, rref(

logarithms

104

) 156

logical double implication,

220

row addition, rowAdd( ) 155

logical implication, 219, 253

logistic regression, Logistic 108

logistic regression, LogisticD 109

Logistic, logistic regression 108

row dimension, rowDim( ) 156

row echelon form, ref( ) 147

row multiplication and addition,

mRowAdd( ) 116

LogisticD, logistic regression 109

loop, Loop 110

Loop, loop 110

row norm, rowNorm( )

row operation, mRow( )

row swap, rowSwap( )

156
116
156

LU, matrix lower-upper

decomposition 110

M

matlist( ), matrix to list 111

matrices

augment/concatenate,

augment( ) 16

submatrix, subMat( ) 180-181

summation, sum( ) 180

transpose, T 182

matrix (1 × 2)

template for 4

matrix (2 × 1)

template for 4

matrix (2 × 2)

template for 4

matrix (m × n)

template for 4

matrix to list, matlist( ) 111

max( ), maximum

111

maximum, max( )

111

mean( ), mean

112

mean, mean( )

112

median( ), median

112

median, median( )

medium-medium line regression,

112

MedMed 113

MedMed, medium-medium line

regression 113

Index 279

mid-string, mid( ) 114 mid( ), mid-string 114 min( ), minimum 115 minimum, min( ) 115 minute notation, ′ 228 mirr( ), modified internal rate of

return 115

mixed fractions, using propFrac(›

with 139 mod( ), modulo 116 mode settings, getMode( ) 83 modes

setting, setMode( ) 162

modified internal rate of return, mirr

( ) 115 modulo, mod( ) 116 mRow( ), matrix row operation 116 mRowAdd( ), matrix row

nor, Boolean operator 123 norm( ), Frobenius norm 124 normal distribution probability,

normCdf( ) 125

normal line, normalLine( ) 124

normalLine( ) 124

normCdf( ) 125

normPdf( ) 125

not equal, ≠ 217

not, Boolean operator 125

nPr( ), permutations 126

npv( ), net present value 126

nSolve( ), numeric solution 127

nth root

template for 1

numeric

derivative, nDeriv( ) 121-122 derivative, nDerivative( ) 121 integral, nInt( ) 122 solution, nSolve( ) 127

O

N

nand, Boolean operator 119 natural logarithm, ln( ) 104 nCr( ), combinations 120 nDerivative( ), numeric derivative 121 negation, entering negative numbers 256 net present value, npv( ) 126 new

objects

create shortcuts to library 96

one-variable statistics, OneVar 128

OneVar, one-variable statistics 128

operators

order of evaluation 255 or (Boolean), or 129 or, Boolean operator 129 ord( ), numeric character code 130

P

PRx( ), rectangular x coordinate PRy( ), rectangular y coordinate

130
131

pass error, PassErr

131

PassErr, pass error 131

Pdf( ) 74

rate 123

nominal rate, nom( ) 123

percent, % 216 permutations, nPr( ) 126 piecewise function (2-piece)

template for 2

280 Index

piecewise function (N-piece)

template for 3 piecewise( ) 132 poissCdf( ) 132 poissPdf( ) 132 polar

proper fraction, propFrac 139

propFrac, proper fraction 139

Q

QR factorization, QR 139

coordinate, RPr( ) 143

QR, QR factorization

139

coordinate, RPθ( ) 142

vector display, Polar 133

quadratic regression, QuadReg

QuadReg, quadratic regression

140
140

polyCoef( ) 133 polyDegree( ) 134 polyEval( ), evaluate polynomial 135 polyGcd( ) 135-136

quartic regression, QuartReg

QuartReg, quartic regression

R

141
141

polynomials

evaluate, polyEval( ) 135

random, randPoly( ) 145

PolyRoots() 136

power of ten, 10^( ) 231

power regression,

PowerReg 136, 149, 151, 187

power, ^ 213

PowerReg, power regression 136

Prgm, define program 137

prime number test, isPrime( ) 93

prime, ′ 230

probability densiy, normPdf( ) 125

prodSeq() 138

product( ), product 138

product, ∏( ) 223

template for 5

product, product( ) 138

programming

define program, Prgm 137 display data, Disp 52, 158 pass error, PassErr 131

programs

defining private library 47

defining public library 47

programs and programming

clear error, ClrErr 25 display I/O screen, Disp 52, 158 end program, EndPrgm 137 end try, EndTry 191 try, Try 191

R, radian 227

RPr( ), polar coordinate 143

RPθ( ), polar coordinate 142

radian, R 227

rand( ), random number 143

randBin, random number 144

randInt( ), random integer 144

randMat( ), random matrix 145

randNorm( ), random norm 145

random

matrix, randMat( )

145

norm, randNorm( )

145

number seed, RandSeed

146

polynomial, randPoly( )

145

random sample

145

randPoly( ), random polynomial

145

randSamp( )

145

RandSeed, random number seed

146

real( ), real

146

real, real( )

146

reciprocal, ^⁻¹

232

rectangular-vector display, Rect

146

rectangular x coordinate, PRx( )

130

rectangular y coordinate, PRy( )

131

reduced row echelon form, rref( )

156

ref( ), row echelon form

147

RefreshProbeVars

regressions

148

cubic, CubicReg 40

exponential, ExpReg 66

Index 281

linear regression, LinRegAx 98 linear regression, LinRegBx 97, 99 logarithmic, LnReg 104

Logistic 108 logistic, Logistic 109 medium-medium line, MedMed 113

MultReg 117

power regression,

PowerReg 136, 149, 151, 187 quadratic, QuadReg 140 quartic, QuartReg 141 sinusoidal, SinReg 169 remain( ), remainder 149 remainder, remain( ) 149

remove

void elements from list 49

Request 149

RequestStr 151

result

display in terms of cosine 29 display in terms of e 63 display in terms of sine 166 result values, statistics 177 results, statistics 176 return, Return 152

Return, return 152 right( ), right 152 right, right( ) 27, 60, 90, 152 rk23( ), Runge Kutta function 152 rotate( ), rotate 154 rotate, rotate( ) 154 round( ), round 155 round, round( ) 155 row echelon form, ref( ) 147 rowAdd( ), matrix row addition 155 rowDim( ), matrix row dimension 156 rowNorm( ), matrix row norm 156 rowSwap( ), matrix row swap 156 rref( ), reduced row echelon form 156

S

sec⁻¹( ), inverse secant 157

sec( ), secant 157

sech⁻¹( ), inverse hyperbolic secant 158 sech( ), hyperbolic secant 158 second derivative

template for 6 second notation, " 228 seq( ), sequence 159 seqGen( ) 159 seqn( ) 160 sequence, seq( ) 159-160 series( ), series 161 series, series( ) 161 set

mode, setMode( ) 162 setMode( ), set mode 162 settings, get current 83 shift( ), shift 163 shift, shift( ) 163 sign( ), sign 165 sign, sign( ) 165 simult( ), simultaneous equations 165 simultaneous equations, simult( ) 165 sin⁻¹( ), arcsine 167 sin( ), sine 166 sine

display expression in terms of 166 sine, sin( ) 166 sinh⁻¹( ), hyperbolic arcsine 168 sinh( ), hyperbolic sine 168

SinReg, sinusoidal regression 169 sinusoidal regression, SinReg 169 solution, deSolve( ) 49 solve( ), solve 170 solve, solve( ) 170

SortA, sort ascending 174

SortD, sort descending 175

sorting

ascending, SortA 174 descending, SortD 175 spherical vector display, Sphere 175 sqrt( ), square root 176

square root

template for 1

square root, √( ) 176, 223

282 Index

standard deviation, stdDev( ) 178, 198 stat.results 176 stat.values 177 statistics

combinations, nCr( ) 120 factorial, ! 220 mean, mean( ) 112 median, median( ) 112 one-variable statistics, OneVar 128 permutations, nPr( ) 126 random norm, randNorm( ) 145 random number seed,

RandSeed 146 standard deviation, stdDev( ) 178, 198 two-variable results, TwoVar 195 variance, variance( ) 198

stdDevPop( ), population standard

deviation 178

stdDevSamp( ), sample standard

deviation 178

Stop command 179

store variable (→) 233

storing

student-t distribution probability,

tCdf( ) 185 student-t probability density, tPdf( ) 190 subMat( ), submatrix 180-181 submatrix, subMat( ) 180-181 substitution with "|" operator 232 subtract, - 210 sum of interest payments 225 sum of principal payments 225 sum( ), summation 180 sum, ∑( ) 224 template for 5 sumIf( ) 180 summation, sum( ) 180 sumSeq() 181

system of equations (2-equation)

template for 3

system of equations (N-equation)

template for 3

T

t test, tTest 192

symbol, & 234

T, transpose

182

string

dimension, dim( ) 52 length 52 string( ), expression to string 179

strings

append, & 220 character code, ord( ) 130 character string, char( ) 22 expression to string, string( ) 179 format, format( ) 73 formatting 73 indirection, # 226 left, left( ) 95 mid-string, mid( ) 114 right, right( ) 27, 60, 90, 152 rotate, rotate( ) 154 shift, shift( ) 163 string to expression, expr( ) 66, 107 using to create variable names 256 within, InString 89

tan⁻¹( ), arctangent 183

tan( ), tangent 182

tangent line, tangentLine( ) 183

tangent, tan( ) 182

tangentLine( ) 183

tanh⁻¹( ), hyperbolic arctangent 184

tanh( ), hyperbolic tangent 184

Taylor polynomial, taylor( ) 185

taylor( ), Taylor polynomial 185

tCdf( ), studentt distribution

probability 185 tCollect( ), trigonometric collection 186 templates

Index 283

indefinite integral 6

limit 6

Log 2

matrix (1 × 2) 4

matrix (2 × 1) 4

matrix (2 × 2) 4

matrix (m × n) 4

nth root 1

piecewise function (2-piece) 2

piecewise function (N-piece) 3

product, ∏( ) 5

second derivative 6

square root 1

sum, ∑( ) 5

system of equations (2-

equation) 3

system of equations (N-

equation) 3

test for void, isVoid( ) 94

Test_2S, 2-sample F test 75

tExpand( ), trigonometric expansion 186

Text command 187

time value of money, Future Value 193

time value of money, Interest 193

time value of money, number of

payments 194

time value of money, payment

amount 194 time value of money, present value 194 tInterval, t confidence interval 187 tInterval_2Samp, twosample t

confidence interval 188

ΔtmpCnv() 189

tmpCnv() 189

tPdf( ), student probability density 190

trace( ) 190

transpose, T 182

trigonometric collection, tCollect( ) 186

trigonometric expansion, tExpand( ) 186

Try, error handling command 191

tTest, t test 192

tTest_2Samp, two-sample t test 192

TVM arguments 195

tvmFV( ) 193

tvmI( ) 193 tvmN( ) 194 tvmPmt( ) 194 tvmPV( ) 194 two-variable results, TwoVar 195

TwoVar, two-variable results 195

U

underscore, _ 230 unit vector, unitV( ) 197 units

convert 231 unitV( ), unit vector 197 unLock, unlock variable or variable

group 197

unlocking variables and variable

groups 197 user-defined functions 46 user-defined functions and

programs 47

V

variable

creating name from a character

string 256

variable and functions

copying 29

variables

clear all single-letter 25 delete, DelVar 48 local, Local 106 variables, locking and unlocking 83, 106, 197 variance, variance( ) 198 varPop( ) 198 varSamp( ), sample variance 198

vectors

cross product, crossP( ) 36

cylindrical vector display,

Cylind 42

dot product, dotP( ) 57

unit, unitV( ) 197

void elements 251

void elements, remove 49

void, test for 94

284 Index

W

Wait command

199

warnCodes( ), Warning codes

200

warning codes and messages

269

when( ), when

200

when, when( )

200

while, While

201

While, while

201

with, |

232

within string, inString( )

89

X

x², square

214

XNOR

220

xor, Boolean exclusive or

201

Z

zeroes( ), zeroes 202 zeroes, zeroes( ) 202 zInterval, z confidence interval 204 zInterval_1Prop, one-proportion z

confidence interval 205

zInterval_2Prop, two-proportion z

confidence interval 205

zInterval_2Samp, two-sample z

confidence interval 206 zTest 206 zTest_1Prop, one-proportion z test 207 zTest_2Prop, two-proportion z test 207 zTest_2Samp, two-sample z test 208

Χ

χ²Cdf( ) 24 χ²GOF 24 χ²Pdf( ) 24

Index 285

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