Learn more about TI Technology through the online help at education.ti.com/eguide.
Except as otherwise expressly stated in the License that accompanies a program, Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely
on an "asis" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the amount set forth in the license for the program. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
© 2020 Texas Instruments Incorporated
Actual products may vary slightly from provided images.
ii
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
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
Autoindentation in Programming Editor 257
Improved Error Messages for TIBasic 257
Online Help 271
Contact TI Support 271
Service and Warranty Information 271
iv
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.
Example:
Note: See also √() (square root), page
223.
Nth root template /l keys
Example:
Note: See also root(), page 154.
Expression Templates 1
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.
Example:
Lets you create expressions and conditions for a twopiece piecewise function. To add
a piece, click in the template and repeat the template.
Note: See also piecewise(), page 132.
2 Expression Templates
Lets you create expressions and conditions for an Npiece 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.
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 (2equation).
Absolute value template Catalog >
Example:
Note: See also abs(), page 8.
Expression Templates 3
dd°mm’ss.ss’’ template Catalog >
Example:
Lets you enter angles in dd°mm’ss.ss’’ format, where dd is the number of decimal degrees, mm is the number of minutes, and ss.ss is the number of seconds.
Matrix template (2 x 2) Catalog >
Example:
Creates a 2 x 2 matrix.
Matrix template (1 x 2) Catalog >
Example:
.
Example:
The template appears after you are prompted to specify the number of rows and columns.
4 Expression Templates
Example:
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.
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
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.
Example:
Note: See also ∫() integral(), page 221.
Limit template Catalog >
Example:
6 Expression Templates
Use − or (−) for left hand limit. Use + for right hand limit.
Note: See also limit(), page 6.
Expression Templates 7
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.
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
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 bitbybit using an and operation. Internally, both integers are converted to signed, 64bit 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(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 twodimensional rectangular coordinate point.
In Degree angle mode: In Gradian angle mode: In Radian angle mode:
ANOVA List1,List2[,List3,...,List20][,Flag]
Performs a oneway 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 twoway 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,...,Len1, 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 >
Expr►approxFraction([Tol]) ⇒
expression
List►approxFraction([Tol]) ⇒ list
Matrix►approxFraction([Tol]) ⇒ matrix
Returns the input as a fraction, using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E14 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.E14 is used.
14 Alphabetical Listing
arccsc() See csc1(), 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.
Alphabetical Listing 15
arctanh() See tanh1(), 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 forwarddifference quotient
(average rate of change).
Expr1 can be a userdefined 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 centraldifference quotient.
16 Alphabetical Listing
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, 64bit 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, 64bit 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(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(0≤X≤upBound)
⇒ number if upBound is a number, list if
upBound is a list
Computes a cumulative probability for the discrete binomial distribution with n number of trials and probability p of success on each trial.
For P(X ≤ upBound), set lowBound=0
binomPdf() 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.
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(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(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 nonreal numbers. This alternative is appropriate if you want factorization with respect to more than one variable.
Alphabetical Listing 21
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 nonreal 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 floatingpoint coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the builtin 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(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(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•I−A)
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 twoway 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 singlecharacter 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 multiline 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(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(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(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(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 a•x2+b•x+c into the form a•(x h)2+k
Alphabetical Listing 27
 or 
Converts a quadratic equation of the form a•x2+b•x+c=d into the form a•(xh)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
(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 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 variablenaming 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(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 1−cos(...)^2
so that any remaining powers of cos(...) have exponents in the range (0, 2). Thus, the result will be free of sin(...) if and only
if sin(...) occurs in the given expression only to even powers.
Note: This conversion operator is not supported in Degree or Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles.
cos() 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
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 X1 and f(A) = X f(B) X1. For example, cos(A) = X cos(B) X1 where:
cos(B) =
All computations are performed using floatingpoint arithmetic.
cos1(Expr1) ⇒ expression
cos1(List1) ⇒ list
cos1(Expr1) returns the angle whose cosine is Expr1 as an expression.
cos1(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
cos1(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 floatingpoint 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 floatingpoint numbers.
In Degree angle mode:
In Radian angle mode:
cosh1(Expr1) ⇒ expression
cosh1(List1) ⇒ list
cosh1(Expr1) returns the inverse
new screenshots format (see Z_ WriterNotes)
hyperbolic cosine of the argument as an
expression.
32 Alphabetical Listing
cosh1(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(...).
cosh1(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 floatingpoint 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(Expr1) ⇒ expression
cot1(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
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.
coth1() Catalog >
coth1(Expr1) ⇒ expression
coth1(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(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
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(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(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:
In Radian angle mode:
csc1() µ key
csc1(Expr1) ⇒expression
csc1(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.
csch1(Expr1) ⇒ expression
csch1(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(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 nonreal 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(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 nonreal 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 nonreal 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
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 nonpolynomial 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 nonreal guess is often necessary to determine a nonreal 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 X, Y[, [Freq] [, Category,
Include]]
Computes the cubic polynomial regression y=a•x3+b•x2+c•x+d on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page
176.)
All the lists must have equal dimension except for Include.
X and Y are lists of independent and dependent variables.
40 Alphabetical Listing
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•x3+b•x2+c•x+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(List1) ⇒ list
Returns a list of the cumulative sums of the elements in List1, starting at element 1.
Alphabetical Listing 41
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 multiline 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(Expr, Var) ⇒list
Returns a list of candidate real and nonreal values of Var that make Expr=0. cZeros() does this by computing exp►list(cSolve(Expr=0,Var),Var). Otherwise, cZeros() is similar to zeros().
Note: See also cSolve(), solve(), and zeros().
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 nonreal 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 nonreal 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
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 nonpolynomial 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 nonreal guess is often necessary to determine a nonreal zero. For convergence, a guess might have to be rather close to a zero.
dbd(date1,date2) ⇒ value
Returns the number of days between date1 and date2 using the actualdaycount method.
44 Alphabetical Listing
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 userdefined 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 builtin 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 userdefined 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
Note for entering the example: For instructions on entering multiline 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 Var = Expression
Define LibPub Function(Param1, Param2,
...) = Expression
Define LibPub Function(Param1, Param2,
...) = Func
Block
EndFunc
Alphabetical Listing 47
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(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.
deSolve() Catalog >
deSolve(1stOr2ndOrderODE, Var,
depVar) ⇒ a general solution
Returns an equation that explicitly or implicitly specifies a general solution to the
1st or 2ndorder 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 1storder equation contains an arbitrary constant of the form ck, where k is an integer suffix from 1 through 255. The solution of a 2ndorder 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(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
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 floatingpoint 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:
5E14 •max(dim
(squareMatrix))•rowNorm
(squareMatrix)
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
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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
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
Please note that the line number is not for the entire screen but for the area immediately following the command/program.
This command allows dashboardlike 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 screenfull 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 18 (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 userdefined variables and functions. In the following example, the expression cannot be simplified because ∫() is a disallowed function.
Alphabetical Listing 55
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, e−1/z at z=0, or ez at z = ∞ or −∞.
If the series or one of its derivatives has a jump discontinuity at Point, the result is likely to contain subexpressions 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() is useful when you want to know the simplest possible expression that is asymptotic to another expression as Var→Point. dominantTerm() is also useful when it isn’t obvious what the degree of
the first nonzero 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: TINspire™ CX II  Draw Commands
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 floatingpoint 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(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
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.
If BooleanExpr1 Then
Block1
ElseIf BooleanExpr2 Then
Block2
⋮
ElseIf BooleanExprN Then
BlockN
EndIf
⋮
Note for entering the example: For instructions on entering multiline program and function definitions, refer to the Calculator section of your product guidebook.
Alphabetical Listing 59
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(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*(100y) 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
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 righthand side that defines the ordinary differential equation (ODE).
SystemOfExpr is the system of righthand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars).
ListOfExpr is a list of righthand 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 twoelement 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(VarMaxVar0) and solutions are returned at Var0+i•VarStep for all i=0,1,2,… such that Var0+i•VarStep
is in [var0,VarMax] (there may not be a solution value at VarMax).
eulerStep is a positive integer (defaults to
1) that defines the number of euler steps
between output values. The actual step size
used by the euler method is
VarStep ⁄ eulerStep.
System of equations:
with y1(0)=2 and y2(0)=5
Alphabetical Listing 61
eval(Expr) ⇒string
eval() is valid only in the TIInnovator™ 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 fadein the red element
Execute the program.
62 Alphabetical Listing
exact(Expr1 [, Tolerance]) ⇒ expression exact(List1 [, Tolerance]) ⇒ list exact(Matrix1 [, Tolerance]) ⇒ matrix
Uses Exact mode arithmetic to return, when possible, the rationalnumber 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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
Function listing:
►exp Catalog >
Expr►exp
Represents Expr in terms of the natural exponential e. This is a display conversion operator. It can be used only at the end of the entry line.
Note: You can insert this operator from the computer keyboard by typing @>exp.
Alphabetical Listing 63
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 floatingpoint numbers.
exp►list(Expr,Var) ⇒ list
Examines Expr for equations that are separated by the word “or,” and returns a list containing the righthand sides of the equations of the form Var=Expr. This gives you an easy way to extract some solution values embedded in the results of the solve(), cSolve(), fMin(), and fMax() functions.
Note: exp►list() is not necessary with the zeros() and cZeros() functions because they return a list of solution values directly.
You can insert this function from the keyboard by typing [email protected]>list(...).
64 Alphabetical Listing
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(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 anglesum and multipleangle 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
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 
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
Expr1 is factored as much as possible toward linear rational factors without introducing new nonreal 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 floatingpoint coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the builtin 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(rationalNumber) returns the rational number factored into primes. For
composite numbers, the computing time grows exponentially with the number of digits in the secondlargest factor. For example, factoring a 30digit 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 secondlargest 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 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(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(Expr, Var) ⇒ Boolean expression
fMax(Expr, Var,lowBound)
fMax(Expr, Var,lowBound,upBound)
fMax(Expr, Var) 
lowBound≤Var≤upBound
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(Expr, Var) ⇒ Boolean expression
fMin(Expr, Var,lowBound) fMin(Expr, Var,lowBound,upBound) fMin(Expr, Var) 
lowBound≤Var≤upBound
Returns a Boolean expression specifying candidate values of Var that minimize Expr or locate its greatest lower bound.
You can use the constraint (“”) operator to restrict the solution interval and/or specify other constraints.
For the Approximate setting of the Auto or Approximate mode, fMin() iteratively searches for one approximate local minimum. This is often faster, particularly if you use the “” operator to constrain the search to a relatively small interval that contains exactly one local minimum.
Note: See also fMax() and min().
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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
72 Alphabetical Listing
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(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.
freqTable►list() Catalog >
freqTable►list(List1,freqIntegerList) ⇒
list
Returns a list containing the elements from
List1 expanded according to the
frequencies in freqIntegerList. This
function can be used for building a
frequency table for the Data & Statistics
application.
List1 can be any valid list.
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(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(n1)<?≤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
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(n1)<?≤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 twosample 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 = n11 
stat.dfDenom  denominator degrees of freedom = n21 
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 userdefined 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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
Define a piecewise function:
Result of graphing g(x)
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
In Auto or Approximate mode, the gcd of fractional floatingpoint 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(1≤X≤upBound)
⇒ number if upBound is a number, list if
upBound is a list
Computes a cumulative geometric probability from lowBound to upBound with the specified probability of success p.
For P(X ≤ upBound), set lowBound = 1.
geomPdf(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 [promptString,] var[, statusVar]
Get [promptString,] func(arg1, ...argn)
[, statusVar]
Example: Request the current value of the hub's builtin lightlevel sensor. Use Get to retrieve the value and assign it to variable lightval.
Alphabetical Listing 77
Programming command: Retrieves a value from a connected TIInnovator™ 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 userdefined 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(Expr1) ⇒ expression
Transforms the argument into an expression having a reduced common denominator, and then returns its denominator.
getKey() Catalog >
getKey([01]) ⇒ returnString
Description:getKey()  allows a TIBasic 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  09  "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  az  alpha = letter pressed (lower 
80 Alphabetical Listing
Handheld Device/Emulator Key  Desktop  Return Value case) ("a"  "z") 
shift az  shift az  alpha = letter pressed "A"  "Z" 
Note: ctrlshift 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  TINspire™ Student Software
Quick Poll Terminate program, handle event
Remote file mgmt Terminate program, handle event
Same as the handheld (TI Nspire™ Student Software, TINspire™ Navigator™ NC Teacher Softwareonly)
Same as the handheld. (TINspire™ Student
Alphabetical Listing 81
Event Device Desktop  TINspire™ Student Software
(Incl. sending 'Exit Press 2
Test' file from another
handheld or desktop
handheld)
End Class Terminate program, handle event
Software, TINspire™ Navigator™ NC Teacher Softwareonly)
Support
(TINspire™ Student Software, TINspire™ Navigator™ NC Teacher Softwareonly)
Event Device Desktop  TINspire™ All
Versions
TIInnovator™ 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(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(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 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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
►Grad Catalog >
Expr1►Grad ⇒ expression
Converts Expr1 to gradian angle measure.
Note: You can insert this operator from the computer keyboard by typing @>Grad.
In Degree angle mode:
In Radian angle mode:
identity(Integer) ⇒ matrix
Returns the identity matrix with a dimension of Integer.
Integer must be a positive integer.
If BooleanExpr
Statement
If BooleanExpr Then
Block
EndIf
86 Alphabetical Listing
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 multiline 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(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
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(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(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.
interpolate(xValue, xList, yList,
yPrimeList) ⇒ list
This function does the following:
Differential equation:
y'=3•y+6•t+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
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(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 (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(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
Computes the inverse cumulative studentt 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
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 secondlargest factor that exceeds about five digits.
Note for entering the example: For instructions on entering multiline 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
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 multiline 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 floatingpoint numbers is their product.
For two lists or matrices, returns the least common multiples of the corresponding elements.
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
Returns the leftmost Num elements contained in List1.
If you omit Num, returns all of List1.
left(Comparison) ⇒ expression
Returns the lefthand 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(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
Limits at positive ∞ and at negative ∞ are always converted to onesided 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 nonzero magnitude might not.
LinRegBx X,Y[,[Freq][,Category,Include]]
Computes the linear regression y = a+b•x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.
X and Y are lists of independent and dependent variables.
Alphabetical Listing 97
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+b•x 
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 X,Y[,[Freq][,Category,Include]]
Computes the linear regression y = m•x+b on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.
98 Alphabetical Listing
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 = m•x+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 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
For Response. Computes a predicted yvalue, 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+b•x 
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 + b•XVal 
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
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.t  tStatistic 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
The first argument must evaluate to a system of linear equations or a single linear equation. Otherwise, an argument error occurs.
For example, evaluating linSolve(x=1 and x=2,x) produces an “Argument Error” result.
ΔList() Catalog >
ΔList(List1) ⇒ list
Note: You can insert this function from the keyboard by typing deltaList(...).
Returns a list containing the differences between consecutive elements in List1. Each element of List1 is subtracted from the next element of List1. The resulting list is always one element shorter than the original List1.
list►mat() Catalog >
list►mat(List [, elementsPerRow]) ⇒
matrix
Returns a matrix filled rowbyrow 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 >
Expr►ln ⇒ 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 floatingpoint 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 X, Y[, [Freq] [, Category, Include]]
Computes the logarithmic regression y = a+b•ln(x) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.
X and Y are lists of independent and dependent variables.
104 Alphabetical Listing
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+b•ln(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 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 multiline function since modifications on global variables are not allowed in a function.
Note for entering the example: For instructions on entering multiline 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(Expr1[,Expr2]) ⇒ expression
log(List1[,Expr2]) ⇒ list
Returns the baseExpr2 logarithm of the first argument.
Note: See also Log template, page 2.
For a list, returns the baseExpr2 logarithm of the elements.
If the second argument is omitted, 10 is used as the base.
log(squareMatrix1[,Expr]) ⇒
squareMatrix
Returns the matrix baseExpr logarithm of squareMatrix1. This is not the same as calculating the baseExpr logarithm of each element. For information about the calculation method, refer to cos().
squareMatrix1 must be diagonalizable. The result always contains floatingpoint 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 >
Expr►logbase(Expr1) ⇒ expression
Causes the input Expression to be simplified to an expression using base Expr1.
Note: You can insert this operator from the computer keyboard by typing @>logbase (...).
Alphabetical Listing 107
Logistic X, Y[, [Freq] [, Category, Include]]
Computes the logistic regression y = (c/ (1+a•ebx)) 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+a•ebx) 
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 X, Y [, [Iterations] , [Freq] [,
Category, Include] ]
Computes the logistic regression y = (c/ (1+a•ebx)+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+a•ebx)+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
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 multiline 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 (lowerupper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatrix, the upper triangular matrix in uMatrix, and the permutation matrix (which describes the row swaps done during the calculation) in pMatrix.
lMatrix•uMatrix = pMatrix•matrix
Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint 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)
110 Alphabetical Listing
The LU factorization algorithm uses partial pivoting with row interchanges.
mat►list() Catalog >
mat►list(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(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
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(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
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 medianmedian line y = (m•x+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 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  Medianmedian line equation: m•x+b 
stat.m, stat.b  Model coefficients 
Alphabetical Listing 113
Output variable  Description 
stat.Resid  Residuals from the medianmedian 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(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
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 nonzero, 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(Expr, Matrix1, Index) ⇒ matrix
Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Expr.
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 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+b1•x1+b2•x2+ ... 
stat.b0, stat.b1, ...  Regression coefficients 
stat.R2  Coefficient of multiple determination 
stat.y List  y List = b0+b1•x1+ ... 
stat.Resid  Residuals from the regression 
MultRegIntervals Catalog >
MultRegIntervals Y, X1[, X2[, X3,…[,
X10]]], XValList[, CLevel]
Computes a predicted yvalue, 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+b1•x1+b2•x2+ ... 
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+b1•x1+b2•x2+ ... 
stat.F  Global F test statistic 
stat.PVal  Pvalue 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  DurbinWatson statistic; used to determine whether firstorder 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 Pvalues for each t statistic 
stat.SEList  List of standard errors for coefficients in bList 
stat.y List  y List = b0+b1•x1+ . . . 
stat.Resid  Residuals from the regression 
stat.sResid  Standardized residuals; obtained by dividing a residual by its standard deviation 
stat.CookDist  Cook’s distance; measure of the influence of an observation based on the residual and leverage 
stat.Leverage  Measure of how far the values of the independent variable are from their mean values 
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
Integer1 nand Integer2 ⇒ integer
Compares two real integers bitbybit using a nand operation. Internally, both integers are converted to signed, 64bit 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•(Expr−1) ... (Expr−posInteger+1) / posInteger!
nCr(Expr, nonInteger) ⇒ expression! / ((Expr−nonInteger)!•nonInteger!)
nCr(List1, List2) ⇒ list
Returns a list of combinations based on the corresponding element pairs in the two lists. The arguments must be the same size list.
nCr(Matrix1, Matrix2) ⇒ matrix
120 Alphabetical Listing
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(numRows, numColumns) ⇒
matrix
Returns a matrix of zeros with the dimension numRows by numColumns.
nfMax(Expr, Var) ⇒ value nfMax(Expr, Var, lowBound) ⇒ value nfMax(Expr, Var, lowBound, upBound) ⇒
value
nfMax(Expr, Var) 
lowBound≤Var≤upBound ⇒ value
Alphabetical Listing 121
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) 
lowBound≤Var≤upBound ⇒ 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(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
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.
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
Integer1 nor Integer2 ⇒ integer
Compares two real integers bitbybit using a nor operation. Internally, both integers
are converted to signed, 64bit 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(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(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, 64bit 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, 64bit 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(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) ... (expression−negInteger))
nPr(Expr, posInteger) ⇒ Expr•(Expr−1) ... (Expr−posInteger+1)
nPr(Expr, nonInteger) ⇒ Expr! / (Expr−nonInteger)!
nPr(List1, List2) ⇒ list
Returns a list of permutations based on the corresponding element pairs in the two lists. The arguments must be the same size list.
nPr(Matrix1, Matrix2) ⇒ matrix
Returns a matrix of permutations based on
the corresponding element pairs in the two
matrices. The arguments must be the same
size matrix.
npv(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
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]) 
lowBound≤Var≤upBound ⇒ number or
error_string
Iteratively searches for one approximate real numeric solution to Equation for its one variable. Specify the variable as:
variable
– or –
variable = real number
For example, x is valid and so is x=3.
nSolve() is often much faster than solve() or zeros(), particularly if the “” operator is used to constrain the search to a small interval containing exactly one simple solution.
nSolve() attempts to determine either one point where the residual is zero or two relatively close points where the residual has opposite signs and the magnitude of the residual is not excessive. If it cannot achieve this using a modest number of sample points, it returns the string “no solution found.”
Note: If there are multiple solutions, you can use a guess to help find a particular solution.
Alphabetical Listing 127
Note: See also cSolve(), cZeros(), solve(), and zeros().
OneVar Catalog >
OneVar [1,]X[,[Freq][,Category,Include]]
OneVar [n,]X1,X2[X3[,…[,X20]]] Calculates 1variable 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 multiline 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
Compares two real integers bitbybit using an or operation. Internally, both integers
are converted to signed, 64bit 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, 64bit 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►Rx(rExpr, θExpr) ⇒ expression P►Rx(rList, θList) ⇒ list P►Rx(rMatrix, θMatrix) ⇒ matrix
Returns the equivalent xcoordinate of the
(r, θ) pair.
130 Alphabetical Listing
In Radian angle mode:
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(...).
P►Ry() Catalog >
P►Ry(rExpr, θExpr) ⇒ expression
P►Ry(rList, θList) ⇒ list
P►Ry(rMatrix, θMatrix) ⇒ matrix
Returns the equivalent ycoordinate 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
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
Note: See also ClrErr, page 25, and Try, page
191.
Note for entering the example: For instructions on entering multiline 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(0≤X≤upBound) ⇒ number if upBound is a number, list if upBound is a list
Computes a cumulative probability for the discrete Poisson distribution with specified mean λ.
For P(X ≤ upBound), set lowBound=0
poissPdf(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 [r∠θ]. The vector
must be of dimension 2 and can be a row or a column.
Note: ►Polar is a displayformat 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 (r∠θ).
• 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
(r∠θ) polar entry.
In Degree angle mode:
polyCoeffs() Catalog >
polyCoeffs(Poly [,Var]) ⇒ list
Alphabetical Listing 133
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(List1, Expr1) ⇒ expression
polyEval(List1, List2) ⇒ expression
Interprets the first argument as the coefficient of a descendingdegree 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(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 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
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
Block
EndPrgm
Template for creating a userdefined program. Must be used with the Define, Define LibPub, or Define LibPriv command.
Calculate GCD and display intermediate results.
Alphabetical Listing 137
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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
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(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.
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 floatingpoint number (9.) in m1 causes results to be calculated in floatingpoint form.
Alphabetical Listing 139
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 floatingpoint 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−14 •max(dim(Matrix)) •rowNorm
(Matrix)
The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using GramSchmidt. The columns in qMatName are the orthonormal
basis vectors that span the space defined by
matrix.
QuadReg X,Y[, Freq][, Category, Include]]
Computes the quadratic polynomial regression y=a•x2+b•x+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
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•x2+b•x+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 X,Y[, Freq][, Category, Include]]
Computes the quartic polynomial regression y = a•x4+b•x3+c• x2+d•x+e on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 176.)
All the lists must have equal dimension except for Include.
Alphabetical Listing 141
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: a•x4+b•x3+c• x2+d•x+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►Pθ() Catalog >
R►Pθ (xExpr, yExpr) ⇒ expression
R►Pθ (xList, yList) ⇒ list
R►Pθ (xMatrix, yMatrix) ⇒ matrix
In Degree angle mode:
142 Alphabetical Listing
Returns the equivalent θcoordinate 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:
R►Pr() Catalog >
R►Pr (xExpr, yExpr) ⇒ expression
R►Pr (xList, yList) ⇒ list
R►Pr (xMatrix, yMatrix) ⇒ matrix
Returns the equivalent rcoordinate 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 >
Expr1►Rad ⇒ 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 randomnumber seed.
Alphabetical Listing 143
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(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(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 Number
If Number = 0, sets the seeds to the factory defaults for the randomnumber 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 displayformat 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
(r∠θ) 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
floatingpoint 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−14 •max(dim(Matrix1)) •rowNorm
(Matrix1)
Avoid undefined elements in Matrix1. They can lead to unexpected results.
For example, if a is undefined in the following expression, a warning message appears and the result is shown as:
Alphabetical Listing 147
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 TIBasic 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
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) x−y•iPart(x/y)
As a consequence, note that remain(−x,y) − remain(x,y). The result is either zero or it has the same sign as the first argument.
Note: See also mod(), page 116.
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
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 userdefined 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
• 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 userdefined 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 [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 multiline 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(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*(100y) and y(0)=10
To see the entire result,
press 5 and then use 7 and 8 to move the cursor.
152 Alphabetical Listing
Uses the RungeKutta 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 righthand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars).
ListOfExpr is a list of righthand 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 twoelement 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(VarMaxVar0) 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 "RungeKutta" Var values.
diftol is the error tolerance (defaults to
0.001).
Same equation with diftol set to 1.E−6
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(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, 64bit 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:
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(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(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(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 floatingpoint 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
• If Tol is omitted or not used, the default tolerance is calculated as:
5E−14 •max(dim(Matrix1)) •rowNorm
(Matrix1)
Note: See also ref(), page 147.
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:
sec1() µ key
sec1(Expr1) ⇒ expression
sec1(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(Expr1) ⇒ expression
sech(List1) ⇒ list
Returns the hyperbolic secant of Expr1 or returns a list containing the hyperbolic secants of the List1 elements.
sech1() Catalog >
sech1(Expr1) ⇒ expression
sech1(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 TIInnovator™ Hub commands to a connected hub.
exprOrString must be a valid
TIInnovator™ 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 userdefined 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 builtin RGB LED for 0.5 seconds.
Example: Request the current value of the hub's builtin lightlevel sensor. A Get command retrieves the value and assigns it to variable lightval.
Example: Send a calculated frequency to the hub's builtin speaker. Use special variable iostr.SendAns to show the hub command with the expression evaluated.
158 Alphabetical Listing
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(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(n1)2/2, with u(1)=2 and VarStep=1.
Example in which Var0=2:
Alphabetical Listing 159
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(n1)/2, with u(1)=2.
160 Alphabetical Listing
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, e−1/z at z=0, or ez at z = ∞ or −∞.
If the series or one of its derivatives has a jump discontinuity at Point, the result is likely to contain subexpressions 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() distributes over 1stargument 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
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 multiline 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(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, 64bit 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
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
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 Expr1≠ 0.
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 floatingpoint 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 floatingpoint 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
• If Tol is omitted or not used, the default tolerance is calculated as:
5E−14 •max(dim(coeffMatrix))
•rowNorm(coeffMatrix)
simult(coeffMatrix, constMatrix[, Tol]) ⇒
matrix
Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants.
Each column in constMatrix must contain the constants for a system of equations. Each column in the resulting matrix contains the solution for the corresponding system.
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 >
Expr►sin
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 1−sin(...)^2
so that any remaining powers of sin(...) have exponents in the range (0, 2). Thus, the result will be free of cos(...) if and only
if cos(...) occurs in the given expression only to even powers.
Note: This conversion operator is not supported in Degree or Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles.
sin() µ key
sin(Expr1) ⇒ expression In Degree angle mode:
166 Alphabetical Listing
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 floatingpoint numbers.
In Gradian angle mode:
In Radian angle mode:
In Radian angle mode:
sin1(Expr1) ⇒ expression
sin1(List1) ⇒ list
sin1(Expr1) returns the angle whose sine is Expr1 as an expression.
sin1(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
Note: You can insert this function from the keyboard by typing arcsin(...).
sin1(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 floatingpoint 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 floatingpoint numbers.
In Radian angle mode:
sinh1(Expr1) ⇒ expression
sinh1(List1) ⇒ list
sinh1(Expr1) returns the inverse hyperbolic sine of the argument as an expression.
168 Alphabetical Listing
sinh1(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(...).
sinh1(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 floatingpoint 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
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: a•sin(bx+c)+d 
stat.a, stat.b, stat.c, stat.d  Regression coefficients 
stat.Resid  Residuals from the regression 
stat.XReg  List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories 
stat.YReg  List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories 
stat.FreqReg  List of frequencies corresponding to stat.XReg and stat.YReg 
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
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
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 nonreal number
For example, x is valid and so is x=3.
172 Alphabetical Listing
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 xaxis. 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 nonpolynomial 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
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 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 >
Vector►Sphere
Note: You can insert this operator from the computer keyboard by typing @>Sphere.
Displays the row or column vector in spherical form [ρ∠θ∠φ].
Vector must be of dimension 3 and can be either a row or a column vector.
Note: ►Sphere is a displayformat 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
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(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(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(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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
string(Expr) ⇒ string
Simplifies Expr and returns the result as a character string.
Alphabetical Listing 179
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() 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(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
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.
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
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:
squareMatrix1 must be diagonalizable. The result always contains floatingpoint numbers.
tan1() µ key
tan1(Expr1) ⇒ expression
tan1(List1) ⇒ list
tan1(Expr1) returns the angle whose tangent is Expr1 as an expression.
tan1(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(...).
tan1(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 floatingpoint numbers.
In Degree angle mode:
In Gradian angle mode:
In Radian angle mode:
In Radian angle mode:
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
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 floatingpoint numbers.
In Radian angle mode:
tanh1(Expr1) ⇒ expression
tanh1(List1) ⇒ list
tanh1(Expr1) returns the inverse hyperbolic tangent of the argument as an expression.
tanh1(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:
tanh1(squareMatrix1) ⇒ squareMatrix In Radian angle mode and Rectangular complex format:
184 Alphabetical Listing
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 floatingpoint 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 nonzero 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(lowBound,upBound,df) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists
Computes the Studentt distribution probability between lowBound and upBound for the specified degrees of freedom df.
For P(X ≤ upBound), set lowBound = ∞.
Alphabetical Listing 185
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 integermultiple 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: Degreemode 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
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 userdefined 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:
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
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 twosample 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.v1v2  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 Studentt 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
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 multiline 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 A•B
Try
Disp "A= ",a Disp "B= ",b Disp " "
Disp "Eigenvalues of A•B are:",eigVl(a*b) Else
If errCode=230 Then
Disp "Error: Product of A•B must be a
square matrix" ClrErr
Else
PassErr
EndIf
EndTry
EndPrgm
Alphabetical Listing 191
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 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
Computes a twosample 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 tstatistic 
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(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
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(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 timevalueofmoney 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
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 x•y values 
stat.r  Correlation coefficient 
stat.MinX  Minimum of x values 
stat.Q1X  1st Quartile of x 
stat.MedianX  Median of x 
stat.Q3X  3rd Quartile of x 
stat.MaxX  Maximum of x values 
stat.MinY  Minimum of y values 
stat.Q1Y  1st Quartile of y 
stat.MedY  Median of y 
stat.Q3Y  3rd Quartile of y 
196 Alphabetical Listing
Output variable  Description 
stat.MaxY  Maximum of y values 
stat.Σ(xv)2  Sum of squares of deviations from the mean of x 
stat.Σ(yw)2  Sum of squares of deviations from the mean of y 
unitV() Catalog >
unitV(Vector1) ⇒ vector
Returns either a row or columnunit vector, depending on the form of Vector1.
Vector1 must be either a singlerow matrix or a singlecolumn matrix.
To see the entire result,
press 5 and then use 7 and 8 to move the cursor.
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
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
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.
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 userdefined 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(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 TINspire™ or TINspire™ 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 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 multiline program and function definitions, refer to the Calculator section of your product guidebook.
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 Integer2⇒ integer
Compares two real integers bitbybit using an xor operation. Internally, both integers are converted to signed, 64bit 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
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, 64bit 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.
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 exp►list(solve (Expr=0,Var),Var).
For some purposes, the result form for zeros() is more convenient than that of solve(). However, the result form of zeros() cannot express implicit solutions, solutions that require inequalities, or solutions that do not involve Var.
Note: See also cSolve(), cZeros(), and solve
().
zeros({Expr1, Expr2},
{VarOrGuess1, VarOrGuess2 [, … ]}) ⇒
matrix
Returns candidate real zeros of the simultaneous algebraic expressions, where each VarOrGuess specifies an unknown whose value you seek.
Optionally, you can specify an initial guess for a variable. Each VarOrGuess must have the form:
202 Alphabetical Listing
variable
– or –
variable = real or nonreal 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 xaxis. 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
If you do not include any guesses and if any expression is nonpolynomial 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 oneproportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 176.)
x is a nonnegative 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 twoproportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 176.)
x1 and x2 are nonnegative 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 twosample 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.x1x2  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
(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 
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
Computes a twoproportion z test. A summary of results is stored in the stat.results variable. (See page 176.)
x1 and x2 are nonnegative 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 σ1,σ2 ,List1,List2[,Freq1
[,Freq2[,Hypoth]]]
(Data list input)
zTest_2Samp σ1,σ2,v1,n1,v2,n2[,Hypoth] (Summary stats input)
Computes a twosample 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
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
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.
Expr1 − Expr2 ⇒ expression
Returns Expr1 minus Expr2.
List1 −List2⇒ list
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.
Expr1•Expr2 ⇒ expression
Returns the product of the two arguments.
List1•List2 ⇒ list
Returns a list containing the products of the corresponding elements in List1 and List2.
Dimensions of the lists must be equal.
Matrix1•Matrix2 ⇒ matrix
Returns the matrix product of Matrix1 and
Matrix2.
The number of columns in Matrix1 must equal the number of rows in Matrix2.
Symbols 211
• (multiply) r key
Expr •List1 ⇒ list
List1•Expr ⇒ list
Returns a list containing the products of
Expr and each element in List1.
Expr •Matrix1 ⇒ matrix
Matrix1•Expr ⇒ matrix
Returns a matrix containing the products of
Expr and each element in Matrix1.
Note: Use .•(dot multiply) to multiply an expression by each element.
⁄ (divide) 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 ^ Expr2⇒ expression
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
Expr12⇒ expression
Returns the square of the argument.
List12 ⇒ list
Returns a list containing the squares of the elements in List1.
squareMatrix12 ⇒ matrix
Returns the matrix square of squareMatrix1. This is not the same as calculating the square of each element. Use
.^2 to calculate the square of each element.
.+ (dot add) ^+ keys
Matrix1 .+ Matrix2 ⇒ matrix
Expr .+ Matrix1⇒ matrix
Matrix1.+Matrix2 returns a matrix that is the sum of each pair of corresponding elements in Matrix1 and Matrix2.
Expr .+ Matrix1 returns a matrix that is the sum of Expr and each element in Matrix1.
Matrix1 .− Matrix2⇒ matrix
Expr .− Matrix1 ⇒matrix
Matrix1.− Matrix2 returns a matrix that is the difference between each pair of corresponding elements in Matrix1 and Matrix2.
Expr .− Matrix1 returns a matrix that is the difference of Expr and each element in Matrix1.
.
214 Symbols
Matrix1 .• Matrix2⇒ matrix
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 . ⁄ Matrix1⇒ matrix
Matrix1 . ⁄ Matrix2 returns a matrix that is the quotient of each pair of corresponding elements in Matrix1 and Matrix2.
Expr . ⁄ Matrix1 returns a matrix that is the quotient of Expr and each element in Matrix1.
.^ (dot power) ^l keys
Matrix1 .^ Matrix2 ⇒ matrix
Expr . ^ Matrix1⇒ matrix
Matrix1.^ Matrix2 returns a matrix where each element in Matrix2 is the exponent for the corresponding element in Matrix1.
Expr .^ Matrix1 returns a matrix where each element in Matrix1 is the exponent for Expr.
− (negate) v key
−Expr1 ⇒ expression
−List1 ⇒ list
−Matrix1 ⇒ matrix
Symbols 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 .
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
Note for entering the example: For instructions on entering multiline program and function definitions, refer to the Calculator section of your product guidebook.
Result of graphing g(x)
≠ (not equal) /= keys
Expr1≠Expr2 ⇒ Boolean expression List1≠List2 ⇒ Boolean list Matrix1≠Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be not equal to Expr2.
Returns false if Expr1 is determined to be equal to Expr2.
Anything else returns a simplified form of the equation.
For lists and matrices, returns comparisons element by element.
Note: You can insert this operator from the keyboard by typing /=
See “=” (equal) example.
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
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
Expr1≤Expr2 ⇒ Boolean expression
List1≤List2 ⇒ Boolean list
Matrix1 ≤Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be less than or equal to Expr2.
Returns false if Expr1 is determined to be greater than Expr2.
Anything else returns a simplified form of the equation.
For lists and matrices, returns comparisons element by element.
Note: You can insert this operator from the keyboard by typing <=
See “=” (equal) example.
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
For lists and matrices, returns comparisons element by element.
≥ (greater or equal) /= keys
Expr1≥Expr2 ⇒ Boolean expression
List1≥List2 ⇒ Boolean list
Matrix1 ≥Matrix2 ⇒ Boolean matrix
Returns true if Expr1 is determined to be greater than or equal to Expr2.
Returns false if Expr1 is determined to be less than Expr2.
Anything else returns a simplified form of the equation.
For lists and matrices, returns comparisons element by element.
Note: You can insert this operator from the keyboard by typing >=
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.
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 antiderivative.
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 nonvariable.
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 antiderivative. A symbolic constant of integration is omitted unless you provide
the Constant argument.
Equally valid antiderivatives 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 builtin 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, Low−1) ⇒ 1
Π(Expr1, Var, Low, High) ⇒ 1/Π(Expr1,
Var, High+1, Low−1) if High < Low−1
The product formulas used are derived from the following reference:
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Reading, Massachusetts: AddisonWesley,
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, Low−1) ⇒ 0
Σ(Expr1, Var, Low, High) ⇒ μ
Σ(Expr1, Var, High+1, Low−1) if High <
Low−1
The summation formulas used are derived from the following reference:
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Reading, Massachusetts: AddisonWesley,
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:
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 nonnegative number
ss.ss A nonnegative number
Returns dd+(mm/60)+(ss.ss/3600). This base60 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 @<.
(Magnitude∠Angle) ⇒ complexValue
(polar input)
Enters a complex value in (r∠θ) 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
1storder differential equation, two prime symbols denote a 2ndorder, and so on.
_ (underscore as an empty element)
See “Empty (Void) Elements,”
_ (underscore as unit designator) /_ keys
Expr_Unit
Designates the units for an Expr. All unit
names must begin with an underscore.
You can use predefined units or create your own units. For a list of predefined 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 predefined 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 floatingpoint numbers.
Symbols 231
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 nonsingular 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
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, oneletter 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, oneletter variables such as a, b, c, x, y, z, and so on.
234 Symbols
© [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 multiline 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
This is a supplemental document for the TINspire™ Reference Guide and the TI Nspire™ CAS Reference Guide. All TINspire™ CX II commands will be incorporated and published in version 5.1 of the TINspire™ Reference Guide and the TINspire™ CAS Reference Guide.
New commands have been added on TINspire™ CX II Handhelds and TINspire™
desktop applications for graphics programming.
The TINspire™ 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 keypress 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 TIBasic 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 TINspire™ CX II Handhelds and the desktop TINspire™ 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 TIBasic program from the incorrect context, an error message is displayed and the TIBasic program
is terminated.
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 TINspire™ CX II  Draw Commands
• The status icons in the top bar (battery status, presstotest 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 TIBasic 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.
TINspire™ CX II  Draw Commands 237
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. 
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 TINspire™ CX II  Draw Commands
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
TINspire™ CX II  Draw Commands 239
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 TINspire™ CX II  Draw Commands
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
TINspire™ CX II  Draw Commands 241
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 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 TINspire™ CX II  Draw Commands
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 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
TINspire™ CX II  Draw Commands 243
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 TINspire™ CX II  Draw Commands
getPlatform()
Returns:
“dt” on desktop software applications
“hh” on TINspire™ CX handhelds
“ios” on TINspire™ CX iPad® app
TINspire™ CX II  Draw Commands 245
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 TINspire™ CX II  Draw Commands
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
TINspire™ CX II  Draw Commands 247
SetColor
Redvalue, Greenvalue, Bluevalue
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 <= 31 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
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 TINspire™ CX II  Draw Commands
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 redrawn in the new configuration.
To reset the window parameters to the default, use:
SetWindow 0,0,0,0
TINspire™ CX II  Draw Commands 249
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 TINspire™ CX II  Draw Commands
When analyzing realworld data, you might not always have a complete data set. TINspire™ 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, freqTable►list, frequency, max, mean, median, product, stDevPop, stDevSamp,
sum, sumIf, varPop, and varSamp, as well as regression calculations, OneVar, TwoVar, and FiveNumSummary statistics, confidence intervals, and stat tests
SortA and SortD move all void elements within the first argument to the bottom.
Empty (Void) Elements 251
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 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(...)
sin1(), cos1(), ... 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
This section describes the Equation Operating System (EOS™) that is used by the TINspire™ 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: degreesminutesseconds (°,',"), 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 TINspire™ CAS software allows you to define your own functions, a variable name followed by an expression in parentheses is considered a “function call” instead of implied multiplication. For example a(b+c) is the function a evaluated by b+c. To multiply the expression b+c by the variable a, use explicit multiplication: a• (b+c).
Indirection
The indirection operator (#) converts a string to a variable or function name. For example, #(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows the creation and modification of variables from inside a program. For example, if 10→r and “r”→s1, then #s1=10.
Post Operators
Post operators are operators that come directly after an argument, such as 5!, 25%, or
60°15' 45". Arguments followed by a post operator are evaluated at the fourth priority
level. For example, in the expression 4^3!, 3! is evaluated first. The result, 6, then
becomes the exponent of 4 to yield 4096.
Exponentiation
Exponentiation (^) and elementbyelement 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
The TINspire™ program editor now autoindents 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 autoindentation 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.
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 
TINspire CX II  TIBasic 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 TINspire CX II  TIBasic 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.
TINspire CX II  TIBasic Programming Features 259
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 6.67408E11 _m3/_kg/_s2
_h Planck's constant 6.626070040E34 _J _s
_k Boltzmann's constant 1.38064852E23 _J/_¡K
_m0 Permeability of a vacuum 1.2566370614359E6 _N/_A2
_mb Bohr magneton 9.274009994E24 _J _m2/_Wb
_Me Electron rest mass 9.10938356E31 _kg
_Mm Muon mass 1.883531594E28 _kg
_Mn Neutron rest mass 1.674927471E27 _kg
_Mp Proton rest mass 1.672621898E27 _kg
_Na Avogadro's number 6.022140857E23 /_mol
_q Electron charge 1.6021766208E19 _coul
_Rb Bohr radius 5.2917721067E11 _m
_Rc Molar gas constant 8.3144598 _J/_mol/_¡K
_Rdb Rydberg constant 10973731.568508/_m
_Re Electron radius 2.8179403227E15 _m
_u Atomic mass 1.660539040E27 _kg
_Vm Molar volume 2.2413962E2 _m3/_mol
_H0 Permittivity of a vacuum 8.8541878176204E12 _F/_m
_s StefanBoltzmann constant 5.670367E8 _W/_m2/_¡K4
_f0 Magnetic flux quantum 2.067833831E15 _Wb
260 Constants and Values
When an error occurs, its code is assigned to variable errCode. Userdefined 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 TINspire™ CAS products, and some apply only to TINspire™ 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^24=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 3element 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^24,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 userdefined 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 reinsert 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  Nonreal 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 Medianmedian 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 TINspire™ CAS. 
1045  Unsupported operator. This operator requires Computer Algebra System. Try TINspire™ CAS. 
1050  Unsupported feature. This operator requires Computer Algebra System. Try TINspire™ 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  Nonreal 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 realvalued 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 2y5x=1 
1260  Argument Error: The first argument of nfMin or nfMax must be an expression in a single variable. It cannot contain a nonvalued 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
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  Nonreal 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
Select your country for more product information.
education.ti.com/ticares
Select your country for technical and other support resources. Service and Warranty Information education.ti.com/warranty
Select your country for information about the length and terms of the warranty or about product service.
Limited Warranty. This warranty does not affect your statutory rights. Texas Instruments Incorporated
12500 TI Blvd. Dallas, TX 75243
General Information 271

, 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
2sample F Test 75
A
abs( ), absolute value 8
absolute value
template for 34
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, oneway variance analysis 10
ANOVA2way, twoway 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( ) 2021, 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( ) 121122 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 240242
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 exp►list( ), 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 243244
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 userdefined 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, list►mat( )
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 list►mat( ), 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, exp►list( ) 64 list to matrix, list►mat( ) 103 matrix to list, mat►list( ) 111 maximum, max( ) 111 midstring, 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, list►mat( )  103 
LnReg, logarithmic regression  104  lowerupper decomposition, LU  110 
local variable, Local  106  matrix to list, mat►list( )  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 lowerupper
decomposition 110
M
mat►list( ), matrix to list 111
matrices
augment/concatenate,
augment( ) 16
submatrix, subMat( ) 180181
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, mat►list( ) 111
max( ), maximum
111
maximum, max( )
111
mean( ), mean
112
mean, mean( )
112
median( ), median
112
median, median( )
mediummedium line regression,
112
MedMed 113
MedMed, mediummedium line
regression 113
Index 279
midstring, mid( ) 114 mid( ), midstring 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( ) 121122 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
onevariable statistics, OneVar 128
OneVar, onevariable statistics 128
operators
order of evaluation 255 or (Boolean), or 129 or, Boolean operator 129 ord( ), numeric character code 130
P
P►Rx( ), rectangular x coordinate P►Ry( ), 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 (2piece)
template for 2
280 Index
piecewise function (Npiece)
template for 3 piecewise( ) 132 poissCdf( ) 132 poissPdf( ) 132 polar
proper fraction, propFrac 139
propFrac, proper fraction 139
Q
QR factorization, QR 139
coordinate, R►Pr( ) 143
QR, QR factorization
139
coordinate, R►Pθ( ) 142
vector display, ►Polar 133
quadratic regression, QuadReg
QuadReg, quadratic regression
140
140
polyCoef( ) 133 polyDegree( ) 134 polyEval( ), evaluate polynomial 135 polyGcd( ) 135136
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
R►Pr( ), polar coordinate 143
R►Pθ( ), 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 
rectangularvector display, ►Rect  146 
rectangular x coordinate, P►Rx( )  130 
rectangular y coordinate, P►Ry( )  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 mediummedium 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( ) 159160 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 onevariable statistics, OneVar 128 permutations, nPr( ) 126 random norm, randNorm( ) 145 random number seed,
RandSeed 146 standard deviation, stdDev( ) 178, 198 twovariable results, TwoVar 195 variance, variance( ) 198
stdDevPop( ), population standard
deviation 178
stdDevSamp( ), sample standard
deviation 178
Stop command 179
store variable (→) 233
storing
studentt distribution probability,
tCdf( ) 185 studentt probability density, tPdf( ) 190 subMat( ), submatrix 180181 submatrix, subMat( ) 180181 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 (2equation)
template for 3
system of equations (Nequation)
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 midstring, 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 (2piece) 2
piecewise function (Npiece) 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, 2sample 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, twosample t test 192
TVM arguments 195
tvmFV( ) 193
tvmI( ) 193 tvmN( ) 194 tvmPmt( ) 194 tvmPV( ) 194 twovariable results, TwoVar 195
TwoVar, twovariable 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 userdefined functions 46 userdefined functions and
programs 47
V
variable
creating name from a character
string 256
variable and functions
copying 29
variables
clear all singleletter 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, oneproportion z
confidence interval 205
zInterval_2Prop, twoproportion z
confidence interval 205
zInterval_2Samp, twosample z
confidence interval 206 zTest 206 zTest_1Prop, oneproportion z test 207 zTest_2Prop, twoproportion z test 207 zTest_2Samp, twosample z test 208
Χ
χ²Cdf( ) 24 χ²GOF 24 χ²Pdf( ) 24
Index 285