TI Nspire cx CAS Guide

8/18/2019 TI Nspire cx CAS Guide

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Important Information

Except as otherwise expressly stated in the License that accompanies a program, TexasInstruments makes no warranty, either express or implied, including but not limited toany implied warranties of merchantability and fitness for a particular purpose,regarding any programs or book materials and makes such materials available solelyon an "as-is" 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 thepurchase or use of these materials, and the sole and exclusive liability of TexasInstruments, regardless of the form of action, shall not exceed the amount set forth inthe license for the program. Moreover, Texas Instruments shall not be liable for anyclaim of any kind whatsoever against the use of these materials by any other party.

License

Please see the complete license installed in C:\Program Files\TI Education\\license.

© 2006 - 2016 Texas Instruments Incorporated


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Contents

Important Information 2

Expression Templates 5

Alphabetical Listing 12

A 12B 21C 24D 48E 59F 67

G 76I 82L 89M 105N 113O 122P 124Q 133R 136S 149T 173U 188V 188W 190X 192Z 193

Symbols 200

Empty (Void) Elements 226

Shortcuts for Entering Math Expressions 228

EOS™ (Equation Operating System) Hierarchy 230

Error Codes and Messages 232

Warning Codes and Messages 240

Support and Service 243

Texas Instruments Support and Service 243

3


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4

Service and Warranty Information 243

Index 245


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Expression Templates

Expression templates give you an easy way to enter math expressions in standardmathematical notation. When you insert a template, it appears on the entry line withsmall blocks at positions where you can enter elements. A cursor shows which elementyou can enter.

Position the cursor on each element, and type a value or expression for the element.

Fraction template /p keys

Note: See also / (divide), page 202.

Example:

Exponent template l key

Note: Type the first value, pressl, andthen type the exponent. To return the cursor

to the baseline, press right arrow (¢).

Note: See also ^ (power), page 203.

Example:

Square root template /q keys

Note: See also √() (square root), page213.

Example:

Nth root template /l keys

Note: See also root(), page 146.

Example:



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6 Expression Templates

Nth root template /l keys

e exponent template u keys

Natural exponential e raised to a powerNote: See also e^(), page 59.

Example:

Log template /s key

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

Note: See also log(), page 101.

Example:

Piecewise template (2-piece) Catalog >

Lets you create expressions and conditionsfor a two-piece piecewise function. To adda piece, click in the template and repeat thetemplate.

Note: See also piecewise(), page 125.

Example:


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Piecewise template (N-piece) Catalog >

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

Note: See also piecewise(), page 125.

Example:

See the example for Piecewisetemplate (2-piece).

System of 2 equations template Catalog >

Creates a system of two equations. To adda row to an existing system, click in thetemplate and repeat the template.

Note: See also system(), page 173.

Example:

System of N equations template Catalog >

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

Note: See also system(), page 173.

Example:

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

Absolute value template Catalog >

Note: See also abs(), page 12.Example:



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Absolute value template Catalog >

dd°mm’ss.ss’’ template Catalog >

Lets you enter angles in dd°mm’ss.ss’’format, where dd is the number of decimaldegrees, mm is the number of minutes, andss.ss is the number of seconds.

Example:

Matrix template (2 x 2) Catalog >

Creates a 2 x 2 matrix.

Example:


.Example:


Example:

Matrix template (m x n) Catalog >

The template appears after you are

prompted to specify the number of rowsand columns.

Example:


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Matrix template (m x n) Catalog >

Note: If you create a matrix with a largenumber of rows and columns, it may take afew moments to appear.

Sum template (Σ) Catalog >

Note: See also Σ() (sumSeq), page 214.

Example:

Product template (Π) Catalog >

Note: See also Π() (prodSeq), page 213.

Example:

First derivative template Catalog >

The first derivative template can also be

used to calculate first derivative at a point.

Note: See also d() (derivative), page 211.

Example:



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Second derivative template Catalog >

The second derivative template can also be

used to calculate second derivative at apoint.


Example:

Nth derivative template Catalog >

The nth derivative template can be used tocalculate the nth derivative.


Example:

Definite integral template Catalog >

Note: See also∫() integral(), page 211.

Example:

Indefinite integral template Catalog >

Note: See also ∫() integral(), page 211.

Example:

Limit template Catalog >

Example:


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Limit template Catalog >

Use − or (−) for left hand limit. Use + forright hand limit.

Note: See also limit(), page 10.



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12 Alphabetical Listing

Alphabetical Listing

Items whose names are not alphabetic (such as +, !, and >) are listed at the end of thissection, page 200. Unless otherwise specified, all examples in this section wereperformed in the default reset mode, and all variables are assumed to be undefined.

A

abs() Catalog >

abs( Expr1) ⇒ expression

abs( List1) ⇒ list abs( Matrix1) ⇒ matrix

Returns the absolute value of the

argument.Note: See also Absolute value template,page 7.

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

Note: All undefined variables are treated asreal variables.

amortTbl() Catalog >

amortTbl( NPmt , N , I , PV , [ Pmt ], [ FV ],[ PpY ], [CpY ], [ PmtAt ], [roundValue]) ⇒matrix

Amortization function that returns a matrixas an amortization table for a set of TVMarguments.

NPmt is the number of payments to beincluded in the table. The table starts withthe first payment.

N , I , PV , Pmt , FV , PpY , CpY , and PmtAt are described in the table of TVMarguments, page 185.

• If you omit Pmt , it defaults to Pmt =tvmPmt( N , I , PV , F V , 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.


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amortTbl() Catalog >

roundValue specifies the number of decimal places for rounding. Default=2.

The columns in the result matrix are in thisorder: Payment number, amount paid tointerest, amount paid to principal, andbalance.

The balance displayed in row n is thebalance after payment n.

You can use the output matrix as input forthe other amortization functions ΣInt() andΣPrn(), page 215, and bal(), page 21.

and Catalog >

BooleanExpr1 and BooleanExpr2 ⇒ Boolean expression

BooleanList1 and BooleanList2 ⇒ Boolean list

BooleanM atrix1 and BooleanMatrix2 ⇒ Boolean matrix

Returns true or false or a simplified form of the original entry.

Integer1 and Integer2 ⇒ integer

Compares two real integers bit-by-bit usingan and operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 1 if both bits are 1;

otherwise, the result is 0. The returnedvalue represents the bit results, and isdisplayed according to the Base mode.

You can enter the integers in any numberbase. For a binary or hexadecimal entry, youmust use the 0b or 0h prefix, respectively.Without a prefix, integers are treated asdecimal (base 10).

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

In Dec base mode:

Note: A binary entry canhave upto 64 digits

(not counting the 0b prefix). A hexadecimalentry can have upto 16 digits.

Alphabe tical Listing 13


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angle() Catalog >

angle( Expr1) ⇒ expression

Returns the angle of the argument,interpreting the argument as a complexnumber.


In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

angle( List1) ⇒ list angle( Matrix1) ⇒ matrix

Returns a list or matrix of angles of theelements in List1 or Matrix1, interpretingeach element as a complex number that

represents a two-dimensional rectangularcoordinate point.

ANOVA Catalog >

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

Performs a one-way analysis of variance forcomparing the means of two to 20 populations. A

summary of results is stored in the stat.resultsvariable. (page 168)

Flag =0 for Data, Flag =1 for Stats

Output variable Description

stat.F Value of the F statistic

stat.PVal Smallestlevel of significance atwhich the null hypothesis canbe rejected

stat.df Degrees of freedom o f the g roups

stat.SS Sum o f squares o f the groups


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stat.MS Mean squares fo r the gro ups

stat.dfError Degrees of freedomof the errors

stat.SSError Sum ofsquares ofthe errors

stat.MSError Mean square for the errors

stat.sp Po oled standard deviation

stat.xbarlist Mean of the input of the lists

stat.CLowerList 95% confidence intervals for the mean of each input list

stat.CUpperList 95% confidence intervals for the mean of each input list

ANOVA2way Catalog >

ANOVA2way List1, List2[, List3,…, List10][,levRow]

Computes a two-way analysis of variance forcomparing the means of two to 10 populations. Asummary of results is stored in the stat.resultsvariable. (See page 168.)

LevRow=0 for Block

LevRow=2,3,..., Len-1, for Two Factor, where Len=length( List1)=length( List2) = … = length( List10) and Len / LevRow Î {2,3,…}

Outputs: Block Design


stat.F F statistic of the column factor


stat.df Degrees of freedomof the columnfactor

stat.SS Sum o f squares o f the column facto r

stat.MS Meansquares for columnfactor

stat.FBlock F statistic for factor

stat.PValBlock Leastprobability at which the null hypothesis can be rejected

stat.dfBlock Degrees of freedom for factor

stat.SSBlock Sum of squares for factor



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stat.MSBlock Mean squares for factor

stat.dfError Degrees of freedomof the errors

stat.SSError Sum ofsquares ofthe errors

stat.MSError Mean squares for the errors

stat.s Standard deviation o f the error

COLUMN FACTOR Outputs


stat.Fcol F statistic of the column factor

stat.PValCol Probability value of the columnfactor

stat.dfCol Degrees o f freedom o f the column factor

stat.SSCol Sum of squares o f the column factor

stat.MSCol Mean squares for column factor

ROW FACTOR Outputs


stat.FRow F statistic of the row factor

stat.PValRo w Pro bability value o f the row facto r

stat.dfRow Degrees o f freedom of the row factor

stat.SSRow Sum of squares of the row factor

stat.MSRow Mean squares for row factor

INTERACTION Outputs


stat.FInteract F statistic of the interaction

stat.PValInteract Probability value of the interaction

stat.dfInteract Degrees of freedomof the interaction

stat.SSInteract Sum o f squares of the interaction

stat.MSInteract Meansquares for interaction

ERROR Outputs


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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 recentlyevaluated expression.

approx() Catalog >

approx( Expr1) ⇒ expression

Returns the evaluation of the argument asan expression containing decimal values,when possible, regardless of the currentAuto or Approximate mode.

This is equivalent to entering the argument

and pressing/·.

approx( List1) ⇒ list approx( Matrix1) ⇒ matrix

Returns a list or matrix where eachelement has been evaluated to a decimal

value, when possible.



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►approxFraction() Catalog > Expr ►approxFraction([Tol]) ⇒expression

List ►approxFraction([Tol ]) ⇒ list

Matrix►approxFraction([Tol ]) ⇒ matrix

Returns the input as a fraction, using atolerance of Tol . If Tol is omitted, atolerance of 5.E-14 is used.

Note: You can insert this function from thecomputer 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 atolerance of Tol . If Tol is omitted, a

tolerance of 5.E-14 is used.

arccos() See cos⁻¹(), page 35.

arccosh() See cosh⁻¹(), page 36.

arccot() See cot⁻¹(), page 37.

arccoth() See coth⁻¹(), page 38.


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arccsc() See csc⁻¹(), page 40.

arccsch() See csch⁻¹(), page 41.

arcLen() Catalog >

arcLen( Expr1,Var ,Start , End ) ⇒expression

Returns the arc length of Expr1 fromStart to End with respect to variable Var .

Arc length is calculated as an integralassuming a function mode definition.

arcLen( List1,Var ,Start , End ) ⇒ list

Returns a list of the arc lengths of eachelement of List1 from Start to End withrespect to Var .

arcsec() See sec⁻¹(), page 150.

arcsech() See sech⁻¹(), page 150.

arcsin() See sin⁻¹(), page 160.

arcsinh() See sinh⁻¹(), page 161.

arctan() See tan⁻¹(), page 174.



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arctanh() See tanh⁻¹(), page 176.

augment() Catalog >

augment( List1, List2) ⇒ list

Returns a new list that is List2 appended tothe end of List1.

augment( Matrix1, Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2appended to Matrix1. When the “,”character is used, the matrices must haveequal row dimensions, and Matrix2 is

appended to Matrix1 as new columns.Does not alter Matrix1 or Matrix2.

avgRC() Catalog >

avgRC( Expr1, Var [=Value] [, Step]) ⇒expression

avgRC( Expr1, Var [=Value] [, List1]) ⇒

list

avgRC( List1, Var [=Value] [, Step]) ⇒list

avgRC( Matrix1, Var [=Value] [, Step]) ⇒matrix

Returns the forward-difference quotient(average rate of change).

Expr1 can be a user-defined function name(see Func).

When Value is specified, it overrides anyprior variable assignment or any current “|”substitution for the variable.

Step is the step value. If Step is omitted, itdefaults to 0.001.

Note that the similar function centralDiff()

uses the central-difference quotient.


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B

bal() Catalog >

bal( NPmt , N , I , PV ,[ Pmt ], [ FV ], [ PpY ],[CpY ], [ PmtAt ], [roundValue]) ⇒ value

bal( NPmt ,amortTable) ⇒ value

Amortization function that calculatesschedule balance after a specified payment.


NPmt specifies the payment number after

which you want the data calculated.


• If you omit Pmt , it defaults to Pmt =tvmPmt( N , I , PV , F V , 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.

roundV alue specifies the number of decimal places for rounding. Default=2.

bal( NPmt ,amortTable) calculates thebalance after payment number NPmt ,based on amortization table amortTable.The amortTable argument must be a

matrix in the form described underamortTbl(), page 12.

Note: See also ΣInt() and ΣPrn(), page 215.

►Base2 Catalog > Integer1 ►Base2 ⇒ integer

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

Converts Integer1 to a binary number.Binary or hexadecimal numbers always



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►Base2 Catalog >have a 0b or 0h prefix, respectively. Use azero, not the letter O, followed by b or h.

0b binaryNumber 0h hexadecimalNumber

A binary number can have up to 64 digits. Ahexadecimal number can have up to 16.

Without a prefix, Integer1 is treated asdecimal (base 10). The result is displayed inbinary, regardless of the Base mode.

Negative numbers are displayed in “two'scomplement” form. For example,

⁻1 is displayed as

0hFFFFFFFFFFFFFFFF in Hex base mode0b111...111 (64 1’s) in Binary base mode

⁻263 is displayed as0h8000000000000000 in Hex base mode0b100...000 (63 zeros) in Binary base mode

If you enter a decimal integer that isoutside the range of a signed, 64-bit binaryform, a symmetric modulo operation is

used to bring the value into the appropriaterange. Consider the following examples of values outside the range.

263 becomes ⁻263 and is displayed as0h8000000000000000 in Hex base mode0b100...000 (63 zeros) in Binary base mode

264 becomes 0 and is displayed as0h0 in Hex base mode

0b0 in Binary base mode⁻263 − 1 becomes 263 − 1 and is displayedas0h7FFFFFFFFFFFFFFF in Hex base mode0b111...111 (64 1’s) in Binary base mode

►Base10 Catalog >

Integer1 ►Base10⇒

integer Note: You can insert this operator from thecomputer keyboard by typing @>Base10.


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►Base10 Catalog >Converts Integer1 to a decimal (base 10)number. A binary or hexadecimal entrymust always have a 0b or 0h prefix,respectively.


Zero, not the letter O, followed by b or h.


Without a prefix, Integer1 is treated asdecimal. The result is displayed in decimal,regardless of the Base mode.

►Base16 Catalog >

Integer1 ►Base16 ⇒ integer

Note: You can insert this operator from thecomputer keyboard by typing @>Base16.

Converts Integer1 to a hexadecimalnumber. Binary or hexadecimal numbersalways have a 0b or 0h prefix, respectively.


Zero, not the letter O, followed by b or h.


Without a prefix, Integer1 is treated asdecimal (base 10). The result is displayed inhexadecimal, regardless of the Base mode.

If you enter a decimal integer that is toolarge for a signed, 64-bit binary form, asymmetric modulo operation is used tobring the value into the appropriate range.For more information, see ►Base2, page21.

binomCdf() Catalog >

binomCdf(n, p) ⇒ number



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binomCdf() Catalog >

binomCdf(n, p,lowBound ,upBound ) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists

binomCdf(n, p,upBound )for P(0≤X≤upBound ) ⇒number if upBound is a number, list if upBound is alist

Computes a cumulative probability for the discretebinomial distribution with n number of trials andprobability p of success on each trial.

For P(X ≤ upBound ), set lowBound =0

binomPdf() Catalog >binomPdf(n, p) ⇒ number

binomPdf(n, p, XVal ) ⇒ number if XVal is a number,list if XVal is a list

Computes a probability for the discrete binomialdistribution with n number of trials and probability pof success on each trial.

C

Catalog >

ceiling( Expr1) ⇒ integer

Returns the nearest integer that is ≥ theargument.

The argument can be a real or a complexnumber.

Note: See also floor().

ceiling( List1) ⇒ list ceiling( Matrix1) ⇒ matrix

Returns a list or matrix of the ceiling of each element.


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centralDiff() Catalog >

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

centralDiff( Expr1,Var [,Step])|Var=Value⇒ expression

centralDiff( Expr1,Var [=Value][, List ]) ⇒list

centralDiff( List1,Var [=Value][,Step]) ⇒list

centralDiff( Matrix1,Var [=Value][,Step])⇒ matrix

Returns the numerical derivative using the

central difference quotient formula.

When Value is specified, it overrides anyprior variable assignment or any current “|”substitution for the variable.

Step is the step value. If Step is omitted, itdefaults to 0.001.

When using List1 or Matrix1, the operationgets mapped across the values in the list oracross the matrix elements.

Note: See also avgRC() and d ().

cFactor() Catalog >

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

cFactor( Expr1) returns Expr1 factored withrespect to all of its variables over acommon denominator.

Expr1 is factored as much as possibletoward linear rational factors even if thisintroduces new non-real numbers. Thisalternative is appropriate if you wantfactorization with respect to more than one

variable.



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cFactor() Catalog >

cFactor( Expr1,Var ) returns Expr1 factoredwith respect to variable Var .

Expr1 is factored as much as possibletoward factors that are linear in Var , withperhaps non-real constants, even if itintroduces irrational constants orsubexpressions that are irrational in othervariables.

The factors and their terms are sorted withVar as the main variable. Similar powers of Var are collected in each factor. IncludeVar if factorization is needed with respectto only that variable and you are willing toaccept irrational expressions in any othervariables to increase factorization withrespect to Var . There might be someincidental factoring with respect to othervariables.

For the Auto setting of the Auto orApproximate mode, including Var alsopermits approximation with floating-pointcoefficients where irrational coefficientscannot be explicitly expressed concisely in

terms of the built-in functions. Even whenthere is only one variable, including Var might yield more complete factorization.

Note: See also factor().

To see the entire result, press£ and then

use¡ and¢ to move the cursor.

char() Catalog >

char( Integer ) ⇒ character

Returns a character string containing thecharacter numbered Integer from thehandheld character set. The valid range for

Integer is 0–65535.


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charPoly() Catalog >

charPoly( squareMatrix,Var ) ⇒ polynomial expression

charPoly( squareMatrix,Expr ) ⇒ polynomial expression

charPoly( squareMatrix1,Matrix2) ⇒ polynomial expression

Returns the characteristic polynomial of squareMatrix. The characteristicpolynomial of n×n matrix A, denoted by p

A(λ), is the polynomial defined by

p A

(λ) = det(λ•I− A)

where I denotes the n×n identity matrix. squareMatrix1 and squareMatrix2 musthave the equal dimensions.

χ 22way Catalog >

χ 22way obsMatrix

chi22way obsMatrix

Computes a χ 2 test for association on the two-waytable of counts in the observed matrix obsMatrix. Asummary of results is stored in the stat.resultsvariable. (page 168)

For information on the effect of empty elements in amatrix, see “Empty (Void) Elements,” page 226.


stat.χ 2 Chi square stat: sum (observed - expected)2/expected

stat.PVal Smallest level of significance at which the null hypothesis canbe rejected

stat.df Degrees of freedomfor the chi squarestatistics

stat.ExpMat Matrix of expectedelemental count table, assuming null hypothesis

stat.CompMat Matrix of elemental chi square statisticcontributions

χ 2Cdf() Catalog >

χ 2Cdf(lowBound ,upBound ,df ) ⇒ number if lowBound and upBound are numbers, list if



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χ 2Cdf() Catalog >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 χ 2 distribution probability betweenlowBound 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 alist, see “Empty (Void) Elements,” page 226.

χ 2GOF Catalog >χ 2GOF obsList ,expList ,df

chi2GOF obsList ,expList ,df

Performs a test to confirm that sample data is froma population that conforms to a specifieddistribution. obsList is a list of counts and mustcontain integers. A summary of results is stored in

the stat.results variable. (See page 168.)For information on the effect of empty elements in alist, see “Empty (Void) Elements,” page 226.


stat.χ 2 Chi square stat: sum((observed - expected)2/expected


stat.df Degreesoffreedom for the chi square statistics

stat.CompList Elemental chi square statisticcontributions

χ 2Pdf() Catalog >χ 2Pdf( XVal ,df ) ⇒ number if XVal is a 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) forthe χ 2 distribution at a specified XVal value for the


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χ 2Pdf() Catalog >specified degrees of freedom df .


ClearAZ Catalog >

ClearAZ

Clears all single-character variables in thecurrent problem space.

If one or more of the variables are locked,this command displays an error messageand deletes only the unlocked variables. See

unLock, page 188.

ClrErr Catalog >

ClrErr

Clears the error status and sets system variableerrCode to zero.

The Else clause of the Try...Else...EndTry block shoulduse ClrErr or PassErr. If the error is to be processed orignored, use ClrErr. If what to do with the error is notknown, use PassErr to send it to the next errorhandler. If there are no more pendingTry...Else...EndTry error handlers, the error dialog boxwill be displayed as normal.

Note: See also PassErr, page 125, and Try, page 182.

Note for entering the example: For instructions on

entering multi-line program and function definitions,refer to the Calculator section of your productguidebook.

For an example of ClrErr, SeeExample 2 under the Trycommand, page 182.

colAugment() Catalog >

colAugment( Matrix1, Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2

appended to Matrix1. The matrices musthave equal column dimensions, and

Matrix2 is appended to Matrix1 as newrows. Does not alter Matrix1 or Matrix2.



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colDim() Catalog >

colDim( Matrix) ⇒ expression

Returns the number of columns containedin Matrix.

Note: See also rowDim().

colNorm() Catalog >

colNorm( Matrix) ⇒ expression

Returns the maximum of the sums of theabsolute values of the elements in thecolumns in Matrix.

Note: Undefined matrix elements are notallowed. See also rowNorm().

comDenom() Catalog >

comDenom( Expr1[,Var ]) ⇒ expressioncomDenom( List1[,Var ]) ⇒ list comDenom( Matrix1[,Var ]) ⇒ matrix

comDenom( Expr1) returns a reduced ratioof a fully expanded numerator over a fullyexpanded denominator.

comDenom( Expr1,Var ) returns a reducedratio of numerator and denominatorexpanded with respect to Var . The termsand their factors are sorted with Var as themain variable. Similar powers of Var arecollected. There might be some incidentalfactoring of the collected coefficients.Compared to omitting Var , this often savestime, memory, and screen space, whilemaking the expression morecomprehensible. It also makes subsequentoperations on the result faster and lesslikely to exhaust memory.

If Var does not occur in Expr1, comDenom( Expr1,Var ) returns a reduced ratio of anunexpanded numerator over an unexpanded

denominator. Such results usually save evenmore time, memory, and screen space.Such partially factored results also makesubsequent operations on the result much


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comDenom() Catalog >

faster and much less likely to exhaustmemory.

Even when there is no denominator, thecomden function is often a fast way toachieve partial factorization if factor() is

too slow or if it exhausts memory.

Hint: Enter this comden() function definitionand routinely try it as an alternative tocomDenom() and factor().

completeSquare () Catalog >

completeSquare( ExprOrEqn, Var ) ⇒

expression or equation

completeSquare( ExprOrEqn, Var^Power )⇒ expression or equation

completeSquare( ExprOrEqn, Var1, Var2[,...]) ⇒ expression or equation

completeSquare( ExprOrEqn, {Var1, Var2[,...]}) ⇒ expression or equation

Converts a quadratic polynomial expressionof the form a•x2+b•x+c into the form a•(x-h)2+k

- or -

Converts a quadratic equation of the forma•x2+b•x+c=d into the form a•(x-h)2=k

The first argument must be a quadratic

expression or equation in standard formwith respect to the second argument.

The Second argument must be a singleunivariate term or a single univariate termraised to a rational power, for examplex, y2, or z(1/3).

The third and fourth syntax attempt tocomplete the square with respect to

variables Var1, Var2 [,… ]).



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conj() Catalog >

conj( Expr1) ⇒ expression

conj( List1) ⇒ list

conj( Matrix1) ⇒ matrix

Returns the complex conjugate of theargument.


constructMat() Catalog >

constructMat

( Expr ,Var1,Var2,numRows,numCols) ⇒matrix

Returns a matrix based on the arguments.

Expr is an expression in variables Var1 andVar2. Elements in the resulting matrix areformed by evaluating Expr for eachincremented value of Var1 and Var2.

Var1 is automatically incremented from 1through numRows. Within each row, Var2is incremented from 1 through numCols.

CopyVar Catalog >

CopyVar Var1, Var2

CopyVar Var1., Var2.

CopyVar Var1, Var2 copies the value of variable Var1 to variable Var2, creatingVar2 if necessary. Variable Var1 must havea value.

If Var1 is the name of an existing user-defined function, copies the definition of that function to function Var2. FunctionVar1 must be defined.

Var1 must meet the variable-namingrequirements or must be an indirectionexpression that simplifies to a variablename meeting the requirements.


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CopyVar Catalog >

CopyVar Var1., Var2. copies all membersof the Var1. variable group to the Var2.group, creating Var2. if necessary.

Var1. must be the name of an existingvariable group, such as the statistics stat .nnresults, or variables created using theLibShortcut() function. If Var2. alreadyexists, this command replaces all membersthat are common to both groups and addsthe members that do not already exist. If one or more members of Var2. are locked,all members of Var2. are left unchanged.

corrMat() Catalog >corrMat( List1, List2[,…[, List20]])

Computes the correlation matrix for the augmentedmatrix [ List1, List2, ..., List20].

►cos Catalog >

Expr ►cos

Note: You can insert this operator from thecomputer keyboard by typing @>cos.

Represents Expr in terms of cosine. This isa display conversion operator. It can beused only at the end of the entry line.

►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 onlyif sin(...) occurs in the given expression onlyto even powers.

Note: This conversion operator is notsupported in Degree or Gradian Anglemodes. Before using it, make sure that theAngle mode is set to Radians and that Expr

does not contain explicit references todegree or gradian angles.



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cos() µ key

cos( Expr1) ⇒ expression

cos( List1) ⇒ list

cos( Expr1) returns the cosine of theargument as an expression.

cos( List1) returns a list of the cosines of allelements in List1.

Note: The argument is interpreted as adegree, gradian or radian angle, accordingto the current angle mode setting. You canuse °, G, or r to override the angle modetemporarily.




cos( squareMatrix1) ⇒ squareMatrix

Returns the matrix cosine of squareMatrix1. This is not the same ascalculating the cosine of each element.

When a scalar function f(A) operates on squareMatrix1 (A), the result is calculatedby the algorithm:

Compute the eigenvalues (λi

) and

eigenvectors (Vi ) of A.

squareMatrix1 must be diagonalizable.Also, it cannot have symbolic variables thathave not been assigned a value.

Form the matrices:



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cos() µ key

Then A = X B X⁻¹ and f(A) = X f(B) X⁻¹. Forexample, cos(A) = X cos(B) X⁻¹ where:

cos(B) =

All computations are performed usingfloating-point arithmetic.

cos⁻¹() µ key

cos⁻¹( Expr1) ⇒ expression

cos⁻¹( List1) ⇒ list

cos⁻¹( Expr1) returns the angle whosecosine is Expr1 as an expression.

cos⁻¹( List1) returns a list of the inversecosines of each element of List1.

Note: The result is returned as a degree,gradian or radian angle, according to thecurrent angle mode setting.

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




cos⁻¹( squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse cosine of

squareMatrix1. This is not the same ascalculating the inverse cosine of eachelement. For information about thecalculation method, refer to cos().

squareMatrix1 must be diagonalizable. Theresult always contains floating-pointnumbers.

In Radian angle mode and RectangularComplex Format:





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cosh() Catalog >

cosh( Expr1) ⇒ expression

cosh( List1) ⇒ list

cosh( Expr1) returns the hyperbolic cosineof the argument as an expression.

cosh( List1) returns a list of the hyperboliccosines of each element of List1.


cosh( squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic cosine of squareMatrix1. This is not the same ascalculating the hyperbolic cosine of eachelement. For information about thecalculation method, refer to cos().



cosh⁻¹() Catalog >cosh⁻¹( Expr1) ⇒ expression

cosh⁻¹( List1) ⇒ list

cosh⁻¹( Expr1) returns the inversehyperbolic cosine of the argument as anexpression.

cosh⁻¹( List1) returns a list of the inversehyperbolic cosines of each element of

List1.

Note: You can insert this function from thekeyboard by typing arccosh(...).

cosh⁻¹( squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse hyperboliccosine of squareMatrix1. This is not thesame as calculating the inverse hyperboliccosine of each element. For informationabout the calculation method, refer to cos().


In Radian angle mode and In RectangularComplex Format:




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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 adegree, gradian or radian angle, accordingto the current angle mode setting. You canuse °, G, or r to override the angle modetemporarily.




cot⁻¹() µ key

cot⁻¹( Expr1) ⇒ expression

cot⁻¹( List1) ⇒ list

Returns the angle whose cotangent is Expr1 or returns a list containing the

inverse cotangents of each element of List1.

Note: The result is returned as a degree,gradian or radian angle, according to thecurrent angle mode setting.

Note: You can insert this function from thekeyboard by typing arccot(...).




coth() Catalog >

coth( Expr1) ⇒ expression

coth( List1) ⇒ list

Returns the hyperbolic cotangent of Expr1or returns a list of the hyperboliccotangents of all elements of List1.



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coth⁻¹() Catalog >coth⁻¹( Expr1) ⇒ expression

coth⁻¹( List1) ⇒ list

Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing theinverse hyperbolic cotangents of eachelement of List1.

Note: You can insert this function from thekeyboard by typing arccoth(...).

count() Catalog >

count(Value1orList1 [,Value2orList2

[,...]]) ⇒ value

Returns the accumulated count of allelements in the arguments that evaluate tonumeric values.

Each argument can be an expression, value,list, or matrix. You can mix data types anduse arguments of various dimensions.

For a list, matrix, or range of cells, eachelement is evaluated to determine if itshould be included in the count.

Within the Lists & Spreadsheet application,you can use a range of cells in place of anyargument.

Empty (void) elements are ignored. Formore information on empty elements, seepage 226.

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.

countif() Catalog >

countif( List ,Criteria) ⇒ value

Returns the accumulated count of allelements in List that meet the specified

Criteria.

Criteria can be:

• A value, expression, or string. For

Counts the number of elements equal to 3.


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countif() Catalog >

example, 3 counts only those elements in List that simplify to the value 3.

• A Boolean expression containing thesymbol ? as a placeholder for eachelement. For example, ?

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 variableVar .

Poly must be a polynomial in one variable.

The second syntax, cPolyRoots( ListOfCoeffs), returns a list of complexroots for the coefficients in ListOfCoeffs.

Note: See also polyRoots(), page 130.



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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 beeither 2 or 3.

crossP(Vector1, Vector2) ⇒ vector

Returns a row or column vector (dependingon the arguments) that is the cross productof Vector1 and Vector2.

Both Vector1 and Vector2 must be rowvectors, or both must be column vectors.

Both vectors must have equal dimension,and the dimension must be either 2 or 3.

csc() µ key

csc( Expr1) ⇒ expression

csc( List1) ⇒ list

Returns the cosecant of Expr1 or returns alist containing the cosecants of all elementsin List1.




csc⁻¹() µ key

csc⁻¹( Expr1) ⇒expression

csc⁻¹( List1) ⇒ list

Returns the angle whose cosecant is Expr1or returns a list containing the inversecosecants of each element of List1.

Note: The result is returned as a degree,




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csc⁻¹() µ key

gradian or radian angle, according to thecurrent angle mode setting.

Note: You can insert this function from thekeyboard by typing arccsc(...).


csch() Catalog >

csch( Expr1) ⇒ expression

csch( List1) ⇒ list

Returns the hyperbolic cosecant of Expr1 orreturns a list of the hyperbolic cosecants of

all elements of List1.

csch⁻¹() Catalog >csch⁻¹( Expr1) ⇒ expression

csch⁻¹( List1) ⇒ list

Returns the inverse hyperbolic cosecant of

Expr1 or returns a list containing theinverse hyperbolic cosecants of eachelement of List1.

Note: You can insert this function from thekeyboard by typing arccsch(...).

cSolve() Catalog >

cSolve( Equation, Var ) ⇒ Booleanexpression

cSolve( Equation, Var=Guess) ⇒ Booleanexpression

cSolve( Inequality , Var ) ⇒ Booleanexpression

Returns candidate complex solutions of anequation or inequality for Var . The goal isto produce candidates for all real and non-real solutions. Even if Equation is real,



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cSolve() Catalog >

cSolve() allows non-real results in Realresult Complex Format.

Although all undefined variables that do notend with an underscore (_) are processedas if they were real, cSolve() can solvepolynomial equations for complex solutions.

cSolve() temporarily sets the domain tocomplex during the solution even if thecurrent domain is real. In the complexdomain, fractional powers having odddenominators use the principal rather thanthe real branch. Consequently, solutionsfrom solve() to equations involving suchfractional powers are not necessarily a

subset of those from cSolve().cSolve() starts with exact symbolicmethods. cSolve() also uses iterativeapproximate complex polynomial factoring,if necessary.

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

Note: If Equation is non-polynomial withfunctions such as abs(), angle(), conj(), real(), or imag(), you should place anunderscore (press/_) at the end of Var . By default, a variable is treated as areal value.

In Display Digits mode of Fix 2:

To see the entire result, press£ and thenuse¡ and¢ to move the cursor.

If you use var _ , the variable is treated ascomplex.

You should also use var _ for any othervariables in Equation that might have

unreal values. Otherwise, you may receiveunexpected results.

cSolve( Eqn1and Eqn2 [and…],VarOrGuess1, VarOrGuess2 [, … ]) ⇒

Boolean expression

cSolve(SystemOfEqns, VarOrGuess1,VarOrGuess2 [, …]) ⇒

Boolean expression

Returns candidate complex solutions to thesimultaneous algebraic equations, where


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cSolve() Catalog >

each varOrGuess specifies a variable thatyou want to solve for.

Optionally, you can specify an initial guessfor a variable. Each varOrGuess must havethe form:

variable – or –variable = real or non-real number

For example, x is valid and so is x=3+i.

If all of the equations are polynomials andif you do NOT specify any initial guesses,cSolve() uses the lexicalGröbner/Buchberger elimination method toattempt to determine all complex solutions.

Note: The following examples use an

underscore (press/_) so that the

variables will be treated as complex.

Complex solutions can include both real andnon-real solutions, as in the example to theright.



Simultaneous polynomial equations canhave extra variables that have no values,but represent given numeric values thatcould be substituted later.



You can also include solution variables thatdo not appear in the equations. Thesesolutions show how families of solutionsmight contain arbitrary constants of theform ck , where k is an integer suffix from 1through 255.

For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list solutionvariables. If your initial choice exhaustsmemory or your patience, try rearrangingthe variables in the equations and/orvarOrGuess list.





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cSolve() Catalog >

If you do not include any guesses and if anyequation is non-polynomial in any variablebut all equations are linear in all solutionvariables, cSolve() uses Gaussianelimination to attempt to determine all

solutions.If a system is neither polynomial in all of itsvariables nor linear in its solution variables,cSolve() determines at most one solutionusing an approximate iterative method. Todo so, the number of solution variablesmust equal the number of equations, andall other variables in the equations mustsimplify to numbers.

A non-real guess is often necessary todetermine a non-real solution. Forconvergence, a guess might have to berather close to a solution.



CubicReg Catalog >

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

Computes the cubic polynomial regressiony=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 168.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependentvariables.

Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency of occurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers ≥ 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 isincluded in this list are included in the calculation.


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CubicReg Catalog >


Outputvariable

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 inthe modified X List actually used in the regression basedonrestrictions of Freq, Category List , and Include Categories

stat.YReg List of data points inthe modifiedY List actually used inthe regression basedonrestrictions of Freq, Category List , and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

cumulativeSum() Catalog >

cumulativeSum( List1) ⇒ list

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

cumulativeSum( Matrix1) ⇒ matrix

Returns a matrix of the cumulative sums of the elements in Matrix1. Each element isthe cumulative sum of the column from topto bottom.

An empty (void) element in List1

or Matrix1 produces a void element in theresulting list or matrix. For moreinformation on empty elements, see page226.

Cycle Catalog >

Cycle

Transfers control immediately to the nextiteration of the current loop (For, While, orLoop).

Function listing that sums the integers from 1

to 100 skipping 50.



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Cycle Catalog >

Cycle is not allowed outside the threelooping structures (For, While, or Loop).

Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your productguidebook.

►Cylind Catalog >Vector ►Cylind

Note: You can insert this operator from thecomputer keyboard by typing @>Cylind .

Displays the row or column vector incylindrical form [r,∠θ, z].

Vector must have exactly three elements.

It can be either a row or a column.

cZeros() Catalog >

cZeros( Expr , Var ) ⇒ list

Returns a list of candidate real and non-realvalues of Var that make Expr =0. cZeros()does this by computingexp

►list(cSolve(

Expr =0,

Var ),

Var ).

Otherwise, cZeros() is similar to zeros().

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

In Display Digits mode of Fix 3:



Note: If Expr is non-polynomial withfunctions such as abs(), angle(), conj(), real(), or imag(), you should place an

underscore (press/_) at the end of Var . By default, a variable is treated as areal value. If you use var_ , the variable istreated as complex.

You should also use var_ for any othervariables in Expr that might have unreal


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cZeros() Catalog >

values. Otherwise, you may receiveunexpected results.

cZeros({ Expr1, Expr2 [, … ] },{VarOrGuess1,VarOrGuess2 [, … ] }) ⇒

matrix

Returns candidate positions where theexpressions are zero simultaneously. EachVarOrGuess specifies an unknown whosevalue you seek.

Optionally, you can specify an initial guessfor a variable. Each VarOrGuess must havethe form:

variable

– or –variable = real or non-real number

For example, x is valid and so is x=3+i.

If all of the expressions are polynomials andyou do NOT specify any initial guesses,cZeros() uses the lexicalGröbner/Buchberger elimination method toattempt to determine all complex zeros.

Note: The following examples use an

underscore _ (press/_) so that the

variables will be treated as complex.

Complex zeros can include both real andnon-real zeros, as in the example to theright.

Each row of the resulting matrix representsan alternate zero, with the componentsordered the same as the VarOrGuess list.To extract a row, index the matrix by [row].

Extractrow2:

Simultaneous polynomials can have extravariables that have no values, but representgiven numeric values that could besubstituted later.



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cZeros() Catalog >

You can also include unknown variables thatdo not appear in the expressions. Thesezeros show how families of zeros mightcontain arbitrary constants of the form ck ,where k is an integer suffix from 1 through

255.For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list unknowns. If your initial choice exhausts memory or yourpatience, try rearranging the variables inthe expressions and/or VarOrGuess list.

If you do not include any guesses and if anyexpression is non-polynomial in any variable

but all expressions are linear in allunknowns, cZeros() uses Gaussianelimination to attempt to determine allzeros.

If a system is neither polynomial in all of itsvariables nor linear in its unknowns, cZeros() determines at most one zero using anapproximate iterative method. To do so, thenumber of unknowns must equal the

number of expressions, and all othervariables in the expressions must simplifyto numbers.

A non-real guess is often necessary todetermine a non-real zero. Forconvergence, a guess might have to berather close to a zero.

D

dbd() Catalog >

dbd(date1,date2) ⇒ value

Returns the number of days between date1and date2 using the actual-day-countmethod.

date1 and date2 can be numbers or lists of

numbers within the range of the dates onthe standard calendar. If both date1 anddate2 are lists, they must be the samelength.


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dbd() Catalog >

date1 and date2 must be between theyears 1950 through 2049.

You can enter the dates in either of twoformats. The decimal placementdifferentiates between the date formats.

MM.DDYY (format used commonly in theUnited States)DDMM.YY (format use commonly inEurope)

►DD Catalog >

Expr1 ►DD ⇒ valueList1►DD ⇒ listMatrix1►DD ⇒ matrix

Note: You can insert this operator from thecomputer keyboard by typing @>DD.

Returns the decimal equivalent of theargument expressed in degrees. Theargument is a number, list, or matrix that isinterpreted by the Angle mode setting in

gradians, radians or degrees.




►Decimal Catalog > Expression1 ►Decimal ⇒ expression

List1 ►Decimal ⇒ expression

Matrix1 ►Decimal ⇒ expression

Note: You can insert this operator from thecomputer keyboard by typing @>Decimal.

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



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Define Catalog >

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

Expression

Defines the variable Var or the user-defined function Function.

Parameters, such as Param1, provideplaceholders for passing arguments to thefunction. When calling a user-definedfunction, you must supply arguments (forexample, values or variables) thatcorrespond to the parameters. When called,the function evaluates Expression usingthe supplied arguments.

Var and Function cannot be the name of asystem variable or built-in function orcommand.

Note: This form of Define is equivalent toexecuting the expression: expression →

Function( Param1,Param2).

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

Block EndFunc

Define Program( Param1, Param2, ...) =Prgm Block EndPrgm

In this form, the user-defined function or

program can execute a block of multiplestatements.

Block can be either a single statement or aseries of statements on separate lines.

Block also can include expressions andinstructions (such as If , Then, Else, and For).

Note for entering the example: Forinstructions on entering multi-line program

and function definitions, refer to theCalculator section of your productguidebook.


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Define Catalog >

Note: See also Define LibPriv, page 51, andDefine LibPub, page 51.

Define LibPriv Catalog >

Define LibPriv Var = ExpressionDefine LibPriv Function( Param1, Param2, ...) =

Expression

Define LibPriv Function( Param1, Param2, ...) = Func Block EndFunc

Define LibPriv Prog ram( P aram1, Param2, ...) =

Prgm Block EndPrgm

Operates the same as Define, except defines aprivate library variable, function, or program. Privatefunctions and programs do not appear in the Catalog.

Note: See also Define, page 50, and Define LibPub,page 51.

Define LibPub Catalog >

Define LibPub Var = ExpressionDefine LibPub Function( Param1, Param2, ...) =

Expression

Define LibPub Function( Param1, Param2, ...) = Func Block EndFunc

Define LibPub Program( Param1, Param2, ...) = Prgm Block EndPrgm

Operates the same as Define, except defines a publiclibrary variable, function, or program. Public functionsand programs appear in the Catalog after the libraryhas been saved and refreshed.

Note: See also Define, page 50, and Define LibPriv,page 51.



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deltaList() See ΔList(), page 97.

deltaTmpCnv()See ΔtmpCnv(), page

181.

DelVar Catalog >

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

DelVar Var .

Deletes the specified variable or variablegroup from memory.

If one or more of the variables are locked,this command displays an error messageand deletes only the unlocked variables. SeeunLock, page 188.

DelVar Var . deletes all members of theVar . variable group (such as the statistics

stat .nn results or variables created using

the LibShortcut() function). The dot (.) inthis form of the DelVar command limits itto deleting a variable group; the simplevariable Var is not affected.

delVoid() Catalog >delVoid( List1) ⇒ list

Returns a list that has the contents of List1with all empty (void) elements removed.

For more information on empty elements,see page 226.

derivative() See d (), page 211.


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deSolve() Catalog >

deSolve(1stOr2ndOrderODE , Var ,depVar ) ⇒ a general solution

Returns an equation that explicitly orimplicitly specifies a general solution to the1st- or 2nd-order ordinary differentialequation (ODE). In the ODE:

• Use a prime symbol (pressº) to denotethe 1st derivative of the dependentvariable with respect to the independentvariable.

• Use two prime symbols to denote thecorresponding second derivative.

The prime symbol is used for derivativeswithin deSolve() only. In other cases, use d().

The general solution of a 1st-order equationcontains an arbitrary constant of the formck , where k is an integer suffix from 1through 255. The solution of a 2nd-orderequation contains two such constants.

Apply solve() to an implicit solution if you

want to try to convert it to one or moreequivalent explicit solutions.

When comparing your results with textbookor manual solutions, be aware that differentmethods introduce arbitrary constants atdifferent points in the calculation, whichmay produce different general solutions.

deSolve(1stOrderODE and initCond , Var ,

depVar ) ⇒ a particular solution

Returns a particular solution that satisfies1stOrderODE and initCond . This is usuallyeasier than determining a general solution,substituting initial values, solving for thearbitrary constant, and then substitutingthat value into the general solution.

initCond is an equation of the form:

depVar (initialIndependentValue) =initialDependentValue



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deSolve() Catalog >

The initialIndependentValue andinitialDependentValue can be variablessuch as x0 and y0 that have no storedvalues. Implicit differentiation can helpverify implicit solutions.

deSolve(2ndOrderODE and initCond1 andinitCond2, Var , depVar )⇒ particular solution

Returns a particular solution that satisfies2nd Order ODE and has a specified valueof the dependent variable and its firstderivative at one point.

For initCond1, use the form:

depVar (initialIndependentValue) =initialDependentValue

For initCond2, use the form:

depVar (initialIndependentValue) =initial1stDerivativeValue

deSolve(2ndOrderODE and bndCond1 andbndCond2, Var , depVar )⇒

a particular solutionReturns a particular solution that satisfies2ndOrderODE and has specified values attwo different points.


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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 thanTolerance. This tolerance is used only if thematrix has floating-point entries and doesnot contain any symbolic variables thathave not been assigned a value. Otherwise,Tolerance is ignored.

• If you use/· or set the Auto orApproximate mode to Approximate,computations are done using floating-point arithmetic.

• If Tolerance is omitted or not used, thedefault tolerance is calculated as:5E⁻14 •max(dim( squareMatrix))•rowNorm( squareMatrix)

diag() Catalog >

diag( List ) ⇒ matrixdiag(rowMatrix) ⇒ matrixdiag(columnMatrix) ⇒ matrix

Returns a matrix with the values in theargument list or matrix in its maindiagonal.

diag( squareMatrix) ⇒ rowMatrix

Returns a row matrix containing the

elements from the main diagonal of squareMatrix.

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}.



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dim() Catalog >

dim(String ) ⇒ integer

Returns the number of characters containedin character string String .

Disp Catalog >

Disp exprOrString1 [, exprOrString2] ...

Displays the arguments in the Calculator history. The arguments are displayed insuccession, with thin spaces as separators.

Useful mainly in programs and functions toensure the display of intermediate

calculations.


►DMS Catalog > Expr ►DMS

List ►DMS

Matrix ►DMS

Note: You can insert this operator from the

computer keyboard by typing @>DMS.

Interprets the argument as an angle anddisplays the equivalent DMS(DDDDDD°MM'SS.ss'') number. See °, ', ''on page 218 for DMS (degree, minutes,seconds) format.

Note: ►DMS will convert from radians todegrees when used in radian mode. If the

input is followed by a degree symbol ° , noconversion will occur. You can use ►DMSonly at the end of an entry line.



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domain() Catalog >

domain( Expr1, Var ) ⇒ expression

Returns the domain of Expr1 with respectto Var .

domain() can be used to examine domains

of functions. It is restricted to real andfinite domain.

This functionality has limitations due toshortcomings of computer algebrasimplification and solver algorithms.

Certain functions cannot be used asarguments for domain(), regardless of whether they appear explicitly or within

user-defined variables and functions. In thefollowing example, the expression cannotbe simplified because ∫() is a disallowedfunction.

dominantTerm() Catalog >

dominantTerm( Expr1, Var [, Point ]) ⇒expression

dominantTerm( Expr1, Var [, Point ]) |Var > Point ⇒ expression

dominantTerm( Expr1, Var [, Point ]) |Var


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dominantTerm() Catalog >

having the same exponent sign.

Point defaults to 0. Point can be ∞ or −∞,in which cases the dominant term will bethe term having the largest exponent of Var rather than the smallest exponent of Var .

dominantTerm(…) returns “dominantTerm(…)” if it is unable to determine such arepresentation, such as for essentialsingularities such as sin(1/ z ) at z =0, e−1/z

at z=0, or ez at z = ∞ or −∞.

If the series or one of its derivatives has a jump discontinuity at Point , the result is

likely to contain sub-expressions of theform sign(…) or abs(…) for a real expansionvariable or (-1)floor(…angle(…)…) for a complexexpansion variable, which is one endingwith “_”. If you intend to use the dominantterm only for values on one side of Point ,then append to dominantTerm(...) theappropriate one of “| Var > Point ”, “| Var

dotP( List1, List2) ⇒ expression

Returns the “dot” product of two lists.dotP(Vector1, Vector2) ⇒ expression

Returns the “dot” product of two vectors.


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dotP() Catalog >

Both must be row vectors, or both must becolumn vectors.

E

e^() u key

e^( Expr1) ⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page6.

Note: Pressingu to display e^( is different

from pressing the characterE on thekeyboard.

You can enter a complex number in reiθpolar form. However, use this form inRadian angle mode only; it causes aDomain error in Degree or Gradian anglemode.

e^( List1) ⇒ list

Returns e raised to the power of eachelement in List1.

e^( squareMatrix1) ⇒ squareMatrix

Returns the matrix exponential of squareMatrix1. This is not the same ascalculating e raised to the power of eachelement. For information about thecalculation method, refer to cos().


eff() Catalog >

eff(nominalRate,CpY ) ⇒ value

Financial function that converts the nominalinterest rate nominalRate to an annualeffective rate, given CpY as the number of compounding periods per year.



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eff() Catalog >

nominalRate must be a real number, andCpY must be a real number > 0.

Note: See also nom(), page 117.

eigVc() Catalog >

eigVc( squareMatrix) ⇒ matrix

Returns a matrix containing theeigenvectors for a real or complex

squareMatrix, where each column in theresult corresponds to an eigenvalue. Notethat an eigenvector is not unique; it may bescaled by any constant factor. The

eigenvectors are normalized, meaning that:

if V = [x1

, x2

, … , xn

]

then x1

2 + x2

2 + … + xn

2 = 1

squareMatrix is first balanced withsimilarity transformations until the row andcolumn norms are as close to the samevalue as possible. The squareMatrix is then

reduced to upper Hessenberg form and theeigenvectors are computed via a Schurfactorization.

In Rectangular Complex Format:



eigVl() Catalog >

eigVl( squareMatrix) ⇒ list

Returns a list of the eigenvalues of a real or

complex squareMatrix. squareMatrix is first balanced withsimilarity transformations until the row andcolumn norms are as close to the samevalue as possible. The squareMatrix is thenreduced to upper Hessenberg form and theeigenvalues are computed from the upperHessenberg matrix.

In Rectangular complex format mode:



Else See If, page 82.


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ElseIf Catalog >

If BooleanExpr1 Then Block1ElseIf BooleanExpr2 Then Block2⋮

ElseIf BooleanExprN Then BlockN EndIf ⋮


EndFor See For, page 72.

EndFunc See Func, page 76.

EndIf See If, page 82.

EndLoop See Loop, page 104.

EndPrgm See Prgm, page 131.

EndTry See Try, page 182.

EndWhile See While, page 191.



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euler () Catalog >

euler( Expr , Var , depVar , {Var0, VarMax},depVar0, VarStep [, eulerStep]) ⇒ matrix

euler(SystemOfExpr , Var , ListOfDepVars,{Var0, VarMax}, ListOfDepVars0,VarStep [, eulerStep]) ⇒ matrix

euler( ListOfExpr , Var , ListOfDepVars,{Var0, VarMax}, ListOfDepVars0,VarStep [, eulerStep]) ⇒ matrix

Uses the Euler method to solve the system

with depVar (Var0)=depVar0 on theinterval [Var0,VarMax]. Returns a matrixwhose first row defines the Var outputvalues and whose second row defines thevalue of the first solution component at thecorresponding Var values, and so on.

Expr is the right-hand side that defines theordinary differential equation (ODE).

SystemOfExpr is the system of right-handsides that define the system of ODEs

(corresponds to order of dependentvariables in ListOfDepVars).

ListOfExpr is a list of right-hand sides thatdefine the system of ODEs (corresponds tothe order of dependent variables in

ListOfDepVars).

Var is the independent variable.

ListOfDepVars is a list of dependent

variables.

{Var0, VarMax} is a two-element list thattells the function to integrate from Var0 toVarMax.

ListOfDepVars0 is a list of initial valuesfor dependent variables.

VarStep is a nonzero number such that sign

(VarStep) = sign(VarMax-Var0) andsolutions are returned at Var0+i•VarStepfor all i=0,1,2,… such that Var0+i•VarStep

Differential equation:y'=0.001*y*(100-y) andy(0)=10



Compare above resultwith CAS exactsolution obtained using deSolve() andseqGen():

System of equations:

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


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euler () Catalog >

is in [var0,VarMax] (there may not be asolution value at VarMax).

eulerStep is a positive integer (defaults to1) that defines the number of euler stepsbetween output values. The actual step sizeused by the euler method isVarStep ⁄ eulerStep.

exact() Catalog >

exact( Expr1 [, Tolerance]) ⇒ expressionexact( List1 [, Tolerance]) ⇒ list exact( Matrix1 [, Tolerance]) ⇒ matrix

Uses Exact mode arithmetic to return,when possible, the rational-numberequivalent of the argument.

Tolerance specifies the tolerance for theconversion; the default is 0 (zero).

Exit Catalog >

Exit

Exits the current For, While, or Loop block.

Exit is not allowed outside the three loopingstructures (For, While, or Loop).


Function listing:



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►exp Catalog > Expr ►exp

Represents Expr in terms of the naturalexponential e. This is a display conversionoperator. It can be used only at the end of the entry line.

Note: You can insert this operator from thecomputer keyboard by typing @>exp.

exp() u key

exp( Expr1) ⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page6.

You can enter a complex number in reiθpolar form. However, use this form inRadian angle mode only; it causes aDomain error in Degree or Gradian anglemode.

exp( List1) ⇒ list

Returns e raised to the power of eachelement in List1.

exp( squareMatrix1) ⇒ squareMatrix

Returns the matrix exponential of squareMatrix1. This is not the same ascalculating e raised to the power of eachelement. For information about thecalculation method, refer to cos().


exp►list() Catalog >exp►list( Expr ,Var ) ⇒ list

Examines Expr for equations that areseparated by the word “or,” and returns alist containing the right-hand sides of theequations of the form Var=Expr . This


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exp►list() Catalog >gives you an easy way to extract somesolution values embedded in the results of the solve(), cSolve(), fMin(), and fMax()functions.

Note: exp►list() is not necessary with thezeros() and cZeros() functions because theyreturn a list of solution values directly.

You can insert this function from thekeyboard by typing exp@>list(...).

expand() Catalog >

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

expand( Expr1) returns Expr1 expandedwith respect to all its variables. Theexpansion is polynomial expansion forpolynomials and partial fraction expansionfor rational expressions.

The goal of expand() is to transform Expr1

into a sum and/or difference of simpleterms. In contrast, the goal of factor() is totransform Expr1 into a product and/orquotient of simple factors.

expand( Expr1,Var ) returns Expr1expanded with respect to Var . Similarpowers of Var are collected. The terms andtheir factors are sorted with Var as themain variable. There might be some

incidental factoring or expansion of thecollected coefficients. Compared toomitting Var , this often saves time,memory, and screen space, while makingthe expression more comprehensible.

Even when there is only one variable, usingVar might make the denominatorfactorization used for partial fraction

expansion more complete.Hint: For rational expressions, propFrac() isa faster but less extreme alternative toexpand().



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expand() Catalog >

Note: See also comDenom() for anexpanded numerator over an expandeddenominator.

expand( Expr1,[Var ]) also distributeslogarithms and fractional powers

regardless of Var . For increaseddistribution of logarithms and fractionalpowers, inequality constraints might benecessary to guarantee that some factorsare nonnegative.

expand( Expr1, [Var ]) also distributesabsolute values, sign(), and exponentials,regardless of Var .

Note: See also tExpand() for trigonometricangle-sum and multiple-angle expansion.

expr() Catalog >

expr(String ) ⇒ expression

Returns the character string contained inString as an expression and immediately

executes it.

ExpReg Catalog >

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

Computes the exponential regression y = a•(b)x onlists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (Seepage 168.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependentvariables.

Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency of occurrence for each corresponding X and Y datapoint. The default value is 1. All elements must be


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ExpReg Catalog >

integers ≥ 0.

Category is a list of category codes for thecorresponding X and Y data.

Include is a list of one or more of the category codes.

Only those data items whose category code isincluded in this list are included in the calculation.


Outputvariable

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 inthe modified X List actually used in the regression based on

restrictions of Freq, Category List , and Include Categories

stat.YReg List of data points inthe modified Y List actually used in the regression based onrestrictions of Freq, Category List , and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

F

factor() Catalog >factor( Expr1[, Var ]) ⇒ expressionfactor( List1[,Var ]) ⇒ list factor( Matrix1[,Var ]) ⇒ matrix

factor( Expr1) returns Expr1 factored withrespect to all of its variables over acommon denominator.

Expr1 is factored as much as possible

toward linear rational factors withoutintroducing new non-real subexpressions.This alternative is appropriate if you wantfactorization with respect to more than onevariable.



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factor() Catalog >

factor( Expr1,Var ) returns Expr1 factoredwith respect to variable Var .

Expr1 is factored as much as possibletoward real factors that are linear in Var ,even if it introduces irrational constants orsubexpressions that are irrational in othervariables.

The factors and their terms are sorted withVar as the main variable. Similar powers of Var are collected in each factor. IncludeVar if factorization is needed with respectto only that variable and you are willing toaccept irrational expressions in any othervariables to increase factorization withrespect to Var . There might be someincidental factoring with respect to othervariables.

For the Auto setting of the Auto orApproximate mode, including Var permitsapproximation with floating-pointcoefficients where irrational coefficientscannot be explicitly expressed concisely interms of the built-in functions. Even when

there is only one variable, including Var might yield more complete factorization.

Note: See also comDenom() for a fast wayto achieve partial factoring when factor() isnot fast enough or if it exhausts memory.

Note: See also cFactor() for factoring all theway to complex coefficients in pursuit of linear factors.

factor(rationalNumber ) returns the rationalnumber factored into primes. Forcomposite numbers, the computing timegrows exponentially with the number of digits in the second-largest factor. Forexample, factoring a 30-digit integer couldtake more than a day, and factoring a 100-digit number could take more than acentury.

To stop a calculation manually,


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factor() Catalog >

• Handheld: Hold down thec key and

press· repeatedly.

• Windows®: Hold down the F12 key andpress Enter repeatedly.

• Macintosh®: Hold down the F5 key andpress Enter repeatedly.

• iPad®: The app displays a prompt. Youcan continue waiting or cancel.

If you merely want to determine if anumber is prime, use isPrime() instead. It ismuch faster, particularly if rationalNumber is not prime and if the second-largest factorhas 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 betweenlowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom.

For P( X ≤ upBound ), set lowBound = 0.

Fill Catalog >

Fill Expr, matrixVar ⇒ matrix

Replaces each element in variablematrixVar with Expr .

matrixVar must already exist.

Fill Expr, listVar ⇒ list

Replaces each element in variable listVar

with Expr .

listVar must already exist.



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FiveNumSummary Catalog >

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

Provides an abbreviated version of the 1-variablestatistics on list X . A summary of results is stored inthe stat.results variable. (See page 168.)

X represents a list containing the data.

Freq is an optional list of frequency values.

TI Nspire cx CAS Guide

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