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Texas Instruments N3/TBL/1L1/J Reference Manual
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Texas Instruments N3/TBL/1L1/J Reference Manual

Texas Instruments N3/TBL/1L1/J Reference Manual

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TI-Nspire™ Reference Guide
This guidebook applies to TI-Nspire™ software version 4.5. To obtain the latest version
of the documentation, go to education.ti.com/go/download.

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Summary of Contents for Texas Instruments N3/TBL/1L1/J

  • Page 1 TI-Nspire™ Reference Guide This guidebook applies to TI-Nspire™ software version 4.5. To obtain the latest version of the documentation, go to education.ti.com/go/download.
  • Page 2 "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 the...
  • Page 3 Contents Important Information Expression Templates Alphabetical Listing...
  • Page 4 Symbols Empty (Void) Elements Shortcuts for Entering Math Expressions EOS™ (Equation Operating System) Hierarchy Constants and Values Error Codes and Messages Warning Codes and Messages Support and Service Texas Instruments Support and Service Service and Warranty Information Index...

  • Page 5: Expression Templates

    Expression Templates Expression templates give you an easy way to enter math expressions in standard mathematical notation. When you insert a template, it appears on the entry line with small blocks at positions where you can enter elements. A cursor shows which element you can enter.
  • Page 6 keys Nth root template keys e exponent template Example: Natural exponential e raised to a power See also e^() , page 43. Note: Log template Example: Calculates log to a specified base. For a default of base 10, omit the base. See also log() , page 86.

  • Page 7: Absolute Value Template

    Piecewise template (N-piece) Catalog > See also piecewise() , page 110. Note: System of 2 equations template Catalog > Example: Creates a system of two linear equations. To add a row to an existing system, click in the template and repeat the template. Note: See also system() , page 150.
  • Page 8 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 is the number of seconds. ss.ss Matrix template (2 x 2) Catalog >...

  • Page 9: First Derivative Template

    Matrix template (m x n) Catalog > If you create a matrix with a large Note: number of rows and columns, it may take a few moments to appear. Sum template ( Σ Catalog > Example: See also Σ () ( sumSeq ), page 186. Note: Product template ( Π...

  • Page 10: Definite Integral Template

    Second derivative template Catalog > The second derivative template can be used to calculate second derivative at a point numerically, using auto differentiation methods. See also d() (derivative) , page 184. Note: Definite integral template Catalog > Example: The definite integral template can be used to calculate the definite integral numerically, using the same method as nInt See also nInt() , page 101.

  • Page 11: Alphabetical Listing

    Alphabetical Listing Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, page 173. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined. Catalog >...
  • Page 12 Catalog > amortTbl() 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 Σ...
  • Page 13 Catalog > angle() Returns the angle of the argument, interpreting the argument as a complex number. In Gradian angle mode: In Radian angle mode: angle( List1 ) ⇒ list angle( Matrix1 ) ⇒ matrix Returns a list or matrix of angles of the elements in List1 or Matrix1 , interpreting each element as a complex number that represents a two-dimensional rectangular...
  • Page 14 Output variable Description stat.MSError Mean square for the errors stat.sp Pooled standard deviation stat.xbarlist Mean of the input of the lists stat.CLowerList 95% confidence intervals for the mean of each input list stat.CUpperList 95% confidence intervals for the mean of each input list Catalog >...
  • Page 15 Output variable Description 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. F col 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...
  • Page 16 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 Standard deviation of the error keys Ans ⇒ value Returns the result of the most recently evaluated expression. Catalog >...
  • Page 17 Catalog > ► approxFraction() You can insert this function from the Note: computer keyboard by typing ... ) . @>approxFraction( approxRational() Catalog > approxRational( Value [, Tol ]) ⇒ value approxRational( List [, Tol ]) ⇒ list approxRational( Matrix [, Tol ]) ⇒ matrix Returns the argument as a fraction using a tolerance of Tol .
  • Page 18 ⁻ ¹ arcsec() See sec (), page 133 . ⁻ ¹ arcsech() See sech (), page 133 . ⁻ ¹ arcsin() See sin (), page 141 . ⁻ ¹ arcsinh() See sinh (), page 142 . ⁻ ¹ arctan() See tan (), page 152 .
  • Page 19 Catalog > avgRC() avgRC( Expr1 , Var [ =Value ] [, Step ]) ⇒ expression avgRC( Expr1 , Var [ =Value ] [, List1 ]) ⇒ list avgRC( List1 , Var [ =Value ] [, Step ]) ⇒ list avgRC( Matrix1 , Var [ =Value ] [, Step ]) ⇒ matrix Returns the forward-difference quotient (average rate of change).
  • Page 20 Catalog > bal() • If you omit , it defaults to =tvmPmt PmtAt • If you omit , it defaults to PmtAt • The defaults for , and are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding.
  • Page 21 Catalog > ► Base2 If you enter a decimal integer that is outside the range of a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. Consider the following examples of values outside the range.
  • Page 22 Catalog > ► 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.
  • Page 23 Catalog > binomPdf() Computes a probability for the discrete binomial distribution with n number of trials and probability p of success on each trial. Catalog > ceiling( Value1 ) ⇒ value Returns the nearest integer that is ≥ the argument. The argument can be a real or a complex number.
  • Page 24 Catalog > centralDiff() When using List1 or Matrix1 , the operation gets mapped across the values in the list or across the matrix elements. See also avgRC() . Note: char() Catalog > char( Integer ) ⇒ character Returns a character string containing the character numbered Integer from the handheld character set.
  • Page 25 Catalog > χ Cdf() chi2Cdf( lowBound , upBound , df ) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the χ distribution probability between lowBound and upBound for the specified degrees of freedom df . For P( X ≤...
  • Page 26 Catalog > χ Pdf() Computes the probability density function (pdf) for the χ 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 27 Catalog > colAugment() 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 >...
  • Page 28 Catalog > constructMat() constructMat ( Expr , Var1 , Var2 , numRows , numCols ) ⇒ matrix Returns a matrix based on the arguments. Expr is an expression in variables Var1 and Var2 . Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2 .
  • Page 29 Catalog > corrMat() corrMat( List1 , List2 [,…[, List20 ]]) Computes the correlation matrix for the augmented matrix [ List1, List2 , ..., List20 ]. µ cos() cos( Value1 ) ⇒ value In Degree angle mode: cos( List1 ) ⇒ list Value1 returns the cosine of the cos(...
  • Page 30 µ cos() Then A = X B X ⁻¹ and f(A) = X f(B) X ⁻¹ . For example, cos(A) = X cos(B) X ⁻¹ where: cos(B) = All computations are performed using floating-point arithmetic. µ ⁻ ¹ In Degree angle mode: cos ⁻¹...
  • Page 31 Catalog > cosh() cosh( Value1 ) ⇒ value cosh( List1 ) ⇒ list Value1 returns the hyperbolic cosine cosh( of the argument. ( List1 ) returns a list of the hyperbolic cosh cosines of each element of List1 . ( squareMatrix1 ) ⇒ squareMatrix cosh In Radian angle mode: Returns the matrix hyperbolic cosine of...
  • Page 32 µ cot() In Degree angle mode: cot( Value1 ) ⇒ value cot( List1 ) ⇒ list Returns the cotangent of Value1 or returns a list of the cotangents of all elements in In Gradian angle mode: List1 . The argument is interpreted as a Note: degree, gradian or radian angle, according to the current angle mode setting.
  • Page 33 ⁻ ¹ Catalog > coth coth ⁻¹ ( Value1 ) ⇒ value coth ⁻¹ ( List1 ) ⇒ list Returns the inverse hyperbolic cotangent of Value1 or returns a list containing the inverse hyperbolic cotangents of each element of List1 . You can insert this function from the Note: keyboard by typing arccoth( ...
  • Page 34 Catalog > countif() example, 3 counts only those elements in Counts the number of elements equal to List that simplify to the value 3. “def.” • A Boolean expression containing the symbol ? as a placeholder for each element. For example, ?<5 counts only List those elements in that are less than...
  • Page 35 Catalog > crossP() 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 .
  • Page 36 Catalog > csch() csch( Value1 ) ⇒ value csch( List1 ) ⇒ list Returns the hyperbolic cosecant of Value1 or returns a list of the hyperbolic cosecants of all elements of List1 . ⁻ ¹ Catalog > csch csch ⁻¹ ( Value ) ⇒ value csch ⁻¹...
  • Page 37 Catalog > CubicReg 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 38 Catalog > Cycle Cycle Function listing that sums the integers from 1 to 100 skipping 50. Transfers control immediately to the next iteration of the current loop ( For , While , or Loop is not allowed outside the three Cycle looping structures ( For , While , or Loop ).
  • Page 39 Catalog > dbd() You can enter the dates in either of two formats. The decimal placement differentiates between the date formats. MM.DDYY (format used commonly in the United States) DDMM.YY (format use commonly in Europe) ► Catalog > Expr1 ► DD ⇒ valueList1 In Degree angle mode: ►...
  • Page 40 Catalog > Define Define Function ( Param1 , Param2 , ...) = Expression Defines the variable Var or the user- defined function Function . Parameters, such as Param1 , provide placeholders for passing arguments to the function. When calling a user-defined function, you must supply arguments (for example, values or variables) that correspond to the parameters.
  • Page 41 Catalog > Define See also Define LibPriv , page 37, and Note: , page 37. Define LibPub Define LibPriv Catalog > Define LibPriv Var = Expression Define LibPriv Function ( Param1 , Param2 , ...) = Expression Define LibPriv Function ( Param1 , Param2 , ...) = Func      Block EndFunc...
  • Page 42 Catalog > Define LibPub See also Define , page 35, and Define Note: , page 37. LibPriv deltaList() List() , page 82 . Δ DelVar Catalog > DelVar Var1 [, Var2 ] [, Var3 ] ... DelVar Var . Deletes the specified variable or variable group from memory.
  • Page 43 Catalog > det() det( squareMatrix [, Tolerance ]) ⇒ expression Returns the determinant of squareMatrix . Optionally, any matrix element is treated as zero if its absolute value is less than Tolerance . This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value.
  • Page 44 Catalog > dim() 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.
  • Page 45 Catalog > DispAt The maximum number is set to 8 Note: since that matches a screen-full of lines on the handheld screen - as long as the lines don't have 2D math expressions. The exact number of lines depends on the content of the displayed information.
  • Page 46 Catalog > DispAt Error conditions: Error Message Description DispAt line number must be between 1 and 8 Expression evaluates the line number outside the range 1-8 (inclusive) Too few arguments The function or command is missing one or more arguments. No arguments Same as current 'syntax error' dialog Too many arguments...
  • Page 47 Catalog > dotP() 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.
  • Page 48 Catalog > eff() 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. See also nom() , page 102.
  • Page 49 Else See If, page 67 . Catalog > ElseIf If BooleanExpr1 Then      Block1 ElseIf BooleanExpr2 Then      Block2 ⋮ ElseIf BooleanExprN Then      BlockN EndIf ⋮ Note for entering the example: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
  • Page 50 EndWhile See While, page 166 . euler () Catalog > euler( Expr , Var , depVar , { Var0, VarMax }, Differential equation: depVar0 , VarStep [, eulerStep ]) ⇒ matrix y'=0.001*y*(100-y) and y(0)=10 euler( SystemOfExpr , Var , ListOfDepVars , { Var0 , VarMax },      ListOfDepVars0 , VarStep [, eulerStep ]) ⇒...
  • Page 51 Catalog > euler () VarStep is a nonzero number such that sign VarStep = sign( VarMax - Var0 ) and solutions are returned at Var0 + i•VarStep for all i =0,1,2,… such that Var0 + i•VarStep is in [ var0 , VarMax ] (there may not be a solution value at VarMax ).
  • Page 52 eval () Hub Menu 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 See also Get  (page 58), GetStr  (page Note: 65), and Send ...
  • Page 53 exp() exp( squareMatrix1 ) ⇒ squareMatrix Returns the matrix exponential of squareMatrix1 . This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.
  • Page 54 Catalog > ExpReg 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 55 Catalog > factor() press Enter repeatedly. • Macintosh®: Hold down the F5 key and press Enter repeatedly. • iPad®: The app displays a prompt. You can continue waiting or cancel. If you merely want to determine if a number is prime, use isPrime() instead. It is much faster, particularly if rationalNumber is not prime and if the second-largest factor has more than five digits.
  • Page 56 Catalog > FiveNumSummary 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 145.) X represents a list containing the data. Freq is an optional list of frequency values.
  • Page 57 Catalog > floor() floor( List1 ) ⇒ list floor( Matrix1 ) ⇒ matrix Returns a list or matrix of the floor of each element. See also ceiling() and int() . Note: Catalog > For Var , Low , High [, Step ]      Block EndFor Executes the statements in Block...
  • Page 58 Catalog > format() 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.
  • Page 59 Catalog > freqTable ► list() freqTable ► list( List1 , freqIntegerList ) ⇒ list Returns a list containing the elements from List1 expanded according to the frequencies in freqIntegerList . This function can be used for building a frequency table for the Data & Statistics application.
  • Page 60 Catalog > frequency() 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 196. Within the Lists & Spreadsheet application, you can use a range of cells in place of both arguments.
  • Page 61 Output variable Description stat.x1_bar Sample means of the data sequences in List 1 List 2 stat.x2_bar stat.n1, stat.n2 Size of the samples Catalog > Func Func Define a piecewise function:      Block EndFunc Template for creating a user-defined function. Block can be a single statement, a series of statements separated with the “:”...
  • Page 62 Catalog > gcd() 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 ≤...
  • Page 63 Hub Menu • 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.
  • Page 64 Catalog > getKey() getKey([0|1]) ⇒ returnString - allows a TI-Basic Description:getKey() Example: 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.
  • Page 65 Handheld Device/Emulator Desktop Return Value "del" "=" trig "trig" 0 through 9 "0" ... "9" Templates "template" Catalog "cat" "^" "square" / (division key) "/" * (multiply key) "*" "exp" 10^x "10power" "+" "-" "(" ")" "." "-" (negate sign) Enter Enter "enter"...
  • Page 66 Handheld Device/Emulator Desktop Return Value "pi" Flag no return "," Return "return" Space Space " " (space) Inaccessible Special Character Keys like The character is returned @,!,^, etc. Function Keys No returned character Special desktop control keys No returned character Inaccessible Other desktop keys that are Same character you get in...
  • Page 67 Event Device Desktop - TI-Nspire™ All Versions TI-Innovator™ Hub Support - Can successfully Same as the handheld connect/disconnect issue commands to the TI- Innovator™ Hub. After you exit the program the TI- Innovator™ Hub is still working with the handheld. getLangInfo() Catalog >...
  • Page 68 Catalog > getMode() getMode( ModeNameInteger ) ⇒ value getMode(0) ⇒ list ModeNameInteger returns a getMode( value representing the current setting of the ModeNameInteger mode. returns a list containing getMode(0) 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.
  • Page 69 Catalog > getNum() getNum( Fraction1 ) ⇒ value Transforms the argument into an expression having a reduced common denominator, and then returns its numerator. GetStr Hub Menu GetStr [ promptString ,] var [, statusVar ] For examples, see Get . GetStr [ promptString ,] func ( arg1 , ...argn ) [, ...
  • Page 70 Catalog > getVarInfo() getVarInfo() ⇒ matrix or string getVarInfo( LibNameString ) ⇒ matrix or string returns a matrix of information getVarInfo() (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".
  • Page 71 Catalog > Goto Goto labelName Transfers control to the label labelName . labelName must be defined in the same function using a Lbl instruction. Note for entering the example: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
  • Page 72 Catalog > If BooleanExpr evaluates to true, executes the single statement Statement or the block of statements Block before continuing execution. If BooleanExpr evaluates to false, continues execution without executing the statement or block of statements. Block can be either a single statement or a sequence of statements separated with the “:”...
  • Page 73 Catalog > ifFn() ifFn( BooleanExpr , Value_If_true [, Value_ If_false [, Value_If_unknown ]]) ⇒ expression, list, or matrix Test value of 1 is less than 2.5, so its Evaluates the boolean expression corresponding BooleanExpr (or each element from BooleanExpr ) and produces a result based Value_If_True element of 5 is copied to on the following rules:...
  • Page 74 Catalog > imag() 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. Indirection See #() , page 188 . inString() Catalog >...
  • Page 75 Catalog > intDiv() 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 ...
  • Page 76 Catalog > inv F () 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. Catalog > invBinom() invBinom Example: Mary and Kevin are playing a dice...
  • Page 77 Catalog > invNorm() 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 . Catalog > invt() invt( Area , df ) Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the...
  • Page 78 Catalog > irr() 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 <...
  • Page 79 Catalog > 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: instructions on entering multi-line program and function definitions, refer to the...
  • Page 80 Catalog > left() Returns the leftmost Num elements contained in List1 . If you omit Num , returns all of List1 . left( Comparison ) ⇒ expression Returns the left-hand side of an equation or inequality. libShortcut() Catalog > libShortcut( LibNameString , This example assumes a properly stored and ShortcutNameString refreshed library document named linalg2...
  • Page 81 Catalog > LinRegBx 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 or string category codes for the corresponding X and Y data.
  • Page 82 Catalog > LinRegMx 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 ≥...
  • Page 83 Catalog > LinRegtIntervals LinRegtIntervals X , Y [, F [,1, Xval [, CLev ]]] For Response. Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable.
  • Page 84 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, Prediction interval for a single observation stat.UpperPred] stat.MEPred Prediction interval margin of error stat.SEPred Standard error for prediction a + b XVal •...
  • Page 85 Catalog > LinRegtTest For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 196. Output variable Description stat.RegEqn Regression equation: a + b • stat.t -Statistic for significance test stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom stat.a, stat.b...
  • Page 86 Catalog > linSolve() 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 produces an “Argument and x=2,x) Error” result. Δ List() Catalog > Δ List( List1 ) ⇒ list You can insert this function from the Note: keyboard by typing deltaList( ...
  • Page 87 keys ln() Returns the natural logarithm of the argument. If complex format mode is Real: For a list, returns the natural logarithms of the elements. If complex format mode is Rectangular: ln( squareMatrix1 ) ⇒ squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix natural logarithm of squareMatrix1 .
  • Page 88 Catalog > LnReg Category is a list of numeric or string 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.
  • Page 89 Catalog > Local 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. Local variables save memory because Note: they only exist temporarily.
  • Page 90 keys log() ⇒ value Value1 [ Value2 ] log( ⇒ list List1 [ Value2 ] log( Returns the base -Value2 logarithm of the first argument. See also Log template , page 2. Note: If complex format mode is Real: For a list, returns the base -Value2 logarithm of the elements.
  • Page 91 Catalog > Logistic 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 ≥...
  • Page 92 Catalog > LogisticD 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.
  • Page 93 Catalog > Loop 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: instructions on entering multi-line program and function definitions, refer to the...
  • Page 94 Catalog > The LU factorization algorithm uses partial pivoting with row interchanges. list() Catalog > ► mat ► list( Matrix ) ⇒ list Returns a list filled with the elements in Matrix . The elements are copied from Matrix row by row. You can insert this function from the Note: computer keyboard by typing mat@>list...
  • Page 95 Catalog > mean() 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 In Rectangular vector format: Returns a row vector of the means of all the columns in Matrix1 .
  • Page 96 Catalog > MedMed MedMed X , Y [, Freq ] [, Category , Include ]] Computes the median-median line y = (m • x+b) on lists X and Y with frequency Freq . A summary of results is stored in the stat.results variable.
  • Page 97 Catalog > mid() mid( sourceString , Start [, Count ]) ⇒ string Returns Count characters from character string sourceString , beginning with character number Start . If Count is omitted or is greater than the dimension of sourceString , returns all characters from sourceString , beginning with character number Start .
  • Page 98 Catalog > min() min( Matrix1 ) ⇒ matrix Returns a row vector containing the minimum element of each column in Matrix1 . See also max(). Note: mirr() Catalog > mirr ( financeRate , reinvestRate , CF0 , CFList [, CFFreq ]) Financial function that returns the modified internal rate of return of an investment.
  • Page 99 Catalog > mod() mod(x,0) = x mod(x,y) = x − y floor(x/y) When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument. If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements.
  • Page 100 Output variable Description stat.RegEqn Regression Equation: b0+b1 • x1+b2 • x2+ ... stat.b0, stat.b1, ... Regression coefficients stat.R Coefficient of multiple determination stat. List List = b0+b1 • x1+ ... stat.Resid Residuals from the regression Catalog > MultRegIntervals MultRegIntervals Y , X1 [, X2 [, X3 ,…[, X10 ]]], XValList [, CLevel ] Computes a predicted y-value, a level C prediction interval for a single observation,...
  • Page 101 Catalog > MultRegTests 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.
  • Page 102 Output Description variable 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 keys nand...
  • Page 103 Catalog > nCr() nCr( Value1 , Value2 ) ⇒ expression For integer Value1 and Value2 with Value1 ≥ Value2≥ 0, is the number of nCr() combinations of Value1 things taken Value2 at a time. (This is also known as a binomial coefficient.) nCr( Value , 0 ) ⇒...
  • Page 104 Catalog > nDerivative() The nDerivative() algorithm has a Note: limitiation: it works recursively through the unsimplified expression, computing the numeric value of the first derivative (and second, if applicable) and the evaluation of each subexpression, which may lead to an unexpected result.
  • Page 105 Catalog > nfMax() 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.
  • Page 106 Catalog > nInt() 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. 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...
  • Page 107 keys 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 ) ⇒...
  • Page 108 Catalog > Returns the one’s complement of a real Important: Zero, not the letter O. integer. Internally, Integer1 is converted to a signed, 64-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement. Results In Bin base mode: are displayed according to the Base mode.
  • Page 109 Catalog > nPr() Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. Catalog > npv() npv( InterestRate , CFO , CFList [, CFFreq ]) Financial function that calculates net present value;...
  • Page 110 Catalog > nSolve() 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. attempts to determine either one nSolve() point where the residual is zero or two relatively close points where the residual...
  • Page 111 Catalog > OneVar 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.
  • Page 112 Catalog > Note for entering the example: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Integer1 or Integer2 ⇒ integer In Hex base mode: Compares two real integers bit-by-bit using an or operation. Internally, both integers are converted to signed, 64-bit binary Important: Zero, not the letter O.
  • Page 113 Catalog > ► Rx() Returns the equivalent x-coordinate of the (r,  θ ) pair. The θ argument is interpreted as Note: either a degree, gradian or radian angle, according to the current angle mode. If the argument is an expression, you can use  ° ,  to override the angle mode setting temporarily.
  • Page 114 Catalog > PassErr Note for entering the example: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Catalog > piecewise() piecewise( Expr1 [, Cond1 [, Expr2 [, Cond2 [, … ]]]]) Returns definitions for a piecewise function in the form of a list.
  • Page 115 Catalog > ► Polar Displays vector in polar form [r ∠ θ ]. The vector must be of dimension 2 and can be a row or a column. is a display-format Note: ► Polar instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans .
  • Page 116 Catalog > polyRoots() 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: { }.
  • Page 117 Catalog > PowerReg For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 196. Output Description variable stat.RegEqn Regression equation: a • stat.a, stat.b Regression coefficients stat.r Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (ln(x), ln(y)) stat.Resid...
  • Page 118 Catalog > Prgm prodSeq() Π (), page 185 . Product (PI) (), page 185 . Π Catalog > product() product( List [, Start [, End ]]) ⇒ expression Returns the product of the elements contained in List . Start and End are optional.
  • Page 119 Catalog > propFrac() rational_expression , Var returns propFrac( 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.
  • Page 120 Catalog > tolerance is calculated as: − • max(dim( Matrix • rowNorm Matrix The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram-Schmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix .
  • Page 121 stat.RegEqn Regression equation: a • • stat.a, Regression coefficients stat.b, stat.c stat.R 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...
  • Page 122 Output variable Description stat.RegEqn Regression equation: a • • • • stat.a, stat.b, Regression coefficients stat.c, stat.d, stat.e stat.R 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...
  • Page 123 Catalog > ► Pr() You can insert this function from the Note: computer keyboard by typing R@>Pr( ... ) . Catalog > ► ⇒ value Value1►Rad In Degree angle mode: Converts the argument to radian angle measure. You can insert this operator from the Note: In Gradian angle mode: computer keyboard by typing @>Rad .
  • Page 124 Catalog > randInt() 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...
  • Page 125 Catalog > randPoly() 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. Catalog >...
  • Page 126 Catalog > ► Rect Vector ► Rect You can insert this operator from the Note: 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: ►...
  • Page 127 Catalog > ref() /· • If you use or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • is omitted or not used, the default tolerance is calculated as: − • max(dim( Matrix1 •...
  • Page 128 Catalog > RefreshProbeVars If status=0 Then StatusVar Status Value Disp "ready" statusVar Normal (continue with the program) For n,1,50 The Vernier DataQuest™ RefreshProbeVars status application is in data collection mode. temperature:=meter.temperature statusVar Note: The Vernier DataQuest™ Disp "Temperature: application must be in meter ",temperature mode for this command to work.
  • Page 129 Catalog > remain() As a consequence, note that remain( − x,y ) − x,y ) . The result is either zero or it remain( has the same sign as the first argument. See also mod() , page 94. Note: Request Catalog >...
  • Page 130 Catalog > Request 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 Result after entering x^3+3x+1 and selecting OK : The program can then use the defined...
  • Page 131 Catalog > RequestStr To stop a program that contains a command inside an infinite loop: RequestStr • Handheld: Hold down the key and · press repeatedly. • Windows®: Hold down the F12 key and press Enter repeatedly. • Macintosh®: Hold down the F5 key and Result after selecting OK (Note that the press Enter repeatedly.
  • Page 132 Catalog > right() right( Comparison ) ⇒ expression Returns the right side of an equation or inequality. rk23 () Catalog > rk23( Expr , Var , depVar , { Var0 , VarMax }, Differential equation: depVar0 , VarStep [, diftol ]) ⇒ matrix y'=0.001*y*(100-y) and y(0)=10 rk23( SystemOfExpr , Var , ListOfDepVars , { Var0 , VarMax }, ListOfDepVars0 ,...
  • Page 133 Catalog > rk23 () { Var0 , VarMax } is a two-element list that tells the function to integrate from Var0 to VarMax . ListOfDepVars0 is a list of initial values for dependent variables. If VarStep evaluates to a nonzero number: sign( VarStep ) = sign( VarMax - Var0 ) and solutions are returned at Var0 +i* VarStep for all i=0,1,2,…...
  • Page 134 Catalog > rotate() If #ofRotations is positive, the rotation is to In Hex base mode: 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.
  • Page 135 Catalog > round() Display digits mode may affect how Note: 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.
  • Page 136 Catalog > rowSwap() rowSwap( Matrix1 , rIndex1 , rIndex2 ) ⇒ matrix Returns Matrix1 with rows rIndex1 and rIndex2 exchanged. Catalog > rref() rref( Matrix1 [, Tol ]) ⇒ matrix Returns the reduced row echelon form of Matrix1 . Optionally, any matrix element is treated as zero if its absolute value is less than Tol .
  • Page 137 µ sec() The argument is interpreted as a Note: degree, gradian or radian angle, according to the current angle mode setting. You can use ° ,  , or to override the angle mode temporarily. µ ⁻ ¹ In Degree angle mode: sec ⁻¹...
  • Page 138 Send Hub Menu Send exprOrString1 [, exprOrString2 ] ... Example: Turn on the blue element of the built-in RGB LED for 0.5 seconds. Programming command: Sends one or more TI-Innovator™ Hub commands to a connected hub. exprOrString must be a valid TI-Innovator™ Example: Request the current value of the Hub Command.
  • Page 139 Catalog > seqGen() seqGen( Expr , Var , depVar , { Var0 , Generate the first 5 terms of the sequence VarMax }[, ListOfInitTerms /2, with (1)= 2 and = 1 . VarStep [, VarStep [, CeilingValue ]]]) ⇒ list Generates a list of terms for sequence depVar ( Var )= Expr as follows: Increments independent variable Var from Var0...
  • Page 140 Catalog > seqn() 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.
  • Page 141 Catalog > setMode() The current mode settings are passed Note: 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: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
  • Page 142 Catalog > shift() If #ofShifts is positive, the shift is to the Important: To enter a binary or left. If #ofShifts is negative, the shift is to hexadecimal number, always use the 0b or the right. The default is − 1 (shift right one 0h prefix (zero, not the letter O).
  • Page 143 Catalog > shift() Characters introduced at the beginning or end of string by the shift are set to a space. sign() Catalog > sign( Value1 ) ⇒ value sign( List1 ) ⇒ list sign( Matrix1 ) ⇒ matrix For real and complex Value1 , returns If complex format mode is Real: Value1 ...
  • Page 144 Catalog > simult() using floating-point arithmetic. • is omitted or not used, the default tolerance is calculated as: − • max(dim( coeffMatrix • rowNorm( coeffMatrix simult( coeffMatrix , constMatrix [, Tol ]) ⇒ Solve: matrix   x + 2y = 1 3x + 4y = −...
  • Page 145 µ sin() squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. µ ⁻ ¹ In Degree angle mode: sin ⁻¹ ( Value1 ) ⇒ value sin ⁻¹ ( List1 ) ⇒ list ⁻¹ Value1 returns the angle whose sine is Value1 .
  • Page 146 Catalog > sinh() sinh( squareMatrix1 ) ⇒ squareMatrix In Radian angle mode: Returns the matrix hyperbolic sine of squareMatrix1 . This is not the same as calculating the hyperbolic sine of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable.
  • Page 147 Catalog > SinReg 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.
  • Page 148 Catalog > SortA SortA List1 [, List2 ] [, List3 ]... SortA Vector1 [, Vector2 ] [, Vector3 ]... Sorts the elements of the first argument in ascending order. If you include additional arguments, sorts the elements of each so that their new positions match the new positions of the elements in the first argument.
  • Page 149 Catalog > ► Sphere ► is a display-format Note: Sphere instruction, not a conversion function. You can use it only at the end of an entry line. Catalog > sqrt() sqrt( Value1 ) ⇒ value sqrt( List1 ) ⇒ list Returns the square root of the argument.
  • Page 150 stat.a stat.dfDenom stat.MedianY stat.Q3X stat.SSBlock stat.AdjR ² stat.dfBlock stat.MEPred stat.Q3Y stat.SSCol stat.b stat.dfCol stat.MinX stat.r stat.SSX ² stat.b0 stat.dfError stat.MinY stat.r stat.SSY stat.b1 stat.dfInteract stat.MS stat.RegEqn stat.SSError stat.b2 stat.dfReg stat.MSBlock stat.Resid stat.SSInteract stat.b3 stat.dfNumer stat.MSCol stat.ResidTrans stat.SSReg σ stat. stat.b4 stat.dfRow stat.MSError stat.SSRow...
  • Page 151 Catalog > stDevPop() stDevPop( List [, freqList ]) ⇒ expression In Radian angle and auto modes: Returns the population standard deviation of the elements in List . Each freqList element counts the number of consecutive occurrences of the corresponding element in List . Note: List must have at least two elements.
  • Page 152 Catalog > stDevSamp() 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 . Matrix1 must have at least two rows.
  • Page 153 Catalog > subMat() subMat( Matrix1 [, startRow ][, startCol ][, endRow ][, endCol ]) ⇒ matrix Returns the specified submatrix of Matrix1 . Defaults: startRow =1, startCol =1, endRow =last row, endCol =last column. Sum (Sigma) (), page 186 . Σ...
  • Page 154 Catalog > sumIf() 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.
  • Page 155 Catalog > T (transpose) Matrix1 T ⇒ matrix Returns the complex conjugate transpose of Matrix1 . You can insert this operator from the Note: computer keyboard by typing @t . µ tan() In Degree angle mode: Value1 ) ⇒ value tan( List1 ) ⇒...
  • Page 156 µ tan() squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. µ ⁻ ¹ tan ⁻¹ ( Value1 ) ⇒ value In Degree angle mode: tan ⁻¹ ( List1 ) ⇒ list ⁻¹ returns the angle whose Value1 tangent is Value1 . In Gradian angle mode: ⁻¹...
  • Page 157 Catalog > tanh() Returns the matrix hyperbolic tangent of squareMatrix1 . This is not the same as calculating the hyperbolic tangent of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.
  • Page 158 Catalog > tCdf() For P(X ≤ upBound ), set lowBound = ⁻ 9 E 999. Catalog > Text Text promptString [, DispFlag ] Define a program that pauses to display each of five random numbers in a dialog Programming command: Pauses the box.
  • Page 159 Catalog > tInterval Computes a t confidence interval. A summary of results is stored in the stat.results variable. (See page 145.) For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 196. Output variable Description stat.CLower, stat.CUpper Confidence interval for an unknown population mean...
  • Page 160 Output variable Description stat.ME Margin of error stat.df Degrees of freedom stat. v 1, stat. v 2 Sample means of the data sequences from the normal random distribution stat. σ x1, stat. σ Sample standard deviations for List 1 List 2 stat.n1, stat.n2 Number of samples in data sequences stat.sp...
  • Page 161 Catalog >      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 162 Catalog > tTest 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...
  • Page 163 Catalog > tTest_2Samp Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See page 145.) Test H : μ 1 = μ 2, against one of the following: For H : μ 1< μ 2, set Hypoth <0 For H : μ...
  • Page 164 Catalog > tvmI() Financial function that calculates the interest rate per year. Arguments used in the TVM functions Note: are described in the table of TVM arguments, page 161. See also amortTbl() , page 7. Catalog > tvmN() tvmN( I , PV , Pmt , FV ,[ PpY ],[ CpY ],[ PmtAt ]) ⇒...
  • Page 165 Description Data type argument* Number of payment periods real number Annual interest rate real number Present value real number Payment amount real number Future value real number Payments per year, default=1 integer > 0 Compounding periods per year, default=1 integer > 0 PmtAt Payment due at the end or beginning of each period, integer (0=end,...
  • Page 166 Catalog > TwoVar An empty (void) element in any of the lists X , Freq , or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists.
  • Page 167 Output variable Description stat.MaxY Maximum of y values stat. Σ (x- v ) Sum of squares of deviations from the mean of x stat. Σ (y- w ) Sum of squares of deviations from the mean of y Catalog > unitV() unitV( Vector1 ) ⇒...
  • Page 168 Catalog > varPop() 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 196. Catalog > varSamp() varSamp( List [, freqList ]) ⇒ expression Returns the sample variance of List .
  • Page 169 Catalog > Wait Suspends execution for a period of timeInSeconds seconds. To wait 1/2 second: is particularly useful in a program that Wait Wait 0.5 needs a brief delay to allow requested data to become available. To wait 1.3 seconds using the variable The argument timeInSeconds must be an seccount expression that simplifies to a decimal value...
  • Page 170 Catalog > when() when( Condition , trueResult [, falseResult ] [, unknownResult ]) ⇒ expression Returns trueResult , falseResult , or unknownResult , depending on whether Condition is true, false, or unknown. Returns the input if there are too few arguments to specify the appropriate result.
  • Page 171 Catalog > 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.
  • Page 172 Catalog > zInterval Computes a z confidence interval. A summary of results is stored in the stat.results variable. (See page 145.) For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 196. Output variable Description stat.CLower, stat.CUpper Confidence interval for an unknown population mean...
  • Page 173 Catalog > zInterval_2Prop Computes a two-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 145.) x1 and x2 are non-negative integers. For information on the effect of empty elements in a list, see “Empty (Void) Elements,”...
  • Page 174 Output variable Description stat. x 1- x 2 Sample means of the data sequences from the normal random distribution stat.ME Margin of error stat. x 1, stat. x 2 Sample means of the data sequences from the normal random distribution stat.
  • Page 175 Catalog > zTest_1Prop Output variable Description stat.p0 Hypothesized population proportion stat.z Standard normal value computed for the proportion stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat. Ç Estimated sample proportion stat.n Size of the sample Catalog >...
  • Page 176 Catalog > zTest_2Samp [, Freq2 [, Hypoth ]]] (Data list input) zTest_2Samp σ , σ ,v 1 , n1 ,v 2 , n2 [, Hypoth ] (Summary stats input) Computes a two-sample z test. A summary of results is stored in the stat.results variable.
  • Page 177 Symbols + (add) Value1 + Value2 ⇒ value 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.
  • Page 178 (subtract) − 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. Value − List1 ⇒ list List1 − Value ⇒ list Subtracts each List1 element from Value or subtracts Value from each List1 element, and returns a list of the results.
  • Page 179 (multiply) • Value •List1 ⇒ list List1•Value ⇒ list Returns a list containing the products of Value and each element in List1 . Value •Matrix1 ⇒ matrix Matrix1•Value ⇒ matrix Returns a matrix containing the products of Value and each element in Matrix1 . Use .
  • Page 180 ^ (power) Value1 ^ Value2⇒ value List1 ^ List2 ⇒ list Returns the first argument raised to the power of the second argument. See also Exponent template , page 1. Note: For a list, returns the elements in List1 raised to the power of the corresponding elements in List2 .
  • Page 181 (square) ⇒ value Value1 Returns the square of the argument. ⇒ list List1 Returns a list containing the squares of the elements in List1 . ⇒ matrix squareMatrix1 Returns the matrix square of squareMatrix1 . This is not the same as calculating the square of each element.
  • Page 182 keys (dot mult.) • Matrix1 . • Matrix2⇒ matrix Value . • Matrix1 ⇒ matrix • Matrix2 returns a matrix that is Matrix1 the product of each pair of corresponding elements in Matrix1 and Matrix2 . Value • Matrix1 returns a matrix containing the products of Value and each element in Matrix1.
  • Page 183 (negate) − Returns the negation of the argument. In Bin base mode: For a list or matrix, returns all the elements Important: Zero, not the letter O. negated. If the argument is a binary or hexadecimal integer, the negation gives the two’s complement.
  • Page 184 = (equal) Note for entering the example: instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. keys (not equal) ≠ Expr1≠Expr2 ⇒ Boolean expression See “=” (equal) example. List1≠List2 ⇒ Boolean list Matrix1≠Matrix2 ⇒...
  • Page 185 keys < (less than) Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. keys ≤ (less or equal) Expr1≤Expr2 ⇒ Boolean expression See “=” (equal) example. List1≤List2 ⇒ Boolean list Matrix1 ≤Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be less than or equal to Expr2 .
  • Page 186 keys (greater or equal) ≥ Expr1≥Expr2 ⇒ Boolean expression See “=” (equal) example. List1≥List2 ⇒ Boolean list Matrix1 ≥Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be greater than or equal to Expr2 . Returns false if Expr1 is determined to be less than Expr2 .
  • Page 187 ⇔ keys (logical double implication, XNOR) 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.
  • Page 188 Catalog > () (derivative) d ( Expr1 , Var [, Order ]) | Var=Value ⇒ value d ( Expr1 , Var [, Order ]) ⇒ value d ( List1 , Var [, Order ]) ⇒ list d ( Matrix1 , Var [, Order ]) ⇒ matrix Except when using the first syntax, you must store a numeric value in variable Var before evaluating d () .
  • Page 189 Catalog > ∫ () (integral) ∫ ( Expr1 , Var , Lower , Upper ) ⇒ value Returns the integral of Expr1 with respect to the variable Var from Lower to Upper . Can be used to calculate the definite integral numerically, using the same method as nInt().
  • Page 190 Π () (prodSeq) Catalog > The product formulas used are derived from the following reference: Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science . Reading, Massachusetts: Addison-Wesley, 1994. Catalog > Σ () (sumSeq) Σ...
  • Page 191 Catalog > Σ Int() 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. PV , Pmt , FV , PpY , CpY , and PmtAt are described in the table of TVM arguments, page 161.
  • Page 192 Catalog > Σ Prn() • If you omit , it defaults to =tvmPmt PmtAt • If you omit , it defaults to PmtAt • The defaults for , and are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding.
  • Page 193 (scientific notation) You can insert this operator from the Note: computer keyboard by typing @E . for example, type 2.3@E4 to enter 2.3 E 4. ¹ (gradian) ⇒ expression Expr1 In Degree, Gradian or Radian mode: ⇒ list List1 ⇒ matrix Matrix1 This function gives you a way to specify a gradian angle while in the Degree or Radian...
  • Page 194 ¹ (radian) Hint: Use if you want to force radians in a function definition regardless of the mode that prevails when the function is used. You can insert this symbol from the Note: computer keyboard by typing @r . ¹ (degree) °...
  • Page 195 ∠ keys (angle) [ Radius , ∠ θ_Angle ] ⇒ vector In Radian mode and vector format set to: (polar input) rectangular [ Radius , ∠ θ_Angle , Z_Coordinate ] ⇒ vector (cylindrical input) [ Radius , ∠ θ_Angle , ∠ θ_Angle ] ⇒ vector cylindrical (spherical input) Returns coordinates as a vector depending...
  • Page 196 Catalog > 10^() 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.
  • Page 197 keys | (constraint operator) • 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 .
  • Page 198 (store) → You can insert this operator from the Note: keyboard by typing =: as a shortcut. For example, type pi/4 =: myvar . keys := (assign) Var := Value Var := List Var := Matrix Function ( Param1 ,...) := Expr Function ( Param1 ,...) := List Function ( Param1 ,...) := Matrix If variable Var does not exist, creates Var...
  • Page 199 keys, keys 0b, 0h 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 In Bin base mode: prefix, a number is treated as decimal (base 10).

  • Page 200: Empty (Void) Elements

    Empty (Void) Elements When analyzing real-world data, you might not always have a complete data set. TI-Nspire™ 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 &...
  • Page 201 List arguments containing void elements In regressions, a void in an X or Y list introduces a void for the corresponding element of the residual. An omitted category in regressions introduces a void for the corresponding element of the residual. A frequency of 0 in regressions introduces a void for the corresponding element of the residual.

  • Page 202: Shortcuts For Entering Math Expressions

    Shortcuts for Entering Math Expressions Shortcuts let you enter elements of math expressions by typing instead of using the Catalog or Symbol Palette. For example, to enter the expression √ 6, you can type sqrt · on the entry line. When you press , the expression sqrt(6) is changed to √...
  • Page 203 To enter this: Type this shortcut: (radians) ° (degrees) (gradians) ∠ (angle) @< ► (conversion) @> , and , @>approxFraction() , and ► Decimal ► approxFraction() @>Decimal so on. so on. Shortcuts for Entering Math Expressions...

  • Page 204: Eos™ (Equation Operating System) Hierarchy

    EOS™ (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOS™) that is used by the TI-Nspire™ 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.
  • Page 205 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 ).” Because the TI-Nspire™...
  • Page 206 Constants and Values The following table lists the constants and their values that are available when performing unit conversions. They can be typed in manually or selected from the list in Utilities > Unit Conversions (Handheld: Press Constants Constant Name Value Speed of light 299792458 _m/_s...

  • Page 207: Error Codes And Messages

    Error Codes and Messages When an error occurs, its code is assigned to variable errCode . User-defined programs and functions can examine errCode to determine the cause of an error. For an example of using errCode , See Example 2 under the Try command, page 157. Some error conditions apply only to TI-Nspire™ CAS products, and some apply Note: only to TI-Nspire™...
  • Page 208 Error Description code Break key was pressed during a long calculation or during program execution. 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.
  • Page 209 Error Description code Inconsistent units Index out of range Indirection string is not a valid variable name Undefined Ans Either the previous calculation did not create Ans, or no previous calculation was entered. Invalid assignment Invalid assignment value Invalid command Invalid for the current mode settings Invalid guess Invalid implied multiply...
  • Page 210 Error Description code Invalid table Invalid use of units Invalid variable name in a Local statement Invalid variable or function name Invalid variable reference Invalid vector syntax Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both ends.
  • Page 211 Error Description code To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. Overflow Program not found A program reference inside another program could not be found in the provided path during execution. Rand type functions not allowed in graphing Recursion too deep Reserved name or system variable Argument error...
  • Page 212 Error Description code 1000 Window variables domain 1010 Zoom 1020 Internal error 1030 Protected memory violation 1040 Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™ CAS. 1045 Unsupported operator. This operator requires Computer Algebra System. Try TI-Nspire™ CAS. 1050 Unsupported feature.
  • Page 213 Error Description code A pathname must be in the form , where: • part can have 1 to 16 characters. • part can have 1 to 15 characters. See the Library section in the documentation for more details. 1170 Invalid use of library pathname •...
  • Page 214 Error Description code Trigonometric conversion operators are not supported in Degree or Gradian angle modes. 1250 Argument Error Use a system of linear equations. Example of a system of two linear equations with variables x and y:   3x+7y=5   2y-5x=-1 1260 Argument Error: The first argument of nfMin or nfMax must be an expression in a single variable.

  • Page 215: Warning Codes And Messages

    Warning Codes and Messages You can use the warnCodes() function to store the codes of warnings generated by evaluating an expression. This table lists each numeric warning code and its associated message. For an example of storing warning codes, see warnCodes() , page 165. Warning code Message...
  • Page 216 Warning code Message 10022 Specifying appropriate lower and upper bounds might produce a solution. 10023 Scalar has been multiplied by the identity matrix. 10024 Result obtained using approximate arithmetic. 10025 Equivalence cannot be verified in EXACT mode. 10026 Constraint might be ignored. Specify constraint in the form "\" 'Variable MathTestSymbol Constant' or a conjunct of these forms, for example 'x<3 and x>-12' Warning Codes and Messages...

  • Page 217: Texas Instruments Support And Service

    Support and Service Texas Instruments Support and Service General Information: North and South America education.ti.com Home Page: education.ti.com/support KnowledgeBase and e-mail inquiries: Phone: (800) TI-CARES / (800) 842-2737 For North and South America and U.S. Territories https://education.ti.com/en/us/customer- International contact information:...
  • Page 218 Index ^, power |, constraint operator -, subtract ′ ′ minute notation !, factorial " +, add ", second notation ≠, not equal #, indirection ≤, less than or equal #, indirection operator ≥, greater than or equal >, greater than =, equal %, percent ∏...
  • Page 219 ►Cylind, display as cylindrical vector add, + ►DD, display as decimal angle amortization table, amortTbl( ) ►Decimal, display result as decimal amortTbl( ), amortization table ►DMS, display as and, Boolean operator degree/minute/second angle( ), angle ►Grad, convert to gradian angle angle, angle( ) ►Polar, display as polar vector ANOVA, one-way variance analysis ►Rad, convert to radian angle ANOVA2way, two-way variance...
  • Page 220 cosine, cos( ) cot⁻¹( ), arccotangent cot( ), cotangent cotangent, cot( ) coth⁻¹( ), hyperbolic arccotangent coth( ), hyperbolic cotangent count days between dates, dbd( ) Cdf( ) count items in a list conditionally , ceiling( ), ceiling countif( ) ceiling, ceiling( ) count items in a list, count( ) centralDiff( ) count( ), count items in a list char( ), character string countif( ), conditionally count items character string, char( )
  • Page 221 definite integral tCdf( ) template for tPdf( ) degree notation, ° χ²2way( ) degree/minute/second display, χ²Cdf( ) ►DMS χ²GOF( ) degree/minute/second notation χ²Pdf( ) delete divide, / void elements from list deleting addition, .+ variable, DelVar division, ./ deltaList() multiplication, .* DelVar, delete variable power, .^ delVoid( ), remove void elements product, dotP( ) derivatives...
  • Page 222 end while, EndWhile For, for EndTry, end try format string, format( ) EndWhile, end while format( ), format string EOS (Equation Operating System) fpart( ), function part equal, = fractions propFrac Equation Operating System (EOS) template for error codes and messages freqTable( ) errors and troubleshooting clear error, ClrErr frequency( ) pass error, PassErr...
  • Page 223 Goto, go to normal distribution) invt( ) gradian notation, g Invχ²( ) greater than or equal, ≥ iPart( ), integer part greater than, > irr( ), internal rate of return greatest common divisor, gcd( ) internal rate of return, irr( ) groups, locking and unlocking isPrime( ), prime test groups, testing lock status isVoid( ), test for void hexadecimal...
  • Page 224 differences in a list, Δlist( ) determinant, det( ) dot product, dotP( ) diagonal, diag( ) empty elements in dimension, dim( ) list to matrix, list►mat( ) dot addition, .+ matrix to list, mat►list( ) dot division, ./ maximum, max( ) dot multiplication, .* mid-string, mid( ) dot power, .^ minimum, min( ) dot subtraction, .- new, newList( )
  • Page 225 maximum, max( ) newMat( ), new matrix mean( ), mean nfMax( ), numeric function maximum mean, mean( ) nfMin( ), numeric function minimum median( ), median nInt( ), numeric integral median, median( ) nom ), convert effective to nominal medium-medium line regression, rate MedMed nominal rate, nom( ) MedMed, medium-medium line nor, Boolean operator regression mid-string, mid( )
  • Page 226 percent, % proper fraction, propFrac permutations, nPr( ) propFrac, proper fraction piecewise function (2-piece) template for piecewise function (N-piece) QR factorization, QR template for QR, QR factorization piecewise( ) quadratic regression, QuadReg poissCdf( ) QuadReg, quadratic regression poissPdf( ) quartic regression, QuartReg polar QuartReg, quartic regression coordinate, R►Pr( ) coordinate, R►Pθ( ) vector display, ►Polar...
  • Page 227 linear regression, LinRegBx seqGen( ) logarithmic, LnReg seqn( ) Logistic sequence, seq( ) 134-135 logistic, Logistic mode, setMode( ) medium-medium line, MedMed setMode( ), set mode MultReg settings, get current power regression, 125-126 shift( ), shift PowerReg quadratic, QuadReg shift, shift( ) quartic, QuartReg sign( ), sign sinusoidal, SinReg sign, sign( ) remain( ), remainder simult( ), simultaneous equations...
  • Page 228 two-variable results, TwoVar sumSeq() variance, variance( ) system of equations (2-equation) template for stdDevPop( ), population standard system of equations (N-equation) deviation template for stdDevSamp( ), sample standard deviation Stop command store variable (→) t test, tTest storing T, transpose symbol, & tan⁻¹( ), arctangent string tan( ), tangent dimension, dim( )
  • Page 229 time value of money, number of variance, variance( ) payments varPop( ) time value of money, payment varSamp( ), sample variance amount vectors time value of money, present value cross product, crossP( ) tInterval, t confidence interval cylindrical vector display, tInterval_2Samp, twosample t ►Cylind confidence interval dot product, dotP( ) tPdf( ), student probability density...
  • Page 230 Χ χ²Cdf( ) χ²GOF χ²Pdf( ) Index 226...

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