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abs()	Catalog >
abs(Expr1) ⇒ expression abs(List1) ⇒ list abs(Matrix1) ⇒ matrix Returns the absolute value of the argument. Note: See also Absolute value template, here. If the argument is a complex number, returns the number’s modulus. Note: All undefined variables are treated as real variables.

abs()

Catalog >

abs(Expr1) ⇒ expression

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

Returns the absolute value of the argument.

Note: See also Absolute value template, here.

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

Note: All undefined variables are treated as real variables.

amortTbl()

Catalog >

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

Amortization function that returns a matrix as an amortization table for a set of TVM arguments.

NPmt is the number of payments to be included in the table. The table starts with the first payment.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, here.

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If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt).

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If you omit FV, it defaults to FV=0.

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The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions.

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

The columns in the result matrix are in this order: Payment number, amount paid to interest, amount paid to principal, and balance.

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

You can use the output matrix as input for the other amortization functions ΣInt() and ΣPrn(), here, and bal(), here.

and	Catalog >
BooleanExpr1 and BooleanExpr2 ⇒ Boolean expression BooleanList1 and BooleanList2 ⇒ Boolean list BooleanMatrix1 and BooleanMatrix2 ⇒ Boolean matrix Returns true or false or a simplified form of the original entry.
Integer1 andInteger2 ⇒ integer Compares two real integers bit-by-bit using an and operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10).	In Hex base mode: Important: Zero, not the letter O. In Bin base mode: In Dec base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits.

and

Catalog >

BooleanExpr1 and BooleanExpr2 ⇒ Boolean expression

BooleanList1 and BooleanList2 ⇒ Boolean list

BooleanMatrix1 and BooleanMatrix2 ⇒ Boolean matrix

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

Integer1 andInteger2 ⇒ integer

Compares two real integers bit-by-bit using an and operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode.

You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10).

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

In Dec base mode:

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

angle()	Catalog >
angle(Expr1) ⇒ expression Returns the angle of the argument, interpreting the argument as a complex number. Note: All undefined variables are treated as real variables.	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 the elements in List1 or Matrix1, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point.

angle()

Catalog >

angle(Expr1) ⇒ expression

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

Note: All undefined variables are treated as real variables.

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 the elements in List1 or Matrix1, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point.

ANOVA	Catalog >
ANOVA List1,List2[,List3,...,List20][,Flag] Performs a one-way analysis of variance for comparing the means of two to 20 populations. A summary of results is stored in the stat.results variable. (here) Flag=0 for Data, Flag=1 for Stats

ANOVA

Catalog >

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

Performs a one-way analysis of variance for comparing the means of two to 20 populations. A summary of results is stored in the stat.results variable. (here)

Flag=0 for Data, Flag=1 for Stats

Output variable	Description
stat.F	Value of the F statistic
stat.PVal	Smallest level of significance at which the null hypothesis can be rejected
stat.df	Degrees of freedom of the groups
stat.SS	Sum of squares of the groups
stat.MS	Mean squares for the groups
stat.dfError	Degrees of freedom of the errors
stat.SSError	Sum of squares of the errors
stat.MSError	Mean square for the errors
stat.sp	Pooled standard deviation
stat.xbarlist	Mean of the input of the lists
stat.CLowerList	95% confidence intervals for the mean of each input list
stat.CUpperList	95% confidence intervals for the mean of each input list

ANOVA2way	Catalog >
ANOVA2way List1,List2[,List3,…,List10][,levRow] Computes a two-way analysis of variance for comparing the means of two to 10 populations. A summary of results is stored in the stat.results variable. (See here.) 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,…}

ANOVA2way

Catalog >

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

Computes a two-way analysis of variance for comparing the means of two to 10 populations. A summary of results is stored in the stat.results variable. (See here.)

LevRow=0 for Block

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

Outputs: Block Design

Output variable	Description
stat.F	F statistic of the column factor
stat.PVal	Smallest level of significance at which the null hypothesis can be rejected
stat.df	Degrees of freedom of the column factor
stat.SS	Sum of squares of the column factor
stat.MS	Mean squares for column factor
stat.FBlock	F statistic for factor
stat.PValBlock	Least probability at which the null hypothesis can be rejected
stat.dfBlock	Degrees of freedom for factor
stat.SSBlock	Sum of squares for factor
stat.MSBlock	Mean squares for factor
stat.dfError	Degrees of freedom of the errors
stat.SSError	Sum of squares of the errors
stat.MSError	Mean squares for the errors
stat.s	Standard deviation of the error

COLUMN FACTOR Outputs

Output variable	Description
stat.Fcol	F statistic of the column factor
stat.PValCol	Probability value of the column factor
stat.dfCol	Degrees of freedom of the column factor
stat.SSCol	Sum of squares of the column factor
stat.MSCol	Mean squares for column factor

ROW FACTOR Outputs

Output variable	Description
stat.FRow	F statistic of the row factor
stat.PValRow	Probability value of the row factor
stat.dfRow	Degrees of freedom of the row factor
stat.SSRow	Sum of squares of the row factor
stat.MSRow	Mean squares for row factor

INTERACTION Outputs

Output variable	Description
stat.FInteract	F statistic of the interaction
stat.PValInteract	Probability value of the interaction
stat.dfInteract	Degrees of freedom of the interaction
stat.SSInteract	Sum of squares of the interaction
stat.MSInteract	Mean squares for interaction

ERROR Outputs

Output variable	Description
stat.dfError	Degrees of freedom of the errors
stat.SSError	Sum of squares of the errors
stat.MSError	Mean squares for the errors
s	Standard deviation of the error

Ans	/v keys
Ans ⇒ value Returns the result of the most recently evaluated expression.

Ans

/v keys

Ans ⇒ value

Returns the result of the most recently evaluated expression.

approx()	Catalog >
approx(Expr1) ⇒ expression Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or Approximate mode. This is equivalent to entering the argument and pressing /·.
approx(List1) ⇒ list approx(Matrix1) ⇒ matrix Returns a list or matrix where each element has been evaluated to a decimal value, when possible.

approx()

Catalog >

approx(Expr1) ⇒ expression

Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or Approximate mode.

This is equivalent to entering the argument and pressing /·.

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

Returns a list or matrix where each element has been evaluated to a decimal value, when possible.

►approxFraction()	Catalog >
Expr►approxFraction([Tol]) ⇒ expression List►approxFraction([Tol]) ⇒ list Matrix►approxFraction([Tol]) ⇒ matrix Returns the input as a fraction, using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used. Note: You can insert this function from the computer keyboard by typing @>approxFraction(...).

►approxFraction()

Catalog >

Expr►approxFraction([Tol]) ⇒ expression

List►approxFraction([Tol]) ⇒ list

Matrix►approxFraction([Tol]) ⇒ matrix

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

Note: You can insert this function from the computer keyboard by typing @>approxFraction(...).

approxRational()	Catalog >
approxRational(Expr[, Tol]) ⇒ expression approxRational(List[, Tol]) ⇒ list approxRational(Matrix[, Tol]) ⇒ matrix Returns the argument as a fraction using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used.

approxRational()

Catalog >

approxRational(Expr[, Tol]) ⇒ expression

approxRational(List[, Tol]) ⇒ list

approxRational(Matrix[, Tol]) ⇒ matrix

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

arccos()	See cos⁻¹(), here.

arccosh()	See cosh⁻¹(), here.

arccot()	See cot⁻¹(), here.

arccoth()	See coth⁻¹(), here.

arccsc()	See csc⁻¹(), here.

arccsch()	See csch⁻¹(), here.

arcLen()	Catalog >
arcLen(Expr1,Var,Start,End) ⇒ expression Returns the arc length of Expr1 from Start to End with respect to variable Var. Arc length is calculated as an integral assuming a function mode definition.
arcLen(List1,Var,Start,End) ⇒ list Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var.

arcLen()

Catalog >

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

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

Arc length is calculated as an integral assuming a function mode definition.

arcLen(List1,Var,Start,End) ⇒ list

Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var.

arcsec()	See sec⁻¹(), here.

arcsech()	See sech⁻¹(), here.

arcsin()	See sin⁻¹(), here.

arcsinh()	See sinh⁻¹(), here.

arctan()	See tan⁻¹(), here.

arctanh()	See tanh⁻¹(), here.

augment()	Catalog >
augment(List1, List2) ⇒ list Returns a new list that is List2 appended to the end of List1.
augment(Matrix1, Matrix2) ⇒ matrix Returns a new matrix that is Matrix2 appended to Matrix1. When the “,” character is used, the matrices must have equal row dimensions, and Matrix2 is appended to Matrix1 as new columns. Does not alter Matrix1 or Matrix2.

augment()

Catalog >

augment(List1, List2) ⇒ list

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

augment(Matrix1, Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2 appended to Matrix1. When the “,” character is used, the matrices must have equal row dimensions, and Matrix2 is appended to Matrix1 as new columns. Does not alter Matrix1 or Matrix2.

avgRC()	Catalog >
avgRC(Expr1, Var [=Value] [, Step]) ⇒ expression avgRC(Expr1, Var [=Value] [, List1]) ⇒ list avgRC(List1, Var [=Value] [, Step]) ⇒ list avgRC(Matrix1, Var [=Value] [, Step]) ⇒ matrix Returns the forward-difference quotient (average rate of change). Expr1 can be a user-defined function name (see Func). When Value is specified, it overrides any prior variable assignment or any current “\|” substitution for the variable. Step is the step value. If Step is omitted, it defaults to 0.001. Note that the similar function centralDiff() uses the central-difference quotient.

avgRC()

Catalog >

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

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

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

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

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

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

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

Step is the step value. If Step is omitted, it defaults to 0.001.

Note that the similar function centralDiff() uses the central-difference quotient.