A

abs()	Catalogue >
abs(Expr1)Þexpression abs(List1)Þlist abs(Matrix1)Þmatrix 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()

Catalogue >

abs(Expr1)Þexpression

abs(List1)Þlist

abs(Matrix1)Þmatrix

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()

Catalogue >

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

Amortisation function that returns a matrix as an amortisation 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.

•

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

•

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

•

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

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

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 amortisation functions ΣInt() and ΣPrn(), here, and bal(), here.

and	Catalogue >
BooleanExpr1 and BooleanExpr2ÞBoolean expression BooleanList1 and BooleanList2ÞBoolean list BooleanMatrix1 and BooleanMatrix2ÞBoolean matrix Returns true or false or a simplified form of the original entry.
Integer1 andInteger2Þinteger 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

Catalogue >

BooleanExpr1 and BooleanExpr2ÞBoolean expression

BooleanList1 and BooleanList2ÞBoolean list

BooleanMatrix1 and BooleanMatrix2ÞBoolean matrix

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

Integer1 andInteger2Þinteger

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()	Catalogue >
angle(Expr1)Þexpression 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)Þlist angle(Matrix1)Þmatrix 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()

Catalogue >

angle(Expr1)Þexpression

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)Þlist

angle(Matrix1)Þmatrix

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	Catalogue >
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

Catalogue >

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	Catalogue >
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 (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

Catalogue >

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 (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
AnsÞvalue Returns the result of the most recently evaluated expression.

Ans

/v keys

AnsÞvalue

Returns the result of the most recently evaluated expression.

approx()	Catalogue >
approx(Expr1)Þexpression 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)Þlist approx(Matrix1)Þmatrix Returns a list or matrix where each element has been evaluated to a decimal value, when possible.

approx()

Catalogue >

approx(Expr1)Þexpression

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)Þlist

approx(Matrix1)Þmatrix

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

4approxFraction()	Catalogue >
Expr 4approxFraction([Tol])Þexpression List 4approxFraction([Tol])Þlist Matrix 4approxFraction([Tol])Þmatrix 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(...).

4approxFraction()

Catalogue >

Expr 4approxFraction([Tol])Þexpression

List 4approxFraction([Tol])Þlist

Matrix 4approxFraction([Tol])Þmatrix

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()	Catalogue >
approxRational(Expr[, Tol])Þexpression approxRational(List[, Tol])Þlist approxRational(Matrix[, Tol])Þmatrix Returns the argument as a fraction using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used.

approxRational()

Catalogue >

approxRational(Expr[, Tol])Þexpression

approxRational(List[, Tol])Þlist

approxRational(Matrix[, Tol])Þmatrix

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/(), here.

arccosh()	See cosh/(), here.

arccot()	See cot/(), here.

arccoth()	See coth/(), here.

arccsc()	See csc/(), here.

arccsch()	See csch/(), here.

arcLen()	Catalogue >
arcLen(Expr1,Var,Start,End) Þexpression 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)Þlist Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var.

arcLen()

Catalogue >

arcLen(Expr1,Var,Start,End) Þexpression

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)Þlist

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

arcsec()	See sec/(), here.

arcsech()	See sech/(), here.

arcsin()	See sin/(), here.

arcsinh()	See sinh/(), here.

arctan()	See tan/(), here.

arctanh()	See tanh/(), here.

augment()	Catalogue >
augment(List1, List2)Þlist Returns a new list that is List2 appended to the end of List1.
augment(Matrix1, Matrix2)Þmatrix 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()

Catalogue >

augment(List1, List2)Þlist

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

augment(Matrix1, Matrix2)Þmatrix

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()	Catalogue >
avgRC(Expr1, Var [=Value] [, Step])Þexpression avgRC(Expr1, Var [=Value] [, List1])Þlist avgRC(List1, Var [=Value] [, Step])Þlist avgRC(Matrix1, Var [=Value] [, Step])Þmatrix 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()

Catalogue >

avgRC(Expr1, Var [=Value] [, Step])Þexpression

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

avgRC(List1, Var [=Value] [, Step])Þlist

avgRC(Matrix1, Var [=Value] [, Step])Þmatrix

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.