factor(rationalNumber) returns the rational number factored into primes. For composite numbers, the computing time grows exponentially with the number of digits in the second-largest factor. For example, factoring a 30-digit integer could take more than a day, and factoring a 100-digit number could take more than a century.

To stop a calculation manually,

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.

FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists

FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists

Computes the F distribution probability between lowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom.

For P(X ≤ upBound), set lowBound = 0.

Fill Expr, listVar ⇒ list

Replaces each element in variable listVar with Expr.

listVar must already exist.

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 here.)

X represents a list containing the data.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1.

Category is a list of numeric category codes for the corresponding X data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. For more information on empty elements, see here.

floor(List1) ⇒ list
floor(Matrix1) ⇒ matrix

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

Note: See also ceiling() and int().

You can use the constraint (“|”) operator to restrict the solution interval and/or specify other constraints.

For the Approximate setting of the Auto or Approximate mode, fMax() iteratively searches for one approximate local maximum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum.

Note: See also fMin() and max().

fMin(Expr, Var) ⇒ Boolean expression

fMin(Expr, Var,lowBound)

fMin(Expr, Var,lowBound,upBound)

fMin(Expr, Var) | lowBound≤Var≤upBound

Returns a Boolean expression specifying candidate values of Var that minimize Expr or locate its greatest lower bound.

You can use the constraint (“|”) operator to restrict the solution interval and/or specify other constraints.

For the Approximate setting of the Auto or Approximate mode, fMin() iteratively searches for one approximate local minimum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local minimum.

Note: See also fMax() and min().

For Var, Low, High [, Step]
     Block
EndFor

Executes the statements in Block iteratively for each value of Var, from Low to High, in increments of Step.

Var must not be a system variable.

Step can be positive or negative. The default value is 1.

Block can be either a single statement or a series of statements separated with the “:” character.

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.

format(Expr[, formatString]) ⇒ string

Returns Expr as a character string based on the format template.

Expr must simplify to a number.

formatString is a string and must be in the form: “F[n]”, “S[n]”, “E[n]”, “G[n][c]”, where [ ] indicate optional portions.

F[n]: Fixed format. n is the number of digits to display after the decimal point.

S[n]: Scientific format. n is the number of digits to display after the decimal point.

E[n]: Engineering format. n is the number of digits after the first significant digit. The exponent is adjusted to a multiple of three, and the decimal point is moved to the right by zero, one, or two digits.

G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. c specifies the group separator character and defaults to a comma. If c is a period, the radix will be shown as a comma.

[Rc]: Any of the above specifiers may be suffixed with the Rc radix flag, where c is a single character that specifies what to substitute for the radix point.

fPart(Expr1) ⇒ expression
fPart(List1) ⇒ list
fPart(Matrix1) ⇒ matrix

Returns the fractional part of the argument.

For a list or matrix, returns the fractional parts of the elements.

The argument can be a real or a complex number.

FPdf(XVal,dfNumer,dfDenom) ⇒ number if XVal is a number, list if XVal is a list

Computes the F distribution probability at XVal for the specified dfNumer (degrees of freedom) and dfDenom.

freqTable►list(List1,freqIntegerList) ⇒ list

Returns a list containing the elements from List1 expanded according to the frequencies in freqIntegerList. This function can be used for building a frequency table for the Data & Statistics application.

List1 can be any valid list.

freqIntegerList must have the same dimension as List1 and must contain non-negative integer elements only. Each element specifies the number of times the corresponding List1 element will be repeated in the result list. A value of zero excludes the corresponding List1 element.

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

Empty (void) elements are ignored. For more information on empty elements, see here.

frequency(List1,binsList) ⇒ list

Returns a list containing counts of the elements in List1. The counts are based on ranges (bins) that you define in binsList.

If binsList is {b(1), b(2), …, b(n)}, the specified ranges are {?≤b(1), b(1)<?≤b(2),…,b(n-1)<?≤b(n), b(n)>?}. The resulting list is one element longer than binsList.

Each element of the result corresponds to the number of elements from List1 that are in the range of that bin. Expressed in terms of the countIf() function, the result is { countIf(list, ?≤b(1)), countIf(list, b(1)<?≤b(2)), …, countIf(list, b(n-1)<?≤b(n)), countIf(list, b(n)>?)}.

Elements of List1 that cannot be “placed in a bin” are ignored. Empty (void) elements are also ignored. For more information on empty elements, see here.

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

Note: See also countIf(), here.

FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]]

FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]]

(Data list input)

FTest_2Samp sx1,n1,sx2,n2[,Hypoth]

FTest_2Samp sx1,n1,sx2,n2[,Hypoth]

(Summary stats input)

Performs a two-sample F test. A summary of results is stored in the stat.results variable. (See here.)

For Ha: σ1 > σ2, set Hypoth>0
For Ha: σ1 ≠ σ2 (default), set Hypoth =0
For Ha: σ1 < σ2, set Hypoth<0

For information on the effect of empty elements in a list, see Empty (Void) Elements, here.

Func
     Block
EndFunc

Template for creating a user-defined function.

Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines. The function can use the Return instruction to return a specific result.

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.