There are therefore permutations of, namely, ,, , and. There are permutations of a list of (distinct) elements, a fact that follows from there being spots to place the first element, spots to place the second element once the first is placed, spots to place the third element once the first two elements are placed and so on until a single spot remains in which to place the last element.
Factorials are best known for counting fixed orderings of the elements of a list, known as permutations, which can be generated using Permutations. Factorials of half integers are given by rational multiples of. For a general complex number, , where the Gamma function is defined by for all complex values of except when is a negative integer (in which case is complex infinity). The special case is defined as 1, consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects. In particular, Factorial returns the factorial of a given number, which, for positive integers, is defined as. Factorial represents the factorial function. Wolfram Language & System Documentation Center. "Factor." Wolfram Language & System Documentation Center. Wolfram Research (1988), Factor, Wolfram Language function, (updated 2022). Factor automatically threads over lists, as well as equations, inequalities and logic functions.Ĭite this as: Wolfram Research (1988), Factor, Wolfram Language function, (updated 2022). 
Factor will extend the domain of coefficients to include any algebraic numbers that appear in poly. With the default setting Extension-> None, Factor will treat algebraic number coefficients in poly like independent variables. When given a rational expression, Factor effectively first calls Together, then factors numerator and denominator. Factor can deal with exponents that are linear combinations of symbolic expressions. The exponents of variables need not be positive integers. If any coefficients in poly are complex numbers, factoring is done allowing Gaussian integer coefficients. Factor factors allowing Gaussian integer coefficients. You may have to use Map, or apply Factor again, to reach other levels. 
Factor applies only to the top algebraic level in an expression.
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