The factors command computes the factorization of a multivariate polynomial over the rationals, an algebraic number field, and with real or complex numeric coefficients.

Unlike the factor function where the input is any expression and the output is a product of sums in the general case, the input to the factors function must be a polynomial or a rational function, and the output is a data structure more suitable for programming purposes.

The factorization is returned in the form  where  where each  (the factor) is a unit normal irreducible polynomial and each  (its multiplicity) is a positive integer.

The call factors(a) factors over the field implied by the coefficients present: thus, if all the coefficients are rational, then the polynomial is factored over the rationals.

If the second argument K is the keyword real or complex, a floating-point factorization is performed over R and C respectively.  Note, at present this is only implemented for univariate polynomials.

The call factors(a, K) factors the polynomial a over the algebraic number field defined by K. K must be a single RootOf, a list or set of RootOfs, a single radical, or a list or set of radicals.