The Factors function is a placeholder for representing the factorization of the multivariate polynomial a over U, a unique factorization domain. The construct Factors(a) produces a data structure of the form  such that , where each f[i] is a primitive irreducible polynomial.

The difference between the Factors function and the Factor function is only the form of the result.  The Factor function, if defined, returns a Maple sum of products more suitable for interactive display and manipulation.

The call Factors(a) mod p computes the factorization of a over the integers modulo p, a prime integer. The polynomial a must have rational coefficients or coefficients over a finite field specified by RootOfs.

The call Factors(a, K) mod p computes the factorization over the finite field defined by K, an algebraic extension of the integers mod p where K is a RootOf.

The call modp1(Factors(a),p) computes the factorization of the polynomial a in the  representation modulo p a prime integer.

The call evala(Factors(a, K)) computes the factorization of the polynomial a over an algebraic number (or function) field defined by the extension K, which is specified as a RootOf or a set of RootOfs. The polynomial a must have algebraic number (or function) coefficients. The factors are monic for the ordering of the variables chosen by Maple.