The Sqrfree function is a placeholder for representing the square-free factorization of the multivariate polynomial or rational function a over a unique factorization domain. It is used in conjunction with either mod, modp1 or evala which define the coefficient domain as described below.

The Sqrfree function returns a data structure of the form  such that  and  is primitive and square-free and  is the leading coefficient of a. That is,  for all  and  for .

The call Sqrfree(a) mod p computes the square-free factorization of the polynomial a modulo p a prime integer. The multivariate polynomial a must have rational coefficients or coefficients from an algebraic extension of the integers modulo p.

The call modp1(Sqrfree(a), p) computes the square-free factorization of the polynomial a in the modp1 representation modulo p a prime integer.

The call evala(Sqrfree(a)) computes the square-free factorization of the polynomial or the rational function a where the coefficients of a are algebraic numbers (or functions) defined by RootOf or radicals. See evala,Sqrfree for more information.