inert square-free factorization function
multivariate polynomial or a multivariate rational function
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 u,f1,e1,...,fn,en such that a=u⁢f1e1⁢⋯⁢fnen and fi is primitive and square-free and u is the leading coefficient of a. That is, Gcd⁡fi,∂∂xjfi=1 for all i and Gcd⁡fi,fj=1 for i≠j.
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.
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