Sqrfree
inert square-free factorization function
Calling Sequence
Parameters
Description
Examples
Sqrfree(a)
a
-
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=uf1e1⋯fnen and fi is primitive and square-free and u is the leading coefficient of a. That is, Gcdfi,∂∂xjfi=1 for all i and Gcdfi,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.
Sqrfree2x2+6x+6mod7
2,x2+3x+3,1
Sqrfree4x2+4x+1mod7
4,x+4,2
aliasα=RootOfx2+x+1
α
Sqrfreeαx3+α+1x2+x+αmod2
α,x+α,3
Sqrfreex2+y2+α+1mod2
1,y+x+α,2
evalaSqrfreex3−2x−212x2+2212
1,x+2,1,x−2,2
evalaSqrfree3x2+6RootOfx2−2x+6
3,RootOf_Z2−2+x,2
See Also
Factors
isqrfree
mod
modp1
RootOf
sqrfree
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