inert square-free factorization function - Maple Help

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Sqrfree - inert square-free factorization function

Calling Sequence

Sqrfree(a)

Parameters

a

-

multivariate polynomial or a multivariate rational function

Description

• 

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 ij.

• 

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.

Examples

Sqrfree2x2+6x+6mod7

2,x2+3x+3,1

(1)

Sqrfree4x2+4x+1mod7

4,x+4,2

(2)

aliasα=RootOfx2+x+1

α

(3)

Sqrfreeαx3+α+1x2+x+αmod2

α,x+α,3

(4)

Sqrfreex2+y2+α+1mod2

1,y+x+α,2

(5)

evalaSqrfreex32x212x2+2212

1,x+2,1,x2,2

(6)

evalaSqrfree3x2+6RootOfx22x+6

3,RootOf_Z22+x,2

(7)

See Also

Factors, isqrfree, mod, modp1, RootOf, sqrfree


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