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Sqrfree

inert square-free factorization function

 

Calling Sequence

Parameters

Description

Examples

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  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.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

See Also

Factors

isqrfree

mod

modp1

RootOf

sqrfree

 


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