5.1.139 sqrfree

Syntax:

sqrfree ( poly_expression )
sqrfree ( poly_expression, 0 )
sqrfree ( poly_expression, 2 )

Type:

list of ideal and intvec

Syntax:

sqrfree ( poly_expression, 1 )

Type:

ideal

Syntax:

sqrfree ( poly_expression, 3 )

Type:

poly

Purpose:

computes the squarefree factors (as an ideal) of the polynomial together with or without the multiplicities (as an intvec) depending on the second argument:

0: returns factors and multiplicities, first factor is a constant. May also be written with only one argument. 1: returns non-constant factors (no multiplicities). 2: returns non-constant factors and multiplicities. 3: returns the product of non-constant factors, i.e. squarefree part

Note:

Not implemented for the coefficient fields real and finite fields of type (p^n,a).

Example:

ring r=3,(x,y,z),dp; poly f=(x-y)^3*(x+z)*(y-z); sqrfree(f); ==> [1]: ==> _[1]=1 ==> _[2]=-xy+xz-yz+z2 ==> _[3]=-x+y ==> [2]: ==> 1,1,3 sqrfree(f,1); ==> _[1]=-xy+xz-yz+z2 ==> _[2]=-x+y sqrfree(f,2); ==> [1]: ==> _[1]=-xy+xz-yz+z2 ==> _[2]=-x+y ==> [2]: ==> 1,3 sqrfree(f,3); ==> x2y-xy2-x2z-xyz-y2z-xz2+yz2