5.1.30 factorize

Syntax:

factorize ( poly_expression )
factorize ( poly_expression, 0 )
factorize ( poly_expression, 2 )

Type:

list of ideal and intvec

Syntax:

factorize ( poly_expression, 1 )

Type:

ideal

Purpose:

computes the irreducible 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.

Note:

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

Example:

ring r=32003,(x,y,z),dp; factorize(9*(x-1)^2*(y+z)); → [1]: → _[1]=9 → _[2]=y+z → _[3]=x-1 → [2]: → 1,1,2 factorize(9*(x-1)^2*(y+z),1); → _[1]=y+z → _[2]=x-1 factorize(9*(x-1)^2*(y+z),2); → [1]: → _[1]=y+z → _[2]=x-1 → [2]: → 1,2

See poly.