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5.1.35 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, finite fields of type (p^n,a) and ZZ/m.
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
  ring rQ=0,x,dp;
  poly f = x2+1;            // irreducible in Q[x]
  factorize(f);
==> [1]:
==>    _[1]=1
==>    _[2]=x2+1
==> [2]:
==>    1,1
  ring rQi = (0,i),x,dp;
  minpoly = i2+1;
  poly f = x2+1;            // splits into linear factors in Q(i)[x]
  factorize(f);
==> [1]:
==>    _[1]=1
==>    _[2]=x+(-i)
==>    _[3]=x+(i)
==> [2]:
==>    1,1,1
See absFactorize; poly.