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5.1.36 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.
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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
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See
absFactorize;
poly.
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