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5.1.145 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
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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
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See
factorize.
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