Home Online Manual
Top
Back: sortvec
Forward: sprintf
FastBack: Functions and system variables
FastForward: Control structures
Up: Functions
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

5.1.140 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
See factorize.