Singular Manual: sqrfree

  | ### 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
  `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.

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