Singular Manual: facstd

  | ### 5.1.34 facstd `Syntax:` `facstd (` ideal_expression `)` `facstd (` ideal_expression`,` ideal_expression `)` `Type:` list of ideals `Purpose:` returns a list of ideals computed by the factorizing Groebner basis algorithm. The intersection of these ideals has the same zero-set as the input, i.e., the radical of the intersection coincides with the radical of the input ideal. In many (but not all!) cases this is already a decomposition of the radical of the ideal. (Note however that in general, no inclusion between the input and output ideals holds.) The second, optional argument gives a list of polynomials which define non-zero constraints: those ideals which contain one of the constraint polynomials are omitted from the output list. Thus the zero set of the intersection of the output ideals is contained in the zero set V of the first input ideal and contains the complement in V of the zero set of the second input ideal. `Note:` Not implemented for baserings over real ground fields and galois fields (that is, only implemented for ground fields for which factorize is implemented). `Example:`
        ring r=32003,(x,y,z),(c,dp);
        ideal I=xyz,x2z;
        facstd(I);
      ==> [1]:
      ==>    _[1]=z
      ==> [2]:
      ==>    _[1]=x
        facstd(I,x);
      ==> [1]:
      ==>    _[1]=z
See ideal; ring; std.

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