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5.1.29 facstd
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Syntax: facstd (ideal_expression)facstd (ideal_expression,ideal_expression)-
Type: list of ideals
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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. Hence, the intersection of the output ideals has a zero-set which is the (closure of the) complement of the zero-set of the second argument in the zero-set of the first argument.-
Note: Not implemented for baserings over real ground fields, galois fields and over algebraic extensions over the rational numbers (that is, only implemented for ground fields for which factorize is implemented).
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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