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5.1.29 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. 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).
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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