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5.1.33 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
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See
ideal;
ring;
std.
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