==> %body 
==>
 
%body
%body
%body %body
%body %body %body
%body SINGULAR - A Computer Algebra System for Polynomial Computations Overview Objects Functionality Libraries Examples Applications Availability History Contributors Future %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Examples Build. Blocks Comb. Appl. HCA Proving
Arrangements Branches Classify Coding Deformations Equidim Part Existence Finite Groups Flatness Genus Hilbert Series Membership Nonnormal Locus Normalization Primdec Puiseux Plane Curves Saturation Solving Space Curves Spectrum %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Applications Robotics Circuit Design Medicine Glass Melting %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
Multivariate factorization internally uses random evaluation points. Therefore the way the factors are ordered is not necessarily the same for different initial random seeds.

When adding a new polynomial, the factorizing Gröbner basis algorithm proceeds by factorizing this polynomial,say f=f1f2, into its factors f1 and f2. Then it reenters, again, this time for

V(I,f1)   and   V(I,f2) \ V(f1).

Thus the algorithm might return a decomposition into a larger or smaller number of components, depending on the random seed.


General remarks on facstd:

  • The intersection of the components returned by facstd has the same radical as the original ideal.
  • The decomposition returned by facstd is usually not a complete decomposition into the components of the variety, it only cuts the decomposition problem into smaller and hence easier problems.
Back
Main Page