A Maple Package for Characteristic Sets
and now a module of Epsilon
CharSets is a Maple package developed by
on the basis of Wu-Ritt's method of characteristic sets. The first
version CharSets 1.0 was made publicly available with Maple's share
library in early 1991. Three subsequent versions 1.1, 1.2, and
2.0 were also distributed.
The current version is CharSets 2.2.
The early versions of CharSets were implemented for computing
characteristic sets and various zero decompositions of polynomial
systems and other related polynomial calculations. Their capabilities
A new module has been added to CharSets (since version 2.0) that contains
eight functions for computing differential characteristic sets
and the corresponding zero decompositions for systems of ordinary
differential polynomials. Some of the routines from the CharSets
package are used by the provers in GEOTHER,
an environment for geometric theorem proving.
- computing (modified) characteristic sets of polynomial sets
(in different senses),
- decomposing polynomial sets into ascending sets and into
irreducible and quasi-irreducible ascending sets,
- decomposing algebraic varieties into irreducible components,
- decomposing polynomial ideals into primary components,
- solving systems of polynomial equations, and
- factorizing multivariate polynomials over algebraic extension
Excerpts with modification from Mathematics Mechanization and
Applications, Academic Press, pp. 498-499 (2000).
Last Modification: June 18, 2003