| Date |
4-3-2003 |
| Time |
16:30 |
| Room/Location |
Sala Conferenza DISI (terzo piano) |
| Title |
Involutive bases of polynomial ideals |
| Speaker |
Vladimir Gerdt |
| Affiliation |
Department of Computer Science University of Rostock |
| Link |
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| Abstract |
In this review talk we present basic ideas, concepts and
constructive methods behind an algorithmic approach to
construction of involutive polynomial bases which are (generally
redundant) Groebner bases of the special form. The approach is
based on the concept of involutive monomial division which is
defined for a (leading) monomial set. Every particular division
provides for each monomial in the set the self-consistent
separation of variables into multiplicative and
non-multiplicative. As a typical representative of involutive
bases we consider those used by Janet for the purpose of algebraic
analysis of partial differential equations. We give also
experimental comparison of computational efficiency of the
involutive algorithm for computing Janet bases and the Buchberger
algorithm for computing reduced Groebner bases. |
