Factorized Gröbner Bases and Polynomial Systems
Date: July 20th (Saturday)
Time: 09:15-09:37.5
Abstract
Solving complicated polynomial systems with special purpose CASs (as
proposed in L. Bernardin's abstract) is often only of restricted benefit
due to the complicated output structure. Especially for systems with
infinitely many solutions, algorithms near to a prime decompositions must
be involved instead to obtain more insight into the structure of the set of
solutions. A central tool for such a purpose is the Gröbner algorithm
with factorization. No special purpose systems offer both facilities (yet)
on a satisfactory level. In my report, I will present both a comparison of
the Gröbner factorizer capabilities of the big general purpose CASs
(as far as these capabilities are accessible) and a survey about the output
quality of this algorithm compared to a full prime decomposition.
