Session 7. Groebner Bases (Web Page)
Aim and Scope
Groebner bases (and related bases like characteristic sets, Groebner bases in differential rings, etc.) have found numerous applications in all areas of science and technology. Since the computation of such bases is known to be intrinsically complex, the improvement of algorithms for their computation and software for the many applications of Groebner bases is of utmost importance. Considerable progress has been made over the past decades and years in this area. Note however that this session is not a forum for the theory of Groebner bases and complexity. We want to focus exclusively on the implementation, software, and application aspect.
Topics (including, but not limited to)
- Practical improvements of the algorithms for computing Groebner bases and related bases
- Generic implementation of Groebner bases
- Particularly efficient implementation of Groebner bases in special domains
- Numerical versions of Groebner bases computation
- Implementation of Groebner bases on parallel machines, high-perfomance computers, special hardware
- Special user interfaces for Groebner bases applications
- Implementation of Groebner bases algorithms in general mathematical software systems
- Special software systems that focus on the computation and applications of Groebner bases
- Case studies for the use and computation of Groebner bases in particularly complex and / or practically important cases
- Success stories and feasibility reports on the use of Groebner bases etc. in science, technology, engineering, economy, medicine etc.
- Success stories and feasibility reports on the use of Groebner bases etc. inside mathematics (mathematical reasoning, geometric reasoning, experimental mathematics, cryptography etc.)
- Comparison (of computing times and other efficiency criteria) of various implementations