**
Olaf Bachmann
Hans Schönemann
Centre for Computer Algebra
Department of Mathematics
University of Kaiserslautern
Kaiserslautern, Germany
**

January 1998

Monomial representations and operations for Gröbner bases
computations are investigated from an implementation point of view.
The technique of vectorized monomial operations is introduced and it
is shown how it expedites computations of Gröbner bases.
Furthermore, a rank-based monomial representation and comparison
technique is examined and it is concluded that this technique does
not yield an additional speedup over vectorized
comparisons. Extensive benchmark tests with the Computer Algebra
System SINGULAR are used to evaluate these concepts.

- 1 Introduction
- 2 Basic monomial operations and representations
- 3 Vectorized monomial operations
- 4 Rank-based monomial representation and comparisons
- 5 Summary
- 6 Acknowledgments
- Bibliography
- Appendix A: Benchmark examples
- Appendix B: Timings on other machines
- About this document ...

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