A Speed-Up Algorithm for Computing Comprehensive Groebner Systems

  • Katsusuke Nabeshima

Research output: Chapter in Book/Report/Conference proceedingConference proceedingspeer-review

Abstract

We introduce a new algorithm for computing comprehensive Groebner systems. There exists the Suzuki-Sato algorithm for computing comprehensive Groebner systems. The Suzuki-Sato algorithm often creates overmuch cells of the parameter space for comprehensive Groebner systems. Therefore the computation becomes heavy. However, by using inequations (``not equal zero''), we can obtain different cells. In many cases, this number of cells of parameter space is smaller than that of Suzuki-Sato's. Therefore, our new algorithm is more efficient than Suzuki-Sato's one, and outputs a nice comprehensive Groebner system. Our new algorithm has been implemented in the computer algebra system Risa/Asir. We compare the runtime of our implementation with the Suzuki-Sato algorithm and find our algorithm superior in many cases.
Original languageEnglish
Title of host publicationISSAC 2007
Editors C. W. Brown
PublisherACM Press
Pages299-306
Number of pages8
ISBN (Print)978-1-59593-743-8
Publication statusPublished - 2007

Fields of science

  • 101 Mathematics
  • 101001 Algebra
  • 101005 Computer algebra
  • 101009 Geometry
  • 101012 Combinatorics
  • 101013 Mathematical logic
  • 101020 Technical mathematics

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