For Publishers
DiscoveryMetadataPeer reviewHostingPublishing
For Researchers
JoinPublishReviewCollect
Register
Blog
About
Search
Advanced search
My ScienceOpen
Search
For Publishers
For Researchers
Blog
About
12
views
9
references
 Top references
cited by
2
    
0 reviews
 Review
0
comments
 Comment
0
recommends
+1 Recommend
0 collections
    0
    shares
      199
      similar
       All similar
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Practical Groebner Basis Computation

      Preprint
      Author(s): ,
      Publication date Created:

      Read this article at

      ScienceOpenArXiv
      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature based Groebner basis algorithms and more traditional variations of the classic Buchberger algorithm. Our conclusions are based on experiments using our new freely available open source standalone C++ library.

          Related collections

          Most cited references9

          • Record: found
          • Abstract: not found
          • Article: not found

          A new efficient algorithm for computing Gröbner bases (F4)

          Jean-Charles Faugère (1999)
          Article 0 comments Cited 135 times – based on 0 reviews     Review now
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Efficiently computing minimal sets of critical pairs

            M. Caboara, M. Kreuzer, L Robbiano (2004)
            Article 0 comments Cited 6 times – based on 0 reviews     Review now
              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              The F5 Criterion revised

              , (2016)
              The purpose of this work is to generalize part of the theory behind Faugere's "F5" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomial ideal I generated by polynomials f_{1},...,f_{m}. A major reason for this is what Faugere called the algorithm's "new" criterion, and we call "the F5 criterion"; it provides a sufficient condition for a set of polynomials G to be a Groebner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination. This paper introduces some new concepts that place the criterion in a more general setting: S-Groebner bases and primitive S-irreducible polynomials. We use these to propose a new, simple algorithm based on a revised F5 criterion. The new concepts also enable us to remove various restrictions, such as proving termination without the requirement that f_{1},...,f_{m} be a regular sequence.
              Article 0 comments Cited 6 times – based on 0 reviews
              Preprint
                   Review now
                Bookmark
                All references

                Author and article information

                Journal
                Publication date Created: 29 June 2012
                Article
                ArXiV ID: 1206.6940
                SO-VID: 301823d0-d936-4344-b84a-eb3302370778
                License:

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Comments Full online version including appendices, 17 pages; Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2012
                Categories cs.SC cs.DS math.AC

                Data availability:

                Comments

                Comment on this article