Skip to main content

Opal: A system for computing noncommutative gröbner bases

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1232)


  • Free Algebra
  • Zero Divisor
  • Path Algebra
  • Artin Algebra
  • Free Associative Algebra

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/3-540-62950-5_83
  • Chapter length: 4 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   99.00
Price excludes VAT (USA)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. M. Auslander, I. Reiten and S. O. Smalø. Representation Theory of Artin Algebras, Cambridge University Press, 1995.

    Google Scholar 

  2. I. Biehl, J. Buchmann and T. Papanikolaou. A Library for Computational Number Theory, Technical Report SFB 124-C1, Fabereich Informatik, Universität Saarlandes, 1995.

    Google Scholar 

  3. D. R. Farkas, C. D. Feustel and E. L. Green. “Synergy in the theories of Gröbner bases and path algebras”, Canadian Journal of Mathematics, 45, 4 (1993) 727–739.

    Google Scholar 

  4. B. Keller. “Alternatives in implementing noncommutative Gröbner basis systems”, Symbolic Rewriting Techniques, Birkhauser-Verlag, (to appear).

    Google Scholar 

  5. B. Keller. Algorithms and Orders for Finding Noncommutative Gröbner Bases, Dissertation, Virginia Polytechnic Institute & State University, (in preparation).

    Google Scholar 

  6. F. Mora. “Groebner bases for noncommutative polynomial rings,” in Algebraic Algorithms and Error-Correcting Codes, J. Calmet (ed.), LNCS# 229, Springer-Verlag, Berlin, 1986, 353–362.

    Google Scholar 

  7. D. Musser and A. Saini. STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library, Addison-Wesley, 1996.

    Google Scholar 

  8. T. Parr and R. Quong. “ANTLR: A predicated-LL(k) parser generator”, Software-Practice and Experience, 25, 4, (1995) 789–810.

    Google Scholar 

  9. B. Reinert. On Gröbner Bases in Monoid and Group Rings, Dissertation, FB Informatik, University of Kaiserslautern, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Green, E.L., Heath, L.S., Keller, B.J. (1997). Opal: A system for computing noncommutative gröbner bases. In: Comon, H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62950-4

  • Online ISBN: 978-3-540-69051-1

  • eBook Packages: Springer Book Archive