skip to main content
poster

General polynomial reduction with TH 9 OREM 8 functors: applications to integro-differential operators and polynomials

Authors Info & Claims
Published:06 February 2009Publication History
First page image

References

  1. G. M. Bergman. The diamond lemma for ring theory. Adv. in Math., 29(2):179--218, 1978.Google ScholarGoogle ScholarCross RefCross Ref
  2. B. Buchberger. An Algorithm for Finding the Bases Elements of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal (German). PhD thesis, Univ. of Innsbruck, 1965. English translation published in J. Symbolic Comput., 41(3-4):475--511, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. B. Buchberger. Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequationes Math., 4:374--383, 1970. English translation in B. Buchberger, F. Winkler (eds.), Gröbner Bases and Applications, Cambridge University Press, 1998.Google ScholarGoogle ScholarCross RefCross Ref
  4. B. Buchberger. Groebner rings and modules. In S. Maruster, B. Buchberger, V. Negru, and T. Jebelean, editors, Proceedings of SYNASC 2001, pages 22--25, 2001.Google ScholarGoogle Scholar
  5. B. Buchberger. Groebner bases in theorema using functors. In J. Faugere and D. Wang, editors, Proceedings of SCC'08, pages 1--15. LMIB Beihang University Press, 2008.Google ScholarGoogle Scholar
  6. B. Buchberger et al. Theorema: Towards computer-aided mathematical theory exploration. J. Appl. Log., 4(4):359--652, 2006.Google ScholarGoogle ScholarCross RefCross Ref
  7. H. Lausch and W. Nöbauer. Algebra of polynomials. North-Holland Publishing Co., Amsterdam, 1973. North-Holland Mathematical Library, Vol. 5.Google ScholarGoogle Scholar
  8. K. Madlener and B. Reinert. Non-commutative reduction rings. Rev. Colombiana Mat., 33(1):27--49, 1999.Google ScholarGoogle Scholar
  9. T. Mora. An introduction to commutative and noncommutative Gröbner bases. Theoret. Comput. Sci., 134(1):131--173, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. G. Regensburger and M. Rosenkranz. An algebraic foundation for factoring linear boundary problems. Ann. Mat. Pura Appl. (4), 2008. DOI:10.1007/s10231-008-0068-3.Google ScholarGoogle Scholar
  11. M. Rosenkranz. A new symbolic method for solving linear two-point boundary value problems on the level of operators. J. Symbolic Comput., 39(2):171--199, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. M. Rosenkranz and G. Regensburger. Integro-differential polynomials and operators. In D. Jeffrey, editor, Proceedings of ISSAC'08. ACM Press, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. M. Rosenkranz and G. Regensburger. Solving and factoring boundary problems for linear ordinary differential equations in differential algebras. J. Symbolic Comput., 43(8):515--544, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. S. Stifter. Gröbner bases of modules over reduction rings. J. Algebra, 159(1):54--63, 1993.Google ScholarGoogle ScholarCross RefCross Ref
  15. W. Windsteiger. Building up hierarchical mathematical domains using functors in THEOREMA. In A. Armando and T. Jebelean, editors, ENTCS, volume 23, pages 401--419. Elsevier, 1999.Google ScholarGoogle Scholar
  16. A. Zapletal. Compilation of Theorema Programs. PhD thesis, Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria, June 2008.Google ScholarGoogle Scholar

Index Terms

  1. General polynomial reduction with TH 9 OREM 8 functors: applications to integro-differential operators and polynomials

              Recommendations

              Comments

              Login options

              Check if you have access through your login credentials or your institution to get full access on this article.

              Sign in

              Full Access

              • Published in

                cover image ACM Communications in Computer Algebra
                ACM Communications in Computer Algebra  Volume 42, Issue 3
                September 2008
                80 pages
                ISSN:1932-2240
                DOI:10.1145/1504347
                Issue’s Table of Contents

                Copyright © 2009 Authors

                Publisher

                Association for Computing Machinery

                New York, NY, United States

                Publication History

                • Published: 6 February 2009

                Check for updates

                Qualifiers

                • poster

              PDF Format

              View or Download as a PDF file.

              PDF

              eReader

              View online with eReader.

              eReader