skip to main content
10.1145/258726.258756acmconferencesArticle/Chapter ViewAbstractPublication PagesissacConference Proceedingsconference-collections
Article
Free Access

Resolvent computations by resultants without extraneous powers

Authors Info & Claims
Published:01 July 1997Publication History
First page image

References

  1. 1.ABDELJAOUED, J. Algorithmes rapides pour le calcul du polyn~me caractgristique. PhD thesis, U.F.R. des sciences et techniques de l'Universitd de Franche-Comtd, Besan(;on, France, March 1997.Google ScholarGoogle Scholar
  2. 2.ARNAUDIES, J.-M., AND VALIBOUZE, A. R~solvantes de Lagrange. Rapport interne 93/61, LITP, d~cembre 1993. To appear in Journal of Pure and Applied Algebra, special issue of MEGA'96.Google ScholarGoogle Scholar
  3. 3.ARNAUDIES, J.-M., AND VALIBOUZE, A. Calculs de rdsolvantes. Rapport interne 94/46, LITP, juillet 1994.Google ScholarGoogle Scholar
  4. 4.BErtKOWlTZ, S. J. On computing the determinant in small parallel time using a small number of processors. Information Processing Letter, 18 (1984), 147-150. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.BErtwlcI<, W. E. H. The condition that a quintic equation should be soluble by radicals. Proceedings of the London Mathematical Society (2) 14 (1915), 301-307.Google ScholarGoogle Scholar
  6. 6.BERWICK, W. E. H. On soluble sextic equations. Proceedings of the London Mathematical Society (2) 29 (1929), 1-28.Google ScholarGoogle Scholar
  7. 7.BrtENT, R. P. Multiple-precision zero-finding methods and the complexity of elementary function evaluation. In Analytic Computational Complexity, J. F. Traub, Ed. Academic Press, 1975, pp. 151-176.Google ScholarGoogle Scholar
  8. 8.CASr'ERSON, D., AND McKAv, J. Symmetric functions, m-sets, and Galois groups. Mathematics of Computation 63, 208 (October 1994), 749-757. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.EICHENLAUB, Y., AND OLIVlErt, M. Computation of galois groups for polynomials with degree up to eleven. Preprint, 1994.Google ScholarGoogle Scholar
  10. 10.GIUSTI, M., LAZArtD, D., AND VALIBOUZE, A. Algebraic transformations of polynomial equations, symmetric polynomials and elimination. In ISSAC'88, LNCS 358, P. Gianni, Ed., Springer, pp. 309-314. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.HENrttCl, P. Automatic computations with power series. Journal of the Association for Computing Machinery 3, 1 (January 1956), 10-15. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.HENrtICX, P. Discrete Fourier Analysis - Cauchy Integrals - Construction of Conformal Maps - Univalent Fhnctions, vol. 3 of Applied and Computational Complex Analysis. John Wiley and Sons, New York, 1986.Google ScholarGoogle Scholar
  13. 13.KOZEN, D., AND LANDAU, S. Polynomial decomposition algorithms. JSC 7 (1989), 445-456. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14.LAGRANGE, J.-L. Rdflexions sur la rdsolution algdbrique des dquations, vol. 3 of (Buvres de Lagrange. Gauthier-Villars, Paris, 1869, pp. 205-421. Nouveaux Mdmoires de l'Acad4mie royale des Sciences et Belles- Lettres de Berlin, armies 1770 et 1771.Google ScholarGoogle Scholar
  15. 15.LEHOBEY, F. Calcul de rdsolvantes r~cursives. In preparation.Google ScholarGoogle Scholar
  16. 16.LEHOBEY, F. Algorithmic methods and practical issues in the computation of Galois group of polynomials. DEA, Universitd de Rennes 1, 1993.Google ScholarGoogle Scholar
  17. 17.SoICSErt, L. The computation of Galois groups. Master's thesis, Concordia University, Montreal, 1981.Google ScholarGoogle Scholar
  18. 18.SOICHER, L. H. An algorithm for computing Galois groups. In Computational Group Theory. Academic Press, London, 1984, pp. 291-296.Google ScholarGoogle Scholar
  19. 19.STAUDUHAR, R.P. The determination of Galois groups. Mathematics of Computation 27, 124 (October 1973), 981-996.Google ScholarGoogle Scholar
  20. 20.VALIBOUZE, A. Galois groups of all polynomials with applications up to degree 7. Private communication, August 1996.Google ScholarGoogle Scholar
  21. 21.VALIBOUZE, A. Modules de Cauchy, polynSmes caractdristiques et rdsolvantes. Rapport interne 95/62, LITP, janvier 1996.Google ScholarGoogle Scholar

Index Terms

  1. Resolvent computations by resultants without extraneous powers

        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
        • Published in

          cover image ACM Conferences
          ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation
          July 1997
          414 pages
          ISBN:0897918754
          DOI:10.1145/258726

          Copyright © 1997 ACM

          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 July 1997

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • Article

          Acceptance Rates

          Overall Acceptance Rate395of838submissions,47%

          Upcoming Conference

          ISSAC '24

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader