Heugcd: How elementary upperbounds generate cheaper data

  • James Davenport
  • Julian Padget
Algebraic Algorithms I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Cauchy, 1829]
    Cauchy, M.A., 1829 Exercies de Mathématiques, Quatrième Année. Les Oeuvres Compiètes d'Augustin Cauchy. IIe Série, Tome IX. (Bibliothèque Nationale, Paris), pp. 122–123.Google Scholar
  2. [Char et al., 1983]
    Char,B.W., Geddes,K.O., Gentleman,W.M., and Gonnet,G.H., The Design of MAPLE: a Compact, Portable and Powerful Computer Algebra System. Proc. EUROCAL 83 (Springer Lecture Notes in Computer Science 162), pp. 101–115.Google Scholar
  3. [Char et al., 1984a]
    Char, B. W., Fee, G. J., Geddes, K. O., Gonnet, G. H., Monagan, M. B., and Watt, S. W., On the Design and Performance of the MAPLE System. University of Waterloo, Research Report CS-84-13, June 1984Google Scholar
  4. [Char et al., 1984b]
    Char, B. W., Geddes, K. O. & Gonnet, G. H., GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation. Proc. EUROSAM 84 (Springer Lecture Notes in Computer Science 174) pp. 285–296.Google Scholar
  5. [Davenport, 1981]
    Davenport, J. H., On the Integration of Algebraic Functions. Springer Lecture Notes in Computer Science 102, 1981.Google Scholar
  6. [Fitch & Norman, 1977]
    Fitch, J. P. & Norman, A. C., Implementing LISP in a High-Level Language. Software — Practice & Expreience 7(1977) pp. 713–725.Google Scholar
  7. [Hearn, 79]
    Hearn, A. C., Non-Modular Computation of Polynomial Gcd Using Trial Division. Proc EUROSAM 79 (Springer Lecture Notes in Computer Science 72), pp. 227–239.Google Scholar
  8. [Hearn, 82]
    Hearn, A. C., REDUCE — A Case Study in Algebra System Development. Proc EUROCAM 82 (Springer Lecture Notes in Computer Science 144), pp. 263–272.Google Scholar
  9. [Landau, 1905]
    Landau, E., Sur queiques théorèmes de M. Petrovic rélatifs aux zeros des fonctions analytiques. Bull. Math. Soc. France 33(1905) pp. 251–261.Google Scholar
  10. [Mignotte, 1974]
    Mignotte, M., An Inequallty About Factors of Polynomials. Math. Comp. 28(1974) pp. 1153–1157.Google Scholar
  11. [Mignotte, 1982]
    Mignotte, M., Some Useful Bounds. Symbolic & Algebraic Computation (Computing Supplementum 4), Springer-Verlag 1982, pp. 259–263.Google Scholar
  12. [Moore & Norman, 1981]
    Moore, P. M. A. & Norman, A. C., Implementing a Polynomial Factorization and GCD Package. Proc. SYMSAC 81, ACM, New York, 1981, pp. 109–116.Google Scholar
  13. [Padget & Davenport, 1985]
    Padget, J. A. & Davenport, J. H., Number Bases in an Algebra System. To appear in SIGSAM Bulletin.Google Scholar
  14. [Stoutemyer, 1984]
    Stoutemyer, D. R., Which Polynomial Representation is Best: Surprises Abound. Proc. 1984 MACSYMA Users' Conference. General Electric. Schenectady, 1984, pp. 221–243.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • James Davenport
    • 1
  • Julian Padget
    • 1
  1. 1.School of MathematicsUniversity of BathBath. AvonEngland

Personalised recommendations