Advertisement

Computations on curves

  • Claire Dicrescenzo
  • Dominique Duval
Algebraic Number Computation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 174)

Abstract

We are implementing this algorithm on REDUCE. As we wrote above, when K is
we may represent any finite family of elements of K as elements of
for some α in K, cf[Ze] ; but we are exploring a more appropriate representation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [B-C]
    A. BAKER, J. COATES. Integer points on curves of genus 1. Proc. Camb. Phil. Soc. 67 (1970), pp. 595–602.Google Scholar
  2. [Co]
    J. COATES. Construction of rational functions on a curve. Proc. Camb. Phil. Soc. 68 (1970), pp. 105–123.Google Scholar
  3. [Da 1]
    J. H. DAVENPORT. Calculs dans les corps. Exposé au Colloque de l'Institut Fourier (1983).Google Scholar
  4. [Da 2]
    J. H. DAVENPORT. On the integration of algebråic functions. Lect. Notes in Computer Sc. 102 (1979).Google Scholar
  5. [Du]
    D. DUVAL. Une méthode géométrique de factorisation des polynômes en deux indéterminées, to appear in Calsyf 3 (1984 ?).Google Scholar
  6. [Fu]
    W. FULTON. Algebraic curves. Benjamin (1969).Google Scholar
  7. [H-S]
    J. HEINTZ, M. SIEVEKING. Absolute primality of polynomials is decidable in random polynomial time in the number of variables. Lect. Notes in Computer Sc. 115 (1981), pp. 16–28.Google Scholar
  8. [Le]
    A. K. LENSTRA. Lattices and factorization of polynomials over algebraic number fields. Computer Algebra Eurocam '82, Lect. Notes in Computer Sc. 144 (1982), pp. 32–39.Google Scholar
  9. [Li]
    J. D. LIPSON. Elements of algebra and algebraic computing. Addison-Wesley (1981).Google Scholar
  10. [Ta]
    E. TAHIRI EL ALAOUI. Solutions formelles d'équation algébrique de deux variables. IMAG R.R. 416 (1983).Google Scholar
  11. [Wa]
    R. WALKER. Algebraic curves. Springer-Verlag (1978).Google Scholar
  12. [Yu]
    D.Y.Y. YUN. Fast algorithm for rational function integration. Proc. IFIP 77 (ed. B. Gilchrist) North-Holland (1977), pp. 493–498.Google Scholar
  13. [Ze]
    H. ZEJLI. Calcul dans les extensions de corps. IMAG, Séminaire 397 (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Claire Dicrescenzo
    • 1
  • Dominique Duval
    • 2
  1. 1.IMAGSt Martin d'Hères Cedex
  2. 2.Institut FourierSt Martin d'Hères Cedex

Personalised recommendations