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.
Bibliography
A. BAKER, J. COATES. Integer points on curves of genus 1. Proc. Camb. Phil. Soc. 67 (1970), pp. 595–602.
J. COATES. Construction of rational functions on a curve. Proc. Camb. Phil. Soc. 68 (1970), pp. 105–123.
J. H. DAVENPORT. Calculs dans les corps. Exposé au Colloque de l'Institut Fourier (1983).
J. H. DAVENPORT. On the integration of algebråic functions. Lect. Notes in Computer Sc. 102 (1979).
D. DUVAL. Une méthode géométrique de factorisation des polynômes en deux indéterminées, to appear in Calsyf 3 (1984 ?).
W. FULTON. Algebraic curves. Benjamin (1969).
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.
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.
J. D. LIPSON. Elements of algebra and algebraic computing. Addison-Wesley (1981).
E. TAHIRI EL ALAOUI. Solutions formelles d'équation algébrique de deux variables. IMAG R.R. 416 (1983).
R. WALKER. Algebraic curves. Springer-Verlag (1978).
D.Y.Y. YUN. Fast algorithm for rational function integration. Proc. IFIP 77 (ed. B. Gilchrist) North-Holland (1977), pp. 493–498.
H. ZEJLI. Calcul dans les extensions de corps. IMAG, Séminaire 397 (1983).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dicrescenzo, C., Duval, D. (1984). Computations on curves. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032834
Download citation
DOI: https://doi.org/10.1007/BFb0032834
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13350-6
Online ISBN: 978-3-540-38893-7
eBook Packages: Springer Book Archive