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Complexity of standard bases in projective dimension zero II

  • Marc Giusti
Submitted Contributions Bases
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)

Abstract

This paper is the continuation of a previous one devoted to the complexity of standard bases in projective dimension zero (see Giusti, 1989). We improve the upper bound on the maximal degree of elements in a standard basis, with respect to any choice of coordinates and any compatible ordering, given in loc.cit. This bound is sharp, being attained for complete intersections and lexicographic ordering.

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References

  1. I. BERMEJO (1990), Sur les degrés d'une base standard minimale pour l'ordre lexicographique d'un idéal dont la variété des zéros est Cohen-Macaulay de dimension 1, Notes aux Compte-Rendus de l'Académie des Sciences de Paris, t. 310, Série I, 591–594.Google Scholar
  2. M. GIUSTI (1988), Combinatorial dimension theory of algebraic varieties, in “Computational Aspects of Commutative Algebra”, special issue, Journal of Symbolic Computation, Academic Press 6, 115–131.Google Scholar
  3. M. GIUSTI (1989), Complexity of standard bases in projective dimension zero, Proceedings of EUROCAL 87 (European Conference on Computer Algebra, Leipzig, RDA), Lecture Notes in Computer Science 378, Springer Verlag, 333–335.Google Scholar
  4. D. LAZARD (1981), Résolution des systèmes d'équations algébriques, Theoretical Computer Science 15, 77–110.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Marc Giusti
    • 1
  1. 1.Laboratoire d'Informatique Ecole PolytechniqueSDI CNRS 6176 “Calcul formel, Algèbre et Géométrie algorithmiques“ (associée au Centre de Mathématiques, URA CNRS D.0169)Palaiseau Cedex

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