Sharp estimates for triangular sets

Xavier Dahan, Éric Schost

Research output: Contribution to conferencePaper

43 Citations (Scopus)

Abstract

We study the triangular representation of zero-dimensional varieties defined over the rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential. We also introduce a rational form of triangular representation, for which our estimates become linear. Experiments show the practical interest of this new representation.

Original languageEnglish
Pages103-110
Number of pages8
DOIs
Publication statusPublished - 2004 Jan 1
Externally publishedYes
EventISSAC 2004 - International Symposium on Symbolic and Algebraic Computation - Santander, Spain
Duration: 2004 Jul 42004 Jul 7

Conference

ConferenceISSAC 2004 - International Symposium on Symbolic and Algebraic Computation
CountrySpain
CitySantander
Period04/7/404/7/7

Keywords

  • Intrinsic bounds
  • Polynomial systems
  • Triangular sets

ASJC Scopus subject areas

  • Computer Science(all)

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    Dahan, X., & Schost, É. (2004). Sharp estimates for triangular sets. 103-110. Paper presented at ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation, Santander, Spain. https://doi.org/10.1145/1005285.1005302