Gcd modulo a primary triangular set of dimension zero

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Computing gcd over a triangular set T is the core routine of the machinery of some triangular decomposition methods, in the realm of polynomial ideal theory. As such it has been studied intensively and is well-understood and implemented in several situations, especially in the case where coefficients are over a radical triangular set; It is not the case over a non-radical one. This paper introduces a gcd notion in this case, when additionally for simplicity 〈T〉 is assumed to be primary. It is built upon the Henselian property of the coefficient ring, and is natural in that it is linked with the subresultant sequence of a and b modulo T. A general algorithm still relies on some assumptions, except for the case of a triangular set T = (T1)x1)) of one variable.

Original languageEnglish
Title of host publicationISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation
EditorsMichael Burr
PublisherAssociation for Computing Machinery
Pages109-116
Number of pages8
ISBN (Electronic)9781450350648
DOIs
Publication statusPublished - 2017 Jul 23
Externally publishedYes
Event42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 - Kaiserslautern, Germany
Duration: 2017 Jul 252017 Jul 28

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
VolumePart F129312

Conference

Conference42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017
Country/TerritoryGermany
CityKaiserslautern
Period17/7/2517/7/28

Keywords

  • Gcd, primary ideal
  • Henselian ring
  • Subresultant
  • Triangular set

ASJC Scopus subject areas

  • Mathematics(all)

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