On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices

Klara Nosan, Amaury Pouly, Sylvain Schmitz, Mahsa Shirmohammadi, James Worrell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We investigate the complexity of computing the Zariski closure of a finitely generated group of matrices. The Zariski closure was previously shown to be computable by Derksen, Jeandel, and Koiran, but the termination argument for their algorithm appears not to yield any complexity bound. In this paper we follow a different approach and obtain a bound on the degree of the polynomials that define the closure. Our bound shows that the closure can be computed in elementary time. We also obtain upper bounds on the length of chains of linear algebraic groups.

Original languageEnglish
Title of host publicationISSAC 2022 - Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022
EditorsAmir Hashemi
PublisherAssociation for Computing Machinery
Pages129-138
Number of pages10
ISBN (Electronic)9781450386883
DOIs
Publication statusPublished - 4 Jul 2022
Externally publishedYes
Event47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022 - Virtual, Online, France
Duration: 4 Jul 20227 Jul 2022

Publication series

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

Conference

Conference47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022
Country/TerritoryFrance
CityVirtual, Online
Period4/07/227/07/22

Keywords

  • algebraic geometry
  • algebraic groups
  • zariski topology

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