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On the computation of the Zariski closure of finitely generated groups of matrices

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 up...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1145/3476446.3536172

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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Oxford college:
Green Templeton College
Role:
Author
Publisher:
Association for Computing Machinery Publisher's website
Pages:
129-138
Host title:
ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation
Publication date:
2022-07-05
Acceptance date:
2022-05-08
Event title:
ISSAC '22: International Symposium on Symbolic and Algebraic Computation
Event location:
Lille, France
Event website:
https://www.issac-conference.org/2022/
Event start date:
2022-07-04T00:00:00Z
Event end date:
2022-07-07T00:00:00Z
DOI:
ISBN:
9781450386883
Language:
English
Keywords:
Pubs id:
1269974
Local pid:
pubs:1269974
Deposit date:
2022-08-08

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