@inproceedings{8ef7e6650a1d4ef58079a1dbce1edc1f,
title = "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 upper bounds on the length of chains of linear algebraic groups.",
keywords = "algebraic geometry, algebraic groups, zariski topology",
author = "Klara Nosan and Amaury Pouly and Sylvain Schmitz and Mahsa Shirmohammadi and James Worrell",
note = "Publisher Copyright: {\textcopyright} 2022 ACM.; 47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022 ; Conference date: 04-07-2022 Through 07-07-2022",
year = "2022",
month = jul,
day = "4",
doi = "10.1145/3476446.3536172",
language = "English",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery",
pages = "129--138",
editor = "Amir Hashemi",
booktitle = "ISSAC 2022 - Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation47th International Symposium on Symbolic and Algebraic Computation, ISSAC 2022",
}