@inproceedings{NosanAmaurySchmitzShirmohammadiWorrell:ISSAC:2022,
    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.},
    Address = {New York, NY, USA},
    Author = {Nosan, Klara and Pouly, Amaury and Schmitz, Sylvain and Shirmohammadi, Mahsa and Worrell, James},
    BookTitle = {Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation},
    ISBN = {9781450386883},
    Keywords = {algebraic groups, algebraic geometry, zariski topology},
    Location = {Villeneuve-d'Ascq, France},
    Pages = {129--138},
    Publisher = {Association for Computing Machinery},
    Series = {ISSAC '22},
    Title = {{On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices}},
    URL = {https://doi.org/10.1145/3476446.3536172},
    Year = {2022},
    bdsk-url-1 = {https://doi.org/10.1145/3476446.3536172},
    date-added = {2022-07-13 11:11:15 +0200},
    date-modified = {2023-08-30 12:26:14 +0200},
    numpages = {10},
    doi = {10.1145/3476446.3536172}
}

@inproceedings{NosanAmaurySchmitzShirmohammadiWorrell:ISSAC:2022, 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.}, Address = {New York, NY, USA}, Author = {Nosan, Klara and Pouly, Amaury and Schmitz, Sylvain and Shirmohammadi, Mahsa and Worrell, James}, BookTitle = {Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}, ISBN = {9781450386883}, Keywords = {algebraic groups, algebraic geometry, zariski topology}, Location = {Villeneuve-d'Ascq, France}, Pages = {129--138}, Publisher = {Association for Computing Machinery}, Series = {ISSAC '22}, Title = {{On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices}}, URL = {https://doi.org/10.1145/3476446.3536172}, Year = {2022}, bdsk-url-1 = {https://doi.org/10.1145/3476446.3536172}, date-added = {2022-07-13 11:11:15 +0200}, date-modified = {2023-08-30 12:26:14 +0200}, numpages = {10}, doi = {10.1145/3476446.3536172} }