On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices
On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices
复制标题
有限生成矩阵群Zariski闭包的计算
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
J. Worrell
中科院分区：
文献类型：
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作者：
Klara Nosan;Amaury Pouly;S. Schmitz;M. Shirmohammadi;J. Worrell
我们研究计算有限生成的矩阵组的 Zariski 闭包的复杂性。 Derksen、Jeandel 和 Koiran 先前已证明 Zariski 闭包是可计算的，但他们算法的终止参数似乎不会产生任何复杂性界限。在本文中，我们采用不同的方法并获得定义闭包的多项式次数的界限。我们的界限表明可以在基本时间内计算闭包。我们还获得了线性代数群链长度的上限。
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.
线性代数群的复曲面包络的度界
影响因子：
2
作者：
Amzallag, Eli;Minchenko, Andrei;Pogudin, Gleb
通讯作者：
Pogudin, Gleb