改进了算术Fuchsian群基本域的计算

Math. Comput. Model. Pub Date : 2021-10-21 DOI:10.1090/mcom/3777

James Rickards

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引用次数: 2

摘要

． Voight给出了一种计算算术Fuchsian群的基本域的实用算法，并在Magma中实现。后来佩奇把它扩展到算术克莱因群的情况。我们结合并改进了这两种算法的部分内容，以产生一种更有效的算法来处理算术Fuchsian群。该算法是在PARI/GP中实现的，我们通过比较运行时间和实时Magma实现来演示改进。

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Improved computation of fundamental domains for arithmetic Fuchsian groups

. A practical algorithm to compute the fundamental domain of an arithmetic Fuchsian group was given by Voight, and implemented in Magma. It was later expanded by Page to the case of arithmetic Kleinian groups. We combine and improve on parts of both algorithms to produce a more eﬃcient algorithm for arithmetic Fuchsian groups. This algorithm is implemented in PARI/GP, and we demonstrate the improvements by comparing running times versus the live Magma implementation.

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Math. Comput. Model.

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