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2006 OPTi's Algorithm for Discreteness Determination
Masaaki Wada
Experiment. Math. 15(1): 61-66 (2006).

Abstract

We summarize how OPTi draws the parameter space. Each point in the picture of a parameter space corresponds to a group, and the program colors the point according to whether the group is discrete or indiscrete. Applying Jørgensen's inequality to certain sets of generators, OPTi first tries to decide indiscreteness of the group. If the process fails for generators up to a certain depth, the program then tries to construct the Ford region. When it succeeds in constructing the Ford region, Poincaré's polyhedron theorem guarantees the discreteness of the group.

Citation

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Masaaki Wada. "OPTi's Algorithm for Discreteness Determination." Experiment. Math. 15 (1) 61 - 66, 2006.

Information

Published: 2006
First available in Project Euclid: 16 June 2006

zbMATH: 1107.30033
MathSciNet: MR2229386

Subjects:
Primary: 20-04
Secondary: 22E40 , 30F40

Keywords: algorithm , Discrete , OPTi

Rights: Copyright © 2006 A K Peters, Ltd.

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