InfoMod: a visual and computational approach to Gauss' binary quadratic forms

被引:0
作者
Zeytin, Ayberk [1 ]
机构
[1] Galatasaray Univ, Ciragan Cad 36 Besiktas, TR-34349 Istanbul, Turkey
关键词
Modular group; Binary quadratic forms; Hyperbolic elements; Geodesics; Visualization;
D O I
10.1007/s00200-020-00460-w
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
InfoMod is a software devoted to the modular group, PSL2 (Z). It consists of algorithms that deal with the classical correspondences among geodesics on the modular surface, elements of the modular group and binary quadratic forms. In addition, the software implements the recently discovered representation of Gauss' indefinite binary quadratic forms and their classes in terms of certain infinite planar graphs (dessins) called carks. InfoMod illustrates various aspects of these forms, i.e. Gauss' reduction algorithm, the representation problem of forms, ambiguous and reciprocal forms. It can be used for visualization, for high performance computation involving these mathematical structures as well as experimenting.
引用
收藏
页码:437 / 455
页数:19
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