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InfoMod: a visual and computational approach to Gauss’ binary quadratic forms
Applicable Algebra in Engineering, Communication and Computing ( IF 0.6 ) Pub Date : 2020-09-19 , DOI: 10.1007/s00200-020-00460-w
Ayberk Zeytin

InfoMod is a new software and application devoted to the modular group, PSL2(Z). It has algorithms that deals with the classical correspondences among continued fractions, geodesics on the modular surface 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 as an educational tool, and might be used to explore some new facts about these objects.

中文翻译:

InfoMod:高斯二元二次型的视觉和计算方法

InfoMod 是一款专门用于模块化组 PSL2(Z) 的新软件和应用程序。它具有处理连分数、模曲面上的测地线和二元二次形式之间的经典对应关系的算法。此外,该软件实现了最近发现的高斯不定二元二次型及其类在称为汽车的某些无限平面图(dessins)方面的表示。InfoMod 说明了这些形式的各个方面,即高斯约简算法、形式的表示问题、模糊形式和互易形式。它可以用作教育工具,也可以用来探索有关这些对象的一些新事实。
更新日期:2020-09-19
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