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

## TL;DR

InfoMod is a software tool that visualizes and computes properties of Gauss' binary quadratic forms, connecting classical theories with modern graph representations for educational and research purposes.

## Contribution

It introduces a novel software that integrates classical and recent theories of binary quadratic forms through visual and computational methods.

## Key findings

- Demonstrates Gauss' reduction algorithm visually
- Provides new insights into form representation and classification
- Facilitates exploration of ambiguous and reciprocal forms

## Abstract

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 \c{c}arks. 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.