Realización de conceptos abstractos de la teoría de grupos por medio de un modelo computacional: implementación de conceptos abstractos relacionados al grupo S3 en el lenguaje de programación C++.

Abstract

This paper focuses on Group Theory, a part of mathematics that helps model physical phenomena through symmetric and dihedral groups. The article presents an implementation of groups using the C++ programming language. Before realizing such a program, a series of preliminary steps must be considered to understand the definitions related to groups. The starting point focuses on the analysis of the presented bibliography, which conceptualizes groups S3 and D3, and the definition of computational structures in the C++ language. Then, the implementation of each group is presented with its respective operators and associated maps with on-screen visualization. In addition, different abstractions of the chosen group are shown through a menu of options and observed on the screen. Finally, through the previously mentioned developments, the proposed definition of the isomorphism function can be proven. Likewise, diverse image representations of said function are presented with user input.