Tools for Calculating Topological Invariants

Juan Pablo Bedoya Giraldo, Aura Lucía Pérez Escobar, Javier Guillermo Valdés Duque

Abstract


In this article there is a description of the process that yielded a software tool which was designed with the purpose of calculating four specific topological invariants, among which we count the Betti numbers, the dimension of the complex, the q-array and the Euler-Poincaré characteristic.

The meaning of all the obtained results is viewed from Professor Luis Eduardo Múnera’s perspective, which in turn proposes a formal mathematical definition of cohesion and coupling, two important criteria when evaluating modularity of a software design. The article also describes the tool itself, its functionality and the importance it has to the professor’s project.

In order to portrait a full comprehensible description of both the process and the tool, an historical framework is established through a brief review of the evolution of the different ideas and concepts behind the project, and the way and pace with which these were assimilated by the student team that were appointed to the task.


Keywords


Modular design; algebraic topology; topological invariants calculations; Betti numbers; complex dimension; Euler/Poincaré characteristic; qarray; cohesion; coupling; Matlab.



DOI: http://dx.doi.org/10.18046/syt.v2i3.931

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