Alexander Polynomial via Python Language

• Autor(a) principal: Miranda, Aldicio José
• Data de Publicação: 2020
• Outros Autores: Souza, Taciana Oliveira, Barros, Rui Marcos de Oliveira
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3862
• topic: Topology; Alexander Polynomial; Python Language; Topologia; Polinômio de Alexander; Linguagem Python

A classic knot is an embedding of an one-dimensional sphere S1 in a real three-dimensional environment, usually R3. Under these conditions it is possible to consider the knot diagram, that is, the planar projection of the embedding. This resembles a curve in which the intersections are exchanged for interruptions in its trace, thus indicating that one arc passes over the other. In Knot Theory we study algebraic invariants extracted from the complement of the embedding, and this complement is visible in the case of embedding S1 --> R3. One of the invariants extracted from the knot diagram is the Alexander Polynomial. In this article we show how the process of determining the Alexander Polynomial of a knot can be transported to an algorithm implemented in Python Language and obtained from a drawn diagram with the aid of a computer mouse.