Knots have been influential in various research fields, particularly in chemistry where properties of molecules, such as proteins, can be studied using special types of knots known as spatial graphs. This work presents a computational development aimed at creating a software program that automates the calculation of a topological invariant, known as the Yamada polynomial. Different examples of the calculation of the polynomial invariant for different types of molecules will also be found, and aspects such as chirality or the distinction of some proteins will be determined through them. For this work, the language Wolfram Mathematica has been used as the primary tool for computing the required algebra in this work.

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A Computational Framework for the Calculation of a Polynomial Invariant in Spatial Graphs

  • Myrian Sadith González Orellana,
  • José Mauricio Alvarenga Rodríguez

摘要

Knots have been influential in various research fields, particularly in chemistry where properties of molecules, such as proteins, can be studied using special types of knots known as spatial graphs. This work presents a computational development aimed at creating a software program that automates the calculation of a topological invariant, known as the Yamada polynomial. Different examples of the calculation of the polynomial invariant for different types of molecules will also be found, and aspects such as chirality or the distinction of some proteins will be determined through them. For this work, the language Wolfram Mathematica has been used as the primary tool for computing the required algebra in this work.