Journal of Mathematics and Statistics

On Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph Coloring

Haridas Kumar Das and Nasim Reza

DOI : 10.3844/jmssp.2018.175.182

Journal of Mathematics and Statistics

Volume 14, 2018

Pages 175-182

Abstract

This paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving a system of polynomial equations (linear and nonlinear) with a finite number of solutions extending the idea of Gröbner basis. Finally we explore the idea of Gröbner basis for coloring the vertices of a given graph. We illustrate the stated results through a number of examples. Moreover, as for auxilary and making comparison with the analytic results, we use Mathematica 9.0.1 to develop some computer algebra.

Copyright

© 2018 Haridas Kumar Das and Nasim Reza. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.