TY  - JOUR
AU  - Das, Haridas Kumar 
AU  - Reza, Nasim 
PY  - 2018
TI  - On Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph Coloring
JF  - Journal of Mathematics and Statistics
VL  - 14
IS  - 1
DO  - 10.3844/jmssp.2018.175.182
UR  - https://thescipub.com/abstract/jmssp.2018.175.182
AB  - 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.