Exploring Gröbner bases for practical problem-solving applications

Gröbner bases serve as a crucial theoretical cornerstone in contemporary (polynomial) ring theory. The development of Gröbner basis theory originated from efforts to address theoretical issues related to ideals in polynomial rings and to solve systems of polynomial equations. This article explores three practical applications of Gröbner basis theory: using Gröbner bases to solve systems of nonlinear polynomial equations, tackling an k-corolability problem, determining the chromatic number of a graph, and presenting a unique example from the automatic geometric proving. By understanding these applications, we can appreciate how Gröbner bases bridge abstract algebraic concepts with tangible computational solutions

کلیدواژه ها:

Fuzzy Numbers ، Fuzzy matrices ، Gröbner Bases ، Fuzzy inverse matrix ، Fuzzy linear equation systems