Solving systems of polynomial equations using Gröbner basis calculations with applications to mechanics

Abstract

Solving systems of algebraic equations is presented using the Gröbner Basis Package of the computer algebra system MAPLE V. The Grobner basis computations allow exact conclusions on the solutions of sets of polynomial equations, such as to decide if the given set is solvable, if the set has (at most) finitely many solutions, to determine the exact number of solutions in case there are finitely many, and their actual computation with arbitrary precision. The Gröbner basis computations are illustrated by two examples: computing the global equilibrium paths of a propped cantilever and of a simple arch.