Algorithmic Search for Flexibility Using Resultants of Polynomial Systems

This paper describes the recent convergence of four topics: polynomial systems, flexibility of three dimensional objects, computational chemistry, and computer algebra. We discuss a way to solve systems of polynomial equations with resultants. Using ideas of Bricard, we find a system of polynomial equations that models a configuration of quadrilaterals that is equivalent to some three dimensional structures. These structures are of interest in computational chemistry, as they represent molecules. We then describe an algorithm that examines the resultant and determines ways that the structure can be flexible.

• Type: Conference
• Year: 2006
• Where: ADG
• Authors: Robert H. Lewis, Evangelos A. Coutsias
• Keywords: ADG 2006, Computational Chemistry, Mathematics, Polynomial Equations, Polynomial Systems