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Algorithmic Search for Flexibility Using Resultants of Polynomial Systems [chapter]

Robert H. Lewis, Evangelos A. Coutsias
Automated Deduction in Geometry  
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
more » ... represent molecules. We then describe an algorithm that examines the resultant and determines ways that the structure can be flexible.
doi:10.1007/978-3-540-77356-6_5 dblp:conf/adg/LewisC06 fatcat:j6daxv5a6rdxjlmotsh74qjvea