Determining Flexibility of Molecules Using Resultants of Polynomial Systems Robert H. Lewis Fordham University http://fordham.academia.edu/RobertLewis Evangelos Coutsias University of New Mexico A new approach to an old subject Abstract This talk 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 and demonstrate an algorithm that examines the resultant and determines ways that the structure can be ﬂexible. We review some ideas about ﬂexibility, from Cauchy (1813) to Bricard (1893) to Connelly (1977) to Steﬀan (1980). 1