Algorithmic search for flexibility using resultants of polynomial systems. (English) Zbl 1195.68115

Lewis, Robert H.; Coutsias, Evangelos A.

Botana, Francisco (ed.) et al., Automated deduction in geometry. 6th international workshop, ADG 2006, Pontevedra, Spain, August 31–September 2, 2006. Revised papers. Berlin: Springer (ISBN 978-3-540-77355-9/pbk). Lecture Notes in Computer Science 4869. Lecture Notes in Artificial Intelligence, 68-79 (2007).

Summary: 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.
For the entire collection see [Zbl 1132.68006].

MSC:

68W30	Symbolic computation and algebraic computation
92-08	Computational methods for problems pertaining to biology
92E10	Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Software:

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