Sparse elimination and applications in kinematics

Abstract

This thesis proposes efficient algorithmic solutions to problems in computational algebra and computational algebraic geometry. Moreover, it considers their application to different areas where algebraic systems describe kinematic and geometric constraints. Given an arbitrary system of nonlinear multivariate polynomial equations, its resultant serves in eliminating variables and reduces root finding to a linear eigenproblem. Our contribution is to describe the first efficient and general algorithms for computing the sparse resultant. The sparse resultant generalizes the classical homogeneous resultant and exploits the structure of the given polynomials. Its size depends only on the geometry of the input Newton polytopes. The first algorithm uses a subdivision of the Minkowski sum and produces matrix...