Multivariate Elimination

Deepak Kapur

Department of Computer Science

State University of New York

Albany, NY 12222

Abstract

Resultants were introduced and studied by Euler, Bezout, Sylvester, Cayley, Dixon and Macaulay to extend linear algebra techniques for solving linear equations to nonlinear polynomial equation solving. A historical account of these developments will be provided with a special focus on Dixon resultants. Recent developments in generalizing Dixon resultants will be presented, and their use for geometric reasoning and computing invariants will be illustrated. Results of these methods on a variety of examples from engineering and artificial intelligence applications including geometry, computer vision, and robotics will be presented and compared with other related methods including Macaulay and sparse resultants.