Tropical Algebraic Geometry in Maple, a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients

Abstract

Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.

20 pages, 8 figures, based on a talk the second author gave at MICA 2008: Milestones in Computer Algebra, a conference in honour of Keith Geddes' 60th Birthday, Stonehaven Bay, Trinidad and Tobago, 1-3 May 2008