Tropical Algebraic Geometry in Maple, a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients
This work offers a novel method for a known bottleneck in symbolic-numeric computing, but the lack of experimental results limits its demonstrated impact.
The paper addresses the problem of finding common factors of multivariate polynomials with approximate coefficients, proposing a preprocessing algorithm that combines tropical algebraic geometry with polyhedral and numerical methods. The approach is illustrated in Maple, but no concrete numerical results are provided.
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.