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

Danko Adrovic and Jan Verschelde

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.

2000 Mathematics Subject Classification. Primary 13P05, 14A99; Secondary 65H10, 68W30.

Key words and phrases. factorization, Newton polygon, Puiseux expansion, symbolic-numeric algorithm, tropical algebraic geometry.