Deciding whether two polynomials in two variables with approximate
coefficients have a common factor is a problem in symbolic-numeric
computing. The tropical viewpoint leads us to compute tropisms.
Tropisms define initial forms of the polynomials which have common
roots. These common roots are the initial coefficients of the
Puiseux series used to grow to representation of the common factor.
The algorithms we use to compute tropisms and coefficients of the
Puiseux series lead to an efficient symbolic-numeric preprocessing
method to decide whether two polynomials share a common factor.
This is joint work with Danko Adrovic.
AMS Special Session on Computational Algebraic and Analytic Geometry for Low-dimensional Varieties. Washington DC, Tuesday 6 January 2009.