We introduce a new approach to multivariate polynomial factorisation
which incorporates ideas from polyhedral geometry, and generalises
Hensel lifting. Our main contribution is to present an algorithm for
factoring bivariate polynomials which is able to exploit to some extent the
sparsity of polynomials. We give details of an implementation which we
used to factor randomly chosen sparse and composite polynomials of high
degree over the binary field.
