  The polyhedral homotopy method of Huber and Sturmfels is a particularly
efficient and robust numerical method for solving system of (Laurent)
polynomial equations. A central component in an implementation of this method
is an efficient and scalable path tracker. While the implementation issues in a
scalable path tracker for computer clusters or multi-core CPUs have been solved
thoroughly, designing good GPU-based implementations is still an active
research topic. This paper addresses the core issue of efficiently evaluate a
multivariate system of Laurent polynomials together with all its partial
derivatives. We propose a simple approach that maps particularly well onto the
parallel computing architectures of modern GPUs. As a by-product, we also
simplify and accelerate the path tracker by consolidating the computation of
Euler and Newton directions.
