  In order to obtain more accurate solutions of polynomial systems with
numerical continuation methods we use multiprecision arithmetic. Our goal is to
offset the overhead of double double arithmetic accelerating the path trackers
and in particular Newton's method with a general purpose graphics processing
unit. In this paper we describe algorithms for the massively parallel
evaluation and differentiation of sparse polynomials in several variables. We
report on our implementation of the algorithmic differentiation of products of
variables on the NVIDIA Tesla C2050 Computing Processor using the NVIDIA CUDA
compiler tools.
