The computation of the tropical prevariety is the first step
in the application of polyhedral methods to compute positive
dimensional solution sets of polynomial systems.
In particular, pretropisms are candidate leading exponents
for the power series developments of the solutions.
The computation of the power series may start as soon as one
pretropism is available, so our parallel computation of the
tropical prevariety has an application in a pipelined solver.
We present a parallel implementation of dynamic enumeration.
Our first distributed memory implementation with forked processes
achieved good speedups, but quite often resulted in large variations
in the execution times of the processes.
The shared memory multithreaded version applies work stealing
to reduce the variability of the run time.
Our implementation applies the thread safe Parma Polyhedral Library (PPL),
in exact arithmetic with the GNU Multiprecision Arithmetic Library (GMP),
aided by the fast memory allocations of TCMalloc.
Our parallel implementation is capable of computing the tropical
prevariety of the cyclic 16-roots problem.
We also report on computational experiments on the n-body
and n-vortex problems;
our computational results compare favorably with Gfan.