  In numerical algebraic geometry witness sets are numerical representations of
positive dimensional solution sets of polynomial systems. Considering the
asymptotics of witness sets we propose certificates for algebraic curves. These
certificates are the leading terms of a Puiseux series expansion of the curve
starting at infinity. The vector of powers of the first term in the series is a
tropism. For proper algebraic curves, we relate the computation of tropisms to
the calculation of mixed volumes. With this relationship, the computation of
tropisms and Puiseux series expansions could be used as a preprocessing stage
prior to a more expensive witness set computation. Systems with few monomials
have fewer isolated solutions and fewer data are needed to represent their
positive dimensional solution sets.
