  The trace test in numerical algebraic geometry verifies the completeness of a
witness set of an irreducible variety in affine or projective space. We give a
brief derivation of the trace test and then consider it for subvarieties of
products of projective spaces using multihomogeneous witness sets. We show how
a dimension reduction leads to a practical trace test in this case involving a
curve in a low-dimensional affine space.
