Trace test

Understand

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.