  In the field of numerical algebraic geometry, positive-dimensional solution
sets of systems of polynomial equations are described by witness sets. In this
paper, we define multiprojective witness sets which encode the multidegree
information of an irreducible multiprojective variety. Our main results
generalize the regeneration solving procedure, a trace test, and numerical
irreducible decomposition to the multiprojective case. Examples are included to
demonstrate this new approach.
