  We generalize the notion of the quandle polynomial to the case of
singquandles. We show that the singquandle polynomial is an invariant of finite
singquandles. We also construct a singular link invariant from the singquandle
polynomial and show that this new singular link invariant generalizes the
singquandle counting invariant. In particular, using the new polynomial
invariant, we can distinguish singular links with the same singquandle counting
invariant.
