  In this paper we give a computer proof of a new polynomial identity, which
extends a recent result of Alladi and the first author. In addition, we provide
computer proofs for new finite analogs of Jacobi and Euler formulas. All
computer proofs are done with the aid of the new computer algebra package
qMultiSum developed by the second author. qMultiSum implements an algorithmic
refinement of Wilf and Zeilberger's multi-q-extension of Sister Celine's
technique utilizing additional ideas of Verbaeten and Wegschaider.
