(joint with Tsung-Lin Lee (Michigan State University))
While the mixed volume computation generates general interests of its own,
its by-product the mixed cells are crucially important in solving
polynomial systems numerically by the polynomial homotopy continuation methods.
In 2005, a software package, MixedVol by T. Gao, T.Y. Li and M. Wu,
emerged which led the existing codes for this purpose by a great margin.
However, after MixedVol was published, T. Mizutani, A. Takeda and
M. Kojima developed a more advanced algorithm based on dynamic evaluations
of the mixed cells which leads MixedVol in speed by a substantial
margin. Recently, we revised the method in MixedVol with different
forms of dynamic evaluations implemented. The preliminary results show
that the new MixedVol code overtakes the lead in speed once again.