**MixedVol-2.0**

**Mixed** **Vol**ume
computation

By Bernshtein’s
theorem [4], the mixed volume of a polynomial system provides an upper bound
for the number of isolated solutions in the algebraic tori and the bound can be reached
when the coefficients of the polynomial system are generic. In general, mixed volume is much less than
the classical Bézout number for a
sparse polynomial system. **MixedVol-2.0**
is a software package which computes the mixed volume of a polynomial system.

**References:**

[1] T.-L. Lee and T.Y. Li, “** Mixed volume computation in
solving polynomial systems**”, Contemporary Mathematics, 556:97-112,
2011.

[2] T. Mizutani, A. Takeda, and M. Kojima
(2007), “** Dynamic enumeration of all mixed cells**”, Disc. & Comput. Geom., 37, pp.
351-367.

[3] T. Gao and T.Y. Li (2003), “** Mixed volume computation for semi-mixed
polynomial systems**”, Disc. & Comput.
Geom., 29, pp. 257-277.

[4] Bernshtein, D.N. (1975), “** The
number of roots of a system of equations**”, Functional Analysis and
Appl., 9(3), 183-185. Translated from Funktsional.
Anal. I Ego Prilozhen., 9(3), 1-4.

**Download:**