Mixed Volume 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.






[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.







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