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PHCpack :: mixedVolume

mixedVolume -- mixed volume of a polynomial system; invokes "phc -m" from PHCpack

Synopsis

Description

The mixed volume of a polynomial system provides an upper bound on the number of complex isolated roots without zero components.

When the coefficients of the system are sufficiently generic, the bound is sharp.
i1 : R=QQ[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : S={y-x^2,z-x^3,x+y+z-1}

         2         3
o2 = {- x  + y, - x  + z, x + y + z - 1}

o2 : List
i3 : m=mixedVolume(S)
using temporary file name /tmp/M2-7482-1PHCinput

o3 = 3

Ways to use mixedVolume :