Background:
There exists a Bernstein theorem for tropical varieties (see Sturmfels'
book on ``Solving systems of polynomial equations''), there also
exists a mixed Monge-Ampère measure whose value at any connected
compact
component 
of the intersection of the considered amoebas is the number
of solutions of the corresponding polynomial system in the pre-image
(in the complex torus) by 
of (see the paper ``Amoebas,
Monge-Ampère
measures and triangulations of the Newton polytope'' from M. Passare and
H. Rullgård).
Questions:
Is it true that this value coincides with the volume of the mixed cell
corresponding to (this volume participates in the Bernstein theorem
for tropical varieties)? Is there a one-to-one correspondence
with the solutions of our system in
and the solutions
of a binomial system corresponding to the mixed cell, and which
sends real solutions to real solutions?
(contributed by Frederic Bihan)
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