Given a compact orientable surface, we determine a complete
set of relations for a function defined on the set of all homotopy
classes of simple loops to be a geometric intersection number function.
As a consequence, Thurston’s space of measured laminations
and Thurston’s compactification of the Teichmüller space are described
by a set of explicit equations. These equations are polynomials
in the max-plus semi-ring structure on the real numbers.
It shows that Thurston’s theory of measured laminations is within
the domain of tropical geometry.