samePolytope -- whether two weights produce the same flow polytope

Synopsis

Usage:

samePolytope(Th1, Th2, TQ)
Inputs:
- Th1, a list,
- Th1, a list,
- TQ, an instance of the type ToricQuiver,
Outputs:
- B, a Boolean value, whether the two weights correspond to the same polytope

Description

This function returns either a boolean value of true or else a string describing why the outcome cannot be determined. It requires that polytopes be smooth and that the set of stable trees for both weights be nonempty. This is computed by calculating the flow polytope for the toric quiver with each of the two weights and comparing the resulting polytopes. The polytopes are considered equal if they are isomorphic, using the areIsomorphic method in the LatticePolytopes package.

i1 : Q = toricQuiver({{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}});

i2 : samePolytope({-3,2,-1,2},{-2,1,-2,3}, Q)

o2 = true

Caveat

This operation is computationally expensive, and may not perform well for quivers whose chamber systems are comprised of many subchambers.

Ways to use samePolytope :

samePolytope(List,List,ToricQuiver)

For the programmer