# coneSystem -- compute the chamber decomposition of weights

## Synopsis

• Usage:
coneSystem Q
• Inputs:
• Outputs:
• L, a list, of Cone instances

## Description

The set of weights th for which the polytope (Q,th) is nonempty lies in a fan CQ. This fan is partitioned into cones by the walls of the toric quiver Q, and for each partition there exists a unique flow polytope.

 i1 : Q = toricQuiver {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}}; i2 : CS = coneSystem Q o2 = {Cone{...1...}, Cone{...1...}, Cone{...1...}, Cone{...1...}, ------------------------------------------------------------------------ Cone{...1...}, Cone{...1...}, Cone{...1...}} o2 : List

## For the programmer

The object coneSystem is .