# potentialWalls -- return the potential walls in the weight chamber decomposition for a given quiver

## Synopsis

• Usage:
potentialWalls Q
• Inputs:
• Outputs:

## Description

every wall can be represented uniquely by a partition of the vertices Q0 of Q into two sets Qplus and Qminus. As a partition can be expressed in terms of only one of the subsets, only one of the two sets Qplus and Qminus is used in every case. Thus we denote the wall W by the subset of vertices Qplus used for defining it.

 i1 : potentialWalls toricQuiver {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}} o1 = {Wall{Qplus => {1, 2, 3}}, Wall{Qplus => {0, 2, 3}}, Wall{Qplus => WallType => (0, 3) WallType => (1, 2) WallType ------------------------------------------------------------------------ {0, 1, 3}}, Wall{Qplus => {0, 1, 2}}, Wall{Qplus => {2, 3} }, => (2, 1) WallType => (3, 0) WallType => (0, 4) ------------------------------------------------------------------------ Wall{Qplus => {1, 3} }, Wall{Qplus => {0, 3} }} WallType => (1, 3) WallType => (2, 2) o1 : List

## Ways to use potentialWalls :

• "potentialWalls(ToricQuiver)"
• potentialWalls(Matrix) (missing documentation)

## For the programmer

The object potentialWalls is .