# chainQuiver -- make a toric quiver on underlying graph in the form of a chain

## Synopsis

• Usage:
chainQuiver E
• Inputs:
• E, a list, number of edges linking each vertex to the next
• Optional inputs:
• Flow (missing documentation) => ..., default value "Canonical", specify what form of flow to use. This input can be either a string with values Canonical or Random, or else a list of integer values.
• Outputs:

## Description

 i1 : Q = chainQuiver {1,2,3} o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1} } IncidenceMatrix => | -1 0 0 0 0 0 | | 1 -1 -1 0 0 0 | | 0 1 1 -1 -1 -1 | | 0 0 0 1 1 1 | Q0 => {0, 1, 2, 3} Q1 => {{0, 1}, {1, 2}, {1, 2}, {2, 3}, {2, 3}, {2, 3}} weights => {-1, -1, -1, 3} o1 : ToricQuiver i2 : Q = chainQuiver ({1,2,3}, Flow=>"Random") o2 = ToricQuiver{flow => {24, 65, 71, 72, 19, 19} } IncidenceMatrix => | -1 0 0 0 0 0 | | 1 -1 -1 0 0 0 | | 0 1 1 -1 -1 -1 | | 0 0 0 1 1 1 | Q0 => {0, 1, 2, 3} Q1 => {{0, 1}, {1, 2}, {1, 2}, {2, 3}, {2, 3}, {2, 3}} weights => {-24, -112, 26, 110} o2 : ToricQuiver i3 : Q = chainQuiver ({1,2,3}, Flow=>{1, 2, 1, 3, 1, 4}) o3 = ToricQuiver{flow => {1, 2, 1, 3, 1, 4} } IncidenceMatrix => | -1 0 0 0 0 0 | | 1 -1 -1 0 0 0 | | 0 1 1 -1 -1 -1 | | 0 0 0 1 1 1 | Q0 => {0, 1, 2, 3} Q1 => {{0, 1}, {1, 2}, {1, 2}, {2, 3}, {2, 3}, {2, 3}} weights => {-1, -2, -5, 8} o3 : ToricQuiver

## For the programmer

The object chainQuiver is .