threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each

Usage:

threeVertexQuiver E
Inputs:
- E, a list, number of edges between each pair of vertices
Optional inputs:
- Flow => ..., 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.
- Height => an integer, default value 10, used in conjunction with the option Flow => Random to set the upper limit of the random number generator
Outputs:
- Q, a toric quiver,

Description

This method can be used to create any quiver in the family of quivers that can be built by defining three vertices and any nonzero number of edges joining each pair of edges

i1 : Q = threeVertexQuiver {1,2,3}

o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1}                            }
                 IncidenceMatrix => | -1 -1 -1 -1 0  0  |
                                    | 1  0  0  0  -1 -1 |
                                    | 0  1  1  1  1  1  |
                 Q0 => {0, 1, 2}
                 Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}}
                 weights => {-4, -1, 5}

o1 : ToricQuiver

i2 : Q = threeVertexQuiver ({1,2,3}, Flow => "Random")

o2 = ToricQuiver{flow => {8, 1, 3, 7, 8, 3}                            }
                 IncidenceMatrix => | -1 -1 -1 -1 0  0  |
                                    | 1  0  0  0  -1 -1 |
                                    | 0  1  1  1  1  1  |
                 Q0 => {0, 1, 2}
                 Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}}
                 weights => {-19, -3, 22}

o2 : ToricQuiver

i3 : Q = threeVertexQuiver ({1,2,3}, Flow => {1, 2, 1, 3, 1, 4})

o3 = ToricQuiver{flow => {1, 2, 1, 3, 1, 4}                            }
                 IncidenceMatrix => | -1 -1 -1 -1 0  0  |
                                    | 1  0  0  0  -1 -1 |
                                    | 0  1  1  1  1  1  |
                 Q0 => {0, 1, 2}
                 Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}}
                 weights => {-7, -4, 11}

o3 : ToricQuiver

Ways to use threeVertexQuiver:

threeVertexQuiver(List)

For the programmer

The object threeVertexQuiver is a method function with options.

The source of this document is in ThinSincereQuivers.m2:3279:0.

threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each

Description

See also

Ways to use threeVertexQuiver:

For the programmer