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

Synopsis

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}}
                 synonym => toric quiver
                 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}}
                 synonym => toric quiver
                 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}}
                 synonym => toric quiver
                 weights => {-7, -4, 11}

o3 : ToricQuiver

See also

Ways to use threeVertexQuiver :

For the programmer

The object threeVertexQuiver is a method function with options.