Macaulay2 » Documentation
Packages » ThinSincereQuivers > mergeOnVertex
next | previous | forward | backward | up | index | toc

mergeOnVertex -- join two quivers together by identifying a vertex from each

Synopsis

Description

This method creates a new quiver from joining two toricQuivers together by identifying vertex $V1$ in $Q1$ with vertex $V2$ in $Q2$. The input matrices must correspond to valid graphs, and the integers must correspond to vertices in each of the provided quiver objects.

i1 : mergeOnVertex (bipartiteQuiver (2, 3), 1, bipartiteQuiver (2, 3), 0)

o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}                                                          }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  0  0  0  0  0  0  |
                                    | 1  0  0  1  0  0  0  0  0  0  0  0  |
                                    | 0  1  0  0  1  0  0  0  0  0  0  0  |
                                    | 0  0  1  0  0  1  0  0  0  0  0  0  |
                                    | 0  0  0  -1 -1 -1 -1 -1 -1 0  0  0  |
                                    | 0  0  0  0  0  0  0  0  0  -1 -1 -1 |
                                    | 0  0  0  0  0  0  1  0  0  1  0  0  |
                                    | 0  0  0  0  0  0  0  1  0  0  1  0  |
                                    | 0  0  0  0  0  0  0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4, 5, 6, 7, 8}
                 Q1 => {{0, 1}, {0, 2}, {0, 3}, {4, 1}, {4, 2}, {4, 3}, {4, 6}, {4, 7}, {4, 8}, {5, 6}, {5, 7}, {5, 8}}
                 synonym => toric quiver
                 weights => {-3, 2, 2, 2, -6, -3, 2, 2, 2}

o1 : ToricQuiver
 
i2 : mergeOnVertex (bipartiteQuiver (2, 3), 1, matrix({{-1,-1,-1,-1},{1,1,0,0},{0,0,1,1}}), 0)

o2 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}                                                }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  0  0  0  0  |
                                    | 1  0  0  1  0  0  0  0  0  0  |
                                    | 0  1  0  0  1  0  0  0  0  0  |
                                    | 0  0  1  0  0  1  0  0  0  0  |
                                    | 0  0  0  -1 -1 -1 -1 -1 -1 -1 |
                                    | 0  0  0  0  0  0  1  1  0  0  |
                                    | 0  0  0  0  0  0  0  0  1  1  |
                 Q0 => {0, 1, 2, 3, 4, 5, 6}
                 Q1 => {{0, 1}, {0, 2}, {0, 3}, {4, 1}, {4, 2}, {4, 3}, {4, 5}, {4, 5}, {4, 6}, {4, 6}}
                 synonym => toric quiver
                 weights => {-3, 2, 2, 2, -7, 2, 2}

o2 : ToricQuiver
 
i3 : mergeOnVertex (matrix({{-1,-1,-1,-1},{1,1,0,0},{0,0,1,1}}), 1, bipartiteQuiver (2, 3), 0)

o3 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}                                                }
                 IncidenceMatrix => | -1 -1 -1 -1 0  0  0  0  0  0  |
                                    | 1  1  0  0  0  0  0  0  0  0  |
                                    | 0  0  1  1  -1 -1 -1 0  0  0  |
                                    | 0  0  0  0  0  0  0  -1 -1 -1 |
                                    | 0  0  0  0  1  0  0  1  0  0  |
                                    | 0  0  0  0  0  1  0  0  1  0  |
                                    | 0  0  0  0  0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4, 5, 6}
                 Q1 => {{0, 1}, {0, 1}, {0, 2}, {0, 2}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}}
                 synonym => toric quiver
                 weights => {-4, 2, -1, -3, 2, 2, 2}

o3 : ToricQuiver

Ways to use mergeOnVertex :

For the programmer

The object mergeOnVertex is a method function.