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Flow

Description

This is an optional argument that can be a string with values Canonical, which assigns a value of 1 to each edge, or Random, which assigns random integer values.

i1 : Q = toricQuiver(matrix({{-1,-1,-1,-1},{1,1,0,0},{0,0,1,1}}), Flow => "Canonical")

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

o1 : ToricQuiver
 
i2 : Q = toricQuiver(matrix({{-1,-1,-1,-1},{0,0,1,1},{1,1,0,0}}), Flow => "Random")

o2 = ToricQuiver{flow => {3, 7, 8, 1}                  }
                 IncidenceMatrix => | -1 -1 -1 -1 |
                                    | 1  1  0  0  |
                                    | 0  0  1  1  |
                 Q0 => {0, 1, 2}
                 Q1 => {{0, 1}, {0, 1}, {0, 2}, {0, 2}}
                 weights => {-19, 10, 9}

o2 : ToricQuiver
 
i3 : Q = bipartiteQuiver(2, 3, Flow => "Random")

o3 = ToricQuiver{flow => {8, 3, 3, 7, 8, 8}                            }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  |
                                    | 0  0  0  -1 -1 -1 |
                                    | 1  0  0  1  0  0  |
                                    | 0  1  0  0  1  0  |
                                    | 0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4}
                 Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}}
                 weights => {-14, -23, 15, 11, 11}

o3 : ToricQuiver

See also

Functions with optional argument named Flow:

  • bipartiteQuiver(...,Flow=>...) -- see bipartiteQuiver -- make a toric quiver on underlying bipartite graph
  • chainQuiver(...,Flow=>...) -- see chainQuiver -- make a toric quiver on underlying graph in the form of a chain
  • threeVertexQuiver(...,Flow=>...) -- see threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
  • toricQuiver(...,Flow=>...) -- see toricQuiver -- the toricQuiver constructor

For the programmer

The object Flow is a symbol.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/ThinSincereQuivers.m2:3291:0.