A toric quiver is a directed graph Q=(Q_0, Q_1) where Q_0 is the set of vertices associated to Q and Q_1 is the set of arrows. Also included in $Q$ is a flow, which associates an integer value to each edge. The canonical flow gives a weight of 1 to each edge.
the ToricQuiver data type is stored as a hash table with the following keys:
i1 : Q = toricQuiver matrix({{-1,-1,-1,-1},{1,1,0,0},{0,0,1,1}}) 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},{1,1,0,0},{0,0,1,1}}), {3, 1, 0, 5}) o2 = ToricQuiver{flow => {3, 1, 0, 5} } 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 => {-9, 4, 5} o2 : ToricQuiver |
i3 : Q = toricQuiver {{0,1},{0,1},{0,2},{0,2}} o3 = 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} o3 : ToricQuiver |
i4 : Q = toricQuiver ({{0,1},{0,1},{0,2},{0,2}}, {1,2,3,4}) o4 = ToricQuiver{flow => {1, 2, 3, 4} } 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 => {-10, 3, 7} o4 : ToricQuiver |
i5 : Q = toricQuiver(matrix({{-1,-1,-1,-1},{1,1,0,0},{0,0,1,1}}), Flow=>"Canonical") o5 = 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} o5 : ToricQuiver |
i6 : Q = toricQuiver(matrix({{-1,-1,-1,-1},{0,0,1,1},{1,1,0,0}}), Flow=>"Random") o6 = ToricQuiver{flow => {24, 65, 71, 72} } IncidenceMatrix => | -1 -1 -1 -1 | | 0 0 1 1 | | 1 1 0 0 | Q0 => {0, 1, 2} Q1 => {{0, 2}, {0, 2}, {0, 1}, {0, 1}} weights => {-232, 143, 89} o6 : ToricQuiver |
i7 : R = toricQuiver(Q) o7 = ToricQuiver{flow => {24, 65, 71, 72} } IncidenceMatrix => | -1 -1 -1 -1 | | 0 0 1 1 | | 1 1 0 0 | Q0 => {0, 1, 2} Q1 => {{0, 2}, {0, 2}, {0, 1}, {0, 1}} weights => {-232, 143, 89} o7 : ToricQuiver |
i8 : R = toricQuiver(Q, {1,2,3,4}) o8 = ToricQuiver{flow => {1, 2, 3, 4} } IncidenceMatrix => | -1 -1 -1 -1 | | 0 0 1 1 | | 1 1 0 0 | Q0 => {0, 1, 2} Q1 => {{0, 2}, {0, 2}, {0, 1}, {0, 1}} weights => {-10, 7, 3} o8 : ToricQuiver |
The object toricQuiver is a method function with options.