This function determines if a given subquiver is stable with respect to the weight saved on Q. A subquiver SQ of the quiver Q is stable if for every subset V of the vertices of Q that is also SQ-successor closed, the sum of the weights associated to V is positive.
i1 : Q = bipartiteQuiver(2, 3); |
i2 : P = Q^{0,1,4,5};
|
i3 : isStable(P, Q) o3 = true |
i4 : isStable ({0, 1}, bipartiteQuiver(2, 3))
o4 = false
|
i5 : Q = bipartiteQuiver(2, 3)
o5 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1} }
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 => {-3, -3, 2, 2, 2}
o5 : ToricQuiver
|
i6 : S = first(subquivers(Q, Format=>"quiver", AsSubquiver=>true))
o6 = ToricQuiver{flow => {1, 0, 0, 0, 0, 0} }
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 => {-1, 0, 1, 0, 0}
o6 : ToricQuiver
|
i7 : isStable (S, Q) o7 = false |
The object isStable is a method function.