This function determines if a given subquiver is semi-stable with respect to the weight saved on Q. A subquiver SQ of the quiver Q is semistable 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 nonnegative.
i1 : isSemistable ({0, 1}, bipartiteQuiver(2, 3))
o1 = false
|
i2 : Q = bipartiteQuiver(2, 3); |
i3 : S = first(subquivers(Q, Format=>"quiver", AsSubquiver=>true))
o3 = 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}
o3 : ToricQuiver
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i4 : isSemistable (S, Q) o4 = false |
The object isSemistable is a method function.