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isStable -- whether a subquiver is semistable with respect to a given weight

Description

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);
i6 : S = first(subquivers(Q, Format => "quiver", AsSubquiver => true));
i7 : isStable (S, Q)

o7 = false

Ways to use isStable:

  • isStable(List,ToricQuiver)
  • isStable(ToricQuiver,ToricQuiver)

For the programmer

The object isStable is a method function.


The source of this document is in ThinSincereQuivers.m2:3279:0.