public void Triangles_AreSelfInjective_WithUnusualFirstVertex()
{
const int FirstVertex = -123;
var qps = Utility.InfiniteRange(2).Select(k => UsefulQPs.GetTriangleQP(k, FirstVertex)).TakeWhile(qp => qp.Quiver.Vertices.Count < 30);
AssertAreSelfInjective(qps);
}
public void ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt_TriforceCorner()
{
var settings = GetSettings(detectNonCancellativity: false);
var qp = UsefulQPs.GetTriangleQP(3);
DoSetup(qp, out var ruleTree);
var representatives = Computer.ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt(qp.Quiver, 1, ruleTree, settings).MaximalNonzeroEquivalenceClassRepresentatives;
var representativeArrowPaths = representatives.Select(path => path.Arrows).ToList();
var expectedRepresentative = new Arrow <int>[] { new Arrow <int>(1, 3), new Arrow <int>(3, 6) };
Assert.That(representativeArrowPaths, Has.Count.EqualTo(1));
Assert.That(representativeArrowPaths.Single(), Is.EqualTo(expectedRepresentative));
}
public void ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt_TriforceInterior()
{
var settings = GetSettings(detectNonCancellativity: false);
var qp = UsefulQPs.GetTriangleQP(3);
DoSetup(qp, out var ruleTree);
var representatives = Computer.ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt(qp.Quiver, 2, ruleTree, settings).MaximalNonzeroEquivalenceClassRepresentatives.ToList();
var representativeArrowPaths = representatives.Select(path => path.Arrows);
var expectedMaximalEquivalenceClasses = new ISet <IEnumerable <Arrow <int> > >[]
{
new HashSet <IEnumerable <Arrow <int> > >
{
new Arrow <int>[] { new Arrow <int>(2, 1), new Arrow <int>(1, 3) },
new Arrow <int>[] { new Arrow <int>(2, 5), new Arrow <int>(5, 3) }
},
};
Assert.That(representatives, Has.Count.EqualTo(expectedMaximalEquivalenceClasses.Length));
foreach (var representative in representativeArrowPaths)
{
Assert.That(expectedMaximalEquivalenceClasses, Has.One.Contains(representative));
}
}
public void Triangles_AreSelfInjective()
{
var qps = Utility.InfiniteRange(2).Select(k => UsefulQPs.GetTriangleQP(k)).TakeWhile(qp => qp.Quiver.Vertices.Count < 20);
AssertAreSelfInjective(qps);
}
