public void Optimise()
{
var groupSize = Size();
var optimisedGroup = new PermutationGroup(Generators[0]);
var optimisedGroupSize = optimisedGroup.Size();
var generatorIndex = 0;
do
{
var copiedOptimised = new PermutationGroup(optimisedGroup.Generators);
copiedOptimised.AddGenerator(Generators[generatorIndex]);
if (copiedOptimised.Size() > optimisedGroupSize)
{
optimisedGroup.AddGenerator(Generators[generatorIndex]);
optimisedGroupSize = optimisedGroup.Size();
}
generatorIndex = (generatorIndex + 1) % Generators.Count;
} while (optimisedGroupSize < groupSize);
Generators.Clear();
InverseGenerators.Clear();
foreach (var generator in optimisedGroup.Generators)
{
AddGenerator(generator);
}
}
public HashSet <Points> OrbitStabiliser(Points partialPoints, out PermutationGroup stabiliser)
{
stabiliser = new PermutationGroup();
var elementLookup = new Dictionary <Points, Element>();
var orbitPoints = new HashSet <Points>(new[] { partialPoints });
var queue = new Queue <Points>(orbitPoints);
elementLookup[partialPoints] = Identity;
while (queue.Any())
{
var headPoints = queue.Dequeue();
for (var i = 0; i < Generators.Count; ++i)
{
var permutedPoints = Apply(i, headPoints);
if (orbitPoints.Contains(permutedPoints))
{
stabiliser.AddGenerator((elementLookup[headPoints].Apply(Generators[i])).Apply(elementLookup[permutedPoints].Inverse()));
continue;
}
orbitPoints.Add(permutedPoints);
queue.Enqueue(permutedPoints);
elementLookup[permutedPoints] = elementLookup[headPoints].Apply(Generators[i]);
}
}
return(orbitPoints);
}
