public void TestTransversal()
{
int size = 4;
// Sym(n) : make the total symmetry group
PermutationGroup group = PermutationGroup.MakeSymN(size);
// Aut(G) : make the automorphism group for a graph
Permutation p1 = new Permutation(2, 1, 0, 3);
Permutation p2 = new Permutation(0, 3, 2, 1);
var generators = new List <Permutation>
{
p1,
p2
};
PermutationGroup subgroup = new PermutationGroup(size, generators);
// generate the traversal
var transversal = group.Transversal(subgroup);
int subgroupOrder = (int)subgroup.Order();
int groupOrder = (int)group.Order();
int transversalSize = transversal.Count;
// check that |Aut(G)| / |Sym(N)| = |Transversal|
Assert.AreEqual(Factorial(size), groupOrder);
Assert.AreEqual(groupOrder / subgroupOrder, transversalSize);
}
