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);
}
public void Test(IAtomContainer mol, int expected)
{
AtomDiscretePartitionRefiner refiner = new AtomDiscretePartitionRefiner();
PermutationGroup group = refiner.GetAutomorphismGroup(mol);
Assert.AreEqual(expected, group.Order());
}
public void OrderTest()
{
int size = 5;
PermutationGroup sym = PermutationGroup.MakeSymN(size);
Assert.AreEqual(Factorial(size), sym.Order());
}
public void EnterTest()
{
int size = 4;
PermutationGroup group = new PermutationGroup(size);
group.Enter(new Permutation(1, 0, 3, 2));
Assert.AreEqual(2, group.Order());
}
/// <summary>
/// Generate a transversal of a subgroup in this group.
/// </summary>
/// <param name="subgroup">the subgroup to use for the transversal</param>
/// <returns>a list of permutations</returns>
public IReadOnlyCollection <Permutation> Transversal(PermutationGroup subgroup)
{
long m = this.Order() / subgroup.Order();
var results = new List <Permutation>();
var transversalBacktracker = new TransversalBacktracker(this, subgroup, m, results);
this.Apply(transversalBacktracker);
return(results);
}
public void GetAutomorphismGroup_StartingPartitionTest()
{
Partition partition = Partition.FromString("0,1|2,3");
string acpString = "C0C1C2C3 0:1(1),0:3(1),1:2(1),2:3(1)";
IAtomContainer ac = AtomContainerPrinter.FromString(acpString, builder);
AtomDiscretePartitionRefiner refiner = new AtomDiscretePartitionRefiner();
PermutationGroup autG = refiner.GetAutomorphismGroup(ac, partition);
Assert.AreEqual(2, autG.Order());
}
public void GetAutomorphismGroupTest()
{
string acpString = "C0C1C2O3 0:1(2),0:2(1),1:3(1),2:3(1)";
IAtomContainer ac = AtomContainerPrinter.FromString(acpString, builder);
AtomDiscretePartitionRefiner refiner = new AtomDiscretePartitionRefiner();
PermutationGroup autG = refiner.GetAutomorphismGroup(ac);
Assert.IsNotNull(autG);
Assert.AreEqual(1, autG.Order());
}
public void RefineTest()
{
string acpString = "C0C1O2O3 0:1(1),0:3(1),1:2(1),2:3(1)";
IAtomContainer ac = AtomContainerPrinter.FromString(acpString, builder);
AtomDiscretePartitionRefiner refiner = new AtomDiscretePartitionRefiner();
refiner.Refine(ac);
PermutationGroup autG = refiner.GetAutomorphismGroup();
Assert.AreEqual(2, autG.Order());
}
public void GetAutomorphismGroup_StartingGroupTest()
{
string acpString = "C0C1C2C3 0:1(1),0:2(1),1:3(1),2:3(1)";
IAtomContainer ac = AtomContainerPrinter.FromString(acpString, builder);
Permutation flip = new Permutation(1, 0, 3, 2);
PermutationGroup autG = new PermutationGroup(4, new[] { flip });
AtomDiscretePartitionRefiner refiner = new AtomDiscretePartitionRefiner();
refiner.GetAutomorphismGroup(ac, autG);
Assert.IsNotNull(autG);
Assert.AreEqual(8, autG.Order());
}
public void Refine_IgnoreBondOrderTest()
{
string acpString = "C0C1C2C3 0:1(2),0:3(1),1:2(1),2:3(2)";
IAtomContainer ac = AtomContainerPrinter.FromString(acpString, builder);
bool ignoreBondOrder = true;
BondDiscretePartitionRefiner refiner = new BondDiscretePartitionRefiner(ignoreBondOrder);
refiner.Refine(ac);
PermutationGroup autG = refiner.GetAutomorphismGroup();
Assert.AreEqual(8, autG.Order());
}
public void GeneratorConstructor()
{
int size = 4;
Permutation p1 = new Permutation(1, 0, 2, 3);
Permutation p2 = new Permutation(1, 2, 3, 0);
var generators = new List <Permutation>
{
p1,
p2
};
PermutationGroup group = new PermutationGroup(size, generators);
Assert.AreEqual(size, group.Count);
Assert.AreEqual(Factorial(size), group.Order());
}