public void IdentityIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(id, group));
}
public void GetSubnormalGroups()
{
IGroup group = new SymmetricGroup(3);
IEnumerable <IGroup> normalsg = GroupUtilities.GetNormalSubgroups(group);
Assert.IsTrue(normalsg.Count() >= 2);
}
public void GetSubnormalGroups()
{
IGroup group = new SymmetricGroup(3);
IEnumerable<IGroup> normalsg = GroupUtilities.GetNormalSubgroups(group);
Assert.IsTrue(normalsg.Count() >= 2);
}
public void SymmetricAreNotCyclic()
{
for (int k = 3; k <= 5; k++)
{
IGroup group = new SymmetricGroup(k);
Assert.IsFalse(GroupUtilities.IsCyclic(group));
}
}
public void MultiplyBeIdempotent()
{
IGroup group = new SymmetricGroup(3);
IGroup group2 = GroupUtilities.Multiply(group, group);
Assert.AreEqual(group.Order, group2.Order);
}
public void GroupAndIdentityAreSubnormalGroups()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
GroupUtilities.IsNormalSubgroup(group, group);
GroupUtilities.IsNormalSubgroup(id, group);
}
public void GetSubgroupsOfSymetricGroupThree()
{
IGroup group = new SymmetricGroup(3);
IEnumerable<IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(6, subgroups.Count());
}
public void GetSubgroupsOfMinimalGroup()
{
IGroup group = new SymmetricGroup(2);
IEnumerable<IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(2, subgroups.Count());
}
public void SymetricGroupSizeFourAreEqualToSymetrycGroup()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
SymmetricGroup group2 = new SymmetricGroup(4);
Assert.AreEqual(group.Order, group2.Order);
Assert.AreEqual(group.GetHashCode(), group2.GetHashCode());
Assert.AreEqual(group, group2);
}
public void GetSubgroupsOfMinimalGroup()
{
IGroup group = new SymmetricGroup(2);
IEnumerable <IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(2, subgroups.Count());
}
public void GetSubgroupsOfSymetricGroupFour()
{
IGroup group = new SymmetricGroup(4);
IEnumerable <IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(30, subgroups.Count());
}
public void SymetricGroupSizeFourAreEqualToSymetrycGroup()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
SymmetricGroup group2 = new SymmetricGroup(4);
Assert.AreEqual(group.Order, group2.Order);
Assert.AreEqual(group.GetHashCode(), group2.GetHashCode());
Assert.AreEqual(group, group2);
}
public void SubgroupsIncludesIdentityAndTotalGroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
IEnumerable <IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsTrue(subgroups.Contains(id));
Assert.IsTrue(subgroups.Contains(group));
}
public void CalculateSymmetricGroupTable()
{
IGroup group = new SymmetricGroup(3);
OperationTable table = new OperationTable(group.Elements);
table.Calculate();
foreach (IElement left in group.Elements)
foreach (IElement right in group.Elements)
Assert.AreEqual(left.Multiply(right), table.GetValue(left, right));
}
public void MultiplyGenerateSymmetricGroup()
{
IGroup group1 = new GeneratedGroup(Element.CreateRotation(4));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4));
IGroup group3 = GroupUtilities.Multiply(group1, group2);
Assert.AreEqual(24, group3.Order);
IGroup symm = new SymmetricGroup(4);
Assert.IsTrue(GroupUtilities.AreEqual(group3, symm));
Assert.IsTrue(group3.Equals(symm));
}
private static void TestSn(uint size, int count, string expectedElements, string expectedSubgroups)
{
var @group = new SymmetricGroup(size);
Assert.AreEqual(count, @group.Count());
var builder = new StringBuilder();
@group.ForEach(element => builder.Append(element).Append('\n'));
Assert.AreEqual(expectedElements, builder.ToString());
builder.Clear();
var gen = GeneratorFactory.Create(@group);
gen.Generate().OrderBy(subgroup => subgroup.Order).ForEach(subgroup => builder.Append(subgroup).Append('\n'));
Assert.AreEqual(expectedSubgroups, builder.ToString());
}
public void CalculateSymmetricGroupTable()
{
IGroup group = new SymmetricGroup(3);
OperationTable table = new OperationTable(group.Elements);
table.Calculate();
foreach (IElement left in group.Elements)
{
foreach (IElement right in group.Elements)
{
Assert.AreEqual(left.Multiply(right), table.GetValue(left, right));
}
}
}
public void GroupIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(group, group));
}
public void MultiplyBeIdempotent()
{
IGroup group = new SymmetricGroup(3);
IGroup group2 = GroupUtilities.Multiply(group, group);
Assert.AreEqual(group.Order, group2.Order);
}
public void MultiplyGenerateSymmetricGroup()
{
IGroup group1 = new GeneratedGroup(Element.CreateRotation(4));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4));
IGroup group3 = GroupUtilities.Multiply(group1, group2);
Assert.AreEqual(24, group3.Order);
IGroup symm = new SymmetricGroup(4);
Assert.IsTrue(GroupUtilities.AreEqual(group3, symm));
Assert.IsTrue(group3.Equals(symm));
}
public void SubgroupsIncludesIdentityAndTotalGroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
IEnumerable<IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsTrue(subgroups.Contains(id));
Assert.IsTrue(subgroups.Contains(group));
}
public void GroupIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(group, group));
}
public void SymmetricAreNotCyclic()
{
for (int k = 3; k <= 5; k++)
{
IGroup group = new SymmetricGroup(k);
Assert.IsFalse(GroupUtilities.IsCyclic(group));
}
}
public void GroupAndIdentityAreSubnormalGroups()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
GroupUtilities.IsNormalSubgroup(group, group);
GroupUtilities.IsNormalSubgroup(id, group);
}
public void IdentityIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(id, group));
}
