public void CreateWithIdentity()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateIdentity(4));
Assert.IsNotNull(group);
Assert.AreEqual(1, group.Order);
}
public void CreateWithSwapOrderTwo()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(2));
Assert.IsNotNull(group);
Assert.AreEqual(2, group.Order);
}
public void CreateSymetricGroupSizeThree()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(3), Element.CreateRotation(3));
Assert.IsNotNull(group);
Assert.AreEqual(6, group.Order);
}
public void CreateWithIdentity()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateIdentity(4));
Assert.IsNotNull(group);
Assert.AreEqual(1, group.Order);
}
public void TwoSymetricGroupsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4, 2), Element.CreateRotation(4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void CreateWithSwapOrderSix()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(6));
Assert.IsNotNull(group);
Assert.AreEqual(2, group.Order);
}
public void TwoGroupsGeneratedByTwoNonOverlappingSwapsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(4), Element.CreateSwap(4, 2));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(6, 2), Element.CreateSwap(6, 4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void CreateSymetricGroupSizeFour()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
Assert.IsNotNull(group);
Assert.AreEqual(24, group.Order);
}
public void IdentityIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(id, group));
}
public void GroupsGeneratedByDiffSizedSwapsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(3));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void CreateSymetricGroupSizeFour()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
Assert.IsNotNull(group);
Assert.AreEqual(24, group.Order);
}
public void CreateSymetricGroupSizeThree()
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(3), Element.CreateRotation(3));
Assert.IsNotNull(group);
Assert.AreEqual(6, group.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 RotationsAreCyclic()
{
for (int k = 1; k <= 7; k++)
{
IGroup group = new GeneratedGroup(Element.CreateRotation(k));
Assert.IsTrue(GroupUtilities.IsCyclic(group));
}
}
public void SwapsAreCyclic()
{
for (int k = 2; k <= 10; k++)
{
IGroup group = new GeneratedGroup(Element.CreateSwap(k));
Assert.IsTrue(GroupUtilities.IsCyclic(group));
}
}
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 GetSubgroupsOfCyclicGroupSeven()
{
IGroup group = new GeneratedGroup(Element.CreateRotation(7));
IEnumerable <IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(2, subgroups.Count());
}
public void GetSubgroupsOfCyclicGroupSeven()
{
IGroup group = new GeneratedGroup(Element.CreateRotation(7));
IEnumerable<IGroup> subgroups = GroupUtilities.GetSubgroups(group);
Assert.IsNotNull(subgroups);
Assert.AreEqual(2, subgroups.Count());
}
public void GroupsGeneratedByDiffPositionSwapsAreNotEqual()
{
IElement swap1 = Element.CreateSwap(3);
IElement swap2 = Element.CreateRotation(4).Multiply(Element.CreateSwap(4));
IGroup group1 = new GeneratedGroup(swap1);
IGroup group2 = new GeneratedGroup(swap2);
Assert.IsFalse(GroupUtilities.AreEqual(group1, group2));
}
public void GroupsGeneratedByDiffPositionSwapsAreIsomorphic()
{
IElement swap1 = Element.CreateSwap(3);
IElement swap2 = Element.CreateSwap(3, 1);
IGroup group1 = new GeneratedGroup(swap1);
IGroup group2 = new GeneratedGroup(swap2);
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
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 PrimeRotationGroupsAreEqual()
{
IElement elementrot = Element.CreateRotation(5);
IElement elementrot2 = elementrot.Multiply(elementrot);
IGroup group1 = new GeneratedGroup(elementrot);
IGroup group2 = new GeneratedGroup(elementrot2);
Assert.IsTrue(GroupUtilities.AreEqual(group1, 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 CreateSymetricGroups()
{
int n = 1;
for (int k = 2; k <= 5; k++)
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(k), Element.CreateRotation(k));
n *= k;
Assert.IsNotNull(group);
Assert.AreEqual(n, group.Order);
}
}
public void CreateSymetricGroups()
{
int n = 1;
for (int k = 2; k <= 5; k++)
{
GeneratedGroup group = new GeneratedGroup(Element.CreateSwap(k), Element.CreateRotation(k));
n *= k;
Assert.IsNotNull(group);
Assert.AreEqual(n, group.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 TwoSymetricGroupsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(4), Element.CreateRotation(4));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4,2), Element.CreateRotation(4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void GroupsGeneratedByDiffPositionSwapsAreNotEqual()
{
IElement swap1 = Element.CreateSwap(3);
IElement swap2 = Element.CreateRotation(4).Multiply(Element.CreateSwap(4));
IGroup group1 = new GeneratedGroup(swap1);
IGroup group2 = new GeneratedGroup(swap2);
Assert.IsFalse(GroupUtilities.AreEqual(group1, group2));
}
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 TwoGroupsGeneratedByTwoNonOverlappingSwapsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(4), Element.CreateSwap(4, 2));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(6, 2), Element.CreateSwap(6, 4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void SwapsAreCyclic()
{
for (int k = 2; k <= 10; k++)
{
IGroup group = new GeneratedGroup(Element.CreateSwap(k));
Assert.IsTrue(GroupUtilities.IsCyclic(group));
}
}
public void GroupsGeneratedByDiffSizedSwapsAreIsomorphic()
{
IGroup group1 = new GeneratedGroup(Element.CreateSwap(3));
IGroup group2 = new GeneratedGroup(Element.CreateSwap(4));
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
public void IdentityIsNormalSubgroup()
{
IGroup group = new SymmetricGroup(3);
IGroup id = new GeneratedGroup(Element.CreateIdentity(3));
Assert.IsTrue(GroupUtilities.IsNormalSubgroup(id, group));
}
public void GroupsGeneratedByDiffPositionSwapsAreIsomorphic()
{
IElement swap1 = Element.CreateSwap(3);
IElement swap2 = Element.CreateSwap(3, 1);
IGroup group1 = new GeneratedGroup(swap1);
IGroup group2 = new GeneratedGroup(swap2);
Assert.IsTrue(GroupUtilities.AreIsomorphic(group1, group2));
}
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 PrimeRotationGroupsAreEqual()
{
IElement elementrot = Element.CreateRotation(5);
IElement elementrot2 = elementrot.Multiply(elementrot);
IGroup group1 = new GeneratedGroup(elementrot);
IGroup group2 = new GeneratedGroup(elementrot2);
Assert.IsTrue(GroupUtilities.AreEqual(group1, group2));
}
public void RotationsAreCyclic()
{
for (int k = 1; k <= 7; k++)
{
IGroup group = new GeneratedGroup(Element.CreateRotation(k));
Assert.IsTrue(GroupUtilities.IsCyclic(group));
}
}
