public void GetGroupsOfOrderFour()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
NamedElement belement = new NamedElement('b');
NamedElement celement = new NamedElement('c');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement, belement, celement
}, true);
IList <OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(4, solutions.Count);
foreach (OperationTable solution in solutions)
{
Assert.IsTrue(solution.IsClosed);
Assert.IsTrue(solution.IsCommutative);
}
IList <IGroup> groups = new List <IGroup>();
foreach (OperationTable ot in solutions)
{
groups.Add(new TableGroup(ot));
}
IList <IGroup> dgroups = GroupUtilities.GetNonIsomorphic(groups);
Assert.IsNotNull(dgroups);
Assert.AreEqual(2, dgroups.Count);
}
public void CreateWithNamedIdentityAndOneElement()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List<IElement>() { identity , aelement}, true);
identity.OperationTable = table;
aelement.OperationTable = table;
table.SetValue(aelement, aelement, identity);
Assert.IsTrue(table.HasIdentity);
Assert.IsTrue(table.IsAssociative);
Assert.IsTrue(table.IsClosed);
Assert.IsTrue(table.IsCommutative);
Assert.AreEqual(2, table.Elements.Count);
Assert.AreEqual(identity, table.GetValue(identity, identity));
Assert.AreEqual(aelement, table.GetValue(aelement, identity));
Assert.AreEqual(aelement, table.GetValue(identity, aelement));
Assert.AreEqual(identity, table.GetValue(aelement, aelement));
Assert.AreEqual(1, identity.Order);
Assert.AreEqual(2, aelement.Order);
}
private static IList <IGroup> GetGroupsOfOrder(int order)
{
IList <IElement> elements = new List <IElement>();
for (int k = 0; k < order; k++)
{
elements.Add(new NamedElement(k));
}
OperationTable table = new OperationTable(elements, true);
IList <OperationTable> solutions = table.GetSolutions().ToList();
foreach (OperationTable solution in solutions)
{
Assert.IsTrue(solution.HasIdentity);
Assert.IsTrue(solution.IsAssociative);
Assert.IsTrue(solution.IsClosed);
}
IList <IGroup> groups = new List <IGroup>();
foreach (OperationTable ot in solutions)
{
groups.Add(new TableGroup(ot));
}
IList <IGroup> dgroups = GroupUtilities.GetNonIsomorphic(groups);
return(dgroups);
}
public void CreateWithNamedIdentityAndOneElement()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement
}, true);
identity.OperationTable = table;
aelement.OperationTable = table;
table.SetValue(aelement, aelement, identity);
Assert.IsTrue(table.HasIdentity);
Assert.IsTrue(table.IsAssociative);
Assert.IsTrue(table.IsClosed);
Assert.IsTrue(table.IsCommutative);
Assert.AreEqual(2, table.Elements.Count);
Assert.AreEqual(identity, table.GetValue(identity, identity));
Assert.AreEqual(aelement, table.GetValue(aelement, identity));
Assert.AreEqual(aelement, table.GetValue(identity, aelement));
Assert.AreEqual(identity, table.GetValue(aelement, aelement));
Assert.AreEqual(1, identity.Order);
Assert.AreEqual(2, aelement.Order);
}
public void SymmetricGroupThreeOperationIsClosed()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsTrue(table.IsClosed);
}
public void SymmetricGroupThreeOperationHasIdentity()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsTrue(table.HasIdentity);
}
public void SymmetricGroupThreeOperationIsNotCommutative()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsFalse(table.IsCommutative);
}
public void RotationGroupThreeOperationIsCommutative()
{
OperationTable table = new OperationTable((new GeneratedGroup(Element.CreateRotation(3))).Elements);
table.Calculate();
Assert.IsTrue(table.IsCommutative);
}
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 GetCompatibleOperationTable()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List<IElement>() { identity, aelement }, true);
identity.OperationTable = table;
aelement.OperationTable = table;
OperationTable table2 = table.GetCompatibleTable(aelement, aelement, identity);
Assert.IsNotNull(table2);
Assert.AreNotSame(table2, table);
}
public void GetIncompatibleOperationTableIfValueIsAlreadyInRowOrColumn()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement
}, true);
identity.OperationTable = table;
aelement.OperationTable = table;
Assert.IsNull(table.GetCompatibleTable(aelement, aelement, aelement));
}
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 GetGroupsOfOrderThree()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
NamedElement belement = new NamedElement('b');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement, belement
}, true);
IList <OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(1, solutions.Count);
Assert.IsTrue(solutions[0].IsClosed);
}
public void CreateWithNamedIdentity()
{
NamedElement identity = new NamedElement('e');
OperationTable table = new OperationTable(new List<IElement>() { identity }, true);
identity.OperationTable = table;
Assert.IsTrue(table.HasIdentity);
Assert.IsTrue(table.IsAssociative);
Assert.IsTrue(table.IsClosed);
Assert.IsTrue(table.IsCommutative);
Assert.AreEqual(identity, table.GetValue(identity, identity));
Assert.AreEqual(1, identity.Order);
}
public void GetCompatibleOperationTable()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement
}, true);
identity.OperationTable = table;
aelement.OperationTable = table;
OperationTable table2 = table.GetCompatibleTable(aelement, aelement, identity);
Assert.IsNotNull(table2);
Assert.AreNotSame(table2, table);
}
public void CreateWithNamedIdentity()
{
NamedElement identity = new NamedElement('e');
OperationTable table = new OperationTable(new List <IElement>()
{
identity
}, true);
identity.OperationTable = table;
Assert.IsTrue(table.HasIdentity);
Assert.IsTrue(table.IsAssociative);
Assert.IsTrue(table.IsClosed);
Assert.IsTrue(table.IsCommutative);
Assert.AreEqual(identity, table.GetValue(identity, identity));
Assert.AreEqual(1, identity.Order);
}
public void GetCompatibleOperationTableUsingAssociationExpansion()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
NamedElement belement = new NamedElement('b');
NamedElement celement = new NamedElement('c');
OperationTable table = new OperationTable(new List <IElement>()
{
identity, aelement, belement, celement
}, true);
identity.OperationTable = table;
aelement.OperationTable = table;
belement.OperationTable = table;
celement.OperationTable = table;
table = table.GetCompatibleTable(aelement, belement, celement);
Assert.IsNotNull(table);
table = table.GetCompatibleTable(belement, aelement, celement);
Assert.IsNotNull(table);
// bc undefined
Assert.IsNull(table.GetValue(belement, celement));
table = table.GetCompatibleTable(belement, celement, identity);
Assert.IsNotNull(table);
// bc = e, ba = c = ab -> cb = e
Assert.AreEqual(identity, table.GetValue(celement, belement));
// but is not complete, yet
Assert.IsFalse(table.IsClosed);
IList <OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(1, solutions.Count);
Assert.IsTrue(solutions[0].IsClosed);
}
public void GetGroupsOfOrderTwo()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List<IElement>() { identity, aelement }, true);
IList<OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(1, solutions.Count);
Assert.IsTrue(solutions[0].IsClosed);
Assert.IsTrue(solutions[0].IsAssociative);
}
private static IList<IGroup> GetGroupsOfOrder(int order)
{
IList<IElement> elements = new List<IElement>();
for (int k = 0; k < order; k++)
elements.Add(new NamedElement(k));
OperationTable table = new OperationTable(elements, true);
IList<OperationTable> solutions = table.GetSolutions().ToList();
foreach (OperationTable solution in solutions)
{
Assert.IsTrue(solution.HasIdentity);
Assert.IsTrue(solution.IsAssociative);
Assert.IsTrue(solution.IsClosed);
}
IList<IGroup> groups = new List<IGroup>();
foreach (OperationTable ot in solutions)
groups.Add(new TableGroup(ot));
IList<IGroup> dgroups = GroupUtilities.GetNonIsomorphic(groups);
return dgroups;
}
public void GetIncompatibleOperationTableIfValueIsAlreadyInRowOrColumn()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
OperationTable table = new OperationTable(new List<IElement>() { identity, aelement }, true);
identity.OperationTable = table;
aelement.OperationTable = table;
Assert.IsNull(table.GetCompatibleTable(aelement, aelement, aelement));
}
public void GetCompatibleOperationTableUsingAssociationExpansion()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
NamedElement belement = new NamedElement('b');
NamedElement celement = new NamedElement('c');
OperationTable table = new OperationTable(new List<IElement>() { identity, aelement, belement, celement }, true);
identity.OperationTable = table;
aelement.OperationTable = table;
belement.OperationTable = table;
celement.OperationTable = table;
table = table.GetCompatibleTable(aelement, belement, celement);
Assert.IsNotNull(table);
table = table.GetCompatibleTable(belement, aelement, celement);
Assert.IsNotNull(table);
// bc undefined
Assert.IsNull(table.GetValue(belement, celement));
table = table.GetCompatibleTable(belement, celement, identity);
Assert.IsNotNull(table);
// bc = e, ba = c = ab -> cb = e
Assert.AreEqual(identity, table.GetValue(celement, belement));
// but is not complete, yet
Assert.IsFalse(table.IsClosed);
IList<OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(1, solutions.Count);
Assert.IsTrue(solutions[0].IsClosed);
}
public void RotationGroupThreeOperationIsCommutative()
{
OperationTable table = new OperationTable((new GeneratedGroup(Element.CreateRotation(3))).Elements);
table.Calculate();
Assert.IsTrue(table.IsCommutative);
}
public void SymmetricGroupThreeOperationHasIdentity()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsTrue(table.HasIdentity);
}
public void SymmetricGroupThreeOperationIsClosed()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsTrue(table.IsClosed);
}
public void GetGroupsOfOrderFour()
{
NamedElement identity = new NamedElement('e');
NamedElement aelement = new NamedElement('a');
NamedElement belement = new NamedElement('b');
NamedElement celement = new NamedElement('c');
OperationTable table = new OperationTable(new List<IElement>() { identity, aelement, belement, celement }, true);
IList<OperationTable> solutions = table.GetSolutions().ToList();
Assert.IsNotNull(solutions);
Assert.AreEqual(4, solutions.Count);
foreach (OperationTable solution in solutions)
{
Assert.IsTrue(solution.IsClosed);
Assert.IsTrue(solution.IsCommutative);
}
IList<IGroup> groups = new List<IGroup>();
foreach (OperationTable ot in solutions)
groups.Add(new TableGroup(ot));
IList<IGroup> dgroups = GroupUtilities.GetNonIsomorphic(groups);
Assert.IsNotNull(dgroups);
Assert.AreEqual(2, dgroups.Count);
}
public void SymmetricGroupThreeOperationIsNotCommutative()
{
OperationTable table = new OperationTable((new SymmetricGroup(3)).Elements);
table.Calculate();
Assert.IsFalse(table.IsCommutative);
}
