public static bool IsGeneratingSetOf <T>(this IEnumerable <T> collection, IFiniteGroup <T> group)
where T : IFiniteGroupElement <T>, new()
{
return(!ReferenceEquals(collection, null) &&
!ReferenceEquals(group, null) &&
group.IsSubsetOf(CreateGroup <T>(collection)));
}
public static IFiniteGroup <T> CreateGroup <T>(this IEnumerable <T> collection)
where T : IFiniteGroupElement <T>, new()
{
List <T> list = new List <T>();
list.Add(new T());
if (!ReferenceEquals(collection, null))
{
foreach (T a in collection)
{
if (!list.Contains(a))
{
list.Add(a);
}
}
int i = 1, count;
do
{
for (count = list.Count; i < count; ++i)
{
T a = list[i];
for (int j = 1; j < count; ++j)
{
T b = list[j], c;
if (!list.Contains(c = a.Add(b)))
{
list.Add(c);
}
if (!list.Contains(c = b.Add(a)))
{
list.Add(c);
}
}
}
} while(count < list.Count);
}
IFiniteGroup <T> group = ToFiniteGroup <T>(list);
list[0] = group.IdentityElement;
return(group);
}
internal static IFiniteSet <T> ToFiniteSet <T>(this IFiniteGroup <T> collection)
where T : IFiniteGroupElement <T>, new()
{
return(ReferenceEquals(collection, null) ?
null : new InternalGroup <T>(collection));
}
internal InternalGroup(IFiniteGroup <T> collection) : base(collection)
{
}
static Polygon120()
{
AllValues = new DihedralGroupD120();
}
