public bool Equals(Coset <T> other)
{
if (other == null)
{
return(false);
}
if (_cosets == other._cosets)
{
return(this.Representative.Equals(other.Representative));
}
return(_members.IsEqualTo(other._members));
}
private IEnumerable <Coset <T> > Cosets(Group <T> h, Func <T, FiniteSet <T> > partition)
{
var setOfCosets = _set.Partition(partition);
var cosets = new Dictionary <T, Coset <T> >();
var list = new List <Coset <T> >();
foreach (FiniteSet <T> set in setOfCosets)
{
var coset = new Coset <T>(this, h, cosets, set, set.First());
foreach (T element in set)
{
cosets.Add(element, coset);
}
list.Add(coset);
}
return(list);
}
public static Coset <T> Inverse(Coset <T> s)
{
return(s._cosets[s.Group.Inverse(s.Representative)]);
}
public static Coset <T> Product(Coset <T> s1, Coset <T> s2)
{
return(s1._cosets[s1.Group.Product(s1.Representative, s2.Representative)]);
}