public bool IsEqualTo(FiniteSet <T> other)
{
if (other is FiniteSet <T> )
{
return(_set.SetEquals(((FiniteSet <T>)other)._set));
}
else
{
return(this.IsSubsetOf(other) && other.IsSubsetOf(this));
}
}
public static bool IsSubgroup(Group <T> group, FiniteSet <T> subset)
{
if (!subset.IsSubsetOf(group.Set))
{
return(false);
}
foreach (T a in subset)
{
foreach (T b in subset)
{
T inverse = group.Inverse(b);
if (!subset.IsMember(group.Product(a, inverse)))
{
return(false);
}
}
}
return(true);
}