/// <summary>
/// Constructs a cyclic group
/// </summary>
/// <param name="order">The order of the cyclic group</param>
/// <exception cref="InvalidGroupException">If the order of the cyclic group is not positive</exception>
public CyclicGroup(int order)
{
if (order <= 0)
{
throw new InvalidGroupException("No cyclic group of negative order");
}
Elements = new ExplicitSet <GroupElement <BigInteger> >();
for (BigInteger i = 0; i < order / 2; ++i)
{
((ExplicitSet <GroupElement <BigInteger> >)Elements).Elements.Add(
new GroupElement <BigInteger>(i, this));
}
}
/// <summary>
/// Create a new Dihedral group
/// </summary>
/// <param name="order">The order of the dihedral group</param>
/// <exception cref="InvalidGroupException">If the order is not even or not positive</exception>
public DihedralGroup(BigInteger order)
{
if (order % 2 != 0 || order <= 0)
{
throw new InvalidGroupException("No Dihedral group of odd order");
}
Elements = new ExplicitSet <GroupElement <BigInteger[]> >();
for (BigInteger i = 0; i < order / 2; ++i)
{
Elements.Elements.Add(new GroupElement <BigInteger[]>(new[] { 0, i }, this));
Elements.Elements.Add(new GroupElement <BigInteger[]>(new[] { 1, i }, this));
}
}
public FiniteGraph(ExplicitSet <N> nodes, ExplicitSet <Tuple <N> > neighbors)
{
this.nodes = nodes;
this.neighbors = neighbors;
}
