static void Main(string[] args)
{
WriteLine("D4: {0}\n", D4); D4.ShowOperationTableColored(); WriteLine();
foreach (var N in D4.NormalProperSubgroups())
{
WriteLine("normal subgroup: N = {0}", N);
}
WriteLine();
foreach (var N in D4.NormalProperSubgroups())
{
WriteLine("normal subgroup: N = {0}", N);
var D4_N = D4.QuotientGroup(N, "N");
WriteLine(" quotient group: D4/N = {0}", D4_N);;
WriteLine(" isomorphic image: {0}", D4_N.IsomorphicImage());
WriteLine(" homomorphisms:");
foreach (var f in D4.GenerateHomomorphisms(D4_N))
{
WriteLine(" {0}", String.Join(" ", D4.Set.Select(elt => (D4.Lookup(elt), f(elt)))));
}
// HomomorphismToString(G, f)
WriteLine();
D4_N.ShowOperationTableColored();
WriteLine();
}
ZxZ(2, 2).ShowOperationTableColored();
}
static void Main(string[] args)
{
WriteLine("normal subgroups: \n");
foreach (var elt in D4.NormalSubgroups())
{
WriteLine(" {0}", elt);
}
WriteLine("----------------------------------------------------------------------");
foreach (var H in D4.NormalSubgroups())
{
WriteLine("normal subgroup: H = {0}", H);
WriteLine(" coset grouping:");
foreach (var elt in D4.CosetGrouping(H, "H"))
{
WriteLine(" each of these: {0} are equal to: {1}", elt.ToMathSet(), elt.Key.ConvertAll(D4.Lookup));
}
WriteLine(" quotient group: D4/H = {0}\n", D4.QuotientGroup(H));
D4.QuotientGroup(H).ShowOperationTableColored();
WriteLine("----------------------------------------------------------------------");
}
WriteLine("NORMAL SUBGROUP QUOTIENT GROUP");
foreach (var H in D4.NormalSubgroups())
{
WriteLine("H = {0,-30} D4/H = {1}", H, D4.QuotientGroup(H));
}
}