static void Main(string[] args)
{
WriteLine("D4: {0}", D4); WriteLine();
D4.ShowOperationTableColored(); WriteLine();
D4.ShowCosets();
}
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("D4: {0}", D4);
D4.ShowOperationTableColored();
void check(GapPerm a, GapPerm b)
{
WriteLine("a {0}", D4.Lookup(a));
WriteLine("b {0}", D4.Lookup(b));
WriteLine("ba {0}", D4.Lookup(b.Compose(a)));
WriteLine("a³b {0}", D4.Lookup(a.Compose(a.Compose(a.Compose(b)))));
}
check(R1, R4); WriteLine();
check(R1, R5); WriteLine();
check(R1, R6); WriteLine();
check(R1, R7); WriteLine();
WriteLine();
D4.ShowCosets();
}