static void Main(string[] args)
{
Console.OutputEncoding = Encoding.UTF8;
Write("S3 "); S3.ShowOperationTableColored(); WriteLine();
var εβσ = S3.Subgroup(new[] { ε, β, σ });
foreach (var elt in S3.CosetGrouping(εβσ, "εβσ"))
{
WriteLine("{0} {1}", elt.ToMathSet(), elt.Key.ConvertAll(S3.Lookup));
}
WriteLine();
Write("S3/εβσ ");
S3
.QuotientGroup(εβσ, coset => new[] { ε, α, β, γ, σ, κ }.ToList().IndexOf(coset.Element).ToString(), "εβσ")
.ShowOperationTableColored();
}
static void Main(string[] args)
{
Console.OutputEncoding = Encoding.UTF8;
Write("S3 "); S3.ShowOperationTableColored(); WriteLine();
foreach (var a in S3.Set)
{
foreach (var b in S3.Set)
{
WriteLine("{0}{1}{2}{3} -> {4}",
S3.Lookup(a),
S3.Lookup(b),
S3.Lookup(S3.Inverse(a)),
S3.Lookup(S3.Inverse(b)),
S3.Lookup(S3.Op_(a, b, S3.Inverse(a), S3.Inverse(b))));
}
//foreach (var b in S3.Set)
//{
// WriteLine("{5}{6}{5}⁻¹{6}⁻¹ -> {0}{1}{2}{3} -> {4}",
// lookup(a),
// lookup(b),
// lookup(S3.Inverse(a)),
// lookup(S3.Inverse(b)),
// lookup(S3.Op_(a, b, S3.Inverse(a), S3.Inverse(b))),
// lookup(a),
// lookup(b));
//}
WriteLine();
}
WriteLine();
foreach (var a in S3.Set)
{
foreach (var b in S3.Set)
{
Write("{0} ", S3.Lookup(S3.Op_(a, b, S3.Inverse(a), S3.Inverse(b))));
}
WriteLine();
}
WriteLine();
void ShowCommutators <T>(Group <T> G)
{
WriteLine("commutators:\n");
var width = G.Set.Select(elt => G.Lookup(elt).Count()).Max();
var color_thunks = new List <Action>()
{
() => { ForegroundColor = ConsoleColor.White; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Red; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Yellow; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Green; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Blue; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Cyan; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.Magenta; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.DarkRed; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.DarkBlue; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.DarkGreen; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.DarkMagenta; BackgroundColor = ConsoleColor.Black; },
() => { ForegroundColor = ConsoleColor.DarkYellow; BackgroundColor = ConsoleColor.Black; }
};
void pick_color(T elt)
{
var i = G.Set.ToList().IndexOf(elt);
color_thunks[i % color_thunks.Count()]();
}
Write("{0}|", "".PadLeft(width));
foreach (var elt in G.Set)
{
pick_color(elt); Write("{0} ", G.Lookup(elt).PadLeft(width));
}
WriteLine();
color_thunks[0](); WriteLine(new String('-', (G.Set.Count() + 1) * (width + 1)));
foreach (var x in G.Set)
{
pick_color(x); Write("{0}", G.Lookup(x).PadLeft(width)); color_thunks[0](); Write("|");
foreach (var y in G.Set)
{
// var elt = G.Op(x, y);
var elt = G.Op_(x, y, G.Inverse(x), G.Inverse(y));
pick_color(elt);
Write("{0} ", G.Lookup(elt).PadLeft(width));
}
WriteLine();
}
ForegroundColor = ConsoleColor.White;
BackgroundColor = ConsoleColor.Black;
}
ShowCommutators(S3);
WriteLine();
// S3.Commutators -> ε β σ
var H = S3.Subgroup(new[] { ε, β, σ });
foreach (var elt in S3.CosetGrouping(H, "H"))
{
WriteLine("{0} {1}",
String.Join(" ", elt.Select(item => String.Format("{0} =", item.ToString()))),
elt.Key.ConvertAll(S3.Lookup));
}
WriteLine();
Write("S3/H ");
S3.QuotientGroup(H, "H").ShowOperationTableColored();
}
