static void Main(string[] args)
{
Console.OutputEncoding = Encoding.UTF8;
foreach (var elt in S3.Set)
{
WriteLine("{0} : {1}", S3.Lookup(elt), elt);
}
WriteLine();
S3.ShowOperationTable(); WriteLine();
foreach (var item in S3.Set)
{
WriteLine("{0} inverse: {1}",
S3.Lookup(item),
S3.Lookup(S3.Inverse(item)));
}
WriteLine();
WriteLine("conjugacy classes (partition of group):");
WriteLine(S3.Set.Select(a => S3.ConjugacyClass(a).ConvertAll(S3.Lookup)).ToMathSet()); WriteLine();
foreach (var a in S3.Set)
{
WriteLine("conjugacy class of {0,4}: {1}",
S3.Lookup(a),
S3.ConjugacyClass(a).ConvertAll(S3.Lookup));
}
WriteLine();
foreach (var a in S3.Set)
{
WriteLine("centralizer of {0,4}: {1}",
S3.Lookup(a),
S3.Centralizer(a).ConvertAll(S3.Lookup));
}
WriteLine();
S3.ShowConjugates();
S3.ShowCentralizers();
}
