static void Main(string[] args)
{
var ε = new GapPerm(0);
var α = new GapPerm("(12)(34)(56)");
var β = new GapPerm("(23)");
var αβ = α.Compose(β);
var βα = β.Compose(α);
var αβα = α.Compose(β.Compose(α));
var βαβ = β.Compose(α.Compose(β));
var αβαβ = α.Compose(β.Compose(α.Compose(β)));
string lookup(GapPerm f)
{
var items = new[] {
(ε, "ε"), (α, "α"), (β, "β"),
(αβ, "αβ"), (βα, "βα"), (αβα, "αβα"), (βαβ, "βαβ"), (αβαβ, "αβαβ")
};
return(items.First(elt => f == elt.Item1).Item2);
}
var G = new Group <GapPerm>
{
Identity = ε,
Set = new MathSet <GapPerm>(new[] { ε, α, β, αβ, βα, αβα, βαβ, αβαβ }),
Op = (a, b) => a.Compose(b),
Lookup = lookup
};
foreach (var elt in G.Set)
{
WriteLine("{0,-4}: {1}", lookup(elt), elt);
}
WriteLine();
G.ShowInverses();
G.ShowOperationTableColored(); WriteLine();
MathSet <int> orbit(Group <GapPerm> grp, int u) => grp.Set.ConvertAll(elt => elt.Apply(u));
WriteLine("orbit of 1: {0}", orbit(G, 1));
WriteLine("orbit of 2: {0}", orbit(G, 2));
WriteLine("orbit of 3: {0}", orbit(G, 3));
WriteLine("orbit of 5: {0}", orbit(G, 5));
WriteLine();
MathSet <GapPerm> stabilizer(Group <GapPerm> grp, int u) =>
grp.Set.Where(elt => elt.Apply(u) == u).ToMathSet();
WriteLine("stabilizer of 1: {0}", stabilizer(G, 1).Select(lookup).ToMathSet());
WriteLine("stabilizer of 2: {0}", stabilizer(G, 2).Select(lookup).ToMathSet());
WriteLine("stabilizer of 4: {0}", stabilizer(G, 4).Select(lookup).ToMathSet());
WriteLine("stabilizer of 5: {0}", stabilizer(G, 5).Select(lookup).ToMathSet());
}
static void Main(string[] args)
{
// Find the order of each of the following permutations
int proc(GapPerm a)
{
var result = new GapPerm();
foreach (var n in Enumerable.Range(1, 100))
{
result = result.Compose(a);
WriteLine("a^{0} = {1}", n, result);
if (result == new GapPerm(0))
{
return(n);
}
}
throw new Exception();
}
proc(new GapPerm("(12)(345)")).Display(); WriteLine();
proc(new GapPerm("(12)(3456)")).Display(); WriteLine();
proc(new GapPerm("(1234)(56789)")).Display(); WriteLine();
}
public void GapPerm_Compose_Identity()
{
var f = new GapPerm();
var g = new GapPerm(0, 2, 1);
Assert.AreEqual(g.Compose(f), g);
}
public void GapPerm_Identity_Compose()
{
var f = new GapPerm();
var g = new GapPerm(0, 2, 1);
Assert.AreEqual(f.Compose(g), g);
}
static int order(GapPerm a)
{
var result = new GapPerm();
foreach (var n in Enumerable.Range(1, 100))
{
result = result.Compose(a);
if (result == new GapPerm(0))
{
return(n);
}
}
throw new Exception();
}
static void Main(string[] args)
{
var perm = new GapPerm("(123)");
{
var f = new GapPerm("(23)");
var g = new GapPerm("(56)");
var h = f.Compose(g);
}
{
var f = new GapPerm("(234)");
var g = new GapPerm("(345)");
var h = f.Compose(g);
}
{
var f = new GapPerm("(12)(34)");
}
{
var f = new GapPerm("(123)");
var result = new[]
{
f.Apply(0),
f.Apply(1),
f.Apply(3),
f.Apply(4)
};
}
{
var f = new GapPerm("(12)");
var g = new GapPerm(0, 2, 1);
WriteLine(f.Equals(g));
WriteLine(f == g);
WriteLine(f.GetHashCode());
WriteLine(g.GetHashCode());
}
{
var f = new GapPerm("(1234)");
var result = f.Inverse();
}
{
var f = new GapPerm(10, 20, 30, 40, 4).Simplify();
}
{
var f = new GapPerm();
var g = new GapPerm(0, 2, 1);
var result_a = f.Apply(10);
var result_b = f.Inverse();
var result_c = f.Compose(g);
var result_d = g.Compose(f);
// var result_e = f.
}
{
var f = new GapPerm(3, 1, 2, 0);
var g = f.Inverse();
}
{
var f = new GapPerm(0, 2, 1, 3);
var g = f.Inverse();
}
{
var f = new GapPerm("(123)(234)(456)").ToDisjointCycles();
var g = new GapPerm("(12)(3456)").ToDisjointCycles();
var h = new GapPerm("(123)(234)(456)");
}
}
[Fact] public static void GapPerm_Compose_000() => Assert.Equal("(135)(246)", a.Compose(a).ToString());