From 2d113029dff8485697404d6f4661476ef34aabf5 Mon Sep 17 00:00:00 2001
From: Ulli Kehrle <ulli.kehrle@rwth-aachen.de>
Date: Wed, 7 Nov 2018 12:36:55 +0100
Subject: Added first draft of the algorithm

---
 subgroupladder.g | 85 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 subgroupladder.g

diff --git a/subgroupladder.g b/subgroupladder.g
new file mode 100644
index 0000000..e1235a1
--- /dev/null
+++ b/subgroupladder.g
@@ -0,0 +1,85 @@
+FindPos := function(list, x)
+	local n, i;
+	n := Length(list);
+	for i in [1..n] do
+		if x in list[i] then
+			return i;
+		fi;
+	od;
+end;
+
+id := function(x)
+	return x;
+end;
+
+Subgroupladder := function(G)
+	local
+		orb,
+		i,
+		k,
+		n,
+		pair,
+		ladder,
+		directfactors,
+		mapping,
+		output,
+		partition;
+		
+
+	if (not IsPermGroup(G)) then
+		ErrorNoReturn("the argument must be a permutation group!\n");
+	fi;
+
+	n := LargestMovedPoint(G);
+
+	orb := List(Orbits(G), x -> x);
+	SortBy(orb, x->-Length(x));
+
+	output := [];
+
+	partition := List(orb, Length);
+	mapping := List([1..n], x -> FindPos(orb, x));
+	ladder := [[List(partition, id), List(mapping, id)]];
+
+
+	while (Length(partition) <> 1 or partition[1] < n) do
+		if (Length(partition) = 1 and partition[1] < n) then
+			mapping[Position(mapping, 0)] := 1;
+			partition[1] := partition[1] + 1;
+			Add(ladder, [List(partition, id), List(mapping, id)]);
+		else 
+			if (partition[2] = 1) then
+				Remove(partition, 2);
+				for i in [1..n] do
+					if (mapping[i]) > 1 then
+						mapping[i] := mapping[i] - 1;
+					fi;
+				od;
+				partition[1] := partition[1] + 1;
+				Add(ladder, [List(partition, id), List(mapping, id)]);
+			else 
+				mapping[Position(mapping, 2)] := Length(partition)+1;
+				partition[2] := partition[2] - 1;
+				Add(partition, 1);
+				Add(ladder, [List(partition, id), List(mapping, id)]);
+
+				mapping[Position(mapping, Length(partition))] := 1;
+				Remove(partition);
+				partition[1] := partition[1] + 1;
+				Add(ladder, [List(partition, id), List(mapping, id)]);
+			fi;
+		fi;
+	od;
+
+	for pair in ladder do
+		k := Length(pair[1]);
+		mapping := pair[2];
+		directfactors := [];
+		for i in [1..k] do
+			Add(directfactors, SymmetricGroup(Filtered([1..n], x -> i = mapping[x])));
+		od;
+		Add(output, DirectProduct(directfactors));
+	od;
+
+	return output;
+end;
-- 
cgit v1.2.3-24-g4f1b