merge default into stable

1 files changed, 102 insertions, 0 deletions

diff --git a/tests/examplefiles/AlternatingGroup.mu b/tests/examplefiles/AlternatingGroup.mu
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+/*++ $Id: AlternatingGroup.mu,v 1.4 2003/09/08 15:00:47 nthiery Exp $
+
+Dom::AlternatingGroup(n) -- the Alternating Group of {1..n}
+
+n	   - integer >= 1
+
+Elements are represented as in Dom::PermutationGroup(n)
+
+Author:	     Nicolas M. Thiéry <nthiery@users.sourceforge.net>
+License:     LGPL
+Created:     August 8th, 1999
+Last update: $Date: 2003/09/08 15:00:47 $
+++*/
+
+domain Dom::AlternatingGroup(n: Type::PosInt)
+    inherits Dom::PermutationGroup(n,toBeDefined);
+    category Cat::PermutationGroup;
+    axiom Ax::canonicalRep;
+
+/*--
+    size
+
+    Size of the group.
+--*/
+
+    size := fact(n)/2;
+
+/*--
+    generators
+
+    A list of generators of the group
+
+    The first 3-cycle (1,2,3), and a maximal even cycle (1,...,n) or
+    (2,...,n) depending on the parity of n
+
+--*/
+
+    generators :=
+    if	 n<=2	     then generators:=[dom([[1]])];
+    elif n=3	     then generators:=[dom([[1,2,3]])];
+    elif n mod 2=0   then generators:=[dom([[1,2,3]]), dom([[$2..n]])];
+    else		  generators:=[dom([[1,2,3]]), dom([[$1..n]])];
+    end_if;
+    
+/*--
+    allElements
+
+    List of all the elements of the group
+--*/
+
+    allElements :=
+    proc()
+	option remember;
+	local p;
+    begin
+	[new(dom,p) $ p in select(combinat::permutations(n),
+				  p->bool(combinat::permutations::sign(p)=1))];
+    end_proc;
+
+/*--
+    cycleTypes:
+
+    Count the elements of the group by cycle type.
+    (Cf Cat::PermutationGroupModule).
+
+    Same algorithm as for Dom::SymmetricGroup, but only even permutations
+    are considered. This is done by disregarding partitions p such
+    that n-length(p) is odd.
+--*/
+
+    cycleTypes :=
+    proc()
+	option remember;
+	local t, p, gen;
+    begin
+	userinfo(3, "cycleTypes: starting computation");
+	t:=table();
+
+	gen := combinat::partitions::generator(n);
+	while (p:=gen()) <> FAIL do
+	    userinfo(5, "working on partition", p);
+	    if(n-nops(p) mod 2=0) then
+		// Compute the size of the conjugacy class of Sn indexed by p
+		// and the cycle type of a permutation in this conjugacy class
+                t[combinat::partitions::toExp(p,n)]
+                  := combinat::partitions::conjugacyClassSize(p);
+	    end_if;
+        end_while;
+	t;
+    end_proc;
+
+begin
+    if testargs() then
+	if args(0) <> 1 then error("wrong no of args"); end_if;
+	if not testtype(n,DOM_INT) then
+	    error("argument must be integer")
+	end_if;
+	if n < 1 then
+	    error("argument must be positive")
+	end_if;
+    end_if;
+end_domain: