lib: allow creating random permutations using a random source

Also add some tests for Random on natural symmetric and alternating groups

lib/gpprmsya.gi

@@ -748,12 +748,12 @@ InstallMethod( Size,
     [ IsNaturalSymmetricGroup ], 0,
     sym -> Factorial( NrMovedPoints(sym) ) );
 
-BindGlobal("FLOYDS_ALGORITHM", function(deg, even)
+BindGlobal("FLOYDS_ALGORITHM", function(rs, deg, even)
     local  rnd, sgn, i, k, tmp;
     rnd := [1..deg];
     sgn := 1;
     for i  in [1..deg-1] do
-        k := Random( [ i .. deg] );
+        k := Random( rs, [ i .. deg] );
         if k <> i then
             tmp := rnd[i];
             rnd[i] := rnd[k];
@@ -771,16 +771,15 @@ end);
 
 
 
-InstallMethod( Random,
-    "symmetric group: floyd's algorithm",
+InstallMethodWithRandomSource( Random,
+    "for a random source and a natural symmetric group: floyd's algorithm",
     true,
-    [ IsNaturalSymmetricGroup ],
-    10, # override perm. gp. method
-function ( G )
+    [ IsRandomSource, IsNaturalSymmetricGroup ],
+    10, # override perm group method
+function ( rs, G )
     local   rnd,        # random permutation, result
-	    deg,
-	    mov;
-
+            deg,
+            mov;
 
     # test for internal rep
     if HasGeneratorsOfGroup(G) and 
@@ -791,34 +790,33 @@ function ( G )
     # use Floyd\'s algorithm
     mov:=MovedPoints(G);
     deg:=Length(mov);
-    rnd := FLOYDS_ALGORITHM(deg,false);
+    rnd:=FLOYDS_ALGORITHM(rs,deg,false);
+
     # return the permutation
     return PermList( rnd )^MappingPermListList([1..deg],mov);
 end);
 
 
-InstallMethod( Random,
-    "alternating group: floyd's algorithm",
+InstallMethodWithRandomSource( Random,
+    "for a random source and a natural alternating group: floyd's algorithm",
     true,
-    [ IsNaturalAlternatingGroup ],
-    10, # override perm gp. method
-function ( G )
+    [ IsRandomSource, IsNaturalAlternatingGroup ],
+    10, # override perm group method
+function ( rs, G )
     local   rnd,        # random permutation, result
-            sgn,        # sign of the permutation so far
-            tmp,        # temporary variable for swapping
-	    deg,
-	    mov,
-            i,  k;      # loop variables
+            deg,
+            mov;
 
     # test for internal rep
     if HasGeneratorsOfGroup(G) and 
       not ForAll(GeneratorsOfGroup(G),IsInternalRep) then
       TryNextMethod();
     fi;
+
     # use Floyd\'s algorithm
     mov:=MovedPoints(G);
     deg:=Length(mov);
-    rnd := FLOYDS_ALGORITHM(deg, true);
+    rnd:=FLOYDS_ALGORITHM(rs,deg,true);
 
     # return the permutation
     return PermList( rnd )^MappingPermListList([1..deg],mov);

tst/testinstall/random.tst

@@ -1,18 +1,36 @@
 gap> START_TEST("random.tst");
 gap> Read( Filename( DirectoriesLibrary( "tst" ), "testrandom.g" ) );
+
+#
 gap> randomTest(Integers, Random);
 gap> randomTest(Rationals, Random);
+
+#
+gap> randomTest(SymmetricGroup(2), Random);
+gap> randomTest(SymmetricGroup(3), Random);
+gap> randomTest(SymmetricGroup(4), Random);
+gap> randomTest(AlternatingGroup(3), Random);
+gap> randomTest(AlternatingGroup(4), Random);
+gap> randomTest(AlternatingGroup(5), Random);
+
+#
 gap> randomTest(Group((1,2),(3,4)), Random);
 gap> randomTest(PrimitiveGroup(5,2), Random);
 gap> randomTest(PrimitiveGroup(5,3), Random);
 gap> randomTest(Group((1,2),(3,4))*(1,2,3), Random);
 gap> randomTest(PrimitiveGroup(5,2)*(1,2,6), Random);
 gap> randomTest(PrimitiveGroup(5,3)*(1,4,6), Random);
+
+#
 gap> randomTest(DoubleCoset(Group((1,2),(3,4)), (1,2,3,4,5,6), Group((1,2,3)) ), Random);
 gap> randomTest(DoubleCoset(Group(()), (1,2), Group((1,2,3)) ), Random);
 gap> randomTest(DoubleCoset(Group((1,2),(3,4)), (), Group((1,2,3)) ), Random);
+
+#
 gap> randomTest([1..10], Random);
 gap> randomTest([1,-6,"cheese", Group(())], Random);
+
+#
 gap> randomTest(PadicExtensionNumberFamily(3, 5, [1,1,1], [1,1]), Random, function(x,y) return IsPadicExtensionNumber(x); end);
 gap> randomTest(PurePadicNumberFamily(2,20), Random, function(x,y) return IsPurePadicNumber(x); end);
 gap> STOP_TEST("random.tst", 1);