Merge pull request #151 from giuliao27/extra-methods

Add computations for the transversal in the extra methods

Author: grahamknockillaree

lib/Orru/sl2methodsExtra.gi

@@ -76,4 +76,55 @@ InstallMethod(CosetRepFunction,
         end;
 
         return cosetRep;
-    end);
+    end);
+
+    ##########################################################################
+##
+## AmbientTransversal( <G> )
+##
+## Right transversal for a congruence subgroup G in its ambient group GG
+     InstallMethod(AmbientTransversal,
+     "Right transversal for a congruence subgroup G in its ambient group",
+     [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
+     function(G)
+        local n, GG, poscan, cosetPos, transversal, ProjLine, cosetOfInt;
+        if DimensionOfMatrixGroup(G) <> 2 then
+            TryNextMethod();
+        fi;
+
+        n:=LevelOfCongruenceSubgroup(G);
+
+        ProjLine := FiniteProjectiveLine(n);
+        
+        GG:=AmbientGroupOfCongruenceSubgroup(G);
+
+        cosetPos:=CosetPosFunction(G);
+
+        cosetOfInt := function(i)
+            local a, c, b, d, gg;
+            a := ProjLine[i][1];
+            c := ProjLine[i][2];
+            if a = 0 then
+                return [[0,-1],[1,0]];
+            fi;
+            gg := Gcdex(a,c);
+            b := -gg.coeff2;
+            d :=  gg.coeff1;
+            return [[a,b],[c,d]];
+        end;
+
+        poscan := function(g)
+            return cosetPos(g^-1);
+        end;
+
+        transversal := List([1..Length(ProjLine)],i->cosetOfInt(i)^-1);
+
+        return Objectify( NewType( FamilyObj( GG ),
+                    IsHapRightTransversalSL2ZSubgroup and IsList and
+                    IsDuplicateFreeList and IsAttributeStoringRep ),
+                    rec( group := GG,
+                         subgroup := G,
+                         cosets:=transversal,
+                         poscan:=poscan 
+                    ));
+     end);

lib/Orru/sl3methods.gi

@@ -77,4 +77,54 @@ InstallMethod(CosetRepFunction,
         end;
 
         return cosetRep;
-     end);
+     end);
+
+     ##
+## AmbientTransversal( <G> )
+##
+## Right transversal for a congruence subgroup G in its ambient group GG
+InstallMethod(AmbientTransversal,
+"Right transversal for a congruence subgroup G in its ambient group",
+[ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
+function(G)
+    local n, GG, poscan, cosetPos, transversal, ProjPlane, cosetOfInt, MatrixInSL3_Hermite;
+
+    if DimensionOfMatrixGroup(G) <> 3 then
+        TryNextMethod();
+    fi;
+
+    n := LevelOfCongruenceSubgroup(G);
+    ProjPlane := FiniteProjectivePlane(n);
+    
+    GG:=AmbientGroupOfCongruenceSubgroup(G);
+    cosetPos:=CosetPosFunction(G);
+
+    MatrixInSL3_Hermite := function(v)
+        local Herm;
+        Herm := HermiteNormalFormIntegerMatTransform([[v[1]],[v[2]],[v[3]]]);
+        return Inverse(Herm!.rowtrans);
+    end;
+
+    cosetOfInt:=function(i)
+        local x,y,z;
+        x := ProjPlane.Reps[i][1];
+        y := ProjPlane.Reps[i][2];
+        z := ProjPlane.Reps[i][3];
+        return MatrixInSL3_Hermite([x,y,z]);
+        end;
+
+    poscan := function(g)
+        return cosetPos(g^-1);
+    end;
+
+    transversal := List([1..Length(ProjPlane.Reps)],i->cosetOfInt(i)^-1);
+
+    return Objectify( NewType( FamilyObj( GG ),
+                IsHapRightTransversalSL2ZSubgroup and IsList and
+                IsDuplicateFreeList and IsAttributeStoringRep ),
+                rec( group := GG,
+                     subgroup := G,
+                     cosets:=transversal,
+                     poscan:=poscan 
+                ));
+end);

lib/Orru/subgroups.gi

@@ -445,7 +445,7 @@ function(G,H)
         TryNextMethod();
     fi;
 
-    HAPCongruenceSubgroupTree(H);
+    #HAPCongruenceSubgroupTree(H);
 
     return HAP_TransversalCongruenceSubgroupInAmbientGroup(G,H);
 end);