CosetRepFunction --> AmbientRepresentation, CosetPosFunction --> AmbientPosition

Author: grahamknockillaree

lib/CongruenceGroups/congGroups.gd

@@ -129,21 +129,21 @@ DeclareAttribute( "AmbientTransversal", IsHAPCongruenceSubgroup );
 
 ############################################################################
 ##
-## CosetPosFunction( <G> )
+## AmbientPosition( <G> )
 ##
 ## returns a function cosetPos(g) that inputs an element g in the ambient 
 ## group GG and returns an integer corresponding to the position of the left
 ## coset gG in the lists of cosets of G in GG. 
-DeclareAttribute( "CosetPosFunction", IsHAPCongruenceSubgroup );
+DeclareAttribute( "AmbientPosition", IsHAPCongruenceSubgroup );
 
 ############################################################################
 ##
-## CosetRepFunction( <G> )
+## AmbientRepresentation( <G> )
 ##
 ## returns a function cosetRep(g) that inputs an element g in the ambient 
 ## group GG and returns a canonical representative in the ambient group GG
 ## of the left coset gG. 
-DeclareAttribute( "CosetRepFunction", IsHAPCongruenceSubgroup );
+DeclareAttribute( "AmbientRepresentation", IsHAPCongruenceSubgroup );
 
 ############################################################################
 ##

lib/CongruenceGroups/congGroups.gi

@@ -103,8 +103,8 @@ InstallMethod( CongruenceSubgroupGamma0, "for integer matrix group and positive
     ## Remaining components to be computed in other functions.
     ProjectiveSpace(G);
     AmbientTransversal(G);
-    CosetPosFunction(G); #A generic method will be used to construct the
-    CosetRepFunction(G); #these two functions except for cases with a
+    AmbientPosition(G); #A generic method will be used to construct the
+    AmbientRepresentation(G); #these two functions except for cases with a
                          #bespoke implementation.
                          #cosetPos and poscan are used interchangably.
 
@@ -180,8 +180,8 @@ InstallMethod( PrincipalCongruenceSubgroup,
     ##
     ## Remaining components to be computer elsewhere.
     AmbientTransversal(G);
-    CosetPosFunction(G); #A generic method will be used to construct the
-    CosetRepFunction(G); #these two functions except for cases with a
+    AmbientPosition(G); #A generic method will be used to construct the
+    AmbientRepresentation(G); #these two functions except for cases with a
                          #bespoke implementation.
                          #cosetPos and poscan are used interchangably.
 
@@ -407,7 +407,7 @@ InstallMethod( IsSubset,
      if Size(StabilizerSubgroup(G))=1 then
          AmbientTree(G);
          nodes:=G!.nodes;
-         poscan:=CosetPosFunction(G); 
+         poscan:=AmbientPosition(G); 
 
      else
      ################################################################
@@ -525,7 +525,7 @@ InstallMethod( IsSubset,
 ## Returns a tree representing the cosets of G in the ambient group GG.
      InstallMethod(AmbientTree,
      "Constructs a coset tree for a congruence subgroup in the ambient group, and uses it to obtain a generating set (faster method)",
-     [ IsHAPCongruenceSubgroup and HasCosetPosFunction and HasCosetRepFunction ],
+     [ IsHAPCongruenceSubgroup and HasAmbientPosition and HasAmbientRepresentation ],
      function(G)
      local GG, ambientGenerators, tree,InGmodU,Ugrp,U,v,p,g,s,n,q,vv,
       leaves,genTriples,generators, InLowDegreeNodesModG, csts, cnt,
@@ -538,8 +538,8 @@ InstallMethod( IsSubset,
      GG:=AmbientGroupOfCongruenceSubgroup(G);
      ambientGenerators:=GeneratorsOfGroup(GG);
      one:=One(GG);
-     cosetPos:=CosetPosFunction(G);
-     cosetRep:=CosetRepFunction(G);
+     cosetPos:=AmbientPosition(G);
+     cosetRep:=AmbientRepresentation(G);
 
      Ugrp:=StabilizerSubgroup(G);
      Ugrp:=Elements(Ugrp);
@@ -616,11 +616,11 @@ InstallMethod( IsSubset,
 
 ##########################################################################
 ##
-## CosetPosFunction( <G> )
+## AmbientPosition( <G> )
 ##
 ## Returns a function cosetPos(g) giving the position of the coset gG in 
 ## the ambient group. 
-     InstallMethod(CosetPosFunction,
+     InstallMethod(AmbientPosition,
      "Returns cosetPos(g) function for the congruence subgroup G",
      [ IsIntegerMatrixGroup and IsHAPPrincipalCongruenceSubgroup ],
      function(G)
@@ -652,11 +652,11 @@ InstallMethod( IsSubset,
 
 ##########################################################################
 ##
-## CosetRepFunction( <G> )
+## AmbientRepresentation( <G> )
 ##
 ## Returns a function cosetRep(g) giving a representative of the coset gG in 
 ## the ambient group. 
-     InstallMethod(CosetRepFunction,
+     InstallMethod(AmbientRepresentation,
      "Returns cosetPos(g) function for the congruence subgroup G",
      [ IsIntegerMatrixGroup and IsHAPPrincipalCongruenceSubgroup ],
      function(G)
@@ -724,9 +724,9 @@ InstallMethod( IsSubset,
 
 ##########################################################################
 ##
-## CosetPosFunction( <G> )
+## AmbientPosition( <G> )
 ##
-     InstallOtherMethod(CosetPosFunction,
+     InstallOtherMethod(AmbientPosition,
      "for a generic congruence subgroup (slow method via ambient tree)",
      [ IsHAPCongruenceSubgroup ],
      function(G)
@@ -746,9 +746,9 @@ InstallMethod( IsSubset,
 
 ##########################################################################
 ##
-## CosetRepFunction( <G> )
+## AmbientRepresentation( <G> )
 ##
-     InstallOtherMethod(CosetRepFunction,
+     InstallOtherMethod(AmbientRepresentation,
      "for a generic congruence subgroup (slow method via ambient tree)",
      [ IsHAPCongruenceSubgroup ],
      function(G)
@@ -892,8 +892,8 @@ G!.ambientMembership:=ambientMembership;
 G!.AmbientGroupOfCongruenceSubgroup:= AmbientGroupOfCongruenceSubgroup(H);
 
 AmbientTransversal(G);
-CosetPosFunction(G);
-CosetRepFunction(G);
+AmbientPosition(G);
+AmbientRepresentation(G);
 
 return G;
 

lib/CongruenceGroups/sl2methods.gi

@@ -55,7 +55,7 @@ InstallMethod(ProjectiveSpace,
      #Now handle case of prime level.
      GG:=AmbientGroupOfCongruenceSubgroup(G);
 
-     cosetPos:=CosetPosFunction(G);
+     cosetPos:=AmbientPosition(G);
      poscan:=function(g) return cosetPos(g^-1); end;
 
      transversal:=List([0..n-1],i->[[1,0],[-i,1]]);
@@ -73,11 +73,11 @@ InstallMethod(ProjectiveSpace,
 
 ##########################################################################
 ##
-## CosetPosFunction( <G> )
+## AmbientPosition( <G> )
 ##
 ## Returns a function cosetPos(g) giving the position of the coset gG in 
 ## the ambient group. 
-     InstallMethod(CosetPosFunction,
+     InstallMethod(AmbientPosition,
      "Returns cosetPos(g) function for the congruence subgroup G",
      [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
      function(G)
@@ -99,11 +99,11 @@ InstallMethod(ProjectiveSpace,
 
 ##########################################################################
 ##
-## CosetRepFunction( <G> )
+## AmbientPosition( <G> )
 ##
 ## Returns a function cosetPos(g) giving a canonical rpresentative of the 
 ## coset gG in the ambient group. 
-     InstallMethod(CosetRepFunction,
+     InstallMethod(AmbientPosition,
      "Returns cosetPos(g) function for the congruence subgroup G",
      [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
      function(G)

lib/Orru/sl2methodsExtra.gi

@@ -1,6 +1,6 @@
 # methods for power of primes
 
-InstallMethod(CosetPosFunction,
+InstallMethod(AmbientPosition,
     "Returns cosetPos(g) function for the congruence subgroup G",
     [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
     function(G)
@@ -77,7 +77,7 @@ InstallMethod(CosetPosFunction,
         return cosetPos;
     end);
 
-InstallMethod(CosetPosFunction,
+InstallMethod(AmbientPosition,
     "Returns cosetPos(g) function for the congruence subgroup G",
     [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
     function(G)
@@ -130,7 +130,7 @@ InstallMethod(CosetPosFunction,
         return cosetPos;
     end);
 
-InstallMethod(CosetRepFunction,
+InstallMethod(AmbientRepresentation,
     "Returns cosetPos(g) function for the congruence subgroup G",
     [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
     function(G)
@@ -161,7 +161,7 @@ InstallMethod(CosetRepFunction,
             return [[a,b],[c,d]];
         end;
 
-        cosetPos := CosetPosFunction(G);
+        cosetPos := AmbientPosition(G);
 
         cosetRep:=function(g);
             return cosetOfInt(cosetPos(g));
@@ -194,7 +194,7 @@ InstallMethod(CosetRepFunction,
 
         GG:=AmbientGroupOfCongruenceSubgroup(G);
 
-        cosetPos:=CosetPosFunction(G);
+        cosetPos:=AmbientPosition(G);
 
         cosetOfInt := function(i)
             local a, c, b, d, gg;

lib/Orru/sl3methods.gi

@@ -20,11 +20,11 @@ InstallMethod(ProjectiveSpace,
      end);
 ##########################################################################
 ##
-## CosetPosFunction( <G> )
+## AmbientPosition( <G> )
 ##
 ## Returns a function cosetPos(g) giving the position of the coset gG in 
 ## the ambient group. 
-InstallMethod(CosetPosFunction,
+InstallMethod(AmbientPosition,
 "Returns cosetPos(g) function for the congruence subgroup G",
 [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
     function(G)
@@ -54,11 +54,11 @@ InstallMethod(CosetPosFunction,
     end);
 ##########################################################################
 ##
-## CosetRepFunction( <G> )
+## AmbientRepresentation( <G> )
 ##
 ## Returns a function cosetPos(g) giving a canonical rpresentative of the 
 ## coset gG in the ambient group. 
-InstallMethod(CosetRepFunction,
+InstallMethod(AmbientRepresentation,
 "Returns cosetRep(g) function for the congruence subgroup G",
 [ IsIntegerMatrixGroup and IsHAPCongruenceSubgroupGamma0 ],
      function(G)
@@ -86,7 +86,7 @@ InstallMethod(CosetRepFunction,
             return MatrixInSL3_Hermite([x,y,z]);
         end;
 
-        cosetPos := CosetPosFunction(G);
+        cosetPos := AmbientPosition(G);
 
         cosetRep:=function(g);
             return cosetOfInt(cosetPos(g));
@@ -113,7 +113,7 @@ function(G)
     ProjPlane := ProjectiveSpace(G);
 
     GG:=AmbientGroupOfCongruenceSubgroup(G);
-    cosetPos:=CosetPosFunction(G);
+    cosetPos:=AmbientPosition(G);
 
     MatrixInSL3_Hermite := function(v)
         local Herm;
@@ -143,4 +143,4 @@ function(G)
                      cosets:=transversal,
                      poscan:=poscan 
                 ));
-end);
+end);