Turn RestrictedNiceMonomorphism into an attribute

Author: fingolfin

lib/factgrp.gi

@@ -523,7 +523,7 @@ InstallMethod(FactorCosetAction,"by right transversal operation, Niceo",
   IsIdenticalObj,[IsGroup and IsHandledByNiceMonomorphism,IsGroup],0,
 function(G,U)
 local hom;
-  hom:=RestrictedNiceMonomorphism(NiceMonomorphism(G),G);
+  hom:=RestrictedNiceMonomorphism(G);
   return hom*DoFactorCosetAction(NiceObject(G),Image(hom,U));
 end);
 
@@ -532,7 +532,7 @@ InstallOtherMethod(FactorCosetAction,
   [IsGroup and IsHandledByNiceMonomorphism,IsGroup,IsGroup],0,
 function(G,U,N)
 local hom;
-  hom:=RestrictedNiceMonomorphism(NiceMonomorphism(G),G);
+  hom:=RestrictedNiceMonomorphism(G);
   return hom*DoFactorCosetAction(NiceObject(G),Image(hom,U),Image(hom,N));
 end);
 

lib/grpmat.gi

@@ -556,26 +556,22 @@ end );
 ##
 BindGlobal( "IsomorphismPermGroupForMatrixGroup",
 function(G)
-local map,H;
-  if HasNiceMonomorphism(G) and IsPermGroup(Range(NiceMonomorphism(G))) then
-    map:=NiceMonomorphism(G);
-  else
+local map;
+  if not HasNiceMonomorphism(G) or not IsPermGroup(Range(NiceMonomorphism(G))) then
     if not HasIsFinite(G) then
       Info(InfoWarning,1,
            "IsomorphismPermGroup: The group is not known to be finite");
     fi;
     map:=NicomorphismOfGeneralMatrixGroup(G,false,false);
     SetNiceMonomorphism(G,map);
   fi;
-  if IsIdenticalObj(Source(map),G) and IsBijective(map) then
-    return map;
+  if IsPermGroup(Range(NiceMonomorphism(G))) then
+    map:=RestrictedNiceMonomorphism(G);
   fi;
-  if IsIdenticalObj(map, NiceMonomorphism(G)) then
-    H:=NiceObject(G);
-  else
-    H:=ImagesSet(map,G);
+  if IsIdenticalObj(Source(map),G) and IsSurjective(map) then
+    return map;
   fi;
-  map:=GeneralRestrictedMapping(map, G, H);
+  map:=GeneralRestrictedMapping(map, G, ImagesSet(map,G));
   SetIsBijective(map, true);
   return map;
 end);

lib/grpnice.gd

@@ -62,13 +62,13 @@ DeclareFilter("IsNiceMonomorphism");
 
 #############################################################################
 ##
-#O  RestrictedNiceMonomorphism(<hom>,<G>)
+#A  RestrictedNiceMonomorphism(<G>)
 ##
 ##  <ManSection>
-##  <Oper Name="RestrictedNiceMonomorphism" Arg='hom, G'/>
+##  <Attr Name="RestrictedNiceMonomorphism" Arg='G'/>
 ##
 ##  <Description>
-##  returns the restriction of the nice monomorphism <A>hom</A> onto
+##  returns the restriction of the nice monomorphism of <A>G</A> onto
 ##  <A>G</A>.
 ##  In contrast to <Ref Func="RestrictedMapping"/>,
 ##  this operation returns an object which has the filter
@@ -89,7 +89,7 @@ DeclareFilter("IsNiceMonomorphism");
 ##  </Description>
 ##  </ManSection>
 ##
-DeclareGlobalFunction("RestrictedNiceMonomorphism");
+DeclareAttribute("RestrictedNiceMonomorphism", IsObject);
 
 #############################################################################
 ##

lib/grpnice.gi

@@ -37,10 +37,16 @@ end);
 
 #############################################################################
 ##
-#O  RestrictedNiceMonomorphism(<hom>,<G>)
+#O  RestrictedNiceMonomorphism(<G>)
 ##
-InstallGlobalFunction(RestrictedNiceMonomorphism,
-function(hom,G)
+InstallMethod(RestrictedNiceMonomorphism,
+  [IsObject],
+function(G)
+  local hom;
+  hom:=NiceMonomorphism(G);
+  if IsIdenticalObj(Source(hom),G) and IsSurjective(hom) then
+    return hom;
+  fi;
   hom:=RestrictedMapping(hom,G:surjective);
 
   # CompositionMapping methods need this to avoid forming an AsGHBI of an
@@ -558,9 +564,9 @@ InstallMethod(IsomorphismPermGroup,"via niceomorphisms",true,
   [ [ IsGroup and IsFinite ], 1 ],
 function(g)
 local mon,iso;
-  mon:=NiceMonomorphism(g);
-  if not IsIdenticalObj(Source(mon),g) then
-    mon:=RestrictedNiceMonomorphism(mon,g);
+  mon:=RestrictedNiceMonomorphism(g);
+  if IsPermGroup(Range(mon)) then
+    return mon;
   fi;
   iso:=IsomorphismPermGroup(NiceObject(g));
   if iso=fail then
@@ -581,9 +587,9 @@ InstallMethod(IsomorphismPcGroup,"via niceomorphisms",true,
   [IsGroup and IsFinite and IsHandledByNiceMonomorphism],0,
 function(g)
 local mon,iso;
-  mon:=NiceMonomorphism(g);
-  if not IsIdenticalObj(Source(mon),g) then
-    mon:=RestrictedNiceMonomorphism(mon,g);
+  mon:=RestrictedNiceMonomorphism(g);
+  if IsPcGroup(Range(mon)) then
+    return mon;
   fi;
   iso:=IsomorphismPcGroup(NiceObject(g));
   if iso=fail then
@@ -604,9 +610,9 @@ InstallOtherMethod(IsomorphismFpGroup,"via niceomorphism",true,
   [IsGroup and IsHandledByNiceMonomorphism,IsString],0,
 function(g,nam)
 local mon,iso;
-  mon:=NiceMonomorphism(g);
-  if not IsIdenticalObj(Source(mon),g) then
-    mon:=RestrictedNiceMonomorphism(mon,g);
+  mon:=RestrictedNiceMonomorphism(g);
+  if IsFpGroup(Range(mon)) then
+    return mon;
   fi;
   iso:=IsomorphismFpGroup(NiceObject(g),nam);
   if iso=fail then
@@ -624,11 +630,8 @@ InstallMethod(IsomorphismFpGroupByGeneratorsNC,"via niceomorphism/w. gens",
   IsFamFamX,[IsGroup and IsHandledByNiceMonomorphism, IsList,IsString],0,
 function(g,c,nam)
 local mon,iso;
-  mon:=NiceMonomorphism(g);
+  mon:=RestrictedNiceMonomorphism(g);
   c:=List(c,i->Image(mon,i));
-  if not IsIdenticalObj(Source(mon),g) then
-    mon:=RestrictedNiceMonomorphism(mon,g);
-  fi;
   iso:=IsomorphismFpGroupByGeneratorsNC(NiceObject(g),c,nam);
   if iso=fail then
     return fail;
@@ -925,9 +928,9 @@ InstallMethod( NaturalHomomorphismByNormalSubgroupOp, IsIdenticalObj,
     function( G, N )
     local   nice;
 
-    nice := RestrictedNiceMonomorphism(NiceMonomorphism( G ),G);
-    G := ImagesSet( nice,G );
-    N := ImagesSet   ( nice, N );
+    nice := RestrictedNiceMonomorphism(G);
+    G := ImagesSet( nice, G );
+    N := ImagesSet( nice, N );
     return CompositionMapping( NaturalHomomorphismByNormalSubgroup( G, N ),
                    nice );
 end );
@@ -946,10 +949,7 @@ local nice,geni,map2,tmp;
   fi;
   tmp := RUN_IN_GGMBI;
   RUN_IN_GGMBI:=true;
-  nice:=NiceMonomorphism(G);
-  if not IsIdenticalObj(Source(nice),G) then
-    nice:=RestrictedNiceMonomorphism(nice,G);
-  fi;
+  nice:=RestrictedNiceMonomorphism(G);
   geni:=List(gens,i->ImageElm(nice,i));
   map2:=GroupGeneralMappingByImagesNC(NiceObject(G),H,geni,imgs);
   RUN_IN_GGMBI:=tmp;