Special setter for size, made IsTrivial<->IsNonTrivial a true method

and changed the corresponding immediate methods to ordinary ones.

Impact on csetgrp b/c ObjectifyWithAttr for Size

lib/coll.gd

@@ -1371,6 +1371,10 @@ InstallFactorMaintenance( IsTrivial,
 ##
 DeclareProperty( "IsNonTrivial", IsCollection );
 
+# true methods to avoid immediate methods 
+InstallTrueMethod(HasIsTrivial,IsNonTrivial);
+InstallTrueMethod(HasIsNonTrivial,IsTrivial);
+
 
 #############################################################################
 ##

lib/coll.gi

@@ -94,7 +94,7 @@ InstallMethod( PrintObj,
 ##
 InstallImmediateMethod( IsEmpty,
     IsCollection and HasSize, 0,
-    C -> Size( C ) = 0 );
+    C->Size( C ) = 0);
 
 InstallMethod( IsEmpty,
     "for a collection",
@@ -120,17 +120,17 @@ InstallMethod( IsTrivial,
     [ IsCollection ],
     C -> Size( C ) = 1 );
 
-InstallImmediateMethod( IsTrivial,
-    IsCollection and HasIsNonTrivial, 0,
+InstallMethod( IsTrivial,
+    [IsCollection and HasIsNonTrivial], 0,
     C -> not IsNonTrivial( C ) );
 
 
 #############################################################################
 ##
 #M  IsNonTrivial( <C> ) . . . . . . . . .  test if a collection is nontrivial
 ##
-InstallImmediateMethod( IsNonTrivial,
-    IsCollection and HasIsTrivial, 0,
+InstallMethod( IsNonTrivial,
+    [IsCollection and HasIsTrivial], 0,
     C -> not IsTrivial( C ) );
 
 InstallMethod( IsNonTrivial,
@@ -173,7 +173,8 @@ InstallMethod( IsWholeFamily,
 #  method, as the immediate method would get called for every group that
 #  knows it is finite but does not know its size -- e.g.  permutation, pc.
 #  The benefit of this is minimal beyond showing off a feature.
-InstallMethod( Size,true, [IsCollection and HasIsFinite], 0,
+InstallMethod( Size,true, [IsCollection and HasIsFinite], 
+  100, # rank above object-specific methods
     function ( C )
     if IsFinite( C ) then
         TryNextMethod();
@@ -3052,6 +3053,20 @@ end);
 InstallMethod( CanComputeIsSubset,"default: no, unless identical",
   [IsObject,IsObject],IsIdenticalObj);
 
+# avoid immediate methods triggering multiple type changes once the Size of
+# an object is known.
+InstallOtherMethod(SetSize,true,[IsObject and IsAttributeStoringRep,IsObject],
+  100, # override system setter
+function(obj,sz)
+  if not HasSize(obj) then
+    SetIsEmpty(obj,sz=0);
+    SetIsTrivial(obj,sz=1);
+    SetIsNonTrivial(obj,sz<>1);
+    SetIsFinite(obj,sz<>infinity);
+  fi;
+  TryNextMethod(); # to enforce size setting
+end);
+
 #############################################################################
 ##
 #E

lib/csetgrp.gi

@@ -573,21 +573,20 @@ end);
 InstallMethod(RightCoset,"use subgroup size",IsCollsElms,
   [IsGroup and HasSize,IsObject],0,
 function(U,g)
-local d,fam;
+local d,fam,typ;
   # noch tests...
 
   fam:=FamilyObj(U);
-  if not IsBound(fam!.rightCosetsDefaultSizeType) then
-    fam!.rightCosetsDefaultSizeType:=NewType(fam,IsRightCosetDefaultRep and
-          HasActingDomain and HasFunctionAction and HasRepresentative and
-	  HasSize and HasCanonicalRepresentativeDeterminatorOfExternalSet);
-  fi;
+  typ:=NewType(fam,IsRightCosetDefaultRep and
+          HasActingDomain and HasFunctionAction and HasRepresentative
+	  and HasCanonicalRepresentativeDeterminatorOfExternalSet);
 
   d:=rec();
-  ObjectifyWithAttributes(d,fam!.rightCosetsDefaultSizeType,
+  ObjectifyWithAttributes(d,typ,
     ActingDomain,U,FunctionAction,OnLeftInverse,Representative,g,
-    Size,Size(U),CanonicalRepresentativeDeterminatorOfExternalSet,
+    CanonicalRepresentativeDeterminatorOfExternalSet,
     RightCosetCanonicalRepresentativeDeterminator);
+  SetSize(d,Size(U)); # as own setter
   return d;
 end);