document the two-argument version of Set

- extend the manual section on `SSortedList`
- fix the `SSortedList` method for list and function
  in the case that list is not dense

lib/coll.gd

@@ -2131,25 +2131,38 @@ DeclareOperation( "SortedList", [ IsListOrCollection ] );
 
 #############################################################################
 ##
-#O SSortedList( <C> ) . . . . . . . . . . . set of elements of a collection
-#O SSortedList( <list> ) . . . . . . . . . . . . . set of elements of a list
-#O Set( <C> )
+#O SSortedList( <C>[, <fun>] ) . . . . . . . set of elements of a collection
+#O SSortedList( <list>[, <fun>] )  . . . . . . . . set of elements of a list
+#O Set( <C>[, <fun>] )
 ##
 ## <#GAPDoc Label="SSortedList">
 ## <ManSection>
-## <Oper Name="SSortedList" Arg='listorcoll'/>
-## <Oper Name="Set" Arg='C'/>
+## <Oper Name="SSortedList" Arg='listorcoll[, fun]'/>
+## <Oper Name="Set" Arg='C[, fun]'/>
 ##
 ## <Description>
 ## <Ref Oper="SSortedList"/> (<Q>strictly sorted list</Q>) returns a new
 ## dense, mutable, and duplicate free list <A>new</A>.
 ## The argument must be a collection or list <A>listorcoll</A>
-## which may contain holes but whose elements lie in the same family
-## (see&nbsp;<Ref Sect="Families"/>).
+## which may contain holes.
+## <P/>
+## If the optional argument <A>fun</A> is not given then
 ## <C>Length( <A>new</A> )</C> is the number of different elements of
 ## <A>listorcoll</A>,
 ## and <A>new</A> contains the different elements in strictly sorted order,
 ## w.r.t.&nbsp;<Ref Oper="\&lt;"/>.
+## For that, any two entries of <A>listorcoll</A> must be comparable via
+## <Ref Oper="\&lt;"/>.
+## (Typically, the entries lie in the same family,
+## see&nbsp;<Ref Sect="Families"/>.)
+## <P/>
+## If <A>fun</A> is given then it must be a unary function.
+## In this case, <A>fun</A> is applied to all elements of <A>listorcoll</A>,
+## <A>new</A> contains the different return values in strictly sorted order,
+## and <C>Length( <A>new</A> )</C> is the number of different such values.
+## For that, any two return values must be comparable via
+## <Ref Oper="\&lt;"/>.
+## <P/>
 ## <C><A>new</A>[<A>pos</A>]</C> executes in constant time
 ## (see&nbsp;<Ref Filt="IsConstantTimeAccessList"/>),
 ## and the size of <A>new</A> in memory is proportional to its length.
@@ -2166,14 +2179,20 @@ DeclareOperation( "SortedList", [ IsListOrCollection ] );
 ## true
 ## true
 ## true
+## gap> SSortedList( Group( (1,2,3) ), Order );
+## [ 1, 3 ]
 ## gap> SSortedList( [ 1, 2, 1,, 3, 2 ] );
 ## [ 1, 2, 3 ]
+## gap> SSortedList( [ 1, 2, 1,, 3, 2 ], x -> x^2 );
+## [ 1, 4, 9 ]
 ## ]]></Example>
 ## </Description>
 ## </ManSection>
 ## <#/GAPDoc>
 ##
 DeclareOperation( "SSortedList", [ IsListOrCollection ] );
+DeclareOperation( "SSortedList", [ IsListOrCollection, IsFunction ] );
+
 DeclareSynonym( "Set", SSortedList );
 
 

lib/list.gi

@@ -677,11 +677,11 @@ end);
 ##
 #M SSortedList( <list> ) . . . . . . . . . . . set of the elements of a list
 ##
-InstallOtherMethod( SSortedList, "for a plist",
+InstallMethod( SSortedList, "for a plist",
  [ IsList and IsPlistRep ],
  SSortedListList );
 
-InstallOtherMethod( SSortedList, "for a list",
+InstallMethod( SSortedList, "for a list",
  [ IsList ],
  l->SSortedListList(AsPlist(l)) );
 
@@ -690,15 +690,15 @@ InstallOtherMethod( SSortedList, "for a list",
 ##
 #M SSortedList( <list>, <func> )
 ##
-InstallOtherMethod( SSortedList,
+InstallMethod( SSortedList,
  "for a list, and a function",
  [ IsList, IsFunction ],
  function ( list, func )
  local res, i, squashsize;
  squashsize := 100;
  res := [];
- for i  in [ 1 .. Length( list ) ] do
- Add( res, func( list[i] ) );
+ for i in list do
+ Add( res, func( i ) );
  if Length(res) > squashsize then
  res := Set(res);
  squashsize := Maximum(100, Size(res) * 2);