Allow function-call syntax for general mappings. (#3901)

lib/mapping.gd

@@ -882,21 +882,27 @@ DeclareOperation( "ImageElm", [ IsMapping, IsObject ] );
 ##  <A>elm</A> of the source of the mapping <A>map</A> under <A>map</A>,
 ##  i.e., the unique element of the range to which <A>map</A> maps
 ##  <A>elm</A>.
-##  This can also be expressed as <A>elm</A><C>^</C><A>map</A>.
+##  This can also be expressed as <A>elm</A><C>^</C><A>map</A> or as 
 ##  Note that <A>map</A> must be total and single valued,
 ##  a multi valued general mapping is not allowed
 ##  (see&nbsp;<Ref Func="Images" Label="set of images of the source of a general mapping"/>).
 ##  <P/>
 ##  <C>Image( <A>map</A>, <A>coll</A> )</C> is the image of the subset
 ##  <A>coll</A> of the source of the mapping <A>map</A> under <A>map</A>,
 ##  i.e., the subset of the range to which <A>map</A> maps elements of
-##  <A>coll</A>.
+##  <A>coll</A>. <P/> 
 ##  <A>coll</A> may be a proper set or a domain.
 ##  The result will be either a proper set or a domain.
 ##  Note that in this case <A>map</A> may also be multi-valued.
 ##  (If <A>coll</A> and the result are lists then the positions of
 ##  entries do in general <E>not</E> correspond.)
 ##  <P/>
+##  <C>Image( <A>map</A>, <A>coll</A> )</C> can also be expressed as <C><A>map</A>(<A>coll</A>)</C> and
+##  <C>Image( <A>map</A>, <A>elm</A> )</C> as  <C><A>map</A>(<A>elm</A>)</C>.
+##  Those using this notation should remember that composition of mappings in &GAP;
+##  still follows the conventions appropriate for mapping acting from the right, so that 
+##  <C>(<A>map1</A>*<A>map2</A>)(<A>x</A>)</C> is equivalent to 
+##  <C><A>map2</A>(<A>map1</A>(<A>x</A>))</C>    <P/>
 ##  <Ref Func="Image" Label="set of images of the source of a general mapping"/>
 ##  delegates to <Ref Attr="ImagesSource"/> when called
 ##  with one argument, and to <Ref Oper="ImageElm"/> resp.

lib/mapping.gi

@@ -152,6 +152,21 @@ InstallGlobalFunction( Image, function ( arg )
                    "Image(<map>,<coll>)" );
 end );
 
+#############################################################################
+##
+#M  <map>(<elm>)
+#M  <map>(<coll>)
+##
+##  Method to alow mappings to be used like functions when appropriate
+
+InstallMethod(CallFuncList, [IsGeneralMapping, IsList],
+        function(map, lst) 
+    if Length(lst) <> 1 then 
+        TryNextMethod(); 
+    fi; 
+    return Image(map, lst[1]); 
+end);
+
 
 #############################################################################
 ##

tst/testinstall/mapping.tst

@@ -271,10 +271,14 @@ gap> IsTotal( map );
 true
 gap> Image( map, Z(3) );
 0*Z(3)
+gap> map(Z(3));
+0*Z(3)
 gap> ImageElm( map, Z(3) );
 0*Z(3)
 gap> Image( map, [ Z(3) ] );
 [ 0*Z(3) ]
+gap> map( [ Z(3) ] );
+[ 0*Z(3) ]
 gap> ImagesElm( map, Z(3) );
 [ 0*Z(3) ]
 gap> ImagesSet( map, [ 0*Z(3), Z(3) ] );
@@ -346,6 +350,18 @@ Error, <elm> must be an element of Source(<map>)
 gap> Image(map, [Z(3), Z(9)]);
 Error, the collection <elm> must be contained in Source(<map>)
 
+# Image in alternative syntax
+gap> map(0*Z(3));
+Error, <map> must be single-valued and total
+gap> mapBijective(Z(5));
+Error, the families of the element or collection <elm> and Source(<map>) don't\
+ match, maybe <elm> is not contained in Source(<map>) or is not a homogeneous \
+list or collection
+gap> mapBijective(Z(9));
+Error, <elm> must be an element of Source(<map>)
+gap> map([Z(3), Z(9)]);
+Error, the collection <elm> must be contained in Source(<map>)
+
 # Images
 gap> Images(x -> x, 1);
 Error, <map> must be a general mapping