ENHANCE: Option generatorNames to select names for free/pc generators

doc/ref/grplib.xml

@@ -99,6 +99,31 @@ calculations.
 <#Include Label="SuzukiGroup">
 <#Include Label="ReeGroup">
 
+<Subsection Label="Generator Names">
+<Heading>Generator Names</Heading>
+For groups created as finitely presented groups of polycyclic groups, the
+generators are labelled, by default, with a letter and a number. Using the
+option <C>generatorNames</C> it is possible to influcence this naming. If
+this option holds a string, the generators are named with this sting and
+numbers, if a list of strings of sufficient length is given, the generator
+names are taken from this list of strings.
+<P/>
+<Example><![CDATA[
+gap> GeneratorsOfGroup(AbelianGroup([5,7]));
+[ f1, f2 ]
+gap> GeneratorsOfGroup(AbelianGroup([5,7]:generatorNames:="a"));
+[ a1, a2 ]
+gap> GeneratorsOfGroup(AbelianGroup([5,7]:generatorNames:=["u","v","w"]));
+[ u, v ]
+gap> AsSSortedList(DihedralGroup(12:generatorNames:="a"));
+[ <identity> of ..., a1, a2, a3, a1*a2, a1*a3, a2*a3, a3^2, a1*a2*a3,
+  a1*a3^2, a2*a3^2, a1*a2*a3^2 ]
+gap> AsSSortedList(DihedralGroup(12:generatorNames:=["a","b","c"]));
+[ <identity> of ..., a, b, c, a*b, a*c, b*c, c^2, a*b*c, a*c^2, b*c^2,
+  a*b*c^2 ]
+]]></Example>
+</Subsection>
+
 </Section>
 
 

lib/grpfree.gi

@@ -449,8 +449,20 @@ InstallGlobalFunction( FreeGroup, function ( arg )
     elif Length( zarg ) = 3 and zarg[1] = infinity then
       names:= InfiniteListOfNames( zarg[2], zarg[3] );
     elif Length( zarg ) = 1 and IsInt( zarg[1] ) and 0 <= zarg[1] then
-      names:= List( [ 1 .. zarg[1] ],
-                    i -> Concatenation( "f", String(i) ) );
+      names:=ValueOption("generatorNames");
+      if names=fail then
+        names:= List( [ 1 .. zarg[1] ],
+                      i -> Concatenation( "f", String(i) ) );
+      elif IsString(names) then
+        names:= List( [ 1 .. zarg[1] ],
+                      i -> Concatenation( names, String(i) ) );
+
+      elif IsList(names) and ForAll(names,IsString) 
+        and Length(names)>=zarg[1] then
+        names:=names{[1..zarg[1]]};
+      else
+        Error("Cannot process `generatorNames` option");
+      fi;
       MakeImmutable( names );
     elif Length( zarg ) = 2 and IsInt( zarg[1] ) and 0 <= zarg[1] then
       names:= List( [ 1 .. zarg[1] ],