change a manual example

such that the output does not depend on which packages are loaded

Author: ThomasBreuer

doc/groups.xml

@@ -408,28 +408,22 @@ gap> gens := [ (1,2,3,4), (1,2)(3,4) ];;
 gap> d8 := Group( gens );;
 gap> SetName( d8, "d8" );
 gap> c2 := Subgroup( d8, [ (2,4) ] );;
-gap> IdempotentEndomorphismsWithImage( gens, c2 );
-[ [ (2,4), () ], [ (), (2,4) ] ]
-gap> IdempotentEndomorphismsData( d8 );
-rec( gens := [ (1,2,3,4), (1,2)(3,4) ], 
-  images := [ [ [ (), () ] ], [ [ (2,4), () ], [ (), (2,4) ] ], 
-      [ [ (1,3), () ], [ (), (1,3) ] ], 
-      [ [ (1,2)(3,4), (1,2)(3,4) ], [ (), (1,2)(3,4) ] ], 
-      [ [ (1,4)(2,3), (1,4)(2,3) ], [ (), (1,4)(2,3) ] ], 
-      [ [ (1,2,3,4), (1,2)(3,4) ] ] ] )
-gap> List( last.images, L -> Length(L) );
+gap> SortedList( IdempotentEndomorphismsWithImage( gens, c2 ) );
+[ [ (), (2,4) ], [ (2,4), () ] ]
+gap> data:= IdempotentEndomorphismsData( d8 );;
+gap> data.images[1];
+[ [ (), () ] ]
+gap> List( data.images, Length );
 [ 1, 2, 2, 2, 2, 1 ]
-gap> IdempotentEndomorphisms( d8 );               
-[ [ (1,2,3,4), (1,2)(3,4) ] -> [ (), () ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (2,4), () ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (), (2,4) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (1,3), () ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (), (1,3) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (1,2)(3,4), (1,2)(3,4) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (), (1,2)(3,4) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (1,4)(2,3), (1,4)(2,3) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (), (1,4)(2,3) ], 
-  [ (1,2,3,4), (1,2)(3,4) ] -> [ (1,2,3,4), (1,2)(3,4) ] ]
+gap> all:= IdempotentEndomorphisms( d8 );;
+gap> Length( all );
+10
+gap> all[1];
+[ (1,2,3,4), (1,2)(3,4) ] -> [ (), () ]
+gap> Size( Image( all[1] ) );
+1
+gap> Last( all ) = IdentityMapping( d8 );
+true
 ]]></Example>
 </Description>
 </ManSection>