Support Nauty digraph6 format

doc/digraph.xml

@@ -193,7 +193,7 @@ true
     old ones, inherit their labels from their parents.
 
     <Example><![CDATA[
-gap> gr := DigraphFromDigraph6String("+D[NGc_");
+gap> gr := DigraphFromDigraph6String("&DHUEe_");
 <digraph with 5 vertices, 11 edges>
 gap> DigraphVertexLabels(gr);
 [ 1 .. 5 ]
@@ -234,7 +234,7 @@ gap> DigraphVertexLabels(gr);
     old ones, inherit their labels from their parents.
 
     <Example><![CDATA[
-gap> gr := DigraphFromDigraph6String("+D[NGc_");
+gap> gr := DigraphFromDigraph6String("&DHUEe_");
 <digraph with 5 vertices, 11 edges>
 gap> DigraphVertexLabel(gr, 3);
 3
@@ -284,7 +284,7 @@ gap> DigraphVertexLabel(gr, 2);
     from old ones, inherit their labels from their parents.
 
     <Example><![CDATA[
-gap> gr := DigraphFromDigraph6String("+D[NGc_");
+gap> gr := DigraphFromDigraph6String("&DHUEe_");
 <digraph with 5 vertices, 11 edges>
 gap> DigraphEdgeLabels(gr);
 [ [ 1 ], [ 1, 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ]
@@ -322,7 +322,7 @@ gap> OutNeighbours(gr);
     See also <Ref Oper="DigraphEdgeLabels"/>.
 
     <Example><![CDATA[
-gap> gr := DigraphFromDigraph6String("+D[NGc_");
+gap> gr := DigraphFromDigraph6String("&DHUEe_");
 <digraph with 5 vertices, 11 edges>
 gap> DigraphEdgeLabel(gr, 3, 1);
 1
@@ -350,7 +350,7 @@ gap> gr := Digraph(["a", "b", "c"], ["a", "b", "b"], ["b", "c", "a"]);
 <digraph with 3 vertices, 3 edges>
 gap> IsMultiDigraph(gr);
 false
-gap> gr := DigraphFromDigraph6String("+Bug");
+gap> gr := DigraphFromDigraph6String("&Bug");
 <digraph with 3 vertices, 6 edges>
 gap> IsDuplicateFree(DigraphEdges(gr));
 true

doc/io.xml

@@ -177,11 +177,11 @@ gap> DigraphFromGraph6String("C]");
 <digraph with 4 vertices, 8 edges>
 gap> DigraphFromGraph6String("H?AAEM{");
 <digraph with 9 vertices, 22 edges>
-gap> DigraphFromDigraph6String("+?");
+gap> DigraphFromDigraph6String("&?");
 <digraph with 0 vertices, 0 edges>
-gap> DigraphFromDigraph6String("+CQFG");
+gap> DigraphFromDigraph6String("&CQFG");
 <digraph with 4 vertices, 6 edges>
-gap> DigraphFromDigraph6String("+IM[SrKLc~lhesbU[F_");
+gap> DigraphFromDigraph6String("&IM[SrKLc~lhesbU[F_");
 <digraph with 10 vertices, 51 edges>
 gap> DigraphFromDiSparse6String(".CaWBGA?b");
 <multidigraph with 4 vertices, 9 edges>

doc/oper.xml

@@ -933,7 +933,7 @@ od;
     between the vertices of a digraph is shown below: <P/>
 
     <Example><![CDATA[
-gap> gr := DigraphFromDigraph6String("+ECGOElR");
+gap> gr := DigraphFromDigraph6String("&EAHQeDB");
 <digraph with 6 vertices, 12 edges>
 gap> func := function(mat, i, j, k)
 >   if mat[i][k] <> -1 and mat[k][j] <> -1 then

doc/orbits.xml

@@ -136,7 +136,7 @@ gap> digraph := CayleyDigraph(AlternatingGroup(4));
 <digraph with 12 vertices, 24 edges>
 gap> DigraphOrbitReps(digraph);
 [ 1 ]
-gap> digraph := DigraphFromDigraph6String("+I?OGg????A?Ci_o_@?");
+gap> digraph := DigraphFromDigraph6String("&IGO??S?`?_@?a?CK?O");
 <digraph with 10 vertices, 14 edges>
 gap> DigraphOrbitReps(digraph);
 [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
@@ -157,7 +157,7 @@ gap> DigraphOrbitReps(digraph);
     vertices of <A>digraph</A>.
 
     <Example><![CDATA[
-gap> digraph := DigraphFromDigraph6String("+GUIQQWWXHHPg");
+gap> digraph := DigraphFromDigraph6String("&GYHPQgWTIIPW");
 <digraph with 8 vertices, 24 edges>
 gap> DigraphStabilizer(digraph, 8);
 Group(())
@@ -215,12 +215,12 @@ gap> DigraphGroup(digraph);
 Group(())
 gap> RepresentativeOutNeighbours(digraph);
 [ [ 2, 1, 3, 4, 5 ], [ 3, 5 ], [ 2 ], [ 1, 2, 3, 5 ], [ 1, 2, 3, 4 ] ]
-gap> digraph := DigraphFromDigraph6String("+GUIQQWWXHHPg");
+gap> digraph := DigraphFromDigraph6String("&GYHPQgWTIIPW");
 <digraph with 8 vertices, 24 edges>
 gap> DigraphGroup(digraph);
 Group([ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,5)(2,6)(3,8)
 (4,7) ])
-gap> RepresentativeOutNeighbours(digraph);
+gap> Set(RepresentativeOutNeighbours(digraph), Set);
 [ [ 2, 3, 5 ] ]]]></Example>
   </Description>
 </ManSection>

gap/io.gi

@@ -812,7 +812,12 @@ end);
 InstallMethod(DigraphFromDigraph6String, "for a string",
 [IsString],
 function(s)
-  local list, i, n, start, range, source, pos, len, j, bpos, tabpos;
+  local legacy, list, n, start, i, range, source, pos, len, j, bpos, tabpos;
+  # NOTE: this package originally used a version of digraph6 that reads down
+  # the columns of an adjacency matrix, and appends a '+' to the start.  This
+  # has been replaced by the Nauty standard, which reads across the rows of the
+  # matrix, and appends a '&' to the start.  For backwards compatibility, this
+  # now accepts both formats, sending an info warning if the old format is used.
 
   s := Chomp(s);
   # Check non-emptiness
@@ -821,8 +826,18 @@ function(s)
                   "the input string <s> should be non-empty,");
   fi;
 
-  # Check for the special '+' character
-  if s[1] <> '+' then
+  # Check for the special '&' character (or the deprecated '+')
+  if s[1] = '&' then
+    legacy := false;
+  elif s[1] = '+' then
+    legacy := true;
+    Info(InfoDigraphs, 1, "Digraph6 strings beginning with '+' use an old");
+    Info(InfoDigraphs, 1, "specification of the Digraph6 format that is");
+    Info(InfoDigraphs, 1, "incompatible with the present standard.  They can");
+    Info(InfoDigraphs, 1, "still be read by the Digraphs package, but are");
+    Info(InfoDigraphs, 1, "unlikely to be recognised by other programs.");
+    Info(InfoDigraphs, 1, "Please consider re-encoding with the new format.");
+  else
     ErrorNoReturn("Digraphs: DigraphFromDigraph6String: usage,\n",
                   "the input string <s> is not in valid digraph6 format,");
   fi;
@@ -867,8 +882,8 @@ function(s)
         i := i / 2;
       else
         tabpos := pos + 6 - bpos;
-        source[len] := (tabpos - 1) mod n + 1;
-        range[len] := (tabpos - source[len]) / n + 1;
+        range[len] := (tabpos - 1) mod n + 1;
+        source[len] := (tabpos - range[len]) / n + 1;
         len := len + 1;
         i := (i - 1) / 2;
       fi;
@@ -877,6 +892,10 @@ function(s)
     pos := pos + 6;
   od;
 
+  if legacy then  # source and range are reversed
+    return Digraph(rec(nrvertices := n, range := source, source := range));
+  fi;
+
   return Digraph(rec(nrvertices := n, range := range, source := source));
 end);
 
@@ -1539,12 +1558,18 @@ InstallMethod(Digraph6String, "for a digraph",
 [IsDigraph],
 function(digraph)
   local list, adj, n, lenlist, tablen, blist, i, j, pos, block;
+  # NOTE: this package originally used a version of digraph6 that reads down
+  # the columns of an adjacency matrix, and appends a '+' to the start.  This
+  # has been replaced by the Nauty standard, which reads across the rows of the
+  # matrix, and appends a '&' to the start.  The old '+' format can be read by
+  # DigraphFromDigraph6String, but can no longer be written by this function.
+
   list := [];
   adj := OutNeighbours(digraph);
   n := Length(DigraphVertices(digraph));
 
-  # First write the special character '+'
-  Add(list, -20);
+  # First write the special character '&'
+  Add(list, -25);
 
   # Now write the number of vertices
   lenlist := DIGRAPHS_Graph6Length(n);
@@ -1555,12 +1580,12 @@ function(digraph)
   fi;
   Append(list, lenlist);
 
-  # Find adjacencies (non-directed)
+  # Find adjacencies
   tablen := n ^ 2;
   blist := BlistList([1 .. tablen + 6], []);
   for i in DigraphVertices(digraph) do
     for j in adj[i] do
-      blist[i + n * (j - 1)] := true;
+      blist[j + n * (i - 1)] := true;
     od;
   od;
 

tst/standard/attr.tst

@@ -1293,7 +1293,7 @@ gap> ChromaticNumber(DigraphDisjointUnion(CompleteDigraph(1),
 > Digraph([[2], [4], [1, 2], [3], [1, 2, 3]])));
 4
 gap> gr := DigraphFromDigraph6String(Concatenation(
-> "+l??O?C?A_@???CE????GAAG?C??M?????@_?OO??G??@?IC???_C?G?o??C?AO???c_??A?",
+> "&l??O?C?A_@???CE????GAAG?C??M?????@_?OO??G??@?IC???_C?G?o??C?AO???c_??A?",
 > "A?S???OAA???OG???G_A??C?@?cC????_@G???S??C_?C???[??A?A?OA?O?@?A?@A???GGO",
 > "??`?_O??G?@?A??G?@AH????AA?O@??_??b???Cg??C???_??W?G????d?G?C@A?C???GC?W",
 > "?????K???__O[??????O?W???O@??_G?@?CG??G?@G?C??@G???_Q?O?O?c???OAO?C??C?G",
@@ -1425,7 +1425,7 @@ gap> IsUndirectedSpanningForest(gr, forest);
 true
 gap> gr = forest;
 true
-gap> gr := DigraphFromDigraph6String("+I?PIMAQc@A?W?ADPP?");
+gap> gr := DigraphFromDigraph6String("&IG@qqW?HO?BSQGA?CG");
 <digraph with 10 vertices, 23 edges>
 gap> IsStronglyConnectedDigraph(gr);
 true

tst/standard/cliques.tst

@@ -219,7 +219,7 @@ gap> DigraphMaximalIndependentSets(gr);
 gap> gr := CompleteDigraph(2);;
 gap> DigraphMaximalIndependentSets(gr);
 [ [ 1 ], [ 2 ] ]
-gap> gr := DigraphFromDigraph6String("+FWSK?[SK_?");
+gap> gr := DigraphFromDigraph6String("&FWsK?WSKC?");
 <digraph with 7 vertices, 14 edges>
 gap> DigraphMaximalIndependentSetsReps(gr);
 [ [ 1, 4 ], [ 1, 5 ], [ 2, 5, 7 ] ]
@@ -307,7 +307,7 @@ gap> DigraphMaximalCliques(gr);
 gap> gr := EmptyDigraph(1);;
 gap> DigraphMaximalCliques(gr);
 [ [ 1 ] ]
-gap> gr := DigraphFromDigraph6String("+D[]]]?");
+gap> gr := DigraphFromDigraph6String("&DNNNF?");
 <digraph with 5 vertices, 15 edges>
 gap> DigraphMaximalCliquesReps(gr);
 [ [ 1, 3 ] ]

tst/standard/display.tst

@@ -179,8 +179,8 @@ node [shape=Mrecord, height=0.5, fixedsize=true]ranksep=1;
 7 -> 5
 8 -> 1
 }
-gap> gr := Concatenation("+XqD?OG???FbueZpzRKGC@?}]sr]nYXnNl[saOEGOgA@w|he?A?",
-> "?}NyxnFlKvbueZpzrLGcHa??A?]NYx_?_GC??AJpzrnw~jm{]srO???_");;
+gap> gr := Concatenation("&X_?_A]|^Vr[nHpmVcy~zy[A????_???G??B]nhtmvcwvJq\\^~",
+> "|m??_AEx]Rb[nHo??__vJy[??A??O_aV~^Zb]njo???_???GZdxMLy}n_");;
 gap> gr := DigraphFromDigraph6String(gr);;
 gap> Print(DotPreorderDigraph(gr){[1 .. 94]}, "\n");
 //dot

tst/standard/grahom.tst

@@ -976,7 +976,7 @@ IdentityTransformation
 gap> gr1 := ChainDigraph(2);;
 gap> MonomorphismsDigraphs(gr1, EmptyDigraph(1));
 [  ]
-gap> gr2 := DigraphFromDigraph6String("+DRZ?L?");;
+gap> gr2 := DigraphFromDigraph6String("&DZTAW?");;
 gap> monos := MonomorphismsDigraphs(gr1, gr2);
 [ IdentityTransformation, Transformation( [ 1, 3, 3 ] ), 
   Transformation( [ 1, 5, 3, 4, 5 ] ), Transformation( [ 2, 1 ] ), 
@@ -1001,7 +1001,7 @@ gap> gr1 := CompleteDigraph(2);;
 gap> gr2 := CompleteDigraph(3);;
 gap> EpimorphismsDigraphs(gr1, gr2);
 [  ]
-gap> gr1 := DigraphFromDigraph6String("+IG????G??I??O?????");;
+gap> gr1 := DigraphFromDigraph6String("&I@??HO???????A????");;
 gap> DigraphEpimorphism(gr1, gr2);
 Transformation( [ 1, 1, 2, 1, 1, 3, 1, 2, 1, 1 ] )
 gap> epis := EpimorphismsDigraphsRepresentatives(gr1, gr2);;

tst/standard/io.tst

@@ -118,7 +118,9 @@ gap> DigraphFromSparse6String(str);
 gap> gr := Digraph([[5], [1, 2, 5], [1], [2], [4]]);
 <digraph with 5 vertices, 7 edges>
 gap> str := Digraph6String(gr);
-"+DWg?[?"
+"&DBeA@?"
+gap> gr = DigraphFromDigraph6String("+DWg?[?");  # deprecated format
+true
 gap> DigraphFromDigraph6String(str);
 <digraph with 5 vertices, 7 edges>
 gap> gr := Digraph(231, [1 .. 100], [1 .. 100] * 0 + 200);
@@ -484,7 +486,7 @@ true
 gap> DigraphFromGraph6String("~llk");
 Error, Digraphs: DigraphFromGraph6String: usage,
 the input string <s> is not in valid graph6 format,
-gap> DigraphFromDigraph6String("+~llk");
+gap> DigraphFromDigraph6String("&~llk");
 Error, Digraphs: DigraphFromDigraph6String: usage,
 the input string <s> is not in valid digraph6 format,
 gap> DigraphFromSparse6String(":~~l");

tst/standard/oper.tst

@@ -15,7 +15,7 @@ gap> LoadPackage("digraphs", false);;
 gap> DIGRAPHS_StartTest();
 
 #  DigraphReverse
-gap> gr := DigraphFromDigraph6String("+D[NGc_");
+gap> gr := DigraphFromDigraph6String("&DHUEe_");
 <digraph with 5 vertices, 11 edges>
 gap> rgr := DigraphReverse(gr);
 <digraph with 5 vertices, 11 edges>
@@ -50,11 +50,11 @@ gap> gr = DigraphReverse(gr);
 true
 
 #  DigraphRemoveLoops
-gap> gr := DigraphFromDigraph6String("+EhxPC?@");
+gap> gr := DigraphFromDigraph6String("&EhxPC?@");
 <digraph with 6 vertices, 11 edges>
 gap> DigraphRemoveLoops(gr);
 <digraph with 6 vertices, 7 edges>
-gap> gr := DigraphFromDigraph6String("+EhxPC?@");
+gap> gr := DigraphFromDigraph6String("&EhxPC?@");
 <digraph with 6 vertices, 11 edges>
 gap> HasDigraphHasLoops(gr);
 false
@@ -99,11 +99,12 @@ gap> last = gr;
 true
 gap> DigraphRemoveEdges(gr, [[1, 2]]);
 <digraph with 2 vertices, 0 edges>
-gap> gr := DigraphFromDigraph6String("+Dv?f`_");
+gap> gr := DigraphFromDigraph6String("&DtGsw_");
 <digraph with 5 vertices, 12 edges>
-gap> DigraphEdges(gr);
-[ [ 1, 2 ], [ 1, 1 ], [ 1, 4 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 3 ], 
-  [ 4, 1 ], [ 4, 5 ], [ 4, 4 ], [ 5, 1 ], [ 5, 5 ] ]
+gap> Set(DigraphEdges(gr)) = Set(
+> [[1, 2], [1, 1], [1, 4], [2, 1], [2, 4], [3, 4],
+>  [3, 3], [4, 1], [4, 5], [4, 4], [5, 1], [5, 5]]);
+true
 gap> gr1 := DigraphRemoveEdges(gr, [[1, 4], [4, 5], [5, 5]]);
 <digraph with 5 vertices, 9 edges>
 gap> DigraphEdges(gr1);
@@ -793,7 +794,7 @@ gap> DigraphVertexLabels(gr2);
 [ 1, Sym( [ 1 .. 2 ] ) ]
 
 #  DigraphRemoveVertex
-gap> gr := DigraphFromDigraph6String("+MW?Gp?GWe?gS?[L?A?f|C@KOCa_gk?F?r_");
+gap> gr := DigraphFromDigraph6String("&MU?GAa?SDCFStK`???d?@LWOq[{DECO?U?");
 <digraph with 14 vertices, 54 edges>
 gap> DigraphRemoveVertex(gr, "a");
 Error, no method found! For debugging hints type ?Recovery from NoMethodFound
@@ -1045,7 +1046,7 @@ gap> func := function(mat, i, j, k)
 >   fi;
 > end;
 function( mat, i, j, k ) ... end
-gap> gr := DigraphFromDigraph6String("+I???@?A`?G?GCCS@??");
+gap> gr := DigraphFromDigraph6String("&I???@?A`?G?GCCS@??");
 <digraph with 10 vertices, 11 edges>
 gap> tclosure := DigraphFloydWarshall(gr, func, 0, 1);;
 gap> grt := DigraphByAdjacencyMatrix(tclosure);
@@ -1104,7 +1105,7 @@ gap> gr = ChainDigraph(14);
 true
 
 #  DigraphEdgeUnion
-gap> gr1 := DigraphFromDigraph6String("+I????O?GO_?C??_OGG");
+gap> gr1 := DigraphFromDigraph6String("&I????@A_?AA???@d??");
 <digraph with 10 vertices, 9 edges>
 gap> gr2 := DigraphFromDiSparse6String(".H`OS?aEMC?bneOY`l_?QCJ");
 <multidigraph with 9 vertices, 20 edges>
@@ -1594,7 +1595,7 @@ gap> DigraphLayers(gr, 9);
 [ [ 9 ], [ 10, 11 ] ]
 gap> DigraphLayers(gr, 10);
 [ [ 10 ] ]
-gap> gr := DigraphFromDigraph6String("+GUIQQWWXHHPg");;
+gap> gr := DigraphFromDigraph6String("&GYHPQgWTIIPW");;
 gap> DigraphGroup(gr);
 Group([ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,5)(2,6)(3,8)(4,7) ])
 gap> DigraphOrbitReps(gr);
@@ -1698,7 +1699,7 @@ the second argument must be a vertex of the digraph,
 gap> DigraphDistanceSet(gr, 10, ["string", 1]);
 Error, Digraphs: DigraphDistanceSet: usage,
 the third argument must be a list of non-negative integers,
-gap> gr := DigraphFromDigraph6String("+GUIQQWWXHHPg");;
+gap> gr := DigraphFromDigraph6String("&GYHPQgWTIIPW");;
 gap> DigraphDistanceSet(gr, 1, [3, 7]);
 [  ]
 gap> DigraphDistanceSet(gr, 1, [1]);
@@ -1772,7 +1773,7 @@ gap> IsUndirectedSpanningForest(gr1, gr2);
 false
 gap> IsUndirectedSpanningForest(gr1, DigraphFromSparse6String(":I`ESyTl^F"));
 true
-gap> gr := DigraphFromDigraph6String("+I?PIMAQc@A?W?ADPP?");
+gap> gr := DigraphFromDigraph6String("&I?PIMAQc@A?W?ADPP?");
 <digraph with 10 vertices, 23 edges>
 gap> IsUndirectedSpanningForest(gr, DigraphByEdges([[2, 7], [7, 2]], 10));
 true
@@ -1782,7 +1783,7 @@ gap> IsUndirectedSpanningTree(EmptyDigraph(1), EmptyDigraph(1));
 true
 gap> IsUndirectedSpanningTree(EmptyDigraph(2), EmptyDigraph(2));
 false
-gap> gr := DigraphFromDigraph6String("+I?PIMAQc@A?W?ADPP?");
+gap> gr := DigraphFromDigraph6String("&I?PIMAQc@A?W?ADPP?");
 <digraph with 10 vertices, 23 edges>
 gap> IsUndirectedSpanningTree(gr, EmptyDigraph(10));
 false
@@ -1995,7 +1996,7 @@ gap> di := Digraph([[1], [1, 2], [1, 3], [1, 2, 3, 4]]);;
 gap> S := AsSemigroup(IsPartialPermSemigroup, di);;
 gap> IsInverseSemigroup(S) and ForAll(Elements(S), IsIdempotent);
 true
-gap> temp := "+P~~}~??o??_?@o??_?@_?W}?O_??o??_?@_FGoA?_?Wo?O_Wt_";;
+gap> temp := "&P_?@_?B`?FrCK_GXoXo_B?_A@aCA`GDroG`_?`?@e??c?@w??_";;
 gap> di := DigraphFromDigraph6String(temp);;
 gap> S := AsSemigroup(IsPartialPermSemigroup, di);;
 gap> IsInverseSemigroup(S) and ForAll(Elements(S), IsIdempotent);