Add OrbitalGraph for a group and a base-pair

gap/OrbitalGraphs.gd

@@ -80,10 +80,10 @@ DeclareOperation("OrbitalGraphs", [IsPermGroup, IsInt]);
 # TODO: Implement constructing the orbital graph with a given base pair
 #! @BeginGroup orbital
 #! @Returns An orbital graph
-#! @Arguments G, u, v
+#! @Arguments G, basepair, n
 #! @Description
 #!   TODO.
-DeclareOperation("OrbitalGraph", [IsPermGroup, IsPosInt, IsPosInt]);
+DeclareOperation("OrbitalGraph", [IsPermGroup, IsHomogeneousList, IsPosInt]);
 #! @EndGroup
 #! @Group orbital
 #! @Arguments G, basepair

gap/OrbitalGraphs.gi

@@ -113,6 +113,45 @@ function(G, points)
 end);
 
 
+# Individual orbital graphs
+
+InstallMethod(OrbitalGraph, "for a permutation group and homogenous list",
+[IsPermGroup, IsHomogeneousList],
+function(G, basepair)
+    if not (Length(basepair) = 2 and ForAll(basepair, IsPosInt)) then
+        ErrorNoReturn("the second argument <basepair> must be a pair of ",
+                      "positive integers");
+    fi;
+    return OrbitalGraph(G, basepair,
+                        Maximum(NrMovedPoints(G), Maximum(basepair)));
+end);
+
+InstallMethod(OrbitalGraph,
+"for a permutation group, homogeneous list, and pos int",
+[IsPermGroup, IsHomogeneousList, IsPosInt],
+function(G, basepair, max)
+    return OrbitalGraph(G, basepair, [1 .. max]);
+end);
+
+InstallMethod(OrbitalGraph,
+"for a permutation group and two homogeneous lists",
+[IsPermGroup, IsHomogeneousList, IsHomogeneousList],
+function(G, basepair, points)
+    local D;
+    if not ForAll(points, IsPosInt) then
+        ErrorNoReturn("the third argument <points> must be... TODO")
+    elif not (Length(basepair) = 2 and IsSubset(points, basepair)) then
+        ErrorNoReturn("the second argument <basepair> must be... TODO");
+    fi;
+    # FIXME This is naive
+    D := DigraphByEdges(Orbit(G, basepair, OnPairs), n);
+    SetFilterObj(D, IsOrbitalGraphOfGroup);
+    SetUnderlyingGroup(D, G);
+    SetBasePair(D, basepair);
+    return D;
+end);
+
+
 # Transformation semigroups
 
 InstallMethod(OrbitalGraphs, "for a transformation semigroup",