Implemented ^ operator for digraphs to delegate to OnDigraphs (issue #580)

gap/oper.gd

@@ -62,6 +62,8 @@ DeclareOperation("DIGRAPHS_GraphProduct", [IsDigraph, IsDigraph, IsFunction]);
 DeclareOperation("SwapDigraphs", [IsMutableDigraph, IsMutableDigraph]);
 
 # 4. Actions . . .
+DeclareOperation("^", [IsDigraph, IsPerm]);
+DeclareOperation("^", [IsDigraph, IsTransformation]);
 DeclareOperation("OnDigraphs", [IsDigraph, IsPerm]);
 DeclareOperation("OnDigraphs", [IsDigraph, IsTransformation]);
 DeclareOperation("OnDigraphsNC", [IsDigraph, IsPerm]);

gap/oper.gi

@@ -1138,6 +1138,16 @@ InstallMethod(DomainForAction, "for a digraph, list or collection and function",
 [IsDigraph, IsListOrCollection, IsFunction],
 ReturnTrue);
 
+# Operator action: D^p  and  D^t
+# Allow D ^ p (digraph and permutation) to call OnDigraphs(D, p)
+# and D ^ t (digraph and transformation) to call OnDigraphs(D, t)
+
+InstallMethod(\^, "digraph acted on by a permutation",
+  [IsDigraph, IsPerm], OnDigraphs);
+
+InstallMethod(\^, "digraph acted on by a transformation",
+  [IsDigraph, IsTransformation], OnDigraphs);
+
 #############################################################################
 # 5. Substructures and quotients
 #############################################################################

tst/standard/oper.tst

@@ -16,6 +16,7 @@
 #@local i1, i2, id, idom, in1, in2, in3, iter, j1, j2, m, m1, m2, mat, n, nbs
 #@local out, out1, out2, out3, p1, p2, path, preorder, qr, r, res, rtclosure, t
 #@local tclosure, u1, u2, x
+#@local D, p, q, t, idp, idt, M
 gap> START_TEST("Digraphs package: standard/oper.tst");
 gap> LoadPackage("digraphs", false);;
 
@@ -109,6 +110,30 @@ gap> gr := DigraphRemoveEdge(gr, [2, 1]);
 gap> DigraphEdges(gr);
 [ [ 1, 2 ] ]
 
+# Tests for digraph operator "^" (implements D ^ p and D ^ t using OnDigraphs)
+gap> D := CycleDigraph(5);
+<immutable cycle digraph with 5 vertices>
+gap> p := (1, 5)(2, 4);;
+gap> D ^ p = DigraphReverse(D);
+true
+gap> OnDigraphs(D, p) = D ^ p;
+true
+gap> idp := ();;
+gap> D ^ idp = D;
+true
+gap> q := (1, 2, 3, 4, 5);;
+gap> (D ^ q) ^ (q ^ -1) = D;
+true
+gap> t := Transformation([2, 3, 4, 5, 1]);;
+gap> D ^ t = OnDigraphs(D, t);
+true
+gap> idt := Transformation([1, 2, 3, 4, 5]);;
+gap> D ^ idt = D;
+true
+gap> M := DigraphMutableCopy(D);;
+gap> M ^ p = OnDigraphs(M, p);
+true
+
 #  OnDigraphs: for a digraph and a perm
 gap> gr := Digraph([[2], [1], [3]]);
 <immutable digraph with 3 vertices, 3 edges>