+// These return references to preallocated common symmetries (similar to
+// the numeric flyweights).
+const symmetry & not_symmetric();
+const symmetry & symmetric2();
+const symmetry & symmetric3();
+const symmetry & symmetric4();
+const symmetry & antisymmetric2();
+const symmetry & antisymmetric3();
+const symmetry & antisymmetric4();
+