Improved verbose option for bigraded_betti_numbers() method

Author: OP5642

src/sage/topology/simplicial_complex.py

@@ -4870,9 +4870,23 @@ def bigraded_betti_numbers(self, base_ring=ZZ, verbose=False):
 
             sage: X = SimplicialComplex([[0,1],[1,2],[1,3],[2,3]])
             sage: Y = SimplicialComplex([[1,2,3],[1,2,4],[3,5],[4,5]])
-            sage: sorted(X.bigraded_betti_numbers().items(), reverse=True)              # needs sage.modules
+            sage: sorted(X.bigraded_betti_numbers(base_ring=QQ).items(), reverse=True)
             [((0, 0), 1), ((-1, 6), 1), ((-1, 4), 2), ((-2, 8), 1), ((-2, 6), 1)]
-            sage: sorted(Y.bigraded_betti_numbers(base_ring=QQ).items(), reverse=True)  # needs sage.modules
+            sage: sorted(Y.bigraded_betti_numbers(verbose=True).items(), reverse=True)
+            (-1, 4): Non-trivial homology Z in dimension 0 of the full
+            subcomplex generated by a set of vertices (1, 5)
+            (-1, 4): Non-trivial homology Z in dimension 0 of the full
+            subcomplex generated by a set of vertices (2, 5)
+            (-1, 4): Non-trivial homology Z in dimension 0 of the full
+            subcomplex generated by a set of vertices (3, 4)
+            (-2, 6): Non-trivial homology Z in dimension 0 of the full
+            subcomplex generated by a set of vertices (1, 2, 5)
+            (-2, 8): Non-trivial homology Z in dimension 1 of the full
+            subcomplex generated by a set of vertices (1, 3, 4, 5)
+            (-2, 8): Non-trivial homology Z in dimension 1 of the full
+            subcomplex generated by a set of vertices (2, 3, 4, 5)
+            (-3, 10): Non-trivial homology Z in dimension 1 of the full
+            subcomplex generated by a set of vertices (1, 2, 3, 4, 5)
             [((0, 0), 1), ((-1, 4), 3), ((-2, 8), 2), ((-2, 6), 1), ((-3, 10), 1)]
 
         If we wish to view them in a form of a table, it is
@@ -4927,7 +4941,7 @@ def bigraded_betti_numbers(self, base_ring=ZZ, verbose=False):
                             B[ind] = ZZ.zero()
                         B[ind] += len(H[j-k-1].gens())
                         if verbose:
-                            print("Non-trivial homology {} in dimension {} of the full subcomplex generated by a set of vertices {}".format(H[j-k-1], j-k-1, x))
+                            print("{}: Non-trivial homology {} in dimension {} of the full subcomplex generated by a set of vertices {}".format(ind, H[j-k-1], j-k-1, x))
 
         self._bbn[base_ring] = B
         self._bbn_all_computed.add(base_ring)