Some more fixes to the isosig decoration: Removing code that flipped …

…slope when there are no matrices. Accounting for the fact that set_peripheral_curves('combinatorial') is not a no-op when the Manifold was just constructed.

cython/core/triangulation.pyx

@@ -2983,6 +2983,10 @@ cdef class Triangulation():
           >>> M.triangulation_isosig(decorated = False, ignore_orientation = False)
           'dLQacccnsnk'
 
+        Note: the decorated triangulation isosig captures the orientation if
+        either ``ignore_orientation = False`` or if both ``ignore_curves = False``
+        and ``ignore_curve_orientations = False``.
+
         Note that a decorated triangulation isosig with the default values
         ``ignore_orientation = True`` but ``ignore_curve_orientations = False``
         still captures the orientations of the triangulation through the

python/decorated_isosig.py

@@ -302,9 +302,6 @@ def candidate_decoration_info(
     if ignore_curves:
         slopes = [ matrix * slope
                    for matrix, slope in zip(matrices, slopes) ]
-        if manifold_orientable:
-            for slope in slopes:
-                slope[0] *= isomorphism_orientation
     else:
         if ignore_curve_orientations:
             for matrix, slope in zip(matrices, slopes):
@@ -345,7 +342,15 @@ def decorated_isosig(manifold, triangulation_class,
         return isosig
 
     N = triangulation_class(isosig, remove_finite_vertices=False)
-    N.set_peripheral_curves('combinatorial')
+    if not (ignore_cusp_ordering and ignore_curves):
+        # Note that data_to_triangulation determines the peripheral
+        # curves before orienting the manifold.
+        # Thus, we get different peripheral curves when calling
+        # N.set_peripheral_curves.
+        # For backwards compatibility (set_peripheral_from_decoration),
+        # we need to keep callingN.set_peripheral_curves here unless there is
+        # no decoration.
+        N.set_peripheral_curves('combinatorial')
 
     manifold_orientable = manifold.is_orientable()
     slopes = manifold.cusp_info('filling')

python/isometry_signature.py

@@ -283,6 +283,8 @@ def drill_manifold_precisions(
 
 def compute_meridian_slopes(isosig, tri):
     isosig_tri = Triangulation(isosig, remove_finite_vertices=False)
+    # Do not call isosig_tri.set_peripheral_curves('combinatorial')
+    # here.
     for iso in tri.isomorphisms_to(isosig_tri):
         cusp_map, = iso.cusp_maps()
         slope = make_vector([cusp_map[0,0], cusp_map[1,0]])

python/test_cases.py

@@ -15,6 +15,58 @@
 >>> T.triangulation_isosig()
 'gLMzQbcdefffaelaaai_acbBaabCbbabbBC'
 
+Test that slopes are computed correctly.
+
+>>> M=Manifold("L14n63023(-5,1)(5,1)(10,1)")
+>>> M.triangulation_isosig(decorated=False, ignore_orientation=False)
+'vLLvvLLMALQQzQQceillmnppqrlmrqtruututiivimllaelaqxrvdoxqltt'
+
+The canonical orientation (used to compute the unoriented isosig)
+is the reverse of the actual orientation:
+
+>>> M.triangulation_isosig(decorated=False)
+'vLLvLLPwPQLAMPQcefikkmnplkopqrsttutuuiixvimqlippawidlabavth'
+>>> Mop = M.copy()
+>>> Mop.reverse_orientation()
+>>> Mop.triangulation_isosig(decorated=False, ignore_orientation=False)
+'vLLvLLPwPQLAMPQcefikkmnplkopqrsttutuuiixvimqlippawidlabavth'
+
+It is not just the triangulation that is chiral, the manifold itself is:
+
+>>> isom_sig_pos = M.isometry_signature(ignore_orientation = False)
+>>> isom_sig_pos
+'KLALvLwLLwMQLQPAMzMzMPzMPcbbeghnklntpqpqvrswtuvxyzABCDEFEGHIJJhhkofnaocnmrlsiaowxfcsaxhxhxhxhjhhhhs'
+>>> isom_sig_neg = Mop.isometry_signature(ignore_orientation = False)
+>>> isom_sig_neg
+'KLAMvMvvAwLvQPPPQMPzMPzMPcbbdegilopoouqtryvuxvwxzzBACDEFEGHIJJhhkhhohahrscaagwxkkgbvwpuxwqxqxwxxxxr'
+
+So we expect the oriented isometry signature to flip when neither the isomorphism
+signature nor its decoration capture the orientation.
+
+>>> for ignore_cusp_ordering in [False, True]:
+...     for ignore_curves in [False, True]:
+...         for ignore_curve_orientations in [False, True]:
+...             for ignore_filling_orientations in [False, True]:
+...                 for ignore_orientation in [False, True]:
+...                     isosig = M.triangulation_isosig(
+...                         ignore_cusp_ordering = ignore_cusp_ordering,
+...                         ignore_curves = ignore_curves,
+...                         ignore_curve_orientations = ignore_curve_orientations,
+...                         ignore_filling_orientations = ignore_filling_orientations,
+...                         ignore_orientation = ignore_orientation)
+...                     isom_sig = (
+...                         Manifold(isosig)
+...                              .isometry_signature(ignore_orientation = False))
+...                     does_ignore_orientation = (
+...                         ignore_orientation and
+...                         (ignore_curve_orientations or ignore_curves))
+...                     expected_isom_sig = (
+...                         isom_sig_neg
+...                         if does_ignore_orientation
+...                         else isom_sig_pos)
+...                     if isom_sig != expected_isom_sig:
+...                         print("Bad")
+
 isometry_signature
 ------------------
 
@@ -54,6 +106,26 @@
 ...
 RuntimeError: Could not compute or verify canonical retriangulation of drilled manifold. Geodesic was: abCDaDAd.
 
+Test isometry_signature's ignore_orientation
+
+>>> M = Manifold("m006")
+>>> M.isometry_signature(ignore_orientation=False)
+'eLMkaccddjgbaj'
+>>> M.isometry_signature(ignore_orientation=True)
+'eLAkaccddngbak'
+>>> M.isometry_signature() # default value
+'eLAkaccddngbak'
+>>> M.dehn_fill((3,4))
+>>> M.isometry_signature(ignore_orientation=False)
+'eLMkaccddjgbaj(-1,4)'
+>>> M.isometry_signature(ignore_orientation=True)
+'eLAkaccddngbak(-3,4)'
+
+Test isometry_signature's of_link and filling.
+
+>>> Manifold("o9_44206(2,3)").isometry_signature(of_link=True)
+'jLLvMQQacggfiihhijkkjkehhtb_abBabBbabaab'
+
 Class hierarchy
 ---------------