Fixed issue where point_on_variety would fail to obtain a good set of…

… orthogonal directions to the variety when the directions were not explicitly provided, thus causing an assertion error. Instead of taking the simplest codim generators as directions, now take the simplest codim independent generators, thus guaranteeing the automatic selection will succeed.

syngular/variety.py

@@ -64,7 +64,11 @@ def point_on_variety(self, field, base_point={}, directions=[], valuations=tuple
 
         # handle directions, i.e. the generators of the sub-ideal of maximal codimension
         if directions == []:
-            directions = sorted(self.generators, key=lambda x: len(x))[:self.codim]
+            for poly in sorted(self.generators, key=lambda x: len(x)):
+                if Ideal(self.ring, directions + [poly, ]).codim > Ideal(self.ring, directions).codim:
+                    directions += [poly, ]
+                if len(directions) == self.codim:
+                    break
             assert Ideal(self.ring, directions).codim == self.codim
         # extra directions in qring
         if isinstance(self.ring, QuotientRing):