ManifoldSubsetPullback: WIP relatively open

src/sage/manifolds/subsets/pullback.py

@@ -27,6 +27,7 @@
 from sage.sets.real_set import RealSet
 from sage.geometry.polyhedron.base import is_Polyhedron
 from sage.geometry.relative_interior import RelativeInterior
+from sage.geometry.convex_set import ConvexSet_base
 
 
 class ManifoldSubsetPullback(ManifoldSubset):
@@ -204,6 +205,13 @@ def __classcall_private__(cls, map, codomain_subset, inverse=None,
                 return map.domain().open_subset(name=name, latex_name=latex_name,
                                                 coord_def=coord_def)
 
+        elif cls._is_relatively_open_convex(codomain_subset):
+
+            data = codomain_subset.affine_hull_projection(return_all_data=True)
+
+            # TODO: Use comm. diagram with map, Euclidean canonical chart, affine hull projection/section
+            #       to define embedded submanifold, return image.
+
         self = super().__classcall__(cls, map, codomain_subset, inverse, name, latex_name)
 
         return self
@@ -279,18 +287,9 @@ def _is_open(codomain_subset):
 
         """
 
-        if isinstance(codomain_subset, ManifoldSubset):
-            return codomain_subset.is_open()
-
-        if isinstance(codomain_subset, RealSet):
+        if isinstance(codomain_subset, (ManifoldSubset, RealSet, ConvexSet_base)):
             return codomain_subset.is_open()
 
-        if is_Polyhedron(codomain_subset):
-            return codomain_subset.is_empty() or codomain_subset.is_universe()
-
-        if isinstance(codomain_subset, RelativeInterior):
-            return codomain_subset.closure().is_full_dimensional()
-
         if codomain_subset in Sets().Finite():
             return codomain_subset.cardinality() == 0
 
@@ -311,6 +310,20 @@ def _is_open(codomain_subset):
 
         return False
 
+    @staticmethod
+    def _is_relatively_open_convex(codomain_subset):
+        """
+        Return whether ``codomain_subset`` is (known to be) a relatively open convex set.
+
+        EXAMPLES::
+
+            sage: from sage.manifolds.subsets.pullback import ManifoldSubsetPullback
+
+        """
+        if isinstance(codomain_subset, ConvexSet_base):
+            return codomain_subset.is_relatively_open()
+        return False
+
     @staticmethod
     def _interval_restriction(expr, interval):
         """