ManifoldSubset.declare_{sub,super}set: New

src/sage/manifolds/manifold.py

@@ -873,9 +873,10 @@ def open_subset(self, name, latex_name=None, coord_def={}):
                                    latex_name=latex_name,
                                    start_index=self._sindex)
         resu._calculus_method = self._calculus_method
-        resu._supersets.update(self._supersets)
-        for sd in self._supersets:
-            sd._subsets.add(resu)
+        if self.is_empty():
+            self.declare_equal(resu)
+        else:
+            self.declare_superset(resu)
         self._top_subsets.add(resu)
         # Charts on the result from the coordinate definition:
         for chart, restrictions in coord_def.items():

src/sage/manifolds/subset.py

@@ -873,9 +873,10 @@ def subset(self, name, latex_name=None, is_open=False):
         if is_open:
             return self.open_subset(name, latex_name=latex_name)
         res = ManifoldSubset(self._manifold, name, latex_name=latex_name)
-        res._supersets.update(self._supersets)
-        for sd in self._supersets:
-            sd._subsets.add(res)
+        if self.is_empty():
+            self.declare_equal(res)
+        else:
+            self.declare_superset(res)
         self._top_subsets.add(res)
         return res
 
@@ -935,16 +936,28 @@ def superset(self, name, latex_name=None, is_open=False):
             res = self._manifold.open_subset(name, latex_name=latex_name)
         else:
             res = ManifoldSubset(self._manifold, name, latex_name=latex_name)
-        res._subsets.update(self._subsets)
-        for sd in self._subsets:
-            sd._supersets.add(res)
+        res.declare_superset(self)
         if is_open and self._is_open:
             res._atlas = list(self._atlas)
             res._top_charts = list(self._top_charts)
             res._coord_changes = dict(self._coord_changes)
             res._def_chart = self._def_chart
         return res
 
+    def declare_subset(self, *supersets):
+        supersets = ManifoldSubsetFiniteFamily.from_subsets_or_families(*supersets)
+        for superset in supersets:
+            superset._subsets.update(self._subsets)
+        for subset in self._subsets:
+            subset._supersets.update(supersets)
+
+    def declare_superset(self, *subsets):
+        subsets = ManifoldSubsetFiniteFamily.from_subsets_or_families(*subsets)
+        for subset in subsets:
+            subset._supersets.update(self._supersets)
+        for superset in self._supersets:
+            superset._subsets.update(subsets)
+
     def intersection(self, other, name=None, latex_name=None):
         r"""
         Return the intersection of the current subset with another subset.