Trac #31727: ManifoldSubset: Add methods subset_family, superset_fami…

…ly, open_superset_family; deprecate method list_of_subsets

Follow-up from #31718.

This ticket proposes to deprecate `list_of_subsets` (note - no other
methods in `sage.manifolds` follow this naming scheme) in favor of a new
method `subset_family`, which prints in a more compact way, is hashable,
and is sorted by name too.

We also add `superset_family` (previously the set of supersets was not
exposed by a method).

We also add `open_superset_family` (to complement `open_superset` added
in #31677).

URL: https://trac.sagemath.org/31727
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Eric Gourgoulhon

src/sage/manifolds/chart.py

@@ -928,12 +928,9 @@ def transition_map(self, other, transformations, intersection_name=None,
         The subset `W`, intersection of `U` and `V`, has been created by
         ``transition_map()``::
 
-            sage: M.list_of_subsets()
-            [1-dimensional topological manifold S^1,
-             Open subset U of the 1-dimensional topological manifold S^1,
-             Open subset V of the 1-dimensional topological manifold S^1,
-             Open subset W of the 1-dimensional topological manifold S^1]
-            sage: W = M.list_of_subsets()[3]
+            sage: F = M.subset_family(); F
+            Set {S^1, U, V, W} of open subsets of the 1-dimensional topological manifold S^1
+            sage: W = F['W']
             sage: W is U.intersection(V)
             True
             sage: M.atlas()
@@ -956,9 +953,8 @@ def transition_map(self, other, transformations, intersection_name=None,
 
         In this case, no new subset has been created since `U \cap M = U`::
 
-            sage: M.list_of_subsets()
-            [2-dimensional topological manifold R^2,
-             Open subset U of the 2-dimensional topological manifold R^2]
+            sage: M.subset_family()
+            Set {R^2, U} of open subsets of the 2-dimensional topological manifold R^2
 
         but a new chart has been created: `(U, (x, y))`::
 

src/sage/manifolds/differentiable/chart.py

@@ -357,12 +357,9 @@ def transition_map(self, other, transformations, intersection_name=None,
         The subset `W`, intersection of `U` and `V`, has been created by
         ``transition_map()``::
 
-            sage: M.list_of_subsets()
-            [1-dimensional differentiable manifold S^1,
-             Open subset U of the 1-dimensional differentiable manifold S^1,
-             Open subset V of the 1-dimensional differentiable manifold S^1,
-             Open subset W of the 1-dimensional differentiable manifold S^1]
-            sage: W = M.list_of_subsets()[3]
+            sage: F = M.subset_family(); F
+            Set {S^1, U, V, W} of open subsets of the 1-dimensional differentiable manifold S^1
+            sage: W = F['W']
             sage: W is U.intersection(V)
             True
             sage: M.atlas()
@@ -385,9 +382,8 @@ def transition_map(self, other, transformations, intersection_name=None,
 
         In this case, no new subset has been created since `U\cap M = U`::
 
-            sage: M.list_of_subsets()
-            [2-dimensional differentiable manifold R^2,
-             Open subset U of the 2-dimensional differentiable manifold R^2]
+            sage: M.subset_family()
+            Set {R^2, U} of open subsets of the 2-dimensional differentiable manifold R^2
 
         but a new chart has been created: `(U, (x, y))`::
 

src/sage/manifolds/differentiable/examples/real_line.py

@@ -229,11 +229,11 @@ class OpenInterval(DifferentiableManifold):
 
     We have::
 
-        sage: I.list_of_subsets()
+        sage: list(I.subset_family())
         [Real interval (0, 1), Real interval (0, pi), Real interval (1/2, 1)]
-        sage: J.list_of_subsets()
+        sage: list(J.subset_family())
         [Real interval (0, 1), Real interval (1/2, 1)]
-        sage: K.list_of_subsets()
+        sage: list(K.subset_family())
         [Real interval (1/2, 1)]
 
     As any open subset of a manifold, open subintervals are created in a
@@ -684,7 +684,7 @@ def open_interval(self, lower, upper, name=None, latex_name=None):
             Real interval (0, pi)
             sage: J.is_subset(I)
             True
-            sage: I.list_of_subsets()
+            sage: list(I.subset_family())
             [Real interval (-4, 4), Real interval (0, pi)]
 
         ``J`` is considered as an open submanifold of ``I``::
@@ -863,7 +863,7 @@ class RealLine(OpenInterval):
         Real interval (0, 1)
         sage: I.manifold()
         Real number line R
-        sage: R.list_of_subsets()
+        sage: list(R.subset_family())
         [Real interval (0, 1), Real number line R]
 
     """

src/sage/manifolds/differentiable/manifold.py

@@ -125,11 +125,8 @@
 
 At this stage, we have four open subsets on `S^2`::
 
-    sage: M.list_of_subsets()
-    [2-dimensional differentiable manifold S^2,
-     Open subset U of the 2-dimensional differentiable manifold S^2,
-     Open subset V of the 2-dimensional differentiable manifold S^2,
-     Open subset W of the 2-dimensional differentiable manifold S^2]
+    sage: M.subset_family()
+    Set {S^2, U, V, W} of open subsets of the 2-dimensional differentiable manifold S^2
 
 `W` is the open subset that is the complement of the two poles::
 
@@ -350,11 +347,8 @@
 
 The following subsets and charts have been defined::
 
-    sage: M.list_of_subsets()
-    [Open subset A of the 1-dimensional complex manifold C*,
-     1-dimensional complex manifold C*,
-     Open subset U of the 1-dimensional complex manifold C*,
-     Open subset V of the 1-dimensional complex manifold C*]
+    sage: M.subset_family()
+    Set {A, C*, U, V} of open subsets of the 1-dimensional complex manifold C*
     sage: M.atlas()
     [Chart (U, (z,)), Chart (V, (w,)), Chart (A, (z,)), Chart (A, (w,))]
 
@@ -775,9 +769,8 @@ def open_subset(self, name, latex_name=None, coord_def={}, supersets=None):
 
         We have then::
 
-            sage: A.list_of_subsets()
-            [Open subset A of the 2-dimensional differentiable manifold M,
-             Open subset B of the 2-dimensional differentiable manifold M]
+            sage: A.subset_family()
+            Set {A, B} of open subsets of the 2-dimensional differentiable manifold M
             sage: B.is_subset(A)
             True
             sage: B.is_subset(M)

src/sage/manifolds/manifold.py

@@ -117,11 +117,8 @@
 
 At this stage, we have four open subsets on `S^2`::
 
-    sage: M.list_of_subsets()
-    [2-dimensional topological manifold S^2,
-     Open subset U of the 2-dimensional topological manifold S^2,
-     Open subset V of the 2-dimensional topological manifold S^2,
-     Open subset W of the 2-dimensional topological manifold S^2]
+    sage: M.subset_family()
+    Set {S^2, U, V, W} of open subsets of the 2-dimensional topological manifold S^2
 
 `W` is the open subset that is the complement of the two poles::
 
@@ -269,11 +266,8 @@
 
 The following subsets and charts have been defined::
 
-    sage: M.list_of_subsets()
-    [Open subset A of the Complex 1-dimensional topological manifold C*,
-     Complex 1-dimensional topological manifold C*,
-     Open subset U of the Complex 1-dimensional topological manifold C*,
-     Open subset V of the Complex 1-dimensional topological manifold C*]
+    sage: M.subset_family()
+    Set {A, C*, U, V} of open subsets of the Complex 1-dimensional topological manifold C*
     sage: M.atlas()
     [Chart (U, (z,)), Chart (V, (w,)), Chart (A, (z,)), Chart (A, (w,))]