Trac #31736: ManifoldSubset: New methods declare_equal, equal_subsets…

…, equal_subset_family

Two subsets are equal if they are subsets of each other.

We add methods `equal_subsets`, `equal_subset_family`; and a method
`declare_equal` to make two or more subsets equal.

We modify the method `subset_poset` and `superset_poset` to quotient out
by equality.

URL: https://trac.sagemath.org/31736
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Eric Gourgoulhon

src/sage/manifolds/differentiable/differentiable_submanifold.py

@@ -18,6 +18,8 @@
 AUTHORS:
 
 - Florentin Jaffredo (2018): initial version
+- Eric Gourgoulhon (2018-2019): add documentation
+- Matthias Koeppe (2021): open subsets of submanifolds
 
 REFERENCES:
 
@@ -26,7 +28,9 @@
 """
 
 # *****************************************************************************
-#  Copyright (C) 2018 Florentin Jaffredo <florentin.jaffredo@polytechnique.edu>
+#  Copyright (C) 2018      Florentin Jaffredo <florentin.jaffredo@polytechnique.edu>
+#  Copyright (C) 2018-2019 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
+#  Copyright (C) 2021      Matthias Koeppe <mkoeppe@math.ucdavis.edu>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/manifolds/differentiable/manifold.py

@@ -411,6 +411,7 @@
 - Eric Gourgoulhon (2015): initial version
 - Travis Scrimshaw (2016): review tweaks
 - Michael Jung (2020): tensor bundles and orientability
+- Matthias Koeppe (2021): refactoring of subsets code
 
 REFERENCES:
 
@@ -424,9 +425,13 @@
 """
 
 # ****************************************************************************
-#       Copyright (C) 2015 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
-#       Copyright (C) 2015 Michal Bejger <bejger@camk.edu.pl>
-#       Copyright (C) 2016 Travis Scrimshaw <tscrimsh@umn.edu>
+#       Copyright (C) 2015-2019 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
+#       Copyright (C) 2015      Michal Bejger <bejger@camk.edu.pl>
+#       Copyright (C) 2015-2016 Travis Scrimshaw <tscrimsh@umn.edu>
+#       Copyright (C) 2017      Karim Van Aelst
+#       Copyright (C) 2019      Hans Fotsing Tetsing
+#       Copyright (C) 2019-2020 Michael Jung
+#       Copyright (C) 2021      Matthias Koeppe
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of

src/sage/manifolds/differentiable/pseudo_riemannian_submanifold.py

@@ -168,6 +168,8 @@
 AUTHORS:
 
 - Florentin Jaffredo (2018): initial version
+- Eric Gourgoulhon (2018-2019): add documentation
+- Matthias Koeppe (2021): open subsets of submanifolds
 
 REFERENCES:
 
@@ -177,7 +179,9 @@
 """
 
 # *****************************************************************************
-#  Copyright (C) 2018 Florentin Jaffredo <florentin.jaffredo@polytechnique.edu>
+#  Copyright (C) 2018      Florentin Jaffredo <florentin.jaffredo@polytechnique.edu>
+#  Copyright (C) 2018-2019 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
+#  Copyright (C) 2021      Matthias Koeppe <mkoeppe@math.ucdavis.edu>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/manifolds/family.py

@@ -11,6 +11,10 @@
 The subclass :class:`ManifoldSubsetFiniteFamily` customizes the print
 representation further.
 
+AUTHORS:
+
+- Matthias Koeppe (2021): initial version
+
 """
 #*****************************************************************************
 #       Copyright (C) 2021 Matthias Koeppe <mkoeppe@math.ucdavis.edu>
@@ -216,6 +220,31 @@ class ManifoldSubsetFiniteFamily(ManifoldObjectFiniteFamily):
 
     """
 
+    @classmethod
+    def from_subsets_or_families(cls, *subsets_or_families):
+        r"""
+        Construct a ManifoldSubsetFiniteFamily from given subsets or iterables of subsets.
+
+        EXAMPLES::
+
+            sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily
+            sage: M = Manifold(2, 'M', structure='topological')
+            sage: A = M.subset('A')
+            sage: Bs = (M.subset(f'B{i}') for i in range(5))
+            sage: Cs = ManifoldSubsetFiniteFamily([M.subset('C0'), M.subset('C1')])
+            sage: ManifoldSubsetFiniteFamily.from_subsets_or_families(A, Bs, Cs)
+            Set {A, B0, B1, B2, B3, B4, C0, C1} of subsets of the 2-dimensional topological manifold M
+        """
+        def generate_subsets():
+            from sage.manifolds.subset import ManifoldSubset
+            for arg in subsets_or_families:
+                if isinstance(arg, ManifoldSubset):
+                    yield arg
+                else:
+                    # arg must be an iterable of ManifoldSubset instances
+                    yield from arg
+        return cls(generate_subsets())
+
     def _repr_object_type(self):
         r"""
         String that describes the type of the elements (plural).

src/sage/manifolds/manifold.py

@@ -310,8 +310,13 @@
 """
 
 #*****************************************************************************
-#       Copyright (C) 2015 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
-#       Copyright (C) 2015 Travis Scrimshaw <tscrimsh@umn.edu>
+#       Copyright (C) 2015-2020 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
+#       Copyright (C) 2015      Travis Scrimshaw <tscrimsh@umn.edu>
+#       Copyright (C) 2016      Andrew Mathas
+#       Copyright (C) 2018      Florentin Jaffredo
+#       Copyright (C) 2019      Hans Fotsing Tetsing
+#       Copyright (C) 2019-2020 Michael Jung
+#       Copyright (C) 2021      Matthias Koeppe <mkoeppe@math.ucdavis.edu>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
@@ -899,9 +904,12 @@ def _init_open_subset(self, resu, coord_def):
             Open subset U of the 2-dimensional topological manifold R^2
         """
         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:
+            resu._supersets.update(self._supersets)
+            for sd in self._supersets:
+                sd._subsets.add(resu)
         self._top_subsets.add(resu)
         # Charts on the result from the coordinate definition:
         for chart, restrictions in coord_def.items():