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@@ -21,3 +21,5 @@ Topological Manifolds | |
| sage/manifolds/topological_submanifold | ||
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| vector_bundle | ||
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| sage/manifolds/family | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,236 @@ | ||
| r""" | ||
| Families of Manifold Objects | ||
| The class :class:`ManifoldObjectFiniteFamily` is a subclass of :class:`FiniteFamily` | ||
| that provides an associative container of manifold objects, indexed by their | ||
| ``_name`` attributes. | ||
| :class:`ManifoldObjectFiniteFamily` instances are totally ordered according | ||
| to their lexicographically ordered element names. | ||
| The subclass :class:`ManifoldSubsetFiniteFamily` customizes the print | ||
| representation further. | ||
| """ | ||
| #***************************************************************************** | ||
| # 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 | ||
| # the Free Software Foundation, either version 2 of the License, or | ||
| # (at your option) any later version. | ||
| # http://www.gnu.org/licenses/ | ||
| #***************************************************************************** | ||
|
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| from functools import total_ordering | ||
| from sage.sets.family import FiniteFamily | ||
|
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| @total_ordering | ||
| class ManifoldObjectFiniteFamily(FiniteFamily): | ||
|
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| r""" | ||
| Finite family of manifold objects, indexed by their names. | ||
| The class :class:`ManifoldObjectFiniteFamily` inherits from | ||
| :class:`FiniteFamily`. Therefore it is an associative container. | ||
| It provides specialized ``__repr__`` and ``_latex_`` methods. | ||
| :class:`ManifoldObjectFiniteFamily` instances are totally ordered | ||
| according to their lexicographically ordered element names. | ||
| EXAMPLES:: | ||
| sage: from sage.manifolds.family import ManifoldObjectFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: C = B.subset('C') | ||
| sage: F = ManifoldObjectFiniteFamily([A, B, C]); F | ||
| Set {A, B, C} of objects of the 2-dimensional topological manifold M | ||
| sage: latex(F) | ||
| \{A, B, C\} | ||
| sage: F['B'] | ||
| Subset B of the 2-dimensional topological manifold M | ||
| All objects must have the same base manifold:: | ||
| sage: N = Manifold(2, 'N', structure='topological') | ||
| sage: ManifoldObjectFiniteFamily([M, N]) | ||
| Traceback (most recent call last): | ||
| ... | ||
| TypeError: all objects must have the same manifold | ||
| """ | ||
| def __init__(self, objects=(), keys=None): | ||
| r""" | ||
| Initialize a new instance of :class:`ManifoldObjectFiniteFamily`. | ||
| TESTS: | ||
| sage: from sage.manifolds.family import ManifoldObjectFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: C = B.subset('C') | ||
| sage: F = ManifoldObjectFiniteFamily([A, B, C]); F | ||
| Set {A, B, C} of objects of the 2-dimensional topological manifold M | ||
| sage: TestSuite(F).run(skip='_test_elements') | ||
| Like ``frozenset``, it can be created from any iterable:: | ||
| sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: I = M.subset('I') | ||
| sage: gen = (subset for subset in (M, I, M, I, M, I)); gen | ||
| <generator object ...> | ||
| sage: ManifoldSubsetFiniteFamily(gen) | ||
| Set {I, M} of subsets of the 2-dimensional topological manifold M | ||
| """ | ||
| if isinstance(objects, dict): | ||
| dictionary = objects | ||
| else: | ||
| dictionary = {object._name: object for object in objects} | ||
| if keys is None: | ||
| keys = sorted(dictionary.keys()) | ||
| FiniteFamily.__init__(self, dictionary, keys) | ||
| names_and_latex_names = sorted((object._name, object._latex_name) | ||
| for object in self) | ||
| self._name = '{' + ', '.join(keys) + '}' | ||
| latex_names = (latex_name for name, latex_name in names_and_latex_names) | ||
| self._latex_name = r'\{' + ', '.join(latex_names) + r'\}' | ||
| try: | ||
| object_iter = iter(self) | ||
| self._manifold = next(object_iter)._manifold | ||
| except StopIteration: | ||
| self._manifold = None | ||
| else: | ||
| if not all(object._manifold == self._manifold for object in object_iter): | ||
| raise TypeError(f'all {self._repr_object_type()} must have the same manifold') | ||
|
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| def _repr_object_type(self): | ||
| r""" | ||
| String that describes the type of the elements (plural). | ||
| TESTS:: | ||
| sage: from sage.manifolds.family import ManifoldObjectFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: ManifoldObjectFiniteFamily([A, B]).__repr__() # indirect doctest | ||
| 'Set {A, B} of objects of the 2-dimensional topological manifold M' | ||
| """ | ||
| return "objects" | ||
|
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| def __lt__(self, other): | ||
| r""" | ||
| Implement the total order on instances of :class:`ManifoldObjectFiniteFamily`. | ||
| TESTS:: | ||
| sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: sorted([ManifoldSubsetFiniteFamily([A, B]), ManifoldSubsetFiniteFamily([]), | ||
| ....: ManifoldSubsetFiniteFamily([B]), ManifoldSubsetFiniteFamily([A])]) | ||
| [{}, | ||
| Set {A} of subsets of the 2-dimensional topological manifold M, | ||
| Set {A, B} of subsets of the 2-dimensional topological manifold M, | ||
| Set {B} of subsets of the 2-dimensional topological manifold M] | ||
| """ | ||
| if not isinstance(other, ManifoldSubsetFiniteFamily): | ||
| return NotImplemented | ||
| return self.keys() < other.keys() | ||
|
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| def __repr__(self): | ||
| r""" | ||
| String representation of the object. | ||
| TESTS:: | ||
| sage: from sage.manifolds.family import ManifoldObjectFiniteFamily | ||
| sage: ManifoldObjectFiniteFamily().__repr__() | ||
| '{}' | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: ManifoldObjectFiniteFamily([A, B]).__repr__() | ||
| 'Set {A, B} of objects of the 2-dimensional topological manifold M' | ||
| """ | ||
| if self: | ||
| return "Set {} of {} of the {}".format(self._name, self._repr_object_type(), self._manifold) | ||
| else: | ||
| return "{}" | ||
|
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| def _latex_(self): | ||
| r""" | ||
| LaTeX representation of ``self``. | ||
| TESTS:: | ||
| sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: ManifoldSubsetFiniteFamily([B, A])._latex_() | ||
| '\\{A, B\\}' | ||
| """ | ||
| return self._latex_name | ||
|
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| class ManifoldSubsetFiniteFamily(ManifoldObjectFiniteFamily): | ||
|
|
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| r""" | ||
| Finite family of subsets of a topological manifold, indexed by their names. | ||
| The class :class:`ManifoldSubsetFiniteFamily` inherits from | ||
| :class:`ManifoldObjectFiniteFamily`. It provides an associative | ||
| container with specialized ``__repr__`` and ``_latex_`` methods. | ||
| :class:`ManifoldSubsetFiniteFamily` instances are totally ordered according | ||
| to their lexicographically ordered element (subset) names. | ||
| EXAMPLES:: | ||
| sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: C = B.subset('C') | ||
| sage: ManifoldSubsetFiniteFamily([A, B, C]) | ||
| Set {A, B, C} of subsets of the 2-dimensional topological manifold M | ||
| sage: latex(_) | ||
| \{A, B, C\} | ||
| All subsets must have the same base manifold:: | ||
| sage: N = Manifold(2, 'N', structure='topological') | ||
| sage: ManifoldSubsetFiniteFamily([M, N]) | ||
| Traceback (most recent call last): | ||
| ... | ||
| TypeError: all... subsets must have the same manifold | ||
| """ | ||
|
|
||
| def _repr_object_type(self): | ||
| r""" | ||
| String that describes the type of the elements (plural). | ||
| TESTS:: | ||
| sage: from sage.manifolds.family import ManifoldSubsetFiniteFamily | ||
| sage: M = Manifold(2, 'M', structure='topological') | ||
| sage: A = M.subset('A') | ||
| sage: B = M.subset('B') | ||
| sage: ManifoldSubsetFiniteFamily([A, B]).__repr__() # indirect doctest | ||
| 'Set {A, B} of subsets of the 2-dimensional topological manifold M' | ||
| """ | ||
| if all(subset.is_open() for subset in self): | ||
| return "open subsets" | ||
| else: | ||
| return "subsets" |
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