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23 | 23 | - [Mil1974]_
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24 | 24 | """
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25 | 25 |
|
26 |
| -#****************************************************************************** |
| 26 | +# **************************************************************************** |
27 | 27 | # Copyright (C) 2019 Michael Jung <[email protected]>
|
28 | 28 | #
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29 | 29 | # Distributed under the terms of the GNU General Public License (GPL)
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30 | 30 | # as published by the Free Software Foundation; either version 2 of
|
31 | 31 | # the License, or (at your option) any later version.
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32 | 32 | # https://www.gnu.org/licenses/
|
33 |
| -#****************************************************************************** |
| 33 | +# **************************************************************************** |
34 | 34 |
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35 | 35 | import sage.rings.abc
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36 | 36 | from sage.categories.vector_bundles import VectorBundles
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@@ -265,16 +265,19 @@ def _init_attributes(self):
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265 | 265 | sage: E = M.vector_bundle(2, 'E')
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266 | 266 | sage: E._init_attributes()
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267 | 267 | """
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268 |
| - self._section_modules = {} # dict of section modules with domains as |
269 |
| - # keys |
| 268 | + self._section_modules = {} |
| 269 | + # dict of section modules with domains as keys |
| 270 | + |
270 | 271 | self._atlas = [] # list of trivializations defined on self
|
271 |
| - self._transitions = {} # dictionary of transition maps (key: pair of |
272 |
| - # of trivializations) |
| 272 | + self._transitions = {} |
| 273 | + # dictionary of transition maps (key: pair of trivializations) |
| 274 | + |
273 | 275 | self._frames = [] # list of local frames for self
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274 | 276 | self._frame_changes = {} # dictionary of changes of frames
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275 |
| - self._coframes = [] # list of local coframes for self |
276 |
| - self._trivial_parts = set() # subsets of base space on which self is |
277 |
| - # trivial |
| 277 | + self._coframes = [] # list of local coframes for self |
| 278 | + self._trivial_parts = set() |
| 279 | + # subsets of base space on which self is trivial |
| 280 | + |
278 | 281 | self._def_frame = None
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279 | 282 |
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280 | 283 | def base_space(self):
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@@ -526,7 +529,7 @@ def atlas(self):
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526 | 529 | Trivialization (phi_V, E|_V),
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527 | 530 | Trivialization (phi_M, E|_M)]
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528 | 531 | """
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529 |
| - return list(self._atlas) # Make a (shallow) copy |
| 532 | + return list(self._atlas) # Make a (shallow) copy |
530 | 533 |
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531 | 534 | def is_manifestly_trivial(self):
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532 | 535 | r"""
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@@ -869,17 +872,19 @@ def total_space(self):
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869 | 872 | sage: M = Manifold(3, 'M', structure='top')
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870 | 873 | sage: E = M.vector_bundle(2, 'E')
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871 | 874 | sage: E.total_space()
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872 |
| - 6-dimensional topological manifold E |
| 875 | + 5-dimensional topological manifold E |
873 | 876 | """
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874 | 877 | if self._total_space is None:
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875 | 878 | from sage.manifolds.manifold import Manifold
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876 | 879 | base_space = self._base_space
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877 |
| - dim = base_space._dim * self._rank |
| 880 | + dim = base_space._dim + self._rank |
878 | 881 | sindex = base_space.start_index()
|
879 |
| - self._total_space = Manifold(dim, self._name, |
880 |
| - latex_name=self._latex_name, |
881 |
| - field=self._field, structure='topological', |
882 |
| - start_index=sindex) |
| 882 | + self._total_space = Manifold( |
| 883 | + dim, self._name, |
| 884 | + latex_name=self._latex_name, |
| 885 | + field=self._field, structure='topological', |
| 886 | + start_index=sindex |
| 887 | + ) |
883 | 888 |
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884 | 889 | # TODO: if update_atlas: introduce charts via self._atlas
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885 | 890 |
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@@ -934,7 +939,7 @@ def set_change_of_frame(self, frame1, frame2, change_of_frame,
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934 | 939 | "section module")
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935 | 940 | if isinstance(change_of_frame, FreeModuleAutomorphism):
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936 | 941 | auto = change_of_frame
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937 |
| - else: # Otherwise try to coerce the input |
| 942 | + else: # Otherwise try to coerce the input |
938 | 943 | auto_group = sec_module.general_linear_group()
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939 | 944 | auto = auto_group(change_of_frame, basis=frame1)
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940 | 945 | sec_module.set_change_of_basis(frame1, frame2, auto,
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