Opened 5 years ago
Last modified 4 years ago
#18529 closed enhancement
Topological manifolds: basics — at Version 19
Reported by:  egourgoulhon  Owned by:  egourgoulhon 

Priority:  major  Milestone:  sage7.1 
Component:  geometry  Keywords:  topological manifolds 
Cc:  mmancini  Merged in:  
Authors:  Eric Gourgoulhon  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  public/manifolds/top_manif_basics  Commit:  4de19a74c83ac6d4d0c4da74e1d1f2afce5c3045 
Dependencies:  #18175  Stopgaps: 
Description (last modified by )
This is the implementation of topological manifolds over a topological field K resulting from the SageManifolds project. See the metaticket #18528 for an overview. By topological manifold over a topological field K it is meant a second countable Hausdorff space M such that every point in M has a neighborhood homeomorphic to K^{n}, with the same nonnegative integer n for all points.
This tickets implements the following Python classes:
TopManifold
: topological manifold over a topological field KTopManifoldPoint
: point in a topological manifoldTopManifoldSubset
: generic subset of a topological manifoldChart
: chart of a topological manifoldRealChart
: chart of a topological manifold over the real field
CoordChange
: transition map between two charts of a topological manifold
TopManifold
is intended to serve as a base class for specific manifolds, like smooth manifolds (K=R) and complex manifolds (K=C).
Documentation:
The reference manual is produced by
sage docbuild reference/manifolds html
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/18529/reference/manifolds/
More documentation (e.g. example worksheets) can be found here.
Change History (19)
comment:1 Changed 5 years ago by
 Description modified (diff)
comment:2 followup: ↓ 4 Changed 5 years ago by
comment:3 Changed 5 years ago by
 Description modified (diff)
comment:4 in reply to: ↑ 2 Changed 5 years ago by
Replying to jhpalmieri:
The phrase "manifold over a field K" sounds odd to me. Is it used in the literature?
Thanks for your comment. You are right: this is an abusive generalization of "manifold over R" and "manifold over C", which are used in the literature.
What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every nonnegative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)
I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.
Thanks for your suggestion; I've modified the ticket description accordingly. I've also added what is meant by "topological manifold over a topological field K".
PS: note that the code in the associated branch is still in a very crude draft state, but should be ready for review within a few days.
comment:5 Changed 5 years ago by
 Commit changed from 89c063c7119f19497e3d21b2a5a9dcb0752122b0 to 5a5722b4a0ef33d8624fdd127bbb1964232ced96
Branch pushed to git repo; I updated commit sha1. New commits:
5a5722b  Add doctests in classes Chart and RealChart

comment:6 Changed 5 years ago by
 Commit changed from 5a5722b4a0ef33d8624fdd127bbb1964232ced96 to 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93
Branch pushed to git repo; I updated commit sha1. New commits:
4f490af  Improve the documentation of coordinate charts

comment:7 Changed 5 years ago by
 Commit changed from 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93 to d8df59f286da79e1e103b56064fdffb702e034ce
Branch pushed to git repo; I updated commit sha1. New commits:
d8df59f  Improve the documentation of TopManifold

comment:8 Changed 5 years ago by
 Commit changed from d8df59f286da79e1e103b56064fdffb702e034ce to fb96562c1e7d4ffc76ca87efcc15d133c6c15190
Branch pushed to git repo; I updated commit sha1. New commits:
fb96562  Open subsets of topological manifolds are now fully considered as topological manifolds.

comment:9 Changed 5 years ago by
 Description modified (diff)
comment:10 Changed 5 years ago by
 Commit changed from fb96562c1e7d4ffc76ca87efcc15d133c6c15190 to 38c3c12cb1d9b4d52a35ad6f7a1a8d0ee666d532
Branch pushed to git repo; I updated commit sha1. New commits:
38c3c12  Improve documentation of classes TopManifold, TopManifoldSubset and TopManifoldPoint

comment:11 Changed 5 years ago by
 Commit changed from 38c3c12cb1d9b4d52a35ad6f7a1a8d0ee666d532 to 7809ebf468f80143e33830e0df75046bf191ce24
Branch pushed to git repo; I updated commit sha1. New commits:
7809ebf  Minor modifications in classes TopManifold and Chart.

comment:12 Changed 5 years ago by
 Commit changed from 7809ebf468f80143e33830e0df75046bf191ce24 to 99cc8c1c94197b1648966eaa7b2a6d04ddab1efc
Branch pushed to git repo; I updated commit sha1. New commits:
99cc8c1  Introduce Chart._init_coordinates() to simplify constructors of Chart and RealChart

comment:13 Changed 5 years ago by
 Commit changed from 99cc8c1c94197b1648966eaa7b2a6d04ddab1efc to 26fc318bbacfc9a27049a9397d43402975525820
Branch pushed to git repo; I updated commit sha1. New commits:
26fc318  Modifications in CoordChange to allow for subclasses.

comment:14 Changed 5 years ago by
 Commit changed from 26fc318bbacfc9a27049a9397d43402975525820 to a74c2e0519c166657b858be5b4b3dc4fd0145d09
Branch pushed to git repo; I updated commit sha1. New commits:
a74c2e0  Add example of padic manifold

comment:15 Changed 5 years ago by
 Commit changed from a74c2e0519c166657b858be5b4b3dc4fd0145d09 to 542b82a9ed134759fe498cd34b682b2d565061c1
Branch pushed to git repo; I updated commit sha1. New commits:
542b82a  Suppress verbose in TestSuite().run; minor improvements in documentation

comment:16 Changed 5 years ago by
 Commit changed from 542b82a9ed134759fe498cd34b682b2d565061c1 to 26c489001c4ee64a95ee70da72210e361180eeb0
Branch pushed to git repo; I updated commit sha1. New commits:
26c4890  Minor improvements in the doc of topological manifolds (basics part)

comment:17 Changed 5 years ago by
 Commit changed from 26c489001c4ee64a95ee70da72210e361180eeb0 to be3ff7424963450c1c2dfa7ca9fbe85eaeab1162
Branch pushed to git repo; I updated commit sha1. New commits:
be3ff74  Introduce open covers on top manifolds

comment:18 Changed 5 years ago by
 Commit changed from be3ff7424963450c1c2dfa7ca9fbe85eaeab1162 to 4de19a74c83ac6d4d0c4da74e1d1f2afce5c3045
Branch pushed to git repo; I updated commit sha1. New commits:
4de19a7  Merge branch 'public/manifolds/top_manif_basics' of git://trac.sagemath.org/sage into sage 6.9

comment:19 Changed 5 years ago by
 Description modified (diff)
 Milestone changed from sage6.8 to sage6.10
 Status changed from new to needs_review
The phrase "manifold over a field K" sounds odd to me. Is it used in the literature? What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every nonnegative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)
I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.