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: sage-7.1
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 egourgoulhon)

This is the implementation of topological manifolds over a topological field K resulting from the SageManifolds project. See the meta-ticket #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 Kn, with the same non-negative integer n for all points.

This tickets implements the following Python classes:

  • TopManifold: topological manifold over a topological field K
  • TopManifoldPoint: point in a topological manifold
  • TopManifoldSubset: generic subset of a topological manifold
  • Chart: chart of a topological manifold
    • RealChart: 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 egourgoulhon

  • Description modified (diff)

comment:2 follow-up: Changed 5 years ago by jhpalmieri

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 non-negative 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.

comment:3 Changed 5 years ago by egourgoulhon

  • Description modified (diff)

comment:4 in reply to: ↑ 2 Changed 5 years ago by egourgoulhon

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 non-negative 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.

Last edited 5 years ago by egourgoulhon (previous) (diff)

comment:5 Changed 5 years ago by git

  • Commit changed from 89c063c7119f19497e3d21b2a5a9dcb0752122b0 to 5a5722b4a0ef33d8624fdd127bbb1964232ced96

Branch pushed to git repo; I updated commit sha1. New commits:

5a5722bAdd doctests in classes Chart and RealChart

comment:6 Changed 5 years ago by git

  • Commit changed from 5a5722b4a0ef33d8624fdd127bbb1964232ced96 to 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93

Branch pushed to git repo; I updated commit sha1. New commits:

4f490afImprove the documentation of coordinate charts

comment:7 Changed 5 years ago by git

  • Commit changed from 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93 to d8df59f286da79e1e103b56064fdffb702e034ce

Branch pushed to git repo; I updated commit sha1. New commits:

d8df59fImprove the documentation of TopManifold

comment:8 Changed 5 years ago by git

  • Commit changed from d8df59f286da79e1e103b56064fdffb702e034ce to fb96562c1e7d4ffc76ca87efcc15d133c6c15190

Branch pushed to git repo; I updated commit sha1. New commits:

fb96562Open subsets of topological manifolds are now fully considered as topological manifolds.

comment:9 Changed 5 years ago by egourgoulhon

  • Description modified (diff)

comment:10 Changed 5 years ago by git

  • Commit changed from fb96562c1e7d4ffc76ca87efcc15d133c6c15190 to 38c3c12cb1d9b4d52a35ad6f7a1a8d0ee666d532

Branch pushed to git repo; I updated commit sha1. New commits:

38c3c12Improve documentation of classes TopManifold, TopManifoldSubset and TopManifoldPoint

comment:11 Changed 5 years ago by git

  • Commit changed from 38c3c12cb1d9b4d52a35ad6f7a1a8d0ee666d532 to 7809ebf468f80143e33830e0df75046bf191ce24

Branch pushed to git repo; I updated commit sha1. New commits:

7809ebfMinor modifications in classes TopManifold and Chart.

comment:12 Changed 5 years ago by git

  • Commit changed from 7809ebf468f80143e33830e0df75046bf191ce24 to 99cc8c1c94197b1648966eaa7b2a6d04ddab1efc

Branch pushed to git repo; I updated commit sha1. New commits:

99cc8c1Introduce Chart._init_coordinates() to simplify constructors of Chart and RealChart

comment:13 Changed 5 years ago by git

  • Commit changed from 99cc8c1c94197b1648966eaa7b2a6d04ddab1efc to 26fc318bbacfc9a27049a9397d43402975525820

Branch pushed to git repo; I updated commit sha1. New commits:

26fc318Modifications in CoordChange to allow for subclasses.

comment:14 Changed 5 years ago by git

  • Commit changed from 26fc318bbacfc9a27049a9397d43402975525820 to a74c2e0519c166657b858be5b4b3dc4fd0145d09

Branch pushed to git repo; I updated commit sha1. New commits:

a74c2e0Add example of p-adic manifold

comment:15 Changed 5 years ago by git

  • Commit changed from a74c2e0519c166657b858be5b4b3dc4fd0145d09 to 542b82a9ed134759fe498cd34b682b2d565061c1

Branch pushed to git repo; I updated commit sha1. New commits:

542b82aSuppress verbose in TestSuite().run; minor improvements in documentation

comment:16 Changed 5 years ago by git

  • Commit changed from 542b82a9ed134759fe498cd34b682b2d565061c1 to 26c489001c4ee64a95ee70da72210e361180eeb0

Branch pushed to git repo; I updated commit sha1. New commits:

26c4890Minor improvements in the doc of topological manifolds (basics part)

comment:17 Changed 5 years ago by git

  • Commit changed from 26c489001c4ee64a95ee70da72210e361180eeb0 to be3ff7424963450c1c2dfa7ca9fbe85eaeab1162

Branch pushed to git repo; I updated commit sha1. New commits:

be3ff74Introduce open covers on top manifolds

comment:18 Changed 5 years ago by git

  • Commit changed from be3ff7424963450c1c2dfa7ca9fbe85eaeab1162 to 4de19a74c83ac6d4d0c4da74e1d1f2afce5c3045

Branch pushed to git repo; I updated commit sha1. New commits:

4de19a7Merge branch 'public/manifolds/top_manif_basics' of git://trac.sagemath.org/sage into sage 6.9

comment:19 Changed 5 years ago by egourgoulhon

  • Description modified (diff)
  • Milestone changed from sage-6.8 to sage-6.10
  • Status changed from new to needs_review
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