Pullbacks (preimages) of manifold subsets under continuous maps #31688

mkoeppe · 2021-04-19T00:13:11Z

Similar to #31653, given a continuous map \Phi: N -> M and a manifold subset S of M, we define the pullback (preimage) of S as the subset of N of points p with \Phi(p) in S.

Given a real scalar field Phi: N -> R and a RealSet S, we define the pullback in the same way.

Also, we view a chart C as a continuous function Phi: C.domain() -> R^n and allow pulling back any subset of R^n (an object with a __contains__ method; for example polyhedra, lattices, linear subspaces, tensor modules) by it as well.

In all cases, because Phi is continuous, topological closures/interiors pull back.

An application is in #31981.

Depends on #31883
Depends on #31904
Depends on #31653
Depends on #31916
Depends on #31644
Depends on #31959
Depends on #31990
Depends on #21243

CC: @egourgoulhon @tscrim @mjungmath

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 4558e26

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31688

The text was updated successfully, but these errors were encountered:

mkoeppe · 2021-05-31T01:22:10Z

Dependencies: #31883

mkoeppe · 2021-05-31T01:31:18Z

Branch: u/mkoeppe/pullbacks_of_manifold_subsets_under_continuous_maps

sagetrac-git · 2021-05-31T02:25:48Z

Commit: 941001b

sagetrac-git · 2021-05-31T02:25:48Z

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

`1942c71`	`ScalarField.codomain: New, put scalar fields in category of continuous maps`
`8829d72`	`Merge #31883`
`941001b`	`ManifoldSubsetPullback: More WIP`

mkoeppe · 2021-05-31T02:26:16Z

Author: Matthias Koeppe

sagetrac-git · 2021-05-31T05:07:03Z

Changed commit from 941001b to 90f763f

sagetrac-git · 2021-05-31T05:07:03Z

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

`90f763f`	`ManifoldSubsetPullback.__contains__: New`

sagetrac-git · 2021-05-31T05:31:13Z

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

`ff34765`	ManifoldSubsetPullback: In `__classcall_private__`, make immutable copies of the maps
`b8dadf3`	`ScalarField.pullback, ContinuousMap.pullback: New`

sagetrac-git · 2021-05-31T05:31:13Z

Changed commit from 90f763f to b8dadf3

sagetrac-git · 2021-06-01T20:57:40Z

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

`5abb86d`	`ManifoldSubsetPullback: More WIP`

sagetrac-git · 2021-06-01T20:57:40Z

Changed commit from b8dadf3 to 5abb86d

sagetrac-git · 2021-06-02T01:57:54Z

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

`e597e6d`	`ManifoldSubsetPullback: Allow pulling back by charts, pulling back polyehdra`

sagetrac-git · 2021-06-02T01:57:54Z

Changed commit from 5abb86d to e597e6d

sagetrac-git · 2021-06-02T19:00:32Z

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

`1623cc5`	`ManifoldSubsetPullback: Move computation of names to __classcall_private__`

sagetrac-git · 2021-06-02T19:00:32Z

Changed commit from e597e6d to 1623cc5

sagetrac-git · 2021-06-03T19:34:05Z

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

`dcc1f9a`	`ManifoldSubsetPullback: Prepare for pullbacks of opens`

sagetrac-git · 2021-06-03T19:34:05Z

Changed commit from 1623cc5 to dcc1f9a

sagetrac-git · 2021-06-04T23:09:52Z

Changed commit from dcc1f9a to a2dd182

sagetrac-git · 2021-06-04T23:09:52Z

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

`a2dd182`	`ManifoldSubsetPullback: Recognize more closed sets`

mkoeppe · 2021-06-05T00:16:10Z

Changed dependencies from #31883 to #31883, #31904

sagetrac-git · 2021-06-05T00:56:51Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`459758e`	`ImageManifoldSubset, ContinuousMap.image: Add optional 'inverse' argument, use it in __contains__`
`26c7e56`	`src/sage/manifolds/continuous_map_image.py: Update doctests`
`3e273bb`	`TopologicalSubmanifold.as_subset: New`
`9726d36`	`Docstring work`
`19762ae`	`ImageManifoldSubset: New parameter domain_subset, use it in ContinuousMap.image`
`964f9f7`	`src/sage/manifolds/continuous_map.py: Update copyright`
`e711215`	`src/sage/manifolds/continuous_map_image.py: Add tests`
`0f3e36d`	`Link in documentation of sage.manifolds.continuous_map_image`
`4a13d8b`	`Merge #31653`
`79232db`	`ContinuousMap.preimage: New, make pullback an alias; add example`

sagetrac-git · 2021-06-22T16:17:29Z

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

`d321b93`	`ContinuousMap: Return domain if the map's codomain is contained in the given subset`

egourgoulhon · 2021-06-24T10:20:41Z

comment:67

A minor point: to generate correctly the documentation, the following change shall be made in the docstring of ManifoldSubsetPullback:

-    - ``map`` - an instance of :class:`ContinuousMap`,
+    - ``map`` - an instance of :class:`~sage.manifolds.continuous_map.ContinuousMap`,
       :class:`ScalarField`, or :class:`Chart`

For :class:`ScalarField` and :class:`Chart`, this is not necessary because these classes are imported in pullback.py.

egourgoulhon · 2021-06-24T13:51:02Z

comment:68

This example in the doctstring of ManifoldSubsetPullback.is_closed is dubious:


        The pullback of finite sets is closed::

            sage: F = Family([vector(QQ, [1, 2], immutable=True), vector(QQ, [2, 3], immutable=True)])
            sage: McF = ManifoldSubsetPullback(c_cart, F, name='McF'); McF
            Subset McF of the 2-dimensional topological manifold R^2
            sage: McF.is_closed()
            False

sagetrac-git · 2021-06-24T16:33:07Z

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

`07aba9e`	`ManifoldSubsetPullback.is_closed: Preimage of finite sets is closed`
`653c651`	`src/sage/manifolds/subsets/pullback.py: Fix docstring markup`

sagetrac-git · 2021-06-24T16:33:07Z

Changed commit from d321b93 to 653c651

mkoeppe · 2021-06-24T16:33:35Z

comment:70

Replying to @egourgoulhon:

This example in the doctstring of ManifoldSubsetPullback.is_closed is dubious:

Indeed. Looks like I had forgotten to actually implement this case. Done now

egourgoulhon · 2021-06-26T09:52:11Z

comment:71

Thanks for the update. As soon as the patchbot visits the ticket and is green, the ticket can be set to positive review.

egourgoulhon · 2021-06-28T19:51:32Z

comment:72

OK, since the changes since the last time the patchbot visited the ticket are quite minor, let us move on without waiting for another visit.

Thank you for the new features introduced here!

mkoeppe · 2021-06-28T20:02:19Z

comment:73

Thanks for the review!

egourgoulhon · 2021-06-30T11:49:15Z

comment:74

Replying to @egourgoulhon:

OK, since the changes since the last time the patchbot visited the ticket are quite minor, let us move on without waiting for another visit.

It seems that we don't have any patchbot at the moment:
https://patchbot.sagemath.org/ticket/0/

sagetrac-git · 2021-07-01T22:59:53Z

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

`4b930ff`	`Merge tag '9.4.beta4' into t/31688/pullbacks_of_manifold_subsets_under_continuous_maps`

sagetrac-git · 2021-07-01T22:59:53Z

Changed commit from 653c651 to 4b930ff

vbraun · 2021-07-07T21:47:41Z

comment:77

sage -t --long --warn-long 41.5 --random-seed=0 src/sage/geometry/polyhedron/base.py
**********************************************************************
File "src/sage/geometry/polyhedron/base.py", line 2975, in sage.geometry.polyhedron.base.Polyhedron_base.incidence_matrix
Failed example:
    M == P.incidence_matrix()
Expected:
    False
Got:
    True
**********************************************************************
1 item had failures:
   1 of  31 in sage.geometry.polyhedron.base.Polyhedron_base.incidence_matrix
    [1737 tests, 1 failure, 35.30 s]
----------------------------------------------------------------------
sage -t --long --warn-long 41.5 --random-seed=0 src/sage/geometry/polyhedron/base.py  # 1 doctest failed
----------------------------------------------------------------------

sagetrac-git · 2021-07-07T23:09:36Z

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

`4558e26`	`Polyhedron_base.incidence_matrix: Remove accidental change to doctest`

sagetrac-git · 2021-07-07T23:09:36Z

Changed commit from 4b930ff to 4558e26

vbraun · 2021-07-18T22:53:36Z

Changed branch from u/mkoeppe/pullbacks_of_manifold_subsets_under_continuous_maps to 4558e26

mkoeppe added this to the sage-9.4 milestone Apr 19, 2021

mkoeppe added c: manifolds labels Apr 19, 2021

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mkoeppe changed the title ~~Pullbacks of manifold subsets under continuous maps~~ Pullbacks (preimages) of manifold subsets under continuous maps Jun 5, 2021

egourgoulhon added s: positive review and removed s: needs review labels Jun 28, 2021

sagetrac-git mannequin added s: needs review and removed s: positive review labels Jul 1, 2021

mkoeppe added s: positive review and removed s: needs review labels Jul 1, 2021

vbraun added s: needs work and removed s: positive review labels Jul 7, 2021

mkoeppe added s: needs review and removed s: needs work labels Jul 7, 2021

vbraun removed the s: positive review label Jul 18, 2021

vbraun closed this as completed in b8585d2 Jul 18, 2021

Pullbacks (preimages) of manifold subsets under continuous maps #31688

Pullbacks (preimages) of manifold subsets under continuous maps #31688

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