Pullbacks (preimages) of manifold subsets under continuous maps

Question

Pullbacks (preimages) of manifold subsets under continuous maps

mkoeppe opened this issue 5 years ago · 115 comments

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

Answer 1 · 2021-05-30T23:53:16.000Z

Description changed:

--- 
+++ 
@@ -1,2 +1,7 @@
 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.
+
+In both cases, because `Phi` is continuous, topological closures/interiors pull back.
+
+

Answer 2 · 2021-05-31T01:22:10.000Z

Dependencies: #31883

Answer 3 · 2021-05-31T01:31:18.000Z

Branch: u/mkoeppe/pullbacks_of_manifold_subsets_under_continuous_maps

Answer 4 · 2021-05-31T02:25:48.000Z

Commit: 941001b

Answer 5 · 2021-05-31T02:25:48.000Z

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`

Answer 6 · 2021-05-31T02:26:16.000Z

Author: Matthias Koeppe

Answer 7 · 2021-05-31T02:26:16.000Z

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 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.
+Given a real scalar field `Phi: N -> R` and a `RealSet` `S`, we define the pullback in the same way.
 
 In both cases, because `Phi` is continuous, topological closures/interiors pull back.

Answer 8 · 2021-05-31T05:07:03.000Z

Changed commit from 941001b to 90f763f

Answer 9 · 2021-05-31T05:07:03.000Z

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

`90f763f`	`ManifoldSubsetPullback.__contains__: New`

Answer 10 · 2021-05-31T05:31:13.000Z

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`

Answer 11 · 2021-05-31T05:31:13.000Z

Changed commit from 90f763f to b8dadf3

Answer 12 · 2021-06-01T20:57:40.000Z

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

`5abb86d`	`ManifoldSubsetPullback: More WIP`

Answer 13 · 2021-06-01T20:57:40.000Z

Changed commit from b8dadf3 to 5abb86d

Answer 14 · 2021-06-02T01:57:54.000Z

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

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

Answer 15 · 2021-06-02T01:57:54.000Z

Changed commit from 5abb86d to e597e6d

Answer 16 · 2021-06-02T02:00:09.000Z

Description changed:

--- 
+++ 
@@ -2,6 +2,8 @@
 
 Given a real scalar field `Phi: N -> R` and a `RealSet` `S`, we define the pullback in the same way.
 
-In both cases, because `Phi` is continuous, topological closures/interiors pull back.
+Also, we view a chart `C` as a continuous function `Phi: C.domain() -> R^n` and allow pulling back by it as well. 
+
+In all cases, because `Phi` is continuous, topological closures/interiors pull back.

Answer 17 · 2021-06-02T18:08:34.000Z

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 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 by it as well. 
+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) by it as well. 
 
 In all cases, because `Phi` is continuous, topological closures/interiors pull back.

Answer 18 · 2021-06-02T19:00:32.000Z

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

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

Answer 19 · 2021-06-02T19:00:32.000Z

Changed commit from e597e6d to 1623cc5

Answer 20 · 2021-06-03T19:34:05.000Z

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

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

Answer 21 · 2021-06-03T19:34:05.000Z

Changed commit from 1623cc5 to dcc1f9a

Answer 22 · 2021-06-04T23:09:52.000Z

Changed commit from dcc1f9a to a2dd182

Answer 23 · 2021-06-04T23:09:52.000Z

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

`a2dd182`	`ManifoldSubsetPullback: Recognize more closed sets`

Answer 24 · 2021-06-05T00:16:10.000Z

Changed dependencies from #31883 to #31883, #31904

Answer 25 · 2021-06-05T00:56:51.000Z

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`

Answer 26 · 2021-06-05T00:56:51.000Z

Changed commit from a2dd182 to 79232db

Answer 27 · 2021-06-05T00:57:26.000Z

Changed dependencies from #31883, #31904 to #31883, #31904, #31653

Answer 28 · 2021-06-05T00:57:26.000Z

Description changed:

Answer 29 · 2021-06-05T18:48:02.000Z

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

`3c6666a`	`ManifoldSubsetPullback: Make pullback of open RealSet under a ScalarField an open set`

Answer 30 · 2021-06-05T18:48:02.000Z

Changed commit from 79232db to 3c6666a

Answer 31 · 2021-06-05T19:02:11.000Z

Changed commit from 3c6666a to e95c897

Answer 32 · 2021-06-05T19:02:11.000Z

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

`235d75a`	`ManifoldSubsetPullback.closure: Adjust doctest`
`aea4554`	`#31904: Fix indentation in _pullback_chart`
`e95c897`	`Merge #31904`

Answer 33 · 2021-06-05T19:13:25.000Z

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 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) by it as well. 
+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, or linear subspaces) by it as well. 
 
 In all cases, because `Phi` is continuous, topological closures/interiors pull back.

Answer 34 · 2021-06-05T20:05:06.000Z

Changed commit from e95c897 to ff5eb8b

Answer 35 · 2021-06-05T20:05:06.000Z

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

`ff5eb8b`	`ManifoldSubsetPullback: Add doctests`

Answer 36 · 2021-06-05T20:35:02.000Z

Changed commit from ff5eb8b to c268d34

Answer 37 · 2021-06-05T20:35:02.000Z

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

`c268d34`	`ManifoldSubsetPullback: Fix example using the embedding map`

Answer 38 · 2021-06-05T21:33:49.000Z

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

`56b22a3`	`ManifoldSubsetPullback.__classcall_private__: Add doc`
`762e0a8`	`ManifoldSubsetPullback.__init__: Add tests`
`2a01a07`	`ManifoldSubsetPullback._an_element_: New`

Answer 39 · 2021-06-05T21:33:49.000Z

Changed commit from c268d34 to 2a01a07

Answer 40 · 2021-06-05T21:37:31.000Z

comment:24

This is not quite ready yet, but comments are very welcome

Answer 41 · 2021-06-06T03:43:51.000Z

Changed commit from 2a01a07 to acc71c3

Answer 42 · 2021-06-06T03:43:51.000Z

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

`e9c670c`	`sage.geometry.polyhedron.relint, Polyhedron_base.relative_interior, Polyhedron_base.interior: New`
`86fc6cd`	`Merge #31916`
`acc71c3`	`ManifoldSubsetPullback: Pulling back interiors of polyhedra`

Answer 43 · 2021-06-06T03:44:16.000Z

Changed dependencies from #31883, #31904, #31653 to #31883, #31904, #31653, #31916

Answer 44 · 2021-06-06T10:03:22.000Z

comment:27

For a possible follow-up, it might be a good idea to bear in mind that the preimage of a regular value of a differentiable map between manifolds of dimension n and m respectively is a differentiable manifold of dimension n-m again.

Answer 45 · 2021-06-06T21:19:55.000Z

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

`9df2104`	`sage.geometry.relative_interior: Move here from sage.geometry.polyhedron.relint`
`b8bfe20`	`ConvexRationalPolyhedralCone: Add methods interior, relative_interior`
`6869673`	`relative_interior: Fix for dimension 0`
`021d073`	`RelativeInterior: Add documentation, tests, comparison methods, method relative_interior`
`8f38e04`	`ConvexRationalPolyhedralCone.interior, relative_interior: Add doctests`
`3a5870e`	`Merge #31916`

Answer 46 · 2021-06-06T21:19:55.000Z

Changed commit from acc71c3 to 3a5870e

Answer 47 · 2021-06-13T16:39:48.000Z

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 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, or linear subspaces) by it as well. 
+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.

Answer 48 · 2021-06-13T19:52:26.000Z

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

`d11280e`	`src/sage/manifolds/subsets/pullback.py: Fixup import`
`cd3ca79`	`Update doctests for refined category of ScalarField`
`105bb8b`	`Merge #31883`
`5f9c852`	`RelativeInterior.interior: New`
`5c089ec`	`RelativeInterior.__eq__, __ne__: Handle comparisons with objects of other types`
`86ce301`	`Polyhedron_base.is_relatively_open: New; fix relative_interior for affine subspaces`
`216cb81`	`ConvexRationalPolyhedralCone.is_relatively_open: New, fix ConvexRationalPolyhedralCone.relative_interior for linear subspaces`
`44cde1e`	`src/doc/en/reference/discrete_geometry/index.rst: Add sage/geometry/relative_interior`
`fa4c2d2`	`Whitespace fixes`
`e802a21`	`Merge #31916`

Answer 49 · 2021-06-13T19:52:26.000Z

Changed commit from 3a5870e to e802a21

Answer 50 · 2021-06-13T19:55:57.000Z

Description changed:

--- 
+++ 
@@ -7,3 +7,5 @@
 In all cases, because `Phi` is continuous, topological closures/interiors pull back.
 
 
+An application is in #31981.
+

Answer 51 · 2021-06-15T03:34:38.000Z

Changed dependencies from #31883, #31904, #31653, #31916 to #31883, #31904, #31653, #31916, #31959

Answer 52 · 2021-06-15T03:35:58.000Z

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

`6bef52b`	`ConvexSet_base._test_convex_set: Run the testsuite of relint`
`6ab5677`	`RelativeInterior.is_universe: New`
`c085d30`	`Polyhedron_base.interior: Handle the empty polyhedron correctly`
`686d0af`	`Polyhedron_base.product: Add doctest for alias 'cartesian_product'`
`2b1d108`	`Merge #31919`
`7323b10`	`ConvexSet_base._test_contains: Only test extension to AA for exact base rings`
`e0d2eeb`	`Merge #31959`
`e6c3ed5`	`RelativeInterior.__hash__: New`
`4c7d57f`	`src/sage/geometry/relative_interior.py: Fix doctest output`
`9ea0cea`	`ManifoldSubsetPullback: Do not trip over relative interiors of cones`

Answer 53 · 2021-06-15T03:35:58.000Z

Changed commit from e802a21 to 9ea0cea

Answer 54 · 2021-06-16T12:49:32.000Z

comment:34

As revealed by the patchbot, there are some doctest failures, as well as some coverage and pyflakes issues.

Answer 55 · 2021-06-16T16:36:29.000Z

Changed commit from 9ea0cea to d591234

Answer 56 · 2021-06-16T16:36:29.000Z

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

`94e6858`	`RelativeInterior.ambient, ambient_vector_space, is_universe: New`
`0c9bc94`	`ConvexSet_base: Add default implementations of ambient, ambient_dim; add doctests`
`d591234`	`Merge #31959`

Answer 57 · 2021-06-16T16:39:17.000Z

comment:36

Thanks for taking a look! Yes, I'll have to add more documentation and examples.

Answer 58 · 2021-06-16T17:19:14.000Z

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

`87f3e30`	`ManifoldSubsetPullback: Add documentation and tests`

Answer 59 · 2021-06-16T17:19:14.000Z

Changed commit from d591234 to 87f3e30

Answer 60 · 2021-06-17T00:58:53.000Z

Changed dependencies from #31883, #31904, #31653, #31916, #31959 to #31883, #31904, #31653, #31916, #31959, #31990

Answer 61 · 2021-06-17T00:59:58.000Z

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

`7d3ae5c`	`Merge #31959`
`2b1040c`	`ConvexSet_base.{an_element,some_elements}, Polyhedron.some_elements, RelativeInterior.some_elements: New`
`a884517`	`PolyhedronFace.some_elements: New`
`f6cc8f7`	`Merge #31990`
`1a4805c`	`ManifoldSubsetPullback: For charts, use .point as the inverse`
`754e002`	`ManifoldSubsetPullback._an_element_, some_elements: Implement`

Answer 62 · 2021-06-17T00:59:58.000Z

Changed commit from 87f3e30 to 754e002

Answer 63 · 2021-06-17T01:28:51.000Z

Changed commit from 754e002 to a8e607c

Answer 64 · 2021-06-17T01:28:51.000Z

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

`a8e607c`	`ManifoldSubsetPullback._coord_def: Add documentation and examples`

Answer 65 · 2021-06-17T05:43:44.000Z

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

`ce91e44`	`src/sage/geometry/relative_interior.py: Fix doctest output`
`b19b3cc`	`Merge #31959`
`c49ab33`	`Merge #31990`

Answer 66 · 2021-06-17T05:43:44.000Z

Changed commit from a8e607c to c49ab33

Answer 67 · 2021-06-17T13:07:33.000Z

Changed commit from c49ab33 to 7ae21da

Answer 68 · 2021-06-17T13:07:33.000Z

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

`f0e7c58`	`ambient_vector_space docstring: Fix bad blocks`
`200d967`	`ConvexSet_base.ambient doctest: Actually test the method`
`1c2bef5`	`Merge #31959`
`ed898e6`	ConvexSet_base.an_element, some_elements: Go through generator method `_some_elements_`, make some_elements return a list
`7ae21da`	`Merge #31990`

Answer 69 · 2021-06-17T20:04:49.000Z

Reviewer: Eric Gourgoulhon

Answer 70 · 2021-06-17T20:04:49.000Z

comment:44

Thanks for the last changes.
Some comments regarding the documentation:

there is no entry for the class ManifoldSubsetPullback in the reference manual
in the files continuous_map.py and subsets/pullback.py, each instance of :class:`ManifoldSubset` should be replaced by :class:`~sage.manifolds.subset.ManifoldSubset`
the docstring of ScalarField.pullback should have an INPUT and OUTPUT sections similar to those of ContinuousMap.preimage. By the way, to be consistent with ContinuousMap.preimage, shouldn't ScalarField.pullback be renamed to ScalarField.preimage, with pullback defined as an alias to preimage?
the INPUT and OUTPUT sections of DiffMap.pullback should be updated to take into account the new arguments.

Answer 71 · 2021-06-18T18:10:39.000Z

Changed dependencies from #31883, #31904, #31653, #31916, #31959, #31990 to #31883, #31904, #31653, #31916, #31644, #31959, #31990

Answer 72 · 2021-06-18T18:47:45.000Z

Changed commit from 7ae21da to 3877c5f

Answer 73 · 2021-06-18T18:47:45.000Z

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

`8d3ad85`	`Merge #31764`
`60505b0`	`Merge #31798`
`b9909c0`	`ManifoldSubsetClosure: Add examples, fix docstring markup`
`16c6a72`	`ManifoldSubsetClosure, ManifoldSubset.closure: Improve documentation`
`2514586`	`Merge #31644`
`3ca139a`	`src/doc/en/reference/manifolds: Add pullback`
`1d430ee`	`src/sage/manifolds/continuous_map.py, src/sage/manifolds/subsets: Use qualified class name in docstrings`
`1266de9`	`src/sage/geometry/convex_set.py: Fix docstring markup`
`df64125`	`ScalarField.preimage: Make pullback an alias; expand documentation`
`3877c5f`	`ManifoldSubsetPullback.is_closed: Remove unfinished NNC_Polyhedron example`

Answer 74 · 2021-06-18T19:31:48.000Z

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

`0c549f0`	`Chart.pullback, preimage: New`
`7bb720e`	`ManifoldSubsetPullback.__contains__: Handle the case of charts, which return tuples of coordinates, not vectors`
`60ea044`	`ContinuousMap.preimage, ScalarField.preimage: Document that output can also be a manifold`

Answer 75 · 2021-06-18T19:31:48.000Z

Changed commit from 3877c5f to 60ea044

Answer 76 · 2021-06-20T05:46:49.000Z

Changed dependencies from #31883, #31904, #31653, #31916, #31644, #31959, #31990 to #31883, #31904, #31653, #31916, #31644, #31959, #31990, #21243

Answer 77 · 2021-06-20T05:47:11.000Z

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

`5b8ceca`	InternalRealInterval, RealSet: Add `_latex_` methods
`69ca854`	`RealSet._repr_: Use unicode cup sign instead of +`
`dbdfc06`	`InternalRealInterval, RealSet: Remove extra whitespace in latex, add documentation`
`a0e3bf5`	`Merge #31880`
`181b128`	`RealSet.is_open, is_closed, closure, interior, boundary: New`
`7f56338`	`PiecewiseFunction: Adjust doctests for changed RealSet repr`
`8cd74b5`	`Merge #31880`
`8fdb104`	`RealSet.boundary: Add another doctest`
`9d41f0e`	`src/sage/sets/real_set.py: Remove unnecessary import`
`c36e43b`	`Merge #21243`

Answer 78 · 2021-06-20T05:47:11.000Z

Changed commit from 60ea044 to c36e43b

Answer 79 · 2021-06-21T17:15:03.000Z

comment:50

In the docstring of ManifoldSubsetPullback:

in the INPUT section, there seems to be no entry for ConvexSet_base in the documentation
in the following part of the EXAMPLES block:

sage: r_squared = M.scalar_field(x^2+y^2)
sage: r_squared.set_immutable()
sage: cl_I = RealSet((1, 4)); cl_I
(1, 4)
sage: cl_O = ManifoldSubsetPullback(r_squared, None, I); cl_O

I guess I in the last line (which, at this stage, is the imaginary number i) should be replaced by cl_I and the subsequent True and False should become False and True respectively. But then, cl_I and cl_O are identical to I and O in the example that follows...

Answer 80 · 2021-06-21T18:05:00.000Z

Changed commit from c36e43b to c540d35

Answer 81 · 2021-06-21T18:05:00.000Z

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

`c540d35`	`ManifoldSubsetPullback: Fix up some doctests with closed intervals`

Answer 82 · 2021-06-21T18:05:37.000Z

comment:52

Thanks for spotting this - I have fixed this and a similar example

Answer 83 · 2021-06-21T18:06:12.000Z

comment:53

Replying to @egourgoulhon:

In the docstring of ManifoldSubsetPullback:

in the INPUT section, there seems to be no entry for ConvexSet_base in the documentation

You may need to run ./sage -docbuild reference/discrete_geometry html

Answer 84 · 2021-06-21T20:02:31.000Z

comment:54

Replying to @mkoeppe:

Replying to @egourgoulhon:

In the docstring of ManifoldSubsetPullback:

in the INPUT section, there seems to be no entry for ConvexSet_base in the documentation

You may need to run ./sage -docbuild reference/discrete_geometry html

Yes indeed!

Answer 85 · 2021-06-21T20:50:04.000Z

comment:55

Replying to @mkoeppe:

Thanks for spotting this - I have fixed this and a similar example

Thanks.

At the moment, we have

sage: M = Manifold(2, 'M')                                                                          
sage: X.<x,y> = M.chart()                                                                           
sage: M.identity_map().preimage(M)                                                                  
Subset Id_M_inv_M of the 2-dimensional differentiable manifold M
sage: M.identity_map().preimage(M) is M                                                             
False
sage: M.zero_scalar_field().preimage(RealSet.point(0))                                              
Subset zero_inv_{0} of the 2-dimensional differentiable manifold M
sage: M.zero_scalar_field().preimage(RealSet.point(0)) is M                                         
False

Do you think it would be easy to have both answers to be True? If no, this should not hamper the current ticket, but be differed to another ticket.

Answer 86 · 2021-06-21T21:10:09.000Z

Changed commit from c540d35 to facad97

Answer 87 · 2021-06-21T21:10:09.000Z

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

`facad97`	`ContinuousMap.preimage: Handle identity_map specially`

Answer 88 · 2021-06-21T21:11:00.000Z

comment:57

Sure, that's easy to do and certainly a good idea. Here it is for ContinuousMap.preimage already, I'll look into the case of the scalar fields

Answer 89 · 2021-06-21T21:20:23.000Z

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

`c2ecf3e`	`ScalarField.preimage: Handle the case of the zero scalar field`

Answer 90 · 2021-06-21T21:20:23.000Z

Changed commit from facad97 to c2ecf3e

Answer 91 · 2021-06-21T21:24:07.000Z

comment:59

More general things such as detecting that the preimage of [0,oo) under squaring is the full domain will have to wait until a follow-up ticket

Answer 92 · 2021-06-22T04:27:46.000Z

comment:60

Replying to @mkoeppe:

Sure, that's easy to do and certainly a good idea. Here it is for ContinuousMap.preimage already,

Thanks. Maybe one can add

if self._is_isomorphism and codomain_subset == self._codomain:
    return self._domain

Answer 93 · 2021-06-22T04:37:09.000Z

comment:61

The patchbot reports a doctest error in src/sage/geometry/polyhedron/base.py as well as pyflakes errors in src/sage/manifolds/subsets/pullback.py.

Answer 94 · 2021-06-22T04:49:47.000Z

comment:62

Replying to @egourgoulhon:

Maybe one can add

if self._is_isomorphism and codomain_subset == self._codomain:
    return self._domain

I think I can do more generally

  if self._codomain.is_subset(codomain_subset):
      return self._domain

Answer 95 · 2021-06-22T04:59:44.000Z

comment:63

Replying to @egourgoulhon:

The patchbot reports a doctest error in src/sage/geometry/polyhedron/base.py

I've seen this one before locally, I don't think it's coming from this ticket, but I have opened #32030 for it

Answer 96 · 2021-06-22T05:22:49.000Z

Changed commit from c2ecf3e to 3b1c428

Answer 97 · 2021-06-22T05:22:49.000Z

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

`3b1c428`	`ManifoldSubsetPullback: Make codomain_subset required 2nd init arg; fix pycodestyle/pyflakes warnings`

Answer 98 · 2021-06-22T08:46:15.000Z

comment:65

Replying to @mkoeppe:

Replying to @egourgoulhon:

Maybe one can add

if self._is_isomorphism and codomain_subset == self._codomain:
    return self._domain

I think I can do more generally

  if self._codomain.is_subset(codomain_subset):
      return self._domain

Yes, indeed! Being an isomorphism is not necessary in that case.

Answer 99 · 2021-06-22T16:17:29.000Z

Changed commit from 3b1c428 to d321b93

Answer 100 · 2021-06-22T16:17:29.000Z

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`