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As preparation for compiling with meson, we replace relative imports by
absolute ones.
Relative imports are not used consistently in the codebase and result in
issues for doctesting with pytest (which admittedly is a limitation of
pytest). We normalize the relative imports in `sage.rings` to be
absolute imports. Small code-style improvements along the way (mainly to
nicely order the imports)

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- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: sagemath#36588
Reported by: Tobias Diez
Reviewer(s): Dima Pasechnik

…{algebras,arith,categories,cpython,data_structures,misc,modular,rings,sat,symbolic}`

    
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<!-- Describe your changes here in detail -->

<!-- Why is this change required? What problem does it solve? -->
Final chunk of the cherry-pick from sagemath#35095 for sagemath#36228, see also
sagemath#36572 (comment)

This PR overlaps with sagemath#36572, sagemath#36588, sagemath#36589, but it does not touch
`.all*` files (no changes there are needed for sagemath#36228), thus avoiding
conflicts with sagemath#35095 (see also
sagemath#36524 (comment))
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- [ ] The description explains in detail what this PR is about.
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- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: sagemath#36666
Reported by: Matthias Köppe
Reviewer(s): David Coudert, John H. Palmieri

…e relative by absolute imports

    
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calculate 1+1"
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<!-- Describe your changes here in detail -->
We restructure the `all.py` files for modularization.

Guided by the technical constraints outlined in
https://groups.google.com/g/sage-devel/c/ozh-7ZZ848s, sagemath#35095 defines
distribution packages (pip-installable packages) **sagemath-{brial,
combinat, eclib, flint, gap, giac, glpk, graphs, groups, homfly, lcalc,
libbraiding, libecm, linbox, modules, mpmath, ntl, pari, plot,
polyhedra, schemes, singular, standard-no-symbolics, symbolics}**.

When a namespace package such as `sage.misc` is filled by modules from
several distribution packages, we create modules named:
- `src/sage/misc/all__sagemath_environment.py`
- `src/sage/misc/all__sagemath_objects.py`
- `src/sage/misc/all__sagemath_repl.py`

Import statements are moved from `src/sage/misc/all.py` to these files
as appropriate, and `src/sage/misc/all.py` imports `*` from there.

Also some imports are replaced by lazy imports.

The new files provide the top level namespaces for the modularized
distribution packages, thus [enabling modularized testing](https://doc.s
agemath.org/html/en/developer/packaging_sage_library.html#testing-
distribution-packages).

This design was introduced in sagemath#29865 (merged in Jan 2022, early in the
Sage 9.6 development cycle).

<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
- Copied from sagemath#35095.
- Part of sagemath#29705

Moreover, applied a one-line command to replace relative by absolute
imports, thus complementing sagemath#36666, which does not touch `.all*` files.

The changes to other files in `sage.modules` etc. come from the PRs
sagemath#36597, sagemath#36572, sagemath#36588, sagemath#36589 merged here and do not need review.

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appropriately. -->

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- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
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- Depends on sagemath#36597 (merged here to resolve merge conflict)
- Depends on sagemath#36572 (merged here to
resolve merge conflict)
- Depends on sagemath#36588 (merged here to
resolve merge conflict)
- Depends on sagemath#36589 (merged here to
resolve merge conflict)
- Depends on sagemath#36449 (merged here to resolve merge conflict)

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URL: sagemath#36676
Reported by: Matthias Köppe
Reviewer(s): David Coudert, John H. Palmieri, Matthias Köppe, Tobias Diez

…e relative by absolute imports

    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes sagemath#1234" use "Introduce new method to
calculate 1+1"
-->
<!-- Describe your changes here in detail -->
We restructure the `all.py` files for modularization.

Guided by the technical constraints outlined in
https://groups.google.com/g/sage-devel/c/ozh-7ZZ848s, sagemath#35095 defines
distribution packages (pip-installable packages) **sagemath-{brial,
combinat, eclib, flint, gap, giac, glpk, graphs, groups, homfly, lcalc,
libbraiding, libecm, linbox, modules, mpmath, ntl, pari, plot,
polyhedra, schemes, singular, standard-no-symbolics, symbolics}**.

When a namespace package such as `sage.misc` is filled by modules from
several distribution packages, we create modules named:
- `src/sage/misc/all__sagemath_environment.py`
- `src/sage/misc/all__sagemath_objects.py`
- `src/sage/misc/all__sagemath_repl.py`

Import statements are moved from `src/sage/misc/all.py` to these files
as appropriate, and `src/sage/misc/all.py` imports `*` from there.

Also some imports are replaced by lazy imports.

The new files provide the top level namespaces for the modularized
distribution packages, thus [enabling modularized testing](https://doc.s
agemath.org/html/en/developer/packaging_sage_library.html#testing-
distribution-packages).

This design was introduced in sagemath#29865 (merged in Jan 2022, early in the
Sage 9.6 development cycle).

<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
- Copied from sagemath#35095.
- Part of sagemath#29705

Moreover, applied a one-line command to replace relative by absolute
imports, thus complementing sagemath#36666, which does not touch `.all*` files.

The changes to other files in `sage.modules` etc. come from the PRs
sagemath#36597, sagemath#36572, sagemath#36588, sagemath#36589 merged here and do not need review.

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appropriately. -->

### 📝 Checklist

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appropriately -->
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here to help! -->
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- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
-->
- Depends on sagemath#36597 (merged here to resolve merge conflict)
- Depends on sagemath#36572 (merged here to
resolve merge conflict)
- Depends on sagemath#36588 (merged here to
resolve merge conflict)
- Depends on sagemath#36589 (merged here to
resolve merge conflict)
- Depends on sagemath#36449 (merged here to resolve merge conflict)

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URL: sagemath#36676
Reported by: Matthias Köppe
Reviewer(s): David Coudert, John H. Palmieri, Kwankyu Lee, Matthias Köppe, Tobias Diez