gh-36136: `sage.combinat.root_system`: Modularization fixes, `# needs`
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Most of the package `sage.combinat.root_system` is intended to be
shipped by the distribution **sagemath-modules**, and much of the
functionality can be tested in the modularized setting.
- Some functionality depends on other distributions, in particular
**sagemath-graphs** (via Dynkin diagrams). The doctests are marked as `#
needs sage.graphs`.
- Other doctests that depend on combinatorics functionality such as
Tableaux are marked `# needs sage.combinat`.
- Use of Weyl and Coxeter groups is marked `# needs sage.libs.gap`, `#
needs sage.rings.number_field`, `# needs sage.symbolic`, or `# needs
sage.groups`.
- Some imports are changed to `lazy_import`; in some places, the changed
code uses the fact that `isinstance(x, cls)` gives False for unresolved
lazy import `cls`.
- Some `_test_...` and `some_elements` methods are changed so that
`ImportError`s do not lead to test failures.
- The hardcoded dependence of `CartanMatrix` on `Matrix_integer_sparse`
(which has complicated compile-time dependencies) is relaxed.
- doctest cosmetics: Breaking long lines in doctest input and output so
that it can be read in the HTML documentation without (or with less)
horizontal scrolling
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- Part of: #29705
- Cherry-picked from: #35095
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- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.
### :hourglass: Dependencies
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URL: https://github.com/sagemath/sage/pull/36136
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe
