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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appropriately. -->

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- [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

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URL: #36136
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe

Author: Release Manager

src/sage/combinat/root_system/ambient_space.py

@@ -117,9 +117,13 @@ def _test_norm_of_simple_roots(self, **options):
         """
         tester = self._tester(**options)
         T = self.cartan_type()
-        D = T.symmetrizer()
-        alpha = self.simple_roots()
-        for C in T.dynkin_diagram().connected_components(sort=False):
+        try:
+            D = T.symmetrizer()
+            alpha = self.simple_roots()
+            DD = T.dynkin_diagram()
+        except ImportError:  # Dynkin diagrams need sage.graphs
+            return
+        for C in DD.connected_components(sort=False):
             tester.assertEqual(len( set( alpha[i].scalar(alpha[i]) / D[i] for i in C ) ), 1)
 
     # FIXME: attribute or method?

src/sage/combinat/root_system/associahedron.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.combinat sage.geometry.polyhedron
 r"""
 Associahedron
 

src/sage/combinat/root_system/braid_move_calculator.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.gap
 """
 Braid Move Calculator
 

src/sage/combinat/root_system/branching_rules.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.gap
 """
 Branching Rules
 """
@@ -54,7 +55,7 @@ def branch_weyl_character(chi, R, S, rule="default"):
       * ``"triality"``
       * ``"miscellaneous"``
 
-    The ``BranchingRule`` class is a wrapper for functions
+    The :class:`BranchingRule` class is a wrapper for functions
     from the weight lattice of `G` to the weight lattice of `H`.
     An instance of this class encodes an embedding of `H` into
     `G`. The usual way to specify an embedding is to supply a