gh-36903: ruff UP details and links to errors in doc in geometry folder
    
This is fixing a few ruff details (code UP) and adding some links to
errors in the doc, in the `geometry` folder.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36903
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/geometry/cone.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Convex rational polyhedral cones
 
@@ -554,7 +553,7 @@ def _ambient_space_point(body, data):
 
     An integral, rational, real algebraic, or numeric point of the
     ambient space of ``body`` is returned if ``data`` were
-    successfully interpreted in such a way. A ``TypeError`` is raised
+    successfully interpreted in such a way. A :class:`TypeError` is raised
     otherwise.
 
     TESTS::
@@ -1664,7 +1663,7 @@ def _contains(self, point, region='whole cone'):
         otherwise, in particular when ``point`` is incompatible with
         the ambient space.
 
-        A ``ValueError`` is raised if ``region`` is not one of the
+        A :class:`ValueError` is raised if ``region`` is not one of the
         three allowed values.
 
         TESTS::
@@ -2340,8 +2339,8 @@ def embed(self, cone):
         or
         :meth:`~sage.geometry.cone.ConvexRationalPolyhedralCone.facet_of`. The
         cone returned by this method will have ``self`` as ambient. If ``cone``
-        does not represent a valid cone of ``self``, ``ValueError`` exception
-        is raised.
+        does not represent a valid cone of ``self``, :class:`ValueError`
+        exception is raised.
 
         .. NOTE::
 
@@ -3017,8 +3016,8 @@ def intersection(self, other):
 
         - :class:`cone <ConvexRationalPolyhedralCone>`.
 
-        Raises ``ValueError`` if the ambient space dimensions are not
-        compatible.
+        This raises :class:`ValueError` if the ambient space dimensions
+        are not compatible.
 
         EXAMPLES::
 
@@ -5349,7 +5348,7 @@ def random_element(self, ring=ZZ):
         Either a lattice element or vector contained in both this cone
         and its ambient vector space. If ``ring`` is ``ZZ``, a lattice
         element is returned; otherwise a vector is returned. If ``ring``
-        is neither ``ZZ`` nor ``QQ``, then a ``NotImplementedError`` is
+        is neither ``ZZ`` nor ``QQ``, then a :class:`NotImplementedError` is
         raised.
 
         EXAMPLES:
@@ -6267,7 +6266,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
 
     A new, randomly generated cone.
 
-    A ``ValueError`` will be thrown under the following conditions:
+    A :class:`ValueError` will be thrown under the following conditions:
 
     * Any of ``min_ambient_dim``, ``max_ambient_dim``, ``min_rays``, or
       ``max_rays`` are negative.
@@ -6425,7 +6424,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
         provided.
 
     If the user requests too many rays in zero, one, or two dimensions,
-    a ``ValueError`` is thrown::
+    a :class:`ValueError` is thrown::
 
         sage: random_cone(max_ambient_dim=0, min_rays=1)
         Traceback (most recent call last):
@@ -6513,7 +6512,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
         sage: random_cone(lattice=L, strictly_convex=True)
         0-d cone in 0-d lattice L
 
-    A ``ValueError`` is thrown if a non-solid cone is requested in a
+    A :class:`ValueError` is thrown if a non-solid cone is requested in a
     zero-dimensional lattice::
 
         sage: L = ToricLattice(0)
@@ -6527,7 +6526,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
         ...
         ValueError: all cones are solid when max_ambient_dim is zero.
 
-    A ``ValueError`` is thrown if a solid cone is requested but the
+    A :class:`ValueError` is thrown if a solid cone is requested but the
     maximum number of rays is too few::
 
         sage: random_cone(min_ambient_dim=4, max_rays=3, solid=True)
@@ -6542,7 +6541,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
         ValueError: max_rays must be at least 5 for a solid cone in this
         lattice.
 
-    A ``ValueError`` is thrown if a non-solid cone is requested but
+    A :class:`ValueError` is thrown if a non-solid cone is requested but
     ``min_rays`` guarantees a solid cone::
 
         sage: random_cone(max_ambient_dim=4, min_rays=10, solid=False)

src/sage/geometry/fan.py

@@ -1956,7 +1956,7 @@ def cone_containing(self, *points):
 
             We think of the origin as of the smallest cone containing no rays
             at all. If there is no ray in ``self`` that contains all ``rays``,
-            a ``ValueError`` exception will be raised.
+            a :class:`ValueError` exception will be raised.
 
         EXAMPLES::
 
@@ -2352,8 +2352,8 @@ def embed(self, cone):
         or
         :meth:`~sage.geometry.cone.ConvexRationalPolyhedralCone.facet_of`. The
         cone returned by this method will have ``self`` as ambient. If ``cone``
-        does not represent a valid cone of ``self``, ``ValueError`` exception
-        is raised.
+        does not represent a valid cone of ``self``, :class:`ValueError`
+        exception is raised.
 
         .. NOTE::
 
@@ -3504,8 +3504,8 @@ def complex(self, base_ring=ZZ, extended=False):
         OUTPUT:
 
         The complex associated to the fan as a :class:`ChainComplex
-        <sage.homology.chain_complex.ChainComplex>`. Raises a
-        ``ValueError`` if the extended complex is requested for a
+        <sage.homology.chain_complex.ChainComplex>`. This raises a
+        :class:`ValueError` if the extended complex is requested for a
         non-complete fan.
 
         EXAMPLES::

src/sage/geometry/fan_morphism.py

@@ -520,8 +520,8 @@ def _ray_index_map(self):
           domain fan is mapped to the origin. If it is `j`, then the `i`-th ray
           of the domain fan is mapped onto the `j`-th ray of the codomain fan.
           If there is a ray in the domain fan which is mapped into the relative
-          interior of a higher dimensional cone, a ``ValueError`` exception is
-          raised.
+          interior of a higher dimensional cone, a :class:`ValueError`
+          exception is raised.
 
         .. NOTE::
 
@@ -601,8 +601,8 @@ def _subdivide_domain_fan(self, check, verbose):
         OUTPUT:
 
         - none, but the domain fan of self is replaced with its minimal
-          refinement, if possible. Otherwise a ``ValueError`` exception is
-          raised.
+          refinement, if possible. Otherwise a :class:`ValueError`
+          exception is raised.
 
         TESTS::
 
@@ -763,11 +763,11 @@ def _subdivide_domain_fan(self, check, verbose):
 
     def _support_error(self):
         r"""
-        Raise a ``ValueError`` exception due to support incompatibility.
+        Raise a :class:`ValueError` exception due to support incompatibility.
 
         OUTPUT:
 
-        - none, a ``ValueError`` exception is raised.
+        - none, a :class:`ValueError` exception is raised.
 
         TESTS:
 
@@ -806,10 +806,10 @@ def _validate(self):
 
         OUTPUT:
 
-        - none, but a ``ValueError`` exception is raised if there is a cone of
-          the domain fan of ``self`` which is not completely contained in a
-          single cone of the codomain fan of ``self``, or if one of these fans
-          does not sit in the appropriate lattice.
+        - none, but a :class:`ValueError` exception is raised if there is
+          a cone of the domain fan of ``self`` which is not completely
+          contained in a single cone of the codomain fan of ``self``,
+          or if one of these fans does not sit in the appropriate lattice.
 
         EXAMPLES::
 

src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 """
 Coercion Maps Between Hyperbolic Plane Models
 
@@ -82,7 +81,7 @@ def _call_(self, x):
         """
         C = self.codomain()
         if not C.is_bounded() and self.domain().is_bounded() and x.is_boundary():
-            msg = u"boundary points are not implemented for the {}"
+            msg = "boundary points are not implemented for the {}"
             raise NotImplementedError(msg.format(C.name()))
 
         y = self.image_coordinates(x.coordinates())

src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Hyperbolic Geodesics
 
@@ -622,7 +621,7 @@ def is_parallel(self, other):
     def ideal_endpoints(self):
         r"""
         Return the ideal endpoints in bounded models.  Raise a
-        ``NotImplementedError`` in models that are not bounded.
+        :class:`NotImplementedError` in models that are not bounded.
 
         EXAMPLES::
 
@@ -660,7 +659,7 @@ def ideal_endpoints(self):
     def complete(self):
         r"""
         Return the geodesic with ideal endpoints in bounded models.  Raise a
-        ``NotImplementedError`` in models that are not bounded.
+        :class:`NotImplementedError` in models that are not bounded.
         In the following examples we represent complete geodesics by a dashed
         line.
 
@@ -817,7 +816,7 @@ def common_perpendicula(self, other):
         r"""
         Return the unique hyperbolic geodesic perpendicular to two given
         geodesics, if such a geodesic exists.  If none exists, raise a
-        ``ValueError``.
+        :class:`ValueError`.
 
         INPUT:
 
@@ -1278,7 +1277,7 @@ def common_perpendicular(self, other):
         r"""
         Return the unique hyperbolic geodesic perpendicular to ``self``
         and ``other``, if such a geodesic exists; otherwise raise a
-        ``ValueError``.
+        :class:`ValueError`.
 
         INPUT:
 

src/sage/geometry/hyperbolic_space/hyperbolic_interface.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Interface to Hyperbolic Models
 

src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Hyperbolic Isometries
 
@@ -489,7 +488,7 @@ def classification(self):
     def translation_length(self):
         r"""
         For hyperbolic elements, return the translation length;
-        otherwise, raise a ``ValueError``.
+        otherwise, raise a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -512,7 +511,7 @@ def translation_length(self):
     def axis(self):
         r"""
         For a hyperbolic isometry, return the axis of the
-        transformation; otherwise raise a ``ValueError``.
+        transformation; otherwise raise a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -593,7 +592,7 @@ def fixed_geodesic(self):
     def repelling_fixed_point(self):
         r"""
         For a hyperbolic isometry, return the attracting fixed point;
-        otherwise raise a ``ValueError``.
+        otherwise raise a :class:`ValueError`.
 
         OUTPUT:
 
@@ -612,7 +611,7 @@ def repelling_fixed_point(self):
     def attracting_fixed_point(self):
         r"""
         For a hyperbolic isometry, return the attracting fixed point;
-        otherwise raise a `ValueError``.
+        otherwise raise a :class:`ValueError`.
 
         OUTPUT:
 
@@ -735,7 +734,7 @@ def classification(self): #UHP
     def translation_length(self): #UHP
         r"""
         For hyperbolic elements, return the translation length;
-        otherwise, raise a ``ValueError``.
+        otherwise, raise a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -843,9 +842,11 @@ def fixed_point_set(self):  # UHP
             return self.domain().get_geodesic(*pts)
         return pts
 
-    def repelling_fixed_point(self): #UHP
+    def repelling_fixed_point(self):  # UHP
         r"""
-        Return the repelling fixed point; otherwise raise a ``ValueError``.
+        Return the repelling fixed point.
+
+        Otherwise, this raises a :class:`ValueError`.
 
         OUTPUT:
 
@@ -867,9 +868,11 @@ def repelling_fixed_point(self): #UHP
             return self.domain().get_point(infinity)
         return self.domain().get_point(v[0] / v[1])
 
-    def attracting_fixed_point(self): #UHP
+    def attracting_fixed_point(self):  # UHP
         r"""
-        Return the attracting fixed point; otherwise raise a ``ValueError``.
+        Return the attracting fixed point.
+
+        Otherwise, this raises a :class:`ValueError`.
 
         OUTPUT:
 

src/sage/geometry/hyperbolic_space/hyperbolic_model.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Hyperbolic Models
 
@@ -156,7 +155,7 @@ def _repr_(self):  # Abstract
             sage: HyperbolicPlane().UHP()
             Hyperbolic plane in the Upper Half Plane Model
         """
-        return u'Hyperbolic plane in the {}'.format(self._name)
+        return 'Hyperbolic plane in the {}'.format(self._name)
 
     def _element_constructor_(self, x, is_boundary=None, **graphics_options):  # Abstract
         """
@@ -260,7 +259,7 @@ def point_in_model(self, p):
     def point_test(self, p):  # Abstract
         r"""
         Test whether a point is in the model.  If the point is in the
-        model, do nothing.  Otherwise, raise a ``ValueError``.
+        model, do nothing.  Otherwise, raise a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -298,7 +297,7 @@ def boundary_point_in_model(self, p):  # Abstract
     def bdry_point_test(self, p):  # Abstract
         r"""
         Test whether a point is in the model.  If the point is in the
-        model, do nothing; otherwise raise a ``ValueError``.
+        model, do nothing; otherwise raise a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -340,7 +339,7 @@ def isometry_test(self, A):  # Abstract
         Test whether an isometry ``A`` is in the model.
 
         If the isometry is in the model, do nothing. Otherwise, raise
-        a ``ValueError``.
+        a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -1173,7 +1172,7 @@ def __init__(self, space):
         # name should really be 'Poincaré Disk Model', but utf8 is not
         # accepted by repr
         HyperbolicModel.__init__(self, space,
-                                 name=u'Poincare Disk Model', short_name="PD",
+                                 name='Poincare Disk Model', short_name="PD",
                                  bounded=True, conformal=True, dimension=2,
                                  isometry_group="PU(1, 1)",
                                  isometry_group_is_projective=True)

src/sage/geometry/hyperbolic_space/hyperbolic_point.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Hyperbolic Points
 

src/sage/geometry/hyperplane_arrangement/arrangement.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Hyperplane Arrangements
 
@@ -2723,7 +2722,7 @@ def region_containing_point(self, p):
 
         OUTPUT:
 
-        A polyhedron. A ``ValueError`` is raised if the point is not
+        A polyhedron. A :class:`ValueError` is raised if the point is not
         interior to a region, that is, sits on a hyperplane.
 
         EXAMPLES::