src/sage/geometry/polyhedron: Fix typos, reformat doctests

src/sage/geometry/polyhedron/backend_field.py

@@ -182,7 +182,7 @@ def _init_from_Vrepresentation(self, vertices, rays, lines,
           verbose output for debugging purposes.
 
         - ``internal_base_ring`` -- the base ring of the generators' components.
-          Defualt is ``None``, in which case, it is set to
+          Default is ``None``, in which case, it is set to
           :meth:`~sage.geometry.polyhedron.base.base_ring`.
 
         EXAMPLES::
@@ -218,7 +218,7 @@ def _init_from_Hrepresentation(self, ieqs, eqns,
           verbose output for debugging purposes.
 
         - ``internal_base_ring`` -- the base ring of the generators' components.
-          Defualt is ``None``, in which case, it is set to
+          Default is ``None``, in which case, it is set to
           :meth:`~sage.geometry.polyhedron.base.base_ring`.
 
         TESTS::

src/sage/geometry/polyhedron/backend_number_field.py

@@ -41,24 +41,31 @@ class Polyhedron_number_field(Polyhedron_field, Polyhedron_base_number_field):
 
         sage: P = Polyhedron(vertices=[[1], [sqrt(2)]], backend='number_field')    # optional - sage.rings.number_field
         sage: P                                                                    # optional - sage.rings.number_field
-        A 1-dimensional polyhedron in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
+        A 1-dimensional polyhedron
+         in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
         sage: P.vertices()                                                         # optional - sage.rings.number_field
         (A vertex at (1), A vertex at (sqrt(2)))
 
         sage: P = polytopes.icosahedron(exact=True, backend='number_field')        # optional - sage.rings.number_field
         sage: P                                                                    # optional - sage.rings.number_field
-        A 3-dimensional polyhedron in (Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?)^3 defined as the convex hull of 12 vertices
-
-        sage: x = polygen(ZZ); P = Polyhedron(vertices=[[sqrt(2)], [AA.polynomial_root(x^3-2, RIF(0,3))]], backend='number_field')    # optional - sage.rings.number_field
+        A 3-dimensional polyhedron
+         in (Number Field in sqrt5 with defining polynomial x^2 - 5
+             with sqrt5 = 2.236067977499790?)^3
+         defined as the convex hull of 12 vertices
+
+        sage: x = polygen(ZZ); P = Polyhedron(                                     # optional - sage.rings.number_field
+        ....:     vertices=[[sqrt(2)], [AA.polynomial_root(x^3-2, RIF(0,3))]],
+        ....:     backend='number_field')
         sage: P                                                                    # optional - sage.rings.number_field
-        A 1-dimensional polyhedron in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
+        A 1-dimensional polyhedron
+         in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
         sage: P.vertices()                                                         # optional - sage.rings.number_field
         (A vertex at (sqrt(2)), A vertex at (2^(1/3)))
 
-
     TESTS:
 
-    Tests from backend_field -- here the data are already either in a number field or in AA.
+    Tests from :class:`~sage.geometry.polyhedron.backend_field.Polyhedron_field` --
+    here the data are already either in a number field or in ``AA``.
 
         sage: p = Polyhedron(vertices=[(0,0),(AA(2).sqrt(),0),(0,AA(3).sqrt())],            # optional - sage.rings.number_field
         ....:                rays=[(1,1)], lines=[], backend='number_field', base_ring=AA)
@@ -68,15 +75,13 @@ class Polyhedron_number_field(Polyhedron_field, Polyhedron_base_number_field):
         sage: p = Polyhedron([(0,0), (1,0), (1/2, sqrt3/2)], backend='number_field')        # optional - sage.rings.number_field
         sage: TestSuite(p).run()                                                            # optional - sage.rings.number_field
 
-    Check that :trac:`19013` is fixed::
-
         sage: K.<phi> = NumberField(x^2-x-1, embedding=1.618)                               # optional - sage.rings.number_field
         sage: P1 = Polyhedron([[0,1], [1,1], [1,-phi+1]], backend='number_field')           # optional - sage.rings.number_field
         sage: P2 = Polyhedron(ieqs=[[-1,-phi,0]], backend='number_field')                   # optional - sage.rings.number_field
         sage: P1.intersection(P2)                                                           # optional - sage.rings.number_field
-        The empty polyhedron in (Number Field in phi with defining polynomial x^2 - x - 1 with phi = 1.618033988749895?)^2
-
-    Check that :trac:`28654` is fixed::
+        The empty polyhedron
+         in (Number Field in phi with defining polynomial x^2 - x - 1
+             with phi = 1.618033988749895?)^2
 
         sage: Polyhedron(lines=[[1]], backend='number_field')
         A 1-dimensional polyhedron in QQ^1 defined as the convex hull of 1 vertex and 1 line