Trac #34160: Fix docstring markup in sage/schemes

Part of #34157:
{{{
sage/schemes/cyclic_covers/cycliccover_finite_field.py:857:1: RST202
Bullet list ends without a blank line; unexpected unindent.
sage/schemes/elliptic_curves/gal_reps_number_field.py:574:1: RST214
Inline literal start-string without end-string.
sage/schemes/elliptic_curves/period_lattice.py:144:1: RST202 Bullet list
ends without a blank line; unexpected unindent.
sage/schemes/elliptic_curves/period_lattice.py:147:1: RST202 Bullet list
ends without a blank line; unexpected unindent.
sage/schemes/elliptic_curves/ell_number_field.py:737:1: RST219 Inline
substitution_reference start-string without end-string.
sage/schemes/elliptic_curves/ell_rational_field.py:6422:1: RST301
Unexpected indentation.
sage/schemes/elliptic_curves/padics.py:1660:1: RST215 Inline interpreted
text or phrase reference start-string without end-string.
sage/schemes/elliptic_curves/padics.py:1665:1: RST301 Unexpected
indentation.
sage/schemes/elliptic_curves/padics.py:1666:1: RST201 Block quote ends
without a blank line; unexpected unindent.
sage/schemes/elliptic_curves/isogeny_class.py:99:1: RST215 Inline
interpreted text or phrase reference start-string without end-string.
sage/schemes/riemann_surfaces/riemann_surface.py:1560:1: RST301
Unexpected indentation.
sage/schemes/curves/zariski_vankampen.py:734:1: RST202 Bullet list ends
without a blank line; unexpected unindent.
}}}

URL: https://trac.sagemath.org/34160
Reported by: klee
Ticket author(s): Frédéric Chapoton
Reviewer(s): Kwankyu Lee, Matthias Koeppe

src/sage/schemes/curves/zariski_vankampen.py

@@ -732,7 +732,7 @@ def geometric_basis(G, E, p):
     - ``G`` -- the graph of the bounded regions of a Voronoi Diagram
 
     - ``E`` -- the subgraph of ``G`` formed by the edges that touch an unbounded
-    region
+      region
 
     - ``p`` -- a vertex of ``E``
 

src/sage/schemes/cyclic_covers/cycliccover_finite_field.py

@@ -855,7 +855,7 @@ def _reduce_vector_vertical_plain(G, s0, s, k=1):
             OUTPUT:
 
             - a vector -- `H \in W_{-1, r*(s - k) + s0}` such that
-            `G y^{-(r*s + s0)} dx \cong H y^{-(r*(s -k) + s0)} dx`
+              `G y^{-(r*s + s0)} dx \cong H y^{-(r*(s -k) + s0)} dx`
             """
             if self._verbose > 2:
                 print(

src/sage/schemes/elliptic_curves/ell_number_field.py

@@ -737,7 +737,7 @@ def _scale_by_units(self):
 
         A model for this elliptic curve, optimally scaled with respect
         to scaling by units, with respect to the logarithmic embedding
-        of |c4|^(1/4)+|c6|^(1/6).  No scaling by roots of unity is
+        of `|c4|^(1/4)+|c6|^(1/6)`. No scaling by roots of unity is
         carried out, so there is no change when the unit rank is 0.
 
         EXAMPLES::

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -6417,10 +6417,12 @@ def S_integral_points_with_bounded_mw_coeffs():
             Return the set of S-integers x which are x-coordinates of
             points on the curve which are linear combinations of the
             generators (basis and torsion points) with coefficients
-            bounded by `H_q`.  The bound `H_q` will be computed at
-            runtime.
+            bounded by `H_q`.
+
+            The bound `H_q` will be computed at runtime.
+
             (Modified version of integral_points_with_bounded_mw_coeffs() in
-             integral_points() )
+            integral_points())
 
             .. TODO::
 

src/sage/schemes/elliptic_curves/gal_reps_number_field.py

@@ -570,11 +570,14 @@ def primes_iter():
         L = [2] + L
     return L
 
+
 def _exceptionals(E, L, patience=1000):
     r"""
-    Determine which primes in L are exceptional for E, using Proposition 19
-    of Section 2.8 of Serre's ``Propriétés Galoisiennes des Points d'Ordre
-    Fini des Courbes Elliptiques'' [Ser1972]_.
+    Determine which primes in L are exceptional for E.
+
+    This is done using Proposition 19 of Section 2.8 of Serre's
+    *Propriétés Galoisiennes des Points d'Ordre Fini des Courbes Elliptiques*
+    [Ser1972]_.
 
     INPUT:
 

src/sage/schemes/elliptic_curves/isogeny_class.py

@@ -97,7 +97,7 @@ def __iter__(self):
 
     def __getitem__(self, i):
         """
-        Return the `i`th curve in the class.
+        Return the `i`-th curve in the class.
 
         EXAMPLES::
 

src/sage/schemes/elliptic_curves/padics.py

@@ -1646,24 +1646,22 @@ def matrix_of_frobenius(self, p, prec=20, check=False, check_hypotheses=True, al
 
     return frob_p.change_ring(Zp(p, prec))
 
+
 def _brent(F, p, N):
     r"""
     This is an internal function; it is used by padic_sigma().
 
-    `F` is a assumed to be a power series over
-    `R = \ZZ/p^{N-1}\ZZ`.
+    `F` is a assumed to be a power series over `R = \ZZ/p^{N-1}\ZZ`.
 
     It solves the differential equation `G'(t)/G(t) = F(t)`
     using Brent's algorithm, with initial condition `G(0) = 1`.
-    It is assumed that the solution `G` has
-    `p`-integral coefficients.
+    It is assumed that the solution `G` has `p`-integral coefficients.
 
     More precisely, suppose that `f(t)` is a power series with
     genuine `p`-adic coefficients, and suppose that
     `g(t)` is an exact solution to `g'(t)/g(t) = f(t)`.
     Let `I` be the ideal
-    `(p^N, p^{N-1} t, \ldots,
-        p t^{N-1}, t^N)`. The input
+    `(p^N, p^{N-1} t, \ldots, p t^{N-1}, t^N)`. The input
     `F(t)` should be a finite-precision approximation to
     `f(t)`, in the sense that `\int (F - f) dt` should
     lie in `I`. Then the function returns a series
@@ -1673,8 +1671,7 @@ def _brent(F, p, N):
     some log-log factors.
 
     For more information, and a proof of the precision guarantees, see
-    Lemma 4 in "Efficient Computation of p-adic Heights" (David
-    Harvey).
+    Lemma 4 in "Efficient Computation of p-adic Heights" (David Harvey).
 
     AUTHORS:
 

src/sage/schemes/elliptic_curves/period_lattice.py

@@ -142,10 +142,10 @@ def __init__(self, E, embedding=None):
           - use the built-in coercion to `\RR` for `K=\QQ`;
 
           - use the first embedding into `\RR` given by
-          ``K.embeddings(RealField())``, if there are any;
+            ``K.embeddings(RealField())``, if there are any;
 
           - use the first embedding into `\CC` given by
-          ``K.embeddings(ComplexField())``, if `K` is totally complex.
+            ``K.embeddings(ComplexField())``, if `K` is totally complex.
 
         .. NOTE::