Trac #20196: some doc corrections in rings and schemes

various minor doc corrections, such as using trac roles, correct rest
formatting, correct sentences

URL: http://trac.sagemath.org/20196
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

src/sage/rings/number_field/number_field.py

@@ -854,7 +854,7 @@ def QuadraticField(D, name='a', check=True, embedding=True, latex_name='sqrt', *
         sage: latex(QuadraticField(-1, 'a', latex_name=None).gen())
         a
 
-    The name of the generator does not interfere with Sage preparser, see #1135::
+    The name of the generator does not interfere with Sage preparser, see :trac:`1135`::
 
         sage: K1 = QuadraticField(5, 'x')
         sage: K2.<x> = QuadraticField(5)

src/sage/rings/number_field/number_field_rel.py

@@ -1242,7 +1242,7 @@ def is_galois_relative(self):
             sage: M.is_galois_relative()
             False
 
-        The following example previously gave the wrong result; see #9390::
+        The next example previously gave a wrong result; see :trac:`9390`::
 
             sage: F.<a, b> = NumberField([x^2 - 2, x^2 - 3])
             sage: F.is_galois_relative()

src/sage/rings/polynomial/laurent_polynomial_ring.py

@@ -483,7 +483,7 @@ def is_integral_domain(self, proof = True):
             sage: LaurentPolynomialRing(QQ,2,'x').is_integral_domain()
             True
 
-        The following used to fail; see #7530::
+        The following used to fail; see :trac:`7530`::
 
             sage: L = LaurentPolynomialRing(ZZ, 'X')
             sage: L['Y']

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -1971,12 +1971,12 @@ def transformed_basis(self, algorithm="gwalk", other_ring=None, singular=singula
     @libsingular_gb_standard_options
     def elimination_ideal(self, variables):
         r"""
-        Returns the elimination ideal this ideal with respect to the
+        Return the elimination ideal of this ideal with respect to the
         variables given in ``variables``.
 
         INPUT:
 
-        - ``variables`` - a list or tuple of variables in ``self.ring()``
+        - ``variables`` -- a list or tuple of variables in ``self.ring()``
 
         EXAMPLE::
 

src/sage/schemes/elliptic_curves/constructor.py

@@ -218,7 +218,7 @@ class EllipticCurveFactory(UniqueFactory):
         Elliptic Curve defined by y^2 = x^3 + x + 1 over Multivariate Polynomial Ring in u, v
         over Integer Ring
 
-    We create a curve and a point over QQbar (see #6879)::
+    We create a curve and a point over ``QQbar`` (see :trac:`6879`)::
 
         sage: E = EllipticCurve(QQbar,[0,1])
         sage: E(0)
@@ -358,7 +358,7 @@ def create_key_and_extra_args(self, x=None, y=None, j=None, minimal_twist=True,
         same base ring and Weierstrass equation; the data in
         ``extra_args`` do not influence comparison of elliptic curves.
         A consequence of this is that passing keyword arguments only
-        works when constructing an elliptic curve the first time:
+        works when constructing an elliptic curve the first time::
 
             sage: E = EllipticCurve('433a1', gens=[[-1, 1], [3, 4]])
             sage: E.gens()

src/sage/schemes/elliptic_curves/period_lattice.py

@@ -1557,7 +1557,9 @@ def elliptic_logarithm(self, P, prec=None, reduce=True):
             sage: L.coordinates(L.elliptic_logarithm(E(e3,0)))
             (0.500000000000000, 0.000000000000000)
 
-        TESTS (see #10026 and #11767)::
+        TESTS:
+
+        (see :trac:`10026` and :trac:`11767`)::
 
             sage: K.<w> = QuadraticField(2)
             sage: E = EllipticCurve([ 0, -1, 1, -3*w -4, 3*w + 4 ])
@@ -1708,7 +1710,7 @@ def elliptic_exponential(self, z, to_curve=True):
             sage: P.parent()
             Abelian group of points on Elliptic Curve defined by y^2 + 1.00000000000000*y = x^3 + (-1.00000000000000)*x over Complex Field with 53 bits of precision
 
-        Very small `z` are handled properly (see #8820)::
+        Very small `z` are handled properly (see :trac:`8820`)::
 
             sage: K.<a> = QuadraticField(-1)
             sage: E = EllipticCurve([0,0,0,a,0])