sage.schemes: Some more cosmetic doctest changes

src/sage/schemes/affine/affine_space.py

@@ -619,13 +619,11 @@ def change_ring(self, R):
 
         - ``R`` -- commutative ring or morphism.
 
-        OUTPUT:
-
-        - affine space over ``R``.
+        OUTPUT: An affine space over ``R``.
 
         .. NOTE::
 
-            There is no need to have any relation between `R` and the base ring
+            There is no need to have any relation between ``R`` and the base ring
             of  this space, if you want to have such a relation, use
             ``self.base_extend(R)`` instead.
 
@@ -840,7 +838,7 @@ def subscheme(self, X, **kwds):
 
     def _an_element_(self):
         r"""
-        Return an element of this affine space,used both for illustration and
+        Return an element of this affine space, used both for illustration and
         testing purposes.
 
         OUTPUT: a point in the affine space
@@ -859,7 +857,7 @@ def _an_element_(self):
 
     def chebyshev_polynomial(self, n, kind='first', monic=False):
         """
-        Generates an endomorphism of this affine line by a Chebyshev polynomial.
+        Generate an endomorphism of this affine line by a Chebyshev polynomial.
 
         Chebyshev polynomials are a sequence of recursively defined orthogonal
         polynomials. Chebyshev of the first kind are defined as `T_0(x) = 1`,
@@ -1101,7 +1099,7 @@ def weil_restriction(self):
         the Weil restriction to the prime subfield.
 
         OUTPUT: Affine space of dimension ``d * self.dimension_relative()``
-                over the base field of ``self.base_ring()``.
+        over the base field of ``self.base_ring()``.
 
         EXAMPLES::
 

src/sage/schemes/generic/algebraic_scheme.py

@@ -1207,17 +1207,17 @@ def irreducible_components(self):
         `\P^4_{\QQ}` then find the irreducible components::
 
             sage: PP.<x,y,z,w,v> = ProjectiveSpace(4, QQ)
-            sage: V = PP.subscheme( (x^2 - y^2 - z^2)*(w^5 -  2*v^2*z^3)* w * (v^3 - x^2*z) )
+            sage: V = PP.subscheme((x^2 - y^2 - z^2) * (w^5 -  2*v^2*z^3) * w * (v^3 - x^2*z))
             sage: V.irreducible_components()
             [
             Closed subscheme of Projective Space of dimension 4 over Rational Field defined by:
-            w,
+              w,
             Closed subscheme of Projective Space of dimension 4 over Rational Field defined by:
-            x^2 - y^2 - z^2,
+              x^2 - y^2 - z^2,
             Closed subscheme of Projective Space of dimension 4 over Rational Field defined by:
-            x^2*z - v^3,
+              x^2*z - v^3,
             Closed subscheme of Projective Space of dimension 4 over Rational Field defined by:
-            w^5 - 2*z^3*v^2
+              w^5 - 2*z^3*v^2
             ]
 
         We verify that the irrelevant ideal is not accidentally returned
@@ -1454,7 +1454,7 @@ def union(self, other):
 
             sage: A.subscheme([x]) + A.subscheme([y^2 - (x^3+1)])
             Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-            x^4 - x*y^2 + x
+              x^4 - x*y^2 + x
 
         Saving and loading::
 
@@ -2037,7 +2037,7 @@ def specialization(self, D=None, phi=None):
 
         - ``D`` -- dictionary (optional)
 
-        - ``phi`` -- SpecializationMorphism (optional)
+        - ``phi`` -- :class:`SpecializationMorphism` (optional)
 
         OUTPUT: :class:`SchemeMorphism_polynomial`
 
@@ -2057,9 +2057,10 @@ def specialization(self, D=None, phi=None):
             sage: P.<x,y,z> = AffineSpace(S, 3)
             sage: X = P.subscheme([x^2 + a*c*y^2 - b*z^2])
             sage: from sage.rings.polynomial.flatten import SpecializationMorphism
-            sage: phi = SpecializationMorphism(P.coordinate_ring(),dict({c:2,a:1}))
+            sage: phi = SpecializationMorphism(P.coordinate_ring(), dict({c: 2, a: 1}))
             sage: X.specialization(phi=phi)
-            Closed subscheme of Affine Space of dimension 3 over Univariate Polynomial Ring in b over Rational Field defined by:
+            Closed subscheme of Affine Space of dimension 3
+            over Univariate Polynomial Ring in b over Rational Field defined by:
               x^2 + 2*y^2 + (-b)*z^2
         """
         if D is None:

src/sage/schemes/generic/morphism.py

@@ -1300,12 +1300,9 @@ def __copy__(self):
 
     def coordinate_ring(self):
         r"""
-        Returns the coordinate ring of the ambient projective space
-        the multivariable polynomial ring over the base ring
+        Return the coordinate ring of the ambient projective space.
 
-        OUTPUT:
-
-        - ring
+        OUTPUT: A multivariable polynomial ring over the base ring.
 
         EXAMPLES::
 
@@ -2079,7 +2076,7 @@ def specialization(self, D=None, phi=None, ambient=None):
             sage: Q.specialization({c: 1})
             (1 : 1)
 
-            ::
+        ::
 
             sage: R.<a,b> = PolynomialRing(QQ)
             sage: P.<x,y> = ProjectiveSpace(R, 1)
@@ -2106,7 +2103,7 @@ def specialization(self, D=None, phi=None, ambient=None):
             (2 : 1)
             sage: Q2.codomain()
             Closed subscheme of Projective Space of dimension 1 over Rational Field defined by:
-                  x - 2*y
+              x - 2*y
 
         ::