one-line outputs (7/7)

src/sage/env.py

@@ -82,9 +82,7 @@ def var(key: str, *fallbacks: Optional[str], force: bool = False) -> Optional[st
       ``True``, skip the environment variable and only use the
       fallbacks.
 
-    OUTPUT:
-
-    The value of the environment variable or its fallbacks.
+    OUTPUT: the value of the environment variable or its fallbacks
 
     EXAMPLES::
 

src/sage/schemes/curves/affine_curve.py

@@ -238,7 +238,7 @@ def projective_closure(self, i=0, PP=None):
         - ``PP`` -- (default: None) ambient projective space to compute the projective closure in. This is
           constructed if it is not given.
 
-        OUTPUT: A curve in projective space.
+        OUTPUT: a curve in projective space
 
         EXAMPLES::
 
@@ -494,7 +494,7 @@ def is_transverse(self, C, P):
 
         - ``P`` -- a point in the intersection of both curves.
 
-        OUTPUT: A boolean.
+        OUTPUT: boolean
 
         EXAMPLES::
 
@@ -550,7 +550,7 @@ def multiplicity(self, P):
 
         - ``P`` -- a point in the ambient space of this curve.
 
-        OUTPUT: An integer.
+        OUTPUT: integer
 
         EXAMPLES::
 
@@ -617,7 +617,7 @@ def tangents(self, P, factor=True):
           curve, or to just return the polynomial corresponding to the union of
           the tangent lines (which requires fewer computations)
 
-        OUTPUT: A list of polynomials in the coordinate ring of the ambient space.
+        OUTPUT: a list of polynomials in the coordinate ring of the ambient space
 
         EXAMPLES::
 
@@ -889,7 +889,7 @@ def projection(self, indices, AS=None):
           this curve, and must have dimension equal to the length of ``indices``.
           This space is constructed if not specified.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a scheme morphism from this curve to affine space of dimension equal
           to the number of coordinates specified in ``indices``
@@ -1050,7 +1050,7 @@ def plane_projection(self, AP=None):
           curve, and must have dimension two. This space will be constructed if
           not specified.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a scheme morphism from this curve into an affine plane
 
@@ -1115,7 +1115,7 @@ def blowup(self, P=None):
         - ``P`` -- (default: None) a point on this curve at which to blow up;
           if ``None``, then ``P`` is taken to be the origin.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a tuple of curves in affine space of the same dimension as the
           ambient space of this curve, which define the blow up in each affine
@@ -1426,7 +1426,7 @@ def resolution_of_singularities(self, extend=False):
           resolved. However, setting ``extend`` to ``True`` will slow down
           computations.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a tuple of curves in affine space of the same dimension as the
           ambient space of this curve, which represent affine patches of the
@@ -1927,7 +1927,7 @@ def riemann_surface(self, **kwargs):
         r"""
         Return the complex Riemann surface determined by this curve
 
-        OUTPUT: A :class:`~sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface` object.
+        OUTPUT: a :class:`~sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface` object
 
         EXAMPLES::
 
@@ -1968,7 +1968,7 @@ def riemann_roch_basis(self, D):
           divisor `Div = d_1P_1 + \dots + d_nP_n`, where `X(F) = \{P_1, \dots,
           P_n\}`.  The ordering is that dictated by ``places_on_curve``.
 
-        OUTPUT: A basis of `L(Div)`.
+        OUTPUT: a basis of `L(Div)`.
 
         EXAMPLES::
 
@@ -2200,7 +2200,7 @@ def function(self, f):
         - ``f`` -- an element of the fraction field of the coordinate ring of
           the ambient space or the coordinate ring of the curve
 
-        OUTPUT: An element of the function field of this curve.
+        OUTPUT: an element of the function field of this curve
 
         EXAMPLES::
 
@@ -2689,7 +2689,7 @@ def places_on(self, point):
 
         - ``point`` -- a closed point of the curve
 
-        OUTPUT: A list of the places of the function field of the curve.
+        OUTPUT: a list of the places of the function field of the curve
 
         EXAMPLES::
 

src/sage/schemes/curves/plane_curve_arrangement.py

@@ -138,9 +138,7 @@ def ncurves(self):
         r"""
         Return the number of curves in the arrangement.
 
-        OUTPUT:
-
-        An integer.
+        OUTPUT: integer
 
         EXAMPLES::
 
@@ -159,9 +157,7 @@ def curves(self):
         r"""
         Return the curves in the arrangement as a tuple.
 
-        OUTPUT:
-
-        A tuple.
+        OUTPUT: a tuple
 
         EXAMPLES::
 
@@ -182,9 +178,7 @@ def _repr_(self):
         r"""
         String representation for a curve arrangement.
 
-        OUTPUT:
-
-        A string.
+        OUTPUT: string
 
         EXAMPLES::
 
@@ -237,9 +231,7 @@ def union(self, other):
         - ``other`` -- a curve arrangement or something that can
           be converted into a curve arrangement
 
-        OUTPUT:
-
-        A new curve arrangement.
+        OUTPUT: a new curve arrangement
 
         EXAMPLES::
 
@@ -334,9 +326,7 @@ def coordinate_ring(self):
         """
         Return the coordinate ring of ``self``.
 
-        OUTPUT:
-
-        The coordinate ring of the curve arrangement.
+        OUTPUT: the coordinate ring of the curve arrangement
 
         EXAMPLES::
 
@@ -499,9 +489,7 @@ def fundamental_group(self, simplified=True, vertical=True,
         - ``projective`` -- boolean (default: ``False``); to be used in the
           method for projective curves
 
-        OUTPUT:
-
-        A finitely presented group.
+        OUTPUT: a finitely presented group
 
         .. NOTE::
 
@@ -832,9 +820,7 @@ def fundamental_group(self, simplified=True):
         - ``simplified`` -- boolean (default: ``True``); set if the group
           is simplified
 
-        OUTPUT:
-
-        A finitely presented group.
+        OUTPUT: a finitely presented group
 
         .. NOTE::
 
@@ -1045,9 +1031,7 @@ def coordinate_ring(self):
         """
         Return the coordinate ring.
 
-        OUTPUT:
-
-        The coordinate ring of the curve arrangement.
+        OUTPUT: the coordinate ring of the curve arrangement
 
         EXAMPLES::
 
@@ -1106,9 +1090,7 @@ def _repr_(self):
         """
         Return a string representation.
 
-        OUTPUT:
-
-        A string.
+        OUTPUT: string
 
         EXAMPLES::
 
@@ -1182,9 +1164,7 @@ def ngens(self):
         """
         Return the number of variables, i.e. 2 or 3, kept for completness.
 
-        OUTPUT:
-
-        An integer, 2 or 3, depending if the arrangement is projective or affine.
+        OUTPUT: an integer, 2 or 3, depending if the arrangement is projective or affine
 
         EXAMPLES::
 
@@ -1201,9 +1181,7 @@ def gens(self):
         """
         Return the coordinates.
 
-        OUTPUT:
-
-        A tuple of linear expressions, one for each linear variable.
+        OUTPUT: a tuple of linear expressions, one for each linear variable
 
         EXAMPLES::
 
@@ -1224,9 +1202,7 @@ def gen(self, i):
 
         - ``i`` -- integer
 
-        OUTPUT:
-
-        A variable.
+        OUTPUT: a variable
 
         EXAMPLES::
 

src/sage/schemes/curves/projective_curve.py

@@ -244,7 +244,7 @@ def affine_patch(self, i, AA=None):
         - ``AA`` -- (default: None) ambient affine space, this is constructed
           if it is not given
 
-        OUTPUT: A curve in affine space.
+        OUTPUT: a curve in affine space
 
         EXAMPLES::
 
@@ -292,7 +292,7 @@ def projection(self, P=None, PS=None):
           ambient space of this curve. This space will be constructed if not
           specified.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a scheme morphism from this curve into a projective space of
           dimension one less than that of the ambient space of this curve
@@ -507,7 +507,7 @@ def plane_projection(self, PP=None):
           as this curve, and must have dimension two. This space is constructed
           if not specified.
 
-        OUTPUT: A tuple of
+        OUTPUT: a tuple of
 
         - a scheme morphism from this curve into a projective plane
 
@@ -644,7 +644,7 @@ def divisor_of_function(self, r):
 
         INPUT: ``r`` is a rational function on X
 
-        OUTPUT: A list. The divisor of r represented as a list of coefficients and
+        OUTPUT: a list. The divisor of r represented as a list of coefficients and
         points. (TODO: This will change to a more structural output in the
         future.)
 
@@ -905,7 +905,7 @@ def degree(self):
 
         For a plane curve, this is just the degree of its defining polynomial.
 
-        OUTPUT: An integer.
+        OUTPUT: integer
 
         EXAMPLES::
 
@@ -1537,7 +1537,7 @@ def is_transverse(self, C, P):
 
         - ``P`` -- a point in the intersection of both curves.
 
-        OUTPUT: A boolean.
+        OUTPUT: boolean
 
         EXAMPLES::
 
@@ -1877,7 +1877,7 @@ def riemann_surface(self, **kwargs):
         r"""
         Return the complex Riemann surface determined by this curve
 
-        OUTPUT: A :class:`~sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface` object.
+        OUTPUT: a :class:`~sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface` object
 
         EXAMPLES::
 
@@ -1905,9 +1905,7 @@ def rational_points_iterator(self):
 
         - ``self`` -- a projective curve
 
-        OUTPUT:
-
-        A generator of all the rational points on the curve defined over its base field.
+        OUTPUT: a generator of all the rational points on the curve defined over its base field
 
         EXAMPLES::
 
@@ -2087,7 +2085,7 @@ def riemann_roch_basis(self, D):
 
         -  ``D`` -- a divisor
 
-        OUTPUT: A list of function field elements that form a basis of the
+        OUTPUT: a list of function field elements that form a basis of the
         Riemann-Roch space.
 
         EXAMPLES::
@@ -2174,7 +2172,7 @@ def rational_points(self, algorithm="enum", sort=True):
           points should be sorted.  If False, the order of the output
           is non-deterministic.
 
-        OUTPUT: A list of all the rational points on the curve, possibly sorted.
+        OUTPUT: a list of all the rational points on the curve, possibly sorted
 
         .. NOTE::
 
@@ -2361,7 +2359,7 @@ def function(self, f):
         - ``f`` -- a fraction of homogeneous polynomials of the coordinate ring
           of the ambient space of the curve
 
-        OUTPUT: An element of the function field.
+        OUTPUT: an element of the function field
 
         EXAMPLES::
 
@@ -2994,7 +2992,7 @@ def Hasse_bounds(q, genus=1):
 
     - ``genus`` (int, default 1) -- a non-negative integer,
 
-    OUTPUT: A tuple. The Hasse bounds (lb,ub) for the cardinality of a curve of
+    OUTPUT: a tuple. The Hasse bounds (lb,ub) for the cardinality of a curve of
     genus ``genus`` defined over `\GF{q}`.
 
     EXAMPLES::