gh-37623: src/sage/rings: Doctest cosmetics
    
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### ⌛ Dependencies

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URL: #37623
Reported by: Matthias Köppe
Reviewer(s): David Coudert

Author: Release Manager

src/sage/rings/complex_conversion.pyx

@@ -9,7 +9,7 @@ cdef class CCtoCDF(Map):
         """
         EXAMPLES::
             sage: from sage.rings.complex_conversion import CCtoCDF
-            sage: f = CCtoCDF(CC, CDF) # indirect doctest
+            sage: f = CCtoCDF(CC, CDF)  # indirect doctest
             sage: f(CC.0)
             1.0*I
             sage: f(exp(pi*CC.0/4))                                                     # needs sage.symbolic

src/sage/rings/complex_mpfr.pyx

@@ -444,7 +444,9 @@ class ComplexField_class(sage.rings.abc.ComplexField):
             sage: CC.gen() + QQ.extension(x^2 + 1, 'I', embedding=None).gen()           # needs sage.rings.number_field
             Traceback (most recent call last):
             ...
-            TypeError: unsupported operand parent(s) for +: 'Complex Field with 53 bits of precision' and 'Number Field in I with defining polynomial x^2 + 1'
+            TypeError: unsupported operand parent(s) for +:
+            'Complex Field with 53 bits of precision' and
+            'Number Field in I with defining polynomial x^2 + 1'
 
         In the absence of arguments we return zero::
 

src/sage/rings/finite_rings/residue_field_givaro.pyx

@@ -123,7 +123,7 @@ class ResidueFiniteField_givaro(ResidueField_generic, FiniteField_givaro):
 
             sage: R.<t> = GF(3)[]; P = R.ideal(t^4 - t^3 + t + 1); k.<a> = P.residue_field()
             sage: V = k.vector_space(map=False); v = V([0,1,2,3])
-            sage: k(v) # indirect doctest
+            sage: k(v)  # indirect doctest
             2*a^2 + a
         """
         try:

src/sage/rings/function_field/function_field_polymod.py

@@ -739,46 +739,50 @@ def free_module(self, base=None, basis=None, map=True):
 
         We convert an element of the vector space back to the function field::
 
-            sage: from_V(V.1)                                                                       # needs sage.modules
+            sage: from_V(V.1)                                                           # needs sage.modules
             y
 
         We define an interesting element of the function field::
 
-            sage: a = 1/L.0; a                                                                      # needs sage.modules
+            sage: a = 1/L.0; a                                                          # needs sage.modules
             (x/(x^4 + 1))*y^4 - 2*x^2/(x^4 + 1)
 
         We convert it to the vector space, and get a vector over the base field::
 
-            sage: to_V(a)                                                                           # needs sage.modules
+            sage: to_V(a)                                                               # needs sage.modules
             (-2*x^2/(x^4 + 1), 0, 0, 0, x/(x^4 + 1))
 
         We convert to and back, and get the same element::
 
-            sage: from_V(to_V(a)) == a                                                              # needs sage.modules
+            sage: from_V(to_V(a)) == a                                                  # needs sage.modules
             True
 
         In the other direction::
 
-            sage: v = x*V.0 + (1/x)*V.1                                                             # needs sage.modules
-            sage: to_V(from_V(v)) == v                                                              # needs sage.modules
+            sage: v = x*V.0 + (1/x)*V.1                                                 # needs sage.modules
+            sage: to_V(from_V(v)) == v                                                  # needs sage.modules
             True
 
         And we show how it works over an extension of an extension field::
 
             sage: R2.<z> = L[]; M.<z> = L.extension(z^2 - y)
-            sage: M.free_module()                                                                   # needs sage.modules
-            (Vector space of dimension 2 over Function field in y defined by y^5 - 2*x*y + (-x^4 - 1)/x, Isomorphism:
+            sage: M.free_module()                                                       # needs sage.modules
+            (Vector space of dimension 2 over Function field in y defined by y^5 - 2*x*y + (-x^4 - 1)/x,
+             Isomorphism:
               From: Vector space of dimension 2 over Function field in y defined by y^5 - 2*x*y + (-x^4 - 1)/x
-              To:   Function field in z defined by z^2 - y, Isomorphism:
+              To:   Function field in z defined by z^2 - y,
+             Isomorphism:
               From: Function field in z defined by z^2 - y
               To:   Vector space of dimension 2 over Function field in y defined by y^5 - 2*x*y + (-x^4 - 1)/x)
 
         We can also get the vector space of ``M`` over ``K``::
 
-            sage: M.free_module(K)                                                                  # needs sage.modules
-            (Vector space of dimension 10 over Rational function field in x over Rational Field, Isomorphism:
+            sage: M.free_module(K)                                                      # needs sage.modules
+            (Vector space of dimension 10 over Rational function field in x over Rational Field,
+             Isomorphism:
               From: Vector space of dimension 10 over Rational function field in x over Rational Field
-              To:   Function field in z defined by z^2 - y, Isomorphism:
+              To:   Function field in z defined by z^2 - y,
+             Isomorphism:
               From: Function field in z defined by z^2 - y
               To:   Vector space of dimension 10 over Rational function field in x over Rational Field)
 
@@ -1271,10 +1275,12 @@ def simple_model(self, name=None):
             sage: L.<y> = K.extension(y^2 - x); R.<z> = L[]
             sage: M.<z> = L.extension(z^2 - y)
             sage: M.simple_model()
-            (Function field in z defined by z^4 + x, Function Field morphism:
+            (Function field in z defined by z^4 + x,
+             Function Field morphism:
                From: Function field in z defined by z^4 + x
                To:   Function field in z defined by z^2 + y
-               Defn: z |--> z, Function Field morphism:
+               Defn: z |--> z,
+             Function Field morphism:
                From: Function field in z defined by z^2 + y
                To:   Function field in z defined by z^4 + x
                Defn: z |--> z
@@ -1444,7 +1450,8 @@ def separable_model(self, names=None):
             sage: L.separable_model()                                                   # needs sage.rings.finite_rings
             Traceback (most recent call last):
             ...
-            NotImplementedError: constructing a separable model is only implemented for function fields over a perfect constant base field
+            NotImplementedError: constructing a separable model is only implemented
+            for function fields over a perfect constant base field
 
         TESTS:
 
@@ -1493,11 +1500,13 @@ def separable_model(self, names=None):
             sage: R.<z> = L[]
             sage: M.<z> = L.extension(z^3 - y)
             sage: M.separable_model()
-            (Function field in z_ defined by z_ + x_^6, Function Field morphism:
+            (Function field in z_ defined by z_ + x_^6,
+             Function Field morphism:
                From: Function field in z_ defined by z_ + x_^6
                To:   Function field in z defined by z^3 + y
                Defn: z_ |--> x
-                     x_ |--> z, Function Field morphism:
+                     x_ |--> z,
+             Function Field morphism:
                From: Function field in z defined by z^3 + y
                To:   Function field in z_ defined by z_ + x_^6
                Defn: z |--> x_
@@ -1606,12 +1615,14 @@ def change_variable_name(self, name):
                     y |--> y
                     x |--> x)
             sage: M.change_variable_name(('zz','yy'))
-            (Function field in zz defined by zz^2 - yy, Function Field morphism:
+            (Function field in zz defined by zz^2 - yy,
+             Function Field morphism:
               From: Function field in zz defined by zz^2 - yy
               To:   Function field in z defined by z^2 - y
               Defn: zz |--> z
                     yy |--> y
-                    x |--> x, Function Field morphism:
+                    x |--> x,
+             Function Field morphism:
               From: Function field in z defined by z^2 - y
               To:   Function field in zz defined by zz^2 - yy
               Defn: z |--> zz
@@ -1687,7 +1698,8 @@ def _inversion_isomorphism(self):
                        From: Function field in T defined by T^3 + (x^4 + x^2 + 1)/x^6
                        To:   Function field in y defined by y^3 + x^6 + x^4 + x^2
                        Defn: T |--> y
-                             x |--> 1/x, Composite map:
+                             x |--> 1/x,
+             Composite map:
                From: Function field in y defined by y^3 + x^6 + x^4 + x^2
                To:   Function field in s defined by s^3 + x^16 + x^14 + x^12
                Defn:   Function Field morphism:

src/sage/rings/polynomial/polynomial_rational_flint.pyx

@@ -336,7 +336,7 @@ cdef class Polynomial_rational_flint(Polynomial):
 
         INPUT:
 
-        - ``singular`` - Singular interpreter (default: default interpreter)
+        - ``singular`` -- Singular interpreter (default: default interpreter)
 
         EXAMPLES::
 

src/sage/rings/puiseux_series_ring_element.pyx

@@ -49,7 +49,9 @@ Mind the base ring. However, the base ring can be changed::
     sage: I*q                                                                           # needs sage.rings.number_field
     Traceback (most recent call last):
     ...
-    TypeError: unsupported operand parent(s) for *: 'Number Field in I with defining polynomial x^2 + 1 with I = 1*I' and 'Puiseux Series Ring in x over Rational Field'
+    TypeError: unsupported operand parent(s) for *:
+    'Number Field in I with defining polynomial x^2 + 1 with I = 1*I' and
+    'Puiseux Series Ring in x over Rational Field'
     sage: qz = q.change_ring(ZZ); qz
     x^(1/3) + x^(1/2)
     sage: qz.parent()

src/sage/rings/qqbar.py

@@ -269,7 +269,8 @@
 Bailey, Yozo, Li and Thompson discusses this result. Evidently it is
 difficult to find, but we can easily verify it. ::
 
-    sage: alpha = QQbar.polynomial_root(x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1, RIF(1, 1.2))
+    sage: alpha = QQbar.polynomial_root(x^10 + x^9 - x^7 - x^6
+    ....:                                - x^5 - x^4 - x^3 + x + 1, RIF(1, 1.2))
     sage: lhs = alpha^630 - 1
     sage: rhs_num = (alpha^315 - 1) * (alpha^210 - 1) * (alpha^126 - 1)^2 * (alpha^90 - 1) * (alpha^3 - 1)^3 * (alpha^2 - 1)^5 * (alpha - 1)^3
     sage: rhs_den = (alpha^35 - 1) * (alpha^15 - 1)^2 * (alpha^14 - 1)^2 * (alpha^5 - 1)^6 * alpha^68
@@ -468,8 +469,10 @@
     0.?e-15
 
     sage: ax = polygen(AA)
-    sage: x2 = AA.polynomial_root(256*ax**8 - 128*ax**7 - 448*ax**6 + 192*ax**5 + 240*ax**4 - 80*ax**3 - 40*ax**2 + 8*ax + 1, RIF(0.9829, 0.983))
-    sage: y2 = (1-x2**2).sqrt()
+    sage: x2 = AA.polynomial_root(256*ax**8 - 128*ax**7 - 448*ax**6 + 192*ax**5
+    ....:                          + 240*ax**4 - 80*ax**3 - 40*ax**2 + 8*ax + 1,
+    ....:                         RIF(0.9829, 0.983))
+    sage: y2 = (1 - x2**2).sqrt()
     sage: x - x2
     0.?e-18
     sage: y - y2
@@ -485,7 +488,8 @@
     sage: x = AA['x'].gen()
     sage: P = 1/(1+x^4)
     sage: P.partial_fraction_decomposition()
-    (0, [(-0.3535533905932738?*x + 1/2)/(x^2 - 1.414213562373095?*x + 1), (0.3535533905932738?*x + 1/2)/(x^2 + 1.414213562373095?*x + 1)])
+    (0, [(-0.3535533905932738?*x + 1/2)/(x^2 - 1.414213562373095?*x + 1),
+         (0.3535533905932738?*x + 1/2)/(x^2 + 1.414213562373095?*x + 1)])
 
 Check that :issue:`22202` is fixed::
 
@@ -2638,7 +2642,8 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
     Things work fine with rational numbers, too::
 
         sage: number_field_elements_from_algebraics((QQbar(1/2), AA(17)))
-        (Rational Field, [1/2, 17], Ring morphism:
+        (Rational Field, [1/2, 17],
+         Ring morphism:
             From: Rational Field
             To:   Algebraic Real Field
             Defn: 1 |--> 1)
@@ -2690,8 +2695,8 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
     It is also possible to have an embedded Number Field::
 
         sage: x = polygen(ZZ)
-        sage: my_num = AA.polynomial_root(x^3-2, RIF(0,3))
-        sage: res = number_field_elements_from_algebraics(my_num,embedded=True)
+        sage: my_num = AA.polynomial_root(x^3 - 2, RIF(0,3))
+        sage: res = number_field_elements_from_algebraics(my_num, embedded=True)
         sage: res[0].gen_embedding()
         1.259921049894873?
         sage: res[2]
@@ -2783,12 +2788,14 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
     Tests trivial cases::
 
         sage: number_field_elements_from_algebraics([], embedded=True)
-        (Rational Field, [], Ring morphism:
+        (Rational Field, [],
+         Ring morphism:
            From: Rational Field
            To:   Algebraic Real Field
            Defn: 1 |--> 1)
         sage: number_field_elements_from_algebraics([1], embedded=True)
-        (Rational Field, [1], Ring morphism:
+        (Rational Field, [1],
+         Ring morphism:
            From: Rational Field
            To:   Algebraic Real Field
            Defn: 1 |--> 1)
@@ -2798,7 +2805,7 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
         sage: # needs sage.libs.gap sage.symbolic
         sage: UCF = UniversalCyclotomicField()
         sage: E = UCF.gen(5)
-        sage: L.<b> = NumberField(x^2-189*x+16, embedding=200)
+        sage: L.<b> = NumberField(x^2 - 189*x + 16, embedding=200)
         sage: x = polygen(ZZ)
         sage: my_nums = [-52*E - 136*E^2 - 136*E^3 - 52*E^4,
         ....:            L.gen()._algebraic_(AA),
@@ -4382,7 +4389,8 @@ def as_number_field_element(self, minimal=False, embedded=False, prec=53):
             sage: AA(elt)
             Traceback (most recent call last):
             ...
-            ValueError: need a real or complex embedding to convert a non rational element of a number field into an algebraic number
+            ValueError: need a real or complex embedding to convert a non rational
+            element of a number field into an algebraic number
             sage: hom(elt) == rt
             True
 
@@ -4391,7 +4399,8 @@ def as_number_field_element(self, minimal=False, embedded=False, prec=53):
             sage: (nf, elt, hom) = rt.as_number_field_element(embedded=True)
             sage: nf.coerce_embedding()
             Generic morphism:
-              From: Number Field in a with defining polynomial y^3 - 2*y^2 - 31*y - 50 with a = 7.237653139801104?
+              From: Number Field in a with defining polynomial y^3 - 2*y^2 - 31*y - 50
+                    with a = 7.237653139801104?
               To:   Algebraic Real Field
               Defn: a -> 7.237653139801104?
             sage: elt
@@ -4518,9 +4527,11 @@ def _exact_field(self):
             sage: QQbar(2)._exact_field()
             Trivial generator
             sage: (sqrt(QQbar(2)) + sqrt(QQbar(19)))._exact_field()
-            Number Field in a with defining polynomial y^4 - 20*y^2 + 81 with a in -3.789313782671036?
+            Number Field in a with defining polynomial y^4 - 20*y^2 + 81
+             with a in -3.789313782671036?
             sage: (QQbar(7)^(3/5))._exact_field()
-            Number Field in a with defining polynomial y^5 - 2*y^4 - 18*y^3 + 38*y^2 + 82*y - 181 with a in 2.554256611698490?
+            Number Field in a with defining polynomial
+             y^5 - 2*y^4 - 18*y^3 + 38*y^2 + 82*y - 181 with a in 2.554256611698490?
         """
         sd = self._descr
         if isinstance(sd, (ANRational, ANExtensionElement)):