PEP8 and typing annotations for function fields

src/sage/rings/function_field/constructor.py

@@ -171,9 +171,9 @@ def create_key(self, polynomial, names):
         """
         if names is None:
             names = polynomial.variable_name()
-        if not isinstance(names,tuple):
+        if not isinstance(names, tuple):
             names = (names,)
-        return (polynomial,names,polynomial.base_ring())
+        return (polynomial, names, polynomial.base_ring())
 
     def create_object(self, version, key, **extra_args):
         """
@@ -197,7 +197,7 @@ def create_object(self, version, key, **extra_args):
         base_field = f.base_ring()
         if isinstance(base_field, function_field_rational.RationalFunctionField):
             k = base_field.constant_field()
-            if k.is_finite(): # then we are in positive characteristic
+            if k.is_finite():  # then we are in positive characteristic
                 # irreducible and separable
                 if f.is_irreducible() and not all(e % k.characteristic() == 0 for e in f.exponents()):
                     # monic and integral

src/sage/rings/function_field/derivations.py

@@ -54,7 +54,7 @@ class FunctionFieldDerivation(RingDerivationWithoutTwist):
         sage: d
         d/dx
     """
-    def __init__(self, parent):
+    def __init__(self, parent) -> None:
         r"""
         Initialize a derivation.
 

src/sage/rings/function_field/derivations_polymod.py

@@ -39,7 +39,7 @@ class FunctionFieldDerivation_separable(FunctionFieldDerivation):
         sage: L.derivation()
         d/dx
     """
-    def __init__(self, parent, d):
+    def __init__(self, parent, d) -> None:
         """
         Initialize a derivation.
 
@@ -164,7 +164,7 @@ def _lmul_(self, factor):
 
 
 class FunctionFieldDerivation_inseparable(FunctionFieldDerivation):
-    def __init__(self, parent, u=None):
+    def __init__(self, parent, u=None) -> None:
         r"""
         Initialize this derivation.
 
@@ -286,7 +286,7 @@ class FunctionFieldHigherDerivation(Map):
           From: Rational function field in x over Finite Field of size 2
           To:   Rational function field in x over Finite Field of size 2
     """
-    def __init__(self, field):
+    def __init__(self, field) -> None:
         """
         Initialize.
 
@@ -386,7 +386,7 @@ class RationalFunctionFieldHigherDerivation_global(FunctionFieldHigherDerivation
         sage: h(x^2, 2)
         1
     """
-    def __init__(self, field):
+    def __init__(self, field) -> None:
         """
         Initialize.
 
@@ -580,7 +580,7 @@ class FunctionFieldHigherDerivation_global(FunctionFieldHigherDerivation):
         ((x^7 + 1)/x^2)*y^2 + x^3*y
     """
 
-    def __init__(self, field):
+    def __init__(self, field) -> None:
         """
         Initialize.
 
@@ -826,7 +826,7 @@ class FunctionFieldHigherDerivation_char_zero(FunctionFieldHigherDerivation):
         sage: h(h(h(e,1),1),1) == 3*2*h(e,3)
         True
     """
-    def __init__(self, field):
+    def __init__(self, field) -> None:
         """
         Initialize.
 

src/sage/rings/function_field/derivations_rational.py

@@ -31,7 +31,7 @@ class FunctionFieldDerivation_rational(FunctionFieldDerivation):
         sage: K.derivation()
         d/dx
     """
-    def __init__(self, parent, u=None):
+    def __init__(self, parent, u=None) -> None:
         """
         Initialize a derivation.
 

src/sage/rings/function_field/differential.py

@@ -98,7 +98,7 @@ class FunctionFieldDifferential(ModuleElement):
         sage: y.differential()                                                          # needs sage.rings.function_field
         ((21/4*x/(x^7 + 27/4))*y^2 + ((3/2*x^7 + 9/4)/(x^8 + 27/4*x))*y + 7/2*x^4/(x^7 + 27/4)) d(x)
     """
-    def __init__(self, parent, f, t=None):
+    def __init__(self, parent, f, t=None) -> None:
         """
         Initialize the differential `fdt`.
 
@@ -116,7 +116,7 @@ def __init__(self, parent, f, t=None):
 
         self._f = f
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return the string representation of the differential.
 
@@ -132,7 +132,7 @@ def _repr_(self):
             sage: f.differential()
             (-1/x^2) d(x)
         """
-        if self._f.is_zero(): # zero differential
+        if self._f.is_zero():  # zero differential
             return '0'
 
         r = 'd({})'.format(self.parent()._gen_base_differential)
@@ -142,7 +142,7 @@ def _repr_(self):
 
         return '({})'.format(self._f) + ' ' + r
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         Return a latex representation of the differential.
 
@@ -155,7 +155,7 @@ def _latex_(self):
             sage: latex(w)                                                              # needs sage.rings.function_field
             \left( x y^{2} + \frac{1}{x} y \right)\, dx
         """
-        if self._f.is_zero(): # zero differential
+        if self._f.is_zero():  # zero differential
             return '0'
 
         r = 'd{}'.format(self.parent()._gen_base_differential)
@@ -165,7 +165,7 @@ def _latex_(self):
 
         return '\\left(' + latex(self._f) + '\\right)\\,' + r
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Return the hash of ``self``.
 
@@ -396,7 +396,7 @@ def divisor(self):
         """
         F = self.parent().function_field()
         x = F.base_field().gen()
-        return self._f.divisor() + (-2)*F(x).divisor_of_poles() + F.different()
+        return self._f.divisor() + (-2) * F(x).divisor_of_poles() + F.different()
 
     def valuation(self, place):
         """
@@ -416,7 +416,7 @@ def valuation(self, place):
         """
         F = self.parent().function_field()
         x = F.base_field().gen()
-        return (self._f.valuation(place) + 2*min(F(x).valuation(place), 0)
+        return (self._f.valuation(place) + 2 * min(F(x).valuation(place), 0)
                 + F.different().valuation(place))
 
     def residue(self, place):
@@ -471,7 +471,7 @@ def residue(self, place):
             sage: sum([QQ(w.residue(p)) for p in d.support()])
             0
         """
-        R,fr_R,to_R = place._residue_field()
+        R, fr_R, to_R = place._residue_field()
 
         # Step 1: compute f such that fds equals this differential.
         s = place.local_uniformizer()
@@ -485,10 +485,10 @@ def residue(self, place):
             return R.zero()
         else:
             g_shifted = g * s**(-r)
-            c = g_shifted.higher_derivative(-r-1, s)
+            c = g_shifted.higher_derivative(-r - 1, s)
             return to_R(c)
 
-    def monomial_coefficients(self, copy=True):
+    def monomial_coefficients(self, copy: bool = True):
         """
         Return a dictionary whose keys are indices of basis elements in the
         support of ``self`` and whose values are the corresponding coefficients.
@@ -600,7 +600,7 @@ class DifferentialsSpace(UniqueRepresentation, Parent):
     """
     Element = FunctionFieldDifferential
 
-    def __init__(self, field, category=None):
+    def __init__(self, field, category=None) -> None:
         """
         Initialize the space of differentials of the function field.
 
@@ -627,7 +627,7 @@ def __init__(self, field, category=None):
         self._gen_base_differential = F.gen()
         self._gen_derivative_inv = ~der(F.gen())  # used for fast computation
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return the string representation of the space of differentials.
 
@@ -770,7 +770,7 @@ class DifferentialsSpaceInclusion(Morphism):
           To:   Space of differentials of Function field in y defined by y^2 - x*y + 4*x^3
     """
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return the string representation of this morphism.
 
@@ -790,7 +790,7 @@ def _repr_(self):
         s += "\n  To:   {}".format(self.codomain())
         return s
 
-    def is_injective(self):
+    def is_injective(self) -> bool:
         """
         Return ``True``, since the inclusion morphism is injective.
 
@@ -849,4 +849,4 @@ def _call_(self, v):
         """
         domain = self.domain()
         F = self.codomain().function_field()
-        return F(v._f)*F(domain._gen_base_differential).differential()
+        return F(v._f) * F(domain._gen_base_differential).differential()