gh-36192: fix E228 then E225 in rings/
    
fix pycodestyle warnings E228 and E225 in rings

done using autopep8

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36192
Reported by: Frédéric Chapoton
Reviewer(s): Frédéric Chapoton, Kwankyu Lee

src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py

@@ -823,7 +823,7 @@ def univariate_decomposition(self):
         for a, m in df:
             am = a**m
             q, r = denominator.quo_rem(am)
-            assert r==0
+            assert r == 0
             numer = p * q.inverse_mod(am) % am
             # The inverse exists because the product and a**m
             # are relatively prime.
@@ -1930,7 +1930,7 @@ def asymptotics_smooth(self, p, alpha, N, asy_var, coordinate=None,
             if v.mod(2) == 0:
                 At_derivs = diff_all(At, T, 2 * N - 2, sub=hderivs1,
                                      sub_final=[Tstar, atP], rekey=AA)
-                Phitu_derivs = diff_all(Phitu, T, 2 * N - 2 +v,
+                Phitu_derivs = diff_all(Phitu, T, 2 * N - 2 + v,
                                         sub=hderivs1, sub_final=[Tstar, atP],
                                         zero_order=v + 1, rekey=BB)
             else:

src/sage/rings/complex_interval_field.py

@@ -558,7 +558,7 @@ def _repr_(self):
             sage: ComplexIntervalField(100) # indirect doctest
             Complex Interval Field with 100 bits of precision
         """
-        return "Complex Interval Field with %s bits of precision"%self._prec
+        return "Complex Interval Field with %s bits of precision" % self._prec
 
     def _latex_(self):
         r"""

src/sage/rings/finite_rings/conway_polynomials.py

@@ -471,7 +471,7 @@ def find_leveller(qindex, level, x, xleveled, searched, i):
         searched[i] = True
         crt_possibles = []
         for j in range(1,len(qlist)):
-            if i==j:
+            if i == j:
                 continue
             if crt[(i,j)][qindex][1] >= level:
                 if xleveled[j]:
@@ -487,7 +487,7 @@ def find_leveller(qindex, level, x, xleveled, searched, i):
 
     def propagate_levelling(qindex, level, x, xleveled, i):
         for j in range(1, len(qlist)):
-            if i==j:
+            if i == j:
                 continue
             if not xleveled[j] and crt[(i,j)][qindex][1] >= level:
                 newxj = x[i][0] + crt[(i,j)][qindex][0]

src/sage/rings/finite_rings/finite_field_givaro.py

@@ -510,7 +510,7 @@ def _pari_modulus(self):
             Mod(1, 3)*a^4 + Mod(2, 3)*a^3 + Mod(2, 3)
         """
         f = pari(str(self.modulus()))
-        return f.subst('x', 'a') * pari("Mod(1,%s)"%self.characteristic())
+        return f.subst('x', 'a') * pari("Mod(1,%s)" % self.characteristic())
 
     def __iter__(self):
         """

src/sage/rings/finite_rings/finite_field_ntl_gf2e.py

@@ -305,4 +305,4 @@ def _pari_modulus(self):
             Mod(1, 2)*a^16 + Mod(1, 2)*a^5 + Mod(1, 2)*a^3 + Mod(1, 2)*a^2 + Mod(1, 2)
         """
         f = pari(str(self.modulus()))
-        return f.subst('x', 'a') * pari("Mod(1,%s)"%self.characteristic())
+        return f.subst('x', 'a') * pari("Mod(1,%s)" % self.characteristic())

src/sage/rings/finite_rings/homset.py

@@ -153,9 +153,9 @@ def _repr_(self):
         D = self.domain()
         C = self.codomain()
         if C == D:
-            return "Automorphism group of %s"%D
+            return "Automorphism group of %s" % D
         else:
-            return "Set of field embeddings from %s to %s"%(D, C)
+            return "Set of field embeddings from %s to %s" % (D, C)
 
     def is_aut(self):
         """

src/sage/rings/function_field/constructor.py

@@ -86,7 +86,7 @@ def create_key(self, F, names):
             sage: K.<x> = FunctionField(QQ) # indirect doctest
         """
         if not isinstance(names, tuple):
-            names=(names,)
+            names = (names,)
         return (F, names)
 
     def create_object(self, version, key,**extra_args):
@@ -112,7 +112,7 @@ def create_object(self, version, key,**extra_args):
             return RationalFunctionField(key[0], names=key[1])
 
 
-FunctionField=FunctionFieldFactory("sage.rings.function_field.constructor.FunctionField")
+FunctionField = FunctionFieldFactory("sage.rings.function_field.constructor.FunctionField")
 
 
 class FunctionFieldExtensionFactory(UniqueFactory):
@@ -171,9 +171,9 @@ def create_key(self,polynomial,names):
 
         """
         if names is None:
-            names=polynomial.variable_name()
+            names = polynomial.variable_name()
         if not isinstance(names,tuple):
-            names=(names,)
+            names = (names,)
         return (polynomial,names,polynomial.base_ring())
 
     def create_object(self,version,key,**extra_args):

src/sage/rings/function_field/divisor.py

@@ -1023,7 +1023,7 @@ def _repr_(self):
             sage: F.divisor_group()
             Divisor group of Function field in y defined by y^2 + 4*x^3 + 4
         """
-        return "Divisor group of %s"%(self._field,)
+        return "Divisor group of %s" % (self._field,)
 
     def _element_constructor_(self, x):
         """

src/sage/rings/function_field/function_field_polymod.py

@@ -280,7 +280,7 @@ def _to_base_field(self, f):
         K = self.base_field()
         if f.element().is_constant():
             return K(f.element())
-        raise ValueError("%r is not an element of the base field"%(f,))
+        raise ValueError("%r is not an element of the base field" % (f,))
 
     def _to_constant_base_field(self, f):
         """
@@ -572,7 +572,7 @@ def _repr_(self):
             sage: L._repr_()
             'Function field in y defined by y^5 - 2*x*y + (-x^4 - 1)/x'
         """
-        return "Function field in %s defined by %s"%(self.variable_name(), self._polynomial)
+        return "Function field in %s defined by %s" % (self.variable_name(), self._polynomial)
 
     def base_field(self):
         """

src/sage/rings/function_field/function_field_rational.py

@@ -220,7 +220,7 @@ def _repr_(self):
             sage: K._repr_()
             'Rational function field in t over Rational Field'
         """
-        return "Rational function field in %s over %s"%(
+        return "Rational function field in %s over %s" % (
             self.variable_name(), self._constant_field)
 
     def _element_constructor_(self, x):
@@ -304,7 +304,7 @@ def _to_constant_base_field(self, f):
             # When K is not exact, f.denominator() might not be an exact 1, so
             # we need to divide explicitly to get the correct precision
             return K(f.numerator()) / K(f.denominator())
-        raise ValueError("only constants can be converted into the constant base field but %r is not a constant"%(f,))
+        raise ValueError("only constants can be converted into the constant base field but %r is not a constant" % (f,))
 
     def _to_polynomial(self, f):
         """
@@ -349,7 +349,7 @@ def _to_bivariate_polynomial(self, f):
         v = f.list()
         denom = lcm([a.denominator() for a in v])
         S = denom.parent()
-        x,t = S.base_ring()['%s,%s'%(f.parent().variable_name(),self.variable_name())].gens()
+        x,t = S.base_ring()['%s,%s' % (f.parent().variable_name(),self.variable_name())].gens()
         phi = S.hom([t])
         return sum([phi((denom * v[i]).numerator()) * x**i for i in range(len(v))]), denom
 

src/sage/rings/function_field/order.py

@@ -259,7 +259,7 @@ def _repr_(self):
             sage: FunctionField(QQ,'y').maximal_order()._repr_()
             'Maximal order of Rational function field in y over Rational Field'
         """
-        return "Maximal order of %s"%(self.function_field(),)
+        return "Maximal order of %s" % (self.function_field(),)
 
 
 class FunctionFieldMaximalOrderInfinite(FunctionFieldMaximalOrder, FunctionFieldOrderInfinite):
@@ -278,4 +278,4 @@ def _repr_(self):
             sage: F.maximal_order_infinite()                                            # needs sage.modules sage.rings.function_field
             Maximal infinite order of Function field in y defined by y^3 + x^6 + x^4 + x^2
         """
-        return "Maximal infinite order of %s"%(self.function_field(),)
+        return "Maximal infinite order of %s" % (self.function_field(),)

src/sage/rings/function_field/order_basis.py

@@ -93,7 +93,7 @@ def __init__(self, basis, check=True):
         R = V.base_field().maximal_order()
         self._module = V.span([to_V(b) for b in basis], base_ring=R)
 
-        self._from_module= from_V
+        self._from_module = from_V
         self._to_module = to_V
         self._basis = tuple(basis)
         self._ring = field.polynomial_ring()

src/sage/rings/function_field/order_polymod.py

@@ -683,7 +683,7 @@ def decomposition(self, ideal):
                 # occurs by constructing a matrix in k, and finding a non-zero
                 # vector in the kernel of the matrix.
 
-                m =[]
+                m = []
                 for g in q.basis_matrix():
                     m.extend(matrix([g * mr for mr in matrices_reduced]).columns())
                 beta  = [c.lift() for c in matrix(m).right_kernel().basis()[0]]
@@ -784,7 +784,7 @@ def _element_constructor_(self, f):
         O = F.base_field().maximal_order_infinite()
         coordinates = self.coordinate_vector(f)
         if not all(c in O for c in coordinates):
-            raise TypeError("%r is not an element of %r"%(f,self))
+            raise TypeError("%r is not an element of %r" % (f,self))
 
         return f
 
@@ -1288,7 +1288,7 @@ def decomposition(self, ideal):
 
                 # p and qgen generates the prime; modulo pO, qgenb generates the prime
                 qgenb = [to(qgen[i]) for i in range(n)]
-                m =[]
+                m = []
                 for i in range(n):
                     m.append(sum(qgenb[j] * mtable[i][j] for j in range(n)))
                 beta  = [fr(coeff) for coeff in matrix(m).left_kernel().basis()[0]]
@@ -1383,7 +1383,7 @@ def add(Ib,Jb):
                 Kb.append(Lb)
 
             # J_1, J_2, ...
-            Jb =[Kb[0]] + [div(Kb[j],Kb[j-1]) for j in range(1,len(Kb))]
+            Jb = [Kb[0]] + [div(Kb[j],Kb[j-1]) for j in range(1,len(Kb))]
 
             # H_1, H_2, ...
             Hb = [div(Jb[j],Jb[j+1]) for j in range(len(Jb)-1)] + [Jb[-1]]
@@ -1455,7 +1455,7 @@ def split(h):
                     # Compute an element beta in O but not in pO. How to find beta
                     # is explained in Section 4.8.3 of [Coh1993]. We keep beta
                     # as a vector over k[x] with respect to the basis of O.
-                    m =[]
+                    m = []
                     for i in range(n):
                         r = []
                         for g in prime._hnf:

src/sage/rings/function_field/order_rational.py

@@ -84,7 +84,7 @@ def _element_constructor_(self, f):
             raise TypeError("unable to convert to an element of {}".format(F))
 
         if not f.denominator() in self.function_field().constant_base_field():
-            raise TypeError("%r is not an element of %r"%(f,self))
+            raise TypeError("%r is not an element of %r" % (f,self))
 
         return f
 

src/sage/rings/function_field/place_polymod.py

@@ -602,7 +602,7 @@ def candidates():
         if deg > 1:
             if isinstance(k, NumberField):
                 if name is None:
-                    name='s'
+                    name = 's'
                 K = k.extension(min_poly, names=name)
 
                 def from_W(e):

src/sage/rings/function_field/place_rational.py

@@ -128,7 +128,7 @@ def to_K(f):
                 d = f.denominator()
 
                 n_deg = n.degree()
-                d_deg =d.degree()
+                d_deg = d.degree()
 
                 if n_deg < d_deg:
                     return K(0)

src/sage/rings/homset.py

@@ -91,7 +91,7 @@ def _repr_(self):
             sage: Hom(ZZ, QQ) # indirect doctest
             Set of Homomorphisms from Integer Ring to Rational Field
         """
-        return "Set of Homomorphisms from %s to %s"%(self.domain(), self.codomain())
+        return "Set of Homomorphisms from %s to %s" % (self.domain(), self.codomain())
 
     def has_coerce_map_from(self, x):
         """
@@ -212,7 +212,7 @@ def natural_map(self):
         """
         f = self.codomain().coerce_map_from(self.domain())
         if f is None:
-            raise TypeError("natural coercion morphism from %s to %s not defined"%(self.domain(), self.codomain()))
+            raise TypeError("natural coercion morphism from %s to %s not defined" % (self.domain(), self.codomain()))
         return f
 
     def zero(self):

src/sage/rings/ideal.py

@@ -316,8 +316,8 @@ def _repr_short(self):
                 s = s.replace('\n','\n  ')
             L.append(s)
         if has_return:
-            return '\n(\n  %s\n)\n'%(',\n\n  '.join(L))
-        return '(%s)'%(', '.join(L))
+            return '\n(\n  %s\n)\n' % (',\n\n  '.join(L))
+        return '(%s)' % (', '.join(L))
 
     def __repr__(self):
         """
@@ -329,7 +329,7 @@ def __repr__(self):
             sage: P*[a^2,a*b+c,c^3] # indirect doctest
             Ideal (a^2, a*b + c, c^3) of Multivariate Polynomial Ring in a, b, c over Rational Field
         """
-        return "Ideal %s of %s"%(self._repr_short(), self.ring())
+        return "Ideal %s of %s" % (self._repr_short(), self.ring())
 
     def random_element(self, *args, **kwds):
         """
@@ -1280,7 +1280,7 @@ def __repr__(self):
             sage: I # indirect doctest
             Principal ideal (x) of Univariate Polynomial Ring in x over Integer Ring
         """
-        return "Principal ideal (%s) of %s"%(self.gen(), self.ring())
+        return "Principal ideal (%s) of %s" % (self.gen(), self.ring())
 
     def is_principal(self):
         r"""
@@ -1693,7 +1693,7 @@ def residue_field(self):
             TypeError: residue fields only supported for polynomial rings over finite fields.
         """
         if not self.is_prime():
-            raise ValueError("The ideal (%s) is not prime"%self)
+            raise ValueError("The ideal (%s) is not prime" % self)
         from sage.rings.integer_ring import ZZ
         if self.ring() is ZZ:
             return ZZ.residue_field(self, check=False)
@@ -1717,7 +1717,7 @@ def __repr__(self):
             sage: Ideal_fractional(K, [a])  # indirect doctest                          # needs sage.rings.number_field
             Fractional ideal (a) of Number Field in a with defining polynomial x^2 + 1
         """
-        return "Fractional ideal %s of %s"%(self._repr_short(), self.ring())
+        return "Fractional ideal %s of %s" % (self._repr_short(), self.ring())
 
 # constructors for standard (benchmark) ideals, written uppercase as
 # these are constructors