gh-36191: fix E228 and E225 in schemes/
    
fix pycodestyle warnings E228 and E225 in schemes

this was 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: #36191
Reported by: Frédéric Chapoton
Reviewer(s): Kwankyu Lee

Author: Release Manager

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -3055,12 +3055,12 @@ def selmer_rank(self, algorithm="pari"):
         try:
             return self.__selmer_rank
         except AttributeError:
-            if algorithm=="pari":
+            if algorithm == "pari":
                 ep = self.pari_curve()
                 lower, upper, s, pts = ep.ellrank()
                 tor = self.two_torsion_rank()
                 return upper + tor + s
-            elif algorithm=="mwrank":
+            elif algorithm == "mwrank":
                 C = self.mwrank_curve()
                 self.__selmer_rank = C.selmer_rank()
                 return self.__selmer_rank
@@ -3110,11 +3110,11 @@ def rank_bound(self, algorithm="pari"):
         try:
             return self.__rank_bound
         except AttributeError:
-            if algorithm=="pari":
+            if algorithm == "pari":
                 ep = self.pari_curve()
                 lower, upper, s, pts = ep.ellrank()
                 return upper
-            elif algorithm=="mwrank":
+            elif algorithm == "mwrank":
                 C = self.mwrank_curve()
                 self.__rank_bound = C.rank_bound()
                 return self.__rank_bound

src/sage/schemes/elliptic_curves/padics.py

@@ -643,7 +643,7 @@ def _multiple_to_make_good_reduction(E):
         li = []
         for p in ps:
             np = u.valuation(p)
-            if Emin.discriminant() %p != 0:
+            if Emin.discriminant() % p != 0:
                 li.append(Emin.Np(p) * p**(np-1))
             elif Emin.has_additive_reduction(p):
                 li.append(E.tamagawa_number(p) * p**np)
@@ -652,7 +652,7 @@ def _multiple_to_make_good_reduction(E):
             else: # non split
                 li.append(E.tamagawa_number(p) * (p+1) * p**(np-1))
         otherbad = Integer(Emin.discriminant()).prime_divisors()
-        otherbad = [p for p in otherbad if u%p != 0 ]
+        otherbad = [p for p in otherbad if u % p != 0 ]
         li += [E.tamagawa_number(p) for p in otherbad]
         n2 = LCM(li)
     return n2

src/sage/schemes/generic/algebraic_scheme.py

@@ -527,7 +527,7 @@ def _repr_(self):
             sage: S._repr_()
             'Subscheme of Projective Space of dimension 3 over Integer Ring'
         """
-        return "Subscheme of %s"%self.__A
+        return "Subscheme of %s" % self.__A
 
     def _homset(self, *args, **kwds):
         """
@@ -819,11 +819,11 @@ def _check_satisfies_equations(self, v):
         coords = list(v)
         for f in self.__X.defining_polynomials():
             if f(coords) != 0:
-                raise TypeError("Coordinates %s do not define a point on %s"%(v,self))
+                raise TypeError("Coordinates %s do not define a point on %s" % (v,self))
         for f in self.__Y.defining_polynomials():
             if f(coords) != 0:
                 return True
-        raise TypeError("Coordinates %s do not define a point on %s"%(v,self))
+        raise TypeError("Coordinates %s do not define a point on %s" % (v,self))
 
     def rational_points(self, **kwds):
         """
@@ -870,9 +870,9 @@ def rational_points(self, **kwds):
 
         if bound == 0:
             if is_RationalField(F):
-                raise TypeError("A positive bound (= %s) must be specified."%bound)
+                raise TypeError("A positive bound (= %s) must be specified." % bound)
             if not isinstance(F, FiniteField):
-                raise TypeError("Argument F (= %s) must be a finite field."%F)
+                raise TypeError("Argument F (= %s) must be a finite field." % F)
         pts = []
         for P in self.ambient_space().rational_points(F):
             try:
@@ -984,11 +984,11 @@ def _check_satisfies_equations(self, v):
         for f in self.defining_polynomials():
             if f(coords) != 0:   # it must be "!=0" instead of "if f(v)", e.g.,
                                  # because of p-adic base rings.
-                raise TypeError("Coordinates %s do not define a point on %s"%(coords,self))
+                raise TypeError("Coordinates %s do not define a point on %s" % (coords,self))
         try:
             return self.ambient_space()._check_satisfies_equations(coords)
         except TypeError:
-            raise TypeError("Coordinates %s do not define a point on %s"%(coords,self))
+            raise TypeError("Coordinates %s do not define a point on %s" % (coords,self))
 
     def base_extend(self, R):
         """
@@ -1463,10 +1463,10 @@ def union(self, other):
             True
         """
         if not isinstance(other, AlgebraicScheme_subscheme):
-            raise TypeError("other (=%s) must be a closed algebraic subscheme of an ambient space"%other)
+            raise TypeError("other (=%s) must be a closed algebraic subscheme of an ambient space" % other)
         A = self.ambient_space()
         if other.ambient_space() != A:
-            raise ValueError("other (=%s) must be in the same ambient space as self"%other)
+            raise ValueError("other (=%s) must be in the same ambient space as self" % other)
         return A.subscheme(self.defining_ideal().intersection(other.defining_ideal()))
 
     def __pow__(self, m):
@@ -1647,10 +1647,10 @@ def intersection(self, other):
               y
         """
         if not isinstance(other, AlgebraicScheme_subscheme):
-            raise TypeError("other (=%s) must be a closed algebraic subscheme of an ambient space"%other)
+            raise TypeError("other (=%s) must be a closed algebraic subscheme of an ambient space" % other)
         A = self.ambient_space()
         if other.ambient_space() != A:
-            raise ValueError("other (=%s) must be in the same ambient space as self"%other)
+            raise ValueError("other (=%s) must be in the same ambient space as self" % other)
         return A.subscheme(self.defining_ideal() + other.defining_ideal())
 
     def complement(self, other=None):
@@ -1706,9 +1706,9 @@ def complement(self, other=None):
             if other == A:
                 other = A.subscheme([])
             else:
-                raise TypeError("Argument other (=%s) must be a closed algebraic subscheme of an ambient space"%other)
+                raise TypeError("Argument other (=%s) must be a closed algebraic subscheme of an ambient space" % other)
         if other.ambient_space() != A:
-            raise ValueError("other (=%s) must be in the same ambient space as self"%other)
+            raise ValueError("other (=%s) must be in the same ambient space as self" % other)
         return AlgebraicScheme_quasi(other, self)
 
     def rational_points(self, **kwds):
@@ -1832,7 +1832,7 @@ def rational_points(self, **kwds):
             try:
                 return X.points(**kwds) # checks for proper bound done in points functions
             except TypeError:
-                raise TypeError("Unable to enumerate points over %s."%F)
+                raise TypeError("Unable to enumerate points over %s." % F)
         elif (self.base_ring() in NumberFields() or self.base_ring() == ZZ)\
           and hasattr(F, 'precision'):
             #we are numerically approximating number field points
@@ -1841,7 +1841,7 @@ def rational_points(self, **kwds):
             X = self.base_extend(F)(F)
             return X.points()
         except TypeError:
-            raise TypeError("Unable to enumerate points over %s."%F)
+            raise TypeError("Unable to enumerate points over %s." % F)
 
     def change_ring(self, R):
         r"""

src/sage/schemes/generic/glue.py

@@ -33,17 +33,17 @@ class GluedScheme(scheme.Scheme):
     def __init__(self, f, g, check=True):
         if check:
             if not morphism.is_SchemeMorphism(f):
-                raise TypeError("f (=%s) must be a scheme morphism"%f)
+                raise TypeError("f (=%s) must be a scheme morphism" % f)
             if not morphism.is_SchemeMorphism(g):
-                raise TypeError("g (=%s) must be a scheme morphism"%g)
+                raise TypeError("g (=%s) must be a scheme morphism" % g)
             if f.domain() != g.domain():
-                raise ValueError("f (=%s) and g (=%s) must have the same domain"%(f,g))
+                raise ValueError("f (=%s) and g (=%s) must have the same domain" % (f,g))
         self.__f = f
         self.__g = g
 
     def gluing_maps(self):
         return self.__f, self.__g
 
     def _repr_(self):
-        return "Scheme obtained by gluing X and Y along U, where\n  X: %s\n  Y: %s\n  U: %s"%(
+        return "Scheme obtained by gluing X and Y along U, where\n  X: %s\n  Y: %s\n  U: %s" % (
             self.__f.codomain(), self.__g.codomain(), self.__f.domain())

src/sage/schemes/generic/hypersurface.py

@@ -95,9 +95,9 @@ def __init__(self, poly, ambient=None):
             True
         """
         if not isinstance(poly, MPolynomial):
-            raise TypeError("Defining polynomial (=%s) must be a multivariate polynomial."%poly)
+            raise TypeError("Defining polynomial (=%s) must be a multivariate polynomial." % poly)
         if not poly.is_homogeneous():
-            raise TypeError("Defining polynomial (=%s) must be homogeneous."%poly)
+            raise TypeError("Defining polynomial (=%s) must be homogeneous." % poly)
         if ambient is None:
             R = poly.parent()
             from sage.schemes.projective.projective_space import ProjectiveSpace
@@ -120,7 +120,7 @@ def _repr_(self):
             sage: H._repr_()
             'Projective hypersurface defined by y^2 + x*z in Projective Space of dimension 2 over Integer Ring'
         """
-        return "Projective hypersurface defined by %s in %s"%(
+        return "Projective hypersurface defined by %s in %s" % (
             self.defining_polynomial(), self.ambient_space())
 
     def defining_polynomial(self):
@@ -185,7 +185,7 @@ def __init__(self, poly, ambient=None):
             True
         """
         if not isinstance(poly, MPolynomial):
-            raise TypeError("Defining polynomial (= %s) must be a multivariate polynomial"%poly)
+            raise TypeError("Defining polynomial (= %s) must be a multivariate polynomial" % poly)
         if ambient is None:
             R = poly.parent()
             from sage.schemes.affine.affine_space import AffineSpace
@@ -208,7 +208,7 @@ def _repr_(self):
             sage: H._repr_()
             'Affine hypersurface defined by y^2 + x*z in Affine Space of dimension 3 over Integer Ring'
         """
-        return "Affine hypersurface defined by %s in %s"%(
+        return "Affine hypersurface defined by %s in %s" % (
             self.defining_polynomial(), self.ambient_space())
 
     def defining_polynomial(self):

src/sage/schemes/generic/morphism.py

@@ -165,7 +165,7 @@ def __init__(self, parent, codomain=None):
         if codomain is not None:
             parent = Hom(parent, codomain)
         if not isinstance(parent, Homset):
-            raise TypeError("parent (=%s) must be a Homspace"%parent)
+            raise TypeError("parent (=%s) must be a Homspace" % parent)
         Element.__init__(self, parent)
         self._codomain = parent.codomain()
 
@@ -261,9 +261,9 @@ def __call__(self, x, *args, **kwds):
                     try:
                         x = D(x)
                     except (TypeError, NotImplementedError):
-                        raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(x, self.domain()))
-                elif self.domain()!=x.codomain():
-                    raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(x, self.domain()))
+                        raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented" % (x, self.domain()))
+                elif self.domain() != x.codomain():
+                    raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented" % (x, self.domain()))
         else:
             x = converter(x)
         if not args and not kwds:
@@ -330,14 +330,14 @@ def _repr_(self):
             NotImplementedError
         """
         if self.is_endomorphism():
-            s = "%s endomorphism of %s"%(self._repr_type(), self.domain())
+            s = "%s endomorphism of %s" % (self._repr_type(), self.domain())
         else:
-            s = "%s morphism:"%self._repr_type()
-            s += "\n  From: %s"%self.domain()
-            s += "\n  To:   %s"%self._codomain
+            s = "%s morphism:" % self._repr_type()
+            s += "\n  From: %s" % self.domain()
+            s += "\n  To:   %s" % self._codomain
         d = self._repr_defn()
         if d != '':
-            s += "\n  Defn: %s"%('\n        '.join(self._repr_defn().split('\n')))
+            s += "\n  Defn: %s" % ('\n        '.join(self._repr_defn().split('\n')))
         return s
 
     def __mul__(self, right):
@@ -396,7 +396,7 @@ def __mul__(self, right):
         if not isinstance(right, SchemeMorphism):
             return coercion_model.bin_op(self, right, operator.mul)
         if right.codomain() != self.domain():
-            raise TypeError("self (=%s) domain must equal right (=%s) codomain"%(self, right))
+            raise TypeError("self (=%s) domain must equal right (=%s) codomain" % (self, right))
         if isinstance(self, SchemeMorphism_id):
             return right
         if isinstance(right, SchemeMorphism_id):
@@ -428,7 +428,7 @@ def __pow__(self, n, dummy=None):
         """
         if not self.is_endomorphism():
             raise TypeError("self must be an endomorphism.")
-        if n==0:
+        if n == 0:
             return self.domain().identity_morphism()
         return generic_power(self, n)
 
@@ -996,11 +996,11 @@ def __init__(self, parent, polys, check=True):
         """
         if check:
             if not isinstance(polys, (list, tuple)):
-                raise TypeError("polys (=%s) must be a list or tuple"%polys)
+                raise TypeError("polys (=%s) must be a list or tuple" % polys)
             source_ring = parent.domain().ambient_space().coordinate_ring()
             target = parent._codomain.ambient_space()
             if len(polys) != target.ngens():
-                raise ValueError("there must be %s polynomials"%target.ngens())
+                raise ValueError("there must be %s polynomials" % target.ngens())
             F = []
             for poly in polys:
                 try:
@@ -1012,7 +1012,7 @@ def __init__(self, parent, polys, check=True):
                         try:
                             p = source_ring(poly.numerator()) / source_ring(poly.denominator())
                         except (TypeError, AttributeError):
-                            raise TypeError("polys (=%s) must be elements of %s"%(polys, source_ring))
+                            raise TypeError("polys (=%s) must be elements of %s" % (polys, source_ring))
                 F.append(p)
             polys = Sequence(F)
 
@@ -1245,7 +1245,7 @@ def _repr_defn(self):
         """
         i = self.domain().ambient_space()._repr_generic_point()
         o = self._codomain.ambient_space()._repr_generic_point(self.defining_polynomials())
-        return "Defined on coordinates by sending %s to\n%s"%(i,o)
+        return "Defined on coordinates by sending %s to\n%s" % (i,o)
 
     def __getitem__(self, i):
         """

src/sage/schemes/generic/point.py

@@ -66,7 +66,7 @@ def _repr_(self):
             sage: P._repr_()
             'Point on Spectrum of Integer Ring'
         """
-        return "Point on %s"%self.__S
+        return "Point on %s" % self.__S
 
 ########################################################
 # Topological points on a scheme
@@ -179,7 +179,7 @@ def __init__(self, S, P, check=False):
         # unfortunately is_prime() is only implemented in a small
         # number of cases
         if check and not P.is_prime():
-            raise ValueError("The argument %s must be a prime ideal of %s"%(P, R))
+            raise ValueError("The argument %s must be a prime ideal of %s" % (P, R))
         SchemeTopologicalPoint.__init__(self, S)
         self.__P = P
 
@@ -197,7 +197,7 @@ def _repr_(self):
             sage: pt._repr_()
             'Point on Projective Space of dimension 2 over Rational Field defined by the Ideal (-x^2 + y*z) of Multivariate Polynomial Ring in x, y, z over Rational Field'
         """
-        return "Point on %s defined by the %s"%(self.scheme(),
+        return "Point on %s defined by the %s" % (self.scheme(),
                                                 self.prime_ideal())
 
     def prime_ideal(self):
@@ -247,7 +247,7 @@ def __init__(self, f):
         self.__f = f
 
     def _repr_(self):
-        return "Point on %s defined by the morphism %s"%(self.scheme(),
+        return "Point on %s defined by the morphism %s" % (self.scheme(),
                                                          self.morphism())
 
     def morphism(self):