fix E713 and E714 in schemes

fchapoton · fchapoton · commit c8499d1a703a · 2021-10-24T21:46:31.000+02:00
diff --git a/src/sage/schemes/affine/affine_homset.py b/src/sage/schemes/affine/affine_homset.py
@@ -398,7 +398,7 @@ def numerical_points(self, F=None, **kwds):
         from sage.schemes.affine.affine_space import is_AffineSpace
         if F is None:
             F = CC
-        if not F in Fields() or not hasattr(F, 'precision'):
+        if F not in Fields() or not hasattr(F, 'precision'):
             raise TypeError('F must be a numerical field')
         X = self.codomain()
         if X.base_ring() not in NumberFields():
diff --git a/src/sage/schemes/affine/affine_subscheme.py b/src/sage/schemes/affine/affine_subscheme.py
@@ -328,7 +328,7 @@ def is_smooth(self, point=None):
             False
         """
         R = self.ambient_space().coordinate_ring()
-        if not point is None:
+        if point is not None:
             self._check_satisfies_equations(point)
             point_subs = dict(zip(R.gens(), point))
             Jac = self.Jacobian().subs(point_subs)
diff --git a/src/sage/schemes/curves/affine_curve.py b/src/sage/schemes/curves/affine_curve.py
@@ -678,7 +678,7 @@ def tangents(self, P, factor=True):
                 # divide T by that power of vars[1]
                 T = self.ambient_space().coordinate_ring()(dict([((v[0],v[1] - t), h) for (v,h) in T.dict().items()]))
             # T is homogeneous in var[0], var[1] if nonconstant, so dehomogenize
-            if not T in self.base_ring():
+            if T not in self.base_ring():
                 if T.degree(vars[0]) > 0:
                     T = T(vars[0], 1)
                     roots = T.univariate_polynomial().roots()
@@ -982,7 +982,7 @@ def projection(self, indices, AS=None):
             raise ValueError("(=%s) must be a list or tuple of length between 2 and (=%s), inclusive" % (indices, n - 1))
         if len(set(indices)) < len(indices):
             raise ValueError("(=%s) must be a list or tuple of distinct indices or variables" % indices)
-        if not AS is None:
+        if AS is not None:
             if not is_AffineSpace(AS):
                 raise TypeError("(=%s) must be an affine space" % AS)
             if AS.dimension_relative() != len(indices):
@@ -2145,11 +2145,11 @@ def _nonsingular_model(self):
         basis = list(gbasis)
         syzygy = {}
         for i in range(n):
-            S = k[R._first_ngens(i+1)]
+            S = k[R._first_ngens(i + 1)]
             while basis:
                 f = basis.pop()
                 if f in S:
-                    if not i in syzygy and f:
+                    if i not in syzygy and f:
                         syzygy[i] = f
                 else:
                     basis.append(f)
diff --git a/src/sage/schemes/curves/curve.py b/src/sage/schemes/curves/curve.py
@@ -320,8 +320,8 @@ def singular_points(self, F=None):
             if not self.base_ring() in Fields():
                 raise TypeError("curve must be defined over a field")
             F = self.base_ring()
-        elif not F in Fields():
-            raise TypeError("(=%s) must be a field"%F)
+        elif F not in Fields():
+            raise TypeError("(=%s) must be a field" % F)
         X = self.singular_subscheme()
         return [self.point(p, check=False) for p in X.rational_points(F=F)]
 
diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
@@ -411,7 +411,7 @@ def projection(self, P=None, PS=None):
             raise TypeError("this curve is already a plane curve")
         if self.base_ring() not in Fields():
             raise TypeError("this curve must be defined over a field")
-        if not PS is None:
+        if PS is not None:
             if not is_ProjectiveSpace(PS):
                 raise TypeError("(=%s) must be a projective space" % PS)
             if PS.dimension_relative() != n - 1:
@@ -455,7 +455,7 @@ def projection(self, P=None, PS=None):
                 Q = self(P)
             except TypeError:
                 pass
-            if not Q is None:
+            if Q is not None:
                 raise TypeError("(=%s) must be a point not on this curve" % P)
             try:
                 Q = self.ambient_space()(P)
diff --git a/src/sage/schemes/elliptic_curves/cm.py b/src/sage/schemes/elliptic_curves/cm.py
@@ -623,9 +623,8 @@ def is_cm_j_invariant(j, method='new'):
         True
     """
     # First we check that j is an algebraic number:
-
     from sage.rings.all import NumberFieldElement, NumberField
-    if not isinstance(j, NumberFieldElement) and not j in QQ:
+    if not isinstance(j, NumberFieldElement) and j not in QQ:
         raise NotImplementedError("is_cm_j_invariant() is only implemented for number field elements")
 
     # for j in ZZ we have a lookup-table:
diff --git a/src/sage/schemes/elliptic_curves/ell_egros.py b/src/sage/schemes/elliptic_curves/ell_egros.py
@@ -447,10 +447,10 @@ def egros_get_j(S=[], proof=None, verbose=False):
             P = urst(P)
             x = P[0]
             y = P[1]
-            j = x**3 /w
-            assert j-1728 == y**2 /w
+            j = x**3 / w
+            assert j - 1728 == y**2 / w
             if is_possible_j(j, S):
-                if not j in jlist:
+                if j not in jlist:
                     if verbose:
                         print("Adding possible j = ", j)
                         sys.stdout.flush()
diff --git a/src/sage/schemes/elliptic_curves/ell_modular_symbols.py b/src/sage/schemes/elliptic_curves/ell_modular_symbols.py
@@ -129,7 +129,7 @@ def modular_symbol_space(E, sign, base_ring, bound=None):
         Modular Symbols space of dimension 1 for Gamma_0(11) of weight 2 with sign -1 over Finite Field of size 37
 
     """
-    if not sign in [-1,0,1]:
+    if sign not in [-1, 0, 1]:
         raise TypeError('sign must -1, 0 or 1')
     N = E.conductor()
     M = ModularSymbols(N, sign=sign, base_ring=base_ring)
@@ -323,12 +323,12 @@ def __init__(self, E, sign, nap=1000):
         """
         from sage.libs.eclib.newforms import ECModularSymbol
 
-        if not sign in [-1,1]:
+        if sign not in [-1, 1]:
             raise TypeError('sign must -1 or 1')
         self._sign = ZZ(sign)
         self._E = E
         self._scaling = 1 if E.discriminant()>0 else ZZ(1)/2
-        self._implementation="eclib"
+        self._implementation = "eclib"
         self._base_ring = QQ
         # The ECModularSymbol class must be initialized with sign=0 to compute minus symbols
         self._modsym = ECModularSymbol(E, int(sign==1), nap)
@@ -436,11 +436,11 @@ def __init__(self, E, sign, normalize="L_ratio"):
             [1, 1, 1, 1, 1, 1, 1, 1]
 
         """
-        if not sign in [-1,1]:
+        if sign not in [-1, 1]:
             raise TypeError('sign must -1 or 1')
         self._sign = ZZ(sign)
         self._E = E
-        self._implementation="sage"
+        self._implementation = "sage"
         self._normalize = normalize
         self._modsym = E.modular_symbol_space(sign=self._sign)
         self._base_ring = self._modsym.base_ring()
diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py
@@ -2376,12 +2376,12 @@ def _compute_gens(self, proof,
             # progress (see trac #1949).
             X = self.mwrank('-p 100 -S '+str(sat_bound))
             verbose_verbose("Calling mwrank shell.")
-            if not 'The rank and full Mordell-Weil basis have been determined unconditionally' in X:
+            if 'The rank and full Mordell-Weil basis have been determined unconditionally' not in X:
                 msg = 'Generators not provably computed.'
                 if proof:
-                    raise RuntimeError('%s\n%s'%(X,msg))
+                    raise RuntimeError('%s\n%s' % (X, msg))
                 else:
-                    verbose_verbose("Warning -- %s"%msg, level=1)
+                    verbose_verbose("Warning -- %s" % msg, level=1)
                 proved = False
             else:
                 proved = True
@@ -4714,8 +4714,9 @@ def isogenies_prime_degree(self, l=None):
         if isinstance(l, list):
             isogs = []
             i = 0
-            while i<len(l):
-                isogenies = [f for f in self.isogenies_prime_degree(l[i]) if not f in isogs]
+            while i < len(l):
+                isogenies = [f for f in self.isogenies_prime_degree(l[i])
+                             if f not in isogs]
                 isogs.extend(isogenies)
                 i += 1
             return isogs
diff --git a/src/sage/schemes/elliptic_curves/isogeny_class.py b/src/sage/schemes/elliptic_curves/isogeny_class.py
@@ -802,7 +802,7 @@ def _compute(self, verbose=False):
 
         def add_tup(t):
             for T in [t, [t[1], t[0], t[2], 0]]:
-                if not T in tuples:
+                if T not in tuples:
                     tuples.append(T)
                     if verbose:
                         sys.stdout.write(" -added tuple %s..." % T[:3])
@@ -818,7 +818,7 @@ def add_tup(t):
                     sys.stdout.flush()
                 add_tup([0,ncurves,d,phi])
                 ncurves += 1
-                if not d in degs:
+                if d not in degs:
                     degs.append(d)
         if verbose:
             sys.stdout.write("... relevant degrees: %s..." % degs)
@@ -909,8 +909,9 @@ def add_tup(t):
         allQs = {} # keys: discriminants d
                    # values: lists of equivalence classes of
                    # primitive forms of discriminant d
-        def find_quadratic_form(d,n):
-            if not d in allQs:
+
+        def find_quadratic_form(d, n):
+            if d not in allQs:
                 from sage.quadratic_forms.binary_qf import BinaryQF_reduced_representatives
 
                 allQs[d] = BinaryQF_reduced_representatives(d, primitive_only=True)
diff --git a/src/sage/schemes/elliptic_curves/isogeny_small_degree.py b/src/sage/schemes/elliptic_curves/isogeny_small_degree.py
@@ -188,7 +188,7 @@ def Psi(l, use_stored=True):
         sage: assert Psi(7, use_stored=True) == Psi(7, use_stored=False)
         sage: assert Psi(13, use_stored=True) == Psi(13, use_stored=False) # not tested (very long time)
     """
-    if not l in [2, 3, 5, 7, 13]:
+    if l not in [2, 3, 5, 7, 13]:
         raise ValueError("Genus zero primes are 2, 3, 5, 7 or 13.")
 
     R = PolynomialRing(ZZ, 2, 'Xt')
@@ -276,7 +276,7 @@ def isogenies_prime_degree_genus_0(E, l=None, minimal_models=True):
         Isogeny of degree 5 from Elliptic Curve defined by y^2 + x*y + y = x^3 - x - 2 over Rational Field to Elliptic Curve defined by y^2 + x*y + y = x^3 - 76*x + 298 over Rational Field]
 
     """
-    if not l in [2, 3, 5, 7, 13, None]:
+    if l not in [2, 3, 5, 7, 13, None]:
         raise ValueError("%s is not a genus 0 prime."%l)
     F = E.base_ring()
     j = E.j_invariant()
@@ -1423,7 +1423,7 @@ def _hyperelliptic_isogeny_data(l):
         ValueError: 37 must be one of [11, 17, 19, 23, 29, 31, 41, 47, 59, 71].
 
     """
-    if not l in hyperelliptic_primes:
+    if l not in hyperelliptic_primes:
         raise ValueError("%s must be one of %s."%(l,hyperelliptic_primes))
     data = {}
     Zu = PolynomialRing(ZZ,'u')
@@ -1692,7 +1692,7 @@ def isogenies_prime_degree_genus_plus_0(E, l=None, minimal_models=True):
         return sum([isogenies_prime_degree_genus_plus_0(E, ell, minimal_models=minimal_models)
                     for ell in hyperelliptic_primes],[])
 
-    if not l in hyperelliptic_primes:
+    if l not in hyperelliptic_primes:
         raise ValueError("%s must be one of %s." % (l, hyperelliptic_primes))
 
     F = E.base_ring()
@@ -1782,7 +1782,7 @@ def isogenies_prime_degree_genus_plus_0_j0(E, l, minimal_models=True):
         sage: isogenies_prime_degree_genus_plus_0_j0(E,17)
         [Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6, Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 5^6 to Elliptic Curve defined by y^2 = x^3 + 2 over Finite Field in a of size 5^6]
     """
-    if not l in hyperelliptic_primes:
+    if l not in hyperelliptic_primes:
         raise ValueError("%s must be one of %s."%(l,hyperelliptic_primes))
     F = E.base_field()
     if E.j_invariant() != 0:
@@ -1873,7 +1873,7 @@ def isogenies_prime_degree_genus_plus_0_j1728(E, l, minimal_models=True):
         sage: [(p,len(isogenies_prime_degree_genus_plus_0_j1728(Emin,p))) for p in [17, 29, 41]]
         [(17, 2), (29, 2), (41, 2)]
     """
-    if not l in  hyperelliptic_primes:
+    if l not in  hyperelliptic_primes:
         raise ValueError("%s must be one of %s."%(l,hyperelliptic_primes))
     F = E.base_ring()
     if E.j_invariant() != 1728:
@@ -2352,10 +2352,10 @@ def isogenies_prime_degree(E, l, minimal_models=True):
     if l==p:
         return isogenies_prime_degree_general(E,l, minimal_models=minimal_models)
 
-    if l in [5,7,13] and not p in [2,3]:
+    if l in [5,7,13] and p not in [2,3]:
         return isogenies_prime_degree_genus_0(E,l, minimal_models=minimal_models)
 
-    if l in hyperelliptic_primes and not p in [2,3]:
+    if l in hyperelliptic_primes and p not in [2,3]:
         return isogenies_prime_degree_genus_plus_0(E,l, minimal_models=minimal_models)
 
     j = E.j_invariant()
diff --git a/src/sage/schemes/elliptic_curves/kraus.py b/src/sage/schemes/elliptic_curves/kraus.py
@@ -809,7 +809,7 @@ def check_Kraus_global(c4, c6, assume_nonsingular=False, debug=False):
     a1list = [d[1] for d in dat]
     a1 = K.solve_CRT(a1list,P2list, check=True)
     # See comment below: this is needed for when we combine with the primes above 3.
-    if not a1 in three: # three.divides(a1) causes a segfault
+    if a1 not in three:  # three.divides(a1) causes a segfault
         a1 = 3*a1
 
     # Using this a1, recompute the local a3's:
diff --git a/src/sage/schemes/generic/scheme.py b/src/sage/schemes/generic/scheme.py
@@ -866,11 +866,11 @@ def __init__(self, R, S=None, category=None):
             <class 'sage.schemes.generic.scheme.AffineScheme_with_category'>
         """
         from sage.categories.commutative_rings import CommutativeRings
-        if not R in CommutativeRings():
+        if R not in CommutativeRings():
             raise TypeError("R (={}) must be a commutative ring".format(R))
         self.__R = R
-        if not S is None:
-            if not S in CommutativeRings():
+        if S is not None:
+            if S not in CommutativeRings():
                 raise TypeError("S (={}) must be a commutative ring".format(S))
             if not R.has_coerce_map_from(S):
                 raise ValueError("There must be a natural map S --> R, but S = {} and R = {}".format(S, R))
diff --git a/src/sage/schemes/plane_conics/con_field.py b/src/sage/schemes/plane_conics/con_field.py
@@ -878,7 +878,7 @@ def parametrization(self, point=None, morphism=True):
             ...
             ValueError: The conic self (=Projective Conic Curve over Rational Field defined by x^2 + y^2) is not smooth, hence does not have a parametrization.
         """
-        if (not self._parametrization is None) and not point:
+        if (self._parametrization is not None) and not point:
             par = self._parametrization
         else:
             if not self.is_smooth():
diff --git a/src/sage/schemes/plane_quartics/quartic_constructor.py b/src/sage/schemes/plane_quartics/quartic_constructor.py
@@ -58,9 +58,9 @@ def QuarticCurve(F, PP=None, check=False):
     if not(F.is_homogeneous() and F.degree()==4):
         raise ValueError("Argument F (=%s) must be a homogeneous polynomial of degree 4"%F)
 
-    if not PP is None:
+    if PP is not None:
         if not is_ProjectiveSpace(PP) and PP.dimension == 2:
-            raise ValueError("Argument PP (=%s) must be a projective plane"%PP)
+            raise ValueError(f"Argument PP (={PP}) must be a projective plane")
     else:
         PP = ProjectiveSpace(P)
 
diff --git a/src/sage/schemes/projective/projective_homset.py b/src/sage/schemes/projective/projective_homset.py
@@ -373,7 +373,7 @@ def numerical_points(self, F=None, **kwds):
         from sage.schemes.projective.projective_space import is_ProjectiveSpace
         if F is None:
             F = CC
-        if not F in Fields() or not hasattr(F, 'precision'):
+        if F not in Fields() or not hasattr(F, 'precision'):
             raise TypeError('F must be a numerical field')
         X = self.codomain()
         if X.base_ring() not in NumberFields():
diff --git a/src/sage/schemes/projective/projective_morphism.py b/src/sage/schemes/projective/projective_morphism.py
@@ -1594,18 +1594,20 @@ def rational_preimages(self, Q, k=1):
         k = ZZ(k)
         if k <= 0:
             raise ValueError("k (=%s) must be a positive integer" % k)
-        #first check if subscheme
+        # first check if subscheme
         from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
         if isinstance(Q, AlgebraicScheme_subscheme_projective):
             return Q.preimage(self, k)
 
-        #else assume a point
+        # else assume a point
         BR = self.base_ring()
         if k > 1 and not self.is_endomorphism():
             raise TypeError("must be an endomorphism of projective space")
-        if not Q in self.codomain():
+        if Q not in self.codomain():
             raise TypeError("point must be in codomain of self")
-        if isinstance(BR.base_ring(),(ComplexField_class, RealField_class,RealIntervalField_class, ComplexIntervalField_class)):
+        if isinstance(BR.base_ring(), (ComplexField_class, RealField_class,
+                                       RealIntervalField_class,
+                                       ComplexIntervalField_class)):
             raise NotImplementedError("not implemented over precision fields")
         PS = self.domain().ambient_space()
         N = PS.dimension_relative()
diff --git a/src/sage/schemes/projective/projective_subscheme.py b/src/sage/schemes/projective/projective_subscheme.py
@@ -434,7 +434,7 @@ def is_smooth(self, point=None):
             sage: H.is_smooth()  # one of the few cases where the cone over the subvariety is smooth
             True
         """
-        if not point is None:
+        if point is not None:
             self._check_satisfies_equations(point)
             R = self.ambient_space().coordinate_ring()
             point_subs = dict(zip(R.gens(), point))
diff --git a/src/sage/schemes/toric/homset.py b/src/sage/schemes/toric/homset.py
@@ -400,7 +400,7 @@ def _finite_field_enumerator(self, finite_field=None):
         variety = self.codomain()
         if finite_field is None:
             finite_field = variety.base_ring()
-        if not finite_field in FiniteFields():
+        if finite_field not in FiniteFields():
             raise ValueError('not a finite field')
         return FiniteFieldPointEnumerator(variety.fan(), finite_field)
 
diff --git a/src/sage/schemes/toric/toric_subscheme.py b/src/sage/schemes/toric/toric_subscheme.py
