Trac #34891: fixing some E502 in tensor, dynamics, modules, plot, numerical

E502 the backslash is redundant between brackets

URL: https://trac.sagemath.org/34891
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Matthias Koeppe

Author: Release Manager

src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py

@@ -239,14 +239,14 @@ def __classcall_private__(cls, dynamical_system, domain=None, ideal=None):
                 try:
                     dynamical_system = DynamicalSystem_affine(dynamical_system)
                 except (TypeError, ValueError):
-                    raise TypeError('domain was affine Berkovich space, but dynamical_system did not ' + \
+                    raise TypeError('domain was affine Berkovich space, but dynamical_system did not '
                         'convert to an affine dynamical system')
         if isinstance(domain, Berkovich_Cp_Projective):
             if not isinstance(dynamical_system, DynamicalSystem_projective):
                 try:
                     dynamical_system = DynamicalSystem_projective(dynamical_system)
                 except (TypeError, ValueError):
-                    raise TypeError('domain was projective Berkovich space, but dynamical_system did not convert ' + \
+                    raise TypeError('domain was projective Berkovich space, but dynamical_system did not convert '
                         'to a projective dynamical system')
 
         if not isinstance(dynamical_system, DynamicalSystem):
@@ -268,7 +268,7 @@ def __classcall_private__(cls, dynamical_system, domain=None, ideal=None):
                         if ideal != domain.ideal():
                             raise ValueError('conflicting inputs for ideal and domain')
             else:
-                raise ValueError('base ring of domain of dynamical_system must be p-adic or a number field ' + \
+                raise ValueError('base ring of domain of dynamical_system must be p-adic or a number field '
                     'not %s' %morphism_domain.base_ring())
 
         if is_AffineSpace(morphism_domain):
@@ -446,6 +446,7 @@ def _repr_(self):
         return "Dynamical system of " + domain_str + " induced by the map" + \
             "\n  Defn: %s"%('\n        '.join(self._system._repr_defn().split('\n')))
 
+
 class DynamicalSystem_Berkovich_projective(DynamicalSystem_Berkovich):
     r"""
     A dynamical system on projective Berkovich space over `\CC_p`.
@@ -528,13 +529,13 @@ def __classcall_private__(cls, dynamical_system, domain=None):
             raise ValueError('domain was not relative dimension 1')
         if not isinstance(R, pAdicBaseGeneric):
             if domain is None:
-                raise TypeError('dynamical system defined over %s, not p-adic, ' %morphism_domain.base_ring() + \
+                raise TypeError('dynamical system defined over %s, not p-adic, ' %morphism_domain.base_ring() +
                     'and domain is None')
             if not isinstance(domain, Berkovich_Cp_Projective):
                 raise TypeError('domain was %s, not a projective Berkovich space over Cp' %domain)
             if domain.base() != morphism_domain:
-                raise ValueError('base of domain was %s, with coordinate ring %s ' %(domain.base(), \
-                    domain.base().coordinate_ring())+ 'while dynamical_system acts on %s, ' %morphism_domain + \
+                raise ValueError('base of domain was %s, with coordinate ring %s ' %(domain.base(),
+                    domain.base().coordinate_ring())+ 'while dynamical_system acts on %s, ' %morphism_domain +
                         'with coordinate ring %s' %morphism_domain.coordinate_ring())
         else:
             domain = Berkovich_Cp_Projective(morphism_domain)
@@ -1007,7 +1008,7 @@ def __classcall_private__(cls, dynamical_system, domain=None):
             raise ValueError('domain not relative dimension 1')
         if not isinstance(R, pAdicBaseGeneric):
             if domain is None:
-                raise TypeError('dynamical system defined over %s, not padic, ' %morphism_domain.base_ring() + \
+                raise TypeError('dynamical system defined over %s, not padic, ' %morphism_domain.base_ring() +
                     'and domain was not specified')
             if not isinstance(domain, Berkovich_Cp_Affine):
                 raise TypeError('domain was %s, not an affine Berkovich space over Cp' %domain)

src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py

@@ -754,7 +754,7 @@ def automorphism_group_QQ_CRT(rational_function, prime_lower_bound=4, return_fun
             # and the gcd of orders over Fp and 24 is 24
             # or if the gcd is equal to the number of automorphisms we have
             if (len(elements) == gcd(orderaut + [24])) or \
-                (gcd(orderaut + [24]) == 24 and \
+                (gcd(orderaut + [24]) == 24 and
                 (len(elements) == 12 or len(elements) == 8)):
                     if iso_type:
                         return elements, which_group(elements)

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -6167,7 +6167,7 @@ def reduced_form(self, **kwds):
                 raise NotImplementedError("smallest coeff only over ZZ or QQ")
             check_min = kwds.get('check_minimal', True)
             from sage.dynamics.arithmetic_dynamics.endPN_minimal_model import smallest_dynamical
-            sm_f, m = smallest_dynamical(self, dynatomic=dynatomic, start_n=start_n,\
+            sm_f, m = smallest_dynamical(self, dynatomic=dynatomic, start_n=start_n,
                  prec=prec, emb=emb, algorithm=algorithm, check_minimal=check_min)
         else:
             #reduce via covariant
@@ -6852,7 +6852,7 @@ def all_periodic_points(self, **kwds):
 
                 if alg != 'lifting':
                     for i in periods[:]:
-                        if (alg == 'dynatomic') or ((N == 1) \
+                        if (alg == 'dynatomic') or ((N == 1)
                                 and i <= pd_bounds[0] and DS.degree() <= pd_bounds[1]):
                             periodic.update(DS.periodic_points(i))
                             periods.remove(i)
@@ -7543,7 +7543,7 @@ def conjugating_set(self, other, R=None, num_cpus=2):
                 #else is_similar went to algebraic closure
                 if base in NumberFields():
                     from sage.rings.qqbar import number_field_elements_from_algebraics
-                    K,mK,phi = number_field_elements_from_algebraics([u for t in list(m) for u in t],\
+                    K,mK,phi = number_field_elements_from_algebraics([u for t in list(m) for u in t],
                                 minimal=True)
                     if K == base:
                         return [matrix(K, M, M, mK)]
@@ -8224,15 +8224,15 @@ def potential_good_reduction(self, prime, return_conjugation=False):
                 hom = old_parent.hom([new_parent.gens()[0]])
                 L = field_of_definition_periodic
                 if hom(K.defining_polynomial()) != L.defining_polynomial():
-                    raise ValueError('prime ideal of %s ' % K + \
-                        'but field of definition of fixed points is %s. ' % L + \
+                    raise ValueError('prime ideal of %s ' % K +
+                        'but field of definition of fixed points is %s. ' % L +
                         'see documentation for examples')
                 embedding = K.embeddings(field_of_definition_periodic)[0]
                 prime = embedding(prime)
         else:
             if field_of_definition_periodic is not QQ:
-                raise ValueError('field of definition of fixed ' + \
-                    'points is %s but prime is in QQ. ' %field_of_definition_periodic)
+                raise ValueError('field of definition of fixed ' +
+                    'points is %s but prime is in QQ. ' % field_of_definition_periodic)
 
         system = self.change_ring(field_of_definition_periodic)
         fixed_points = system.periodic_points(1)

src/sage/dynamics/arithmetic_dynamics/wehlerK3.py

@@ -113,7 +113,6 @@ def random_WehlerK3Surface(PP):
 
 class WehlerK3Surface_ring(AlgebraicScheme_subscheme_product_projective):
     r"""
-
     A K3 surface in `\mathbb{P}^2 \times \mathbb{P}^2` defined as the
     intersection of a bilinear and biquadratic form. [Weh1998]_
 
@@ -807,7 +806,7 @@ def degenerate_fibers(self):
         vars = list(PSX.gens())
         K = FractionField(PSX.base_ring())
         R0 = PolynomialRing(K, 3, vars)
-        I = R.ideal(self.Gpoly(1, 0), self.Gpoly(1, 1), self.Gpoly(1, 2), self.Hpoly(1, 0,1 ), \
+        I = R.ideal(self.Gpoly(1, 0), self.Gpoly(1, 1), self.Gpoly(1, 2), self.Hpoly(1, 0,1 ),
                     self.Hpoly(1, 0, 2), self.Hpoly(1, 1, 2))
         phi = R.hom(vars + [0, 0, 0], R0)
         I = phi(I)
@@ -838,7 +837,7 @@ def degenerate_fibers(self):
         vars = list(PSY.gens())
         K = FractionField(PSY.base_ring())
         R0 = PolynomialRing(K, 3, vars)
-        I = R.ideal(self.Gpoly(0, 0), self.Gpoly(0, 1), self.Gpoly(0, 2), self.Hpoly(0, 0, 1), \
+        I = R.ideal(self.Gpoly(0, 0), self.Gpoly(0, 1), self.Gpoly(0, 2), self.Hpoly(0, 0, 1),
                     self.Hpoly(0, 0, 2), self.Hpoly(0, 1, 2))
         phi = PP.coordinate_ring().hom([0, 0, 0] + vars, R0)
         I = phi(I)
@@ -1108,16 +1107,16 @@ def sigmaX(self, P, **kwds):
                     raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(P, self))
         pt = list(P[0]) + [0, 0, 0]
         if P[1][0] != 0:
-            [a,b,c] = [P[1][0]*self.Gpoly(1, 0)(*pt),\
-                       -1*P[1][0]*self.Hpoly(1, 0, 1)(*pt) - P[1][1]*self.Gpoly(1, 0)(*pt),\
+            [a,b,c] = [P[1][0]*self.Gpoly(1, 0)(*pt),
+                       -1*P[1][0]*self.Hpoly(1, 0, 1)(*pt) - P[1][1]*self.Gpoly(1, 0)(*pt),
                        -P[1][0]*self.Hpoly(1, 0, 2)(*pt) - P[1][2]*self.Gpoly(1, 0)(*pt)]
         elif P[1][1] != 0:
-            [a,b,c] = [-1*P[1][1]*self.Hpoly(1, 0, 1)(*pt)-P[1][0]*self.Gpoly(1, 1)(*pt),\
-                        P[1][1]*self.Gpoly(1, 1)(*pt),\
+            [a,b,c] = [-1*P[1][1]*self.Hpoly(1, 0, 1)(*pt)-P[1][0]*self.Gpoly(1, 1)(*pt),
+                        P[1][1]*self.Gpoly(1, 1)(*pt),
                        -P[1][1]*self.Hpoly(1, 1, 2)(*pt)-P[1][2]*self.Gpoly(1, 1)(*pt)]
         else:
-            [a,b,c] = [-1*P[1][2]*self.Hpoly(1, 0, 2)(*pt) - P[1][0]*self.Gpoly(1, 2)(*pt),\
-                       -P[1][2]*self.Hpoly(1, 1, 2)(*pt) - P[1][1]*self.Gpoly(1, 2)(*pt),\
+            [a,b,c] = [-1*P[1][2]*self.Hpoly(1, 0, 2)(*pt) - P[1][0]*self.Gpoly(1, 2)(*pt),
+                       -P[1][2]*self.Hpoly(1, 1, 2)(*pt) - P[1][1]*self.Gpoly(1, 2)(*pt),
                        P[1][2]*self.Gpoly(1, 2)(*pt)]
         Point = [P[0][0], P[0][1], P[0][2], a, b, c]
 
@@ -1148,13 +1147,13 @@ def sigmaX(self, P, **kwds):
             t = w1 - t1
             phi = R.hom([s1*(t) + s0*P[0][0]/P[0][2], s0*w1, s0, z0, z1, z2], S)
 
-        #Blow-up the fiber
-        T = [phi(self.L),phi(self.Q),\
-             phi(self.Gpoly(1, 0)),\
-             phi(self.Gpoly(1, 1)),\
-             phi(self.Gpoly(1, 2)),\
-            -phi(self.Hpoly(1, 0, 1)),\
-            -phi(self.Hpoly(1, 0, 2)),\
+        # Blow-up the fiber
+        T = [phi(self.L),phi(self.Q),
+             phi(self.Gpoly(1, 0)),
+             phi(self.Gpoly(1, 1)),
+             phi(self.Gpoly(1, 2)),
+            -phi(self.Hpoly(1, 0, 1)),
+            -phi(self.Hpoly(1, 0, 2)),
             -phi(self.Hpoly(1, 1, 2))]
         maxexp = []
 
@@ -1182,11 +1181,11 @@ def sigmaX(self, P, **kwds):
         #on the fiber
         RR = PolynomialRing(BR, 5,'s0, s1, z0, z1, z2',order = 'lex')
         s0, s1, z0, z1, z2 = RR.gens()
-        I = RR.ideal([RR(T[0]), \
-                      RR(T[1]), \
-                      RR(T[2]) - P[1][0]*z0, RR(T[3]) - P[1][1]*z1, RR(T[4])-P[1][2]*z2, \
-                      RR(T[5]) - (P[1][0]*z1 + P[1][1]*z0), \
-                      RR(T[6]) - (P[1][0]*z2 + P[1][2]*z0), \
+        I = RR.ideal([RR(T[0]),
+                      RR(T[1]),
+                      RR(T[2]) - P[1][0]*z0, RR(T[3]) - P[1][1]*z1, RR(T[4])-P[1][2]*z2,
+                      RR(T[5]) - (P[1][0]*z1 + P[1][1]*z0),
+                      RR(T[6]) - (P[1][0]*z2 + P[1][2]*z0),
                       RR(T[7]) - (P[1][1]*z2 + P[1][2]*z1)])
 
         #Find the points
@@ -1225,13 +1224,13 @@ def sigmaX(self, P, **kwds):
             for i in range(2,len(T)):
                 newT[i] = newT[i]/s**e
             #Create the new ideal
-            II = SS.ideal([SS(newT[0]), \
-                           SS(newT[1]), \
-                           SS(newT[2]) - P[1][0]*z0, \
-                           SS(newT[3]) - P[1][1]*z1, \
-                           SS(newT[4]) - P[1][2]*z2, \
-                           SS(newT[5]) - (P[1][0]*z1 + P[1][1]*z0), \
-                           SS(newT[6]) - (P[1][0]*z2 + P[1][2]*z0), \
+            II = SS.ideal([SS(newT[0]),
+                           SS(newT[1]),
+                           SS(newT[2]) - P[1][0]*z0,
+                           SS(newT[3]) - P[1][1]*z1,
+                           SS(newT[4]) - P[1][2]*z2,
+                           SS(newT[5]) - (P[1][0]*z1 + P[1][1]*z0),
+                           SS(newT[6]) - (P[1][0]*z2 + P[1][2]*z0),
                            SS(newT[7]) - (P[1][1]*z2 + P[1][2]*z1)])
 
             #Find the points
@@ -1350,16 +1349,16 @@ def sigmaY(self,P, **kwds):
                     raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(P, self))
         pt = [0, 0, 0] + list(P[1])
         if P[0][0] != 0:
-            [a, b, c] = [P[0][0]*self.Gpoly(0, 0)(*pt), \
-                      -1*P[0][0]*self.Hpoly(0, 0, 1)(*pt) - P[0][1]*self.Gpoly(0, 0)(*pt), \
+            [a, b, c] = [P[0][0]*self.Gpoly(0, 0)(*pt),
+                      -1*P[0][0]*self.Hpoly(0, 0, 1)(*pt) - P[0][1]*self.Gpoly(0, 0)(*pt),
                       -P[0][0]*self.Hpoly(0, 0, 2)(*pt) - P[0][2]*self.Gpoly(0, 0)(*pt)]
         elif P[0][1] != 0:
-            [a, b, c] = [-1*P[0][1]*self.Hpoly(0, 0, 1)(*pt) - P[0][0]*self.Gpoly(0, 1)(*pt),\
-                       P[0][1]*self.Gpoly(0, 1)(*pt), \
+            [a, b, c] = [-1*P[0][1]*self.Hpoly(0, 0, 1)(*pt) - P[0][0]*self.Gpoly(0, 1)(*pt),
+                       P[0][1]*self.Gpoly(0, 1)(*pt),
                        -P[0][1]*self.Hpoly(0, 1, 2)(*pt) - P[0][2]*self.Gpoly(0, 1)(*pt)]
         else:
-            [a, b, c] = [-1*P[0][2]*self.Hpoly(0, 0, 2)(*pt) - P[0][0]*self.Gpoly(0, 2)(*pt), \
-                       - P[0][2]*self.Hpoly(0, 1, 2)(*pt) - P[0][1]*self.Gpoly(0, 2)(*pt), \
+            [a, b, c] = [-1*P[0][2]*self.Hpoly(0, 0, 2)(*pt) - P[0][0]*self.Gpoly(0, 2)(*pt),
+                       - P[0][2]*self.Hpoly(0, 1, 2)(*pt) - P[0][1]*self.Gpoly(0, 2)(*pt),
                        P[0][2]*self.Gpoly(0, 2)(*pt)]
         Point = [a, b, c, P[1][0], P[1][1], P[1][2]]
         if [a, b, c] != [0, 0, 0]:
@@ -1391,13 +1390,13 @@ def sigmaY(self,P, **kwds):
             phi = R.hom([z0, z1, z2, s1*(t) + s0*P[1][0]/P[1][2], s0*w1, s0], S)
 
         #Blow-up the fiber
-        T = [phi(self.L),\
-         phi(self.Q),\
-         phi(self.Gpoly(0, 0)), \
-         phi(self.Gpoly(0, 1)), \
-         phi(self.Gpoly(0, 2)), \
-        -phi(self.Hpoly(0, 0, 1)), \
-        -phi(self.Hpoly(0, 0, 2)), \
+        T = [phi(self.L),
+         phi(self.Q),
+         phi(self.Gpoly(0, 0)),
+         phi(self.Gpoly(0, 1)),
+         phi(self.Gpoly(0, 2)),
+        -phi(self.Hpoly(0, 0, 1)),
+        -phi(self.Hpoly(0, 0, 2)),
         -phi(self.Hpoly(0, 1, 2))]
         maxexp = []
 
@@ -1422,13 +1421,13 @@ def sigmaY(self,P, **kwds):
         # on the fiber
         RR = PolynomialRing(BR, 5, 's0, s1, z0, z1, z2', order='lex')
         s0, s1, z0, z1, z2 = RR.gens()
-        I = RR.ideal([RR(T[0]), \
-                      RR(T[1]), \
-                      RR(T[2]) - P[0][0]*z0, \
-                      RR(T[3]) - P[0][1]*z1, \
-                      RR(T[4]) - P[0][2]*z2, \
-                      RR(T[5]) - (P[0][0]*z1 + P[0][1]*z0), \
-                      RR(T[6]) - (P[0][0]*z2 + P[0][2]*z0), \
+        I = RR.ideal([RR(T[0]),
+                      RR(T[1]),
+                      RR(T[2]) - P[0][0]*z0,
+                      RR(T[3]) - P[0][1]*z1,
+                      RR(T[4]) - P[0][2]*z2,
+                      RR(T[5]) - (P[0][0]*z1 + P[0][1]*z0),
+                      RR(T[6]) - (P[0][0]*z2 + P[0][2]*z0),
                       RR(T[7]) - (P[0][1]*z2 + P[0][2]*z1)])
         #Find the points
         SS = PolynomialRing(BR, 4, 's, z0, z1, z2', order = 'lex')
@@ -1465,14 +1464,14 @@ def sigmaY(self,P, **kwds):
             for i in range(2,len(T)):
                 newT[i] = newT[i]/s**e
             #Create the new ideal
-            II = SS.ideal([SS(newT[0]), \
-                           SS(newT[1]), \
-                           SS(newT[2]) - P[0][0]*z0, \
-                            SS(newT[3]) - P[0][1]*z1, \
-                            SS(newT[4]) - P[0][2]*z2, \
-                            SS(newT[5]) - (P[0][0]*z1 + P[0][1]*z0), \
-                            SS(newT[6]) - (P[0][0]*z2 + P[0][2]*z0), \
-                            SS(newT[7]) - (P[0][1]*z2 + P[0][2]*z1)])
+            II = SS.ideal([SS(newT[0]),
+                           SS(newT[1]),
+                           SS(newT[2]) - P[0][0]*z0,
+                           SS(newT[3]) - P[0][1]*z1,
+                           SS(newT[4]) - P[0][2]*z2,
+                           SS(newT[5]) - (P[0][0]*z1 + P[0][1]*z0),
+                           SS(newT[6]) - (P[0][0]*z2 + P[0][2]*z0),
+                           SS(newT[7]) - (P[0][1]*z2 + P[0][2]*z1)])
             # Find the points
             SSS = PolynomialRing(BR, 3, 'z0, z1, z2', order='lex')
             z0, z1, z2 = SSS.gens()
@@ -1633,11 +1632,11 @@ def lambda_plus(self, P, v, N, m, n, prec = 100):
             K = Qp(v, prec)
         PK = P.change_ring(K)
         W = self.change_ring(K)
-        Rx = W.ambient_space().coordinate_ring().hom(\
-             list(W.ambient_space()[0].coordinate_ring().gens())+[0, 0, 0], \
+        Rx = W.ambient_space().coordinate_ring().hom(
+             list(W.ambient_space()[0].coordinate_ring().gens()) + [0, 0, 0],
              W.ambient_space()[0].coordinate_ring())
-        Ry = W.ambient_space().coordinate_ring().hom(\
-             [0, 0, 0] + list(W.ambient_space()[1].coordinate_ring().gens()), \
+        Ry = W.ambient_space().coordinate_ring().hom(
+             [0, 0, 0] + list(W.ambient_space()[1].coordinate_ring().gens()),
              W.ambient_space()[1].coordinate_ring())
         beta = R(2 + sqrt(3))
         L = [x.abs() for x in list(PK[0])]
@@ -1730,10 +1729,10 @@ def lambda_minus(self, P, v, N, m, n, prec=100):
             K = Qp(v, prec)
         PK = P.change_ring(K)
         W = self.change_ring(K)
-        Rx = W.ambient_space().coordinate_ring().hom(list(W.ambient_space()[0].coordinate_ring().gens())\
-            +[0, 0, 0],W.ambient_space()[0].coordinate_ring())
-        Ry = W.ambient_space().coordinate_ring().hom([0, 0, 0] + \
-                list(W.ambient_space()[1].coordinate_ring().gens()), \
+        Rx = W.ambient_space().coordinate_ring().hom(list(W.ambient_space()[0].coordinate_ring().gens())
+            + [0, 0, 0], W.ambient_space()[0].coordinate_ring())
+        Ry = W.ambient_space().coordinate_ring().hom([0, 0, 0] +
+                list(W.ambient_space()[1].coordinate_ring().gens()),
                 W.ambient_space()[1].coordinate_ring())
         beta = R(2 + sqrt(3))
         L = [x.abs() for x in list(PK[0])]

src/sage/dynamics/complex_dynamics/mandel_julia.py

@@ -283,10 +283,11 @@ def mandelbrot_plot(f=None, **kwds):
                     max_iteration = 50
 
                 # Mandelbrot of General Polynomial Map
-                return polynomial_mandelbrot(f, parameter, x_center, y_center, \
-                 image_width, max_iteration, pixel_count, level_sep, \
+                return polynomial_mandelbrot(f, parameter, x_center, y_center,
+                 image_width, max_iteration, pixel_count, level_sep,
                  number_of_colors, base_color)
 
+
 def external_ray(theta, **kwds):
     r"""
     Draws the external ray(s) of a given angle (or list of angles)