fix all remaining E251 warnings

Author: fchapoton

src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py

@@ -126,7 +126,7 @@ def automorphism_group_QQ_fixedpoints(rational_function, return_functions=False,
     else:
         elements = [matrix(F, 2, [1,0,0,1])]
 
-    rational_roots = h.roots(multiplicities = False)
+    rational_roots = h.roots(multiplicities=False)
 
     min_poly = 1
 
@@ -743,7 +743,7 @@ def automorphism_group_QQ_CRT(rational_function, prime_lower_bound=4, return_fun
             # compute automorphisms mod p
             phi_p = f.change_ring(GF(p))/g.change_ring(GF(p))
             sorted_automorphisms = automorphism_group_FF(phi_p)
-            sorted_automorphisms.sort(key = PGL_order)
+            sorted_automorphisms.sort(key=PGL_order)
             orders = [PGL_order(A) for A in sorted_automorphisms]
 
             automorphisms.append(sorted_automorphisms)

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -4519,7 +4519,7 @@ def preperiodic_points(self, m, n, **kwds):
                     # we now deform by a parameter t
                     T = R['t']
                     t = T.gens()[0]
-                    Pt = ProjectiveSpace(N-1, R=T, names = [str(i) for i in CR.gens()])
+                    Pt = ProjectiveSpace(N-1, R=T, names=[str(i) for i in CR.gens()])
                     deformed_polys = [poly + t*Pt.gens()[-1]**d for poly in new_f.defining_polynomials()[:-1]]
                     deformed_polys += [new_f.defining_polynomials()[-1]]
                     f_deformed = DynamicalSystem(deformed_polys)
@@ -4869,7 +4869,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
                             # we now deform by a parameter t
                             T = R['t']
                             t = T.gens()[0]
-                            Pt = ProjectiveSpace(N-1, R=T, names = [str(i) for i in CR.gens()])
+                            Pt = ProjectiveSpace(N-1, R=T, names=[str(i) for i in CR.gens()])
                             deformed_polys = [poly + t*Pt.gens()[-1]**d for poly in new_f.defining_polynomials()[:-1]]
                             deformed_polys += [new_f.defining_polynomials()[-1]]
                             f_deformed = DynamicalSystem(deformed_polys)
@@ -5694,7 +5694,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
                 # we now deform by a parameter t
                 T = base_ring['k']
                 k = T.gens()[0]
-                Pt = ProjectiveSpace(N, R=T, names = [str(i) for i in CR.gens()])
+                Pt = ProjectiveSpace(N, R=T, names=[str(i) for i in CR.gens()])
                 deformed_polys = [poly + k*Pt.gens()[-1]**d for poly in new_f.defining_polynomials()[:-1]]
                 deformed_polys += [new_f.defining_polynomials()[-1]]
                 f_deformed = DynamicalSystem(deformed_polys)
@@ -6331,7 +6331,7 @@ def _is_preperiodic(self, P, err=0.1, return_period=False):
 
         # we calculate the canonical height without considering
         # if the domain is a subscheme
-        h = f.canonical_height(P, error_bound = err)
+        h = f.canonical_height(P, error_bound=err)
         # we know canonical height 0 if and only if preperiodic
         # however precision issues can occur so we can only tell *not* preperiodic
         # if the value is larger than the error

src/sage/dynamics/arithmetic_dynamics/wehlerK3.py

@@ -815,7 +815,7 @@ def degenerate_fibers(self):
         for n in range(3):
             affvars = list(R0.gens())
             del affvars[n]
-            R1 = PolynomialRing(K, 2, affvars, order = 'lex')
+            R1 = PolynomialRing(K, 2, affvars, order='lex')
             mapvars = list(R1.gens())
             mapvars.insert(n,1)
             phi1 = R0.hom(mapvars, R1)
@@ -846,7 +846,7 @@ def degenerate_fibers(self):
         for n in range(3):
             affvars = list(R0.gens())
             del affvars[n]
-            R1 = PolynomialRing(K, 2, affvars, order = 'lex')
+            R1 = PolynomialRing(K, 2, affvars, order='lex')
             mapvars = list(R1.gens())
             mapvars.insert(n, 1)
             phi1 = R0.hom(mapvars,R1)
@@ -867,7 +867,7 @@ def degenerate_fibers(self):
         return [xFibers,yFibers]
 
     @cached_method
-    def degenerate_primes(self,check = True):
+    def degenerate_primes(self,check=True):
         r"""
         Determine which primes `p` self has degenerate fibers over `GF(p)`.
 
@@ -1179,7 +1179,7 @@ def sigmaX(self, P, **kwds):
 
         #Defines the ideal whose solution gives `(s0, s1)` and the two points
         #on the fiber
-        RR = PolynomialRing(BR, 5,'s0, s1, z0, z1, z2',order = 'lex')
+        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]),
@@ -1189,7 +1189,7 @@ def sigmaX(self, P, **kwds):
                       RR(T[7]) - (P[1][1]*z2 + P[1][2]*z1)])
 
         #Find the points
-        SS = PolynomialRing(BR, 4,'s, z0, z1, z2', order = 'lex')
+        SS = PolynomialRing(BR, 4,'s, z0, z1, z2', order='lex')
         s, z0, z1, z2 = SS.gens()
         phi = RR.hom([s, 1, z0, z1, z2], SS)
         J = phi(I)
@@ -1234,7 +1234,7 @@ def sigmaX(self, P, **kwds):
                            SS(newT[7]) - (P[1][1]*z2 + P[1][2]*z1)])
 
             #Find the points
-            SSS = PolynomialRing(BR, 3, 'z0, z1, z2', order = 'lex')
+            SSS = PolynomialRing(BR, 3, 'z0, z1, z2', order='lex')
             z0,z1,z2 = SSS.gens()
             phi = SS.hom([0, z0, z1, z2], SSS)
             J2 = phi(II)
@@ -1248,7 +1248,7 @@ def sigmaX(self, P, **kwds):
                 [a, b, c] = [V[0][z0], V[0][z1], V[0][z2]]
 
             if len(V) == 0 or [a,b,c] == [0, 0, 0]:
-                SS = PolynomialRing(BR, 3, 'z0, z1, z2', order = 'lex')
+                SS = PolynomialRing(BR, 3, 'z0, z1, z2', order='lex')
                 z0,z1,z2 = SS.gens()
                 phi = RR.hom([1, 0, z0, z1, z2], SS)
                 J = phi(I)
@@ -1430,7 +1430,7 @@ def sigmaY(self,P, **kwds):
                       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')
+        SS = PolynomialRing(BR, 4, 's, z0, z1, z2', order='lex')
         s, z0, z1, z2 = SS.gens()
         phi = RR.hom([s, 1, z0, z1, z2], SS)
         J = phi(I)
@@ -1486,7 +1486,7 @@ def sigmaY(self,P, **kwds):
             if len(V) == 1:
                 [a, b, c] = [V[0][z0], V[0][z1], V[0][z2]]
             if len(V) == 0 or [a,b,c] == [0, 0, 0]:
-                SS = PolynomialRing(BR, 3, 'z0, z1, z2', order = 'lex')
+                SS = PolynomialRing(BR, 3, 'z0, z1, z2', order='lex')
                 z0,z1,z2 = SS.gens()
                 phi = RR.hom([1, 0, z0, z1, z2], SS)
                 J = phi(I)
@@ -1584,7 +1584,7 @@ def psi(self,a, **kwds):
         kwds.update({"check":False})
         return self.sigmaX(A, **kwds)
 
-    def lambda_plus(self, P, v, N, m, n, prec = 100):
+    def lambda_plus(self, P, v, N, m, n, prec=100):
         r"""
         Evaluates the  local canonical height plus function of Call-Silverman at
         the place ``v`` for ``P`` with ``N`` terms of the series.
@@ -1744,7 +1744,7 @@ def lambda_minus(self, P, v, N, m, n, prec=100):
         local_height = beta*R((PK[1][i]/PK[1][n]).abs()).log() - R((PK[0][j]/PK[0][m]).abs()).log()
         for e in range(N):
             #Take the next iterate
-            Q = W.psi(PK, check = False)
+            Q = W.psi(PK, check=False)
             L = [x.abs() for x in list(Q[0])]
             l = L.index(max(L))
             L = [y.abs() for y in list(Q[1])]

src/sage/dynamics/complex_dynamics/mandel_julia.py

@@ -206,21 +206,21 @@ def mandelbrot_plot(f=None, **kwds):
 
     from ipywidgets.widgets import FloatSlider, IntSlider, ColorPicker, interact
     widgets = dict(
-                   x_center = FloatSlider(min=-1.0, max=1.0, step=EPS,
+                   x_center=FloatSlider(min=-1.0, max=1.0, step=EPS,
                                           value=x_center, description="Real center"),
-                   y_center = FloatSlider(min=-1.0, max=1.0, step=EPS,
+                   y_center=FloatSlider(min=-1.0, max=1.0, step=EPS,
                                           value=y_center, description="Imag center"),
-                   image_width = FloatSlider(min=EPS, max=4.0, step=EPS,
+                   image_width=FloatSlider(min=EPS, max=4.0, step=EPS,
                                              value=image_width, description="Width"),
-                   max_iteration = IntSlider(min=0, max=1000,
+                   max_iteration=IntSlider(min=0, max=1000,
                                              value=max_iteration, description="Iterations"),
-                   pixel_count = IntSlider(min=10, max=1000,
+                   pixel_count=IntSlider(min=10, max=1000,
                                            value=pixel_count, description="Pixels"),
-                   level_sep = IntSlider(min=1, max=20,
+                   level_sep=IntSlider(min=1, max=20,
                                          value=level_sep, description="Color sep"),
-                   color_num = IntSlider(min=1, max=100,
+                   color_num=IntSlider(min=1, max=100,
                                          value=number_of_colors, description="# Colors"),
-                   base_color = ColorPicker(value=Color(base_color).html_color(),
+                   base_color=ColorPicker(value=Color(base_color).html_color(),
                                             description="Base color"),
                    )
 
@@ -729,25 +729,25 @@ def julia_plot(f=None, **kwds):
             from ipywidgets.widgets import FloatSlider, IntSlider, \
                                            ColorPicker, interact
             widgets = dict(
-                c_real = FloatSlider(min=-2.0, max=2.0, step=EPS,
+                c_real=FloatSlider(min=-2.0, max=2.0, step=EPS,
                                   value=c_real, description="Real c"),
-                c_imag = FloatSlider(min=-2.0, max=2.0, step=EPS,
+                c_imag=FloatSlider(min=-2.0, max=2.0, step=EPS,
                                   value=c_imag, description="Imag c"),
-                x_center = FloatSlider(min=-1.0, max=1.0, step=EPS,
+                x_center=FloatSlider(min=-1.0, max=1.0, step=EPS,
                                   value=x_center, description="Real center"),
-                y_center = FloatSlider(min=-1.0, max=1.0, step=EPS,
+                y_center=FloatSlider(min=-1.0, max=1.0, step=EPS,
                                   value=y_center, description="Imag center"),
-                image_width = FloatSlider(min=EPS, max=4.0, step=EPS,
+                image_width=FloatSlider(min=EPS, max=4.0, step=EPS,
                                   value=image_width, description="Width"),
-                max_iteration = IntSlider(min=0, max=1000,
+                max_iteration=IntSlider(min=0, max=1000,
                                   value=max_iteration, description="Iterations"),
-                pixel_count = IntSlider(min=10, max=1000,
+                pixel_count=IntSlider(min=10, max=1000,
                                   value=pixel_count, description="Pixels"),
-                level_sep = IntSlider(min=1, max=20,
+                level_sep=IntSlider(min=1, max=20,
                                   value=level_sep, description="Color sep"),
-                color_num = IntSlider(min=1, max=100,
+                color_num=IntSlider(min=1, max=100,
                                   value=number_of_colors, description="# Colors"),
-                base_color = ColorPicker(value=base_color.html_color(),
+                base_color=ColorPicker(value=base_color.html_color(),
                                          description="Base color"),
             )
             if mandelbrot:

src/sage/modules/free_module.py

@@ -2592,7 +2592,7 @@ def basis_matrix(self, ring=None):
         except AttributeError:
             MAT = sage.matrix.matrix_space.MatrixSpace(self.coordinate_ring(),
                             len(self.basis()), self.degree(),
-                            sparse = self.is_sparse())
+                            sparse=self.is_sparse())
             if self.is_ambient():
                 A = MAT.identity_matrix()
             else:
@@ -5378,7 +5378,7 @@ def _dense_module(self):
             sage: M is S._dense_module()
             True
         """
-        return FreeModule(base_ring=self.base_ring(), rank = self.rank(), sparse=False)
+        return FreeModule(base_ring=self.base_ring(), rank=self.rank(), sparse=False)
 
     def _sparse_module(self):
         """
@@ -5394,7 +5394,7 @@ def _sparse_module(self):
             sage: M._sparse_module() is S
             True
         """
-        return FreeModule(base_ring=self.base_ring(), rank = self.rank(), sparse=True)
+        return FreeModule(base_ring=self.base_ring(), rank=self.rank(), sparse=True)
 
     def echelonized_basis_matrix(self):
         """
@@ -6683,7 +6683,7 @@ def _echelonized_basis(self, ambient, basis):
         # Return the first rank rows (i.e., the nonzero rows).
         d = self._denominator(basis)
         MAT = sage.matrix.matrix_space.MatrixSpace(
-            ambient.base_ring(), len(basis), ambient.degree(), sparse = ambient.is_sparse())
+            ambient.base_ring(), len(basis), ambient.degree(), sparse=ambient.is_sparse())
         if d != 1:
             basis = [x*d for x in basis]
         A = MAT(basis)
@@ -7051,7 +7051,7 @@ def user_to_echelon_matrix(self):
                 rows = sum([self.echelon_coordinates(b,check=False) for b in self.basis()], [])
                 M = sage.matrix.matrix_space.MatrixSpace(self.base_ring().fraction_field(),
                                              self.dimension(),
-                                             sparse = self.is_sparse())
+                                             sparse=self.is_sparse())
                 self.__user_to_echelon_matrix = M(rows)
         return self.__user_to_echelon_matrix
 

src/sage/modules/submodule.py

@@ -165,7 +165,7 @@ def matrix(self):
         """
         from sage.matrix.matrix_space import MatrixSpace
         MAT = MatrixSpace(self.base_ring(), len(self.gens()), self.degree(),
-                          sparse = self.is_sparse())
+                          sparse=self.is_sparse())
         A = MAT(self.gens())
         A.set_immutable()
         return A

src/sage/modules/with_basis/morphism.py

@@ -1127,7 +1127,7 @@ def cokernel_basis_indices(self):
             raise NotImplementedError("cokernel_basis_indices implemented only for morphisms with a finite dimensional codomain")
         return [i for i in self.codomain().basis().keys() if self._inverse_on_support(i) is None]
 
-    def cokernel_projection(self, category = None):
+    def cokernel_projection(self, category=None):
         """
         Return a projection on the co-kernel of ``self``.
 
@@ -1517,7 +1517,7 @@ def __invert__(self):
         """
         return self.codomain().module_morphism(
             diagonal=pointwise_inverse_function(self._diagonal),
-            codomain=self.domain(), category = self.category_for())
+            codomain=self.domain(), category=self.category_for())
 
 
 def pointwise_inverse_function(f):