gh-35892: fixing some pep8 warnings in schemes/toric
    
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### 📚 Description

fixes some pycodestyle warning in `schemes/toric`

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URL: #35892
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/schemes/toric/fano_variety.py

@@ -107,15 +107,14 @@
 # The first example of the tutorial is taken from
 # CPRFanoToricVariety_field.anticanonical_hypersurface
 
-
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2010 Andrey Novoseltsev <[email protected]>
 #       Copyright (C) 2010 William Stein <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 import re
 
@@ -527,7 +526,7 @@ def CPRFanoToricVariety(Delta=None,
             raise ValueError("the origin (point #%d) cannot be used for a "
                 "coordinate!\nGot: %s"
                 % (Delta_polar.origin(), coordinate_points))
-    point_to_ray = dict()
+    point_to_ray = {}
     for n, point in enumerate(coordinate_points):
         point_to_ray[point] = n
     # This can be simplified if LatticePolytopeClass is adjusted.
@@ -568,7 +567,7 @@ def CPRFanoToricVariety(Delta=None,
                         make_simplicial=make_simplicial)
     # Now create yet another fan making sure that the order of the rays is
     # the same as requested (it is a bit difficult to get it from the start)
-    trans = dict()
+    trans = {}
     for n, ray in enumerate(fan.rays()):
         trans[n] = rays.index(ray)
     cones = tuple(tuple(sorted(trans[r] for r in cone.ambient_ray_indices()))
@@ -1147,7 +1146,7 @@ def cartesian_product(self, other,
             Delta_polar = LatticePolytope(fan.rays())
 
             points = Delta_polar.points()
-            point_to_ray = dict()
+            point_to_ray = {}
             coordinate_points = []
             for ray_index, ray in enumerate(fan.rays()):
                 point = points.index(ray)
@@ -1230,7 +1229,7 @@ def resolve(self, **kwds):
                              "subdivision!" % Delta_polar.origin())
         if new_points:
             coordinate_points = coordinate_points + new_points
-            point_to_ray = dict()
+            point_to_ray = {}
             for n, point in enumerate(coordinate_points):
                 point_to_ray[point] = n
         else:

src/sage/schemes/toric/ideal.py

@@ -227,17 +227,17 @@ def __init__(self, A,
         """
         self._A = matrix(ZZ, A)
         if polynomial_ring:
-            if (names!='z') or (base_ring is not QQ):
+            if names != 'z' or base_ring is not QQ:
                 raise ValueError('you must not specify both variable names and a polynomial ring')
-            self._names = [str(_) for _ in polynomial_ring.gens()]
+            self._names = [str(g) for g in polynomial_ring.gens()]
             self._base_ring = polynomial_ring.base_ring()
             ring = polynomial_ring
         else:
             self._names = names
             self._base_ring = base_ring
             ring = self._init_ring('degrevlex')
 
-        if algorithm=='HostenSturmfels':
+        if algorithm == 'HostenSturmfels':
             ideal = self._ideal_HostenSturmfels()
         else:
             raise ValueError(f'algorithm = {algorithm} is not known')
@@ -396,9 +396,9 @@ def _ideal_quotient_by_variable(self, ring, ideal, n):
         """
         N = self.nvariables()
         y = list(ring.gens())
-        x = [ y[i-n] for i in range(N) ]
-        y_to_x = dict(zip(x,y))
-        x_to_y = dict(zip(y,x))
+        x = [y[i - n] for i in range(N)]
+        y_to_x = dict(zip(x, y))
+        x_to_y = dict(zip(y, x))
         # swap variables such that the n-th variable becomes the last one
         J = ideal.subs(y_to_x)
 
@@ -410,7 +410,7 @@ def _ideal_quotient_by_variable(self, ring, ideal, n):
         # x_n = y[0]   # the cheapest variable in the revlex order
         def subtract(e, power):
             l = list(e)
-            return tuple([l[0]-power] + l[1:])
+            return tuple([l[0] - power] + l[1:])
 
         def divide_by_x_n(p):
             d_old = p.dict()

src/sage/schemes/toric/library.py

@@ -27,16 +27,16 @@
     Multivariate Polynomial Ring in x, y, z over Rational Field
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2010 Volker Braun <[email protected]>
 #       Copyright (C) 2010 Andrey Novoseltsev <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.structure.sage_object import SageObject
 
@@ -121,30 +121,30 @@
          (-1, -1, -1), (-1, 1, -1), (1, -1, -1), (1, 1, -1)],
         [[0,1,2,3],[4,5,6,7],[0,1,7,6],[4,5,3,2],[0,2,5,7],[4,6,1,3]] ],
     'BCdlOG':[
-        [(-1, 0, 0, 2, 3),  #  0
-         ( 0,-1, 0, 2, 3),  #  1
-         ( 0, 0,-1, 2, 3),  #  2
-         ( 0, 0,-1, 1, 2),  #  3
-         ( 0, 0, 0,-1, 0),  #  4
-         ( 0, 0, 0, 0,-1),  #  5
-         ( 0, 0, 0, 2, 3),  #  6
-         ( 0, 0, 1, 2, 3),  #  7
-         ( 0, 0, 2, 2, 3),  #  8
-         ( 0, 0, 1, 1, 1),  #  9
+        [(-1, 0, 0, 2, 3),  # 0
+         ( 0,-1, 0, 2, 3),  # 1
+         ( 0, 0,-1, 2, 3),  # 2
+         ( 0, 0,-1, 1, 2),  # 3
+         ( 0, 0, 0,-1, 0),  # 4
+         ( 0, 0, 0, 0,-1),  # 5
+         ( 0, 0, 0, 2, 3),  # 6
+         ( 0, 0, 1, 2, 3),  # 7
+         ( 0, 0, 2, 2, 3),  # 8
+         ( 0, 0, 1, 1, 1),  # 9
          ( 0, 1, 2, 2, 3),  # 10
          ( 0, 1, 3, 2, 3),  # 11
-         ( 1, 0, 4, 2, 3)], # 12
-        [ [0,6,7,1,4],   [0,6,10,2,4],  [0,6,1,2,4],   [0,9,7,1,5],  [0,6,7,1,5],
-          [0,6,10,2,5],  [0,6,1,2,5],   [0,9,1,4,5],   [0,6,10,4,11],[0,6,7,4,11],
-          [0,6,10,5,11], [0,9,7,5,11],  [0,6,7,5,11],  [0,9,4,5,11], [0,10,4,5,11],
-          [0,9,7,1,8],   [0,9,1,4,8],   [0,7,1,4,8],   [0,9,7,11,8], [0,9,4,11,8],
-          [0,7,4,11,8],  [0,10,2,4,3],  [0,1,2,4,3],   [0,10,2,5,3], [0,1,2,5,3],
-          [0,10,4,5,3],  [0,1,4,5,3],   [12,6,7,1,4],  [12,6,10,2,4],[12,6,1,2,4],
-          [12,9,7,1,5],  [12,6,7,1,5],  [12,6,10,2,5], [12,6,1,2,5], [12,9,1,4,5],
+         ( 1, 0, 4, 2, 3)],  # 12
+        [ [0,6,7,1,4], [0,6,10,2,4], [0,6,1,2,4], [0,9,7,1,5], [0,6,7,1,5],
+          [0,6,10,2,5], [0,6,1,2,5], [0,9,1,4,5], [0,6,10,4,11],[0,6,7,4,11],
+          [0,6,10,5,11], [0,9,7,5,11], [0,6,7,5,11], [0,9,4,5,11], [0,10,4,5,11],
+          [0,9,7,1,8], [0,9,1,4,8], [0,7,1,4,8], [0,9,7,11,8], [0,9,4,11,8],
+          [0,7,4,11,8], [0,10,2,4,3], [0,1,2,4,3], [0,10,2,5,3], [0,1,2,5,3],
+          [0,10,4,5,3], [0,1,4,5,3], [12,6,7,1,4], [12,6,10,2,4],[12,6,1,2,4],
+          [12,9,7,1,5], [12,6,7,1,5], [12,6,10,2,5], [12,6,1,2,5], [12,9,1,4,5],
           [12,6,10,4,11],[12,6,7,4,11], [12,6,10,5,11],[12,9,7,5,11],[12,6,7,5,11],
-          [12,9,4,5,11], [12,10,4,5,11],[12,9,7,1,8],  [12,9,1,4,8], [12,7,1,4,8],
+          [12,9,4,5,11], [12,10,4,5,11],[12,9,7,1,8], [12,9,1,4,8], [12,7,1,4,8],
           [12,9,7,11,8], [12,9,4,11,8], [12,7,4,11,8], [12,10,2,4,3],[12,1,2,4,3],
-          [12,10,2,5,3], [12,1,2,5,3],  [12,10,4,5,3], [12,1,4,5,3] ]  ],
+          [12,10,2,5,3], [12,1,2,5,3], [12,10,4,5,3], [12,1,4,5,3] ]  ],
     'BCdlOG_base':[
         [(-1, 0, 0),
          ( 0,-1, 0),
@@ -535,7 +535,7 @@ def P(self, n, names='z+', base_ring=QQ):
         if n <= 0:
             raise ValueError("only projective spaces of positive dimension "
                              "can be constructed!\nGot: %s" % n)
-        m = identity_matrix(n).augment(matrix(n, 1, [-1]*n))
+        m = identity_matrix(n).augment(matrix(n, 1, [-1] * n))
         charts = [list(range(i)) + list(range(i + 1, n + 1))
                   for i in range(n + 1)]
         return CPRFanoToricVariety(
@@ -935,9 +935,15 @@ def Cube_deformation(self,k, names=None, base_ring=QQ):
         if k < 0:
             raise ValueError("cube deformations X_k are defined only for "
                              "non-negative k!\nGot: %s" % k)
-        rays = lambda kappa: matrix([[ 1, 1, 2*kappa+1],[ 1,-1, 1],[-1, 1, 1],[-1,-1, 1],
-                                       [-1,-1,-1],[-1, 1,-1],[ 1,-1,-1],[ 1, 1,-1]])
-        cones = [[0,1,2,3],[4,5,6,7],[0,1,7,6],[4,5,3,2],[0,2,5,7],[4,6,1,3]]
+
+        def rays(kappa):
+            return matrix([[1, 1, 2 * kappa + 1], [1, -1, 1],
+                           [-1, 1, 1], [-1, -1, 1],
+                           [-1, -1, -1], [-1, 1, -1],
+                           [1, -1, -1], [1, 1, -1]])
+
+        cones = [[0, 1, 2, 3], [4, 5, 6, 7], [0, 1, 7, 6],
+                 [4, 5, 3, 2], [0, 2, 5, 7], [4, 6, 1, 3]]
         fan = Fan(cones, rays(k))
         return ToricVariety(fan, coordinate_names=names)
 
@@ -1277,7 +1283,7 @@ def WP(self, *q, **kw):
 
         L = ToricLattice(m)
         L_sub = L.submodule([L(q)])
-        Q = L/L_sub
+        Q = L / L_sub
         rays = []
         cones = []
         w = list(range(m))
@@ -1286,7 +1292,7 @@ def WP(self, *q, **kw):
             b = L_basis[i]
             v = Q.coordinate_vector(Q(b))
             rays = rays + [v]
-            w_c = w[:i] + w[i+1:]
+            w_c = w[:i] + w[i + 1:]
             cones = cones + [tuple(w_c)]
         fan = Fan(cones,rays)
         return ToricVariety(fan, coordinate_names=names, base_ring=base_ring)

src/sage/schemes/toric/morphism.py

@@ -344,7 +344,7 @@
     1 connected components over (1, 2), each with 2 irreducible components.
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2011 Volker Braun <[email protected]>
 #       Copyright (C) 2010 Andrey Novoseltsev <[email protected]>
 #       Copyright (C) 2006 William Stein <[email protected]>
@@ -353,8 +353,8 @@
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 # For now, the scheme morphism base class cannot derive from Morphism
 # since this would clash with elliptic curves. So we derive only on
@@ -640,7 +640,7 @@ def _reverse_ray_map(self):
         """
         orbit = self.parent().domain()
         codomain_fan = self.parent().codomain().fan()
-        reverse_ray_dict = dict()
+        reverse_ray_dict = {}
         for n1, n2 in self._ray_map.items():
             ray_index = codomain_fan.rays().index(n1)
             if n2.is_zero():
@@ -760,7 +760,7 @@ def pullback_divisor(self, divisor):
         codomain_rays = self.codomain().fan().rays()
         for ray in self.domain().fan().rays():
             ray = codomain_rays[self._reverse_ray_map()[ray]]
-            value = divisor.function_value(ray) - m*ray
+            value = divisor.function_value(ray) - m * ray
             values.append(value)
         return self.domain().divisor(values)
 
@@ -855,9 +855,9 @@ def __init__(self, parent, fan_morphism, check=True):
                     to Rational polyhedral fan in 1-d lattice N.
         """
         SchemeMorphism.__init__(self, parent)
-        if check and self.domain().fan()!=fan_morphism.domain_fan():
+        if check and self.domain().fan() != fan_morphism.domain_fan():
             raise ValueError('the fan morphism domain must be the fan of the domain')
-        if check and self.codomain().fan()!=fan_morphism.codomain_fan():
+        if check and self.codomain().fan() != fan_morphism.codomain_fan():
             raise ValueError('the fan morphism codomain must be the fan of the codomain')
         self._fan_morphism = fan_morphism
 
@@ -1816,7 +1816,7 @@ def _make_fiber_component(self):
         ker = fm.kernel().basis()
         m = fm.matrix() * base_cone.lattice().basis_matrix()
         base_cone_preimg = [m.solve_left(r) for r in base_cone.rays()]
-        L = fm.domain_fan().lattice().span(ker+base_cone_preimg).saturation()
+        L = fm.domain_fan().lattice().span(ker + base_cone_preimg).saturation()
 
         cone_L = Cone([L.coordinates(r) for r in defining_cone.rays()])
         L_quotient = cone_L.sublattice_quotient()
@@ -1833,7 +1833,7 @@ def projection(ray):
             cones.append(Cone(projected_rays))
         fiber_fan = Fan(cones)
 
-        ray_index_map = dict()
+        ray_index_map = {}
         for ray in star_rays:
             ray_index = fm.domain_fan().rays().index(ray)
             projected_ray = fiber_fan.lattice()(projection(ray))
@@ -1939,7 +1939,7 @@ def _image_ray_multiplicity(self, fiber_ray):
             d = gcd(ray)
             if d * fiber_ray != ray:
                 continue
-            if multiplicity is not None and d>multiplicity:
+            if multiplicity is not None and d > multiplicity:
                 continue
             multiplicity = d
             image_ray_index = index
@@ -1984,7 +1984,7 @@ def pullback_divisor(self, divisor):
         for ray in self.domain().fan().rays():
             image_ray_index, multiplicity = self._image_ray_multiplicity(ray)
             image_ray = codomain_rays[image_ray_index]
-            value = divisor.function_value(image_ray) - m*image_ray
+            value = divisor.function_value(image_ray) - m * image_ray
             value /= multiplicity
             values.append(value)
         return self.domain().divisor(values)