pep8 fixes in schemes/toric

src/sage/schemes/toric/ideal.py

@@ -354,8 +354,8 @@ def _naive_ideal(self, ring):
         x = ring.gens()
         binomials = []
         for row in self.ker().matrix().rows():
-            xpos = prod(x[i]**max( row[i],0) for i in range(0,len(x)))
-            xneg = prod(x[i]**max(-row[i],0) for i in range(0,len(x)))
+            xpos = prod(x[i]**max(row[i], 0) for i in range(len(x)))
+            xneg = prod(x[i]**max(-row[i], 0) for i in range(len(x)))
             binomials.append(xpos - xneg)
         return ring.ideal(binomials)
 
@@ -445,6 +445,6 @@ def _ideal_HostenSturmfels(self):
         J = self._naive_ideal(ring)
         if J.is_zero():
             return J
-        for i in range(0,self.nvariables()):
+        for i in range(self.nvariables()):
             J = self._ideal_quotient_by_variable(ring, J, i)
         return J

src/sage/schemes/toric/library.py

@@ -58,44 +58,44 @@
 # The combinatorial data of the toric varieties is stored separately here
 # since we might want to use it later on to do the reverse lookup.
 toric_varieties_rays_cones = {
-    'dP6':[
+    'dP6': [
         [(0, 1), (-1, 0), (-1, -1), (0, -1), (1, 0), (1, 1)],
-        [[0,1],[1,2],[2,3],[3,4],[4,5],[5,0]] ],
-    'dP7':[
+        [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]]],
+    'dP7': [
         [(0, 1), (-1, 0), (-1, -1), (0, -1), (1, 0)],
-        [[0,1],[1,2],[2,3],[3,4],[4,0]] ],
-    'dP8':[
-        [(1,1), (0, 1), (-1, -1), (1, 0)],
-        [[0,1],[1,2],[2,3],[3,0]]
+        [[0, 1], [1, 2], [2, 3], [3, 4], [4, 0]]],
+    'dP8': [
+        [(1, 1), (0, 1), (-1, -1), (1, 0)],
+        [[0, 1], [1, 2], [2, 3], [3, 0]]
         ],
-    'P1xP1':[
+    'P1xP1': [
         [(1, 0), (-1, 0), (0, 1), (0, -1)],
-        [[0,2],[2,1],[1,3],[3,0]] ],
-    'P1xP1_Z2':[
+        [[0, 2], [2, 1], [1, 3], [3, 0]]],
+    'P1xP1_Z2': [
         [(1, 1), (-1, -1), (-1, 1), (1, -1)],
-        [[0,2],[2,1],[1,3],[3,0]] ],
-    'P1':[
+        [[0, 2], [2, 1], [1, 3], [3, 0]]],
+    'P1': [
         [(1,), (-1,)],
-        [[0],[1]] ],
-    'P2':[
-        [(1,0), (0, 1), (-1, -1)],
-        [[0,1],[1,2],[2,0]] ],
-    'A1':[
+        [[0], [1]]],
+    'P2': [
+        [(1, 0), (0, 1), (-1, -1)],
+        [[0, 1], [1, 2], [2, 0]]],
+    'A1': [
         [(1,)],
-        [[0]] ],
-    'A2':[
+        [[0]]],
+    'A2': [
         [(1, 0), (0, 1)],
-        [[0,1]] ],
-    'A2_Z2':[
+        [[0, 1]]],
+    'A2_Z2': [
         [(1, 0), (1, 2)],
-        [[0,1]] ],
-    'P1xA1':[
+        [[0, 1]]],
+    'P1xA1': [
         [(1, 0), (-1, 0), (0, 1)],
-        [[0,2],[2,1]] ],
-    'Conifold':[
+        [[0, 2], [2, 1]]],
+    'Conifold': [
         [(0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)],
-        [[0,1,2,3]] ],
-    'dP6xdP6':[
+        [[0, 1, 2, 3]]],
+    'dP6xdP6': [
         [(0, 1, 0, 0), (-1, 0, 0, 0), (-1, -1, 0, 0),
          (0, -1, 0, 0), (1, 0, 0, 0), (1, 1, 0, 0),
          (0, 0, 0, 1), (0, 0, -1, 0), (0, 0, -1, -1),
@@ -108,74 +108,74 @@
          [3, 4, 8, 9], [3, 4, 9, 10], [3, 4, 10, 11], [3, 4, 6, 11],
          [4, 5, 6, 7], [4, 5, 7, 8], [4, 5, 8, 9], [4, 5, 9, 10],
          [4, 5, 10, 11], [4, 5, 6, 11], [0, 5, 6, 7], [0, 5, 7, 8],
-         [0, 5, 8, 9], [0, 5, 9, 10], [0, 5, 10, 11], [0, 5, 6, 11]] ],
-    'Cube_face_fan':[
+         [0, 5, 8, 9], [0, 5, 9, 10], [0, 5, 10, 11], [0, 5, 6, 11]]],
+    'Cube_face_fan': [
         [(1, 1, 1), (1, -1, 1), (-1, 1, 1), (-1, -1, 1),
          (-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]] ],
-    'Cube_sublattice':[
+        [[0, 1, 2, 3], [4, 5, 6, 7], [0, 1, 7, 6], [4, 5, 3, 2], [0, 2, 5, 7], [4, 6, 1, 3]]],
+    'Cube_sublattice': [
         [(1, 0, 0), (0, 1, 0), (0, 0, 1), (-1, 1, 1),
          (-1, 0, 0), (0, -1, 0), (0, 0, -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]] ],
-    'Cube_nonpolyhedral':[
+        [[0, 1, 2, 3], [4, 5, 6, 7], [0, 1, 7, 6], [4, 5, 3, 2], [0, 2, 5, 7], [4, 6, 1, 3]]],
+    'Cube_nonpolyhedral': [
         [(1, 2, 3), (1, -1, 1), (-1, 1, 1), (-1, -1, 1),
          (-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':[
+        [[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
-         ( 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],
-          [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],
-          [12,9,7,11,8], [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] ]  ],
-    'BCdlOG_base':[
+         (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],
+          [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, 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]]],
+    'BCdlOG_base': [
         [(-1, 0, 0),
-         ( 0,-1, 0),
-         ( 0, 0,-1),
-         ( 0, 0, 1),
-         ( 0, 1, 2),
-         ( 0, 1, 3),
-         ( 1, 0, 4)],
-        [[0,4,2],[0,4,5],[0,5,3],[0,1,3],[0,1,2],
-         [6,4,2],[6,4,5],[6,5,3],[6,1,3],[6,1,2]] ],
-    'P2_112':[
-        [(1,0), (0, 1), (-1, -2)],
-        [[0,1],[1,2],[2,0]] ],
-    'P2_123':[
-        [(1,0), (0, 1), (-2, -3)],
-        [[0,1],[1,2],[2,0]] ],
-    'P4_11169':[
+         (0, -1, 0),
+         (0, 0, -1),
+         (0, 0, 1),
+         (0, 1, 2),
+         (0, 1, 3),
+         (1, 0, 4)],
+        [[0, 4, 2], [0, 4, 5], [0, 5, 3], [0, 1, 3], [0, 1, 2],
+         [6, 4, 2], [6, 4, 5], [6, 5, 3], [6, 1, 3], [6, 1, 2]]],
+    'P2_112': [
+        [(1, 0), (0, 1), (-1, -2)],
+        [[0, 1], [1, 2], [2, 0]]],
+    'P2_123': [
+        [(1, 0), (0, 1), (-2, -3)],
+        [[0, 1], [1, 2], [2, 0]]],
+    'P4_11169': [
         [(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (-9, -6, -1, -1)],
-        [[0,1,2,3],[0,1,2,4],[0,1,3,4],[0,2,3,4],[1,2,3,4]] ],
-    'P4_11169_resolved':[
+        [[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [1, 2, 3, 4]]],
+    'P4_11169_resolved': [
         [(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (-9, -6, -1, -1), (-3, -2, 0, 0)],
         [[0, 1, 2, 3], [0, 1, 3, 4], [0, 1, 2, 4], [1, 3, 4, 5], [0, 3, 4, 5],
-         [1, 2, 4, 5], [0, 2, 4, 5], [1, 2, 3, 5], [0, 2, 3, 5]] ],
-    'P4_11133':[
+         [1, 2, 4, 5], [0, 2, 4, 5], [1, 2, 3, 5], [0, 2, 3, 5]]],
+    'P4_11133': [
         [(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (-3, -3, -1, -1)],
-        [[0,1,2,3],[0,1,2,4],[0,1,3,4],[0,2,3,4],[1,2,3,4]] ],
-    'P4_11133_resolved':[
+        [[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [1, 2, 3, 4]]],
+    'P4_11133_resolved': [
         [(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (-3, -3, -1, -1), (-1, -1, 0, 0)],
         [[0, 1, 2, 3], [0, 1, 3, 4], [0, 1, 2, 4], [1, 3, 4, 5], [0, 3, 4, 5],
-         [1, 2, 4, 5], [0, 2, 4, 5], [1, 2, 3, 5], [0, 2, 3, 5]] ]
+         [1, 2, 4, 5], [0, 2, 4, 5], [1, 2, 3, 5], [0, 2, 3, 5]]]
 }
 
 
@@ -264,7 +264,7 @@ def _make_CPRFanoToricVariety(self, name, coordinate_names, base_ring):
             polytope = LatticePolytope(rays, lattice=ToricLattice(len(rays[0])))
             points = [tuple(_) for _ in polytope.points()]
             ray2point = [points.index(r) for r in rays]
-            charts = [ [ray2point[i] for i in c] for c in cones ]
+            charts = [[ray2point[i] for i in c] for c in cones]
             self.__dict__[dict_key] = \
                 CPRFanoToricVariety(Delta_polar=polytope,
                                     coordinate_points=ray2point,
@@ -868,7 +868,7 @@ def Cube_nonpolyhedral(self, names='z+', base_ring=QQ):
         """
         return self._make_ToricVariety('Cube_nonpolyhedral', names, base_ring)
 
-    def Cube_deformation(self,k, names=None, base_ring=QQ):
+    def Cube_deformation(self, k, names=None, base_ring=QQ):
         r"""
         Construct, for each `k\in\ZZ_{\geq 0}`, a toric variety with
         `\ZZ_k`-torsion in the Chow group.
@@ -1268,7 +1268,7 @@ def WP(self, *q, **kw):
             rays = rays + [v]
             w_c = w[:i] + w[i + 1:]
             cones = cones + [tuple(w_c)]
-        fan = Fan(cones,rays)
+        fan = Fan(cones, rays)
         return ToricVariety(fan, coordinate_names=names, base_ring=base_ring)
 
     def torus(self, n, names='z+', base_ring=QQ):

src/sage/schemes/toric/sheaf/klyachko.py

@@ -605,7 +605,7 @@ def cohomology_complex(self, m):
         C = fan.complex()
         CV = []
         F = self.base_ring()
-        for dim in range(1,fan.dim()+1):
+        for dim in range(1, fan.dim()+1):
             codim = fan.dim() - dim
             d_C = C.differential(codim)
             d_V = []
@@ -616,7 +616,7 @@ def cohomology_complex(self, m):
                     sigma = fan(dim-1)[i]
                     if sigma.is_face_of(tau):
                         pr = self.E_quotient_projection(sigma, tau, m)
-                        d = d_C[i,j] * pr.matrix().transpose()
+                        d = d_C[i, j] * pr.matrix().transpose()
                     else:
                         E_sigma = self.E_quotient(sigma, m)
                         E_tau = self.E_quotient(tau, m)
@@ -695,7 +695,7 @@ def cohomology(self, degree=None, weight=None, dim=False):
             except KeyError:
                 HH[d] = FreeModule(self.base_ring(), 0)
         if dim:
-            HH = vector(ZZ, [HH[i].rank() for i in range(space_dim+1) ])
+            HH = vector(ZZ, [HH[i].rank() for i in range(space_dim+1)])
         return HH
 
     def __richcmp__(self, other, op):

src/sage/schemes/toric/toric_subscheme.py

@@ -328,14 +328,14 @@ def pullback_polynomial(p):
             result = R.zero()
             for coefficient, monomial in p:
                 exponent = monomial.exponents()[0]
-                exponent = [ exponent[i] for i in cone.ambient_ray_indices() ]
-                exponent = vector(ZZ,exponent)
+                exponent = [exponent[i] for i in cone.ambient_ray_indices()]
+                exponent = vector(ZZ, exponent)
                 m = n_rho_matrix.solve_right(exponent)
                 assert all(x in ZZ for x in m), \
-                    'The polynomial '+str(p)+' does not define a ZZ-divisor!'
+                    f'The polynomial {p} does not define a ZZ-divisor!'
                 m_coeffs = dualcone.Hilbert_coefficients(m)
                 result += coefficient * prod(R.gen(i)**m_coeffs[i]
-                                             for i in range(0,R.ngens()))
+                                             for i in range(R.ngens()))
             return result
 
         # construct the affine algebraic scheme to use as patch
@@ -353,7 +353,7 @@ def pullback_polynomial(p):
         if cone.is_smooth():
             x = ambient.coordinate_ring().gens()
             phi = []
-            for i in range(0,fan.nrays()):
+            for i in range(fan.nrays()):
                 if i in cone.ambient_ray_indices():
                     phi.append(pullback_polynomial(x[i]))
                 else:
@@ -371,11 +371,10 @@ def pullback_polynomial(p):
         # it remains to find the preimage of point
         # map m to the monomial x^{D_m}, see reference.
         F = ambient.coordinate_ring().fraction_field()
-        image = []
-        for m in dualcone.Hilbert_basis():
-            x_Dm = prod([ F.gen(i)**(m*n) for i,n in enumerate(fan.rays()) ])
-            image.append(x_Dm)
-        patch._embedding_center = tuple( f(list(point)) for f in image )
+        image = [prod([F.gen(i)**(m * n)
+                       for i, n in enumerate(fan.rays())])
+                 for m in dualcone.Hilbert_basis()]
+        patch._embedding_center = tuple(f(list(point)) for f in image)
         return patch
 
     def _best_affine_patch(self, point):
@@ -487,7 +486,7 @@ def neighborhood(self, point):
         phi_reduced = [S(t) for t in phi]
 
         patch._embedding_center = patch(point_preimage)
-        patch._embedding_morphism = patch.hom(phi_reduced,self)
+        patch._embedding_morphism = patch.hom(phi_reduced, self)
         return patch
 
     def dimension(self):
@@ -513,7 +512,7 @@ def dimension(self):
         if '_dimension' in self.__dict__:
             return self._dimension
         npatches = self.ambient_space().fan().ngenerating_cones()
-        dims = [ self.affine_patch(i).dimension() for i in range(0,npatches) ]
+        dims = [self.affine_patch(i).dimension() for i in range(npatches)]
         self._dimension = max(dims)
         return self._dimension
 
@@ -582,7 +581,8 @@ def is_smooth(self, point=None):
         if '_smooth' in self.__dict__:
             return self._smooth
         npatches = self.ambient_space().fan().ngenerating_cones()
-        self._smooth = all(self.affine_patch(i).is_smooth() for i in range(0,npatches))
+        self._smooth = all(self.affine_patch(i).is_smooth()
+                           for i in range(npatches))
         return self._smooth
 
     def is_nondegenerate(self):
@@ -692,7 +692,7 @@ def restrict(cone):
                                 enumerate(SR.subs(divide).gens())])
             return ideal, Jac_patch + SR_patch
 
-        for dim in range(0, fan.dim() + 1):
+        for dim in range(fan.dim() + 1):
             for cone in fan(dim):
                 ideal1, ideal2 = restrict(cone)
                 if ideal1.is_zero() or ideal2.dimension() != -1: