fix W2 and W3 in geometry, rings, schemes

Author: fchapoton

src/sage/geometry/hyperplane_arrangement/affine_subspace.py

@@ -131,7 +131,7 @@ def __hash__(self):
         """
         # note that the point is not canonically chosen, but the linear part is
         return hash(self._linear_part)
-    
+
     def _repr_(self):
         r"""
         String representation for an :class:`AffineSubspace`.

src/sage/geometry/hyperplane_arrangement/check_freeness.py

@@ -120,7 +120,7 @@ def next_step(indices, prev, T):
             ret = next_step(I, Y, U)
             if ret is not None:
                 return [prev] + ret
-        return None                
+        return None
 
     T = matrix.identity(S, r)
     for i in indices:

src/sage/geometry/hyperplane_arrangement/plot.py

@@ -410,7 +410,7 @@ def plot_hyperplane(hyperplane, **kwds):
     # the extra keywords have now been handled
     # now create the plot
     if hyperplane.dimension() == 0:  # a point on a line
-        x, = hyperplane.A() 
+        x, = hyperplane.A()
         d = hyperplane.b()
         p = point((d/x,0), size=pt_size, **kwds)
         if has_hyp_label:
@@ -456,7 +456,7 @@ def plot_hyperplane(hyperplane, **kwds):
             s0, s1 = -3, 3
             t0, t1 = -3, 3
         p = parametric_plot3d(pnt+s*w[0]+t*w[1], (s,s0,s1), (t,t0,t1), **kwds)
-        if has_hyp_label: 
+        if has_hyp_label:
             if has_offset:
                 b0, b1, b2 = label_offset
             else:
@@ -518,7 +518,7 @@ def legend_3d(hyperplane_arrangement, hyperplane_colors, length):
     for i in range(N):
         p += line([(0,0),(0,0)], color=hyperplane_colors[i], thickness=8,
                 legend_label=labels[i], axes=False)
-    p.set_legend_options(title='Hyperplanes', loc='center', labelspacing=0.4, 
+    p.set_legend_options(title='Hyperplanes', loc='center', labelspacing=0.4,
             fancybox=True, font_size='x-large', ncol=2)
     p.legend(True)
     return p

src/sage/geometry/ribbon_graph.py

@@ -460,16 +460,16 @@ def contract_edge(self, k):
         #the following two lines convert the list of tuples to list of lists
         aux_sigma = [list(x) for x in self._sigma.cycle_tuples(singletons=True)]
         aux_rho = [list(x) for x in self._rho.cycle_tuples()]
-        #The following ''if'' rules out the cases when we would be 
-        #contracting a loop (which is not admissible since we would 
+        #The following ''if'' rules out the cases when we would be
+        #contracting a loop (which is not admissible since we would
         #lose the topological type of the graph).
-        if (_find(aux_sigma, aux_rho[k][0])[0] == 
+        if (_find(aux_sigma, aux_rho[k][0])[0] ==
                 _find(aux_sigma, aux_rho[k][1])[0]):
             raise ValueError("the edge is a loop and cannot be contracted")
         #We store in auxiliary variables the positions of the vertices
         #that are the ends of the edge to be contracted and we delete
         #from them the darts corresponding to the edge that is going
-        #to be contracted. We also delete the contracted edge 
+        #to be contracted. We also delete the contracted edge
         #from aux_rho
         pos1 = _find(aux_sigma, aux_rho[k][0])
         pos2 = _find(aux_sigma, aux_rho[k][1])
@@ -582,7 +582,7 @@ def extrude_edge(self, vertex, dart1, dart2):
         for val in val_one:
             repr_sigma += [[val]]
 
-        # We find which is the highest value a dart has, in order to 
+        # We find which is the highest value a dart has, in order to
         # add new darts that do not conflict with previous ones.
         k = max(darts_rho)
 
@@ -627,7 +627,7 @@ def genus(self):
         """
         #We now use the same procedure as in _repr_ to get the vertices
         #of valency 1 and distinguish them from the extra singletons of
-        #the permutation sigma. 
+        #the permutation sigma.
         repr_sigma = [list(x) for x in self._sigma.cycle_tuples()]
         repr_rho = [list(x) for x in self._rho.cycle_tuples()]
         darts_rho = flatten(repr_rho)
@@ -637,10 +637,10 @@ def genus(self):
         #the total number of vertices of sigma is its number of cycles
         #of length >1 plus the number of singletons that are actually
         #vertices of valency 1
-        
+
         vertices = len(self._sigma.cycle_tuples()) + len(val_one)
         edges = len(self._rho.cycle_tuples())
-        #formula for the genus using that the thickening is homotopically 
+        #formula for the genus using that the thickening is homotopically
         #equivalent to the graph
         g = (-vertices + edges - self.number_boundaries() + 2) // 2
 
@@ -720,13 +720,13 @@ def boundary(self):
         bound = []
 
         #since lists of tuples are not modifiable, we change the data to a
-        #list of lists 
+        #list of lists
         aux_perm = (self._rho * self._sigma).cycle_tuples(singletons=True)
 
-        #the cycles of the permutation rho*sigma are in 1:1 correspondence with 
+        #the cycles of the permutation rho*sigma are in 1:1 correspondence with
         #the boundary components of the thickening (see function number_boundaries())
         #but they are not the labeled boundary components.
-        #With the next for, we convert the cycles of rho*sigma to actually 
+        #With the next for, we convert the cycles of rho*sigma to actually
         #the labelling of the edges. Each edge, therefore, should appear twice
 
         for i,p in enumerate(aux_perm):
@@ -799,16 +799,16 @@ def reduced(self):
             aux_sigma = [list(x) for x in aux_ribbon._sigma.cycle_tuples(singletons=True)]
             aux_rho = [list(x) for x in aux_ribbon._rho.cycle_tuples()]
             for j in range(len(aux_rho)):
-                if (_find(aux_sigma, aux_rho[j][0])[0] != 
+                if (_find(aux_sigma, aux_rho[j][0])[0] !=
                         _find(aux_sigma, aux_rho[j][1])[0]):
                     aux_ribbon = aux_ribbon.contract_edge(j)
-                    aux_rho = [list(x) for 
+                    aux_rho = [list(x) for
                     x in aux_ribbon._rho.cycle_tuples()]
                     break
         #finally we change the data to a list of tuples and return the
-        #information as a ribbon graph. 
+        #information as a ribbon graph.
         return aux_ribbon
-    
+
     #the next function computes a basis of homology, it uses
     #the previous function.
 
@@ -960,15 +960,15 @@ def homology_basis(self):
 
         basis = [[list(x)] for x in self.reduced()._rho.cycle_tuples()]
 
-        #Now we define center as the set of edges that were contracted 
-        #in reduced() this set is contractible and can be define as the 
+        #Now we define center as the set of edges that were contracted
+        #in reduced() this set is contractible and can be define as the
         #complement of reduced_rho in rho
 
-        center = [list(x) for x in self._rho.cycle_tuples() 
+        center = [list(x) for x in self._rho.cycle_tuples()
                   if (x not in self.reduced()._rho.cycle_tuples())]
 
         #We define an auxiliary list 'vertices' that will contain the
-        #vertices (cycles of sigma) corresponding to each half edge. 
+        #vertices (cycles of sigma) corresponding to each half edge.
 
         vertices = []
 
@@ -1013,7 +1013,7 @@ def homology_basis(self):
                     basis[i][j][0], basis[i][j][1] = \
                         basis[i][j][1], basis[i][j][0]
 
-        #the variable basis is a LIST of Lists of lists. Each List 
+        #the variable basis is a LIST of Lists of lists. Each List
         #corresponds to an element of the basis and each list in a List
         #is just a 2-tuple which corresponds to an ''ordered'' edge of rho.
 
@@ -1056,7 +1056,7 @@ def normalize(self):
         darts_rho = flatten(aux_rho)
         darts_sigma = flatten(aux_sigma)
         val_one = [x for x in darts_rho if x not in darts_sigma]
- 
+
         #We add them to aux_sigma
         for i in range(len(val_one)):
             aux_sigma += [[val_one[i]]]
@@ -1147,7 +1147,7 @@ def make_ribbon(g, r):
         repr_sigma[1].append(i+(2*g+2)+1)
         repr_rho += [[i+2,i+(2*g+2)+1]]
 
-    #finally we add an edge for each additional boundary component. 
+    #finally we add an edge for each additional boundary component.
     max_dart = 4*g+2
     for j in range(r-1):
         repr_sigma[0].insert(0, max_dart+2*(j+1)-1)

src/sage/geometry/triangulation/point_configuration.py

@@ -1899,7 +1899,7 @@ def contained_simplex(self, large=True, initial_point=None, point_order=None):
             # PointConfiguration are actually ignored.
         if not points:
             return tuple()
-                         
+
         if initial_point is None:
             origin = points.pop()
         else:
@@ -2005,7 +2005,7 @@ def facets_of_simplex(simplex):
 
         # input verification
         self._assert_is_affine()
-        
+
         point_order_is_given = point_order is not None
         if point_order is None:
             point_order = list(self.points())

src/sage/rings/continued_fraction.py

@@ -1018,7 +1018,7 @@ def __bool__(self):
         """
         return bool(self.quotient(0)) or self.quotient(1) is not Infinity
 
-    
+
 
     def is_zero(self):
         r"""

src/sage/rings/function_field/ideal.py

@@ -1266,7 +1266,7 @@ def __bool__(self):
         """
         return self._hnf.nrows() != 0
 
-    
+
 
     def __hash__(self):
         """

src/sage/rings/number_field/number_field.py

@@ -6288,7 +6288,7 @@ def _normalize_prime_list(self, v):
             v = []
         elif not isinstance(v, (list, tuple)):
             v = [v]
-        
+
         v = [ZZ(p).abs() for p in v]
         v = sorted(set(v))
 

src/sage/rings/number_field/splitting_field.py

@@ -378,7 +378,7 @@ def splitting_field(poly, name, map=False, degree_multiple=None, abort_degree=No
         abort_rel_degree = abort_degree//absolute_degree
         if abort_rel_degree and rel_degree_divisor > abort_rel_degree:
             raise SplittingFieldAbort(absolute_degree * rel_degree_divisor, degree_multiple)
-        
+
         # First, factor polynomials in Lred and store the result in L
         verbose("SplittingData to factor: %s"%[s._repr_tuple() for s in Lred])
         t = cputime()

src/sage/rings/polynomial/all.py

@@ -22,7 +22,7 @@
 # Quotient of polynomial ring
 from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing
 from sage.rings.polynomial.polynomial_quotient_ring_element import PolynomialQuotientRingElement
- 
+
 # Univariate Polynomial Rings
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.polynomial_ring import polygen, polygens