suggested fix

Author: fchapoton

src/sage/modular/abvar/homspace.py

@@ -168,15 +168,15 @@
 - Craig Citro, Robert Bradshaw (2008-03): Rewrote with modabvar overhaul
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2007 William Stein <[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 copy import copy
@@ -188,7 +188,6 @@
 
 from . import morphism
 
-import sage.rings.integer_ring
 from sage.rings.infinity import Infinity
 
 from sage.rings.ring import Ring
@@ -276,7 +275,7 @@ def _matrix_space(self):
             sage: Hom(J0(11), J0(22))._matrix_space
             Full MatrixSpace of 2 by 4 dense matrices over Integer Ring
         """
-        return MatrixSpace(ZZ,2*self.domain().dimension(), 2*self.codomain().dimension())
+        return MatrixSpace(ZZ, 2*self.domain().dimension(), 2*self.codomain().dimension())
 
     def _element_constructor_from_element_class(self, *args, **keywords):
         """
@@ -479,7 +478,7 @@ def free_module(self):
         """
         self.calculate_generators()
         V = ZZ**(4*self.domain().dimension() * self.codomain().dimension())
-        return V.submodule([ V(m.matrix().list()) for m in self.gens() ])
+        return V.submodule([V(m.matrix().list()) for m in self.gens()])
 
     def gen(self, i=0):
         """
@@ -570,7 +569,7 @@ def calculate_generators(self):
             return
 
         if (self.domain() == self.codomain()) and (self.domain().dimension() == 1):
-            self._gens = ( identity_matrix(ZZ,2), )
+            self._gens = (identity_matrix(ZZ, 2),)
             return
 
         phi = self.domain()._isogeny_to_product_of_powers()
@@ -583,9 +582,9 @@ def calculate_generators(self):
         Mt = psi.complementary_isogeny().matrix()
 
         R = ZZ**(4*self.domain().dimension()*self.codomain().dimension())
-        gens = R.submodule([ (M*self._get_matrix(g)*Mt).list()
-                             for g in im_gens ]).saturation().basis()
-        self._gens = tuple([ self._get_matrix(g) for g in gens ])
+        gens = R.submodule([(M*self._get_matrix(g)*Mt).list()
+                            for g in im_gens]).saturation().basis()
+        self._gens = tuple([self._get_matrix(g) for g in gens])
 
     def _calculate_product_gens(self):
         """
@@ -746,7 +745,8 @@ def _calculate_simple_gens(self):
         Mf = f.matrix()
         Mg = g.matrix()
 
-        return [ Mf * self._get_matrix(e) * Mg for e in ls ]
+        return [Mf * self._get_matrix(e) * Mg for e in ls]
+
 
 # NOTE/WARNING/TODO:  Below in the __init__, etc. we do *not* check
 # that the input gens are give something that spans a sub*ring*, as apposed
@@ -820,7 +820,7 @@ def __init__(self, A, gens=None, category=None):
         if gens is None:
             self._gens = None
         else:
-            self._gens = tuple([ self._get_matrix(g) for g in gens ])
+            self._gens = tuple([self._get_matrix(g) for g in gens])
         self._is_full_ring = gens is None
 
     def _repr_(self):
@@ -903,7 +903,7 @@ def index_in_saturation(self):
         A = self.abelian_variety()
         d = A.dimension()
         M = ZZ**(4*d**2)
-        gens = [ x.matrix().list() for x in self.gens() ]
+        gens = [x.matrix().list() for x in self.gens()]
         R = M.submodule(gens)
         return R.index_in_saturation()
 
@@ -934,8 +934,8 @@ def discriminant(self):
             2
         """
         g = self.gens()
-        M = Matrix(ZZ,len(g), [ (g[i]*g[j]).trace()
-                                for i in range(len(g)) for j in range(len(g)) ])
+        M = Matrix(ZZ, len(g), [(g[i]*g[j]).trace()
+                                for i in range(len(g)) for j in range(len(g))])
         return M.determinant()
 
     def image_of_hecke_algebra(self, check_every=1):
@@ -1002,18 +1002,18 @@ def image_of_hecke_algebra(self, check_every=1):
         EndVecZ = ZZ**(4*d**2)
 
         if d == 1:
-            self.__hecke_algebra_image = EndomorphismSubring(A, [[1,0,0,1]])
+            self.__hecke_algebra_image = EndomorphismSubring(A, [[1, 0, 0, 1]])
             return self.__hecke_algebra_image
 
         V = EndVecZ.submodule([A.hecke_operator(1).matrix().list()])
 
-        for n in range(2,M.sturm_bound()+1):
+        for n in range(2, M.sturm_bound()+1):
             if (check_every > 0 and
                     n % check_every == 0 and
                     V.dimension() == d and
                     V.index_in_saturation() == 1):
                 break
-            V += EndVecZ.submodule([ A.hecke_operator(n).matrix().list() ])
+            V += EndVecZ.submodule([A.hecke_operator(n).matrix().list()])
 
         self.__hecke_algebra_image = EndomorphismSubring(A, V.basis())
         return self.__hecke_algebra_image