a few pep8 details in modules/

Author: fchapoton

src/sage/modules/filtered_vector_space.py

@@ -99,14 +99,14 @@
     in Vector space of dimension 3 over Algebraic Field
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #       Copyright (C) 2013 Volker Braun <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  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.rings.all import QQ, ZZ, RDF, RR, Integer
 from sage.rings.infinity import InfinityRing, infinity, minus_infinity
@@ -275,7 +275,7 @@ def construct_from_dim_degree(dim, max_degree, base_ring, check):
     dim = ZZ(dim)
     from sage.matrix.constructor import identity_matrix
     generators = identity_matrix(base_ring, dim).columns()
-    filtration = dict()
+    filtration = {}
     if max_degree is None:
         max_degree = infinity
     filtration[normalize_degree(max_degree)] = range(dim)
@@ -314,7 +314,7 @@ def normalize_gen(v):
     generators = tuple(sorted(generators))
 
     # normalize filtration data
-    normalized = dict()
+    normalized = {}
     for deg, gens_deg in filtration.items():
         indices = [generators.index(normalize_gen(v)) for v in gens_deg]
         normalized[deg] = tuple(indices)
@@ -373,13 +373,13 @@ def construct_from_generators_indices(generators, filtration, base_ring, check):
         v.set_immutable()
 
     # normalize filtration data
-    normalized = dict()
+    normalized = {}
     for deg, gens in filtration.items():
         deg = normalize_degree(deg)
-        gens = [ZZ(i) for i in gens]
-        if any(i < 0 or i >= len(generators) for i in gens):
+        gens = tuple(sorted(ZZ(i) for i in gens))
+        if gens[0] < 0 or gens[-1] >= len(generators):
             raise ValueError('generator index out of bounds')
-        normalized[deg] = tuple(sorted(gens))
+        normalized[deg] = gens
     try:
         del normalized[minus_infinity]
     except KeyError:
@@ -389,8 +389,6 @@ def construct_from_generators_indices(generators, filtration, base_ring, check):
     return FilteredVectorSpace_class(base_ring, dim, generators, filtration, check=check)
 
 
-
-
 class FilteredVectorSpace_class(FreeModule_ambient_field):
 
     def __init__(self, base_ring, dim, generators, filtration, check=True):
@@ -734,7 +732,7 @@ def graded(self, d):
             Basis matrix:
             [1 1]
         """
-        return self.get_degree(d).quotient(self.get_degree(d+1))
+        return self.get_degree(d).quotient(self.get_degree(d + 1))
 
     def presentation(self):
         """
@@ -760,7 +758,7 @@ def presentation(self):
             generators.update(V.echelonized_basis())
         generators = tuple(sorted(generators))
 
-        filtration = dict()
+        filtration = {}
         for d, V in filt:
             indices = [ZZ(generators.index(v)) for v in V.echelonized_basis()]
             filtration[d] = tuple(indices)
@@ -770,6 +768,8 @@ def _repr_field_name(self):
         """
         Return an abbreviated field name as string
 
+        .. NOTE: This should rather be a method of fields and rings.
+
         RAISES:
 
         ``NotImplementedError``: The field does not have an
@@ -1001,15 +1001,15 @@ def direct_sum(self, other):
         self_gens, self_filt = self.presentation()
         other_gens, other_filt = other.presentation()
         generators = \
-            [ list(v) + [base_ring.zero()]*other.dimension() for v in self_gens  ] + \
-            [ [base_ring.zero()]*self.dimension() + list(v)  for v in other_gens ]
+            [list(v) + [base_ring.zero()] * other.dimension() for v in self_gens] + \
+            [[base_ring.zero()] * self.dimension() + list(v) for v in other_gens]
 
         # construct the filtration dictionary
         def join_indices(self_indices, other_indices):
             self_indices = tuple(self_indices)
             other_indices = tuple(i + len(self_gens) for i in other_indices)
             return self_indices + other_indices
-        filtration = dict()
+        filtration = {}
         self_indices = set()
         other_indices = set()
         degrees = list(self_filt) + list(other_filt)
@@ -1071,7 +1071,7 @@ def tensor_product(self, other):
         W_coll = VectorCollection(W_generators, base_ring, W.dimension())
         T = TensorOperation([V_coll, W_coll], 'product')
 
-        filtration = dict()
+        filtration = {}
         for V_deg in V.support():
             for W_deg in W.support():
                 deg = V_deg + W_deg
@@ -1112,7 +1112,7 @@ def _power_operation(self, n, operation):
         T = TensorOperation([V] * n, operation)
 
         iters = [self.support()] * n
-        filtration = dict()
+        filtration = {}
         from sage.categories.cartesian_product import cartesian_product
         for degrees in cartesian_product(iters):
             deg = sum(degrees)
@@ -1124,7 +1124,6 @@ def _power_operation(self, n, operation):
             filtration[deg] = filt_deg
         return FilteredVectorSpace(T.vectors(), filtration, base_ring=self.base_ring())
 
-
     def exterior_power(self, n):
         """
         Return the `n`-th graded exterior power.
@@ -1204,7 +1203,7 @@ def dual(self):
             sage: F.dual().support()
             (-2, 0)
         """
-        filtration = dict()
+        filtration = {}
         prev_deg = minus_infinity
         for deg, V in self._filt[1:]:
             filtration[-prev_deg] = V.complement().echelonized_basis()
@@ -1226,7 +1225,7 @@ def shift(self, deg):
             (-5, -3)
         """
         generators, filtration = self.presentation()
-        shifted = dict()
+        shifted = {}
         for d, indices in filtration.items():
             shifted[d + deg] = indices
         return FilteredVectorSpace(generators, shifted, base_ring=self.base_ring())
@@ -1269,7 +1268,7 @@ def random_deformation(self, epsilon=None):
         R = self.base_ring()
         if epsilon is None:
             epsilon = R.one()
-        filtration = dict()
+        filtration = {}
         for deg, filt in self._filt[1:]:
             generators = [v + epsilon * random_vector(R, self.rank())
                           for v in filt.echelonized_basis()]

src/sage/modules/free_module.py

@@ -4611,7 +4611,7 @@ def span_of_basis(self, basis, base_ring=None, check=True, already_echelonized=F
                 M = self.change_ring(base_ring)
             except TypeError:
                 raise ValueError("Argument base_ring (= %s) is not compatible with the base field (= %s)." % (
-                    base_ring, self.base_field() ))
+                    base_ring, self.base_field()))
             try:
                 return M.span_of_basis(basis)
             except TypeError:
@@ -5653,7 +5653,7 @@ def basis(self):
         """
         try:
             return self.__basis
-        except  AttributeError:
+        except AttributeError:
             ZERO = self(0)
             one = self.coordinate_ring().one()
             w = []
@@ -6600,7 +6600,7 @@ def _echelon_matrix_richcmp(self, other, op):
         lx = self.ambient_vector_space()
         rx = other.ambient_vector_space()
         if lx != rx:
-            return lx._echelon_matrix_richcmp( rx, op)
+            return lx._echelon_matrix_richcmp(rx, op)
 
         lx = self.dimension()
         rx = other.dimension()

src/sage/modules/free_quadratic_module_integer_symmetric.py

@@ -349,7 +349,7 @@ def IntegralLatticeDirectSum(Lattices, return_embeddings=False):
     basis = [matrix.block(1, 3, [matrix.zero(dims[i], sum_degree[i]),
                                  Lattices[i].basis_matrix(),
                                  matrix.zero(dims[i], sum_degree[-1] - sum_degree[i+1])
-                                ])  for i in range(N)]
+                                ]) for i in range(N)]
     basis_matrix = matrix.block(N, 1, basis)
     ipm = ambient.inner_product_matrix()
     direct_sum = FreeQuadraticModule_integer_symmetric(ambient=ambient,
@@ -363,6 +363,7 @@ def IntegralLatticeDirectSum(Lattices, return_embeddings=False):
            for i in range(N)]
     return [direct_sum, phi]
 
+
 def IntegralLatticeGluing(Lattices, glue, return_embeddings=False):
     r"""
     Return an overlattice of the direct sum as defined by ``glue``.
@@ -1092,7 +1093,7 @@ def maximal_overlattice(self, p=None):
                 for t in D:
                     if t != 0 and t.q() == 0:
                         break
-                if t.q() != 0 :
+                if t.q() != 0:
                     # no isotropic vector left
                     break
                 L = L.overlattice([t.lift()])

src/sage/modules/matrix_morphism.py

@@ -1236,7 +1236,7 @@ def is_identity(self):
         # testing for the identity matrix will only work for
         #   endomorphisms which have the same basis for domain and codomain
         #   so we test equality on a basis, which is sufficient
-        return all( self(u) == u for u in self.domain().basis() )
+        return all(self(u) == u for u in self.domain().basis())
 
     def is_zero(self):
         r"""
@@ -1369,7 +1369,7 @@ def is_equal_function(self, other):
         if self.codomain() != other.codomain():
             return False
         # check agreement on any basis of the domain
-        return all( self(u) == other(u) for u in self.domain().basis() )
+        return all(self(u) == other(u) for u in self.domain().basis())
 
     def restrict_domain(self, sub):
         """

src/sage/modules/torsion_quadratic_module.py

@@ -144,7 +144,7 @@ def _mul_(self, other):
             1/4
         """
         value_module = self.parent().value_module()
-        return value_module( self.lift().inner_product(other.lift()) )
+        return value_module(self.lift().inner_product(other.lift()))
 
     inner_product = _mul_
     b = _mul_
@@ -296,7 +296,6 @@ def __init__(self, V, W, gens, modulus, modulus_qf):
         self._modulus = modulus
         self._modulus_qf = modulus_qf
 
-
     def _repr_(self):
         r"""
         Return a string representation of ``self``.
@@ -313,10 +312,10 @@ def _repr_(self):
             [0 0 0]
             [0 0 0]
         """
-        return ( "Finite quadratic module over %s with invariants %s\n"
-                 % (self.base_ring(), self.invariants()) +
-                 "Gram matrix of the quadratic form with values in %r:\n%r"
-                 % (self.value_module_qf(), self.gram_matrix_quadratic()))
+        return ("Finite quadratic module over %s with invariants %s\n"
+                % (self.base_ring(), self.invariants()) +
+                "Gram matrix of the quadratic form with values in %r:\n%r"
+                % (self.value_module_qf(), self.gram_matrix_quadratic()))
 
     def _module_constructor(self, V, W, check=False):
         r"""

src/sage/modules/with_basis/cell_module.py

@@ -357,7 +357,7 @@ def _acted_upon_(self, scalar, self_on_left=False):
                 # Temporary needed by coercion (see Polynomial/FractionField tests).
                 if not P._algebra.has_coerce_map_from(scalar.parent()):
                     return None
-                scalar = P._algebra( scalar )
+                scalar = P._algebra(scalar)
 
             if self_on_left:
                 raise NotImplementedError

src/sage/modules/with_basis/morphism.py

@@ -403,18 +403,19 @@ def __call__(self, *args):
         mc = x.monomial_coefficients(copy=False)
         if self._is_module_with_basis_over_same_base_ring:
             return self.codomain().linear_combination(
-                    (self._on_basis(*(before+(index,)+after)), coeff )
-                    for (index, coeff) in mc.items())
+                (self._on_basis(*(before + (index,) + after)), coeff)
+                for (index, coeff) in mc.items())
         else:
-            return sum((coeff * self._on_basis(*(before+(index,)+after))
-                       for (index, coeff) in mc.items()), self._zero)
+            return sum((coeff * self._on_basis(*(before + (index,) + after))
+                        for (index, coeff) in mc.items()), self._zero)
 
     # As per the specs of Map, we should in fact implement _call_.
     # However we currently need to abuse Map.__call__ (which strict
     # type checking) for multi-parameter module morphisms
     # To be cleaned up
     _call_ = __call__
 
+
 class TriangularModuleMorphism(ModuleMorphism):
     r"""
     An abstract class for triangular module morphisms
@@ -683,10 +684,9 @@ def __init__(self, triangular="upper", unitriangular=False,
         self._inverse = inverse
 
         if inverse_on_support == "compute":
-            inverse_on_support = {
-                self._dominant_item(on_basis(i))[0] : i
-                for i in self.domain().basis().keys()
-            }.get
+            inverse_on_support = {self._dominant_item(on_basis(i))[0]: i
+                                  for i in self.domain().basis().keys()
+                                  }.get
 
         self._inverse_on_support = inverse_on_support
 
@@ -883,7 +883,7 @@ def _invert_on_basis(self, i):
             sage: phi._invert_on_basis(2)
             B[2] - B[3]
         """
-        return self.preimage( self.codomain().monomial(i) )
+        return self.preimage(self.codomain().monomial(i))
 
     def preimage(self, f):
         r"""
@@ -1351,13 +1351,13 @@ def __init__(self, domain, matrix, codomain=None, category=None, side="left"):
             matrix = matrix.transpose()
         if matrix.nrows() != len(indices):
             raise ValueError("The dimension of the matrix (%s) does not match with the dimension of the domain (%s)"
-                             %(matrix.nrows(), len(indices)))
+                             % (matrix.nrows(), len(indices)))
         if matrix.ncols() != codomain.dimension():
             raise ValueError("The dimension of the matrix (%s) does not match with the dimension of the codomain (%s)"
-                             %(matrix.ncols(), codomain.dimension()))
+                             % (matrix.ncols(), codomain.dimension()))
         self._matrix = matrix
-        d = { xt: codomain.from_vector(matrix.row(rank_domain(xt)))
-              for xt in domain.basis().keys() }
+        d = {xt: codomain.from_vector(matrix.row(rank_domain(xt)))
+             for xt in domain.basis().keys()}
 
         ModuleMorphismByLinearity.__init__(self, on_basis=d.__getitem__,
                                            domain=domain, codomain=codomain,