remove many unused imports

Author: fchapoton

src/sage/algebras/jordan_algebra.py

@@ -1298,7 +1298,6 @@ def basis(self):
             sage: len(B)
             27
         """
-        import itertools
         R = self.base_ring()
         OB = self._O.basis()
         base = [R.zero()] * 3 + [self._O.zero()] * 3

src/sage/algebras/lie_algebras/verma_module.py

@@ -28,11 +28,9 @@
 from sage.categories.homset import Hom, Homset
 from sage.monoids.indexed_free_monoid import IndexedFreeAbelianMonoid
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.modules.free_module_element import vector
 from sage.sets.family import Family
 from sage.structure.richcmp import richcmp
 from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
 
 
 class ModulePrinting:

src/sage/categories/kahler_algebras.py

@@ -17,16 +17,14 @@
 
 from sage.categories.category_types import Category_over_base_ring
 from sage.categories.graded_algebras_with_basis import GradedAlgebrasWithBasis
-from sage.categories.finite_dimensional_algebras_with_basis import FiniteDimensionalAlgebrasWithBasis
-from sage.categories.filtered_modules_with_basis import FilteredModulesWithBasis
 from sage.misc.abstract_method import abstract_method
 from sage.quadratic_forms.quadratic_form import QuadraticForm
-from sage.misc.cachefunc import cached_method
 
 
 class KahlerAlgebras(Category_over_base_ring):
     r"""
     The category of graded algebras satisfying the Kähler package.
+
     A finite-dimensional graded algebra `\bigoplus_{k=1}^{r}A^k` satisfies
     the *Kähler package* if the following properties hold:
 
@@ -197,4 +195,4 @@ def hodge_riemann_relations(self, k):
             for i,el in enumerate(basis_k):
                 for j in range(i, len(basis_k)):
                     coeff.append((el * (lefschetz_el ** (r-(2*k)) * basis_k[j])).degree())
-            return QuadraticForm(self.base_ring(), len(basis_k), coeff)
+            return QuadraticForm(self.base_ring(), len(basis_k), coeff)

src/sage/coding/guruswami_sudan/utils.py

@@ -8,20 +8,18 @@
 - David Lucas, ported the original implementation in Sage
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #       Copyright (C) 2015 David Lucas <[email protected]>
 #                     2015 Johan S. R. Nielsen <[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.arith.misc import integer_floor as floor
-from sage.misc.lazy_import import lazy_import
 from sage.misc.functional import sqrt
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer

src/sage/combinat/combinat.py

@@ -170,15 +170,12 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.integer import Integer
-from sage.rings.infinity import infinity
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.misc.misc_c import prod
 from sage.misc.cachefunc import cached_function
 from sage.structure.sage_object import SageObject
-from sage.structure.parent import Parent
 from sage.misc.lazy_import import lazy_import
-from sage.misc.lazy_attribute import lazy_attribute
 from .combinat_cython import _stirling_number2
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.structure.element import Element

src/sage/combinat/root_system/reflection_group_complex.py

@@ -196,26 +196,25 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.misc.cachefunc import cached_method, cached_function
-from sage.misc.misc_c import prod
 from sage.categories.category import Category
-from sage.categories.permutation_groups import PermutationGroups
 from sage.categories.complex_reflection_groups import ComplexReflectionGroups
 from sage.categories.coxeter_groups import CoxeterGroups
+from sage.categories.permutation_groups import PermutationGroups
+from sage.combinat.root_system.cartan_matrix import CartanMatrix
 from sage.combinat.root_system.reflection_group_element import ComplexReflectionGroupElement, _gap_return
-from sage.sets.family import Family
-from sage.structure.unique_representation import UniqueRepresentation
 from sage.groups.perm_gps.permgroup import PermutationGroup_generic
-from sage.combinat.permutation import Permutation
-from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
+from sage.interfaces.gap3 import gap3
 from sage.matrix.constructor import matrix
 from sage.matrix.special import identity_matrix
-from sage.structure.element import Matrix
-from sage.interfaces.gap3 import gap3
-from sage.modules.free_module_element import vector
-from sage.combinat.root_system.cartan_matrix import CartanMatrix
+from sage.misc.cachefunc import cached_method, cached_function
+from sage.misc.misc_c import prod
 from sage.misc.sage_eval import sage_eval
+from sage.modules.free_module_element import vector
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.sets.family import Family
+from sage.structure.element import Matrix
+from sage.structure.unique_representation import UniqueRepresentation
 
 
 class ComplexReflectionGroup(UniqueRepresentation, PermutationGroup_generic):

src/sage/combinat/specht_module.py

@@ -34,7 +34,6 @@
 from sage.matrix.constructor import matrix
 from sage.rings.rational_field import QQ
 from sage.modules.with_basis.subquotient import SubmoduleWithBasis, QuotientModuleWithBasis
-from sage.modules.free_module_element import vector
 from sage.categories.modules_with_basis import ModulesWithBasis
 
 

src/sage/crypto/key_exchange/diffie_hellman.py

@@ -17,22 +17,17 @@
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-
-from sage.misc.superseded import experimental
+from typing import Union
 
 from sage.crypto.key_exchange.key_exchange_scheme import KeyExchangeScheme
-
-from sage.arith.misc import is_prime
 from sage.misc.prandom import randint
-from sage.rings.integer import Integer
+from sage.misc.superseded import experimental
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.rings.finite_rings.finite_field_prime_modn import \
-    FiniteField_prime_modn
+from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
 from sage.rings.finite_rings.integer_mod import IntegerMod_abstract
+from sage.rings.integer import Integer
 from sage.structure.proof.proof import WithProof
 
-from typing import Union
-
 
 class DiffieHellman(KeyExchangeScheme):
 

src/sage/crypto/util.py

@@ -11,21 +11,19 @@
   ``is_blum_prime``, ``least_significant_bits``, ``random_blum_prime``.
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #       Copyright (c) 2009, 2010 Minh Van Nguyen <[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.arith.functions import lcm
 from sage.arith.misc import is_prime, primes, random_prime
 from sage.misc.lazy_import import lazy_import
 from sage.rings.finite_rings.integer_mod import Mod as mod
-from sage.rings.integer import Integer
 
 lazy_import('sage.arith.misc', ('carmichael_lambda'), deprecation=34719)
 lazy_import('sage.monoids.string_monoid', 'BinaryStrings')

src/sage/env.py

@@ -47,7 +47,6 @@
 import sys
 import sysconfig
 from . import version
-from pathlib import Path
 import subprocess