sage.{crypto,databases,dynamics,lfunctions,quadratic_forms}: Consolidate imports from the same module

Author: Matthias Koeppe

src/sage/crypto/classical.py

@@ -55,8 +55,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-from sage.arith.misc import XGCD as xgcd
-from sage.arith.misc import inverse_mod
+from sage.arith.misc import inverse_mod, XGCD as xgcd
 from random import randint
 from sage.matrix.matrix_space import MatrixSpace
 

src/sage/crypto/lwe.py

@@ -91,26 +91,25 @@
 - [CGW2013]_
 """
 
+from sage.arith.misc import euler_phi, next_prime
 from sage.functions.log import log
 from sage.functions.other import floor, ceil
-from sage.misc.functional import sqrt
 from sage.misc.functional import cyclotomic_polynomial, round
-from sage.misc.randstate import set_random_seed
+from sage.misc.functional import sqrt
 from sage.misc.prandom import randint
+from sage.misc.randstate import set_random_seed
 from sage.modules.free_module import FreeModule
 from sage.modules.free_module_element import random_vector, vector
 from sage.numerical.optimize import find_root
-from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+from sage.rings.integer_ring import ZZ
 from sage.rings.real_mpfr import RR
-from sage.arith.misc import next_prime
-from sage.arith.misc import euler_phi
+from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
+from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 from sage.structure.element import parent
 from sage.structure.sage_object import SageObject
 from sage.symbolic.constants import pi
 from sage.symbolic.ring import SR
-from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
-from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 
 
 class UniformSampler(SageObject):

src/sage/crypto/public_key/blum_goldwasser.py

@@ -30,19 +30,17 @@
 
 from operator import xor
 
-from sage.crypto.cryptosystem import PublicKeyCryptosystem
-from sage.crypto.util import is_blum_prime
-from sage.crypto.util import least_significant_bits
-from sage.crypto.util import random_blum_prime
+from sage.arith.misc import GCD as gcd, power_mod, XGCD as xgcd
 from sage.functions.log import log
 from sage.functions.other import Function_floor
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.misc import GCD as gcd
-from sage.arith.misc import power_mod
-from sage.arith.misc import XGCD as xgcd
 from sage.rings.finite_rings.integer_mod import Mod as mod
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 
+from .cryptosystem import PublicKeyCryptosystem
+from .util import is_blum_prime, least_significant_bits, random_blum_prime
+
+
 floor = Function_floor()
 IntegerModRing = IntegerModFactory("IntegerModRing")
 

src/sage/crypto/stream.py

@@ -12,17 +12,16 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .cryptosystem import SymmetricKeyCryptosystem
-from .stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
-
-from sage.crypto.util import random_blum_prime
+from sage.arith.misc import GCD as gcd, power_mod
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.misc import GCD as gcd
-from sage.arith.misc import power_mod
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 from sage.rings.polynomial.polynomial_element import Polynomial
 
+from .cryptosystem import SymmetricKeyCryptosystem
+from .stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
+from .util import random_blum_prime
+
 
 IntegerModRing = IntegerModFactory("IntegerModRing")
 

src/sage/crypto/util.py

@@ -20,17 +20,16 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.misc import is_prime
 from sage.arith.functions import lcm
-from sage.arith.misc import primes
-from sage.arith.misc import random_prime
-from sage.rings.integer import Integer
+from sage.arith.misc import is_prime, primes, random_prime
+from sage.misc.lazy_import import lazy_import
+from sage.monoids.string_monoid import BinaryStrings
 from sage.rings.finite_rings.integer_mod import Mod as mod
+from sage.rings.integer import Integer
 
-from sage.misc.lazy_import import lazy_import
 lazy_import('sage.arith.misc', ('carmichael_lambda'), deprecation=34719)
 
+
 def ascii_integer(B):
     r"""
     Return the ASCII integer corresponding to the binary string ``B``.

src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py

@@ -22,26 +22,23 @@
 from copy import copy, deepcopy
 from itertools import permutations, combinations, product
 
+from sage.arith.functions import lcm
+from sage.arith.misc import CRT, divisors, GCD as gcd, is_square
+from sage.combinat.permutation import Arrangements
 from sage.combinat.subset import Subsets
-from sage.misc.functional import sqrt
 from sage.matrix.constructor import matrix
-from sage.structure.element import is_Matrix
+from sage.misc.functional import sqrt
 from sage.misc.misc_c import prod
+from sage.parallel.use_fork import p_iter_fork
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Integers
 from sage.rings.integer_ring import ZZ
 from sage.rings.number_field.number_field import NumberField
-from sage.arith.misc import GCD as gcd
-from sage.arith.functions import lcm
-from sage.arith.misc import CRT
-from sage.arith.misc import is_square
-from sage.arith.misc import divisors
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 from sage.sets.primes import Primes
 from sage.sets.set import Set
-from sage.combinat.permutation import Arrangements
-from sage.parallel.use_fork import p_iter_fork
+from sage.structure.element import is_Matrix
 
 
 def automorphism_group_QQ_fixedpoints(rational_function, return_functions=False, iso_type=False):

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -52,29 +52,29 @@ class initialization directly.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.arith.misc import is_prime
+from copy import copy
+from itertools import count, product
+
+import sage.rings.abc
+
+from sage.arith.functions import lcm
+from sage.arith.misc import binomial, GCD as gcd, is_prime, moebius, next_prime, primes
 from sage.calculus.functions import jacobian
 from sage.categories.fields import Fields
+from sage.categories.finite_fields import FiniteFields
 from sage.categories.function_fields import FunctionFields
-from sage.categories.number_fields import NumberFields
 from sage.categories.homset import End
-from sage.dynamics.arithmetic_dynamics.generic_ds import DynamicalSystem
-from sage.misc.functional import sqrt
+from sage.categories.number_fields import NumberFields
 from sage.functions.other import ceil
 from sage.libs.pari.all import PariError
 from sage.matrix.constructor import matrix, identity_matrix
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import typecall
+from sage.misc.functional import sqrt
 from sage.misc.mrange import xmrange
 from sage.modules.free_module_element import vector
-from sage.rings.integer import Integer
-from sage.arith.misc import GCD as gcd
-from sage.arith.functions import lcm
-from sage.arith.misc import next_prime
-from sage.arith.misc import binomial
-from sage.arith.misc import primes
-from sage.arith.misc import moebius
-from sage.categories.finite_fields import FiniteFields
+from sage.parallel.ncpus import ncpus
+from sage.parallel.use_fork import p_iter_fork
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
 from sage.rings.complex_mpfr import ComplexField
 from sage.rings.finite_rings.finite_field_base import FiniteField
@@ -83,6 +83,7 @@ class initialization directly.
 from sage.rings.fraction_field import (FractionField, is_FractionField, FractionField_1poly_field)
 from sage.rings.fraction_field_element import is_FractionFieldElement, FractionFieldElement
 from sage.rings.function_field.function_field import is_FunctionField
+from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.flatten import FlatteningMorphism, UnflatteningMorphism
 from sage.rings.morphism import RingHomomorphism_im_gens
@@ -94,31 +95,27 @@ class initialization directly.
 from sage.rings.qqbar import QQbar, number_field_elements_from_algebraics
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.rational_field import QQ
-import sage.rings.abc
 from sage.rings.real_mpfr import RealField
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
-from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
+from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
 from sage.schemes.projective.projective_morphism import (
     SchemeMorphism_polynomial_projective_space,
     SchemeMorphism_polynomial_projective_space_field,
     SchemeMorphism_polynomial_projective_space_finite_field)
-from sage.schemes.projective.projective_space import (ProjectiveSpace,
-                                                      is_ProjectiveSpace)
-from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
+from sage.schemes.projective.projective_space import ProjectiveSpace, is_ProjectiveSpace
+from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
 from sage.structure.element import get_coercion_model
 from sage.symbolic.constants import e
-from copy import copy
-from sage.parallel.ncpus import ncpus
-from sage.parallel.use_fork import p_iter_fork
-from sage.dynamics.arithmetic_dynamics.projective_ds_helper import (_fast_possible_periods,_all_periodic_points)
-from itertools import count, product
+
 from .endPN_automorphism_group import (
     automorphism_group_QQ_CRT,
     automorphism_group_QQ_fixedpoints,
     conjugating_set_helper,
     conjugating_set_initializer,
     is_conjugate_helper)
 from .endPN_automorphism_group import automorphism_group_FF
+from .generic_ds import DynamicalSystem
+from .projective_ds_helper import _fast_possible_periods, _all_periodic_points
 
 
 class DynamicalSystem_projective(SchemeMorphism_polynomial_projective_space,

src/sage/lfunctions/zero_sums.pyx

@@ -18,21 +18,21 @@ AUTHORS:
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sage_object cimport SageObject
-from sage.rings.integer_ring import ZZ
-from sage.rings.real_double import RDF
-from sage.rings.complex_double import CDF
-from sage.rings.infinity import PlusInfinity
-from sage.arith.misc import prime_powers
-from sage.arith.misc import next_prime
+from sage.arith.misc import next_prime, prime_powers
 from sage.functions.log import log, exp
 from sage.functions.other import real, imag
-from sage.symbolic.constants import pi, euler_gamma
+from sage.libs.flint.ulong_extras cimport n_is_prime
 from sage.libs.pari.all import pari
 from sage.misc.verbose import verbose
 from sage.parallel.decorate import parallel
 from sage.parallel.ncpus import ncpus as num_cpus
-from sage.libs.flint.ulong_extras cimport n_is_prime
+from sage.rings.complex_double import CDF
+from sage.rings.infinity import PlusInfinity
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_double import RDF
+from sage.structure.sage_object cimport SageObject
+from sage.symbolic.constants import euler_gamma, pi
+
 
 cdef extern from "<math.h>":
     double c_exp "exp"(double)

src/sage/quadratic_forms/count_local_2.pyx

@@ -2,15 +2,11 @@ r"""
 Optimized counting of congruence solutions
 """
 
-from sage.arith.misc import valuation
-from sage.arith.misc import kronecker as kronecker_symbol
-from sage.arith.misc import is_prime
+from sage.arith.misc import is_prime, kronecker as kronecker_symbol, valuation
+from sage.rings.finite_rings.integer_mod cimport IntegerMod_gmp
 from sage.rings.finite_rings.integer_mod import Mod
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-
 from sage.rings.integer_ring import ZZ
-
-from sage.rings.finite_rings.integer_mod cimport IntegerMod_gmp
 from sage.sets.set import Set
 
 

src/sage/quadratic_forms/quadratic_form__equivalence_testing.py

@@ -5,16 +5,17 @@
 
 - Anna Haensch (2014-12-01): added test for rational isometry
 """
-from sage.arith.misc import hilbert_symbol
-from sage.arith.misc import prime_divisors
-from sage.arith.misc import is_prime
-from sage.arith.misc import valuation
-from sage.arith.misc import GCD
-from sage.arith.misc import legendre_symbol
+
+from sage.arith.misc import (hilbert_symbol,
+                             GCD,
+                             is_prime,
+                             legendre_symbol,
+                             prime_divisors,
+                             valuation)
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 
-from sage.quadratic_forms.quadratic_form import is_QuadraticForm
+from .quadratic_form import is_QuadraticForm
 
 
 ##############################################################################