sage.schemes: Consolidate imports from the same module

src/sage/schemes/elliptic_curves/ell_finite_field.py

@@ -23,24 +23,24 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.groups.generic as generic
 
-from sage.schemes.curves.projective_curve import Hasse_bounds
-from .ell_field import EllipticCurve_field
-from .constructor import EllipticCurve
-from sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field import HyperellipticCurve_finite_field
+from sage.arith.functions import lcm
+from sage.arith.misc import binomial, GCD as gcd
+from sage.groups.additive_abelian.additive_abelian_wrapper import AdditiveAbelianGroupWrapper
+from sage.misc.cachefunc import cached_method
+from sage.rings.finite_rings.element_base import is_FiniteFieldElement
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.polynomial.polynomial_ring import polygen
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
-import sage.groups.generic as generic
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+from sage.schemes.curves.projective_curve import Hasse_bounds
+from sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field import HyperellipticCurve_finite_field
+
 from . import ell_point
-from sage.arith.misc import GCD as gcd
-from sage.arith.functions import lcm
-from sage.arith.misc import binomial
-from sage.misc.cachefunc import cached_method
-from sage.groups.additive_abelian.additive_abelian_wrapper import AdditiveAbelianGroupWrapper
+from .constructor import EllipticCurve
+from .ell_field import EllipticCurve_field
 
 
 class EllipticCurve_finite_field(EllipticCurve_field, HyperellipticCurve_finite_field):

src/sage/schemes/elliptic_curves/ell_modular_symbols.py

@@ -87,22 +87,22 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.structure.sage_object import SageObject
-from sage.modular.modsym.all import ModularSymbols
+from sage.arith.misc import (kronecker as kronecker_symbol,
+                             next_prime,
+                             prime_divisors,
+                             valuation)
 from sage.databases.cremona import parse_cremona_label
-
-from sage.arith.misc import next_prime
-from sage.arith.misc import kronecker as kronecker_symbol
-from sage.arith.misc import prime_divisors
-from sage.arith.misc import valuation
+from sage.misc.verbose import verbose
+from sage.modular.cusps import Cusps
+from sage.modular.modsym.all import ModularSymbols
 from sage.rings.infinity import unsigned_infinity as infinity
 from sage.rings.integer import Integer
-from sage.modular.cusps import Cusps
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.misc.verbose import verbose
+from sage.structure.sage_object import SageObject
+
+from .constructor import EllipticCurve
 
-from sage.schemes.elliptic_curves.constructor import EllipticCurve
 
 oo = Cusps(infinity)
 zero = Integer(0)

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -76,10 +76,9 @@
 import sage.rings.all as rings
 from sage.rings.power_series_ring import PowerSeriesRing
 from sage.rings.infinity import Infinity as oo
-from sage.rings.integer_ring import ZZ
+from sage.rings.integer_ring import ZZ, IntegerRing
 from sage.rings.rational_field import QQ
 from sage.rings.integer import Integer
-from sage.rings.integer_ring import IntegerRing
 from sage.rings.real_mpfr import RealField
 from sage.rings.complex_mpfr import ComplexField
 from sage.rings.rational_field import RationalField

src/sage/schemes/elliptic_curves/gal_reps_number_field.py

@@ -45,18 +45,17 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sage_object import SageObject
-from sage.rings.number_field.number_field import NumberField
+from sage.arith.misc import legendre_symbol, primes
+from sage.misc.functional import cyclotomic_polynomial
 from sage.modules.free_module import VectorSpace
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.misc.functional import cyclotomic_polynomial
-from sage.arith.misc import legendre_symbol
-from sage.arith.misc import primes
-from sage.sets.set import Set
+from sage.rings.infinity import Infinity
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
+from sage.rings.number_field.number_field import NumberField
 from sage.rings.rational_field import QQ
-from sage.rings.infinity import Infinity
+from sage.sets.set import Set
+from sage.structure.sage_object import SageObject
 
 
 class GaloisRepresentation(SageObject):

src/sage/schemes/elliptic_curves/heegner.py

@@ -92,41 +92,34 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-
-from sage.misc.misc_c import prod
-from sage.misc.verbose import verbose
-from sage.misc.cachefunc import cached_method
-
-from sage.structure.sage_object import SageObject
-from sage.structure.richcmp import (richcmp_method, richcmp,
-                                    richcmp_not_equal, rich_to_bool)
-
 import sage.rings.abc
 import sage.rings.number_field.number_field_element
 import sage.rings.number_field.number_field as number_field
 import sage.rings.all as rings
-from sage.rings.integer_ring import ZZ
-from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
-from sage.rings.rational_field import QQ
+
+from sage.arith.functions import lcm
+from sage.arith.misc import (binomial, factorial, prime_divisors,
+                             GCD as gcd, XGCD as xgcd)
+from sage.matrix.constructor import Matrix as matrix
+from sage.matrix.matrix_space import MatrixSpace
+from sage.misc.cachefunc import cached_method
+from sage.misc.misc_c import prod
+from sage.misc.verbose import verbose
+from sage.modular.modsym.p1list import P1List
 from sage.rings.complex_double import CDF
-from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as Integers
-from sage.rings.real_mpfr import RealField
 from sage.rings.complex_mpfr import ComplexField
-from sage.rings.number_field.number_field import QuadraticField
-from sage.arith.misc import GCD as gcd
-from sage.arith.misc import XGCD as xgcd
-from sage.arith.functions import lcm
-from sage.arith.misc import prime_divisors
-from sage.arith.misc import factorial
-from sage.arith.misc import binomial
 from sage.rings.factorint import factor_trial_division
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as Integers
+from sage.rings.integer_ring import ZZ
+from sage.rings.number_field.number_field import QuadraticField
+from sage.rings.rational_field import QQ
+from sage.rings.real_mpfr import RealField
 from sage.quadratic_forms.all import (BinaryQF,
                                       BinaryQF_reduced_representatives)
-from sage.matrix.matrix_space import MatrixSpace
-from sage.matrix.constructor import Matrix as matrix
-
-from sage.modular.modsym.p1list import P1List
-
+from sage.structure.sage_object import SageObject
+from sage.structure.richcmp import (richcmp_method, richcmp,
+                                    richcmp_not_equal, rich_to_bool)
 
 ###############################################################################
 #

src/sage/schemes/elliptic_curves/hom_velusqrt.py

@@ -122,21 +122,17 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sequence import Sequence
-from sage.structure.all import coercion_model as cm
-
 from sage.misc.cachefunc import cached_method
-
 from sage.misc.misc_c import prod
 from sage.rings.generic import ProductTree, prod_with_derivative
-
-from sage.structure.richcmp import op_EQ
-
 from sage.rings.integer import Integer
+from sage.structure.all import coercion_model as cm
+from sage.structure.richcmp import op_EQ
+from sage.structure.sequence import Sequence
 
-from sage.schemes.elliptic_curves.constructor import EllipticCurve
-from sage.schemes.elliptic_curves.ell_finite_field import EllipticCurve_finite_field
-from sage.schemes.elliptic_curves.hom import EllipticCurveHom, compare_via_evaluation
+from .constructor import EllipticCurve
+from .ell_finite_field import EllipticCurve_finite_field
+from .hom import EllipticCurveHom, compare_via_evaluation
 
 
 def _choose_IJK(n):
@@ -1214,11 +1210,11 @@ def _random_example_for_testing():
         True
     """
     from sage.rings.fast_arith import prime_range
-    from sage.misc.prandom import choice
-    from sage.misc.prandom import randrange
+    from sage.misc.prandom import choice, randrange
     from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
     from sage.arith.functions import lcm
     from sage.rings.finite_rings.integer_mod import Mod
+
     while True:
         p = choice(prime_range(2, 100))
         e = randrange(1,5)

src/sage/schemes/elliptic_curves/mod_sym_num.pyx

@@ -164,18 +164,16 @@ AUTHORS:
 from cysignals.memory cimport sig_malloc, sig_free, sig_realloc
 from cysignals.signals cimport sig_check
 
+from sage.arith.misc import euler_phi, kronecker as kronecker_symbol
 from sage.misc.cachefunc import cached_method
-
+from sage.misc.misc_c import prod
+from sage.misc.verbose import verbose
 from sage.rings.complex_mpfr cimport ComplexNumber
 from sage.rings.complex_mpfr import ComplexField
-from sage.rings.real_mpfr cimport RealNumber, RealField
-from sage.rings.rational cimport Rational
 from sage.rings.integer cimport Integer
+from sage.rings.rational cimport Rational
+from sage.rings.real_mpfr cimport RealNumber, RealField
 
-from sage.misc.misc_c import prod
-from sage.misc.verbose import verbose
-from sage.arith.misc import kronecker as kronecker_symbol
-from sage.arith.misc import euler_phi
 
 cdef extern from "<math.h>":
     double log(double)

src/sage/schemes/elliptic_curves/padic_lseries.py

@@ -61,35 +61,33 @@
 #                  https://www.gnu.org/licenses/
 ######################################################################
 
-from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
-from sage.rings.padics.factory import Qp
-from sage.rings.infinity import infinity
-from sage.rings.laurent_series_ring import LaurentSeriesRing
-from sage.rings.power_series_ring import PowerSeriesRing
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as Integers
-
-from sage.rings.integer import Integer
-from sage.arith.misc import valuation
-from sage.arith.misc import binomial
-from sage.arith.misc import kronecker as kronecker_symbol
-from sage.arith.misc import GCD as gcd
-from sage.arith.misc import prime_divisors
-from sage.arith.functions import lcm as LCM
-
-from sage.structure.sage_object import SageObject
-from sage.structure.richcmp import richcmp_method, richcmp
-
-from sage.misc.functional import denominator
-from sage.misc.verbose import verbose, get_verbose
-
-from sage.modules.free_module_element import vector
 import sage.matrix.all as matrix
 import sage.schemes.hyperelliptic_curves.monsky_washnitzer
+
+from sage.arith.functions import lcm as LCM
+from sage.arith.misc import (binomial,
+                             GCD as gcd,
+                             prime_divisors,
+                             kronecker as kronecker_symbol,
+                             valuation)
 from sage.functions.log import log
 from sage.functions.other import floor
 from sage.misc.cachefunc import cached_method
+from sage.misc.functional import denominator
+from sage.misc.verbose import get_verbose, verbose
+from sage.modules.free_module_element import vector
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as Integers
+from sage.rings.infinity import infinity
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import ZZ
+from sage.rings.laurent_series_ring import LaurentSeriesRing
+from sage.rings.padics.factory import Qp
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+from sage.rings.power_series_ring import PowerSeriesRing
+from sage.rings.rational_field import QQ
+from sage.structure.richcmp import richcmp_method, richcmp
+from sage.structure.sage_object import SageObject
+
 
 @richcmp_method
 class pAdicLseries(SageObject):

src/sage/schemes/elliptic_curves/padics.py

@@ -21,25 +21,28 @@
 #                  https://www.gnu.org/licenses/
 ######################################################################
 
+import math
 
-import sage.rings.all as rings
-from . import padic_lseries as plseries
 import sage.arith.all as arith
-from sage.rings.padics.factory import Qp
-from sage.rings.padics.factory import Zp
+import sage.matrix.all as matrix
+import sage.misc.misc as misc
+import sage.rings.all as rings
+import sage.schemes.hyperelliptic_curves.hypellfrob
+import sage.schemes.hyperelliptic_curves.monsky_washnitzer
+
+from sage.misc.cachefunc import cached_method
+from sage.rings.big_oh import O
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as Integers
 from sage.rings.integer import Integer
-from sage.rings.big_oh import O
-from sage.rings.power_series_ring import PowerSeriesRing
 from sage.rings.laurent_series_ring import LaurentSeriesRing
+from sage.rings.padics.factory import Qp, Zp
+from sage.rings.power_series_ring import PowerSeriesRing
 from sage.rings.rational_field import RationalField
-import math
-import sage.misc.misc as misc
-import sage.matrix.all as matrix
+
+from . import padic_lseries as plseries
+
 sqrt = math.sqrt
-import sage.schemes.hyperelliptic_curves.monsky_washnitzer
-import sage.schemes.hyperelliptic_curves.hypellfrob
-from sage.misc.cachefunc import cached_method
+
 
 def __check_padic_hypotheses(self, p):
     r"""

src/sage/schemes/elliptic_curves/period_lattice.py

@@ -96,22 +96,22 @@
 
 """
 
+import sage.rings.abc
+
+from sage.libs.pari.all import pari
+from sage.misc.cachefunc import cached_method
 from sage.modules.free_module import FreeModule_generic_pid
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.complex_mpfr import ComplexNumber
+from sage.rings.infinity import Infinity
 from sage.rings.integer_ring import ZZ
+from sage.rings.number_field.number_field import refine_embedding
+from sage.rings.qqbar import AA, QQbar
 from sage.rings.rational_field import QQ
 from sage.rings.real_mpfr import RealField
-from sage.rings.complex_mpfr import ComplexField
-from sage.rings.qqbar import QQbar
-from sage.rings.qqbar import AA
-import sage.rings.abc
-from sage.rings.complex_mpfr import ComplexNumber
 from sage.rings.real_mpfr import RealNumber as RealNumber
-from sage.rings.number_field.number_field import refine_embedding
-from sage.rings.infinity import Infinity
 from sage.schemes.elliptic_curves.constructor import EllipticCurve
-from sage.misc.cachefunc import cached_method
 from sage.structure.richcmp import richcmp_method, richcmp, richcmp_not_equal
-from sage.libs.pari.all import pari
 
 
 class PeriodLattice(FreeModule_generic_pid):