sage -fiximports src/sage/schemes

src/sage/schemes/affine/affine_morphism.py

@@ -59,7 +59,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
 
-from sage.arith.all import gcd
+from sage.arith.misc import GCD as gcd
 
 from sage.rings.integer import Integer
 from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField

src/sage/schemes/elliptic_curves/BSD.py

@@ -2,7 +2,9 @@
 "Birch and Swinnerton-Dyer formulas"
 
 from sage.arith.misc import prime_divisors
-from sage.rings.all import ZZ, Infinity, QuadraticField
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.infinity import Infinity
+from sage.rings.number_field.number_field import QuadraticField
 from sage.functions.other import ceil
 
 
@@ -480,7 +482,7 @@ def prove_BSD(E, verbosity=0, two_desc='mwrank', proof=None, secs_hi=5,
         # We do not know BSD(E,p) for even a single p, since it's
         # an open problem to show that L^r(E,1)/(Reg*Omega) is
         # rational for any curve with r >= 2.
-        from sage.sets.all import Primes
+        from sage.sets.primes import Primes
         BSD.primes = Primes()
         if return_BSD:
             BSD.rank = rank_lower_bd

src/sage/schemes/elliptic_curves/cardinality.py

@@ -21,7 +21,10 @@
 # ****************************************************************************
 from .constructor import EllipticCurve, EllipticCurve_from_j
 from sage.schemes.curves.projective_curve import Hasse_bounds
-from sage.rings.all import Integer, ZZ, GF, polygen
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
+from sage.rings.polynomial.polynomial_ring import polygen
 from sage.groups.generic import order_from_bounds
 
 

src/sage/schemes/elliptic_curves/cm.py

@@ -34,12 +34,12 @@
 # ****************************************************************************
 
 from sage.interfaces.magma import magma
-from sage.rings.all import (Integer,
-                            QQ,
-                            ZZ,
-                            IntegerRing,
-                            is_fundamental_discriminant,
-                            PolynomialRing)
+from sage.rings.integer import Integer
+from sage.rings.rational_field import Q as QQ
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.integer_ring import IntegerRing
+from sage.rings.number_field.number_field import is_fundamental_discriminant
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 from sage.misc.cachefunc import cached_function
 
@@ -124,7 +124,8 @@ def hilbert_class_polynomial(D, algorithm=None):
         raise ValueError("%s is not a valid algorithm" % algorithm)
 
     from sage.quadratic_forms.binary_qf import BinaryQF_reduced_representatives
-    from sage.rings.all import RR, ComplexField
+    from sage.rings.real_mpfr import RR
+    from sage.rings.complex_mpfr import ComplexField
     from sage.functions.all import elliptic_j
 
     # get all primitive reduced quadratic forms, (necessary to exclude
@@ -623,7 +624,8 @@ def is_cm_j_invariant(j, method='new'):
         True
     """
     # First we check that j is an algebraic number:
-    from sage.rings.all import NumberFieldElement, NumberField
+    from sage.rings.number_field.number_field_element import NumberFieldElement
+    from sage.rings.number_field.number_field import NumberField
     if not isinstance(j, NumberFieldElement) and j not in QQ:
         raise NotImplementedError("is_cm_j_invariant() is only implemented for number field elements")
 

src/sage/schemes/elliptic_curves/descent_two_isogeny.pyx

@@ -19,8 +19,8 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring import polygen
 cdef object x_ZZ = polygen(ZZ)
 from sage.rings.polynomial.real_roots import real_roots
-from sage.arith.all import prime_divisors
-from sage.all import ntl
+from sage.arith.misc import prime_divisors
+import sage.libs.ntl.all as ntl
 
 from sage.rings.integer cimport Integer
 from sage.libs.gmp.mpz cimport *

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

@@ -2486,7 +2486,7 @@ def __compute_omega_general(self, E, psi, psi_pr, phi, phi_pr):
         # thesis are wrong, the correct formulas
         # are coded below
 
-        from sage.arith.all import binomial
+        from sage.arith.misc import binomial
 
         for j in range(n - 1):
             psi_prpr += binomial(j+2, 2) * psi[j+2] * cur_x_pow

src/sage/schemes/elliptic_curves/ell_field.py

@@ -1426,7 +1426,7 @@ def isogenies_prime_degree(self, l=None, max_l=31):
             raise NotImplementedError("This code could be implemented for QQbar, but has not been yet.")
 
         if l is None:
-            from sage.rings.all import prime_range
+            from sage.rings.fast_arith import prime_range
             L = prime_range(max_l + 1)
         else:
             try:

src/sage/schemes/elliptic_curves/ell_finite_field.py

@@ -28,11 +28,17 @@
 from .ell_field import EllipticCurve_field
 from .constructor import EllipticCurve
 from sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field import HyperellipticCurve_finite_field
-from sage.rings.all import Integer, ZZ, PolynomialRing, GF, polygen
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import Z as 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 . import ell_point
-from sage.arith.all import gcd, lcm, binomial
+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
 

src/sage/schemes/elliptic_curves/ell_generic.py

@@ -62,7 +62,7 @@
 import sage.groups.additive_abelian.additive_abelian_group as groups
 import sage.groups.generic as generic
 
-from sage.arith.all import lcm
+from sage.arith.functions import lcm
 import sage.rings.all as rings
 from sage.misc.cachefunc import cached_method
 from sage.misc.fast_methods import WithEqualityById

src/sage/schemes/elliptic_curves/ell_modular_symbols.py

@@ -91,7 +91,10 @@
 from sage.modular.modsym.all import ModularSymbols
 from sage.databases.cremona import parse_cremona_label
 
-from sage.arith.all import next_prime, kronecker_symbol, prime_divisors, valuation
+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.rings.infinity import unsigned_infinity as infinity
 from sage.rings.integer import Integer
 from sage.modular.cusps import Cusps

src/sage/schemes/elliptic_curves/ell_number_field.py

@@ -388,7 +388,7 @@ def height_pairing_matrix(self, points=None, precision=None, normalised=True):
             RR = RealField()
         else:
             RR = RealField(precision)
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         M = MatrixSpace(RR, r)
         mat = M()
         for j in range(r):
@@ -3892,7 +3892,7 @@ def saturation(self, points, verbose=False,
             raise ValueError("points not linearly independent in saturation()")
         sat_reg = reg
 
-        from sage.rings.all import prime_range
+        from sage.rings.fast_arith import prime_range
         if full_saturation:
             if lower_ht_bound is None:
                 # TODO (robertwb): verify this for rank > 1

src/sage/schemes/elliptic_curves/ell_point.py

@@ -2836,7 +2836,9 @@ def archimedean_local_height(self, v=None, prec=None, weighted=False):
             4.0000000000000000000000000000000000000000000000000000000000
         """
         from sage.rings.number_field.number_field import refine_embedding
-        from sage.all import RealField, ComplexField, Infinity
+        from sage.rings.real_mpfr import RealField
+        from sage.rings.complex_mpfr import ComplexField
+        from sage.rings.infinity import Infinity
 
         E = self.curve()
         K = E.base_ring()
@@ -3257,7 +3259,9 @@ def elliptic_logarithm(self, embedding=None, precision=100,
             0.70448375537782208460499649302 - 0.79246725643650979858266018068*I
         """
         from sage.rings.number_field.number_field import refine_embedding
-        from sage.rings.all import RealField, ComplexField, QQ
+        from sage.rings.real_mpfr import RealField
+        from sage.rings.complex_mpfr import ComplexField
+        from sage.rings.rational_field import Q as QQ
 
         # Check the trivial case:
 

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -74,13 +74,15 @@
 
 import sage.arith.all as arith
 import sage.rings.all as rings
-from sage.rings.all import (
-    PowerSeriesRing,
-    infinity as oo,
-    ZZ, QQ,
-    Integer,
-    IntegerRing, RealField,
-    ComplexField, RationalField)
+from sage.rings.power_series_ring import PowerSeriesRing
+from sage.rings.infinity import Infinity as oo
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.rational_field import Q as 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
 
 from sage.structure.coerce import py_scalar_to_element
 from sage.structure.element import Element
@@ -3436,7 +3438,7 @@ def Lambda(self, s, prec):
             sage: E.Lambda(1.4+0.5*I, 50)
             -0.354172680517... + 0.874518681720...*I
         """
-        from sage.all import pi
+        from sage.symbolic.constants import pi
 
         s = C(s)
         N = self.conductor()
@@ -6013,7 +6015,7 @@ def point_preprocessing(free,tor):
             roots.remove(e3)
             e1,e2 = roots
 
-        from sage.all import pi
+        from sage.symbolic.constants import pi
         e = R(1).exp()
         pi = R(pi)
 
@@ -7054,7 +7056,7 @@ def elliptic_curve_congruence_graph(curves):
         Graph on 12 vertices
     """
     from sage.graphs.graph import Graph
-    from sage.arith.all import lcm
+    from sage.arith.functions import lcm
     from sage.rings.fast_arith import prime_range
     from sage.misc.misc_c import prod
     G = Graph()

src/sage/schemes/elliptic_curves/ell_tate_curve.py

@@ -44,7 +44,7 @@
 from sage.rings.padics.factory import Qp
 from sage.structure.sage_object import SageObject
 from sage.structure.richcmp import richcmp, richcmp_method
-from sage.arith.all import LCM
+from sage.arith.functions import lcm as LCM
 from sage.modular.modform.constructor import EisensteinForms, CuspForms
 from sage.schemes.elliptic_curves.constructor import EllipticCurve
 from sage.functions.log import log

src/sage/schemes/elliptic_curves/ell_torsion.py

@@ -26,7 +26,7 @@
 # ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
-from sage.rings.all import RationalField
+from sage.rings.rational_field import RationalField
 import sage.groups.additive_abelian.additive_abelian_wrapper as groups
 from sage.structure.richcmp import richcmp_method, richcmp
 

src/sage/schemes/elliptic_curves/formal_group.py

@@ -16,7 +16,7 @@
 
 import sage.misc.misc as misc
 import sage.rings.all as rings
-from sage.rings.all import O
+from sage.rings.big_oh import O
 
 
 class EllipticCurveFormalGroup(SageObject):

src/sage/schemes/elliptic_curves/gal_reps.py

@@ -121,7 +121,8 @@
 import sage.misc.all as misc
 from sage.misc.verbose import verbose
 import sage.rings.all as rings
-from sage.rings.all import RealField, GF
+from sage.rings.real_mpfr import RealField
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 
 from math import sqrt
 from sage.libs.pari.all import pari

src/sage/schemes/elliptic_curves/gal_reps_number_field.py

@@ -50,9 +50,13 @@
 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.all import legendre_symbol, primes
+from sage.arith.misc import legendre_symbol
+from sage.arith.misc import primes
 from sage.sets.set import Set
-from sage.rings.all import Integer, ZZ, QQ, Infinity
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.rational_field import Q as QQ
+from sage.rings.infinity import Infinity
 
 
 class GaloisRepresentation(SageObject):

src/sage/schemes/elliptic_curves/heegner.py

@@ -105,14 +105,25 @@
 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.all import (ZZ, GF, QQ, CDF,
-                            Integers, RealField, ComplexField, QuadraticField)
-from sage.arith.all import (gcd, xgcd, lcm, prime_divisors, factorial,
-        binomial)
+from sage.rings.integer_ring import Z as ZZ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
+from sage.rings.rational_field import Q as QQ
+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.quadratic_forms.all import (BinaryQF,
                                       BinaryQF_reduced_representatives)
-from sage.matrix.all import MatrixSpace, matrix
+from sage.matrix.matrix_space import MatrixSpace
+from sage.matrix.constructor import Matrix as matrix
 
 from sage.modular.modsym.p1list import P1List
 
@@ -6822,7 +6833,7 @@ def heegner_index_bound(self, D=0, prec=5, max_height=None):
     else:
         H = 4*h
     p = 3
-    from sage.all import next_prime
+    from sage.arith.misc import next_prime
     while True:
         c = H/(2*p**2) + B
         if c < max_height:

src/sage/schemes/elliptic_curves/height.py

@@ -42,7 +42,8 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.misc.mrange import cartesian_product_iterator
-from sage.arith.all import lcm, factorial
+from sage.arith.functions import lcm
+from sage.arith.misc import factorial
 from sage.ext.fast_callable import fast_callable
 from sage.functions.log import log, exp
 from sage.symbolic.ring import SR

src/sage/schemes/elliptic_curves/hom_velusqrt.py

@@ -1213,7 +1213,12 @@ def _random_example_for_testing():
         sage: 5 <= K.order()
         True
     """
-    from sage.all import prime_range, choice, randrange, GF, lcm, Mod
+    from sage.rings.fast_arith import prime_range
+    from sage.misc.prandom import choice
+    from sage.misc.prandom import 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/isogeny_class.py

@@ -770,7 +770,7 @@ def _compute(self, verbose=False):
             True
         """
         from sage.schemes.elliptic_curves.ell_curve_isogeny import fill_isogeny_matrix
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         from sage.sets.set import Set
         self._maps = None
 
@@ -1055,7 +1055,7 @@ def _compute(self):
             [0 2 0 0 0 0]
         """
         algorithm = self._algorithm
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         self._maps = None
         if algorithm == "database":
             try:
@@ -1183,8 +1183,8 @@ def isogeny_degrees_cm(E, verbose=False):
         print("CM case, discriminant = %s" % d)
 
     from sage.libs.pari.all import pari
-    from sage.sets.all import Set
-    from sage.arith.all import kronecker_symbol
+    from sage.sets.set import Set
+    from sage.arith.misc import kronecker as kronecker_symbol
 
     n = E.base_field().absolute_degree()
     if not E.has_rational_cm():

src/sage/schemes/elliptic_curves/isogeny_small_degree.py

@@ -536,7 +536,7 @@ def _sporadic_Q_data(j):
         ....:     g = E.division_polynomial(ell)
         ....:     assert g % f == 0
     """
-    from sage.rings.all import RealField
+    from sage.rings.real_mpfr import RealField
     from sage.misc.misc_c import prod
     ell = sporadic_j[j]
     E = EllipticCurve(j=j).short_weierstrass_model()