gh-35033: sage.schemes: Replace imports from sage.*.all for namespace…

… packages

    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes #1234" use "Introduce new method to
calculate 1+1"
-->
### 📚 Description

<!-- Describe your changes here in detail -->
<!-- Why is this change required? What problem does it solve? -->
<!-- If it resolves an open issue, please link to the issue here. For
example "Closes #1337" -->
Closes #34951

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->

- [x] I have made sure that the title is self-explanatory and the
description concisely explains the PR.
- [x] I have linked an issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies
<!-- List all open pull requests that this PR logically depends on -->
<!--
- #xyz: short description why this is a dependency
- #abc: ...
-->
    
URL: #35033
Reported by: Matthias Köppe
Reviewer(s): Lorenz Panny

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 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 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 QQ
+from sage.rings.integer_ring import 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

@@ -1434,7 +1434,7 @@ 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

@@ -25,18 +25,24 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.groups.generic as generic
 
+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 import polygen
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 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.rings.all import Integer, ZZ, PolynomialRing, GF, 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.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_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

@@ -87,19 +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.all import next_prime, kronecker_symbol, prime_divisors, 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_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):
@@ -3897,7 +3897,7 @@ 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

@@ -2833,7 +2833,9 @@ 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()
@@ -3254,7 +3256,9 @@ 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 QQ
 
         # Check the trivial case:
 

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -74,13 +74,14 @@
 
 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 ZZ, IntegerRing
+from sage.rings.rational_field import QQ
+from sage.rings.integer import Integer
+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 +3437,7 @@ 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 +6014,7 @@ 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 +7055,7 @@ 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

@@ -45,14 +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.all import legendre_symbol, primes
+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.sets.set import Set
-from sage.rings.all import Integer, ZZ, QQ, Infinity
+from sage.structure.sage_object import SageObject
 
 
 class GaloisRepresentation(SageObject):

src/sage/schemes/elliptic_curves/heegner.py

@@ -92,30 +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.all import (ZZ, GF, QQ, CDF,
-                            Integers, RealField, ComplexField, QuadraticField)
-from sage.arith.all import (gcd, xgcd, lcm, prime_divisors, factorial,
-        binomial)
+
+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.complex_mpfr import ComplexField
 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.all import MatrixSpace, 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)
 
 ###############################################################################
 #
@@ -6822,7 +6826,7 @@ 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: