Trac #34191: Remove imports from sage.rings.all in sage.modular

Part of Meta-ticket #34201: Replace imports from sage.*.all for
namespace packages

Also clean up some other outdated importing practices.

URL: https://trac.sagemath.org/34191
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): David Ayotte

src/sage/modular/abvar/abvar.py

@@ -29,46 +29,53 @@
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
+
 from copy import copy
 from random import randrange
 
+from sage.arith.functions import lcm as LCM
+from sage.arith.misc import divisors, next_prime, is_prime
+from sage.categories.modular_abelian_varieties import ModularAbelianVarieties
+from sage.matrix.constructor import matrix
+from sage.matrix.special import block_diagonal_matrix, identity_matrix
 from sage.misc.lazy_import import lazy_import
-
-from sage.categories.all import ModularAbelianVarieties
-from sage.structure.sequence import Sequence, Sequence_generic
-from sage.structure.richcmp import (richcmp_method, richcmp_not_equal,
-                                    rich_to_bool)
-from sage.structure.parent import Parent
-from .morphism import HeckeOperator, Morphism, DegeneracyMap
-from .torsion_subgroup import RationalTorsionSubgroup, QQbarTorsionSubgroup
-from .finite_subgroup import (FiniteSubgroup_lattice, FiniteSubgroup,
-                              TorsionPoint)
-from .cuspidal_subgroup import (CuspidalSubgroup, RationalCuspidalSubgroup,
-                                RationalCuspSubgroup)
-from sage.rings.all import ZZ, QQ, QQbar, Integer
-from sage.arith.all import LCM, divisors, prime_range, next_prime
-from sage.rings.ring import is_Ring
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.infinity import infinity
-from sage.modules.free_module import is_FreeModule
-from sage.modular.arithgroup.all import (is_CongruenceSubgroup, is_Gamma0,
-                                         is_Gamma1, is_GammaH)
-from sage.modular.modsym.all import ModularSymbols
-from sage.modular.modsym.space import ModularSymbolsSpace
+from sage.misc.misc_c import prod
+from sage.modular.arithgroup.congroup_gamma0 import is_Gamma0
+from sage.modular.arithgroup.congroup_gamma1 import is_Gamma1
+from sage.modular.arithgroup.congroup_gammaH import is_GammaH
+from sage.modular.arithgroup.congroup_generic import is_CongruenceSubgroup
 from sage.modular.modform.constructor import Newform
-from sage.matrix.all import matrix, block_diagonal_matrix, identity_matrix
+from sage.modular.modsym.modsym import ModularSymbols
+from sage.modular.modsym.space import ModularSymbolsSpace
+from sage.modular.quatalg.brandt import BrandtModule
+from sage.modules.free_module import is_FreeModule
 from sage.modules.free_module_element import vector
-from sage.misc.misc_c import prod
-from sage.arith.misc import is_prime
+from sage.rings.fast_arith import prime_range
+from sage.rings.infinity import infinity
+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.qqbar import QQbar
+from sage.rings.rational_field import QQ
+from sage.rings.ring import is_Ring
 from sage.schemes.elliptic_curves.constructor import EllipticCurve
 from sage.sets.primes import Primes
-
-from . import homspace
-from . import lseries
+from sage.structure.parent import Parent
+from sage.structure.richcmp import richcmp_method, richcmp_not_equal, rich_to_bool
+from sage.structure.sequence import Sequence, Sequence_generic
 
 lazy_import('sage.databases.cremona',
             ['cremona_letter_code', 'CremonaDatabase'])
 
+from . import homspace
+from . import lseries
+from .morphism import HeckeOperator, Morphism, DegeneracyMap
+from .torsion_subgroup import RationalTorsionSubgroup, QQbarTorsionSubgroup
+from .finite_subgroup import (FiniteSubgroup_lattice, FiniteSubgroup,
+                              TorsionPoint)
+from .cuspidal_subgroup import (CuspidalSubgroup, RationalCuspidalSubgroup,
+                                RationalCuspSubgroup)
+
 
 def is_ModularAbelianVariety(x) -> bool:
     """
@@ -4929,7 +4936,6 @@ def brandt_module(self, p):
         if self.level().valuation(p) != 1:
             raise ValueError("p must exactly divide the level")
         M = self.level() / p
-        from sage.modular.all import BrandtModule
         V = BrandtModule(p, M)
         # now cut out version of self in B
         S = self.modular_symbols(sign=1)

src/sage/modular/abvar/cuspidal_subgroup.py

@@ -69,11 +69,14 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .finite_subgroup                import FiniteSubgroup
-from sage.rings.all                 import infinity, QQ, ZZ
-from sage.matrix.all                import matrix
+from sage.matrix.constructor        import matrix
 from sage.modular.arithgroup.all    import is_Gamma0
 from sage.modular.cusps             import Cusp
+from sage.rings.infinity            import infinity
+from sage.rings.integer_ring        import ZZ
+from sage.rings.rational_field      import QQ
+
+from .finite_subgroup               import FiniteSubgroup
 
 
 class CuspidalSubgroup_generic(FiniteSubgroup):

src/sage/modular/abvar/finite_subgroup.py

@@ -103,8 +103,11 @@
 from sage.structure.gens_py import abelian_iterator
 from sage.structure.sequence import Sequence
 from sage.structure.richcmp import richcmp_method, richcmp
-from sage.rings.all import QQ, ZZ, QQbar, Integer
-from sage.arith.all import lcm
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import ZZ
+from sage.rings.qqbar import QQbar
+from sage.rings.rational_field import QQ
+from sage.arith.functions import lcm
 from sage.misc.misc_c import prod
 from sage.structure.element import coercion_model
 

src/sage/modular/abvar/homology.py

@@ -50,9 +50,12 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+from sage.modular.hecke.module import HeckeModule_free_module
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.ring import CommutativeRing
 from sage.structure.richcmp import richcmp_method, richcmp, richcmp_not_equal
-from sage.modular.hecke.all import HeckeModule_free_module
-from sage.rings.all import Integer, ZZ, QQ, CommutativeRing
 
 # TODO: we will probably also need homology that is *not* a Hecke module.
 

src/sage/modular/abvar/torsion_subgroup.py

@@ -88,16 +88,19 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.structure.richcmp import richcmp_method, richcmp
+from sage.arith.misc import divisors, gcd
+from sage.misc.misc_c import prod
 from sage.modular.abvar.torsion_point import TorsionPoint
-from sage.modules.module            import Module
-from .finite_subgroup                import FiniteSubgroup
-from sage.rings.all                 import ZZ, QQ
-from sage.sets.primes               import Primes
-from sage.modular.arithgroup.all    import is_Gamma0, is_Gamma1
-from sage.all                       import divisors, gcd, prime_range
-from sage.modular.dirichlet         import DirichletGroup
-from sage.misc.misc_c               import prod
+from sage.modular.arithgroup.all import is_Gamma0, is_Gamma1
+from sage.modular.dirichlet import DirichletGroup
+from sage.modules.module import Module
+from sage.rings.fast_arith import prime_range
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.sets.primes import Primes
+from sage.structure.richcmp import richcmp_method, richcmp
+
+from .finite_subgroup import FiniteSubgroup
 
 
 @richcmp_method

src/sage/modular/arithgroup/arithgroup_generic.py

@@ -16,7 +16,7 @@
 from sage.groups.old import Group
 from sage.categories.groups import Groups
 from sage.rings.integer_ring import ZZ
-from sage.arith.all import lcm
+from sage.arith.functions import lcm
 from sage.misc.cachefunc import cached_method
 from copy import copy # for making copies of lists of cusps
 from sage.modular.modsym.p1list import lift_to_sl2z

src/sage/modular/arithgroup/arithgroup_perm.py

@@ -98,14 +98,18 @@
 #
 ################################################################################
 
+from sage.arith.functions import lcm
+from sage.arith.misc import CRT_basis
+from sage.groups.perm_gps.constructor import PermutationGroupElement as PermutationConstructor
+from sage.groups.perm_gps.permgroup import PermutationGroup
+from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
+from sage.misc.cachefunc import cached_method
+from sage.misc.misc_c import prod
+from sage.rings.integer_ring import ZZ
+
 from .all import SL2Z
 from .arithgroup_generic import ArithmeticSubgroup
-from sage.rings.integer_ring import ZZ
-from sage.misc.cachefunc import cached_method
-import sage.arith.all as arith
 
-from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
-from sage.groups.perm_gps.constructor import PermutationGroupElement as PermutationConstructor
 
 Idm = SL2Z([1,0,0,1])    # identity
 
@@ -206,8 +210,7 @@ def eval_sl2z_word(w):
         [ 66 -59]
         [ 47 -42]
     """
-    from sage.all import prod
-    mat = [Lm,Rm]
+    mat = [Lm, Rm]
     w0 = Idm
     w1 = w
     return w0 * prod((mat[a[0]]**a[1] for a in w1), Idm)
@@ -243,7 +246,6 @@ def word_of_perms(w, p1, p2):
             G = G2
             p1 = G(p1)
         else:
-            from sage.groups.perm_gps.all import PermutationGroup
             G = PermutationGroup([p1,p2])
             p1 = G(p1)
             p2 = G(p2)
@@ -431,8 +433,6 @@ def ArithmeticSubgroup_Permutation(
 
         # Check transitivity. This is the most expensive check, so we do it
         # last.
-        from sage.groups.perm_gps.all import PermutationGroup
-
         G = PermutationGroup(gens)
         if not G.is_transitive():
             raise ValueError("Permutations do not generate a transitive group")
@@ -676,7 +676,6 @@ def perm_group(self):
             sage: ap.HsuExample10().perm_group()
             Permutation Group with generators [(1,2)(3,4)(5,6)(7,8)(9,10), (1,8,3)(2,4,6)(5,7,10), (1,4)(2,5,9,10,8)(3,7,6), (1,7,9,10,6)(2,3)(4,5,8)]
         """
-        from sage.groups.perm_gps.all import PermutationGroup
         # we set canonicalize to False as otherwise PermutationGroup changes the
         # order of the generators.
         return PermutationGroup([self.S2(), self.S3(), self.L(), self.R()], canonicalize=False)
@@ -1288,7 +1287,7 @@ def generalised_level(self):
             sage: G.generalised_level()
             3
         """
-        return arith.lcm(self.cusp_widths())
+        return lcm(self.cusp_widths())
 
     def congruence_closure(self):
         r"""
@@ -1477,7 +1476,7 @@ def is_congruence(self):
             # e>1, m>1
             onehalf = ZZ(2).inverse_mod(m) # i.e. 2^(-1) mod m
             onefifth = ZZ(5).inverse_mod(e) # i.e. 5^(-1) mod e
-            c,d = arith.CRT_basis([m, e])
+            c, d = CRT_basis([m, e])
             # c=0 mod e, c=1 mod m; d=1 mod e, d=0 mod m
             a = L**c
             b = R**c

src/sage/modular/arithgroup/congroup_gamma.py

@@ -10,18 +10,21 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .congroup_generic import CongruenceSubgroup
-from sage.misc.misc_c import prod
-from sage.rings.all import ZZ, Zmod, QQ
-from sage.rings.integer import GCD_list
+from sage.arith.misc import gcd
 from sage.groups.matrix_gps.finitely_generated import MatrixGroup
 from sage.matrix.constructor import matrix
+from sage.misc.misc_c import prod
 from sage.modular.cusps import Cusp
-from sage.arith.all import gcd
+from sage.rings.finite_rings.integer_mod_ring import Zmod
+from sage.rings.integer import GCD_list
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 from sage.structure.richcmp import richcmp_method, richcmp
 
+from .congroup_generic import CongruenceSubgroup
 from .congroup_sl2z import SL2Z
 
+
 _gamma_cache = {}
 def Gamma_constructor(N):
     r"""

src/sage/modular/arithgroup/congroup_gamma0.py

@@ -10,18 +10,17 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .congroup_gammaH import GammaH_class
-from .congroup_gamma1 import is_Gamma1
-from sage.modular.modsym.p1list import lift_to_sl2z
-from .congroup_generic import CongruenceSubgroup
-
-from sage.modular.cusps import Cusp
+from sage.arith.misc import kronecker_symbol, divisors, euler_phi, gcd, moebius
 from sage.misc.cachefunc import cached_method
-from sage.rings.all import IntegerModRing, ZZ
-from sage.arith.all import kronecker_symbol
 from sage.misc.misc_c import prod
-import sage.modular.modsym.p1list
-import sage.arith.all as arith
+from sage.modular.cusps import Cusp
+from sage.modular.modsym.p1list import lift_to_sl2z, P1List
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+from sage.rings.integer_ring import ZZ
+
+from .congroup_gamma1 import is_Gamma1
+from .congroup_gammaH import GammaH_class
+from .congroup_generic import CongruenceSubgroup
 
 
 def is_Gamma0(x):
@@ -211,7 +210,6 @@ def _list_of_elements_in_H(self):
         """
         N = self.level()
         if N != 1:
-            gcd = arith.gcd
             H = [x for x in range(1, N) if gcd(x, N) == 1]
         else:
             H = [1]
@@ -321,7 +319,7 @@ def coset_reps(self):
         if N == 1: # P1List isn't very happy working modulo 1
             yield SL2Z([1,0,0,1])
         else:
-            for z in sage.modular.modsym.p1list.P1List(N):
+            for z in P1List(N):
                 yield SL2Z(lift_to_sl2z(z[0], z[1], N))
 
     @cached_method
@@ -455,8 +453,8 @@ def _find_cusps(self):
         N = self.level()
         s = []
 
-        for d in arith.divisors(N):
-            w = arith.gcd(d, N//d)
+        for d in divisors(N):
+            w = gcd(d, N//d)
             if w == 1:
                 if d == 1:
                     s.append(Cusp(1,0))
@@ -466,8 +464,8 @@ def _find_cusps(self):
                     s.append(Cusp(1,d))
             else:
                 for a in range(1, w):
-                    if arith.gcd(a, w) == 1:
-                        while arith.gcd(a, d//w) != 1:
+                    if gcd(a, w) == 1:
+                        while gcd(a, d//w) != 1:
                             a += w
                         s.append(Cusp(a,d))
         return sorted(s)
@@ -484,7 +482,7 @@ def ncusps(self):
             [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
         """
         n = self.level()
-        return sum([arith.euler_phi(arith.gcd(d,n//d)) for d in n.divisors()])
+        return sum([euler_phi(gcd(d,n//d)) for d in n.divisors()])
 
 
     def nu2(self):
@@ -595,7 +593,6 @@ def dimension_new_cusp_forms(self, k=2, p=0):
              sage: all(Gamma0(N).dimension_new_cusp_forms(2)==100 for N in L)
              True
         """
-        from sage.arith.all import moebius
         from sage.functions.other import floor
 
         N = self.level()

src/sage/modular/arithgroup/congroup_gamma1.py

@@ -17,7 +17,7 @@
 from sage.misc.misc_c import prod
 from .congroup_gammaH import GammaH_class, is_GammaH, GammaH_constructor
 from sage.rings.integer_ring import ZZ
-from sage.arith.all import euler_phi as phi, moebius, divisors
+from sage.arith.misc import euler_phi as phi, moebius, divisors
 from sage.modular.dirichlet import DirichletGroup
 
 

src/sage/modular/arithgroup/congroup_gammaH.py

@@ -20,7 +20,8 @@
 #
 ################################################################################
 
-from sage.arith.all import euler_phi, lcm, gcd, divisors, get_inverse_mod, get_gcd, factor, xgcd
+from sage.arith.functions import lcm
+from sage.arith.misc import euler_phi, gcd, divisors, get_inverse_mod, get_gcd, factor, xgcd
 from sage.modular.modsym.p1list import lift_to_sl2z
 from .congroup_generic import CongruenceSubgroup
 from sage.modular.cusps import Cusp