sage.modular: Modularization fixes for imports

Author: Matthias Koeppe

src/sage/modular/abvar/abvar.py

@@ -33,6 +33,8 @@
 from copy import copy
 from random import randrange
 
+import sage.rings.abc
+
 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
@@ -55,7 +57,6 @@
 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
@@ -66,6 +67,8 @@
 
 lazy_import('sage.databases.cremona',
             ['cremona_letter_code', 'CremonaDatabase'])
+lazy_import('sage.rings.qqbar', 'QQbar')
+
 
 from . import homspace
 from . import lseries
@@ -798,7 +801,7 @@ def _Hom_(self, B, cat=None):
             L = B.base_field()
             if K == L:
                 F = K
-            elif K == QQbar or L == QQbar:
+            elif isinstance(K, sage.rings.abc.AlgebraicField) or isinstance(L, sage.rings.abc.AlgebraicField):
                 F = QQbar
             else:
                 # TODO -- improve this

src/sage/modular/abvar/finite_subgroup.py

@@ -97,6 +97,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+from sage.misc.lazy_import import lazy_import
 from sage.modular.abvar.torsion_point import TorsionPoint
 from sage.modules.module import Module
 from sage.modules.free_module import is_FreeModule
@@ -105,12 +106,13 @@
 from sage.structure.richcmp import richcmp_method, richcmp
 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
 
+lazy_import('sage.rings.qqbar', 'QQbar')
+
 
 @richcmp_method
 class FiniteSubgroup(Module):
@@ -521,7 +523,7 @@ def _repr_(self):
             'Finite subgroup with invariants [3, 3, 3, 3, 3, 3, 3, 3, 3, 3] over QQ of Abelian variety J0(42) of dimension 5'
         """
         K = self.__field_of_definition
-        if K == QQbar:
+        if isinstance(K, sage.rings.abc.AlgebraicField):
             field = "QQbar"
         elif K == QQ:
             field = "QQ"
@@ -815,7 +817,7 @@ def invariants(self):
 
 
 class FiniteSubgroup_lattice(FiniteSubgroup):
-    def __init__(self, abvar, lattice, field_of_definition=QQbar, check=True):
+    def __init__(self, abvar, lattice, field_of_definition=None, check=True):
         """
         A finite subgroup of a modular abelian variety that is defined by a
         given lattice.
@@ -841,6 +843,8 @@ def __init__(self, abvar, lattice, field_of_definition=QQbar, check=True):
             sage: G = J.finite_subgroup([[1/3,0], [0,1/5]]); G
             Finite subgroup with invariants [15] over QQbar of Abelian variety J0(11) of dimension 1
         """
+        if field_of_definition is None:
+            field_of_definition = QQbar
         if check:
             from .abvar import is_ModularAbelianVariety
             if not is_FreeModule(lattice) or lattice.base_ring() != ZZ:

src/sage/modular/arithgroup/all.py

@@ -9,7 +9,8 @@
 from .congroup_gamma import Gamma_constructor as Gamma, is_Gamma
 from .congroup_sl2z import SL2Z, is_SL2Z
 
-from .arithgroup_perm import ArithmeticSubgroup_Permutation
+from sage.misc.lazy_import import lazy_import
+lazy_import('sage.modular.arithgroup.arithgroup_perm', 'ArithmeticSubgroup_Permutation')
 
 from .congroup import (degeneracy_coset_representatives_gamma0,
                             degeneracy_coset_representatives_gamma1)

src/sage/modular/btquotients/btquotient.py

@@ -42,7 +42,6 @@
 from collections import deque
 
 from sage.arith.misc import gcd, xgcd, kronecker_symbol, fundamental_discriminant
-from sage.libs.pari.all import pari
 from sage.matrix.constructor import Matrix
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
@@ -59,16 +58,17 @@
 from sage.rings.finite_rings.integer_mod_ring import Zmod
 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.padics.factory import Qp, Zp
 from sage.rings.padics.precision_error import PrecisionError
 from sage.rings.rational_field import QQ
 from sage.structure.sage_object import SageObject
 from sage.structure.unique_representation import UniqueRepresentation
 
 lazy_import('sage.algebras.quatalg.quaternion_algebra', 'QuaternionAlgebra')
 lazy_import('sage.graphs.graph', 'Graph')
+lazy_import('sage.libs.pari.all', 'pari')
 lazy_import('sage.plot.colors', 'rainbow')
+lazy_import('sage.rings.number_field.number_field', 'NumberField')
+lazy_import('sage.rings.padics.factory', ['Qp', 'Zp'])
 
 
 class DoubleCosetReduction(SageObject):

src/sage/modular/btquotients/pautomorphicform.py

@@ -46,6 +46,7 @@
 
 from sage.matrix.constructor import Matrix, zero_matrix
 from sage.matrix.matrix_space import MatrixSpace
+from sage.misc.lazy_import import lazy_import
 from sage.misc.verbose import verbose
 from sage.modular.btquotients.btquotient import DoubleCosetReduction
 from sage.modular.hecke.all import AmbientHeckeModule, HeckeModuleElement
@@ -56,14 +57,16 @@
 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.rational_field import QQ
 from sage.rings.real_mpfr import RR
 from sage.structure.element import ModuleElement
 from sage.structure.richcmp import op_EQ, op_NE
 from sage.structure.unique_representation import UniqueRepresentation
 
+lazy_import('sage.rings.padics.factory', 'Qp')
+
+
 # Need this to be pickleable
 
 

src/sage/modular/local_comp/local_comp.py

@@ -23,14 +23,16 @@
 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.rings.qqbar               import QQbar
 from sage.misc.abstract_method      import abstract_method
 from sage.misc.cachefunc            import cached_method
+from sage.misc.lazy_import          import lazy_import
 from sage.misc.verbose              import verbose
 from sage.misc.flatten              import flatten
 from sage.modular.modform.element   import Newform
 from sage.structure.sequence        import Sequence
 
+lazy_import('sage.rings.qqbar', 'QQbar')
+
 from .type_space                    import TypeSpace
 from .smoothchar                    import SmoothCharacterGroupQp, SmoothCharacterGroupUnramifiedQuadratic, SmoothCharacterGroupRamifiedQuadratic
 

src/sage/modular/local_comp/smoothchar.py

@@ -49,22 +49,24 @@
 from sage.categories.rings import Rings
 from sage.misc.abstract_method import abstract_method
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.misc.mrange import xmrange
 from sage.misc.verbose import verbose
 from sage.modular.dirichlet import DirichletGroup
-from sage.rings.finite_rings.conway_polynomials import conway_polynomial
 from sage.rings.finite_rings.integer_mod_ring import Zmod
 from sage.rings.infinity import Infinity
 from sage.rings.integer_ring import ZZ
-from sage.rings.number_field.number_field import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 from sage.structure.element import MultiplicativeGroupElement, parent
 from sage.structure.parent import Parent
 from sage.structure.richcmp import richcmp_not_equal, richcmp
 from sage.structure.sequence import Sequence
 
+lazy_import('sage.rings.finite_rings.conway_polynomials', 'conway_polynomial')
+lazy_import('sage.rings.number_field.number_field', 'NumberField')
+
 
 class SmoothCharacterGeneric(MultiplicativeGroupElement):
     r"""

src/sage/modular/modform/all.py

@@ -14,9 +14,10 @@
 
 from .theta import theta_qexp, theta2_qexp
 
-from .j_invariant import j_invariant_qexp
+from sage.misc.lazy_import import lazy_import
 
-from .vm_basis import victor_miller_basis, delta_qexp
+lazy_import('sage.modular.modform.j_invariant', 'j_invariant_qexp')
+lazy_import('sage.modular.modform.vm_basis', ['victor_miller_basis', 'delta_qexp'])
 
 from .hecke_operator_on_qexp import hecke_operator_on_qexp, hecke_operator_on_basis
 

src/sage/modular/modform/cuspidal_submodule.py

@@ -41,12 +41,14 @@
 from sage.matrix.constructor import Matrix
 from sage.matrix.special import identity_matrix
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.misc.verbose  import verbose
 from sage.rings.integer import Integer
 from sage.rings.rational_field import QQ
 
+lazy_import('sage.modular.modform.vm_basis', 'victor_miller_basis')
+
 from .submodule import ModularFormsSubmodule
-from . import vm_basis
 from . import weight1
 
 class CuspidalSubmodule(ModularFormsSubmodule):
@@ -316,8 +318,7 @@ def _compute_q_expansion_basis(self, prec=None):
             prec = self.prec()
         else:
             prec = Integer(prec)
-        return vm_basis.victor_miller_basis(self.weight(), prec,
-                                            cusp_only=True, var='q')
+        return victor_miller_basis(self.weight(), prec, cusp_only=True, var='q')
 
     def _pari_init_(self):
         """

src/sage/modular/modform/eis_series.py

@@ -14,16 +14,17 @@
 
 from sage.arith.functions import lcm
 from sage.arith.misc import bernoulli, divisors, is_squarefree
+from sage.misc.lazy_import import lazy_import
 from sage.misc.timing import cputime
 from sage.modular.arithgroup.congroup_gammaH import GammaH_class
 from sage.modular.dirichlet import DirichletGroup
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.number_field.number_field import CyclotomicField
 from sage.rings.power_series_ring import PowerSeriesRing
 from sage.rings.rational_field import QQ
 
-from .eis_series_cython import eisenstein_series_poly, Ek_ZZ
+lazy_import('sage.modular.modform.eis_series_cython', ['eisenstein_series_poly', 'Ek_ZZ'])
+lazy_import('sage.rings.number_field.number_field', 'CyclotomicField')
 
 
 def eisenstein_series_qexp(k, prec=10, K=QQ, var='q', normalization='linear'):