sage.modular: Work around lazy_import limitations

Author: Matthias Koeppe

src/sage/modular/abvar/abvar.py

@@ -67,7 +67,6 @@
 
 lazy_import('sage.databases.cremona',
             ['cremona_letter_code', 'CremonaDatabase'])
-lazy_import('sage.rings.qqbar', 'QQbar')
 
 
 from . import homspace
@@ -802,7 +801,7 @@ def _Hom_(self, B, cat=None):
             if K == L:
                 F = K
             elif isinstance(K, sage.rings.abc.AlgebraicField) or isinstance(L, sage.rings.abc.AlgebraicField):
-                F = QQbar
+                from sage.rings.qqbar import QQbar as F
             else:
                 # TODO -- improve this
                 raise ValueError("please specify a category")
@@ -1000,7 +999,7 @@ def intersection(self, other):
                 for v in V.coordinate_module(S).basis()]
 
         if A.dimension() > 0:
-            finitegroup_base_field = QQbar
+            from sage.rings.qqbar import QQbar as finitegroup_base_field
         else:
             finitegroup_base_field = self.base_field()
         G = self.finite_subgroup(gens, field_of_definition=finitegroup_base_field)
@@ -3129,7 +3128,7 @@ def finite_subgroup(self, X, field_of_definition=None, check=True):
                     raise ValueError("X must be a subgroup of self.")
 
         if field_of_definition is None:
-            field_of_definition = QQbar
+            from sage.rings.qqbar import QQbar as field_of_definition
 
         return FiniteSubgroup_lattice(
             self, X, field_of_definition=field_of_definition, check=check)

src/sage/modular/abvar/finite_subgroup.py

@@ -113,8 +113,6 @@
 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):
@@ -754,6 +752,8 @@ def subgroup(self, gens):
             sage: H == G.subgroup([[1/11,0,0,0]])
             True
         """
+        from sage.rings.qqbar import QQbar
+
         if not isinstance(gens, (tuple, list)):
             raise TypeError("gens must be a list or tuple")
         A = self.abelian_variety()
@@ -846,7 +846,7 @@ def __init__(self, abvar, lattice, field_of_definition=None, check=True):
             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
+            from sage.rings.qqbar import QQbar as field_of_definition
         if check:
             from .abvar import is_ModularAbelianVariety
             if not is_FreeModule(lattice) or lattice.base_ring() != ZZ:

src/sage/modular/arithgroup/arithgroup_generic.py

@@ -885,20 +885,21 @@ def index(self):
 
     def generalised_level(self):
         r"""
-        Return the generalised level of self, i.e. the least common multiple of
+        Return the generalised level of ``self``, i.e., the least common multiple of
         the widths of all cusps.
 
-        If self is *even*, Wohlfart's theorem tells us that this is equal to
-        the (conventional) level of self when self is a congruence subgroup.
-        This can fail if self is odd, but the actual level is at most twice the
+        If ``self`` is *even*, Wohlfart's theorem tells us that this is equal to
+        the (conventional) level of ``self`` when ``self`` is a congruence subgroup.
+        This can fail if ``self`` is odd, but the actual level is at most twice the
         generalised level. See the paper by Kiming, Schuett and Verrill for
         more examples.
 
         EXAMPLES::
 
             sage: Gamma0(18).generalised_level()
             18
-            sage: sage.modular.arithgroup.arithgroup_perm.HsuExample18().generalised_level()
+            sage: from sage.modular.arithgroup.arithgroup_perm import HsuExample18
+            sage: HsuExample18().generalised_level()
             24
 
         In the following example, the actual level is twice the generalised

src/sage/modular/modform_hecketriangle/hecke_triangle_group_element.py

@@ -25,7 +25,7 @@
 from sage.rings.infinity import infinity
 from sage.rings.cc import CC
 
-lazy_import('sage.rings.qqbar', ['AA', 'QQbar'])
+lazy_import('sage.rings.qqbar', 'AA')
 
 from sage.groups.matrix_gps.group_element import MatrixGroupElement_generic
 from sage.geometry.hyperbolic_space.hyperbolic_interface import HyperbolicPlane
@@ -774,6 +774,8 @@ def _primitive_block_decomposition_data(self):
             if self.parent().n() == infinity:
                 raise NotImplementedError
 
+            from sage.rings.qqbar import QQbar
+
             emb = self.root_extension_embedding(QQbar)
             p = self.fixed_points()[0]
             embp = emb(p)

src/sage/modular/modsym/heilbronn.pyx

@@ -111,7 +111,8 @@ cdef class Heilbronn:
 
         EXAMPLES::
 
-            sage: H = sage.modular.modsym.heilbronn.Heilbronn()
+            sage: from sage.modular.modsym.heilbronn import Heilbronn
+            sage: H = Heilbronn()
             sage: H._initialize_list()
             Traceback (most recent call last):
             ...
@@ -343,6 +344,7 @@ cdef class HeilbronnCremona(Heilbronn):
 
         EXAMPLES::
 
+            sage: from sage.modular.modsym.heilbronn import HeilbronnCremona
             sage: H = HeilbronnCremona.__new__(HeilbronnCremona)
             sage: H.p = 5
             sage: H
@@ -457,6 +459,7 @@ cdef class HeilbronnMerel(Heilbronn):
 
         EXAMPLES::
 
+            sage: from sage.modular.modsym.heilbronn import HeilbronnMerel
             sage: H = HeilbronnMerel.__new__(HeilbronnMerel)
             sage: H.n = 5
             sage: H