sage.modular: Update # needs, doctest cosmetics

src/sage/modular/abvar/abvar.py

@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# sage.doctest: needs sage.libs.flint sage.libs.pari
 """
 Base class for modular abelian varieties
 
@@ -317,7 +317,7 @@ def base_extend(self, K):
 
             sage: A = J0(37); A
             Abelian variety J0(37) of dimension 2
-            sage: A.base_extend(QQbar)
+            sage: A.base_extend(QQbar)                                                  # needs sage.rings.number_field
             Abelian variety J0(37) over Algebraic Field of dimension 2
             sage: A.base_extend(GF(7))
             Abelian variety J0(37) over Finite Field of size 7 of dimension 2

src/sage/modular/abvar/abvar_newform.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.pari
 """
 Abelian varieties attached to newforms
 

src/sage/modular/abvar/finite_subgroup.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.pari
 r"""
 Finite subgroups of modular abelian varieties
 
@@ -178,7 +179,8 @@ def lattice(self):
         EXAMPLES::
 
             sage: J = J0(33); C = J[0].cuspidal_subgroup(); C
-            Finite subgroup with invariants [5] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [5] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
             sage: C.lattice()
             Free module of degree 6 and rank 2 over Integer Ring
             Echelon basis matrix:
@@ -197,7 +199,8 @@ def _relative_basis_matrix(self):
             sage: A = J0(43)[1]; A
             Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
             sage: C = A.cuspidal_subgroup(); C
-            Finite subgroup with invariants [7] over QQ of Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
+            Finite subgroup with invariants [7] over QQ of
+             Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
             sage: C._relative_basis_matrix()
             [  1   0   0   0]
             [  0 1/7 6/7 5/7]
@@ -262,7 +265,7 @@ def __richcmp__(self, other, op):
 
     def is_subgroup(self, other):
         """
-        Return True exactly if self is a subgroup of other, and both are
+        Return ``True`` exactly if ``self`` is a subgroup of ``other``, and both are
         defined as subgroups of the same ambient abelian variety.
 
         EXAMPLES::
@@ -302,8 +305,9 @@ def __add__(self, other):
 
         An example where the parent abelian varieties are different::
 
-            A = J0(48); A[0].cuspidal_subgroup() + A[1].cuspidal_subgroup()
-            Finite subgroup with invariants [2, 4, 4] over QQ of Abelian subvariety of dimension 2 of J0(48)
+            sage: A = J0(48); A[0].cuspidal_subgroup() + A[1].cuspidal_subgroup()
+            Finite subgroup with invariants [2, 4, 4] over QQ of
+             Abelian subvariety of dimension 2 of J0(48)
         """
         if not isinstance(other, FiniteSubgroup):
             raise TypeError("only addition of two finite subgroups is defined")
@@ -330,7 +334,8 @@ def exponent(self):
 
             sage: t = J0(33).hecke_operator(7)
             sage: G = t.kernel()[0]; G
-            Finite subgroup with invariants [2, 2, 2, 2, 4, 4] over QQ of Abelian variety J0(33) of dimension 3
+            Finite subgroup with invariants [2, 2, 2, 2, 4, 4] over QQ of
+             Abelian variety J0(33) of dimension 3
             sage: G.exponent()
             4
         """
@@ -343,7 +348,7 @@ def exponent(self):
 
     def intersection(self, other):
         """
-        Return the intersection of the finite subgroups self and other.
+        Return the intersection of the finite subgroups ``self`` and ``other``.
 
         INPUT:
 
@@ -358,12 +363,15 @@ def intersection(self, other):
             sage: E11a0, E11a1, B = J0(33)
             sage: G = E11a0.torsion_subgroup(6); H = E11a0.torsion_subgroup(9)
             sage: G.intersection(H)
-            Finite subgroup with invariants [3, 3] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [3, 3] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
             sage: W = E11a1.torsion_subgroup(15)
             sage: G.intersection(W)
-            Finite subgroup with invariants [] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
             sage: E11a0.intersection(E11a1)[0]
-            Finite subgroup with invariants [5] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [5] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
 
         We intersect subgroups of different abelian varieties.
 
@@ -372,27 +380,35 @@ def intersection(self, other):
             sage: E11a0, E11a1, B = J0(33)
             sage: G = E11a0.torsion_subgroup(5); H = E11a1.torsion_subgroup(5)
             sage: G.intersection(H)
-            Finite subgroup with invariants [5] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [5] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
             sage: E11a0.intersection(E11a1)[0]
-            Finite subgroup with invariants [5] over QQ of Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
+            Finite subgroup with invariants [5] over QQ of
+             Simple abelian subvariety 11a(1,33) of dimension 1 of J0(33)
 
         We intersect abelian varieties with subgroups::
 
             sage: t = J0(33).hecke_operator(7)
             sage: G = t.kernel()[0]; G
-            Finite subgroup with invariants [2, 2, 2, 2, 4, 4] over QQ of Abelian variety J0(33) of dimension 3
+            Finite subgroup with invariants [2, 2, 2, 2, 4, 4] over QQ of
+             Abelian variety J0(33) of dimension 3
             sage: A = J0(33).old_subvariety()
             sage: A.intersection(G)
-            Finite subgroup with invariants [2, 2, 2, 2] over QQ of Abelian subvariety of dimension 2 of J0(33)
+            Finite subgroup with invariants [2, 2, 2, 2] over QQ of
+             Abelian subvariety of dimension 2 of J0(33)
             sage: A.hecke_operator(7).kernel()[0]
-            Finite subgroup with invariants [2, 2, 2, 2] over QQ of Abelian subvariety of dimension 2 of J0(33)
+            Finite subgroup with invariants [2, 2, 2, 2] over QQ of
+             Abelian subvariety of dimension 2 of J0(33)
             sage: B = J0(33).new_subvariety()
             sage: B.intersection(G)
-            Finite subgroup with invariants [4, 4] over QQ of Abelian subvariety of dimension 1 of J0(33)
+            Finite subgroup with invariants [4, 4] over QQ of
+             Abelian subvariety of dimension 1 of J0(33)
             sage: B.hecke_operator(7).kernel()[0]
-            Finite subgroup with invariants [4, 4] over QQ of Abelian subvariety of dimension 1 of J0(33)
+            Finite subgroup with invariants [4, 4] over QQ of
+             Abelian subvariety of dimension 1 of J0(33)
             sage: A.intersection(B)[0]
-            Finite subgroup with invariants [3, 3] over QQ of Abelian subvariety of dimension 2 of J0(33)
+            Finite subgroup with invariants [3, 3] over QQ of
+             Abelian subvariety of dimension 2 of J0(33)
         """
         from .abvar import is_ModularAbelianVariety
         A = self.abelian_variety()
@@ -736,13 +752,15 @@ def subgroup(self, gens):
 
             sage: J = J0(23)
             sage: G = J.torsion_subgroup(11); G
-            Finite subgroup with invariants [11, 11, 11, 11] over QQ of Abelian variety J0(23) of dimension 2
+            Finite subgroup with invariants [11, 11, 11, 11] over QQ of
+             Abelian variety J0(23) of dimension 2
 
         We create the subgroup of the 11-torsion subgroup of `J_0(23)`
         generated by the first `11`-torsion point::
 
             sage: H = G.subgroup([G.0]); H
-            Finite subgroup with invariants [11] over QQbar of Abelian variety J0(23) of dimension 2
+            Finite subgroup with invariants [11] over QQbar of
+             Abelian variety J0(23) of dimension 2
             sage: H.invariants()
             [11]
 
@@ -773,7 +791,8 @@ def invariants(self):
 
             sage: J = J0(38)
             sage: C = J.cuspidal_subgroup(); C
-            Finite subgroup with invariants [3, 45] over QQ of Abelian variety J0(38) of dimension 4
+            Finite subgroup with invariants [3, 45] over QQ of
+             Abelian variety J0(38) of dimension 4
             sage: v = C.invariants(); v
             [3, 45]
             sage: v[0] = 5
@@ -786,12 +805,14 @@ def invariants(self):
         ::
 
             sage: C * 3
-            Finite subgroup with invariants [15] over QQ of Abelian variety J0(38) of dimension 4
+            Finite subgroup with invariants [15] over QQ of
+             Abelian variety J0(38) of dimension 4
 
         An example involving another cuspidal subgroup::
 
             sage: C = J0(22).cuspidal_subgroup(); C
-            Finite subgroup with invariants [5, 5] over QQ of Abelian variety J0(22) of dimension 2
+            Finite subgroup with invariants [5, 5] over QQ of
+             Abelian variety J0(22) of dimension 2
             sage: C.lattice()
             Free module of degree 4 and rank 4 over Integer Ring
             Echelon basis matrix:
@@ -843,7 +864,8 @@ def __init__(self, abvar, lattice, field_of_definition=None, check=True):
 
             sage: J = J0(11)
             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
+            Finite subgroup with invariants [15] over QQbar of
+             Abelian variety J0(11) of dimension 1
         """
         if field_of_definition is None:
             from sage.rings.qqbar import QQbar as field_of_definition
@@ -868,7 +890,8 @@ def lattice(self):
 
             sage: J = J0(11)
             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
+            Finite subgroup with invariants [15] over QQbar of
+             Abelian variety J0(11) of dimension 1
             sage: G.lattice()
             Free module of degree 2 and rank 2 over Integer Ring
             Echelon basis matrix:

src/sage/modular/abvar/homology.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.flint sage.libs.pari
 r"""
 Homology of modular abelian varieties
 
@@ -37,7 +38,8 @@
     [-4  0]
     [ 0 -4]
     sage: a.T(7)
-    Hecke operator T_7 on Submodule of rank 2 of Integral Homology of Abelian variety J0(43) of dimension 3
+    Hecke operator T_7 on
+     Submodule of rank 2 of Integral Homology of Abelian variety J0(43) of dimension 3
 """
 
 # ****************************************************************************
@@ -272,7 +274,8 @@ def hecke_matrix(self, n):
 
             sage: J = J0(23)
             sage: J.homology(QQ[I]).hecke_matrix(3).parent()
-            Full MatrixSpace of 4 by 4 dense matrices over Number Field in I with defining polynomial x^2 + 1 with I = 1*I
+            Full MatrixSpace of 4 by 4 dense matrices over
+             Number Field in I with defining polynomial x^2 + 1 with I = 1*I
         """
         raise NotImplementedError
 
@@ -694,16 +697,19 @@ def hecke_bound(self):
 
     def hecke_matrix(self, n):
         """
-        Return the matrix of the n-th Hecke operator acting on this
+        Return the matrix of the `n`-th Hecke operator acting on this
         homology group.
 
         EXAMPLES::
 
             sage: d = J0(125).homology(GF(17)).decomposition(2); d
             [
-            Submodule of rank 4 of Homology with coefficients in Finite Field of size 17 of Abelian variety J0(125) of dimension 8,
-            Submodule of rank 4 of Homology with coefficients in Finite Field of size 17 of Abelian variety J0(125) of dimension 8,
-            Submodule of rank 8 of Homology with coefficients in Finite Field of size 17 of Abelian variety J0(125) of dimension 8
+            Submodule of rank 4 of Homology with coefficients in Finite Field of size 17
+             of Abelian variety J0(125) of dimension 8,
+            Submodule of rank 4 of Homology with coefficients in Finite Field of size 17
+             of Abelian variety J0(125) of dimension 8,
+            Submodule of rank 8 of Homology with coefficients in Finite Field of size 17
+             of Abelian variety J0(125) of dimension 8
             ]
             sage: t = d[0].hecke_matrix(17); t
             [16 15 15  0]

src/sage/modular/abvar/homspace.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.flint sage.libs.pari
 """
 Spaces of homomorphisms between modular abelian varieties
 
@@ -16,7 +17,8 @@
     Simple abelian subvariety 37b(1,37) of dimension 1 of J0(37)
     ]
     sage: D[0].intersection(D[1])
-    (Finite subgroup with invariants [2, 2] over QQ of Simple abelian subvariety 37a(1,37) of dimension 1 of J0(37),
+    (Finite subgroup with invariants [2, 2] over QQ of
+      Simple abelian subvariety 37a(1,37) of dimension 1 of J0(37),
      Simple abelian subvariety of dimension 0 of J0(37))
 
 As an abstract product, since these newforms are distinct, the
@@ -218,7 +220,8 @@ def __init__(self, domain, codomain, cat):
         EXAMPLES::
 
             sage: H = Hom(J0(11), J0(22)); H
-            Space of homomorphisms from Abelian variety J0(11) of dimension 1 to Abelian variety J0(22) of dimension 2
+            Space of homomorphisms from Abelian variety J0(11) of dimension 1
+             to Abelian variety J0(22) of dimension 2
             sage: Hom(J0(11), J0(11))
             Endomorphism ring of Abelian variety J0(11) of dimension 1
             sage: type(H)

src/sage/modular/abvar/lseries.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.flint
 """
 `L`-series of modular abelian varieties
 
@@ -99,29 +100,29 @@ def __call__(self, s, prec=53):
         EXAMPLES::
 
             sage: L = J0(23).lseries()
-            sage: L(1)
+            sage: L(1)                                                                  # needs sage.symbolic
             0.248431866590600
-            sage: L(1, prec=100)
+            sage: L(1, prec=100)                                                        # needs sage.symbolic
             0.24843186659059968120725033931
 
             sage: L = J0(389)[0].lseries()
-            sage: L(1) # long time (2s) abstol 1e-10
+            sage: L(1)                          # abstol 1e-10          # long time (2s), needs sage.symbolic
             -1.33139759782370e-19
-            sage: L(1, prec=100) # long time (2s) abstol 1e-20
+            sage: L(1, prec=100)                # abstol 1e-20          # long time (2s), needs sage.symbolic
             6.0129758648142797032650287762e-39
             sage: L.rational_part()
             0
 
             sage: L = J1(23)[0].lseries()
-            sage: L(1)
+            sage: L(1)                                                                  # needs sage.symbolic
             0.248431866590600
 
             sage: J = J0(11) * J1(11)
-            sage: J.lseries()(1)
+            sage: J.lseries()(1)                                                        # needs sage.symbolic
             0.0644356903227915
 
             sage: L = JH(17,[2]).lseries()
-            sage: L(1)
+            sage: L(1)                                                                  # needs sage.symbolic
             0.386769938387780
 
         """

src/sage/modular/abvar/morphism.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.flint
 r"""
 Hecke operators and morphisms between modular abelian varieties
 

src/sage/modular/abvar/torsion_point.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.rings.number_field
 """
 Torsion points on modular abelian varieties
 
@@ -30,10 +31,10 @@ class TorsionPoint(ModuleElement):
     - ``parent`` -- a finite subgroup of a modular abelian variety
 
     - ``element`` -- a `\QQ`-vector space element that represents
-       this element in terms of the ambient rational homology
+      this element in terms of the ambient rational homology
 
     - ``check`` -- bool (default: ``True``): whether to check that
-       element is in the appropriate vector space
+      element is in the appropriate vector space
 
     EXAMPLES:
 
@@ -78,7 +79,8 @@ def element(self):
 
             sage: J = J0(11)
             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
+            Finite subgroup with invariants [15] over QQbar of
+             Abelian variety J0(11) of dimension 1
             sage: G.0.element()
             (1/3, 0)
 
@@ -194,7 +196,7 @@ def _richcmp_(self, right, op):
         INPUT:
 
         - ``self, right`` -- elements of the same finite abelian
-           variety subgroup.
+          variety subgroup.
 
         - ``op`` -- comparison operator (see :mod:`sage.structure.richcmp`)
 
@@ -255,10 +257,12 @@ def _relative_element(self):
 
         EXAMPLES::
 
+            sage: # needs sage.libs.flint
             sage: A = J0(43)[1]; A
             Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
             sage: C = A.cuspidal_subgroup(); C
-            Finite subgroup with invariants [7] over QQ of Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
+            Finite subgroup with invariants [7] over QQ of
+             Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)
             sage: x = C.0; x
             [(0, 1/7, 0, 6/7, 0, 5/7)]
             sage: x._relative_element()