[with patch, positive review] modularSymbol complement fails for E=128a

[syazdani]

The following code raises the following exception:

sage: E=EllipticCurve("128a")
sage: ME=E.modular_symbol_space()
sage: ME.complement()
---------------------------------------------------------------------------
<type 'exceptions.RuntimeError'>          Traceback (most recent call last)

/net/mathserv/1/home/syazdani/research/programs/<ipython console> in <module>()

/home/syazdani/sage/local/lib/python2.5/site-packages/sage/modular/hecke/submodule.py in complement(self, bound)
    200         else:
    201             # failed
--> 202             raise RuntimeError, "Computation of complementary space failed (cut down to rank %s, but should have cut down to rank %s)."%(V.rank(), self.rank())
    203
    204

<type 'exceptions.RuntimeError'>: Computation of complementary space failed (cut down to rank 18, but should have cut down to rank 1).

[mabshoff]

This remains unfixed in Sage 2.9.

Cheers,

Michael

[mabshoff]

And it is still open in Sage 2.10.

Cheers,

Michael

[mabshoff]

And it is still broken in Sage 3.0.3. This looks like a job for Craig Citro :)

Cheers,

Michael

[mabshoff]

Could #2535 be related?

Cheers,

Michael

[AlexGhitza]

For the record, there are other failures for conductors 144, 192, 225. These are the only conductors smaller than 250 that fail.

The patch implements a naive fix.

[craigcitro]

I'd review this, but I helped write it. :)

[robertwb]

I'm still getting

sage: E = EllipticCurve("128a") 
sage: E.congruence_number()
------------------------------------------------------------
Traceback (most recent call last):
  File "<ipython console>", line 1, in <module>
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line 2618, in congruence_number
    self.__congruence_number = W.congruence_number(V)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 938, in congruence_number
    W = other.q_expansion_module(prec, ZZ)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 770, in q_expansion_module
    return self._q_expansion_module_integral(prec)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 910, in _q_expansion_module_integral
    V = self.q_expansion_module(prec, QQ)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 772, in q_expansion_module
    return self._q_expansion_module_rational(prec)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 861, in _q_expansion_module_rational
    return self._q_expansion_module(prec)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 820, in _q_expansion_module
    return A.span([f.padded_list(prec) for f in self.q_expansion_basis(prec, algorithm)])
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 602, in q_expansion_basis
    return Sequence(self._q_expansion_basis_hecke_dual(prec), cr=True)
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/modsym/space.py", line 1073, in _q_expansion_basis_hecke_dual
    v = [self.dual_hecke_matrix(n).column(i) for n in range(1,prec)]
  File "/Users/robert/sage/sage-3.1.3/local/lib/python2.5/site-packages/sage/modular/hecke/module.py", line 797, in dual_hecke_matrix
    T = self._compute_dual_hecke_matrix(n)
  File "/Users/robert/sage/current/local/lib/python2.5/site-packages/sage/modular/hecke/submodule.py", line 110, in _compute_dual_hecke_matrix
    return A.restrict(self.dual_free_module(), check=check)
  File "/Users/robert/sage/current/local/lib/python2.5/site-packages/sage/modular/hecke/submodule.py", line 320, in dual_free_module
    "(cut down to rank %s, but should have cut down to rank %s)."%(V.rank(), self.rank())
RuntimeError: Computation of embedded dual vector space failed (cut down to rank 9, but should have cut down to rank 8).

[robertwb]

This is a separate issue, see #5080. The patch fixes the issue that was raised.

[mabshoff]

Merged in Sage 3.3.alpha2

Cheers,

Michael