On Thu, May 21, 2009 at 3:42 AM, rje <[email protected]> wrote:
>
> Transcript below. Ironically, no error is produced by the related
> command
> sage: time f=D[6].q_eigenform(7,'a')
> rje
> *************************************************************************************************
>
> rev...@sobolev:~% sage
> ----------------------------------------------------------------------
> | Sage Version 3.4.2, Release Date: 2009-05-05 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: time G=DirichletGroup(525,CyclotomicField(4));X=G.list();Y=X
> [15];
> M=ModularSymbols(Y,3,sign=1)
> CPU times: user 94.43 s, sys: 0.10 s, total: 94.53 s
> Wall time: 94.52 s
> sage: M
> Modular Symbols space of dimension 160 and level 525, weight 3,
> character
> [-1, -zeta4, -1], sign 1, over Cyclotomic Field of order 4 and degree
> 2
> sage: time D=M.cuspidal_subspace().new_subspace().decomposition()
> CPU times: user 6833.46 s, sys: 303.90 s, total: 7137.37 s
> Wall time: 7136.81 s
> sage: D
>
> [
> Modular Symbols subspace of dimension 2 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 2 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 4 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 4 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 4 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 4 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 8 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 8 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 16 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2,
> Modular Symbols subspace of dimension 40 of Modular Symbols space of
> dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
> sign 1,
> over Cyclotomic Field of order 4 and degree 2
> ]
> sage: time f=D[4].q_eigenform(7,'a') #HERE IS THE OFFENDING
> COMMAND
> ---------------------------------------------------------------------------
> IndexError Traceback (most recent call
> last)
>
> /base/people/revans/<ipython console> in <module>()
>
> /usr/local/sage/local/lib/python2.5/site-packages/IPython/iplib.pyc
> in
> ipmagic(self, arg_s)
> 951 else:
> 952 magic_args = self.var_expand(magic_args,1)
> --> 953 return fn(magic_args)
> 954
> 955 def ipalias(self,arg_s):
>
> /usr/local/sage/local/lib/python2.5/site-packages/IPython/Magic.pyc
> in
> magic_time(self, parameter_s)
> 1909 else:
> 1910 st = clk()
> -> 1911 exec code in glob
> 1912 end = clk()
> 1913 out = None
>
> /base/people/revans/<timed exec> in <module>()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/modular/modsym/
> space.pyc
> in q_eigenform(self, prec, names)
> 1077 return
> self.plus_submodule(compute_dual=True).q_eigenform(prec, names)
> 1078 raise ArithmeticError, "self must be simple."
> -> 1079 a2 = self.eigenvalue(2, names)
> 1080 R = PowerSeriesRing(a2.parent(), "q")
> 1081 q = R.gen(0)
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
> module.pyc
> in eigenvalue(self, n, name)
> 907
> 908 if (arith.is_prime(n) or n==1):
> --> 909 Tn_e = self._eigen_nonzero_element(n)
> 910 an = self._element_eigenvalue(Tn_e, name=name)
> 911 dict_set(ev, n, name, an)
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
> module.pyc
> in _eigen_nonzero_element(self, n)
> 394 raise ArithmeticError, "the rank of self must be
> positive"
> 395 A = self.ambient_hecke_module()
> --> 396 i = self._eigen_nonzero()
> 397 return A._hecke_image_of_ith_basis_vector(n, i)
> 398
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
> module.pyc
> in _eigen_nonzero(self)
> 375 pass
> 376 A = self.ambient_hecke_module()
> --> 377 V = self.dual_free_module()
> 378 B = V.basis()
> 379 for i in range(V.degree()):
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
> submodule.pyc
> in dual_free_module(self, bound, anemic, use_star)
> 401 f = self.hecke_polynomial(p)
> 402 T = A.dual_hecke_matrix(p)
> --> 403 V = T.kernel_on(V, poly=f, check=False)
> 404 if V.dimension() <= self.dimension():
> 405 break
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
> matrix2.so in
> sage.matrix.matrix2.Matrix.kernel_on (sage/matrix/matrix2.c:11763)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_element.so
> in sage.rings.polynomial.polynomial_element.Polynomial.__call__
> (sage/rings/polynomial/polynomial_element.c:6824)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in
> sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval
> (sage/rings/polynomial/polynomial_compiled.c:1254)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.pd_eval
> (sage/rings/polynomial/polynomial_compiled.c:2296)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.mul_pd.eval
> (sage/rings/polynomial/polynomial_compiled.c:4111)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.pd_eval
> (sage/rings/polynomial/polynomial_compiled.c:2296)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.sqr_pd.eval
> (sage/rings/polynomial/polynomial_compiled.c:3378)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.pd_eval
> (sage/rings/polynomial/polynomial_compiled.c:2296)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
> polynomial/polynomial_compiled.so
> in sage.rings.polynomial.polynomial_compiled.sqr_pd.eval
> (sage/rings/polynomial/polynomial_compiled.c:3389)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/structure/
> element.so
> in sage.structure.element.Matrix.__mul__ (sage/structure/element.c:
> 12803)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
> matrix_cyclo_dense.so
> in
> sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense._matrix_times_matrix_
> (sage/matrix/matrix_cyclo_dense.cpp:6167)()
>
> /usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
> matrix_integer_dense.so
> in sage.matrix.matrix_integer_dense._lift_crt
> (sage/matrix/matrix_integer_dense.c:35969)()
>
> IndexError: list index out of range
>
I found and fixed that bug recently:
http://trac.sagemath.org/sage_trac/ticket/5974
(it's in there). This will be part of sage-4.0.
-- William
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