L-Series Group

247 days ago by pub

Most Relevant Source Code: http://code.google.com/p/purplesage/source/browse/psage/lseries/eulerprod.py

There are some examples at the bottom of the above file, such as:
from psage.lseries.eulerprod import LSeries K.<a> = NumberField(x^2 + 1) L = LSeries(K); L 
        
Dedekind Zeta function of Number Field in a with defining polynomial x^2
+ 1
Dedekind Zeta function of Number Field in a with defining polynomial x^2 + 1
L(5) 
        
1.03294370043647
1.03294370043647
L.anlist(20) 
        
[0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2]
[0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2]
L.epsilon() 
        
1
1
L = LSeries(J0(33)); L 
        
L-series attached to Abelian variety J0(33) of dimension 3
L-series attached to Abelian variety J0(33) of dimension 3
L(1) 
        
0.0481553138900504
0.0481553138900504
L.analytic_rank() 
        
0
0
L.factor() 
        
(L-series of a degree 1 newform of level 11 and weight 2)^2 * (L-series
of a degree 1 newform of level 33 and weight 2)
(L-series of a degree 1 newform of level 11 and weight 2)^2 * (L-series of a degree 1 newform of level 33 and weight 2)
L0 = L[0][0]; L0 
        
L-series of a degree 1 newform of level 11 and weight 2
L-series of a degree 1 newform of level 11 and weight 2
L0.anlist(20) 
        
Traceback (click to the left of this block for traceback)
...
ValueError: max() arg is an empty sequence
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_22.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("TDAuYW5saXN0KDIwKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp1rLJWn/___code___.py", line 3, in <module>
    exec compile(u'L0.anlist(_sage_const_20 )
  File "", line 1, in <module>
    
  File "/sagenb/sage_install/purplesage/psage/lseries/eulerprod.py", line 1132, in anlist
    self._precompute_local_factors(bound+1, prec=prec)
  File "/sagenb/sage_install/purplesage/psage/lseries/eulerprod.py", line 2072, in _precompute_local_factors
    self._do_precompute(primes, prec)
  File "/sagenb/sage_install/purplesage/psage/lseries/eulerprod.py", line 2075, in _do_precompute
    E, v = self._M.compact_system_of_eigenvalues(primes)
  File "/sagenb/sage_install/sage-4.7/local/lib/python2.6/site-packages/sage/modular/modsym/space.py", line 187, in compact_system_of_eigenvalues
    E = M.hecke_images(nz, v) * self.dual_free_module().basis_matrix().transpose()
  File "/sagenb/sage_install/sage-4.7/local/lib/python2.6/site-packages/sage/modular/hecke/ambient_module.py", line 549, in hecke_images
    return self._hecke_images(i, v)
  File "/sagenb/sage_install/sage-4.7/local/lib/python2.6/site-packages/sage/modular/modsym/ambient.py", line 2941, in _hecke_images
    return heilbronn.hecke_images_gamma0_weight2(c.u,c.v,N, v, self.manin_gens_to_basis())
  File "heilbronn.pyx", line 594, in sage.modular.modsym.heilbronn.hecke_images_gamma0_weight2 (sage/modular/modsym/heilbronn.c:5634)
ValueError: max() arg is an empty sequence

Hey, I found a bug.