CoCalc -- dokchitser.ipynb

Kernel: SageMath 8.0

Tim Dokchitser's $L$ -functions code is in Sage:

http://doc.sagemath.org/html/en/reference/lfunctions/sage/lfunctions/dokchitser.html

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L = Dokchitser(conductor=1, gammaV=[0,1], weight=12, eps=1)

In [2]:

pari_precode = 'tau(n)=(5*sigma(n,3)+7*sigma(n,5))*n/12 - 35*sum(k=1,n-1,(6*k-4*(n-k))*sigma(k,3)*sigma(n-k,5))'

In [0]:

L.init_coeffs?

WARNING: In Jupyter for some reason this gets stuck.

Use sage directly or a Sage worksheet

In [3]:

L.init_coeffs('tau(k)', pari_precode=pari_precode, max_asymp_coeffs=15)

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
<ipython-input-3-e254409c7eb3> in <module>()
----> 1 L.init_coeffs('tau(k)', pari_precode=pari_precode, max_asymp_coeffs=Integer(15))

/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/lfunctions/dokchitser.pyc in init_coeffs(self, v, cutoff, w, pari_precode, max_imaginary_part, max_asymp_coeffs)
    341 
    342         self.__init = (v, cutoff, w, pari_precode, max_imaginary_part, max_asymp_coeffs)
--> 343         gp = self.gp()
    344         if pari_precode != '':
    345             self._gp_eval(pari_precode)
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/lfunctions/dokchitser.pyc in gp(self)
    225             logfile = os.path.join(DOT_SAGE, 'dokchitser.log')
    226             g = sage.interfaces.gp.Gp(script_subdirectory='dokchitser', logfile=logfile)
--> 227             g.read('computel.gp')
    228             self.__gp = g
    229             self._gp_eval('default(realprecision, %s)'%(self.prec//3 + 2))
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/interface.pyc in read(self, filename)
    192             sage: os.unlink(filename)
    193         """
--> 194         self.eval(self._read_in_file_command(filename))
    195 
    196     def _read_in_file_command(self, filename):
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/expect.pyc in eval(self, code, strip, synchronize, locals, allow_use_file, split_lines, **kwds)
   1295                 elif split_lines:
   1296                     return '\n'.join([self._eval_line(L, allow_use_file=allow_use_file, **kwds)
-> 1297                                         for L in code.split('\n') if L != ''])
   1298                 else:
   1299                     return self._eval_line(code, allow_use_file=allow_use_file, **kwds)
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/gp.pyc in _eval_line(self, line, allow_use_file, wait_for_prompt, restart_if_needed)
    439         a = Expect._eval_line(self, line,
    440                               allow_use_file=allow_use_file,
--> 441                               wait_for_prompt=wait_for_prompt)
    442         if a.find("the PARI stack overflows") != -1:
    443             verbose("automatically doubling the PARI stack and re-executing current input line")
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/expect.pyc in _eval_line(self, line, allow_use_file, wait_for_prompt, restart_if_needed)
    903         try:
    904             if self._expect is None:
--> 905                 self._start()
    906             E = self._expect
    907             try:
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/gp.pyc in _start(self, alt_message, block_during_init)
    239 
    240     def _start(self, alt_message=None, block_during_init=True):
--> 241         Expect._start(self, alt_message, block_during_init)
    242         # disable timer
    243         self._eval_line('default(timer,0);')
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/expect.pyc in _start(self, alt_message, block_during_init)
    500             self._expect = None
    501             self._session_number = BAD_SESSION
--> 502             raise RuntimeError("unable to start %s" % self.name())
    503         self._expect.timeout = None
    504 
RuntimeError: unable to start pari

In [0]: