CoCalc Shared Filescode / dokchitser.ipynb

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))'

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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 
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