I tried running the limit through Maple, and it couldn't do it (it just
returned an unevaluated form), and Wolphram Alpha times out. Any idea what the
answer should be?
Aaron Meurer
On Oct 9, 2010, at 8:27 PM, Aaron S. Meurer wrote:
> I've never seen it before, and I didn't come up with anything in the issues
> when I searched for the error message, so I think it is safe to report this
> one. :)
>
> Any idea what is happening, by the way?
>
> Aaron Meurer
>
> On Oct 9, 2010, at 8:21 PM, Ben Goodrich wrote:
>
>> Hi,
>>
>> I didn't see this problem exactly when I searched through the Issues,
>> but I wanted to check that it was not a known problem first.
>>
>> Thanks,
>> Ben
>>
>> In [32]: c,n,r = symbols('cnr')
>>
>> In [33]: limit( (( 2*n*(n-r+1)/(n + r*(n-r+1)) )**c + (r-1)*( n*(n-r
>> +2)/(n + r*(n-r+1)) )**c - n)/(n**c - n), n, oo )
>> ---------------------------------------------------------------------------
>> TypeError Traceback (most recent call
>> last)
>>
>> /tmp/<ipython console> in <module>()
>>
>> /usr/lib/pymodules/python2.6/sympy/series/limits.pyc in limit(e, z,
>> z0, dir)
>> 89
>> 90 try:
>> ---> 91 r = gruntz(e, z, z0, dir)
>> 92 except PoleError:
>> 93 r = heuristics(e, z, z0, dir)
>>
>> /usr/lib/pymodules/python2.6/sympy/series/gruntz.pyc in gruntz(e, z,
>> z0, dir)
>> 496 #convert all limits to the limit z->oo
>>
>> 497 elif z0 == oo:
>> --> 498 return limitinf(e, z)
>> 499 elif z0 == -oo:
>> 500 return limitinf(e.subs(z,-z), z)
>>
>> /usr/lib/pymodules/python2.6/sympy/series/gruntz.pyc in limitinf(e, x)
>> 337 if e.has(log):
>> 338 e = e.normal()
>> --> 339 c0, e0 = mrv_leadterm(e,x)
>> 340 sig=sign(e0,x)
>> 341 if sig==1: return S.Zero # e0>0: lim f = 0
>>
>> /usr/lib/pymodules/python2.6/sympy/series/gruntz.pyc in
>> mrv_leadterm(e, x, Omega)
>> 395 e_up = moveup([e],x)[0]
>> 396 #calculate the lead term
>>
>> --> 397 mrv_leadterm_up = mrv_leadterm(e_up, x, Omega_up)
>> 398 #move the result (c0, e0) down
>>
>> 399 return tuple(movedown(mrv_leadterm_up, x))
>>
>> /usr/lib/pymodules/python2.6/sympy/series/gruntz.pyc in
>> mrv_leadterm(e, x, Omega)
>> 404 wsym = Symbol("w", real=True, positive=True, dummy=True)
>> 405 f, logw=rewrite(e, set(Omega), x, wsym)
>> --> 406 series = calculate_series(f, wsym)
>> 407 series=series.subs(log(wsym), logw)
>> 408 return series.leadterm(wsym)
>>
>> /usr/lib/pymodules/python2.6/sympy/series/gruntz.pyc in
>> calculate_series(e, x)
>> 370
>> 371 f = e
>> --> 372 series=f.nseries(x, 0, 2).removeO()
>> 373 if series == 0:
>> 374 #we need to calculate more terms, let's try 4:
>>
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/mul.pyc in _eval_nseries(self,
>> x, x0, n)
>> 934 def _eval_nseries(self, x, x0, n):
>> 935 from sympy import powsimp
>> --> 936 terms = [t.nseries(x, x0, n) for t in self.args]
>> 937 return powsimp(Mul(*terms).expand(), combine='exp',
>> deep=True)
>> 938
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/add.pyc in _eval_nseries(self,
>> x, x0, n)
>> 178
>> 179 def _eval_nseries(self, x, x0, n):
>> --> 180 terms = [t.nseries(x, x0, n) for t in self.args]
>> 181 return Add(*terms)
>> 182
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/mul.pyc in _eval_nseries(self,
>> x, x0, n)
>> 934 def _eval_nseries(self, x, x0, n):
>> 935 from sympy import powsimp
>> --> 936 terms = [t.nseries(x, x0, n) for t in self.args]
>> 937 return powsimp(Mul(*terms).expand(), combine='exp',
>> deep=True)
>> 938
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/power.pyc in
>> _eval_nseries(self, x, x0, n)
>> 700 lt = b.as_leading_term(x)
>> 701 o = order * lt**(1-e)
>> --> 702 bs = b.nseries(x, x0, n-e)
>> 703 if bs.is_Add:
>> 704 bs = bs.removeO()
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/mul.pyc in _eval_nseries(self,
>> x, x0, n)
>> 934 def _eval_nseries(self, x, x0, n):
>> 935 from sympy import powsimp
>> --> 936 terms = [t.nseries(x, x0, n) for t in self.args]
>> 937 return powsimp(Mul(*terms).expand(), combine='exp',
>> deep=True)
>> 938
>>
>> /usr/lib/pymodules/python2.6/sympy/core/basic.pyc in nseries(self, x,
>> x0, n)
>> 2253 See also lseries().
>> 2254 """
>> -> 2255 return self._eval_nseries(x, x0, n)
>> 2256
>> 2257 def _eval_nseries(self, x, x0, n):
>>
>> /usr/lib/pymodules/python2.6/sympy/core/power.pyc in
>> _eval_nseries(self, x, x0, n)
>> 656 from sympy.functions import ceiling
>> 657 terms = [1/prefactor]
>> --> 658 for m in xrange(1,ceiling(n/l)):
>> 659 new_term = terms[-1]*(-rest)
>> 660 if new_term.is_Pow:
>>
>> TypeError: an integer is required
>>
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