On Thu, Jul 30, 2009 at 5:39 PM, Phillip M. Feldman<[email protected]> wrote:
>
> When I type something like the following, I would expect to get a
> result of oo, indicating that the sum diverges to infinity:
>
> sum(1/n, (n, 2, oo))
>
> Instead, I get the same thing back (actually not quite-- the 's'
> changes to a capital 'S'). Any idea why this doesn't work?
This is what I get:
In [1]: sum(1/n, (n, 2, oo))
Out[1]: Sum(1/n, (n, 2, oo))
This just returns the Sum instance, meaning, that you can do stuff on it, like:
In [2]: a = sum(1/n, (n, 2, oo))
In [3]: a.n()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/home/ondrej/repos/sympy/<ipython console> in <module>()
/home/ondrej/repos/sympy/sympy/core/evalf.pyc in Basic_evalf(x, n, **options)
1006 options['maxprec'] = max(prec, DEFAULT_MAXPREC)
1007 try:
-> 1008 result = evalf(x, prec+4, options)
1009 except NotImplementedError:
1010 # Fall back to the ordinary evalf
/home/ondrej/repos/sympy/sympy/core/evalf.pyc in evalf(x, prec, options)
946 try:
947 rf = evalf_table[x.func]
--> 948 r = rf(x, prec, options)
949 except KeyError:
950 #r = finalize_complex(x._eval_evalf(prec)._mpf_, fzero, prec)
/home/ondrej/repos/sympy/sympy/core/evalf.pyc in evalf_sum(expr, prec, options)
854 raise NotImplementedError
855 # Use fast hypergeometric summation if possible
--> 856 v = hypsum(func, n, int(a), prec2)
857 delta = prec - fastlog(v)
858 if fastlog(v) < -10:
/home/ondrej/repos/sympy/sympy/core/evalf.pyc in hypsum(expr, n, start, prec)
818 raise ValueError("Sum diverges like (%i)^n" % abs(1/g))
819 if p < 1 or (p == 1 and not alt):
--> 820 raise ValueError("Sum diverges like n^%i" % (-p))
821 # We have polynomial convergence: use Richardson extrapolation
822 # Need to use at least quad precision because a lot of
cancellation
ValueError: Sum diverges like n^-1
E.g. this tells you that the sum diverges.
Maybe the sum could return oo immediately.
Ondrej
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