On Tue, Apr 22, 2008 at 5:47 PM, Helio Perroni Filho <[EMAIL PROTECTED]> wrote:
> Hello all,
>
> I've been trying to use SAGE to find the positive infinity limit of this
> function:
>
> f(x) = ln(x^x) / ln(x!)
>
> However, if I try defining it in SAGE like this:
>
> f(x) = ln(x^x) / ln(factorial(x))
>
> I get the following error message:
>
> ---------------------------------------------------------------------------
> <type 'exceptions.TypeError'> Traceback (most recent call last)
>
> /Users/erios/<ipython console> in <module>()
>
> /Applications/SAGE/local/lib/python2.5/site-packages/sage/rings/arith.py in
> factorial(n, algorithm)
> 273 Z = integer_ring.ZZ
> 274 if algorithm == 'gmp':
> --> 275 return Z(n).factorial()
> 276 elif algorithm == 'pari':
> 277 return Z(pari('%s!'%Z(n)))
>
> /Users/erios/integer_ring.pyx in
> sage.rings.integer_ring.IntegerRing_class.__call__()
>
> <type 'exceptions.TypeError'>: unable to convert x (=x) to an integer
>
> I have tried several variations of the above code, including alternative
> ways to define the function, but they all stumble, one way or the other, in
> an apparent inability of SAGE to convert a SymbolicVariable into an Integer.
> Is there some way to corner SAGE into converting a SymbolicVariable into an
> Integer, or to avoid having to – perhaps with a symbolic-calculus-friendly
> factorial function?
Unfortunately, there is currently no support for a symbolic version
of factorial in Sage. Even if there were one, Maxima (which sage uses
in this case to compute the limit) asks all kinds of (annoying) interactive
questions. So here's how to do it in Maxima (which comes with Sage),
where I literally type "positive;" below in each case.
sage: !maxima
(%i2) limit(log(x^x)/log(x!), x, inf);
Is x! positive or negative?
positive;
Is x (2 log(x) - 2) + log(x) positive, negative, or zero?
positive;
(%o2) 1
(%i3)
Yes, the interactive nature of Maxima above is incredibly clunky.
It is on our list to somehow deal with this in a much better way.
-- William
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