Sage does have the Gamma function implemented for real and complex
arguments, but it does not seem able to treat it as a symbolic
function which can be passed to maxima. Is that something which could
be changed?
sage: factorial(5)
120
sage: factorial(5) == gamma(6)
True
sage: gamma(2.3)
1.16671190519816
sage: gamma(2.3+4.5*I)
0.00134894116108760 - 0.0333573062633992*I
sage: gamma(x)
---------------------------------------------------------------------------
<type 'exceptions.TypeError'> Traceback (most recent call last)
(etc)
John
2008/4/23 William Stein <[EMAIL PROTECTED]>:
>
>
> 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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