Re: [Axiom-developer] [Bug?] "error in library; negative log"

[Martin Rubey]

Dear all,

Martin Rubey <address@hidden> writes:

> If you file a bug report concerning limit((-1/2)^n,n=%plusInfinity), I'll file
> a patch :-)

Today I tried to do so, but alas, the patch is not so easy... Furthermore, it
seems that it would be wasted work, because of

On Computing Limits in a Symbolic Manipulation System [Abstract] [Postscript] 
Dominik Gruntz. ETH Diss 11432, 1996. 

which can be obtained from

http://www.cs.fh-aargau.ch/~gruntz/publications2.html

Somehow sad, since the algorithm in Axiom is quite elaborate, while Gruntz's
algorithm seems to be much shorter. It is in fact implemented in MuPAD.

Still, here is the reason for Axiom's failure:

(1/2)^(1/x) has an essential singularity at x=0, thus no Puiseux expansion can
be computed. Thus, Axiom computes an exponential expansion, which, in this
simple case is

%e^(- log 2 * 1/x)

Next it checks that - log 2 is negative, thus the exponent goes to -infinity
and we are done.

For 

(-1/2)^(1/x) 

or

(-1/2)^(1/x) + (1/3)^(1/x)

this doesn't work, since we would obtain negative numbers in the exponent...

Martin