Is %i an integer?



Mike Hansen wrote:
> Hello,
>
> Is the following intended behavior?
>
> Maxima 5.18.1 http://maxima.sourceforge.net
> Using Lisp ECL 9.4.1
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) integrate(exp(-x^(%i)),x,0,1);
> Is %i an integer?
>
> --Mike
>
>   
looks like an error to me.  Though the expression  "x^%i" is kind of 
peculiar.
using changevar() one can alter the expression to
%i*integrate(t^(-%i-1)*%e^(-t),t) with t=x^%i


Note that the indefinite integral returns 
%i*gamma_incomplete(-%i,x^%i)*x*(x^%i)^%i
which appears to be correct.
or the changed integral is
%i*gamma_incomplete(-%i,t)


The commercial Macsyma leaves the definite integral unchanged (even 
after setting intanalysis:false), and transforms but does not solve the 
indefinite integral.
Mathematica 6.0 does nothing with the integral.

if you change the integrand to
%e^(-%e^(%i*log(x)))
which I think is the same :)
the indefinite integral in Maxima is not done.
and the definite integral says
Maxima encountered a Lisp error:
 inverting $finite?

These are also bugs; perhaps different.


RJF