Is %i an integer? - Adding more facts to the database

I had a look at the problem of the bug report "integrate(exp(-x^(%i)),x,0,1); =>
Is %i an integer?" - ID: 2811926.

I think at first we should give Maxima more knowledge about known facts.

I have added the following facts to the database:

   (kind $%i $imaginary)
   (kind $%pi $real)
   (kind $%gamma $real)
   (kind $%phi $real)

Next I have improved the function NONINTEGERP.

;	  ((atom e) (kindp e '$noninteger))
          ((atom e) (or (kindp e '$noninteger)
                        (kindp e '$rational)
                        (kindp e '$real)
                        (kindp e '$complex)))

With this change symbols wich are declared to be rational, real, or complex are
a noninteger too.

With this changes we get:

(%i3) featurep(%i,imaginary);
(%o3) true

and

(%i4) askinteger(%i);
(%o4) no

Because we have %pi declared to be real we get:

(%i5) featurep(%pi,real);
(%o5) true

(%i6) askinteger(%pi);
(%o6) no

With this extension we no longer get the question "Is %i an integer?". Maxima
tries to give a result. I have not checked the result.

(%i7) integrate(exp(-x^(%i)),x,0,1);
(%o7) %i*(%i*('limit(%i*gamma_incomplete(-%i,-log(x+1))/2
                      -%i*gamma_incomplete(%i,-log(x+1))/2,x,0,minus)
             +%i*gamma_incomplete(%i,1)/2-%i*gamma_incomplete(-%i,1)/2)
         +'limit(-gamma_incomplete(%i,-log(x+1))/2
                  -gamma_incomplete(-%i,-log(x+1))/2,x,0,minus)
         +gamma_incomplete(%i,1)/2+gamma_incomplete(-%i,1)/2)

Maxima gives the correct indefinite integral:
 
(%i8) integrate(exp(-x^(%i)),x);
(%o8) %i*gamma_incomplete(-%i,x^%i)*x*(x^%i)^%i

The testsuite and the share_testsuite has no problems with this extension. I
think we should do this extension.

Dieter Kaiser