Am Dienstag, den 09.03.2010, 12:59 -0500 schrieb Raymond Toy:
> On 2/28/10 1:53 PM, Dieter Kaiser wrote:
> > I have implemented a small extension to get more integrals for special
> > functions. The idea is to support a special routine which is looked up
> > in the routine INTFORM, if Maxima does not get a result for the desired
> > special function.
> >
> > This is the implementation in INTFORM:
> >
> >
> [snip]
> > The testsuite has no problems. We get no slow down, because the new code
> > is only executed, if a special function is part of the integrand. We
> > only get new integrals.
> >
> > If the implementation is of interest I would like to commit the code.
> >
> Is there any kind of general theory we can use for these integrals?
> Kind of like how specint works by converting the integrand to a
> hypergeometric form and integrating that? I mostly just curious.
One more general approach is to integrate the hypergeometric
representation of special functions. The only problem is that we need to
extend the hypergeometric code to get a lot more simplifications in
terms of special functions too.
> Another thing that we might want to look into is TILU (table of
> integrals by lookup). Richard Fateman has obtained permission for us to
> use that and he sent out the code sometime ago. I meant to look into
> integrating that into maxima, but I never got around to it. (Some
> design issues need investigating, like where the integrals are stored.
> As part of maxima? Some webserver somewhere? Something else?)
Yes, I have thought about this too. Therefore, I have hesitated to
commit anything. I had a look at the code already introduced with
abs_integrate and I think it might be much better to extend this code
and not the Lisp integrator.
Another point is, that the integrator might be improved further in its
core functionality to support more general problems.
Dieter Kaiser