Yes, I know that a lot of special functions aren't implemented. In the cases
Maxima can't handle the integral I have just given the output in the tabulated
form and don't try to convert it in an expression Maxima knows.
I have collected all the examples to have a working reference to improve the
code of $specint. So the implementation of missing functions would be one task.
Another task would be to give the user better access to the internal functions
$specint knows e.g.
%l[n,0](z) --> laguerre(n,z)
(But the code for the function %l has a bug).
The algorithmen of the user function laplace are much more special. I think that
it might be a good idea to improve the more general algorithmen of $specint to
handle a much wider range of special functions correctly.
Dieter Kaiser
-----Urspr?ngliche Nachricht-----
Von: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] Im
Auftrag von Alexey Beshenov
Gesendet: Montag, 12. Mai 2008 01:25
An: maxima at math.utexas.edu
Betreff: Re: [Maxima] Problems with the function $specint
On Sunday 11 May 2008 22:40, Dieter Kaiser wrote:
> I started to look at the code of the Maxima function $specint which
> calculate the Laplace transform. I have rearranged the code, drawn flow
> charts and added a lot of debug information to find the problems.
>
> To get an overview of the problems with the code I have taken the tabulated
> Laplace transforms from the website of EqWorld. There are 99 Examples
> tabulated. 47 examples pass the test. 53 examples don't give the tabulated
> answer. The file test_eqworld.mac includes comments to the examples which
> fails. Some answers of Maxima might be correct, but I can't show that the
> result is identical to the tabulated answer. I run this test file with the
> Maxima CVS-Version and GCL 2.6.8.
1. Unit step function is called "unit_step", not "u". Anyway, Laplace
transform code doesn't handle it.
2. Many special integral functions (Ei, Ci, Si, etc.) are not implemented in
Maxima, so you shouldn't expect them in output.
3. Maxima doesn't handle well "abs" in integration or Laplace transform.
4. You should look at "laplace" if you're expecting nouns instead of strange
Lisp symbols in output (it's a well-known bug in "specint").
--
Alexey Beshenov <al at beshenov.ru>
http://beshenov.ru/