Re: [Maxima-discuss] inverse Laplace transform

[Robert D. <rob...@gm...>]

On 2017-08-22, Richard Fateman <fa...@be...> wrote:

> It might be easier for matching if the arguments were reversed, that is,
>
> reverse_arg_ilt(x,t, ....) , ....)
>
> because then x and t would be bound before trying to match the main 
> argument.

I tried that approach in another project (share/z_transforms) but
eventually settled on having a top-level rule which captures the
variable names, and then applies a bunch of other rules for specific
cases.

It seems to me that this general approach could be applied to other
integral transforms such as the ILT. There is the problem that the
existing ILT code doesn't make use of it (instead implementing a similar
method via hand-written Lisp code); if someone creates new rules for ILT
via pattern-matching rules, we might try to unify them with the existing
code, or we might just let the two code bases exist separately. 

On looking at the existing ILT code in src/laplac.lisp, I see that
Maxima's ilt function handles only a few cases -- the only nontrivial
one is a ratio of polynomials, if I'm not mistaken. Given that, it seems
worth considering to reimplemnt the whole thing via pattern matching
rules.

Incidentally I would take the opportunity to press for renaming 'ilt' to
something more self-explanatory such as 'inverse_laplace'.

best

Robert Dodier