green's functions, passing functions to a routine

John,

Though it is possible to work in terms of functions in Maxima, in general it
is easier to work in terms of *expressions*.

So instead of writing

        h1(x,t) := ''(ratsimp(integrate(g1(x,t),t)));       -- function
approach

you'd write

        h1 : ratsimp(integrate(g1,t))       -- expression approach

As for piecewise-defined functions, Maxima is currently rather weak in that
area; integration etc. do not work with them, not even in the most trivial
cases, e.g.

       integrate(if x>=0 then 1 else 0, x, 0, 1) => noun form
-- x>=0 over the whole integration interval!

I don't know if there are plans to fix this in the short term.

                -s


On Mon, Sep 1, 2008 at 12:35 AM, John Lapeyre <pdl at johnlapeyre.com> wrote:

> I am trying to find convenient ways to deal with a
> one dimensional Green's function problem. Here are some
> questions that came up.
>
> 1) how can one pass functions as arguments to another function?
>   Eg,
>
>  /*WRONG*/
>  ygen(f,x,L) :=  integrate(f(t)*g2(x,t),t,0,x)
>         + integrate(f(t)*g1(x,t),t,x,L);
>
>  this does not do what I am trying to do.
>
> 2) I want to integrate g1 and make a function h1 from the
>   result. Is there  a good idiom? This seems to work ok.
>
>   h1(x,t) := ''(ratsimp(integrate(g1(x,t),t)));
>
> 3) Piecewise defined functions.
>   f(x) := if x > 3 then 0 else x;
>   integrate(f(x),[x,0,4]); /* FAILS */
>   fails to give a useful result.
>   Of course, eventually, one would like a more complicated
>   problem with 3 replaced by say, a.
>