Re: [Axiom-mail] Defining piece-wise functions and drawing, integrating, ...

[Martin Rubey]

"Sumant S.R. Oemrawsingh" <address@hidden> writes:

> Hi,
> 
> Thanks for the reply. Too bad integration over such functions can't be done
> symbolically. I also don't quite understand why for the draw function, the
> function si compiled with type Variable x -> Polynomial Integer, when
> x=-1..1 is a range in R.

yes, that's very strange and should be debugged.  Maybe you could file a report
on IssueTracker?

> I was hoping I could write down all my stuff in Axiom (symbolically), so that
> I would, say, never have to go through stacks of paper, manually calculating
> overlap integrals of two different, piece-wise functions, or stuff like
> that. It would appear that I still have to do all this manually, if I would
> like a symbolic answer :(

But you can still do this, if you know the boundaries of the functions!  Use
something like

-- lf...list of functions
-- x...integration variable
-- lb...list of boundaries
integratePiecewise(lf: List EXPR INT, x: Symbol, lb: List EXPR INT): EXPR INT ==
    reduce(+, [integrate(f, x=b1..b2) for f in lf for b1 in lb for b2 in rest 
lb], 0)

Maybe you could even take a single f which is a piecewise defined function, and
extract the necessary information, but that will need a little detective work.


Martin