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

[Sumant S.R. Oemrawsingh]

Hi,

I filed a report on IssueTracker, but accidentally filed it twice (n00bs...)
Sorry for that. The latter filing is more complete and  correctly categorised.

Integrating over a list of functions with a list of boundaries is certainly
a clever way of doing this, but alas, I do not know a priori what the
boundaries of integration are. In other words, some of these functions will
be displaced and some boundaries will come before others. I've always done
this integration by hand, as well as the ordering of the boundaries, but
things are getting more and more ridiculous now, with many, many different
cases. I was hoping that Axiom could figure all this out itself.

I will try to see if I can do some clever extraction and ordering, making
both the boundaries and the functions a function of the displacement.

Thanks for the tips, though,

Sumant


On Wed, May 30, 2007 at 09:11:43AM +0200, Martin Rubey wrote:
> "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
> 

-- 
Sumant S. R. Oemrawsingh
address@hidden