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

[Ralf Hemmecke]

On 06/03/2007 07:30 PM, Raymond E. Rogers wrote:
> Ralf Hemmecke wrote:
> > Agreed, but what about telling Axiom the following:
> >
> > (1) -> g(x)==if x>0 then x else -x
> >                                 Type: Void
> >
> > (
> I am sorry for being a nuisance but I would like to point out:
> This function can be expressed as
> g(x)=  -x +2*DD^2
> Where DD is the second order of the Dirac Delta function;  and DD^2 =
> int(int(DD*1)) , a ramp starting at 0.  The point is that piecewise
> polynomials  can be handled as generalized functions.
> The integral int(g(x),a,b) would be [-(x^2/2)+DD^3]^b_a 
>
>  I am retiring soon and perhaps will implement the useful parts of using
> the Dirac Delta function in Axiom. 
>
> Ray Rogers

I don't know whether one can easily explain to a not so well trained 
user what a "generalised function" is and that instead of

g(x)==if x>0 then x else -x

he/she should rather write

g(x)=  -x +2*DD^2,

but I would love to see your contribution to Axiom. Hopefully you never 
retire from using and contributing to Axiom.

All the best

Ralf