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

[Sumant S.R. Oemrawsingh]

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.

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 I've got loads of other stuff to throw at Axiom, I'll see what happens
there! :)

Thanks again,

S.

On Sun, May 27, 2007 at 08:55:38AM +0200, Martin Rubey wrote:
> Dear Sumant,
> 
> You have sent an excellent example!
> 
> "Sumant S.R. Oemrawsingh" <address@hidden> writes:
> 
> > Say, I wish to define a piece-wise function,
> > 
> > (1) -> f(x|x<0)==-x**2
> >                                                                    Type: 
> > Void
> > (2) -> f(x)==x**2
> >                                                                    Type: 
> > Void
> > (3) -> draw(f(x),x=-1..1)
> >    Compiling function f with type Variable x -> Polynomial Integer 
> 
> Reading this line, you might find out what happened: axiom interprets your
> function f as being from Variable x to Polynomial Integer.  Try - in a fresh
> session -
> 
>   )set message bottom on
> 
> (or shorter, )se me bo on) and
> 
>   x<0
> 
> You will see, x is interpreted as a polynomial integer! Thus, the inequality
> x<0 in your function definition will never hold!
> 
> There is a way out though: tell axiom to draw a function from DoubleFloat to
> DoubleFloat:
> 
>   draw(f, -1..1)
> 
> Look carefully at the messages, and look up "draw" in HyperDoc or with
> 
>   )display operations draw
> 
> (shorter: )di op draw)
> 
> 
> > If I now continue to integrate,
> > 
> > (4) -> integrate(f(x),x=-1..1)
> 
> Here, I think, you are out of luck.  axiom's Expression Domain does not yet
> provide piecewise functions.  You can only do it numerically:
> 
> (19) -> romberg(f, -1,1,0.1,0.1,10,20)
> 
>    (19)  [value= 0.0,error= 0.0,totalpts= 2049,success= true]
>    Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)
> 
> hope that helps,
> 
> Martin
> 

-- 
Sumant S. R. Oemrawsingh
address@hidden