Re: [Axiom-mail] How to expand a fraction (like Maple does with 'expand')?

[Francois Maltey]

Hello Thomas, 

Thanks for your interest for axiom !

> > expand(((-r1*r2*uoff)+((r2+r1)*r3+r1*r2)*ue)/(r2*r3));
>                            r1 uoff        ue r1   ue r1
>                          - ------- + ue + ----- + -----
>                              r3            r2      r3
> 

So you are looking for expand fraction as maple and mupad :
(A+B+C+D)/E gives A/E + B/E + C/E + D/E where (A, B, C, D) are monomials.

Are you also looking for a << partFrac >> functions as :

   x/(x^2-1) = (1/2)/(x-1) + (1/2)/(x+1)
or x/(x+1)^2 = 1/(x+1) - 1/(x+1)^2.

I don't know if this is possible.

Axiom doesn't play with expressions as 
x^2-y^2 or (x-y)(x+y) but only with expanded or sparse polynomials.

So (x-y)(x+y) doesn't exist, but only x^2-y^2.

The great advantage of this data structure is his normal form :
    ((x+y)-x*y) + z - ((x+y)-x*y) * z 
and ((y+z)-y*z) + x - ((y+z)-y*z) * x 
are equal without any expand command. Axiom uses expanded form.

It's also possible to factor polynoms : try factor (x^2-y^2).

But it's (almost) impossible to factor a fraction as 
(cos x + 1) * (cos x + 2) * (cos x + 3) / (cos x + 4) / (cos x + 5)

And other transforms as x^2/(x-1) = 1 + x + 1/(x-1) aren't so obvious.

> I am writing a quit overview about CA Systems for hobby electronics
> and  want to explain some usual tasks in different CA Systems.

What CAS do you explain ?

Have a nice day !

Francois