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

[Bill Page]

On January 23, 2007 2:02 PM Wiesner Thomas wrote:
> 
> I'm sorry that i bug you with this (probably) simple
> problem:
> 
> How can i do the following (from Maple) in Axiom:
> 
> > expand(((-r1*r2*uoff)+((r2+r1)*r3+r1*r2)*ue)/(r2*r3));
>                            r1 uoff        ue r1   ue r1
>                          - ------- + ue + ----- + -----
>                              r3            r2      r3
> 
> I've been trying and googling for hours. I've tried MPOLY but 
> have only managed to to pull one variable in front of the
> fraction and didn't find out how to split it up completely.
> 
> I found the MPOLY approach in the Rosetta pages  
> (http://wiki.axiom-developer.org/RosettaStone)
> but it doesn't do what i want.
> 
> This seems to be such a simple task and I can't find out.
> 
> I am writing a quit overview about CA Systems for hobby 
> electronics and want to explain some usual tasks in
> different CA Systems.
> 

I would suggest the following computation:

(1) -> ex1:=((-r1*r2*uoff)+((r2+r1)*r3+r1*r2)*ue)/(r2*r3)

        - r1 r2 uoff + ((r2 + r1)r3 + r1 r2)ue
   (1)  --------------------------------------
                         r2 r3
Type: Fraction Polynomial Integer

(2) -> ex1::DMP([r1,ue,uoff],FRAC POLY INT)

        r3 + r2          1
   (2)  ------- r1 ue - -- r1 uoff + ue
         r2 r3          r3
Type: DistributedMultivariatePolynomial([r1,ue,uoff],
        Fraction Polynomial Integer)

The reason why this apparently simple task might seem difficult
at first to a novice Axiom user is because Axiom is strongly-
typed. Unlike Maple (and most other CA systems) expressions in
Axiom always have some type (domain) that explicitly defines the
operations appearing in the expression. Instead of "expanding"
an expression within a given domain, we are often faced with
"coercing" (represented by the :: symbol) expressions from one
domain to another more suitable for our task.

In my opinion learning to deal with the Axiom type system is
what makes Axiom's learning curve very steep at the beginning,
but this initial investment pays off later in more sophisticated
applications.

In (2) above, the reason that the first term is not expanded
further is that Axiom does not have any domain (as far as I
know) that has

       ue r1   ue r1
       ----- + -----
        r2      r3

as separate terms.

Regards,
Bill Page.