RE: Factorizing an expression

On Wednesday, November 08, 2006 9:30 AM Ludovic Courtès wrote:
> 
> I'm looking for a way to turn an expression into a factor of another
> one.  For instance, given this equation:
> 
>   (a/b)^2 + (a/b)y + 3(a/b)x
> 
> tell Axiom to somehow turn this into:
> 
>   (a/b).((a/b) + y + 3x)
> 
> Apologize if this is answered elsewhere but I couldn't find it in the
> book.
> 

Here is what I would do:


(1) -> p:MPOLY([x,y],FRAC POLY INT):=(a/b)^2 + (a/b)*y + 3*(a/b)*x

                      2
        3a     a     a
   (1)  -- x + - y + --
         b     b      2
                     b
              Type: MultivariatePolynomial([x,y],Fraction Polynomial Integer)
(2) -> factor p

        3a      1      a
   (2)  -- (x + - y + --)
         b      3     3b
     Type: Factored MultivariatePolynomial([x,y],Fraction Polynomial Integer)
(3) ->

--------

p is a multivariate polynomial in x and y with coefficients from
the ring of polynomial fractions. At first glance this construction
might seem rather strange from a mathmatical point of view, but it
in Axiom's formal approach the only requirement to form a multi-
variate polynomial is to supply a list of variables and the name
of some ring from which the coefficients are drawn. Axiom takes care
of keeping track what is a polynomial variable and what is a
coefficient.

This sort of construction is one of the things that sets Axiom
apart from most other computer algebra systems.

Regards,
Bill Page.