Re: [Axiom-math] How reads axiom Expressions ?

[Dylan Thurston]

On Mon, Oct 13, 2003 at 08:37:06AM +0200, address@hidden wrote:
> Hello, 
> 
> I type this example in axiom :
> 
> (4) ->  (sin (x)+1/2)*(cos(x)+1/2)
>         (4cos(x) + 2)sin(x) + 2cos(x) + 1
>    (4)  ---------------------------------
>                         4
> 
> I don't understand the result : 
> it's _not_ an expanded product, and it's _not_ a factorised product.
> What does axiom ?

I don't think it's specific to sin/cos:

(9) -> (x + 1/2) * (y + 1/2)

             1     1     1
   (9)  (x + -)y + - x + -
             2     2     4
                                            Type: Polynomial Fraction Integer

From reading the tutorial, I believe that Axiom by default is writing
this as a polynomial in the variable 'y', which is the lexicographically
largest variable.

Hmm, it seems that here we're probably really seeing the differences
between Axiom's approach and a tree-based approach like in the three Ms.
Axiom seems to be storing this polynomial as a polynomial, and not just
as a tree of expressions; as such, I'm guessing that it is put in a
canonical form using Groebner bases and such.

Peace,
        Dylan

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