Re: [Axiom-developer] about Expression Integer

[Francois Maltey]

Hello !

So I try :

> P := DistributedMultivariatePolynomial([x,y],Expression Integer)
> a: P := x
> a/x

> However, I guess, most people find this confusing.
Indeed...

Why axiom doesn't see the denominator as a DMP ([x,y], Expr Int) ?
The numerator is a DMP ([x,y], Expr Int).

Numerator and denominator of any fraction are in the same ring, 
and have the same type.

The x variable can't be a variable of the Expression Integer Ring, 
because this a is one of the polynomial.

// 1 //
I was waiting that axiom read a/x as (a::P)/(x::P) because I wait
the same calculus from my students on a sheet of paper.

Is it too difficult ?

// 2 //
I also wait a fail result for the command :
b := monomial(x,[0,0]::DirectProduct(2,NNI))$P

I understand wat is R[X], (R[X])[Y], (R[Y])[X], R[X,Y] and R[Y,X].

I don't understand what is (R[X])[X], so axiom might forget it.

And I don't understand why it's not interessing to add this patch :
.....
However for our purposes something rather primitive is sufficient: 
All domains that contain variables need to export a function 
variables2: % -> List Symbol. Then we can say in 'QFCAT':

 if S has variables2: S -> List Symbol then
   variables2: % -> List Symbol
   variables2 f ==
      merge(variables2(numer(f)), variables2(denom(f)))

and add the following to UP and 'MPOLY':

 if R has variables2: R -> List Symbol then
   coerce(r:R):% ==
     if member?(x, variables2(r)) then
       error "coefficient contains variable"
     else coerce(r)$Rep
......

// 3 // 
Why DMP doesn't accept OrderedSet but only List Symbol ?

* one writes a new domain with a new representation. For
  'DistributedExpression' I failed to do so, since the proper representation
  would be 'DMP', but this only accepts a 'List Symbol' as variables, for
  expressions I need to allow an arbitrary 'OrderedSet' however.

If I'm right Expression are built over POLY which accept OrderedSet 
or <<kernel>> as sin x and so.