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[Axiom-developer] RE: How can I get every term of an expression ?

From: Page, Bill
Subject: [Axiom-developer] RE: How can I get every term of an expression ?
Date: Mon, 19 Sep 2005 21:20:39 -0400

On Sunday, September 18, 2005 4:23 PM Francois Maltey wrote:
> I start from ... an Expression : 
> (2*log(x)+3*exp(y))*(4*sin(z)+2*log(x))
> And I want to get every term : ... 6 %e^y log(x), etc. 
> and get easily the integer 6, 8, 12 or 4.
> ... 
> I want to play with expression, not polynomial ; 
> then what coerce must I do ?

Tim Daly answered the part of Francois' question concerning the
case of polynomials (which I have omitted above) but in this case
the example expression is not a polynomial. It is assumed by Axiom
to be of type Expression Integer and cannot be converted to any
of the polynomial types except in a trivial manner, e.g.
DistributedMultivariatePolynomial([x,y,z],Expression Integer)

I have not been able to find any acceptible answer to Francois'

How can I persuade Axiom to write out

(1) -> (2*log(x)+3*exp(y))*(4*sin(z)+2*log(x))

as a "sum of products"? E.g.

(2) -> 8*log(x)*sin(z)+4*log(x)^2+12*exp(y)*sin(z)+6*exp(y)*log(x)

In Axiom, both of these expressions are rendered as

    (8log(x) + 12exp(y))sin(z) + 4log(x)  + 6exp(y)log(x)
                Type: Expression Integer

Why does Axiom choose this peculiar form instead of (1) or (2)?

Why can't Axiom factor and expand such expressions?

In the case of polynomials I can write:

(3) -> ((2*x+3*y)*(4*z+2*x))::DMP([x,y,z],INT)

   (3)  4x  + 6x y + 8x z + 12y z
           Type: DistributedMultivariatePolynomial([x,y,z],Integer)

But there does not seem to be anything type equivalent to

           Type: DistributedExpression Integer

Why not?

Would it make sense to define Distributed as a generic domain
constructor similar to Complex?

Would it be possible to write

  Distributed MultivariatePolynomial([x.y.z],Integer)


  Distributed Expression Integer?

(Note the space between Distributed and MultivariatePolynomial.)

Would it be simple to "extend" Expression to a new domain were
expressions are represented (when possible) as sums of products?

Bill Page.

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