Re: [Axiom-mail] A polynomial question

[Bill Page]

Alasdair,

Axiom does not have an polynomial type having symbolic exponents. As
far as I know Expression is the only applicable domain.

Is this anything like you wanted to do?

(1) -> x:UP(x,EXPR INT)
                                                                   Type: Void

(2) -> x

   (2)  x

                Type: UnivariatePolynomial(x,Expression Integer)

(3) -> k*(b+1)^(k-1)*x

                 k - 1
   (3)  k (b + 1)     x

                  Type: UnivariatePolynomial(x,Expression Integer)

(4) -> % * x*(b+1)

                        k - 1 2
   (4)  (b + 1)k (b + 1)     x

                  Type: UnivariatePolynomial(x,Expression Integer)

(5) -> monicDivide(%%(4),x)

                                   k - 1
   (5)  [quotient= (b + 1)k (b + 1)     x,remainder= 0]

Type: Record(quotient: UnivariatePolynomial(x,Expression
Integer),remainder: UnivariatePolynomial(x,Expression Integer))

(6) ->

Regards,
Bill Page.


On 2/7/08, Alasdair McAndrew wrote:

> I was doing some algebra relating to a proof by induction, and
> I had a polynomial containing terms of the form
>
> k(b+1)^(k-1)*x
>
> where b is a constant.  I wanted to multiply through by x(b+1)
> or similar.  How to I tell Axiom that b is a constant, k is a positive
> integer, and x is the polynomial's variable?  I tried setting the type
> to UP(x,POLY INT), but I just got Expression Integer instead.
> This didn't help, as I wanted to perform a monicDivide (w.r.t. x)
> later on.
>
> Thanks,
> Alasdair