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## RE: [Axiom-developer] [Q] How to classify integrate(z) vs integra te(z^1

 From: Page, Bill Subject: RE: [Axiom-developer] [Q] How to classify integrate(z) vs integra te(z^1) Date: Thu, 17 Feb 2005 19:56:18 -0500

```Since in Axiom

(1) -> z^1

(1)  z
Type: Polynomial
Integer
(2) -> z

(2)  z
Type: Variable
z

What you show below is entirely normal behaviour for Axiom.
Axiom knows how to integrate something that it can coerce to
a univariate polynomial such as the polynomial z^1, but it
does not know what to do with the variable z.

I agree that this is a bit bizzarre - especially for new users.

Actually I think it might make sense to allow coersion from
the domain Variable to Symbol from which the interpret can get
to UnivariatePolynomial. In which case one would see the same
result as

integrate(z::Symbol)

Regards,
Bill Page.

On Thursday, February 17, 2005 7:14 PM Vladimir Bondarenko wrote:
>
> AXIOM connoisseurs help is highly appreciated.
>
> How to interpret the following behavior?
>
> ...
>
> -> integrate(z^1)
>
>      1  2
>      - z
>      2
>                                Type:
> UnivariatePolynomial(z,Fraction Integer)
>
> but
>
> -> integrate(z)
>
>    There are 5 exposed and 2 unexposed library operations named
>       integrate having 1 argument(s) but none was determined to be
>       applicable. Use HyperDoc Browse, or issue
>                             )display op integrate
>       package-calling the operation or using coercions on the
> arguments
>       will allow you to apply the operation.
>
>    Cannot find a definition or applicable library operation named
>       integrate with argument type(s)
>                                  Variable z
>
>       Perhaps you should use "@" to indicate the required return type,
>       or "\$" to specify which version of the function you need.

```