RE: Axiom's integration non-deterministic?

On Friday, March 24, 2006 5:56 PM Igor Khavkine wrote:
> ... 
> Start up Axiom, and type in the following integral
> 
>   integrate(sqrt(1+x^(-2/3)),x)
> 
> Then type in the same integral again
> ... 
> Clearly, Axiom takes two different paths through the integration
> algorithm, even when give identical input. What is the cause of
> the branch? Is there a non-deterministic step somewhere in the
> algorithm?

I don't know the cause of this behaviour but I get the same effect
on the Windows version of Axiom.

> 
> Incidentally, is there a canonical form for radical expressions
> in which the two forms of the answer can be compared and directly
> shown to be the same?
> 

It's not based on a canonical form, but this seems to work:

A1 := integrate(sqrt(1+x^(-2/3)),x)
A2 := integrate(sqrt(1+x^(-2/3)),x)
A1-A2

Surprised? :)

Regards,
Bill Page.