RE: [Axiom-developer] SuchThat

[Bill Page]

On Monday, October 11, 2004 2:09 PM I wrote:
> ... 
> I was looking for a non-trivial example of 'numeric' versus
> 'symbolic' mathematics to discuss at the AMS meeting this
> weekend. Symbolic eigenvalue computations have been of
> interest to me before. So I loooked at section 8.4 of the
> AXIOM book (page 241 in the original book). When I tried
> the example eq. (1) I found that it produced a result
> slightly different than the book.
> 
http://page.axiom-developer.org/zope/Plone/Members/billpage/MathAction2
>
> The 'extra' result was in the form of a SuchThat type.
>
> So in the end, this did not (quite) turn out to be the
> numeric computational result that I had expected!

In fact the more I think about it, I wonder why the
author choose to return the 2nd and 3rd eigenvalues
in this problem only implicitly. Was it only for
compactness? In the case of problems of low degree the
roots could easily have been given numerically as shown
in the calculation. Perhaps it was for generality?
There is some new algorithm, isn't there, for finding
roots of polynomials of any degree?

Regards,
Bill Page.