On 5/18/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
>
> Given: I'm currently taking undergrad algebra, and I'm not as well-steeped in 
> fields as I'd like.  But Wikipedia tells me that a polynomial ring over any 
> field is Euclidean... so this seems horribly, horribly wrong.
>

That is indeed a bug.  Many thanks for pointing it out!
I've fixed it (the issue was with the very
state-based behavior of Singular.)  See attached patch.

> {{{
> F.<u> = GF(31^2,'u')
> R.<x,y,z> = F['x','y','z']
> p = x^3 + (1+u)*y^3 + z^3
> q = p^3
> print gcd(p,q)
> print gcd(p,q)
> print gcd(p,q)
> print gcd(p,q)
> ///
> 1
> x^3 + (u + 1)*y^3 + z^3
> 1
> x^3 + (u + 1)*y^3 + z^3
> }}}
>
>
>
>
> >
>


-- 
William Stein
Associate Professor of Mathematics
University of Washington
http://www.williamstein.org

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Attachment: 4504.patch
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