That looks like a good reference.
I was thinking of the remark in Ian Connell;s (free online) lecture
notes on elliptic curves, available from
http://www.math.mcgill.ca/connell/public/ECH1/, where he says (bottom
of first page of Chapter 2)
The pitfall to avoid here is that the isomorphic rings $A((T_1))((T_2))$ and
$A((T_2))((T_1))$
cannot be identified in the same way as $A[[T_1]][[T_2]]=A[[T_2]][[T_1]]$
since, for example, $\sum_{i=0}^{\infty}T_1^{-i}T_2^i$ is a member of the
first ring, but not the second.
On 16/11/2007, Georg Muntingh <[EMAIL PROTECTED]> wrote:
>
> I think you want the multivariate Laurent series to form a field. For
> x + y to have an inverse, you should additionally make a choice of an
> ordering x < y or y < x to decide what its series expansion looks
> like. The best definition might therefore be the iterated Laurent
> series, as described in Chapter 2 of this PhD thesis:
> http://arxiv.org/pdf/math/0405133.
> This might also be the easiest to implement.
> >
>
--
John Cremona
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
