On Sun, Mar 23, 2008 at 7:50 PM, Alex Ghitza <[EMAIL PROTECTED]> wrote: > > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > Hi all, > > Martin Albrecht brought up the following issue, in relation to > http://trac.sagemath.org/sage_trac/ticket/2634 > > "I am not convinced that it is actually desired to allow 0 generators > for multivariate polynomial rings. We allowed that before and thus I > reintroduced that behaviour but I would like to get rid of it: It will > be a no fun to support once the generic multivariate polynomials get > closer to C and I don't see the point." > > > I'm not sure whether the pun at the end of the quote was intended or > not. But we definitely want to be able to work with zero-dimensional > schemes (points), e.g. A0 = AffineSpace(ZZ, 0, 'a'). As far as I can > tell, the trouble comes up only in A0.coordinate_ring(), which currently > looks at this as a multivariate polynomial ring in zero variables. I > think we can just make coordinate_ring() return the base ring in the > case of dimension zero, and this would allow Martin to get rid of > zero-variable ring. > > Thoughts?
I definitely think multivariate polynomial rings with 0 generators should be supported for exactly the same reason matrices with 0 rows or columns should be supported -- algorithms are much more likely to work in corner cases and code is cleaner. I've been incredibly glad on numerous occasions that across the board Sage works very well with matrices that have 0 rows or columns, though this took a lot of extra work initially. The only argument put forth for removing multivariate polynomials rings with 0 generators is "It will be a no fun to support". That is not compelling. William -- William --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
