On Nov 2, 2006, at 8:28 PM, David Harvey wrote: > On Nov 2, 2006, at 11:11 PM, Robert Bradshaw wrote: > >>> This is much harder. I agree it would be nice, but how would you >>> handle something like >>> >>> sage: R.<x> = ZZ["x"] >>> sage: S.<y> = ZZ["y"] >>> sage: x*y >>> >>> ?? >>> >>> David >> >> Now you could return that as an element of ZZ['x', 'y'], but I'm not >> sure that would be a good idea. (non-common parents could be good >> runtime indicators that something could be wrong, and efficiency >> could really drop...) > > Hmmm... it sounds like what you're asking for is the following. > > If x is in R, and y is in S, and there is a natural coercion from R > to T and a natural coercion from S to T, then > > sage: x * y > > should be smart enough to coerce both into T, and perform the > multiplication there. (I've left out complications involving scalar > multiplications...) > > Also, I guess you want T to be minimal in some sense.
Yes, that's what I'm saying, though I don't know how feasible it would be in general. In terms of scalar multiplications, that's actually what my original motivation was. > One thing I definitely don't like about this is that the > multiplication operator has to conjure up a whole new ring. But I > guess this already happens for things like this: > > sage: R.<x> = PolynomialRing(ZZ) > sage: (x/2).parent() > Fraction Field of Univariate Polynomial Ring in x over Integer Ring Yes, it already goes on with division. I think being inefficient is better than throwing an error (and for those interested in speed they should be doing everything over the same ring...) I have to admit that this specific example bothers me...I can see where it comes from but I _want_ it to be an element of Univariate Polynomial Ring in x over Rational Field, i.e. x/2 = 1/2 * x. > > Must sleep now. > > David > > > --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
