On Sun, 29 Oct 2006 04:08:02 -0700, Bill Hart <[EMAIL PROTECTED]> wrote:
> > Actually, I am wrong. It is no more difficult to decide whether the > user should be allowed to coerce something from one ring into another > than it is to have sage do it automatically. So the user should not > have to specify coersions all the time. > > If SAGE were being really clever, the only rings it would know how to > coerce would be its base rings defined upon startup. As it went, it > would construct a table of possible automatic coersions. That's the plan. And currently it sort of does that on the fly, except it doesn't actually store the results in a table. > Polynomials would be automatically coerced into another ring if the > base rings can be coerced one into the other, so this decision would be > a recursive one. Yep, that's the plan. > Other coersions could occur along homomorphisms, to quotient rings and > from subrings. > > The problem comes if there is an isomorphism from one ring to another, > or even just a homomorphism in both ways. Coecion is defined only if the composition in both directions is an isomorphism; otherwise, it isn't defined. > So basically, sage uses its wits, trying to determine canonical > homomorphisms (i.e. specifically inclusions) and beyond that, expects > the user to specify what a canonical isomorphism should be. Natural quotient maps in addition to inclusions. > Maybe you guys have already had this discussion. Yep. That you're coming up with the same answer is encouraging. 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
