On Nov 19, 6:22 am, Dima Pasechnik <dimp...@gmail.com> wrote: > Perhaps the coersion system itself might be a bit confused, but > it looks like here we talk rigour for the sake of rigour, without > any benefits.
One benefit is error detection and picking proper normalizations. For instance, if you create a "reduction map" from a projective variety to one over GF(p), denominators need to be cleared. First you need to clear them from the equations, but assuming you did that, it's also important that you properly clear denominators from the representatives for your projective points (i.e, the projective point (1:1/p) should be represented by (p:1) before it gets mapped over). However, projective points over Q usually do normalized with a 1 in a given coordinate, forcing denominators elsewhere. With an automatic coercion you may well succeed in defining a map, only to find it doesn't evaluate in points where you thought it should. Nasty complications with the coercion framework always happen a couple of levels removed from the source of the problems, so I've given up on only guarding against problems I can "imagine" and prefer the more defensive stance of sticking with what is mathematically guaranteed to work. If we ensure there are reasonable ways to loosen the stringent defaults I think we can still end up with a workable system. > Conceptually, field division is a partial map too. Yes, and it always is. So assuming it's not will surely be a bug. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
