I like Robert's suggestion. If the user wants n independent generic points, construct a large enough field (transcendence degree n) to contain them.
A useful change Magma made relatively recently (a couple of years or so ago) was to aloow points on an elliptic curve to have coordinates in an extension of the base field of the curve -- as one would when working mathematically. e.g. given a curve defined over QQ you can define points on E(K) for e.g. K=a number field, or K=a function field (such as the function field of E, to get a generic point). Of course, these points "know" what their curve is so you can do point arithmetic on them and so on. I don't see why this should be workable in Sage too (maybe it is already? if so I will retire shame-faced from the discussion...) John On 15/01/2008, Nick Alexander <[EMAIL PROTECTED]> wrote: > > > Perhaps something like > > > > P, Q = generic_points(2) > > P+Q # this works (assuming we can do the fraction field arithmetic > > efficiently enough) > > > > where P and Q are defined over the same ring large enough to make > > them independent. (I'm not returning the new curve here because with > > a variable number of points I think this would be more cumbersome, > > but one can always do E.parent()). > > Do it like objgens(): > > E, (P, Q) = generic_points(2) > > Nick > > > > -- John Cremona --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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/ -~----------~----~----~----~------~----~------~--~---
