Yes I just started looking at this again about an hour ago. It looks like the way Sage gets the map is only by doing linear changes of coordinates on P^2 and a Cremona, as outlined here: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCwQFjAA&url=http%3A%2F%2Ftrac.sagemath.org%2Fraw-attachment%2Fticket%2F3416%2Fcubic_to_weierstrass_documentation.pdf&ei=mASBU4zHJ6KlsATngYHQCA&usg=AFQjCNHyMPTkzhy9KhgNr-MB0pI6pJXNTw&sig2=AORDehO_tzL8xrZTO7OLZg&bvm=bv.67720277,d.cWc&cad=rja In fact I followed the procedure there by hand since I didn't look at the actual Sage code and the output was the same exact equation.
On Saturday, May 24, 2014 4:38:48 PM UTC-4, Nils Bruin wrote: > > On Saturday, May 24, 2014 9:18:29 AM UTC-7, Volker Braun wrote: >> >> Its a 4:1 map so you can't invert it... >> > > I would find that surprising. For a general plane cubic, there are good > recipes for getting a 9:1 map to a Weierstrass model in general and a 1:1 > map when a rational point is specified. A 4:1 map is rather unnatural to > get in that situation. You'd expect that from a y^2=quartic in x model. > > Indeed, the map returned is invertible, the inverse being: > > [ -12*x*z - 4*y*z, 32*x*z, x^2 - 28*x*z - 4*y*z] > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
