On Saturday, 28 October 2023 at 18:50:12 UTC-7 Nils Bruin wrote: On Saturday, 28 October 2023 at 15:26:35 UTC-7 Kwankyu wrote:
f1, f2, f3 are univariate polynomials (say in y) over rational function field (say in x). Then x and y are not always the variables X and Y of the coordinate ring of the affine plane. Things are more complicated if the curve is in space (of dim > 2). Sure. But you did get x,y somehow from the model with which C was given. Most likely, the A2 on which x,y are coordinates is obtained via projection from whatever model C was given by? Even if it is not a linear map, there are still expressions through which you can pull back x,y to the original model. You're right that the representations may get rather bad, but I'm not sure there's really something you can do about that. The most pressing problem in sage at the moment seems to be that presently there only seem to be morphisms between schemes. You need rational maps for this (especially from a singular model, the map to a canonical model might only be a rational map). So I think we'd first need a bit of a push to get some infrastructure for rational maps. In fact "maps" between schemes in magma are just rational maps. So presently there is really a difference in functionality. There are some conceptual problems with the main "map" type between schemes being a rational map. But it is very convenient and certainly for curves a much better fit than maps that are clearly morphisms. I might be overlooking something ... currently sage allows for the construction of a rational map P2 -> P2, but then asking for the image of a curve C in P2 leads to TypeError: map must be a morphism (which should probably be a ValueError). Perhaps the code is just unnecessarily picky? -- 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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/efdf5070-97a8-49b1-876b-1cdce5b61455n%40googlegroups.com.
