thanks. On Tuesday, February 3, 2015 at 8:09:45 AM UTC-5, John Cremona wrote: > > On 3 February 2015 at 13:00, Ben Hutz <bn4...@gmail.com <javascript:>> > wrote: > > I'm not a member yet of those groups, so my cross-post attempt failed. > If > > you could do so that would be appreciated. > > Done -- and I also approved your application to join sage-nt! We set > up sage-nt to discuss number-theory-specific things in Sage, and I > think there are several people who follow that but do not read all > sage-devel. > > John > > > > > On Tuesday, February 3, 2015 at 4:03:22 AM UTC-5, John Cremona wrote: > >> > >> This would be great to have. Why don't you cross-post to sage-nt (and > >> perhaps also sage-algebra)? > >> > >> John > >> > >> On 3 February 2015 at 01:59, Ben Hutz <bn4...@gmail.com> wrote: > >> > I'm interested in implementing Weil restriction (restriction of > scalars) > >> > for > >> > affine schemes. I see from #5569, that there is an implementation for > >> > ideals. I'd like to extend this to affine schemes/points/morphisms. > >> > There is > >> > also an aborted attempt of Weil restriction for projective models of > >> > elliptic curves #13266 that does not seem to be going anywhere. > >> > > >> > While the code for the restriction for each of these (affine) objects > is > >> > not > >> > difficult, this seems like something that should be implemented as a > >> > functor > >> > as you'd like the resulting schemes/points/morphisms to all play > nicely > >> > together. However, I know little about functors in Sage. I've looked > >> > around > >> > in the code a little bit hoping to find an example where something > like > >> > this > >> > was done before, but I'm having some trouble. I see where Spec is > >> > implemented as a functor, but I'm not sure that is helpful. I've also > >> > seen > >> > the documentation about which functions a new functor class should > >> > override. > >> > I'm sure I'm going to get this wrong, but as a place to start this > >> > discussion would an implementation look something like this > >> > > >> > 1) create a new functor class WeilRestrictionAffineFunctor which > >> > implements > >> > _coerce_into_domain(self, x) > >> > _apply_functor(self, x) > >> > _apply_functor_to_morphism(self, f) > >> > > >> > although it doesn't seem like any of these three would apply to the > >> > points > >> > of the affine scheme. > >> > > >> > 2) Given an affine scheme A and a morphism f:A -> A, have the methods > >> > A.weil_restriction() and f.weil_restriction() call the functor so > that > >> > domains/codomains all match-up nicely? For example, I'd like > something > >> > like > >> > this to work > >> > > >> > sage: K.<w>=QuadraticField(3) > >> > sage: A.<x,y>=AffineSpace(K,2) > >> > sage: X=A.subscheme([y^2-x^2]) > >> > sage: H=End(X) > >> > sage: f=H([y,x]) > >> > sage: P=X(-1,1) > >> > sage: f(P).weil_restriction() == > >> > f.weil_restriction(P.weil_restriction()) > >> > True > >> > > >> > > >> > I'm sure I could make this work manually by caching the > weil_restriction > >> > of > >> > a scheme so that a new one is only created when it doesn't already > exist > >> > (like 'homogenize' does) but, at least mathematically, this really > >> > should be > >> > a functor. I guess my first question is then: Is a functor the > 'right' > >> > choice for implementation of Weil restriction in Sage? If yes, is > there > >> > anywhere else in Sage something like this is done from which I can > base > >> > this > >> > new functionality? > >> > > >> > Thanks, > >> > Ben > >> > > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sage-devel" group. > >> > To unsubscribe from this group and stop receiving emails from it, > send > >> > an > >> > email to sage-devel+...@googlegroups.com. > >> > To post to this group, send email to sage-...@googlegroups.com. > >> > Visit this group at http://groups.google.com/group/sage-devel. > >> > For more options, visit https://groups.google.com/d/optout. > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to sage-devel+...@googlegroups.com <javascript:>. > > To post to this group, send email to sage-...@googlegroups.com > <javascript:>. > > Visit this group at http://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/d/optout. >
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