Now with (draft) PR https://github.com/sagemath/sage/pull/36592
the ask.sagemath problem is solved by P2.<x,y,z> = ProjectiveSpace(QQ, 2) f = 2*x^5 - 4*x^3*y*z + x^2*y*z^2 + 2*x*y^3*z + 2*x*y^2*z^2+ y^5 C = Curve(f) kC = C.function_field() K = kC.gen().differential().divisor() # canonical divisor basis = (-K).basis_function_space() Basis = [C._pull_from_function_field(f) for f in basis] phi = C.hom(Basis, P2) D = phi.image() # conic assert D.degree() == 2 D On Monday, October 30, 2023 at 8:11:05 AM UTC+9 Kwankyu wrote: > This is simpler > > sage: psi = C.hom(liftedbasis, P2) > sage: psi.image() > Closed subscheme of Projective Space of dimension 2 over Rational Field > defined by: > x^2 + x*y + 2*y*z > > > On Monday, October 30, 2023 at 5:45:27 AM UTC+9 Nils Bruin wrote: > > > > On Monday, 30 October 2023 at 00:19:47 UTC+13 Kwankyu wrote: > > What is your code? > > P2.<x,y,z> = ProjectiveSpace(QQ, 2) > f = 2*x^5 - 4*x^3*y*z + x^2*y*z^2 + 2*x*y^3*z + 2*x*y^2*z^2+ y^5 > C = Curve(f) > kC = C.function_field() > D = kC(kC.base_field().gen(0)).differential().divisor() > L,m,s = (-D).function_space() > #the routine below is a bit of a shortcut based on how the affine patch > for kC > #is chosen. In more general code this would need to be a little more > sophisticated > def liftkC(u): > return sum([(m.numerator()(y/x))/(m.denominator()(y/x))*(z/x)^i for > i,m in enumerate(u.list())]) > liftedbasis = [liftkC(m(b)) for b in L.basis()] > den = lcm([b.denominator() for b in liftedbasis]) > liftedbasis = [parent(x)(b*den) for b in liftedbasis] > phi = P2.hom(liftedbasis,P2) > phi(C) # this fails > C._forward_image(phi,check=False) #this seems to work! > > Of course, one could also do some linear algebra with > (-D).function_space() and (-2*D).function_space() to figure out this image. > > -- 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/79431f03-f623-4654-a4c6-cbfe8425c49bn%40googlegroups.com.
