This is now #3964. John
2008/8/27 John Cremona <[EMAIL PROTECTED]>: > You are definitely right. The problem lies (as far as I can see) in > sage.schemes.generic in the __init__ funtion of class > SchemeMorphism_on_points_projective_space. (I only found this out by > tring to construct a morphism from P^1 to P^1 using 3 polynomials, > which did raise an error in this very function.) > > It appears that the only check this function does is that the number > of polys is correct. It does not check that they are actually polys, > or have the right number of variables, let alone that they are coprime > and homogeneous of the same degree: > > sage: S.<u,v,w> = QQ[] > sage: f = H([u,v]) > sage: f = H([u*v*w,u+v+w]) > sage: f = H([exp(u),exp(v)]) > sage: f > > Scheme endomorphism of Projective Space of dimension 1 over Rational Field > Defn: Defined on coordinates by sending (x : y) to > (e^u : e^v) > > with H as in your example. > > This definitely deserves a ticket, which I will create. now. > > John > > 2008/8/27 Alex Ghitza <[EMAIL PROTECTED]>: >> >> Hi, >> >> I am fairly certain the following two things are bugs, but I want to >> double-check that I'm not doing something stupid before submitting a ticket: >> >> sage: R.<x,y> = QQ[] >> sage: P1 = ProjectiveSpace(R) >> sage: H = P1.Hom(P1) >> sage: f = H([x-y, x*y]) >> sage: f >> >> Scheme endomorphism of Projective Space of dimension 1 over Rational Field >> Defn: Defined on coordinates by sending (x : y) to >> (x - y : x*y) >> >> >> This is nonsense: there is no morphism from P1 to P1 given by those >> equations, since the two polynomials x-y and x*y are not homogeneous of >> the same degree. I think Sage should throw a ValueError here. >> >> The second example: >> >> sage: R.<x,y> = QQ[] >> sage: P1 = ProjectiveSpace(R) >> sage: H = P1.Hom(P1) >> sage: f = H([x^2, x*y]) >> sage: f >> >> Scheme endomorphism of Projective Space of dimension 1 over Rational Field >> Defn: Defined on coordinates by sending (x : y) to >> (x^2 : x*y) >> >> >> This is also bad: the two polynomials are now homogeneous of degree 2, >> but they are not relatively prime (and so this is not a morphism from P1 >> to P1, but rather a rational map since it is not defined at (0 : y)). I >> think Sage should also throw a ValueError here. >> >> (Or maybe I'm doing things wrong, in which case I'd love to find out how >> to make this work.) >> >> Cheers, >> Alex >> >> >> >> -- >> Alexandru Ghitza >> Lecturer, Pure Mathematics >> Department of Mathematics and Statistics >> The University of Melbourne >> Parkville, VIC, 3010 >> Australia >> >> >> >> >> > --~--~---------~--~----~------------~-------~--~----~ 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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
