On Nov 21, 6:22 am, VictorMiller <[email protected]> wrote: > sage: T.<t1,t2,u1,u2> = QQ[] > sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1- > u2)^2 -1]) > sage: TJ.genus() > 4294967295 > sage: TJ.dimension() > 1
Yes, there is a bug in the code. If I try Sage 32 bits, the answer to TJ.genus() is -1. Is I use Sage 64 bits I get your result. The genus -1 looks like the ideal is not (absolutely) prime. This looks odd at first sight since the ideal is prime over the rationals and the projection onto [t1,t2] or [u1,u2] gives rational curves. But, after a little research the answer looks right. sage: T.<t1,t2,u1,u2,t>=QQ[sqrt(3)][] sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1- u2)^2 -1]) sage: TJ.is_prime() False sage: TJ.primary_decomposition() [Ideal (3*t2 + (-2*sqrt3)*u1 + (sqrt3)*u2, 3*t1 + (-sqrt3)*u1 + (2*sqrt3)*u2, 4*u1^2 - 4*u1*u2 + 4*u2^2 - 3) of Multivariate Polynomial Ring in t1, t2, u1, u2, t over Number Field in sqrt3 with defining polynomial x^2 - 3, Ideal (3*t2 + (2*sqrt3)*u1 + (-sqrt3)*u2, 3*t1 + (sqrt3)*u1 + (-2*sqrt3)*u2, 4*u1^2 - 4*u1*u2 + 4*u2^2 - 3) of Multivariate Polynomial Ring in t1, t2, u1, u2, t over Number Field in sqrt3 with defining polynomial x^2 - 3] The ideal is the union of two rational conjugate curves. -- 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 URL: http://www.sagemath.org
