Thanks. It looks like the error occurs in integralbasis.lib. It's last version data is fairly recent, so the file may be under active maintenance.
sagemath has grown enough divisor machinery that it can probably compute a conic model of a genus 0 curve, which would be more standard to try and parametrize. Alternatively, with point searching methods (which may not be implemented comprehensively in sage) one could perhaps find a degree 1 place on the genus 0 curve directly and use Riemann-Roch machinery to compute the parametrization without going through a conic model. So, if this functionality in integralbasis.lib in singular is not comprensive enough, it may be a doable project to do it in sage directly now. Note that algcurves is sometimes a little too eager in finding a parametrization: it might just adjoin a point over an extension to get a parametrization (also when that's not required). If you need the parametrization for arithmetic applications, that's a problem. But indeed, Mark van Hoeij did an amazing job on that maple package! On Wednesday 17 April 2024 at 08:12:35 UTC-7 ypf...@googlemail.com wrote: The following code raises a SingularError in SageMath version 10.4.beta3 (with system singular enabled), and the same at https://sagecell.sagemath.org/ : R.<x, y> = QQ[] f = -2*x^2*y^2 - x^3 - x^2*y + x*y^2 + y^3 + 2*x^2 + 2*y^2 - 2 C = Curve(f) assert C.genus() == 0 print(C.rational_parameterization()) The polynomial f is absolutely irreducible, and the given curve is rationally parametrized e.g. by (x, y) = (1/2*(t^3+t^2+t-1)/t^2, 1/2/t*(t^3+t^2-t+1)). -- Peter Mueller PS: To me as a naive end user, it looks like Singular has had recurring problems with basic things for many years that have worked smoothly in systems like Maple (and its algcurves package) for more than 30 years. -- 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+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/4c71470a-aba1-4808-b5d1-a00118edc661n%40googlegroups.com.
