Although Sage uses the pari library for number field computations, and by default the pari library does make assumptions such as the GRH, for speed, Sage's philosophy is that computations should not make any silent assumptions, so that the results obtained from the pari library are certified by Sage. Hence, unless you explicitly ask Sage to assume GRH -- which is often useful as it can speed up computations considerably -- the output will be unconditional.
John Cremona On Tue, 12 Jan 2021 at 10:26, Subramani Muthukrishnan <[email protected]> wrote: > > Dear All, > > I am M. Subramani, working at the Indian Institute of Information Technology > D&M, Chennai. I would like to know whether the following sage code uses GRH > or not. Kindly looking forward to your suggestions/comments. > > sage: x = polygen(QQ) > sage: K.<a,b> = NumberField([x^2+67,x^2+163]) > sage: K.absolute_discriminant() > sage: UK = UnitGroup(K); UK > sage: UK.gens_values() > sage: f = K.factor(47); f > sage: [i.residue_class_degree() for i, _ in f] > sage: g = K.factor(167); g > sage: [i.residue_class_degree() for i, _ in g] > sage: I = K.ideal((102005618195957366438*b - 670427217454663892839)*a + > 859657055484696603731/2*b + 21319906288123697979267/2)^2 > sage: I.small_residue(-113532749239375013512100611401835237324223211*a + > 72788832531850093592405531048689006688627546*b)^(71*35) > > Thanking you in advance, > > with regards, > M. Subramani > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/e76436ab-1d89-4fcb-a3dd-42179da61494n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/CAD0p0K7eQhBVSqOzogxYk3h9S9R9FNod%3DXmSVMSbbaEidDzqHg%40mail.gmail.com.
