Adding to what John said, in case, you're interested in using GRH in your computations.
Methods that have speedups based on conjectures often have a "proof" parameter that is True by default (meaning, it won't use the conjecture) (example: https://doc.sagemath.org/html/en/reference/number_fields/sage/rings/number_field/class_group.html#sage.rings.number_field.class_group.ClassGroup). Setting it False will make use of the speedups. It can also be set globally (https://doc.sagemath.org/html/en/reference/structure/sage/structure/proof/proof.html). On Tuesday, January 12, 2021 at 2:47:25 AM UTC-8 John Cremona wrote: > 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/7e2478bd-6a12-4e4c-b05b-72f15f3889b7n%40googlegroups.com.
