On Fri, Dec 13, 2024 at 3:04 PM 'Martin R' via sage-devel <sage-devel@googlegroups.com> wrote: > > Well, only if the ring of integers is just a subset of K. > > Essentially, that means that we cannot really compute with O - eg., compute > the gcd of two polynomials over O. polynomials over rings are tricky.
sage: P.<t>=O[] sage: c*t^2-2 (2*a + 4)*t^2 - 2 sage: (c*t^2-2).gcd(2*t+2) --------------------------------------------------------------------------- KeyError Traceback (most recent call last) ... NotImplementedError: Maximal Order generated by a in Number Field in a with defining polynomial x^2 - 3 does not provide a gcd implementation for univariate polynomials > > Martin > On Friday, 13 December 2024 at 21:07:50 UTC+1 dim...@gmail.com wrote: >> >> On Fri, Dec 13, 2024 at 1:38 PM 'Martin R' via sage-devel >> <sage-...@googlegroups.com> wrote: >> > >> > This does not look right, does it? >> > >> > sage: K.<a> = NumberField(x^2-3) >> > sage: O = K.ring_of_integers() >> > sage: c = O(2*a + 4) >> > sage: isinstance(O, Field) >> > False >> > sage: isinstance(c, FieldElement) >> > True >> >> c is an element of K, by construction. >> >> > >> > Martin >> > On Thursday, 12 December 2024 at 23:35:40 UTC+1 Nils Bruin wrote: >> >> >> >> On Thursday, 12 December 2024 at 12:39:46 UTC-8 axio...@yahoo.de wrote: >> >> >> >> Great, thank you! This - almost - provides a performance test: >> >> >> >> >> >> Yes, you would need to convince sage that this is indeed a euclidean ring >> >> (I think for this one the usual norm actually is a euclidean norm). I >> >> don't think that simply being a UFD will do it for you. >> > >> > -- >> > 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+...@googlegroups.com. >> > To view this discussion visit >> > https://groups.google.com/d/msgid/sage-devel/35043e34-7915-4c54-9c74-29521c3762e1n%40googlegroups.com. > > -- > 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 visit > https://groups.google.com/d/msgid/sage-devel/a8ab4860-50d3-49e8-8e9c-896bc41e350en%40googlegroups.com. -- 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 visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq3Drb%3DGbPJg79ofC2ib_xRYfEWUY-T-asKO0c_Nco27ow%40mail.gmail.com.
