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.
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.
