Indeed, Magma's AlgebraicallyClosedField is not embedded into CC; it also has no version of AA. And Nils meant what he said about large *finite* fields being used to keep track. I find QQbar easier to use -- but when Magma's AlgebraicallyClosedField was first developed it was a really original idea and state of the art, there is at least one paper describing how it works (Nils, I cannot remember the author -- is it Allan Steele?).
John On Wed, 4 Sept 2024 at 07:26, Kwankyu Lee <ekwan...@gmail.com> wrote: > > > On Wednesday, September 4, 2024 at 1:41:30 PM UTC+9 Nils Bruin wrote: > > .. Indeed, Magma's algebraic closure of QQ does not use an embedding into > CC but instead tracks conjugate labels using a large finite field. > > > You mean a large number field? > > From QQbar doc: > > As with many other implementations of the algebraic numbers, we try > hard to avoid computing a number field and working in the number > field; instead, we use floating-point interval arithmetic whenever > possible (basically whenever we need to prove non-equalities), and > resort to symbolic computation only as needed (basically to prove > equalities). > > Thus QQbar assumes a complex embedding from the ground, perhaps unlike > Magma. > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-devel" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-devel/s81ieq2vpVo/unsubscribe. > To unsubscribe from this group and all its topics, 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/afb486c5-7efb-4b6c-94f9-dc230a1108fen%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/afb486c5-7efb-4b6c-94f9-dc230a1108fen%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAD0p0K6uPrKHZ8h6pF8syrR%2BBffwyQHpOKY44V-6-%2B7a9SXKRg%40mail.gmail.com.
