On Fri, Oct 23, 2020 at 8:38 AM Kwankyu Lee <ekwan...@gmail.com> wrote:
> Currently working on that (see http://fredrikj.net/calcium/ and >> http://fredrikj.net/blog/2020/09/benchmarking-exact-dft-computation/). >> > > Looks great! The standard question is then: do you think your library fits > for the throne of RealField and could rule peacefully other "real fields" > of Sage? > I'm not sure if there can be such a field. For exact use, perhaps. In general, Calcium will be much slower than RR or RBF if you just want numerical values. It will be terrible for plotting, for example. In any case, there would probably not be a unique "Calcium field" -- you would be able to create different fields with different internal simplification behavior (absolute vs relative algebraic numbers, expanding complex exponentials into real and imaginary parts, etc.). The other main alternative that I can see would be lightweight symbolic expression DAGs for "lazy computable numbers" (something I'm also interested in). That would give you relatively cheap numerical evaluation and the opportunity to fall back to exact simplification for deciding predicates. The problem is when expressions start building up without simplifying, say (((((x+1)-1)+1)-1)...). Again, no silver bullet. Fredrik -- 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/CAJdUXTL3N_9wOhBHY77a%2BMKo-o98eZkw1OaV9vG9bmeCnTZgFQ%40mail.gmail.com.
