On Wed, Oct 21, 2020 at 11:56 AM Vincent Delecroix <20100.delecr...@gmail.com> wrote: > > Thanks Dima. To my mind, the thread has shown that some > questions have to be settled first. I am trying to gather > the relevant comments, ignoring completely the genuine > real field (which is one motivation but not the purpose > of the ticket). This is a personal interpretation of what > happened. Feel free to correct me. > > > One proposal consisted to discard the "field" terminology > (J. Cremona, S. Lelievre) > > "Real Floating-Point Numbers with x bits of precision" > > or > > "Real Floats with x bits of precision" > > These proposals describe somehow accurately the set but > completely discard the importance of the underlying algebraic > structure. Here was proposed "pseudo-field" and "quasi-field" > (M. Jung). I think that both of these names are bad because > "pseudo" and "quasi" are used in many mathematical concepts > but here would refer to non standard terminology. I proposed > "numerical field" which is also an invented concept > but has the advantage to fit well with the "is_exact()" > method already present on some parents. > > So question number 1: > > 1. Should we drop any reference to the algebraic structure > for numerical approximations? > (J. Cremona, S. Lelievre) > > 2. Should we have a common adjective for all approximations? > Which one "pseudo", "quasi", "numerical", "nonexact", ...? > Should we differentiate various kind of approximations (eg > floating-point vs balls/intervals, various flavors of p-adics)?
Unfortunately nobody has written an adapted to mathematicians version of the classic "What Every Computer Scientist Should Know About Floating-Point Arithmetic", by David Goldberg :-) I gather that (ignoring NaNs and +/-infinities) the addition and multiplication are commutative here, but not associative, and not distributive. Moreover none of these is a quasigroup. Looks like not enough to coordinatise a projective plane. :-) As far as I am concerned, putting Field in "" will do, to raise the awareness that it's not a field. > > Parallel to this question is the "categorical" version > > 1'. Should RealField simply be a member of the Sets() category? > > 2'. Should we develop some categorical machinery to differentiate > exact fields from approximate fields? Which one? > > Best > Vincent > > -- > 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/b4e612ec-e4cc-23ac-25c3-e409b93102df%40gmail.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 on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq33HBavwuerRN9nrNg5UVGsnuTCxdWe65N37WXzZpTd2Q%40mail.gmail.com.
