¿¡Qué estás diciendo!?
On Monday, July 13, 2015 at 9:14:51 PM UTC+2, Dima Pasechnik wrote: > > > > On Monday, 13 July 2015 18:49:48 UTC+1, William wrote: >> >> On Mon, Jul 13, 2015 at 10:15 AM, Simon King <simon...@uni-jena.de> >> wrote: >> > Hi! >> > >> > On 2015-07-13, Nathann Cohen <nathan...@gmail.com> wrote: >> >> sage: sqrt(2) # a symbolic ring element >> >> sqrt(2) >> >> sage: QQbar(sqrt(2)) # an algebraic value >> >> 1.414213562373095? >> >> >> >> It is true that this final '?' sounds more like a '...', as if some >> additional >> >> digits were hidden in a value stored as a float/double. Yet it is >> exact. >> >> >> >> How could we replace it? Ideally, that would be a 'sqrt(2)' but can we >> always >> >> provide such a representation cheaply? Could we display it as >> 'sqrt(2)' at least >> >> when it is free to do so? >> > >> > The elements of QQbar are the solutions of algebraic equations. As you >> > probably know, the solutions of algebraic equations of degree > 4 can, >> in >> > general, not be expressed that nicely. But it seems like an appealing >> > idea to show a nice expression for algebraic numbers of degree up to 4. >> > >> >> If we cannot get rid totally of this numerical representation, what >> would you >> >> think of replacing this '?' by a 'alg', which would be (slightly) more >> >> informative, e.g.: >> > >> > 1.4142134... looks exact to me: "..." seems to suggest that Sage knows >> all >> > (potentially infinitely many) digits but can't show them all, whereas >> "?" seems >> > to suggest that the last shown digit is questionable (i.e., subject to >> rounding >> > errors), i.e., "?" seems to suggest that Sage doesn't know the exact >> value. >> >> Yes. Also, with interval arithmetic, that is precisely what it means: >> >> sage: RealIntervalField(53)(sqrt(2)) >> 1.414213562373095? >> sage: QQbar(sqrt(2)) >> 1.414213562373095? >> >> It's certainly not good that the above two print in the same way. >> The (mysterious [1]) person who made those design choices -- Carl >> Witty -- isn't contributing anymore, or I'd ask his opinion. >> > > As we now allow unicode, we can probably find a better character than '?'. > Say ⇘, or ↴, or even ¿. > > > >> >> >> [1] http://stackoverflow.com/users/684532/carl-witty >> >> > >> > So, I'd prefer to display elements of QQbar as floating point numbers >> > (what default precision?), always rounded DOWN to the last digit that >> is >> > displayed, and followed by "..." (not "?") unless the displayed value >> is >> > exact. So, what is displayed is an initial part of the potentially >> > infinite sequence of digits. >> > >> > Best regards, >> > Simon >> > >> > >> > -- >> > 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 post to this group, send email to sage-...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sage-devel. >> > For more options, visit https://groups.google.com/d/optout. >> >> >> >> -- >> William (http://wstein.org) >> > -- 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 post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
