I agree with Simon, although finding a nice expression like sqrt(2)+3^(1/3) can be very costly deppending on how the algebraic number was constructed. Anyways we could have such an expression for the cases where it is evident from the number construction.
Related to that, i think the current 17? digits are way too much for a visually nice representation. I would prefear to see 1.4142... than 1.414213562373095? inside an expression. El lunes, 13 de julio de 2015, 19:15:40 (UTC+2), Simon King escribió: > > Hi! > > On 2015-07-13, Nathann Cohen <nathan...@gmail.com <javascript:>> 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. > > 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+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.
