On Monday, October 7, 2013 3:37:22 PM UTC-7, Peter Bruin wrote: > > > I think a case could be made for having two versions of the current RR: > one like the current one (more like a model of the extended real line) and > one where overflow or division by zero raises an exception instead of > returning +/- infinity (more like a model of the usual real numbers). I > can think of at least two reasons for having the latter: > > (1) it has a better field-like behaviour; this will always be imperfect > due to rounding errors, but not having infinity avoids many violations of > the field axioms; > > (2) it interacts better with the complex numbers; R embeds into C and this > extends to an identification of R + R*i with C, but the current > implementation acts as if this is true with R replaced by the extended real > line. This leads to the undesirable fact that Sage's CC now contains many > different infinities (namely, all a + b*i where at least one of a, b is > infinite; note that this is completely different from e.g. having all > r*exp(i*t) with r = Infinity and t in [0, 2*pi), as well as from the fact > that in the usual compactification of C (the Riemann sphere) there is only > one point at infinity). The question that Greg originally posed (why > imag(CC(infinity)) = 0 instead of undefined) stems from this. > > In my experience it often seems like it often seems desirable to have a "field" R that tries to behave a little closer to being a field, but upon closer inspection, the nasty implementation details of floating point numbers will require for any somewhat serious application a special treatment anyway.
Thus, before embarking on the laborious task of trying to program such a field, I recommend you first try to find a non-trivial scenario that would genuinely benefit from this work. I suspect that when someone stumbles into this unexpected infinity problem, then removal of this problem would just let the person stumble into a more fundamental difference between RR and the real numbers before getting any worthwhile results. Doing a lot of work just for cosmetics might not be worth the investment. -- 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/groups/opt_out.
