> > Any number cos(rational x pi) is algebraic and equality of algebraic > numbers is decidable. Moreover, it is not because something is > undecidable that Sage should return a wrong answer. In that case, it > would be good to have a third party in comparison (either returning > Unknown or raising exception). >
Yes, in this particular case, you are right (and in fact, you can check for equality of those two elements if you convert them to AA), but in general, determining if a real number given by a symbollic expression involving e,pi, rationals, roots, logarithms... is zero or not is not doable. So, no matter how you implement this new field of real numbers, it will have "broken" comparison. But maybe you are right about the "Unknown" answer. Although it might cause some other problems: you cannot know if you can take the inverse, or the logarithm of a real numbers. We could have then something like the NaN problem: an "unknown" thing that contaminates everything it touches. I don't really think we can find a good solution. -- 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.
