On Wed, Apr 29, 2009 at 10:41 AM, William Stein <wst...@gmail.com> wrote: > > On Wed, Apr 29, 2009 at 10:18 AM, John H Palmieri > <jhpalmier...@gmail.com> wrote: >> >> On Apr 29, 9:51 am, mark mcclure <mcmcc...@unca.edu> wrote: >>> >>> On the other hand, I'll happily go on record as saying that I find >>> Wolfram's explanation of "Why You Do Not Usually Need to Know >>> about Internals" personally offensive. You can read that >>> here:http://reference.wolfram.com/mathematica/tutorial/WhyYouDoNotUsuallyN... >>> >>> The funny thing about that statement is that no one who believes >>> it could possibly be inquisitive enough to be employed in a >>> technical position at Wolfram in the first place. I honestly >>> assume that virtually nobody there believes it. >> >> One interesting thing from this page, though: >> >> In[7]:= N[Sin[10^50], 20] >> Out[7]= -0.78967... (I can't copy and paste from that page, but this >> is how the number starts) >> In[8] := Sin[10.^50] >> Out[8] := 0.669369 >> >> Sage doesn't get the right answer here (assuming that -0.78967... is >> the right answer): >> >> sage: sin(10^50).n >> (10) >> 0.74 >> sage: sin(10^50).n >> (20) >> 0.82842 >> sage: sin(10^50).n >> (40) >> -0.052373001636 >> sage: sin(10^50).n >> (80) >> 0.90620599081868764998830 >> sage: sin >> (10.^50) >> -0.480500143493759 >> > > The Sage implementation of numerical_approx currently (and correctly) > simply does all the arithmetic in the expression tree using the given > bits of precision for the leaf nodes, and by that definition the above > output by Sage is correct. I thought that I had clearly documented > this in the numerical_approx docstring, but I haven't. > > I would not be opposed to somebody rewriting numerical_approx to > instead use interval arithmetic, and hence given a proven number of > correct digits of precision of output, which would fix the above > problem. This should be easy given how good Cwitty's RIF and CIF is > now.
I myself prefer if .n(20) returns the 20 correct digits. sage: sin(10^50).n(10) 0.74 sage: from sympy import sin sage: sin(10^50).n(10) -0.7896724934 sage: sin(10^50).n(20) -0.78967249342931008271 O. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
