On Tuesday, March 10, 2015 at 9:04:14 AM UTC-7, Dima Pasechnik wrote: > > On 2015-03-10, M M <mirette...@gmail.com <javascript:>> wrote: > > I get different results from Sage when I try to get a numerical > > approximation for an expression and if I use evaluate a preparse of the > > string. I get different results on different versions of sage as well. > Here > > are samples: > > Integration is done by Maxima, and it is a bloody mess; e.g. >
It is, but I suspect that's not the cause here. I think it's just numerical instability. sage: sage: integral(x/(x^3-x+1), x, 1, 2).n(100) 0.56579991645642210974671290281 sage: sage: integral(x/(x^3-x+1), x, 1, 2).simplify_full().n(100) 0.56579991645643344322713389324 i.e., approximating the exact result just needs some more digits to be accurate. The default "n" only specifies the precision *used* using evaluation, so the error in the numerical approximation isn't a priori controlled and depends on the particular evaluation scheme chosen for the expression (expect that to be just "left to right evaluate" as you would do on a calculator). Specifying more digits to work with should give a better result for well-behaved expressions. In principle, using the RealIntervalField you should get guaranteed digits: sage: I=integral(x/(x^3-x+1), x, 1, 2) sage: RealIntervalField(53)(I) [-infinity .. +infinity] sage: RealIntervalField(60)(I) 1.? sage: RealIntervalField(70)(I) 0.566? sage: RealIntervalField(90)(I) 0.565799917? Needless to say, probably numerical integration is the better way of getting a numerical approximation. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
