On 2015-03-11, Nils Bruin <nbr...@sfu.ca> wrote: > On Wednesday, March 11, 2015 at 2:46:25 AM UTC-7, Dima Pasechnik wrote: >> >> I tried this integral directly in Maxima, and taking bfloat of it >> outputs nonsense. >> > > I have noticed before that bfloats aren't infectious enough: operations on > bfloats can easily result in a normal "double". I think there are ways to > convince maxima to use bfloats more pervasively. Perhaps a global precision > setting somewhere? > > >> I wish there was a more accessible full implementation of Risch >> algorithm... >> > > This is a rational function, so a first calculus course would already teach > you the relevant part of the Risch algorithm. It's a little more tricky to
Risch, as implemented in Axiom, does not do factorisation (i.e. no partial fractions). In this example at least it produces much nicer looking antiderivative, no huge integers. http://axiom-wiki.newsynthesis.org/ExampleIntegration Dima > get an ostensibly real-valued function as an antiderivative. Anyway, sympy > produces a reasonable-looking antiderivative. > > Interestingly, we have: > > sage: I=integral(x/(x^3-x+1), x, 1, 2, algorithm='sympy') > sage: RIF(I) > TypeError: unable to simplify to a real interval approximation > > The offending subexpression seems to be: > > sage: A=(299838966359964800*69^(5/6)*2^(2/3) - > 11515081166050000*69^(2/3)*2^(1/3)*(25*sqrt(69) + 207)^(1/3) - > 99785894223312000*sqrt(69)*(25*sqrt(69) + 207)^(2/3) + > 2271318237097115625*69^(1/3)*2^(2/3) - > 99785894223312000*69^(1/6)*2^(1/3)*(25*sqrt(69) + 207)^(1/3) - > 497728835949744*9522^(1/3)*(25*sqrt(69) + 207)^(1/3) - > 828883890137982336*(25*sqrt(69) + 207)^(2/3) + > 219331275901257879*276^(1/3))^(QQ(-1)) > sage: RIF(A) > TypeError: unable to simplify to a real interval approximation > > Note the *rational* exponent -1. If that's an integer there's no problem. > Using RealIntervalField(200) has the same problem. Using RealField(...) > seems to work fine. > -- 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.
