On Wed, Mar 11, 2015 at 2:07 PM, Dima Pasechnik <[email protected]> wrote: > > > On Wednesday, 11 March 2015 16:44:32 UTC, William wrote: >> >> On Wed, Mar 11, 2015 at 9:35 AM, Dima Pasechnik <[email protected]> wrote: >> > On 2015-03-11, Nils Bruin <[email protected]> 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 >> >> For what it's worth, here's how to mostly do that Axiom session, but >> in a SageMathCloud worksheet... >> >> >> https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-03-11-093745-axiom-integral.sagews > > > here is a better version (all the stuff works): > https://cloud.sagemath.com/projects/bb6fd6ca-6304-4dda-be31-bd2dd5eb3d98/files/support/2015-03-11-093745-axiom-integral.sagews >
Thanks! I replaced mine by yours. William > Dima > >> >> >> William >> >> > >> >> 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 [email protected]. >> > To post to this group, send email to [email protected]. >> > Visit this group at http://groups.google.com/group/sage-support. >> > For more options, visit https://groups.google.com/d/optout. >> >> >> >> -- >> William (http://wstein.org) > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- William (http://wstein.org) -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
