On Dec 12, 11:50 am, "David Joyner" <[EMAIL PROTECTED]> wrote:
> On Dec 12, 2007 3:20 AM, pgdoyle <[EMAIL PROTECTED]> wrote:
>
>
>
>
>
> > The description of Bessel_K functions in the Sage Cookbook is
> > confusing about the order of the arguments.
> >http://sagemath.org/doc/html/const/node96.html
> > Here's what it says:
>
> > >Here's an example using SAGE's interface to pari's special functions.
>
> > >sage: pari('2+I').besselk(3)
> > >0.04559077184075505871203211094 + 0.02891929465820812820828883526*I #
> > >32-bit
> > >0.045590771840755058712032110938791854704 +
> > >0.028919294658208128208288835257608789842*I # 64-bit
> > >sage: pari('2').besselk(3) # random
> > >0.061510458471742038
>
> > >The last command can also be executed using the SAGE command
>
> > >sage: bessel_K(3,2)
> > >0.647385390948634
> > >sage: bessel_K(3,2,100)
> > >0.64738539094863415315923557097
>
> > But in fact the answer 0.061510458471742038 is correct, not random:
>
> "Random" here doesn't mean what you think. All SAGE docs are
> tested for correctness by an automatic testing program written by
> William Stein. Since it is run on different machines, and different
> machines give
We really need to kill all of those and add "..." to account for the
imprecision caused by different CPUs/operating systems/compilers. That
was we can still catch obviously incorrect results while ignoring
numerical noise. I will open a ticket for that shortly and grep
through the tree for all occurrences of "#random". We might not kill
all of them, but we should be able to eliminate the vast majority of
them.
Cheers,
Michael
> slightly different round-off errors at the last few places, those last
> few places are "random". Here "# random" is a key word that indicates
> to the tester that the last few places are possibly different.
>
>
>
> > sage: bessel_K(2,3)
> > 0.0615104584717420
> > sage: bessel_K(2,3,100)
> > 0.061510458471742037656820071453
>
> > I believe the confusion resulted because in earlier versions of Sage
> > the order of arguments to
> > bessel_K was backwards. For instance in Sage 2.8.5:
>
> > sage: bessel_K(2,3)
> > 0.647385390948634 # WRONG!!!
>
> > Cheers,
>
> > Peter
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