[Axiom-developer] Re: Sage and Special Functions??

[TimDaly]

in the first paragraph s/chunck/chunk/
page 3 s/fucntions/functions/


The DLMF copyright section states:

The material on this site is copyrighted ((c)) by NIST and/or the
respective authors, and subject to the usual copyright restrictions.

Does that imply DLMF can be used by open source programs?
If the copyrights remain with the authors rather than with NIST
it might not be possible to use the electronic form without
permission.

Are you planning to show implementations of the functions
using multiple systems (ala CATS) or using a sage+single
underlying system?

I did validation and verification of solutions to a couple of the
tables of integrals presented by the early edition of Spiegel's
mathematical handbook using Axiom. Several of the more
complex functions turned out to be in error. Curiously they
were dropped from the latest Schaums version. The validation
of the tables took a significant amount of time and effort
because the computer solution and the hand solution often
differed wildly. Proving they were equal (or not) took a fair amount
of manipulation.

Another particularly challenging aspect is the handling of the
provisos. That is, the clauses like
  1/x provided x <>  0
and their propagation, manipulation, and combination  thru the
validation of the computer proof.

That said, I hope that you get such a proposal funded. I think it
is vitally important to get some reference version of computational
mathematics in electronic form. A common set of standards (e.g.
branch cuts), whether -7 is prime, etc. needs to be established
and agreed upon. I suspect that the effort to try to validate DLMF
will highlight these fundamental issues since they are almost
certainly not constant in the DLMF.

Tim

On Dec 14, 8:29 pm, "William Stein" <address@hidden> wrote:
> Hi,
>
> This is a (very short!) Sage proposal that we're putting together for
> NSF.   It's
> getting close to being finished.  Any comments, including on typos are 
> welcome:
>
>    http://wstein.org/grants/2007-cdi-reinhardt/
>
> Thanks!
>
>  -- William
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org