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

[William Stein]

Tim,

Many thanks for your thoughts about the proposal!

On Dec 14, 2007 6:46 PM, TimDaly <address@hidden> wrote:
>
> 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.

We are actually in close communication with NIST, so no matter
what there wouldn't be any use of their materials without their permissions.
Reinhardt has been deeply involved in the DLMF project from the start
10 years ago...

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

Multiple systems.

> 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.

We'll definitely consult with you if we get funded!


> 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.

Thanks!

William