[om] Specfun CD's (was: library)

[J H Davenport]

On Thu, 9 Aug 2001, Bruce Miller wrote:
> Two points are explicitly raised:
>  1) Multiple CDs with short function names (eg. Bessel:J)
>    vs.
>     A single CD with longer names (eg. BesselJ)
>
>  2) Currying (eg. \BesselJ_\nu)
>    vs.
>     not (eg. forall z: \BesselJ_\nu(z)).
>
> And an implied one:
>  3) deciding on `standard' branch cuts.
>
> *** Some questions:
>
> Point 1: What is the impact of such a choice?
> Clearly, a finer granularity might make it
> easier to revise (sub)CDs in the future, at the
> cost of having more CDs to cope with.
> Are there other issues?
Yes, I think there, as regards the name of the symbol (assuming that, in
general, one doesn't beileve that
<OMS name="E" cd="specfun"/> is acceptable): BesselJ or J.
BesselJ is slightly easier for the algebra system whose name we have
chosen to use; J is easier for (any) rendered.
>
> Point 2: It's not clear from the example (on page 21)
> how the CD itself depends on this choice, as opposed
> to the OpenMath core or the corresponding STS.
>
> Perhaps I need to re-read the OM specs, but if F is
> intended for 2 arguments, is
>   <OMA><OMS name="F"/><OMV name="x"/></OMA>
> not implicitly curried?  Or an error?
I believe it currently to be an error, and it is certainly aviolation of
STS. I believe again that one has to use lamba explcitly to build a
functional
> If the latter, can you point to examples of how
> currying is explicitly handled?
Possibly the best is in the current draft of logic3.ocd (currently with
Olga Caprotti for looking at, but I have placed a copy at
http://staff.bath.ac.uk/masjhd/cd/logic3.ocd
with David's HTML version at
http://www.bath.ac.uk/~masjhd/cdfiles/html/extra/logic3.html)
>
> Point 3 is difficult.  Clearly something is needed.
> I have a _definite_ bias, here, but I think that the
> only viable resource for these determinations are
> the Editors & Authors of the DLMF project.
I would agree, with one reservation. When we looked at the paper A=S for
our article
Corless,R.M., Davenport,J.H., Jeffrey,D.J. & Watt,S.M.,
According to Abramowitz and Stegun.
SIGSAM Bulletin 34(2000) 2, pp. 58--65
we found that A+S was not always clear about what took place on the branch
cut itself. One can argue that it doesn't matter numerically (though I
wouldn't) but it clearly matters symbolically.
> However, when I've raised such questions in the past
> the answers have been somewhat ambivalent "Oh, the
> branch cuts are whereever you need them -- use
> analytic continuation"    Perhaps I'm misrepresenting
> thier point-of-view, and the comment really translates
> into "Oh, please dont make me think about that _now_"
> But, it may be difficult...
It is. There are some comments in our paper in AISC 2000:
http://www.apmaths.uwo.ca/~djeffrey/offprints.html
and more in a follow-up article in press - should I post a copy? In
particular, thanks to David Jeffrey, we destroy the "it's a Riemann
surface" point of view as a computational tool.

> *** Some Comments on my submitted CD.
I'll answer these later.
James


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