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RE: [Axiom-developer] SuchThat

From: Bill Page
Subject: RE: [Axiom-developer] SuchThat
Date: Mon, 11 Oct 2004 14:09:01 -0400

On Monday, October 11, 2004 2:02 PM Tim Daly address@hidden
> My thesis topic was on "Provisos". These are fundamental
> mathematical constraints on the domain and range of
> functions. Every computation should produce them, carry
> them, and compute the interaction between them.

Yes. I think Maple and Mathematica both are moving in this
direction, albiet not with the notion of a Type. Instead they
are tending to return more results as 'piecewise' conditionals.

> I do have some documents moldering in the history pile but
> it's probably better if I write the SuchThat docs from
> scratch. In fact, there are several improvements I could make.

Ok everyone, let's encourage Tim to do this!

> ... 
> The interaction between provisos, the domains, and the elements
> of the domains is quite complex and absolutely fundamental to
> computational mathematics. I never really published anything
> about my investigations of the subject.

Now would be a good time to do it - looks of space available
on MathAction :)

> I understand how to compute with them and have some
> interesting research results.  I even have a primitive
> implementation somewhere on a floppy disk (which I probably
> can't read anymore). Axiom clearly needs to develop the
> proviso capability but that's a real research issue and
> the NSF no longer supports that kind of research. Perhaps
> one of Buchberger, Bronstein, or Davenport's students will
> take up the torch.

Ok, we have got advertise!

> What sparked your interest in SuchThat?

I was looking for a non-trivial example of 'numeric' versus
'symbolic' mathematics to discuss at the AMS meeting this
weekend. Symbolic eigenvalue computations have been of
interest to me before. So I loooked at section 8.4 of the
AXIOM book (page 241 in the original book). When I tried
the example eq. (1) I found that it produced a result
slightly different than the book.

The 'extra' result was in the form of a SuchThat type.

So in the end, this did not (quite) turn out to be the
numeric computational result that I had expected!

Bill Page.

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