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Re: [Axiom-developer] SuchThat

From: root
Subject: Re: [Axiom-developer] SuchThat
Date: Mon, 11 Oct 2004 14:01:47 -0400

Ah, would that I did have my PhD thesis online. Since I don't have a
PhD (after 11 years :-) ) it's unlikely to ever be online.  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. SuchThat
is essentially a "storage" mechanism to wrap results with provisos.
Axiom output should be qualified not just by type but also with the
corresponding provisos. You see this all the time in math textbooks.

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.

I didn't write the domains that use it. That was Manuel Bronstein.
He and I had several discussions about the subject.

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. 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.

What sparked your interest in SuchThat?


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