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[Axiom-developer] Provisos generalize intervals.

From: root
Subject: [Axiom-developer] Provisos generalize intervals.
Date: Sun, 12 Mar 2006 14:55:41 -0500


I've taken a step back and am reviewing Moore's book again in 
preparation for a deeper reading of your book.

It seems that the fundamental difference between the work that you and
Moore have pursued and the work I've been doing lies in the definition
of the endpoints of the intervals. Correct me if I'm wrong but it appears
that the endpoints of your intervals are all ordered numbers.

The endpoints of the intervals I'm looking at for provisos are not
numbers and, in most cases, are ordered by explicit constraints. My
work assumes that the endpoints can be pretty much anything, complex
numbers, vectors, symbols, polynomials, etc.

Thus I raise the question of intervals whose endpoints specify the 
inner and outer radius of two bounding surfaces. For example, the
inner and outer radius of two spheres or the upper and lower bounding
surfaces of a function during integration. This is useful symbolically
since if I can show that the two bounding surfaces tends to zero I can
conclude that the integral tends to zero even if the actual function
is too complex to compute.

Provisos generalize intervals.


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