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RE: [Axiom-developer] Exact Number Domain

From: Bertfried Fauser
Subject: RE: [Axiom-developer] Exact Number Domain
Date: Thu, 21 Sep 2006 15:54:28 +0200 (CEST)

Dear Tim,

a very cute question indeed. The approach proposed by Bill Page is quite
interesting in that way, that the completition of a number field can be
done in different ways using ideas from topos theory. I don't even see how
to manage the wealth of possibilities here. However what about truncating
computations in a sort of p-adic way along with a stream like

To pick up Ralf Hemmeke's example, if you want to represent pi, you might
want it to expand in powers of some prime number, eg 3

pi= a1*3^1+a0*3^0+ .....

a stram like object could represent the n-th power truncated version of
such expansions. The inductive limit of these objects would actually (but
infinitely) represent the number.

Over all it seems to be very complicated and I would not expect such a
representation to be helpful for numeric calculations (speedwise) at all.


% PD Dr Bertfried Fauser
%     Institution: Max Planck Institute for Math, Leipzig 
%   Privat Docent: University of Konstanz, Phys Dept 
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