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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
reprsentations?
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.
ciao
BF.
% PD Dr Bertfried Fauser
% Institution: Max Planck Institute for Math, Leipzig
<http://www.mis.mpg.de>
% Privat Docent: University of Konstanz, Phys Dept
<http://www.uni-konstanz.de>
% contact|->URL : http://clifford.physik.uni-konstanz.de/~fauser/
% Phone : Leipzig +49 341 9959 735 Konstanz +49 7531 693491