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## RE: [Axiom-developer] Exact Number Domain

**From**: |
Page, Bill |

**Subject**: |
RE: [Axiom-developer] Exact Number Domain |

**Date**: |
Thu, 21 Sep 2006 11:20:57 -0400 |

Bertfried,
On Thursday, September 21, 2006 9:54 AM you wrote:
>* ... *
>* 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.*
>* *
For a practical implementation see the RealLib Project:
http://www.brics.dk/~barnie/RealLib
by Branimir Lambov
http://www.brics.dk/~barnie/
and especially his paper:
A two-layer approach to the computability and complexity of
real functions
http://www.brics.dk/~barnie/RealPaper.pdf
The Sage developers are working on an interface to RealLib
http://sage-wiki.axiom-developer.org/RealLib3
http://sage-wiki.axiom-developer.org/DidierDeshommes
http://modular.math.washington.edu/sage/packages/optional
I would like to be able to do this in Axiom.
Regards,
Bill Page.