RE: [Axiom-developer] Exact Number Domain

[Page, Bill]

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.