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## Re: [Axiom-mail] New to Axiom: Implement 'Balanced' FiniteField ?

**From**: |
Martin Rubey |

**Subject**: |
Re: [Axiom-mail] New to Axiom: Implement 'Balanced' FiniteField ? |

**Date**: |
Wed, 30 Mar 2005 12:13:12 +0200 |

It will roughly work as follows:
)abbrev domain BAL Balanced
Balanced(n:PositiveInteger):Exports == Implementation where
Exports == with
coerce: PrimeField n -> $
coerce: $ -> OutputForm
-- coerce: $ -> PrimeField n
Implementation == add
Rep := Integer
coerce(a: PrimeField n):$ == convert(a)@Integer - n
coerce(x:%):OutputForm == coerce(x)$Rep
-------------------------------------------------------------------------------
If you need explanation, ask for it. (No time right now)
Martin
jim kraai writes:
>* Greetings,*
>* *
>* (I'm more of a pencil-n-paper math guy.)*
>* *
>* A BalancedFiniteField representation of an integer n would be:*
>* the same as FiniteField (base) if n <= floor(n/2)*
>* else base - floor(n/2)*
>* *
>* Examples:*
>* *
>* base of 4 base of 5 *
>* n FF BFF n FF BFF *
>* ---------- ----------*
>* 0 0 0 0 0 0 *
>* 1 1 1 1 1 1 *
>* 2 2 2 2 2 2 *
>* 3 3 -1 3 3 -2 *
>* 4 0 0 4 0 -1 *
>* 5 1 1 5 1 0 *
>* 6 0 0 *
>* *
>* After reading the book chapters on Packages, Categorys, and Domains, I find *
>* that I'm no more clear on which is an effective way to get this output.*
>* *
>* Thanks for any help,*
>* *
>* --jim*
>* *
>* *
>* *
>* *
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