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

[Martin Rubey]

Changes http://page.axiom-developer.org/zope/mathaction/AxiomMail/diff
--
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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