Re: Announcing cdrskin-0.7.2

["Thomas Schmitt" <scdbackup@gmx.net>]

Hi,

> Why are the two logs added as integers (+) rather than
> as polynumials (^)?

One can prove the theorem

  log(a*b) = log(a) + log(b)

by

  a = x^log(a)
  b = x^log(b)
  a*b = x^log(a)*x^log(b)
      = x*x...x * x*x...x
        \____/    \____/
    log(a) many   log(b) many
 
This breaks down the computation to counting
the number of polynomial multiplications.
That counting happens on natural numbers, not
on polynoms.

I.e. the indice of the power and log table
represent natural numbers, not polynomials.

(The polynomial addition is not an iteration
of increments, and the polynomial multiplication
is not an iteration of polynomial additions.
It is a bit mind twisting indeed if one does
not base a field on an extension of the natural
numbers.)


>  Why do you do % 255 rather than 256?

The periodicity of the x^n enumeration is
256-1 because the 0 does not participate.
Similar as with groups the enumeration
cycles through all other values until it
hits its start value again.


Have a nice day :)

Thomas