Talk:Irish logarithm

Discrete logarithms?
It looks like the A. W. Faber Model 366 uses true discrete logarithms. However, this seems to use an ad-hoc scheme created by Ludgate. It would be interesting to see if (a) Ludgate's system were to correspond to some true discrete logarithm scheme, and, if not, (b) how many non-trivial functions f: Z -> Z, over some reasonable subset of Z, have the discrete-logarithm-like property f(ab) = f(a) + f(b). -- The Anome (talk) 12:21, 13 April 2021 (UTC)


 * (a) Ludgate's system were to correspond to some true discrete logarithm scheme
 * - no, it is not. It's more similar to regular logarithms, I think.
 * (b) how many non-trivial functions f: Z -> Z, over some reasonable subset of Z, have the discrete-logarithm-like property f(ab) = f(a) + f(b).
 * - There are infinitely many such functions. For functions over natural numbers (1,2,3,...) any non-zero linear combination of exponents in the prime factorization of a can be used as f(a). Excluding the value for 0, the Ludgate's system is a specific example of a function in this class: it's exponent of 2 plus seven exponents of 3, etc. I don't think I can find a reference for this, but it looks like a simple arithmetic and therefore may be exempt from the original research policy. Should it be added to the article? Teaktl17 (talk) 17:45, 29 June 2022 (UTC)
 * I've added some material from citable sources that addresses some of this. &mdash; The Anome (talk) 19:01, 2 October 2023 (UTC)

Constraint programming problem
It would be interesting to consider the problem of generating integer pseudo-log functions using constraint programming. It certainly looks from the cited sources that Ludgate's tables naturally arise from a reasonably simple greedy search; I wonder what the shortest practical derivation of such a function would be? &mdash; The Anome (talk) 19:01, 2 October 2023 (UTC)