Talk:Zech's logarithm

Untitled 2004 comment
I foound the literature on this a bit confusing, last time I looked. But I would have expect 'logarithm' to mean the inverse of the mapping indicated. That is, the log map would be


 * polynomial in &alpha; (reduced) &rarr; n

where n is the power you need to take ...

Charles Matthews 21:54, 7 Dec 2004 (UTC)


 * When discussing Zech's logarithms in particular you start with a lot of high power polynomials and then the set of logarithms is the set of sums of reduced powers. So I believe the power-reducing nature lead to the naming.  That being said, I've only seen Zech's logarithms described in lecture notes and mentioned referentially in a couple of papers, and I'm not even sure where they were first introduced.  I tried many different searches on search engines to try to figure out who Zech is and ultimately posted here, to no avail.  So, if you can dig up some more info on the subject perhaps you can set things straight (if they aren't already). CryptoDerk 23:46, Dec 7, 2004 (UTC)

Who is Zech? If possible, the article should say who this concept is named after. Michael Hardy 22:11, 22 July 2005 (UTC)

Addition in a finite field
Zech's logarithms are used to perform addition in a finite field, not to reduce a high degree polynomial to one of a lesser degree. The description given in the article seems totally spurious to me. Bekant 10:06, 11 December 2006 (UTC)


 * I agree. I've made a large revision to the article to correct this problem. Hurkyl (talk) 18:51, 1 June 2012 (UTC)

The title should be Zech logarithms since one needs to refer to Zech himself. . There IS literature on Zech. May be hard to find. See [Lam and McKay] Collected algorithms A.C.M. Nov 1973 No. 469 for computing them. John McKay24.200.155.110 (talk) 01:01, 7 February 2009 (UTC)

Two further references are John H. Conway (MR 0237467) (1968) and in Fletcher, Miller, Rosenhead Mathematical Tables. The purpose of the Zech logarithm is to do rational arithmetic (originally over the reals I believe). The index set includes {-\infinity} to produce a consistent notation. The name \v{Z}ech is common but one should be able to find more biographical details. —Preceding unsigned comment added by 66.130.86.141 (talk) 22:26, 25 August 2009 (UTC)