Talk:Damm algorithm

This article was nominated for deletion on 22 December 2012 (UTC). The result of the discussion was keep.

Contested PROD

This article was proposed for deletion with rationale This article presents original research, which is not permitted by our policies. Unless you can add reliable and independent sources, which attest to the subject's notability, your article will be deleted. Thank you for your understanding. This seems wrong and I have contested the PROD since the article does indeed cite reliable sources, namely a peer-reviewed academic journal, and our policy on original research is a prohibition on editors directly publishing their own unsupported work in an article -- it does not mean that we cannot report research published in independent reliable sources, which this appears to do. Deltahedron (talk) 07:33, 22 December 2012 (UTC)[reply]

totally anti-symmetric

What does "totally anti-symmetric" mean in the context of this article? What other wikipedia article talks about the kind of "anti-symmetric" and "totally anti-symmetric" alluded to here?

At first I thought maybe that phrase should link to antisymmetric matrix, but the table given in this article doesn't seem to meet the definition given in that article. --DavidCary (talk) 17:29, 30 May 2014 (UTC)[reply]

The references define this. Example:

A quasigroup

(Q,*)

is called totally anti-symmetric if

(c * x)* y =(c * y)* x \Rightarrow x = y

and

x * y = y * x \Rightarrow x = y

.

Good catch, though, this article should define this. —Quondum 20:32, 30 May 2014 (UTC)[reply]

Dear reader,

I suspect this idea of a "totally anti-symmetric quasigroup" may be more widely useful than this one particular algorithm, and so should be mentioned -- or perhaps already is mentioned, using some other name -- in other Wikipedia articles.

If you know some other name for this idea, or some other Wikipedia article where it is relevant, please mention it here or in the article.

Thank you, Quondum, for adding that definition to the article. --DavidCary (talk) 19:57, 8 June 2014 (UTC)[reply]

Algorithm?

I can't find description of algorithm that would match the one given in this article and used in example. References define that an m-digit sequence $d_{m}d_{m-1}d_{m-2}\ldots d_{1}$ with a check digit $d_{0}$ shall satisfy $((\ldots ((d_{m}*d_{m-1})*d_{m-2})*\ldots )*d_{1})*d_{0}=0$ where $d_{m},\ldots ,d_{0}\in Q$ and $(Q,*)$ is a totally anti-symmetric quasigroup. The step-by-step description of algorithm in this article uses interim digit with fixed initial value of 0 which means that a slightly different equation is used, i.e. $((\ldots ((0*d_{m})*d_{m-1})*\ldots )*d_{1})*d_{0}=0$ . I don't see any problem with this itself, because it's the same as computing with tacitly leading zero prefix, so all the properties should still hold. However, the example then uses a quasigroup which not totally anti-symmetric, because, for example 2 * 5 = 5 * 2. It is only weak totally anti-symmetric. With weak totally anti-symmetric quasigroup, check digit calculated using the original formula as given in references would fail to detect adjacent transpositions, e.g. both 257 and 527 would have a correct check digit. The scheme, nevertheless, appears to work exactly because of the fixed initial 0. The recent edit added possible justification for this stating that for this modified equation only a weak totally anti-symmetric quasigroup with additional property of $x * x = 0$ is needed. I can easily see that other statements (definition of weak totally anti-symmetric, and that existence of weak of given order implies existence of totally anti-symmetric and that one can be constructed from another with appropriate permutation) are present in the referenced dissertation (and they are restated later in English in ScienceDirect article, referenced as well), but I can't find anything about using fixed prefix. Did I miss something or are we missing some important references? — mwgamera (talk) 19:11, 29 June 2014 (UTC)[reply]