Talk:Damm algorithm: Difference between revisions

Revision as of 19:11, 29 June 2014

Revision as of 19:15, 29 June 2014

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a slightly different equation is used, i.e. <math>((\ldots((0*d_m)*d_{m-1})*\ldots)*d_1)*d_0 = 0</math>.

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. (AsWith aweak sidetotally noteanti-symmetric Iquasigroup, thinkcheck thisdigit namecalculated isusing the original formula as given in references would fail to detect adjacent transpositions, e.g. both 257 and 527 would have a misleadingcorrect becausecheck )digit.

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 [https://en.wikipedia.org/w/index.php?title=Damm_algorithm&diff=prev&oldid=614858206 edit] added possible justification for this stating that for this modified equation only a weak totally anti-symmetric quasigroup with additional property of {{math|1=''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? — [[User:MwGamera|mwgamera]] ([[User talk:MwGamera|talk]]) 19:11, 29 June 2014 (UTC)