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Subject: [OASIS Issue Tracker] Commented: (OFFICE-2289) GCD

    [ http://tools.oasis-open.org/issues/browse/OFFICE-2289?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17448#action_17448 ] 

Dennis Hamilton commented on OFFICE-2289:

I'm puzzled by the Gnumeric failures.  

The cases gcd(0,n)  = gcd(n,0) = n for n > 0 are commonly accepted.  See p.103 in [Graham, Ronald L., Knuth, Donald E., Patashnik, Oren.  Concrete Mathematics.  Addison-Wesley (Reading, MA: 1989) ISBN 0-201-14236-8].  In computational mathematics, gcd(0,0) is considered mathematically undefined as you note.

Knuth (Art of Computer Programming, vol.1) and the Wikipedia article on "Gretaest Common Denominator" both demonstrate that one can determine an extended gcd(m,n) > 0 for all integers m and n, positive or negative, so long as they are not both zero.  (The Wikipedia article strikes me as a little flakey not going directly to Euclid's algorithm, but that's just me.)  

There are other ways to define a computational function, gcd(-m,n), etc., so I suppose it is safer to ciostrain the arguments to be non-negative and not both zero.  One might consider that the behavior for any of m and n being negative is implementation defined, but I think I would insist that gcd(m,n) > 0 always, if at all possible.

The Mathematica rational GCD(r, s, t, ..) can be safely ignored, I think.

> GCD 
> ----
>                 Key: OFFICE-2289
>                 URL: http://tools.oasis-open.org/issues/browse/OFFICE-2289
>             Project: OASIS Open Document Format for Office Applications (OpenDocument) TC
>          Issue Type: Sub-task
>          Components: OpenFormula
>    Affects Versions: ODF 1.2
>            Reporter: Robert Weir 
>            Assignee: Andreas Guelzow 
> == 6.15.35 GCD ==
> "Return the largest value that can be evenly divided (no remainder) into 
> the given numbers." should be "Return the largest value that can divide 
> the given numbers evenly (no remainder)."

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