Re: finite domains

• To: mathgroup at smc.vnet.net
• Subject: [mg53053] Re: finite domains
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 22 Dec 2004 04:52:43 -0500 (EST)
• Organization: The University of Western Australia
• References: <cp3t2v\$9ai\$1@smc.vnet.net> <200412201134.GAA02658@smc.vnet.net> <cq8u48\$h47\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <cq8u48\$h47\$1 at smc.vnet.net>, János <janos.lobb at yale.edu>
wrote:

> I looked at the article and I understand that for that particular case.
> However that case fell back in the definition on an already existing
> infinite domain of the same order namely Z. There is also a similar
> definition in the Book for Odd numbers.
>
> In my case I cannot fall back on an existing finite domain, or I do not
> know how to explore/exploite it with Boolean.
>
> I am thinking of a domain named Irany having elements
> {North,East,South,West}. How can I do that without a reference to a
> more basic domain as foundation and expect that
> Element[NorthWest,Irany] will give me False?

The following code does what _you_ want:

Irany /: Element[x_, Irany]:= MemberQ[{North,East,South,West}, #]& /@ x

Element[{North, West}, Irany]

Element[NorthWest, Irany]

However, this violates the "spirit" of Mathematica because, for an
arbitrary symbol, the definition should return the unevaluated
expression -- but if you try

Element[y, Irany]

you get false, rather than the unevaluated expression. Now, y could be
North, or it could be NorthWest ...

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
The University of Western Australia      (CRICOS Provider No 00126G)
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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