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Topic: Re: [mg5345] Argument types
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Jens-Peer Kuska

Posts: 12
Registered: 12/7/04
Re: [mg5345] Argument types
Posted: Dec 1, 1996 11:20 PM
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> From mathgroup-adm@smc.vnet.net Wed Nov 27 15:54:45 1996
> From: Olivier Georg <olivier.georg@studi.epfl.ch>
> To: mathgroup@smc.vnet.net
> Subject: [mg5345] Argument types
> Organization: EPF Lausanne
> Content-Length: 1083
> X-Lines: 22
>
> Hi,
>
> I recently disovered that you could specify the type of the arguments
> of a function being defined. For exemple, f[x_Integer] if you want x
> to be an integer. There's also List, Real, Complex and Symbol. But
> there's also ?MatrixQ which is not in the Mathematica book, to specify
> a matrix. Are there other types?
>
> Olivier


Hi Olivier,

You *must* decide between a pattern with a given head like _Integer,
_Rational, _Plus and a test like _?VectorQ and _?MatrixQ. The first
one refers to a expression with a certain head where _?MatrixQ refers
to a test MatrixQ[expr]. The aquivalent to

f[x_?MatrixQ]:= ..

is

f[x: {{__}..}] /; Equal @@ (Length /@ x):= ...

because the pattern {{__}..} say that You what a list of lists with at
least one element in the sublists, the appended condition says that You
only what lists of lists with equal length.

Since MatrixQ is a test and not a (you say type but is a) head You
can add any function with one argument to test the pattern. Beside
EvenQ, PolynomQ in

f[x_?EvenQ] :=
..

you can invent Your own tests like

f[x_?(Head[#]==List && EvenQ[Length[#]] &)] :=

to test if x is a list with a even number of arguments.

There is probably a infinite number of such possible tests
and to list them all in the Mathematica book will increase
the sufficiently.

Hope that helps
Jens







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