Re: Argument types
- To: mathgroup at smc.vnet.net
- Subject: [mg5359] Re: [mg5345] Argument types
- From: jpk at apex.mpe.FTA-Berlin.de (Jens-Peer Kuska)
- Date: Thu, 5 Dec 1996 14:50:09 -0500
- Sender: owner-wri-mathgroup at wolfram.com
> From mathgroup-adm at smc.vnet.net Wed Nov 27 15:54:45 1996
> From: Olivier Georg <olivier.georg at studi.epfl.ch>
To: mathgroup at smc.vnet.net
> To: mathgroup at 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