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Functions with data hidden in them

• To: mathgroup at smc.vnet.net
• Subject: [mg81831] Functions with data hidden in them
• From: Neil Stewart <neil.stewart at warwick.ac.uk>
• Date: Thu, 4 Oct 2007 04:29:26 -0400 (EDT)
• Reply-to: Neil Stewart <neil.stewart at warwick.ac.uk>

The Interpolation[] function somehow "hides" the data passed to it in the
InterpolationFunction object that it returns. In the example below, when
f[1] is evaluated it is using information from the list data, but does not
have the list data passed to it as parameter.

In[1]:= data = {{1, 1}, {2, 2}, {3, 3}}

In[2]:=  f = Interpolation[data]

In[3]:= f[1]
Out[3]= 1

How can I write my own function that stores data inside itself in the same
way that Interpolation does? I'm aiming to write a functions that takes a
number as a parameter and consults a large data set to return a number. I'm
not sure where to start - any ideas very welcome!

Thanks,
Neil.