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Re: Combined Set, SetDelayed

• To: mathgroup at smc.vnet.net
• Subject: [mg100805] Re: Combined Set, SetDelayed
• From: Simon <simonjtyler at gmail.com>
• Date: Sun, 14 Jun 2009 05:41:47 -0400 (EDT)
• References: <h0vteh$6v2$1@smc.vnet.net>

Hi Sid,

if you check the grouping of the expression it is

f[x_,y_] := ( f[x, y] = ... )

thus if f[x,y] is not in the downvalues of f for the particular x and
y it will do the calculation.  If it is in the downvalues, it simply
returns the value it knows.
( NB this is dangerous if you change your definition of f, but do not
clear all the previously calculated specific values )

it can be used whenever the calculation of f[x,y] is computationally
expensive (and memory isn't too much of a problem)...
the famous example (I think given in the documentation centre) is that
of the Fibonacci numbers - a naive recursive definition

f[0]=f[1]=1;
f[n_Integer?Positive]:=f[n-1]+f[n-2]

becomes unusable for relatively small values of n.

Simon