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Re: Conditional SetDelayed with Replacement

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92808] Re: Conditional SetDelayed with Replacement
  • From: Szabolcs Horvat <szhorvat at gmail.com>
  • Date: Tue, 14 Oct 2008 04:54:55 -0400 (EDT)
  • Organization: University of Bergen
  • References: <gcv7d5$e1i$1@smc.vnet.net>

Raffy wrote:
> I've been having difficulty getting the following code to work as
> desired.
> 
> Clear[f];
> Do[f[x_ /; x < i^2] = i, {i, 5}];
> 
> The problem should be obvious: the i^2 is not be evaluated (since its
> held by SetDelayed).
> 
> The only solution I've found thus far, has been doing the following:
> 
> Clear[f];
> (f[x_ /; x < #^2] = #)& /@ Range[5]
> or
> Do[(f[x_ /; x < #^2] = #)&[i], {i, 5}];
> 
> What kind of Hold, ReleaseHold, Evalulate, or Pattern Replacement
> would be needed to get the first example working without using a pure-
> function for replacement?
> 

With[] can be used to inject values into held expressions:

Clear[f]
Do[With[{i = j}, f[x_ /; x < i^2] = i], {j, 5}]

ReplaceAll works too, but it's somewhat messier:

Clear[f]
Do[Unevaluated[f[x_ /; x < i^2] = i] /. i -> j, {j, 5}]


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