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MathGroup Archive 2006

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Re: Modify a list of pure functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70827] Re: [mg70812] Modify a list of pure functions
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Sat, 28 Oct 2006 23:38:00 -0400 (EDT)
  • References: <200610280921.FAA16098@smc.vnet.net>

You are running into problems with the HoldAll Attribute of Function.
ReplaceAll can replace things inside held expressions, but I would
really recommend using non-pure "functions" instead of trying to be
precise with ReplaceAll.

On 10/28/06, . <ggroup at sarj.ca> wrote:
> Hi all,
>
> I have a problem where I need to build up a list of pure functions that
> have been modified from a base pure function.  I'm not having much luck
> in getting it to work correctly, and was wondering if anyone had some
> good ideas.  A toy version of the problem is:
>
> f = Sin[#]&
> listF = Table[(i f[##])&, {i, 5}]
>
> What I'd hope to get is listF containing:
> {Sin[##]&, (2 Sin[##])&, (3 Sin[##])&, (4 Sin[##])&, (5 Sin[##])&}
>
> But instead, I get something where neither i nor f have been evaluated.
>  As I say, this is a toy example.  One thing that does partially work
> for the toy case, but does not seem to work for more complicated
> situations is to use ReplaceAll:
>
> listF2 = Table[{j f[##])& /. j->i, {i,5}]
>
> This does give:
> {1 f[##1] &, 2 f[##1] &, 3 f[##1]&, 4 f[##1] &, 5 f[##1] &}
>
> However, all that has been done is the index has been inserted; no
> significant evaluation seems to have occurred.  So this method doesn't
> work in more complicated situations.  For example, suppose insted of
> using the index i directly, it actually referred to a list:
>
> coeffs = Reverse[ Range[5] ];
> listF3 = Table[ (coeffs[[j]] f[##]) & /. j->i, {i, 5}]
>
> This just gives:
> {coeffs[[1]]*f[##1] & , coeffs[[2]]*f[##1] & , coeffs[[3]]*f[##1] & ,
> coeffs[[4]]*f[##1] & , coeffs[[5]]*f[##1] & }
>
> Which is no good if coeffs is a temporary variable.
>
> Any suggestions would be most appreciated.  Thanks!
>
>


-- 
http://chris.chiasson.name/


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