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MathGroup Archive 2004

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RE: A question about function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49328] RE: [mg49308] A question about function
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 14 Jul 2004 07:29:34 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Feng-Yin,

You could use the Through command.

g[i_] := {Min, Max}[i] // Through

g[{1, 3, 2, 7}]
{1, 7}

But if you try to do something like...

g[i_] := {Max - Min, (Max + Min)/2}[i] // Through

g[{1, 3, 2, 7}]
{(Max - Min)[{1, 3, 2, 7}], ((Max + Min)/2)[
   {1, 3, 2, 7}]}

Through does not push far enough and it is difficult to complete the action.
You have to instead use a complete functional form in the list.

g[i_] := {Max[#] - Min[#] &, (Max[#] + Min[#])/2 &}[i] // Through

g[{1, 3, 2, 7}]
{6, 4}

I find the following routine useful in these cases.

PushOnto::usage =
    "PushOnto[argslist, ontolist][expr] is a form of the Through command
that \
pushes arguments only onto forms given in the ontolist.\n\
PushOnto[ontolist][(head)[args]] pushes args onto forms given in the \
ontolist";

PushOnto[argslist_List, ontolist_List][expr_] :=
  Module[{onto = Alternatives @@ ontolist},
    expr /. (h_ /; ¬ FreeQ[h, onto]) @@
          argslist :> (h /. a_ /; MatchQ[a, onto] -> a @@ argslist)
    ]

PushOnto[ontolist_List][(head_)[arglist___]] :=
  Module[{onto = Alternatives @@ ontolist},
    head /. a_ /; MatchQ[a, onto] :> a[arglist]
    ]

Then you can write...

g[i_] := {Max - Min, (Max + Min)/2}[i] // PushOnto[{Max, Min}]

g[{1, 3, 2, 7}]
{6, 4}

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/



From: Feng-Yin Chang [mailto:fychang at slac.stanford.edu]
To: mathgroup at smc.vnet.net

Hi all,
      I have a small question which bother me for a while.
      For a  variable i(for any data type), I want to define a function
      like
      g[i_]:={a[i],b[i],c[i],d[i]....} .
      (g,a,b,c,d,...are all functions or command)

      for example
      g[i]:={Max[i],Min[i]}

      Is it possible to  gather the list of  function like
      g[i_]:={a,b,c,d,..}[i] in Mathematica?

     It is convenient to have a list of testing different functions.

                                                      Regards,
                                                      Feng-Yin Chang





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