Re: Combining several pure functions into a single pure function

• To: mathgroup at smc.vnet.net
• Subject: [mg7287] Re: [mg7262] Combining several pure functions into a single pure function
• From: penny at suu.edu (Des Penny)
• Date: Thu, 22 May 1997 09:19:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```>I am working with a little program that generates several pure
>functions which are "Boolean" in nature -- i.e., each of them, when
>applied to an argument, evaluates to True or False.  These functions,
>when they are initially produced, are connected with logical operators
>-- for example:
>
>        (Function[x,Plus[x]>9] && Function[x,Length[x]==4]) ||
>        (Function[x,Plus[x]<3] && Function[x,Length[x]==6])
>
>In this form, however, they are useless since, as a group, they do not
>constitute a pure function and cannot be applied to an argument.
>Thus, I need to convert the foregoing into a single pure Boolean
>function, which would (using the above example) look like this:
>
>        Function[x,(Plus[x]>9 && Length[x]==4) ||
>        (Plus[x]<3 && Length[x]==6)]

Hi Robert:

Is this what you need?

=================================================
test=
(((Plus @@ #  >9) && (Length[#]==4)) || ((Plus @@ #  >3)&&(Length[#]==6)))&;

test[{1,-2,3,1,1,1}]

Out: True
=================================================

I was initially confused about x in your code.  I finally decided that it
had to be a list.  However Plus[{1,2}], returns {1,2}.  I believe what you
need is the Apply function:

Apply[Plus,{1,2}]

Which returns 3.

This can also be written:  Plus @@ {1,2}.  This is the form I've used above.

Hope this helps.

Cheers,

Des Penny

-------------------------------
Des Penny
Physical Science Dept.
Southern Utah University
Cedar City, UT 84720

VOICE: (Office): (801) 586-7708
(Home)  : (801) 586-2286
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e-mail: penny at suu.edu
-------------------------------

```

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