Re: strange function that defines a function---how do I do it?

• To: mathgroup at smc.vnet.net
• Subject: [mg15229] Re: strange function that defines a function---how do I do it?
• From: dreissBLOOP at bloop.earthlink.net (David Reiss)
• Date: Wed, 23 Dec 1998 01:04:06 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Here is one way to do it  (I allow you to give the head  of the function
that you define as the first argument):

In[1]:=

Clear[FunMake1];

FunMake1[f_,x_List,expr_]:=

(
Clear[f];
f[Sequence@@(Pattern[#,_]&)/@x]:=expr
)

In[2]:= FunMake1[h, {x,y,z},x^2 + y/z]

In[3]:= ?h

"Global`h"

h[x_, y_, z_] := x^2 + y/z

In[4]:= h[a,b,c]

Out[4]=

\!\(a\^2 + b\/c\)

Also, if you wan to add a NumberQ condition you can write:

In[5]:=
Clear[FunMake2];

FunMake2[f_,x_List,expr_]:=

(
Clear[f];
f[Sequence@@(Pattern[#,_?NumberQ]&)/@x]:=expr
)

In[6]:= FunMake2[g, {x,y,z,t},x^2 + y/z+Sin[t]]

In[7]:= ?g

"Global`g"

g[x:_?NumberQ, y:_?NumberQ, z:_?NumberQ, t:_?NumberQ] := x^2 + y/z +
Sin[t]

In[8]:= g[a,1,2,3]

Out[8]= g[a,1,2,3]

In[9]:= g[3,4,5,6]

Out[9]= \!\(49\/5 + Sin[6]\)

Regards,

David

In article <75no5e\$sgj at smc.vnet.net>, belotto at vassar.edu (Benjamin
Lotto) wrote:

> Working with Mathematica 3.0:
>
> Suppose I define
>
>    makefunction[var_, expr_]:=f[var_?NumberQ]:=NIntegrate[expr,{x,0,1}]
>
> Then I can do something like
>
>    z=x^2
>    makefunction[x,z]
>
> and it will be just as if I typed
>
>    f[x_?NumberQ]:=NIntegrate[x^2,{x,0,1}]
>
> In fact, entering
>
>    ?f
>
> at this point yields
>
>    "Global`f"
>
>    f[(x_)?NumberQ] := NIntegrate[x^2, {x, 0, 1}]
>
> OK, now suppose I have a list of variables  x1  up through  xn.  Suppose
> they're in a list:
>
>    list={x1,x2,...,xn}
>
> I want something like "makefunction" above so that when I type
>
>    makefunction[list,expr]
>
> it will be just as if I typed
>
>    f[x1_?NumberQ,x2_?NumberQ,...,xn_?NumberQ]:=expr
>
> analogous to the above.  Can anyone help me?
>
> Thanks in advance.  Y'all out there have been very helpful in the past.

--
David Reiss