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Re: strange function that defines a function---how do I do it?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg15250] Re: strange function that defines a function---how do I do it?
*From*: dreissBLOOP at bloop.earthlink.net (David Reiss)
*Date*: Sun, 27 Dec 1998 03:58:40 -0500
*Organization*: EarthLink Network, Inc.
*References*: <75no5e$sgj@smc.vnet.net> <75q118$20o@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <75q118$20o at smc.vnet.net>, "Allan Hayes"
<hay at haystack.demon.co.uk> wrote:
> Benjamin Lotto wrote in message <75no5e$sgj at smc.vnet.net>...
> >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.
> >
>
> Benjamin:
>
> One way
>
> Clear["`*"]
>
> makefunction[var_, expr_] :=
> Block[{f, SetDelayed}, f @@ (#_?NumberQ & /@ var) := expr]
>
> list = {x1, x2};
>
> makefunction[list, 6]
>
> Check
>
> ?f
>
> Global`f
> f[x1 _?NumberQ, x2 _?NumberQ] := 6
>
>
> We can get problems if f is not blocked and there are no tests
>
> Clear["`*"]
>
> makefunction[var_, expr_] := Block[{SetDelayed}, f @@ (#_ & /@ var) :=
> expr]
>
> list = {x1, x2};
>
> makefunction[list, 6]
>
> ?f
>
> Global`f
> f[x1 _, x2 _] := 6
>
> But if we define a second time then f[x1_,x_2] evaluates to 6 before
> the setting is made and the definition fails:
>
> makefunction[list, 6]
>
> SetDelayed::"setraw": "Cannot assign to raw object 6."
>
> $Failed
>
> Allan
>
> ---------------------
> Allan Hayes
> Mathematica Training and Consulting
> www.haystack.demon.co.uk
> hay at haystack.demon.co.uk
> Voice: +44 (0)116 271 4198
> Fax: +44 (0)870 164 0565
Hi Alan,
Unfortunately this approach uncovers a bug or feature concerning the
use of a pattern in a pure function. If we follow through with your
example one step further
In[1]:=
Clear[makefunction];
makefunction[var_, expr_] :=
Block[{f, SetDelayed}, f @@ (#_?NumberQ & /@ var) := expr]
In[2]:= list = {x1, x2};
In[3]:= makefunction[list, 6]
In[4]:= ?f
"Global`f"
f[x1*_?NumberQ, x2*_?NumberQ] := 6
If all were well we would expect the following to give 6 as the result
In[5]:= f[2,3]
Out[5]= f[2,3]
However, this does
In[6]:= f[x1 2,x2 3]
Out[6]= 6
What seems to be happening is the following
In[7]:= (#_&)@z
Out[7]= z _
Note the space between the z and the _
In[8]:= FullForm[%]
Out[8]//FullForm=
Times[z,Blank[]]
So, typing the two characters # and _ into an input cell is inperpreted
by the frontend as the product #*_ rather than what we want, which is
#_. Indeed when these two characters are typed, the frontend
automatically puts a space between them in the same wayit does when a
symbol is preceeded by a number as in
In[9]:= 2x
Out[9]=
2 x
I tried initially to use the pattern #_ in a pure function, but ran
into this problem, so I used the following instead
In[10]:= Pattern[#,_]&[z]
Out[10]= z_
So, do you think that this auto-formatting of #_ into # _ is a bug or
feature?
--
David Reiss
dreissBLOOP at bloop.earthlink.net
To send personal email, remove the words "bloop" and "BLOOP" from the
email address
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