Is it possible to "pre-evaluate" parts of pure function?

• To: mathgroup at smc.vnet.net
• Subject: [mg70286] Is it possible to "pre-evaluate" parts of pure function?
• From: "Philpp" <piotr at bigpond.net.au>
• Date: Wed, 11 Oct 2006 01:54:12 -0400 (EDT)

```This is a problem that's been bugging me for a long time now. Consider
the following function definition:

In[1]:=  Clear[f];
f[x_, opts___] :=
Module[
{multiplierfun =
MultiplierFunction /. {opts} /. Options[f]},
multiplierfun[x^2]
];
Options[f] = {MultiplierFunction :> (2 # &)};

In[4]:=  f[2]
Out[4]=  8

Changing the MultiplierFunction option changes the result

In[5]:=  f[2, MultiplierFunction :> (3 # &)]
Out[5]=  12

Now, consider the following

In[6]:=  const = 4;
f[2, MultiplierFunction :> (const # &)]
Out[7]=  16

Again, the result is as expected.

>From now on, I would like to "fix" the pure function with the present
value of const. The solution that immediately comes to mind is

In[8]:=  SetOptions[f, MultiplierFunction :> (const # &)]
Out[8]=  {MultiplierFunction :> (const #1 &)}

this is not what I intended, I expected

{MultiplierFunction :> (4 #1 &)}

since the const value is 4.

Trying any of the following doesn't work either

In[9]:=  SetOptions[f, MultiplierFunction -> (const # &)]
SetOptions[f, MultiplierFunction -> Evaluate[(const # &)]]
SetOptions[f, MultiplierFunction -> ReleaseHold[(const # &)]]

Out[9]=  {MultiplierFunction -> (const #1 &)}
Out[10]= {MultiplierFunction -> (const #1 &)}
Out[11]= {MultiplierFunction -> (const #1 &)}

the symbol const remains unevaluated.

The only way to even approach what I want is to define a named function
g

In[12]:= (Clear[r, g]; g[r_] = (const r))
SetOptions[f, MultiplierFunction -> g]

Out[12]= 4 r
Out[13]= {MultiplierFunction -> g}

In[14]:= ?g
g[r_] = 4 r

However, this is not a solution to my problem. It only shifts the focus
from const onto g symbol, i.e., now g could be redefined before f is
executed.

So, is it possible to "pre-evaluate" parts of pure function?

Can anybody offer any suggestions?

Cheers,

Philipp

```

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