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Re: Best practice passing expressions to functions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg85303] Re: Best practice passing expressions to functions
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Tue, 5 Feb 2008 19:40:35 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <fo9gvu$t1l$1@smc.vnet.net>
Remo Aschwanden wrote:
> I want to write procedures that accept expressions as parameters and be
> able define functions based on these expressions, i.e.
>
> f[exp_]:=Module[
> "g[x_] := exp "
> ]
>
> The code between the " " should clarify what I intend to do. Calling
> f[x^2-2x+4]
> should lead to the definition of a function (or pattern)
> g[x_]:=x^2-2x+4;
>
> What's the best way to do this? How can I do this without being
> dependent on the variables used in the expressions ("x")?
One possible way, though I do not know whether it qualifies as best
practice, is as follows.
The first argument of f, exp_, is the expression that is going to be
transformed into a function definition, function definition that depends
on the variable var_, which is passed as second argument and as default
value, say, x.
The transformation rule applied to the pattern p_ looks for a pattern
named p$ rather than p since Mathematica renames p_ as p$_ (you can see
that by using the command *Trace*).
In[1]:= f[exp_, var_: x] := g[p_ /. p$ -> var] := exp
In[2]:= f[x^2 - 2 x y + 4 y]
g[3]
Out[3]= 9 - 2 y
In[4]:= f[x^2 - 2 x y + 4 y, x]
g[3]
Out[5]= 9 - 2 y
In[6]:= f[x^2 - 2 x y + 4 y, y]
g[3]
Out[7]= 12 - 6 x + x^2
Regards,
--
Jean-Marc
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