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Re: Impossible?

• To: mathgroup@smc.vnet.net
• Subject: [mg10504] Re: [mg10458] Impossible?
• From: Daniel Lichtblau <danl@wolfram.com>
• Date: Tue, 20 Jan 1998 02:22:52 -0500
• References: <199801160934.EAA08231@smc.vnet.net.>

Arturas Acus wrote:
> 
> Hello,
> 
> I would like to construct a function which gives me an absolute Level of
> subexpression in expression.  For example I want:
> 
> a*(b+c*(d+AbsoluteLevelQ[e]))
> 
> evaluate to
> 
> Level[a*(b+c*(d+e)),e].
> ( AbsoiuteLevelQ climbs up until reaches  In[], after  that calls Level
> )
> 
> More generally, I would like to control absolute level (level in respect
> to In[%]) at  which patter matching take place. For example if pattern
> matches at Level n>3,  then rule is applied,  but if it matches at
> Level n<3 then not.
> 
> I suspect, that evaluation machinery here is hardly involved. Do
> Mathematica language provides tools for such a control? Please comment
> if solution don't exist.
> 
>                                       Arturas Acus
> ....

Something along the following lines might get you started.

ruls = {f_[e1___, al[e_Symbol], e2___] :> al[f[e1,e,e2], e],
	f_[e1___, al[e2_,e_Symbol], e3___] :> al[f[e1,e2,e3], e]}

In[81]:= (a*(b+c*(d+al[e])) //. ruls) /. al->Level Level::level: Level
specification e is not of the form n, {n}, or {m, n}.
Out[81]= Level[a (b + c (d + e)), e]

But, while this gives the output you specified, I doubt it is what you
want. Maybe you have in mind a nesting-depth-counter? Could do

In[1]:= ruls2 = {al[e_] :> al[e,1],
    f_[e1___, al[e2_,n_Integer], e3___] :> al[f[e1,e2,e3], n+1]}

In[2]:= (a*(b+c*(d+al[e])) //. ruls2) Out[2]= al[a (b + c (d + e)), 5]

or perhaps

FindLevel[e_] := Module[{pos, len},
    len = Length[pos = Position[e, al[_]]];
    Length[pos[[1]]] +1 /; len==1
    ]

In[16]:= FindLevel[a*(b+c*(d+al[e]))] Out[16]= 5


Daniel Lichtblau
Wolfram Research

• References:
  • Impossible?
    • From: "Arturas Acus" <acus@itpa.lt>