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MathGroup Archive 1998

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Re: Impossible?



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
> Institute of Theoretical
> Physics and Astronomy
> Gostauto 12, 2600,Vilnius
> Lithuania
> 
> E-mail: acus@itpa.lt
>    Fax: 370-2-225361
>    Tel: 370-2-612906


Every mathematica expression is a list of some sort. If you type in an
algebraic expression like:

In[6]:=
f=x*Sin[y]+3*Exp[-x^3-4 x +7];

The various "elements" of f can be found just like in a regular list.  I
show a few examples below:

In[7]:=
f[[0]]
Out[7]=
Plus
In[8]:=
f[[1]]
Out[8]=
3*E^(7 - 4*x - x^3)
In[9]:=
f[[2]]
Out[9]=
x Sin[y]
In[12]:=
Dimensions[f[[1]]]
Out[12]=
{2}
In[13]:=
f[[1,1]]
Out[13]=
3
In[14]:=
f[[1,2]]
Out[14]=
E^(7 - 4*x - x^3)

You might also check out the LeafCount,TreeForm, Level, Depth, Position
etc. in chapter 2.1.4 of the mathematica book.  In particular,
something like
 
MatrixForm[Table[Level[f,n],{n,1,Depth[f]}]]

can give you a graphic representation of the data available and

Level[f,Depth[f]]

returns a list of all possible subexpressions.

{3, E, 7, -4, x, -4*x, -1, x, 3, x^3, -x^3, 7 - 4*x - x^3, 
  E^(7 - 4*x - x^3), 3*E^(7 - 4*x - x^3), x, y, Sin[y], 
  x*Sin[y]}

To find the complete location of one of those elements, say 7, use:


Position[f,7,Depth[f]]

which returns an exact description of where in the expression you can
find that subexpression:

{{1,2,2,1}}


Hope that helps.
-- 
Remove the _nospam_ in the return address to respond.



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