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MathGroup Archive 1994

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Re: Question about Cases command.

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Question about Cases command.
  • From: withoff (David Withoff)
  • Date: Tue, 28 Jun 1994 15:45:07 -0500

> In[2]:= myterms = {Derivative[1,2][a][x,y], Derivative[1,1][b][x,y]};
> 
> In[3]:= Map[Head, myterms]
> 
>           (1,2)   (1,1)
> Out[3]= {a     , b     }
> 
> 	Now try to uses Cases:
> 
> In[4]:= Cases[myterms,_Derivative[__][a]]
> 
> Out[4]= {}
> 
> 	Why didn't it select the "a" term out?  Try:
> 
> In[5]:= Cases[myterms, _Derivative[__][_]]
> 
> Out[5]= {}
> 
> In[6]:= Cases[myterms, _Derivative[__][__]]
>  
>            3       2
>           d a     d b
> Out[6]= {------, ------}
>            1  2    1  1
>          dx dy   dx dy
> 
> 	Ok, now why must I use two underscores in this form?  ( In[6] )
> 	The "a" and the "b" are single elements.
> 
> 
> Scott A. Herod
> Program in Applied Mathematics
> University of Colorado, Boulder
> (sherod at newton.colorado.edu)

Compare

In[9]:= FullForm[myterms[[1]]]

Out[9]//FullForm= Derivative[1, 2][a][x, y]

with

In[10]:= FullForm[_Derivative[__][_]]

Out[10]//FullForm= Blank[Derivative][BlankSequence[]][Blank[]]

The pattern will match anything with a single argument and
with a head that matches Blank[Derivative][BlankSequence[]],
which means that the head must be something with one or more
elements and the head of the head must match Blank[Derivative].

The expression

    Derivative[1, 2][a][x, y]

has two elements, so it fails the first test.

The pattern Blank[h] does literal comparisons of the head.
It does not use the Head function, and does not allow for
the effects of special pattern expressions (things like __).
For example:

In[13]:= MatchQ[f[0][], Blank[f[0]]]

Out[13]= True

In[14]:= MatchQ[f[0][], Blank[f[_]]]

Out[14]= False

In[15]:= MatchQ[f[_][], Blank[f[_]]]

Out[15]= True

Also, the special input notation _h for Blank[h] works only
if h is a symbol.  The FullForm must be used if h is not
a symbol.  That is, _f[0] parses as Blank[f][0], and will match
expressions, with element 0 and a head that matches _f, not
expressions with a head of f[0].  The pattern that matches
expressions with head f[0] must be entered as Blank[f[0]].

Dave Withoff
Research and Development
Wolfram Research





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