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Re: Question about Cases command.
*To*: mathgroup at yoda.physics.unc.edu (Mathgroup)
*Subject*: Re: Question about Cases command.
*From*: leszek (Leszek Sczaniecki)
*Date*: Tue, 28 Jun 1994 14:30:47 -0500
> From: Scott Herod <sherod at gauss.colorado.edu>
> Subject: Question about Cases command.
> To: mathgroup at yoda.physics.unc.edu (Mathgroup)
> Date: Mon, 27 Jun 1994 14:58:29 -0600 (MDT)
>
> I am trying to grab a list of the derivatives of functions that
> appears in a large list of differential equations. I have been using
> the Cases command to do this and have a question about some curious
> behavior.
>
> Consider the list of two derivatives:
>
> In[1]:= {Derivative[1,2][a][x,y], Derivative[1,1][b][x,y]}
>
> 3 2
> d a d b
> Out[1]= {------, ------}
> 1 2 1 1
> dx dy dx dy
>
>
> I would like to select the derivatives of "a" . First let's
> check the Head of the terms:
>
> In[2]:= myterms = %;
>
> 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.
>
> BTW. Here is something which works.
>
> In[7]:= derivdepfn[deriv_] := Head[deriv][[1]];
>
> In[9]:= Select[myterms, (derivdepfn[#1] === a) &]
>
> 3
> d a
> Out[9]= {------}
> 1 2
> dx dy
>
>
>
> Scott A. Herod
> Program in Applied Mathematics
> University of Colorado, Boulder
> (sherod at newton.colorado.edu)
>
In[5]:= expr = {Derivative[1,2][a][x,y], Derivative[1,1][b][x,y]}
Out[5]=
(1,2) (1,1)
{a [x, y], b [x, y]}
In[25]:= Cases[expr, Derivative[__][a][__]]
Out[25]=
(1,2)
{a [x, y]}
You may consider to use Select
In[41]:= expr1 = {Sqrt[Derivative[1,2][a][x,y]], Derivative[1,1][b][x,y]}
Out[41]=
(1,2) (1,1)
{Sqrt[a [x, y]], b [x, y]}
In[42]:= Select[expr1, !FreeQ[#, Derivative[__][a]]&]
Out[42]=
(1,2)
{Sqrt[a [x, y]]}
I hope it helps,
Leszek
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