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Re: pattern in list of derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22729] Re: pattern in list of derivatives
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Fri, 24 Mar 2000 03:27:13 -0500 (EST)
  • References: <8b9n7a$997@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Klaus Duellmann" <k.duellmann at uni-mannheim.de> wrote in message
news:8b9n7a$997 at smc.vnet.net...
> Dear Mathgroup Member,
>
> I can extract all derivatives from
>
> e.g. s1 = a u'[x] + a u''[x]
>
> by Cases[{s1}, Derivative[_][u][x],-1] and get
>
> {u'[x],u''[x]}
>
>
> But for mixed derivatives
>
> e.g. {a u[x,y]^(0,1) + c u[x,y]^(1,1)}
>
> the correponding command Cases[{s1}, Derivative[_][u][x,y],-1]
> doesn't work and I receive only the empty list {}.
>
> Any help is much appreciated!
>
>
> Klaus Duellmann
> Mannheim University
>
> E-mail: k.duellmann at uni-mannheim.de
>

Klaus,
Two points:

1. u[x,y]^(1,1) will not be interpreted as a derivalive.
The InputForm of what you want is
    Derivative[1,1][u][x,y]
This can be converted to Traditional or Standard form by selecting it and
using the menu Cell > Convert To.

2. Cases sees the input form (more generally, the FullForm) so we need
    Cases[s2, Derivative[__][u][x, y], -1]
with the double underscore __  inside Derivative to match with one or more
entries.

Putting these together, the following works.

s2 = a Derivative[0, 1][u][x, y] +
    c Derivative[1, 1][u][x, y];

Cases[s2, Derivative[__][u][x, y], -1]


Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565





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