Re: Pattern matching problem

• To: mathgroup at smc.vnet.net
• Subject: [mg88538] Re: Pattern matching problem
• From: dh <dh at metrohm.ch>
• Date: Thu, 8 May 2008 04:11:17 -0400 (EDT)
• References: <fvs2kf\$eo4\$1@smc.vnet.net>

```
Hi Charlie,

use ReplaceAll (/.) instead of Count. ReplaceAll treats any piece at

most once. Here is an example, where "expression" is your expression. We

prevent any evaluation of the found multiplicity by my[..] and use Total

to add all arguments to my:

t=expression/. D[u[x],{x,i_}]^k_.:>my[i k]

Cases[t,my[x_]:>x,Infinity]//Total

hope this helps, Daniel

Charlie Brummitt wrote:

> Hi all,

> Here is my problem: Given a polynomial in the variables u[x,t] and its

> spatial derivatives (for example, the polynomial could be 1 + u +

> u_xx*u_xxx^2), count the number of spatial derivatives with multiplicity.

> That is, after writing the above polynomial as

>

>

> 1 + u + u_xx * u_xxx * u_xxx

>

> the output should be 2 + 3 + 3 (basically, you count the number of x's).

>

> I have tried implementing this using a pattern matching approach. Here is

> what I tried:

>

> f[equation_ ] :=  Sum[ k * j * Count[ equation , D[ u[x, t], {x, j} ] ^ k ,

> {0, \infinity} ], {j, 1, 50}, {k, 1, 50}]

>

> This fails to work on, for example, the input u_xx^2, because it outputs 6

> when it should output 4. This is because the u_xx is counted (+2 to the

> sum), and the u_xx^2 is counted (+4 to the sum). This is because the u_xx is

> nested inside the Power[    , 2] in its representation in Mathematica and so

> it gets counted too many times in my formula. I can't seem to figure out a

> way to use the "provided that" operator /; to make this formula work.

>

> I've also tried doing some replacement methods, but to no success.

>

>

> -Charlie

>

>

```

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