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. > > Thanks for any help you may be able to provide. > > -Charlie > >