Re: Pattern matching problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg88593] Re: [mg88516] Pattern matching problem*From*: DrMajorBob <drmajorbob at att.net>*Date*: Fri, 9 May 2008 03:25:34 -0400 (EDT)*References*: <29931163.1210271316984.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

If you don't want to multiply by the power, then don't: f[equation_] := Sum[j*Count[equation, D[u[x, t], {x, j}]^k, {0, Infinity}], {j, 1, 50}, {k, 1, 50}] eg = D[u[x, t], {x, 2}]^2; f[eg] 4 Bobby On Wed, 07 May 2008 06:07:52 -0500, Charlie Brummitt <cbrummitt at wisc.edu > 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 th e > 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 > > > -- DrMajorBob at longhorns.com