Re: A pattern matching problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg72544] Re: A pattern matching problem*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 6 Jan 2007 03:38:30 -0500 (EST)*References*: <enksb3$9nt$1@smc.vnet.net>

Hi, what is with r = u[t + h] - 2*u[t] + u[t - h] + a2*u'[t + h/2] + 4*u'[t - h/4] + c* u''[t + alfa*h]/12; (Cases[r, u[_] | Derivative[__][u][_], Infinity] /. {u[ arg_] :> {0, arg}, Derivative[i_][u][arg_] :> {i, arg}}) /. {order_Integer, arg_} :> {order, D[arg, h]} Regards Jens carlos at colorado.edu wrote: > Here is an interesting challenge in pattern matching. Suppose > you are given an algebraic-differential expression exemplified by > > r = u[t+h]-2*u[t]+u[t-h]+a^2*u'[t+h/2]+4*u'[t-h/4]+ > c*u''[t+alfa*h]/12; > > Here u[t] is a function of time t, assumed infinitely differentiable, > h is a time interval, and primes denote derivatives wrt t. > Relation r==0 is called a delay-differential equation, and is the > basic stuff in delayed automatic control (h is the signal "lag"). > > The function name u and the lag h are always symbolic. > Function u and its derivatives appear linearly in r, while > h always appears linearly in arguments. > Coefficients of h may be numeric or symbolic. > Coefficients of u & derivatives may be numeric or symbolic. > > The challenge: given r, get the coefficients of h as a 2D list, > row-ordered by derivative order. Zero coefficients may be omitted. > For the above r, it should return > > {{1,-1},{1/2,-1/4},{alfa}} > > Envisioned module invocation: clist=LagCoefficients[r,u,t,h,m] > with m=max u-derivative order to be considered. Skeleton: > > LagCoefficients[r_,u_,t_,h_,m_]:=Module[ {clist={}}, > ?????? > Return[clist]]; > > Any ideas for ????? >

**Follow-Ups**:**Re: Re: A pattern matching problem***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>