Re: Rule replacement doesn't work after NDSolve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg124019] Re: Rule replacement doesn't work after NDSolve?*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Fri, 6 Jan 2012 04:13:35 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <je3vls$eao$1@smc.vnet.net>

On 2012.01.05. 11:57, Bill Rowe wrote: > On 1/4/12 at 5:03 AM, g.crlsn at gmail.com (gac) wrote: > >> Thanks very much for the reply. Your suggestion works as you say, >> but I'm still confused. I thought that the replacement is for the >> function, not the arguments. > > Replacement rules are not limited to either functions or > arguments. For example, I can do: > > In[3]:= Cos[y] /. Cos -> Sin > > Out[3]= Sin[y] > > replacing the Cos function with Sin or > > In[4]:= Cos[y] /. y -> 2 x > > Out[4]= Cos[2*x] > > replacing the argument y with 2 x > > The thing to keep in mind with replacement rules is a litteral > match is made between the FullForm of the expression you want to > operate on and the left hand side of the replacement rule. For > example, this does nothing: > > In[5]:= -2 I /. I -> -I > > Out[5]= -2*I > > since > > In[6]:= FullForm[-2 I] > > Out[6]//FullForm= Complex[0,-2] > > and there is nothing to match the left hand side of the > replacement rule > It is an interesting example your bring up here. Although FullForm[I+1] shows Complex[1,1], we can also check that AtomQ[I+1] === True, i.e. Complex[1,1] doesn't have a structure as an expression. In this sense it is quite different from the expressions Complex[a,b] or Complex[_,_] (a pattern), which *do* have a structure that can be broken down: check that AtomQ[Complex[_,_]] === False. Despite this MatchQ[ 1+I, Complex[_,_] ] *does* match. This was surprising for me. SparseArray is atomic too, and it matches too in similar situations. Graph (also atomic) doesn't, however: MatchQ[Graph[{1 -> 2}], Graph[_, __]] even though FullForm gives Graph[List[1,2],List[DirectedEdge[1,2]]] My point is that one should be careful when looking at the *apparent* FullForm of atomic objects and matching against them. Or perhaps the different behaviour of Graph is an oversight or bug? -- Szabolcs Horvát Mma QA site proposal: http://area51.stackexchange.com/proposals/37304