One of my students was surprised at what happened after this command: > plot([sign(x), 'sign(x)' ],x=-1..1,color=[green,red]); I was too. One would expect to see an overlay of the green and red graphs. You don't. Curious. Jim Herod

I do not understand why these parts give different results. Part 1. > restart; > u:=(t,x)->sum(a[n](t)*sin(n*Pi*x),n=1..2); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE IS WHAT A HUMAN WOULD GET. Part 2. > restart; > N:=2; > u:=(t,x)->sum(a[n](t)*sin(n*Pi*x),n=1..N); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE IS 0, curiously. Part 3. > restart; > N:=2; > u:=(t,x)->add(a[n](t)*sin(n*Pi*x),n=1..N); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE ECHOES THE REQUEST. > I prefer the output of Part 1, of course. I can tolerate the output of Part 3. But, the output of Part 2 seems wrong. What am I not understanding?

I was doing some stuff with the quadratic nonlinearities that interest me. The quadratic nonlinearities involve structure having the form <>, where <> represents the usual dot product, A is a matrix, and v is a vector. I didn't want to use complex numbers with what I was doing, so I assumed things were real valued. I was surprised by what happened as a result. I have simplified the curious behavior so that it can be observed in a few lines. I can live with this, but it was a surprise.

Here are two illustrations for how one might want to check to see if g is the same as f. The attached file is a Maple 10 worksheet.