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 want to ask about a small problem. I will present a paper at a conference in February. Because it involves time consuming calculations of numerical solutions for several onerous systems, I will do the calculations at home before the talk, save the results, and show the output to the conference. The folks attending the conference are not necessarily Maple Folks, so I do not want to have to explain the tilde after characters for which I have made assumptions. Of course, I know about
interface(showassumed=0);
After making the calculations here at home, traveling to the meeting, opening the file to make the presentation then, alas, the tildes are back again. Try this.
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.
