## 105 Reputation

18 years, 160 days

## sign(x)...

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

## n=1..2, or n=1..N where N = 2...

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?

## tildes all over again...

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.

## Surprise behavior with assume...

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.

## Two Illustrations of "Is g the same as f...

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.

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