Maple used to be very good for large-scale work, meaning that one could deal with thousands (even tens of thousands) of files easily. But now that more and more functionality is buried in the GUI, Maple is actually becoming less useful for that kind of large-scale work. It's not that people at Maplesoft don't know about this -- I know of people who have been forced to manually open ~800 worksheets, make a minor change, and save it again. All because there was no scriptable way to get the same effect. What an utter waste of time! Even on the Mac there are ways to script many things. And in the Hallowed Halls of GUI Supremacy that is the Mac, that really means something. Apparently the new features seem to be directed at small-scale work, with a human forcibly in the loop.

I am a little surprised that no one seemed to have followed-up on your post. If what you say is true, this is definitely a step backwards, and thus a bug that ought to be fixed.

PARI/GP is indeed a ``computer algebra system'' in the literal sense of those words, and a rather good one at that. Unfortunately, Maple still sometimes describes itself as a CAS, although that is a rather outdated view. It is more like a computational assistant for a wide variety of mathematics that goes far beyond "algebra". PARI/GP sticks to algebra, and is very good at it. Maple is not, however, a "mathematical assistant", since it does not help with proofs. It helps (a lot) with computations, and more generally exploration, while also being decent for exposition. But it still has no facilities for proofs, thus not being able to embrace the full spectrum of mathematical activities.

The issue goes much deeper. The ``problem'' is that -1 and 1/(-1) are subtly different. More precisely, -1 = exp(I*Pi), but 1/(-1) = 1/(exp(I*Pi)) = exp(-I*Pi). Of course, projected onto the complex plane, exp(-I*Pi) = -1. However, sqrt(-1) = exp(Pi*I/2) = I, but sqrt(exp(-I*Pi)) = exp(-I*Pi/2) = -I. In other words, when you move a unit from the denominator of a rational function to the numerator, that changes the values on the negative real axis from being ``on top'' to ``underneath'' -- which can be seen once a function (like sqrt or log) which can detect this is applied.

The issue goes much deeper. The ``problem'' is that -1 and 1/(-1) are subtly different. More precisely, -1 = exp(I*Pi), but 1/(-1) = 1/(exp(I*Pi)) = exp(-I*Pi). Of course, projected onto the complex plane, exp(-I*Pi) = -1. However, sqrt(-1) = exp(Pi*I/2) = I, but sqrt(exp(-I*Pi)) = exp(-I*Pi/2) = -I. In other words, when you move a unit from the denominator of a rational function to the numerator, that changes the values on the negative real axis from being ``on top'' to ``underneath'' -- which can be seen once a function (like sqrt or log) which can detect this is applied.

But I am off to Calculemus (and its satellite events) in a couple of hours, so I might not get to it for a few days. I need to find a way to remind myself to come back to this thread (since right now it is marked as 'read').

But I am off to Calculemus (and its satellite events) in a couple of hours, so I might not get to it for a few days. I need to find a way to remind myself to come back to this thread (since right now it is marked as 'read').

Have you considered doing some math advocacy at your local schools? Stories like this might actually get through to some kids.

Have you considered doing some math advocacy at your local schools? Stories like this might actually get through to some kids.

I agree - both with the default being "Plain Text" and with it being a per-user setting (and, like you, I would change mine to HTML).

I agree - both with the default being "Plain Text" and with it being a per-user setting (and, like you, I would change mine to HTML).

Collecting the insights you have gathered while you have learned Maple can really be useful to others. Your questions were perfectly topical for this forum.

Collecting the insights you have gathered while you have learned Maple can really be useful to others. Your questions were perfectly topical for this forum.

Darn, looks like I did forget ;-). Speaking of smileys, it would be nice if I could insert the more classical ones in some posts -- but how?

[That does seem like a bug] But why go numeric when symbolics work?

> dsolve({y(0)=4,diff(y(x),x)=8*x^3*y(x)},y(x));
                                          4
                          y(x) = 4 exp(2 x )

From the answer, it is fairly clear why a numerical integrator might find this difficult!