If you ask Maple to calculate sum(a/x, x = 1 .. infinity) assuming a > 0 Maple correctly returns infinity. But if you ask Maple to calculate the sum given by Evan Stanley, Maple returns unevaluated. So Maple did not determine that Evan's sum diverges.

You say that you "hate" document mode. The examples that you give, however, have nothing to do with document mode. They relate to a facility that is available with 2-D input, in both worksheet mode and document mode. (I have pointed out the distinction between 1-D/2-D and document/worksheet above, four times.) If you do not like the primes facility, turn it off: View > Typesetting Rules > Differential Options (parsing only) > Prime Derivatives. The setting defaults to the usage that is common in mathematical analysis; I suppose you could argue about the default. I do not see any reason to criticize 2-D input though. As for MS Word, it is not just for, or even primarily for, students. Even for students, though, spell-check surely does aid in learning spelling, etc.

You say that you "hate" document mode. The examples that you give, however, have nothing to do with document mode. They relate to a facility that is available with 2-D input, in both worksheet mode and document mode. (I have pointed out the distinction between 1-D/2-D and document/worksheet above, four times.) If you do not like the primes facility, turn it off: View > Typesetting Rules > Differential Options (parsing only) > Prime Derivatives. The setting defaults to the usage that is common in mathematical analysis; I suppose you could argue about the default. I do not see any reason to criticize 2-D input though. As for MS Word, it is not just for, or even primarily for, students. Even for students, though, spell-check surely does aid in learning spelling, etc.

The solve function is supposed to give exact solutions. Numerical issues apply to fsolve, but not to solve. I think I see what's happening though. solve does give the exact solution. The only issue is that Maple doesn't easily do the simplfication of the imaginary part to zero (which is fine).

The solve function is supposed to give exact solutions. Numerical issues apply to fsolve, but not to solve. I think I see what's happening though. solve does give the exact solution. The only issue is that Maple doesn't easily do the simplfication of the imaginary part to zero (which is fine).

This sounds like more special cases to remember. I like the currently-implemented approach.

This sounds like more special cases to remember. I like the currently-implemented approach.

Okay, though I think that the Help for solve should mention this. Even so, I still don't really understand. The solutions from solve (not fsolve) are supposed to be exact. Yet the solutions are not exactly real (as they must be). So what's going on?

Okay, though I think that the Help for solve should mention this. Even so, I still don't really understand. The solutions from solve (not fsolve) are supposed to be exact. Yet the solutions are not exactly real (as they must be). So what's going on?

Sorry I'm confused here. Aren't the fonts in Document Mode and Worksheet Mode identical? Are you comparing 1-D input to 2-D input? (My question assumes use of 2-D input.)

Sorry I'm confused here. Aren't the fonts in Document Mode and Worksheet Mode identical? Are you comparing 1-D input to 2-D input? (My question assumes use of 2-D input.)

Being able to do a Google-type search in Help would definitely be nice. At a minimum, it should be possible to search for a quoted string. Although the Help pages are uneven in depth/quality, I do not find this to be a serious issue. The one exception is that the links given under "See Also" are sometimes really poor, and yet links to other pages can be critical for someone looking to improve their knowledge of Maple. In June 2005, I e-mailed the Maple developers with a small list of recommendations to improve the Help pages, particularly via additional links. This would have taken them about an hour to implement. Yet none of the recommendations have been made to Maple 11. So it seems that Maplesoft doesn't care. I agree with you that Help improvements have high importance.

I join the throng of people who would like to be able to resize the matrix browser window. This functionality was in Maple a couple versions ago, but was removed (for reasons unstated). Maybe too there could be a "maximize" button, in the window's top right-hand corner?

This is an interesting point. But then shouldn't the help page for save mention this? (In Maple 11, it doesn't.)
Does LibraryTools:-Save fully obsolete save?

With the Optimization and Statistics (and GlobalOptimization) packages, Maple's skill at data analysis became greatly better. The new extensions to hardware float support are also useful. It would be really good to do more with data analysis. Here are three suggestions. First, given some two-dimensional data, find an interpolating curve with minimal total squared curvature (minκ²). People commonly use splines for interpolating unmodelled data, but splines have problems: they tend to wiggle around too much, the effect of shifting a point is non-local, etc. The minκ² curve is what most folks want in practice (even if they do not realize it). It is also the curve with minimal energy when bending a beam, and so arises in engineering. A Mathematica program to find minκ² was described by A.Alon & S.Bergmann [JPhysicsA 35: 3877-3898 (2002)]. (The authors also found minκⁿ for any n, but I do not see this as useful.) Some related work is by J.A.Edwards [ACM TOMS 18: 174-192 (1992); doi: 10.1145/146847.146925]. There is also some two-point work in the Maple Application Center, Engineering. Second, generalize the above for when the data ordinates have (normally-distributed) errors; i.e. so the curve does not exactly interpolate, but smooths the data, with the amount of smoothing controlled by a parameter. For this problem, the smoothing spline is commonly used; generalization of the above is much preferable, if it can be done without too much computation time. (No one else has done this, to my knowledge.) Third, include support for time series. ARMA models are supported by NAG (so that might be easy to implement); other models would also be nice to have.