I'm just curious - and I don't work for Maplesoft :) - but what do people here actually use Maple for ? What sorts of problems are you tackling, and what commands/packages do you typically use ? I'm also interested to hear about how people use Maple in teaching (for those that do).

Myself I use Maple for research in computer algebra - mostly topics related to polynomial systems. For example, I may be trying to find algorithms to compute in new domains. I like Maple because it is very easy to program mathematical algorithms. It is not quite so easy to get them to run fast, but that gives me something to work on :) I mostly use my own software (PolynomialIdeals + recent code), but I also use the Groebner package and now the RegularChains package (new in Maple 10). I make a point of trying all the other packages every once in a while, since you never know when something is going to be useful. I use the plot commands a lot as well.

Anyway, I would like to know what other people are doing. What parts of the system do you think are really good, and what parts do you think are weak ? Personally I find the LinearAlgebra package to be a burden when the matrix entries are exact rational numbers - I think it really could be a lot better if it used modular methods. Oddly enough, the LinearAlgebra:-Modular package seems to be one of the strongest Maple packages. It almost always does what I need, although it lacks support for sparse matrices.