What are you using for symbolic computation? What are the pluses and minuses of different software packages? Anything new worth checking out?
I'm especially interested in open source packages.
 A: Someone should also mention Axiom, which started out as commercial package developed by IBM but after a long and tortuous journey is now open source. As I understand it, it is built on a strongly typed, mathematically oriented and user extensible type hierarchy. So it knows what groups, rings and fields are, and it lets you define your own and do computation in them.
A: I tend to use Macaulay2 for research related stuff
Some points about it.


*

*It is open source

*It is specific to algebraic geometry/commutative algebra (but since this is a large community on mathoverflow...)

*Is actively being developed (it seems to have several conferences devoted to it each year in recent years).

*It is a unix program so you need cygwin to run it on windows.

*The preferred environment to run it seems to be in an emacs window (although various people are working on other interfaces I understand).


I've also heard good things about Sage but haven't tried it.
A: If you haven't already, you should try Sage.
Advantages:


*

*Open source.

*Includes many different packages (including GAP, Maxima, Singular, PARI/GP, and R, just to name a few), and provides a common interface for them.

*Has a built-in Python interpreter.

*You can install it on a server and allow people to run it remotely, through a web browser.

*Is still actively being developed.


(Possible) Disadvantage:


*

*No native Windows version. (You can still run it on Windows, but you have to run it under a virtual machine. This is fairly straightforward, though.)

A: I suggest you to try Reduce, it is OpenSource and there are RPM packeges. It looks like this: 
alt text http://static.itmages.ru/i/10/1012/h_1286887665_4af06aa049.png
A: The only open-source CAS (Computer Algebra System) that I know of is called Maxima, but as I have not used it, I cannot say whether it is any good. I own a copy of Mathematica 7.0, and can say that it is superb. The programming language is easy to learn, and in many ways quite similar to that of the TI-89. The university I attend uses Maple 13, which from my experience is not as strong as Mathematica in the area of purely symbolic manipulation, but is superior in terms of numerical modeling.
A: For quick calculations, I use Wolfram|Alpha, which is not open source but is a free web service.
