What is the best mathematics software for Linux? What is the best general mathematics software, the best computer algebra system? What's the best software for learners?
Which is the easiest to use, while at the same being very full-featured?
If at all possible, please list what the most high-quality, full-featured, easy-to-use software is. I would appreciate a list of software for people who aren't great at mathematics, but are in the process of learning. To put it another way, software that you don't have to know much or learn too much to use, but that as you get better you can put to very good use (without having to switch over to different software), and that you can use for simpler things, also. Taking all of this into consideration, plotting is a must.

Look into maxima/wxmaxima. It is a full-featured, easy-to-use CAS, and can do simple 2-D and 3-D plotting.

Other math tools I've used include gsl (GNU Scientific Libraries), and Coq (an automated proof checker), but these require programming skills and/or more advanced math knowledge to use.

--jrtayloriv

A lot of people are using "R" on Linux: http://www.r-project.org/
People with a Matlab background usually like "octave": http://www.gnu.org/software/octave/

I goofed around with R before, but not for long enough to really learn about it. I mostly used examples, just to get some idea of it.
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Do you think learning Lisp is at all important if you want to use Maxima well?

I'm sure it wouldn't hurt. But I don't know any Lisp, and I've never run into an area where this has caused me problems.

Take a look at Octave (MATLAB clone) and SciLab. I use MATLAB for my studies, and I've found Octave to be a very good free replacement (for when I work at home). I've never used SciLab, but have heard good things.

In general, they're pretty straightforward to use, though you obviously have to learn their syntax. At its simplest, Octave/MATLAB is just like a calculator:They get progressively more powerful depending on what you want to achieve.

I'd say octave, but SciPy is turning out to be a pretty cool math environment.

Really? I'm in the process of learning about Python right now ...
I installed Octave yesterday, but haven't started reading about it yet.
The main reasons I installed Octave is because it's GNU, and it's mostly compatible with MATLAB (which I've heard a lot about, and is very popular).
I goofed around with Maxima before when I was using Windows XP. It seemed to me like you wouldn't really need to learn all about Lisp, but that at least learning how to put it to general use would be nice (to save time thinking about it if you ever have to do a little tinkering with things).

in college i used matlab and systemview (systemview is more for digital system processing).
theres also autocad and labview.

I am going to say +1 to SciPy, even though I have not had a chance to use it yet. However, I started going through the Python tutorials while waiting for builds, and I was struck by how similar some of the Python syntax is to Matlab.

One of the problems with Octave is that it is incredibly slow compared with Matlab. If Python has solved this problem, then it is worth switching. After I investigate SciPy further, I will come back to either confirm or revoke my "+1 to SciPy".

Octave will do it.
SciLab is good too, but it's less intuitive.

R is mostly for statistics.

download SAGE: http://sagemath.org/
It's designed to replace Mathematica, Matlab, Maple, etc.