Numerical anylasis on linux

daniel_i_l

I just started to take a numerical anylasis course. Throughout the course we need to solve various problems using different numerical methods. I'm looking for a free linux-compatable program that'll let me plot graphs and implement numerical algorithms. I also need to be able to specify the degree of accuracy (decimal points in floating point arithmetic) that it uses while performing calculations.
I'm currently trying to decide between Octave, Maxima, and Scilab but I'm open to suggestions.
Also, what are the advantages/disadvantages to using a library like NumPy rather than complete software such as the programs I mentioned? I'm already familiar with python so it'd probably have an easier learning curve but does it give the same functionality as the other packages?
Thanks.