I have always used R and Python for statistical analyses and object-oriented programming. Now, I have to perform relatively demanding (long to perform) mathematical analyses such as derivations and integrations of big functions, large matrix multiplication, finding general solutions to recurrence relations, analysis of Markov models, etc...
From the comment and answer I got from this question it seems to me that R might not be an optimal programming language for this kind of mathematical analysis. Therefore, I am asking:
What free programming language/softwares would you recommend to perform linear algebra calculations and (stochastic) function analyses?
Is R really a poor choice for this kind of tasks?
Note: This question has been considered off-topic on stack overflow. Hope that will be accepted here.
I agree that R, a statistical computing language, is probably less than ideal for your needs. I recommend Sage. It's free and open-source and allows you to call on a bunch of other tools, like GAP. It's built off of Python, so it's very easy to read and intuitive to learn.