I like a lot of things about Wolfram's Mathematica software; it is an extremely useful tool for symbolic mathematical manipulations and visualization of various functions.  However, it is expensive software so recently I have been exploring if there is a free alternative.  In doing this I came across Cantor that can run SageMath as a backend, which in turn is built on top of Maxima and other packages.

In the screenshot above I took it for a test drive.  In the first lines I set up an equation and told it to solve for .  In the next lines it integrated one of the solutions,

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Right after that I had it display the TeX code for typesetting the equation, which I can reuse to get it displayed below.

Next is a five by five matrix of random numbers, from this the eigenvalues (a summary of how the matrix transformation tends to behave when applied to a system) are calculated and in this example two of them happen to be complex numbers (which indicates that the system has a rotational quality in two of its five dimensions).  Last there is a plot to visualize the matrix entries but it is cut off at the bottom of the window in this image.

I am impressed.  It is still not capable of all the tools built into mathematica but I am glad I came across this.