I've found this Wolfram Demonstrations applet illustrating Sendov's Conjecture very interesting to play around with and have been working on writing my own version in the MATLAB language. I thought that would be faster than learning to create interactive applets in Mathematica. Moreover, I have a free option, Octave, which uses the MATLAB language.
The shortfall of this is that, as far as I know, Octave doesn't support dynamic interactivity. I'm wondering what other free software is out there that would be better-suited to creating a program like the applet I linked to.
EDIT: To be more specific, by "dynamic" I'm thinking of the sort of drag-and-drop capabilities that Mathematica demonstrates in the link above. In that example, Mathematica reevaluates the polynomial's critical points in real time as a root is dragged.
Thank you for reading!