Show HN: Interactive polynomial roots toy

69 points by duetosymmetry 7 years ago | 9 comments
  • raverbashing 7 years ago
    For those curious what practical usage this might have, there is a control technique that uses the position of roots to determine how a system will behave as the feedback gain is changed https://en.wikipedia.org/wiki/Root_locus

    Or basically, how loud can you crank an amplifier before you hear feedback (and how does it behave with different levels of feedback)

    • BucketSort 7 years ago
      This is GREAT! Reminds me of the http://explorabl.es/ project. The library it links to is very cool as well - http://jsxgraph.uni-bayreuth.de/wp/
      • lancebeet 7 years ago
        Cool, really enjoyable to play around with. This made me notice a cute (probably trivial) phenomenon that I haven't seen before. If you take x^n+...+1 and move one of the roots to 1 (equivalently, divide x^(n+1)-1 by (x-z) where z is some nth root of unity), then the resulting polynomial's coefficients seem to be the nth roots of unity.

        By the way, it doesn't seem to prevent you from entering a degree higher than 7 if you enter the number manually even though it gives off a warning. Not sure if this is intentional.

        • duetosymmetry 7 years ago
          I wanted to keep the UI from getting too busy, which is why I limited the degree to 7. But if somebody really wants to play with higher-degree polynomials, I'm not going to stop them!
        • Aditya_Garg 7 years ago
          Could you open source the code? I think this tool would be really helpful for one of my professors in explaining gain margin for feedback systems.
        • anigbrowl 7 years ago
          This is unreasonably enjoyable. Would also make a great musical toy...
          • ttoinou 7 years ago
            Very cool to see one graph moving when changing the other graph. I must find a way to make cools fractals with that concept