6 ms·

Show HN: Interactive polynomial roots toy

69 points by duetosymmetry 9y ago

raverbashing 9y 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 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)
ttoinou 9y 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
- Strilanc 9y ago
  If you restrict the possible coefficients, and limit the maximum degree, you get interesting fractal patterns: https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-of-roots/ https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-o...
anigbrowl 9y ago
This is unreasonably enjoyable. Would also make a great musical toy...
BucketSort 9y ago
This is GREAT! Reminds me of the http://explorabl.es/ http://explorabl.es/ project. The library it links to is very cool as well - http://jsxgraph.uni-bayreuth.de/wp/ http://jsxgraph.uni-bayreuth.de/wp/
lancebeet 9y 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 9y 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 9y 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.
- duetosymmetry 9y ago
  Hi, yes, it's open source. My web site's github repo is at https://github.com/duetosymmetry/web-site/tree/customization https://github.com/duetosymmetry/web-site/tree/customization . The JS for controlling the web toy is at https://github.com/duetosymmetry/web-site/blob/customization/assets/js/poly-root-toy.js https://github.com/duetosymmetry/web-site/blob/customization... . This relies on a modified version of Polynomial.js which I will hopefully get accepted upstream, but for now it's just on my fork at https://github.com/duetosymmetry/Polynomial.js/tree/Aberth https://github.com/duetosymmetry/Polynomial.js/tree/Aberth (though this is also behind my local repo).

69 points by duetosymmetry 9y 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 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)

ttoinou 9y 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

Strilanc 9y ago
If you restrict the possible coefficients, and limit the maximum degree, you get interesting fractal patterns: https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-of-roots/ https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-o...

anigbrowl 9y ago

This is unreasonably enjoyable. Would also make a great musical toy...

BucketSort 9y ago

This is GREAT! Reminds me of the http://explorabl.es/ http://explorabl.es/ project. The library it links to is very cool as well - http://jsxgraph.uni-bayreuth.de/wp/ http://jsxgraph.uni-bayreuth.de/wp/

lancebeet 9y 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 9y 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 9y 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.

duetosymmetry 9y ago
Hi, yes, it's open source. My web site's github repo is at https://github.com/duetosymmetry/web-site/tree/customization https://github.com/duetosymmetry/web-site/tree/customization . The JS for controlling the web toy is at https://github.com/duetosymmetry/web-site/blob/customization/assets/js/poly-root-toy.js https://github.com/duetosymmetry/web-site/blob/customization... . This relies on a modified version of Polynomial.js which I will hopefully get accepted upstream, but for now it's just on my fork at https://github.com/duetosymmetry/Polynomial.js/tree/Aberth https://github.com/duetosymmetry/Polynomial.js/tree/Aberth (though this is also behind my local repo).