[![Coverage Status](https://coveralls.io/repos/github/FlorisSteenkamp/FloPoly/badge.svg?branch=master)](https://coveralls.io/github/FlorisSteenkamp/FloPoly?branch=master) [![Build Status](https://travis-ci.org/FlorisSteenkamp/FloPoly.svg?branch=master)](https://travis-ci.org/FlorisSteenkamp/FloPoly) # Overview The focus is to find real roots of real coefficient polynomials from degree 1 up to about degree 20 as accurately and as fast as possible, e.g. ```typescript // some polynomial with double precision coefficients, i.e. x^6 - 21x^5 + 175x^4 - 735x^3 + 1624x^2 - 1764 + 720 const p = [1, -21, 175, -735, 1624, -1764, 720]; allRoots(p); //=> [0.9999999999999997, 2.0000000000000013, 2.9999999999999316, 4.00000000000096, 5.000000000000012, 6.00000000000028] ``` However, the above function, `allRoots`, does not take error bounds into account and can thus be inaccurate if the roots have high condition numbers. For extremely accurate (no matter how high the condition number) certified results use e.g.: ```typescript const p = [1, -21, 175, -735, 1624, -1764, 720]; // some polynomial with double precision coefficients allRootsCertifiedSimplified(p); ``` or for a more flexible function that takes the input polynomial coefficients as double-double precision and the ability to specify error bounds on the coefficients in addition to a fallback function to specify exact coefficients (in the form of [Shewchuk expansions](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf)) use `allRootsCertified`. Though the focus is on root finding, the library include numerous useful operators on polynomials with `double`, `double-double`, `Shewchuk expansion` and `bigint` coefficients, e.g ```typescript add([1,2,3], [3,4]); //=> [1,5,7] ``` ## Why only up to about degree 20? This isn't a hard limit. Roughly speaking, since the roots are found using [Rolle's Theorem](https://en.wikipedia.org/wiki/Rolle%27s_theorem) it becomes asymptotically slower (compared to [Descartes Methods](https://en.wikipedia.org/wiki/Descartes%27_rule_of_signs)), i.e. roughly `O(n²)` vs `O(n)` the higher the polynomial degree, `n`. Another reason is that evaluation of the polynomial at `x` when `|x| >> 1` can result in overflow when the result is larger than about `1.8 x 10^308` (the max value a double precision floating point value can be). # Documentation For more in-depth documentation please [read the docs!](https://florissteenkamp.github.io/FloPoly). # Installation ```cli npm install flo-poly ``` This package is [ESM only](https://gist.github.com/sindresorhus/a39789f98801d908bbc7ff3ecc99d99c) and can be used in `Node.js` or in a browser. For direct browser support (without using a bundler), `index.js` and `index.min.js` are provided in the `./browser` folder. # Usage ### Node.js ```JavaScript import { allRoots } from 'flo-poly'; // some polynomial with double precision coefficients, i.e. x^6 - 21x^5 + 175x^4 - 735x^3 + 1624x^2 - 1764 + 720 const p = [1, -21, 175, -735, 1624, -1764, 720]; const roots = allRoots(p); if (roots.length === 6) { console.log('success! 😁'); // we should get to here! } else { console.log('failure! 😥'); // ...and not here } ``` ### Browsers - directly, without a bundler, using the pre-bundled minified .js file Please note that no tree shaking will take place in this case. ```html Check the console. ``` ### Bundlers (Webpack, Rollup, ...) Webpack will be taken as an example here. Since your webpack config file might still use `CommonJS` you must rename `webpack.config.js` to `webpack.config.cjs`. If you are using TypeScript: This is an [ESM only](https://gist.github.com/sindresorhus/a39789f98801d908bbc7ff3ecc99d99c) library. Follow this [guide](https://gist.github.com/sindresorhus/a39789f98801d908bbc7ff3ecc99d99c#how-can-i-make-my-typescript-project-output-esm).