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.

// 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.:

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) 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

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 it becomes asymptotically slower (compared to Descartes Methods), 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!.

Installation

npm install flo-poly

In TypeScript or Node simply import whatever you need, e.g.:

import { allRoots } from 'flo-poly';

or if you prefer using a script and global var in the browser (not recommended):

<script src='node_modules/flo-poly/browser/index.min.js'></script>

and then use the global named FloPoly

const { allRoots } = FloPoly;

// ...