flo-poly/src/factor/expansion/e-content.ts

A practical, root-focused JavaScript polynomial utility library.

import { eGcdInts as eGcdInts_ } from "../../gcd/expansion/e-integer-gcd.js";
import { eSign as eSign_ } from "big-float-ts";
import { eNegativeOf as eNegativeOf_ } from "big-float-ts";

// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗ Otherwise code is too slow❗
const eGcdInts = eGcdInts_;
const eSign = eSign_;
const eNegativeOf = eNegativeOf_;


/**
 * Returns cont(p), i.e. the content of the given polynomial defined as the 
 * greatest common divisor of its coefficients.
 * 
 * * the sign is chosen such that dividing the polynomial by cont(p) will
 * always result in a positive leading coefficient
 * 
 * * see e.g. [Factorization of polynomials](https://en.wikipedia.org/wiki/Factorization_of_polynomials)
 * 
 * * example: let `p = -10x² + 5x + 5 = (-5)(2x² - x - 1)` so that `-5` is the 
 * content of `p` and `2x² - x - 1` is its primitive part.
 * 
 * @param p a polynomial with coefficients given densely as an array of
 * Shewchuk expansions from highest to lowest power, e.g. `[[5],[-3],[0]]` 
 * represents the polynomial `5x^2 - 3x`
 * 
 * @doc
 */
function eContent(p: number[][]): number[] {
    if (p.length === 0) { 
        // the zero polynomial
        return [1];
    }
    return eSign(p[0]) < 0 ? eNegativeOf(eGcdInts(p)) : eGcdInts(p);
}


export { eContent }