flo-poly/src/factor/expansion/e-primitive-part.ts

A practical, root-focused JavaScript polynomial utility library.

import { eContent as eContent_ } from "./e-content.js";
import { eDiv as eDiv_ } 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 eContent = eContent_;
const eDiv = eDiv_;


/**
 * Returns the primitive part of the given polynomial.
 * 
 * * the sign is chosen such that the leading term coefficient is positive
 * 
 * * 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 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 ePrimitivePart(p: number[][]): number[][] {
    const c = eContent(p);

    const p_: number[][] = [];

    for (let i=0; i<p.length; i++) {
        p_.push(eDiv(p[i], c, 0));
    }

    return p_;
}


export { ePrimitivePart }