flo-poly/src/factor/bigint/b-primitive-part.ts

A practical, root-focused JavaScript polynomial utility library.

import { bContent as bContent_ } from "./b-content.js";

// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗ Otherwise code is too slow❗
const bContent = bContent_;


/**
 * Returns the primitive part of the given polynomial.
 * 
 * * see e.g. [Factorization of polynomials](https://en.wikipedia.org/wiki/Factorization_of_polynomials)
 * 
 * * the sign is chosen such that the leading term coefficient is positive
 * 
 * * 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
 * bigints from highest to lowest power, e.g. `[5n,-3n,0n]` represents the 
 * polynomial `5x^2 - 3x`
 * 
 * @doc
 */
function bPrimitivePart(p: bigint[]): bigint[] {
    const c = bContent(p);

    const p_: bigint[] = [];

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

    return p_;
}


export { bPrimitivePart }