import { bPdivTrivial } from "../../euclidean-division-related/bigint/b-pdiv-trivial.js";


/**
 * Returns `true` if the polynomial `b` divides the polynomial `a`, i.e. if
 * there exists a polynomial `r` such that `a = b*r`.
 * 
 * @param a 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`
 * @param b another polynomial
 */
function bDivides(
        b: bigint[],
        a: bigint[]) {

    if (b.length === 0) { return a.length === 0; }
    if (a.length === 0) { return false; }

    const { q, r } = bPdivTrivial(a, b);
    
    if (r.length !== 0) { return false; }

    const d = a.length - b.length + 1;
    const multiplier = b[0] ** BigInt(d);
    for (const c of q) {
        if (c % multiplier !== 0n) {
            return false;
        }
    }

    return true;
}


export { bDivides }


// Quokka tests
// import { bMultiply } from "./b-multiply.js";

// const a = bMultiply([1n,1n],[1n,-1n]);//?
// const { r } = bPdivTrivial([1n, 0n, -1n], [6n, -6n]);//?
// bDivides([4n, 0n, -4n], [2n,2n]);//?