import { bSturmChain } from "../../../euclidean-division-related/bigint/b-sturm-chain.js";
import { bSignChanges } from "./b-sign-changes.js";
import { bEvaluateAt1 } from "../../../evaluate/bigint/b-evaluate-at-1.js";


/**
 * Returns the *exact* number of *distinct* real roots in the **closed**
 * interval `[0,1]` of the given polynomial.
 * 
 * @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 bNumRootsIn01(
        p: bigint[]): number {

    // Check for root at 0
    let numRootsAt0 = 0;
    while (p.length > 0 && p[p.length-1] === 0n) {
        p = p.slice(0, p.length - 1);
        numRootsAt0++;
    }

    const ps = bSturmChain(p);
    const as = ps.map(p => p[p.length-1]);    // evaluate at 0
    const bs = ps.map(p => bEvaluateAt1(p));  // evaluate at 1

    return bSignChanges(as) - bSignChanges(bs) + numRootsAt0;
}


export { bNumRootsIn01 }