const bChangeVariablesScale = bScale;


 /**
 * Returns the polynomial `p(s·x)`, i.e. the coefficient of `xⁱ` scaled by `sⁱ`.
 * 
 * @param p a polynomial with coefficients given densely as an array of bigint
 * numbers from highest to lowest power, e.g. `[5n,-3n,0n]` 
 * represents the polynomial `5x^2 - 3x`
 * @param s a scaling factor, i.e. the `s` in `p(x) <- p(sx)`
 * 
 * @example
 * ```typescript
 * bScale([1n,2n,7n], 3n); //=> [9n, 6n, 7n]
 * ```
 * 
 * @doc
 */
function bScale(
        p: bigint[],
        s: bigint): bigint[] {

    const n = p.length - 1;
    if (n < 0) { return []; }

    const r = new Array<bigint>(n + 1);
    r[n] = p[n];

    let sPow = s;
    for (let i=1; i<=n; i++) {
        r[n - i] = p[n - i] * sPow;
        sPow *= s;
    }

    return r;
}


/**
 * Returns the polynomial `p((1/s)·x)`, i.e. the coefficient of `xⁱ` scaled by `(1/s)ⁱ`.
 * 
 * * it is assumed that all coefficients are exactly divisible by `s`.
 * 
 * @param p a polynomial with coefficients given densely as an array of bigint
 * numbers from highest to lowest power, e.g. `[5n,-3n,0n]` 
 * represents the polynomial `5x^2 - 3x`
 * @param a a scaling factor, i.e. the `s` in `p(x) <- p((1/s)x)`
 * 
 * @example
 * ```typescript
 * bInvScale([16n, 8n, 7n], 4n); //=> [1n, 2n, 7n]
 * ```
 * 
 * @doc
 */
function bInvScale(
        p: bigint[],
        s: bigint): bigint[] {

    const n = p.length - 1;
    if (n < 0) { return []; }

    const r = new Array<bigint>(n + 1);
    r[n] = p[n];

    let sPow = s;
    for (let i=1; i<=n; i++) {
        r[n - i] = p[n - i] / sPow;
        sPow *= s;
    }

    return r;
}


export { bScale, bInvScale, bChangeVariablesScale }