/**
 * Returns the result of reflecting the given polynomial about the Y-axis, i.e. 
 * perform the change of variables: p(x) <- p(-x).
 * 
 * @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`
 * 
 * @example
 * ```typescript
 * bReflectAboutYAxis([5n, 4n, 3n, 2n, 1n]); //=> [5n, -4n, 3n, -2n, 1n]
 * ```
 * 
 * @doc
 */
function bReflectAboutYAxis(
        p: bigint[]): bigint[] {

    const d = p.length-1;

    if (d < 0) { return []; }

    const result = p.slice();
    for (let i=0; i<d+1; i++) {
        if (i % 2 === (d - 1) % 2) {
            result[i] = -result[i]; 
        }
    }
    
    return result;
}


export { bReflectAboutYAxis }