//--------------------------
// SUPERSEDED BY `taylorShift` !!
//--------------------------

// /**
//  * Returns the result of performing a change of variables of the 
//  * form: p(x) <- p(x + b) in double precision.
//  * 
//  * * see [this stackoverflow question](http://stackoverflow.com/questions/141422/how-can-a-transform-a-polynomial-to-another-coordinate-system)
//  * 
//  * @param p a polynomial with coefficients given densely as an array of double
//  * floating point numbers from highest to lowest power, e.g. `[5,-3,0]` 
//  * represents the polynomial `5x^2 - 3x`
//  * @param b the `b` in `x + b`
//  * 
//  * @example
//  * ```typescript
//  * changeVariablesTranslateX([1,2,7], 3); //=> [1, 8, 22]
//  * ```
//  * 
//  * @doc
//  */
// function changeVariablesTranslateX(
//         p: number[], 
//         b: number): number[] {

//     // We let the coefficients of p(x + b) be denoted by d_i in the code below. 
//     // d_i is calculated as d = T*c, where c are the original coefficients.
     
//     const d = p.length-1;

//     if (d < 0) { return []; }
    
//     // Initialize a zero matrix
//     const t = new Array<number[]>(d+1);
//     for (let i=0; i<d+1; i++) {
//         t[i] = new Array(d+1).fill(0);
//     }

//     // Calculate the triangular matrix T
//     t[0][0] = 1;
//     for (let j=1; j<=d; j++) {
//         t[0][j] = b*t[0][j-1];
//         for (let i=1; i<=j; i++) {
//             t[i][j] = b*t[i][j-1] + t[i-1][j-1];
//         }
//     }
    
//     // Multiply
//     const res: number[] = new Array(d+1).fill(0);
//     for (let i=0; i<=d; i++) {
//         res[d-i] = 0;
//         for (let j=i; j<=d; j++) {
//             res[d-i] += t[i][j] * p[d-j];
//         }
//     }
    
//     return res;
// }


// export { changeVariablesTranslateX }