import { scale } from './scale.js';
import { taylorShift } from './taylor-shift.js';

/**
 * Returns the result of performing a change of variables of the 
 * form: p(x) <- p(ax + 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 a the `a` in `ax + b`
 * @param b the `b` in `ax + b`
 * 
 * @example
 * ```typescript
 * changeVariablesLinear([1,2,7], 3, 4); //=> [9, 30, 31]
 * ```
 * 
 * @doc
 */
function changeVariablesLinear(
        p: number[], 
        a: number, 
        b: number): number[] {

    return scale(taylorShift(p, b), a);
}


export { changeVariablesLinear }