import { eScale } from './e-scale.js';
import { eTaylorShift } from './e-taylor-shift.js';


/**
 * Returns the exact result (bar underflow / overflow) of performing a change 
 * of variables of the form: p(x) <- p(ax + b) on the given polynomial (with
 * coefficients given as Shewchuk expansions).
 * 
 * * 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 Shewchuk
 * floating point expansions 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
 * eChangeVariablesLinear([[1],[2],[7]], 3, 4); //=> [[9], [30], [31]]
 * ```
 * 
 * @doc
 */
function eChangeVariablesLinear(
        p: number[][], 
        a: number, 
        b: number): number[][] {

    return eScale(eTaylorShift(p, b), a);
}


export { eChangeVariablesLinear }