flo-poly/src/basic/expansion/e-product.ts

A practical, root-focused JavaScript polynomial utility library.

import { eMultiply } from "./e-multiply.js";


/**
 * Returns the exact result (bar underflow / overflow) of the product of 0 or 
 * more polynomials. 
 * 
 * * see [polynomial arithmetic](https://en.wikipedia.org/wiki/Polynomial_arithmetic)
 * * see [polynomial multiplication](https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Polynomial_multiplication)
 * * see [polynomial multiplication](http://web.cs.iastate.edu/~cs577/handouts/polymultiply.pdf)
 * 
 * @param ps an array of polynomials each 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`
 * 
 * @example
 * ```typescript
 * eProduct([[[1],[2],[3]], [[2],[5],[3],[5]]]); //=> [[2], [9], [19], [26], [19], [15]]
 * ```
 * 
 * @doc
 */
function eProduct(ps: number[][][]): number[][] {
	if (ps.length === 0) { return [[1]]; }

	let p = ps[0];
	for (let i=1; i<ps.length; i++) {
		p = eMultiply(p, ps[i]);
	}

	return p;
}


export { eProduct }