flo-poly/src/basic/bigint/b-multiply.ts

A practical, root-focused JavaScript polynomial utility library.

/**
 * Returns the result of multiplying 2 polynomials with bigint coefficients.
 * 
 * * 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 a 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`
 * @param b another polynomial.
 * 
 * @example
 * ```typescript
 * bMultiply([1n,2n,3n], [2n,5n,3n,5n]); //=> [2n, 9n, 19n, 26n, 19n, 15n]
 * ```
 * 
 * @doc
 */
function bMultiply(a: bigint[], b: bigint[]): bigint[] {
	const da = a.length-1;
	const db = b.length-1;

	// if either or both is the zero polynomial
	if (da < 0 || db < 0) { 
		return [];
	}

	const d = da + db;
	
	const r: bigint[] = new Array(d+1).fill(0n);
	for (let i=0; i<da+1; i++) {
		for (let j=0; j<db+1; j++) {
			r[d-(i+j)] += (a[da-i] * b[db-j]); 				
		}
	}

	return r;
}


export { bMultiply }