/**
 * Returns the result of multiplying 2 polynomials in double precision.
 *
 * * 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 p1 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 p2 another polynomial.
 *
 * @example
 * ```typescript
 * multiply([1,2,3], [2,5,3,5]); //=> [2, 9, 19, 26, 19, 15]
 * ```
 *
 * @doc
 */
declare function multiply(p1: number[], p2: number[]): number[];
/**
 * Returns the result of multiplying 2 polynomials in double precision using
 * the [Karatsuba](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
 * divide-and-conquer algorithm (`O(n^log2(3)) ≈ O(n^1.585)`).
 *
 * @param p1 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 p2 another polynomial.
 *
 * @example
 * ```typescript
 * multiplyKaratsuba([1,2,3], [2,5,3,5]); //=> [2, 9, 19, 26, 19, 15]
 * ```
 *
 * @doc
 */
declare function multiplyKaratsuba(p1: number[], p2: number[]): number[];
export { multiply, multiplyKaratsuba };