#pragma once

#include <vector>

#include <Eigen/Core>

#include "drake/common/symbolic/polynomial.h"

namespace drake {
namespace solvers {

/**
 * Given input polynomial p, outputs a set M of monomials with the following
 * guarantee: if p = f1*f1 + f2*f2 + ... + fn*fn for some (unknown) polynomials
 * f1, f2, ..., fn, then the span of M contains f1, f2, ..., fn,  Given M, one
 * can then find the polynomials fi using semidefinite programming; see,
 * e.g., Chapter 3 of Semidefinite Optimization and Convex Algebraic Geometry
 * by G. Blekherman, P. Parrilo, R. Thomas.
 * @param p A polynomial
 * @return A vector whose entries are the elements of M
 */
[[nodiscard]] drake::VectorX<symbolic::Monomial> ConstructMonomialBasis(
    const drake::symbolic::Polynomial& p);
}  // namespace solvers
}  // namespace drake