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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::AddMulAssign;
use malachite_base::num::basic::traits::Zero;
use malachite_base::polynomial::L2NormSquared;
impl L2NormSquared for &NaturalPolynomial {
type Output = Natural;
/// Computes the sum of the squares of a [`NaturalPolynomial`]'s coefficients, which is the
/// square of its $L^2$ norm.
///
/// $$
/// f(p) = \sum_i p_i^2.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::L2NormSquared;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^2+3*x+2")
/// .unwrap()
/// .l2_norm_squared(),
/// 14u32
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("0").unwrap().l2_norm_squared(),
/// 0u32
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("5").unwrap().l2_norm_squared(),
/// 25u32
/// );
/// ```
///
/// This is the dot product of the coefficients with themselves that `_fmpz_poly_2norm` in
/// `fmpz_poly/2norm.c`, FLINT 3.6.0, computes before taking the square root.
fn l2_norm_squared(self) -> Natural {
let mut sum = Natural::ZERO;
for c in &self.coefficients {
let a = c;
sum.add_mul_assign(a, a);
}
sum
}
}