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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::Rational;
use crate::rational_polynomial::RationalPolynomial;
use malachite_base::num::arithmetic::traits::Square;
use malachite_base::polynomial::L2NormSquared;
impl L2NormSquared for &RationalPolynomial {
type Output = Rational;
/// Computes the sum of the squares of a [`RationalPolynomial`]'s coefficients, which is the
/// square of its $L^2$ norm.
///
/// $$
/// f(p) = \sum_i p_i^2.
/// $$
///
/// With the polynomial written as $x/d$ in lowest terms, this is the integer sum of the squares
/// of the coefficients of $x$ over $d^2$, reduced.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::L2NormSquared;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// RationalPolynomial::from_str("1/2*x^2-1/3")
/// .unwrap()
/// .l2_norm_squared()
/// .to_string(),
/// "13/36"
/// );
/// assert_eq!(
/// RationalPolynomial::from_str("1/2*x+1/2")
/// .unwrap()
/// .l2_norm_squared()
/// .to_string(),
/// "1/2"
/// );
/// assert_eq!(
/// RationalPolynomial::from_str("x-3")
/// .unwrap()
/// .l2_norm_squared()
/// .to_string(),
/// "10"
/// );
/// ```
#[inline]
fn l2_norm_squared(self) -> Rational {
Rational::from_naturals(
(&self.numerator).l2_norm_squared(),
(&self.denominator).square(),
)
}
}