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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_polynomial::RationalPolynomial;
use malachite_base::num::arithmetic::traits::{Square, SquareAssign};
impl Square for RationalPolynomial {
type Output = Self;
/// Squares a [`RationalPolynomial`], taking it by value.
///
/// $$
/// f(p) = p^2.
/// $$
///
/// With $p = x/a$ in lowest terms, $x^2/a^2$ is in lowest terms too: by Gauss's lemma the
/// content of $x^2$ is the square of the content of $x$, which is coprime to $a$. So no GCD is
/// needed.
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is the largest
/// number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// RationalPolynomial::from_str("1/2*x+1/3")
/// .unwrap()
/// .square()
/// .to_string(),
/// "1/4*x^2+1/3*x+1/9"
/// );
/// assert_eq!(
/// RationalPolynomial::from_str("x-1")
/// .unwrap()
/// .square()
/// .to_string(),
/// "x^2-2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_mul` from `fmpq_poly/mul.c`, FLINT 3.6.0, with both factors
/// the same polynomial.
fn square(self) -> Self {
Self {
numerator: self.numerator.square(),
denominator: self.denominator.square(),
}
}
}
impl Square for &RationalPolynomial {
type Output = RationalPolynomial;
/// Squares a [`RationalPolynomial`], taking it by reference.
///
/// $$
/// f(p) = p^2.
/// $$
///
/// With $p = x/a$ in lowest terms, $x^2/a^2$ is in lowest terms too: by Gauss's lemma the
/// content of $x^2$ is the square of the content of $x$, which is coprime to $a$. So no GCD is
/// needed.
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is the largest
/// number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .square()
/// .to_string(),
/// "1/4*x^2+1/3*x+1/9"
/// );
/// assert_eq!(
/// (&RationalPolynomial::from_str("x-1").unwrap())
/// .square()
/// .to_string(),
/// "x^2-2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_mul` from `fmpq_poly/mul.c`, FLINT 3.6.0, with both factors
/// the same polynomial.
fn square(self) -> RationalPolynomial {
RationalPolynomial {
numerator: (&self.numerator).square(),
denominator: (&self.denominator).square(),
}
}
}
impl SquareAssign for RationalPolynomial {
/// Squares a [`RationalPolynomial`] in place.
///
/// $$
/// p \gets p^2.
/// $$
///
/// No GCD is needed; see the [`Square`] implementation for why.
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is the largest
/// number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::SquareAssign;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("1/2*x+1/3").unwrap();
/// p.square_assign();
/// assert_eq!(p.to_string(), "1/4*x^2+1/3*x+1/9");
/// ```
///
/// This is equivalent to `fmpq_poly_mul` from `fmpq_poly/mul.c`, FLINT 3.6.0, with both factors
/// the same polynomial.
fn square_assign(&mut self) {
self.numerator.square_assign();
self.denominator.square_assign();
}
}