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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 crate::rational_polynomial::arithmetic::mul_truncated::canonicalize_truncated;
use core::mem::take;
use malachite_base::num::arithmetic::traits::Square;
use malachite_base::polynomial::{SquareTruncated, SquareTruncatedAssign};
impl SquareTruncated for RationalPolynomial {
type Output = Self;
/// Squares a [`RationalPolynomial`], keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking it by value.
///
/// $$
/// f(p, n) = p^2 \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the square of its image modulo $x^n$.
/// Truncation can leave the numerator sharing a factor with the denominator, so the result is
/// reduced afterwards.
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `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::polynomial::SquareTruncated;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// // The square is 1/4*x^2+1/3*x+1/9; its low two coefficients.
/// assert_eq!(
/// RationalPolynomial::from_str("1/2*x+1/3")
/// .unwrap()
/// .square_truncated(2)
/// .to_string(),
/// "1/3*x+1/9"
/// );
/// // The square is 1/4*x^4+x^3+2*x^2+2*x+1; once the quartic term is cut, nothing is left over
/// // 4.
/// assert_eq!(
/// RationalPolynomial::from_str("1/2*x^2+x+1")
/// .unwrap()
/// .square_truncated(3)
/// .to_string(),
/// "2*x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_mullow` from `fmpq_poly/mullow.c`, FLINT 3.6.0, with both
/// factors the same polynomial.
#[inline]
fn square_truncated(self, len: u64) -> Self {
canonicalize_truncated(
self.numerator.square_truncated(len),
self.denominator.square(),
)
}
}
impl SquareTruncated for &RationalPolynomial {
type Output = RationalPolynomial;
/// Squares a [`RationalPolynomial`], keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking it by reference.
///
/// $$
/// f(p, n) = p^2 \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the square of its image modulo $x^n$.
/// Truncation can leave the numerator sharing a factor with the denominator, so the result is
/// reduced afterwards.
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `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::polynomial::SquareTruncated;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// // The square is 1/4*x^2+1/3*x+1/9; its low two coefficients.
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .square_truncated(2)
/// .to_string(),
/// "1/3*x+1/9"
/// );
/// // The square is 1/4*x^4+x^3+2*x^2+2*x+1; once the quartic term is cut, nothing is left over
/// // 4.
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x^2+x+1").unwrap())
/// .square_truncated(3)
/// .to_string(),
/// "2*x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_mullow` from `fmpq_poly/mullow.c`, FLINT 3.6.0, with both
/// factors the same polynomial.
#[inline]
fn square_truncated(self, len: u64) -> RationalPolynomial {
canonicalize_truncated(
(&self.numerator).square_truncated(len),
(&self.denominator).square(),
)
}
}
impl SquareTruncatedAssign for RationalPolynomial {
/// Squares a [`RationalPolynomial`] in place, keeping only the coefficients of $x^i$ for $i$
/// less than `len`.
///
/// $$
/// p \gets p^2 \bmod x^n.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n^{\log_2 3} m \log m \log\log m + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `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::polynomial::SquareTruncatedAssign;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("1/2*x^2+x+1").unwrap();
/// p.square_truncated_assign(3);
/// assert_eq!(p.to_string(), "2*x^2+2*x+1");
/// ```
///
/// This is equivalent to `fmpq_poly_mullow` from `fmpq_poly/mullow.c`, FLINT 3.6.0, with both
/// factors the same polynomial.
fn square_truncated_assign(&mut self, len: u64) {
*self = take(self).square_truncated(len);
}
}