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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::Pow;
use malachite_base::polynomial::{PowTruncated, PowTruncatedAssign};
impl PowTruncated for RationalPolynomial {
type Output = Self;
/// Raises a [`RationalPolynomial`] to a power, keeping only the coefficients of $x^i$ for $i$
/// less than `len`, taking it by value.
///
/// $$
/// f(p, e, n) = p^e \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the power of its image modulo $x^n$.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0. Truncation can
/// leave the numerator sharing a factor with the denominator, so the result is reduced
/// afterwards.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm) + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is `exp` times the
/// largest number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncated;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// (RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .pow_truncated(3, 2)
/// .to_string(),
/// "1/6*x+1/27"
/// );
/// // The low coefficients of the cube have no denominator left.
/// assert_eq!(
/// (RationalPolynomial::from_str("1/2*x^2+x+1").unwrap())
/// .pow_truncated(3, 2)
/// .to_string(),
/// "3*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_pow_trunc` from `fmpq_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that the truncated power of the numerator is computed over the integers and reduced
/// against the power of the denominator once, at the end, where FLINT reduces after every
/// truncated multiplication.
#[inline]
fn pow_truncated(self, exp: u64, len: u64) -> Self {
canonicalize_truncated(
self.numerator.pow_truncated(exp, len),
self.denominator.pow(exp),
)
}
}
impl PowTruncated for &RationalPolynomial {
type Output = RationalPolynomial;
/// Raises a [`RationalPolynomial`] to a power, keeping only the coefficients of $x^i$ for $i$
/// less than `len`, taking it by reference.
///
/// $$
/// f(p, e, n) = p^e \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the power of its image modulo $x^n$.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0. Truncation can
/// leave the numerator sharing a factor with the denominator, so the result is reduced
/// afterwards.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm) + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is `exp` times the
/// largest number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncated;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .pow_truncated(3, 2)
/// .to_string(),
/// "1/6*x+1/27"
/// );
/// // The low coefficients of the cube have no denominator left.
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x^2+x+1").unwrap())
/// .pow_truncated(3, 2)
/// .to_string(),
/// "3*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_pow_trunc` from `fmpq_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that the truncated power of the numerator is computed over the integers and reduced
/// against the power of the denominator once, at the end, where FLINT reduces after every
/// truncated multiplication.
#[inline]
fn pow_truncated(self, exp: u64, len: u64) -> RationalPolynomial {
canonicalize_truncated(
(&self.numerator).pow_truncated(exp, len),
(&self.denominator).pow(exp),
)
}
}
impl PowTruncatedAssign for RationalPolynomial {
/// Raises a [`RationalPolynomial`] to a power in place, keeping only the coefficients of $x^i$
/// for $i$ less than `len`.
///
/// $$
/// p \gets p^e \bmod x^n.
/// $$
///
/// The polynomial need not already be truncated: this is the power of its image modulo $x^n$.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0. Truncation can
/// leave the numerator sharing a factor with the denominator, so the result is reduced
/// afterwards.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm) + n m (\log m)^2 \log\log m)$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `len`, and $m$ is `exp` times the
/// largest number of significant bits of any numerator coefficient or of the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncatedAssign;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("1/2*x+1/3").unwrap();
/// p.pow_truncated_assign(3, 2);
/// assert_eq!(p.to_string(), "1/6*x+1/27");
///
/// // The low coefficients of the cube have no denominator left.
/// let mut p = RationalPolynomial::from_str("1/2*x^2+x+1").unwrap();
/// p.pow_truncated_assign(3, 2);
/// assert_eq!(p.to_string(), "3*x+1");
/// ```
///
/// This is equivalent to `fmpq_poly_pow_trunc` from `fmpq_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that the truncated power of the numerator is computed over the integers and reduced
/// against the power of the denominator once, at the end, where FLINT reduces after every
/// truncated multiplication.
#[inline]
fn pow_truncated_assign(&mut self, exp: u64, len: u64) {
*self = take(self).pow_truncated(exp, len);
}
}