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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::{Pow, PowAssign};
impl Pow<u64> for RationalPolynomial {
type Output = Self;
/// Raises a [`RationalPolynomial`] to a power, taking it by value.
///
/// $$
/// f(p, e) = p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. No GCD is needed: the numerator and
/// the denominator are raised to the power separately, and by Gauss's lemma the content of the
/// numerator's power is the power of its content, which stays coprime to the power of the
/// denominator.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, 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::num::arithmetic::traits::Pow;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// (RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .pow(3)
/// .to_string(),
/// "1/8*x^3+1/4*x^2+1/6*x+1/27"
/// );
/// assert_eq!(
/// (RationalPolynomial::from_str("1/2*x-1").unwrap())
/// .pow(4)
/// .to_string(),
/// "1/16*x^4-1/2*x^3+3/2*x^2-2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_pow` from `fmpq_poly/pow.c`, FLINT 3.6.0, except that the
/// numerator is raised to the power as in [`Pow`] for
/// [`IntegerPolynomial`](malachite_nz::integer_polynomial::IntegerPolynomial).
#[inline]
fn pow(mut self, exp: u64) -> Self {
self.pow_assign(exp);
self
}
}
impl Pow<u64> for &RationalPolynomial {
type Output = RationalPolynomial;
/// Raises a [`RationalPolynomial`] to a power, taking it by reference.
///
/// $$
/// f(p, e) = p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. No GCD is needed: the numerator and
/// the denominator are raised to the power separately, and by Gauss's lemma the content of the
/// numerator's power is the power of its content, which stays coprime to the power of the
/// denominator.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, 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::num::arithmetic::traits::Pow;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x+1/3").unwrap())
/// .pow(3)
/// .to_string(),
/// "1/8*x^3+1/4*x^2+1/6*x+1/27"
/// );
/// assert_eq!(
/// (&RationalPolynomial::from_str("1/2*x-1").unwrap())
/// .pow(4)
/// .to_string(),
/// "1/16*x^4-1/2*x^3+3/2*x^2-2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpq_poly_pow` from `fmpq_poly/pow.c`, FLINT 3.6.0, except that the
/// numerator is raised to the power as in [`Pow`] for
/// [`IntegerPolynomial`](malachite_nz::integer_polynomial::IntegerPolynomial).
#[inline]
fn pow(self, exp: u64) -> RationalPolynomial {
RationalPolynomial {
numerator: (&self.numerator).pow(exp),
denominator: (&self.denominator).pow(exp),
}
}
}
impl PowAssign<u64> for RationalPolynomial {
/// Raises a [`RationalPolynomial`] to a power in place.
///
/// $$
/// p \gets p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. No GCD is needed: the numerator and
/// the denominator are raised to the power separately, and by Gauss's lemma the content of the
/// numerator's power is the power of its content, which stays coprime to the power of the
/// denominator.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, 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::num::arithmetic::traits::PowAssign;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("1/2*x+1/3").unwrap();
/// p.pow_assign(3);
/// assert_eq!(p.to_string(), "1/8*x^3+1/4*x^2+1/6*x+1/27");
///
/// let mut p = RationalPolynomial::from_str("1/2*x-1").unwrap();
/// p.pow_assign(4);
/// assert_eq!(p.to_string(), "1/16*x^4-1/2*x^3+3/2*x^2-2*x+1");
/// ```
///
/// This is equivalent to `fmpq_poly_pow` from `fmpq_poly/pow.c`, FLINT 3.6.0, except that the
/// numerator is raised to the power as in [`Pow`] for
/// [`IntegerPolynomial`](malachite_nz::integer_polynomial::IntegerPolynomial).
#[inline]
fn pow_assign(&mut self, exp: u64) {
self.numerator.pow_assign(exp);
self.denominator.pow_assign(exp);
}
}