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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::integer_polynomial::arithmetic::pow::{pow_assign_vec, pow_ref};
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::{Pow, PowAssign};
impl Pow<u64> for NaturalPolynomial {
type Output = Self;
/// Raises a [`NaturalPolynomial`] to a power, taking it by value.
///
/// $$
/// f(p, e) = p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. Depending on the length of the
/// polynomial, the size of its coefficients, and the exponent, the power is computed by the
/// binomial theorem, by J. C. P. Miller's recurrence for the coefficients of a power, by an
/// addition chain, or by repeated squaring.
///
/// # 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 of its
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x+1")
/// .unwrap()
/// .pow(3)
/// .to_string(),
/// "x^3+3*x^2+3*x+1"
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("2*x+1")
/// .unwrap()
/// .pow(4)
/// .to_string(),
/// "16*x^4+32*x^3+24*x^2+8*x+1"
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("x^2+x")
/// .unwrap()
/// .pow(0)
/// .to_string(),
/// "1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_pow` from `fmpz_poly/pow.c`, FLINT 3.6.0, except that a
/// factor of $x^k$ is removed before powering, and that the algorithm is chosen by measured
/// criteria, which include addition chains.
#[inline]
fn pow(mut self, exp: u64) -> Self {
self.pow_assign(exp);
self
}
}
impl Pow<u64> for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Raises a [`NaturalPolynomial`] to a power, taking it by reference.
///
/// $$
/// f(p, e) = p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. Depending on the length of the
/// polynomial, the size of its coefficients, and the exponent, the power is computed by the
/// binomial theorem, by J. C. P. Miller's recurrence for the coefficients of a power, by an
/// addition chain, or by repeated squaring.
///
/// # 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 of its
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x+1").unwrap())
/// .pow(3)
/// .to_string(),
/// "x^3+3*x^2+3*x+1"
/// );
/// assert_eq!(
/// (&NaturalPolynomial::from_str("2*x+1").unwrap())
/// .pow(4)
/// .to_string(),
/// "16*x^4+32*x^3+24*x^2+8*x+1"
/// );
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+x").unwrap())
/// .pow(0)
/// .to_string(),
/// "1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_pow` from `fmpz_poly/pow.c`, FLINT 3.6.0, except that a
/// factor of $x^k$ is removed before powering, and that the algorithm is chosen by measured
/// criteria, which include addition chains.
#[inline]
fn pow(self, exp: u64) -> NaturalPolynomial {
NaturalPolynomial {
coefficients: pow_ref(&self.coefficients, exp),
}
}
}
impl PowAssign<u64> for NaturalPolynomial {
/// Raises a [`NaturalPolynomial`] to a power in place.
///
/// $$
/// p \gets p^e.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1. Depending on the length of the
/// polynomial, the size of its coefficients, and the exponent, the power is computed by the
/// binomial theorem, by J. C. P. Miller's recurrence for the coefficients of a power, by an
/// addition chain, or by repeated squaring.
///
/// # 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 of its
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::PowAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x+1").unwrap();
/// p.pow_assign(3);
/// assert_eq!(p.to_string(), "x^3+3*x^2+3*x+1");
///
/// let mut p = NaturalPolynomial::from_str("2*x+1").unwrap();
/// p.pow_assign(4);
/// assert_eq!(p.to_string(), "16*x^4+32*x^3+24*x^2+8*x+1");
///
/// let mut p = NaturalPolynomial::from_str("x^2+x").unwrap();
/// p.pow_assign(0);
/// assert_eq!(p.to_string(), "1");
/// ```
///
/// This is equivalent to `fmpz_poly_pow` from `fmpz_poly/pow.c`, FLINT 3.6.0, except that a
/// factor of $x^k$ is removed before powering, and that the algorithm is chosen by measured
/// criteria, which include addition chains.
#[inline]
fn pow_assign(&mut self, exp: u64) {
pow_assign_vec(&mut self.coefficients, exp);
}
}