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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_truncated::{
pow_truncated_assign_vec, pow_truncated_ref,
};
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::polynomial::{PowTruncated, PowTruncatedAssign};
impl PowTruncated for NaturalPolynomial {
type Output = Self;
/// Raises a [`NaturalPolynomial`] 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 $x^n$,
/// so only its first `len` coefficients are read. The zeroth power of every polynomial is 1,
/// truncated to 0 when `len` is 0. The power is computed by repeated truncated squaring and
/// multiplication.
///
/// # 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 `len`, and $m$ is `exp` times the
/// largest number of significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (NaturalPolynomial::from_str("x+1").unwrap())
/// .pow_truncated(5, 3)
/// .to_string(),
/// "10*x^2+5*x+1"
/// );
/// // The power is a multiple of x^4.
/// assert_eq!(
/// (NaturalPolynomial::from_str("x^2+x").unwrap())
/// .pow_truncated(4, 4)
/// .to_string(),
/// "0"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_pow_trunc` from `fmpz_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that a factor of $x^k$ is removed before powering, and that the intermediate powers
/// are kept at their own lengths rather than padded to `len`.
#[inline]
fn pow_truncated(mut self, exp: u64, len: u64) -> Self {
self.pow_truncated_assign(exp, len);
self
}
}
impl PowTruncated for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Raises a [`NaturalPolynomial`] 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 $x^n$,
/// so only its first `len` coefficients are read. The zeroth power of every polynomial is 1,
/// truncated to 0 when `len` is 0. The power is computed by repeated truncated squaring and
/// multiplication.
///
/// # 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 `len`, and $m$ is `exp` times the
/// largest number of significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x+1").unwrap())
/// .pow_truncated(5, 3)
/// .to_string(),
/// "10*x^2+5*x+1"
/// );
/// // The power is a multiple of x^4.
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+x").unwrap())
/// .pow_truncated(4, 4)
/// .to_string(),
/// "0"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_pow_trunc` from `fmpz_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that a factor of $x^k$ is removed before powering, and that the intermediate powers
/// are kept at their own lengths rather than padded to `len`.
#[inline]
fn pow_truncated(self, exp: u64, len: u64) -> NaturalPolynomial {
NaturalPolynomial {
coefficients: pow_truncated_ref(&self.coefficients, exp, len),
}
}
}
impl PowTruncatedAssign for NaturalPolynomial {
/// Raises a [`NaturalPolynomial`] 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 $x^n$,
/// so only its first `len` coefficients are read. The zeroth power of every polynomial is 1,
/// truncated to 0 when `len` is 0. The power is computed by repeated truncated squaring and
/// multiplication.
///
/// # 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 `len`, and $m$ is `exp` times the
/// largest number of significant bits of any of the first `len` coefficients of the polynomial.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PowTruncatedAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x+1").unwrap();
/// p.pow_truncated_assign(5, 3);
/// assert_eq!(p.to_string(), "10*x^2+5*x+1");
///
/// // The power is a multiple of x^4.
/// let mut p = NaturalPolynomial::from_str("x^2+x").unwrap();
/// p.pow_truncated_assign(4, 4);
/// assert_eq!(p.to_string(), "0");
/// ```
///
/// This is equivalent to `fmpz_poly_pow_trunc` from `fmpz_poly/pow_trunc.c`, FLINT 3.6.0,
/// except that a factor of $x^k$ is removed before powering, and that the intermediate powers
/// are kept at their own lengths rather than padded to `len`.
#[inline]
fn pow_truncated_assign(&mut self, exp: u64, len: u64) {
pow_truncated_assign_vec(&mut self.coefficients, exp, len);
}
}