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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::natural_polynomial::NaturalPolynomial;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::polynomial::{DivPowerOfX, DivPowerOfXAssign, Polynomial};
impl DivPowerOfX for NaturalPolynomial {
type Output = Self;
/// Divides a [`NaturalPolynomial`] by $x^n$, discarding the remainder, taking it by value.
/// Every coefficient moves down by $n$ places, and the lowest $n$ are dropped.
///
/// $$
/// f(p, n) = \sum_{i \geq n} p_ix^{i-n}.
/// $$
///
/// The result is zero when $n$ is at least the number of coefficients, and dividing by $x^0$
/// changes nothing. Multiplying the result by $x^n$ and adding back the dropped low part, the
/// truncation to $n$ coefficients, gives the polynomial back.
///
/// # Worst-case complexity
/// $T(m) = O(m)$
///
/// $M(m) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $m$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::DivPowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!(p.div_power_of_x(2).to_string(), "x+3");
/// let p = NaturalPolynomial::from_str("5*x").unwrap();
/// assert_eq!(p.div_power_of_x(1).to_string(), "5");
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!(p.div_power_of_x(10), NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_shift_right` from `fmpz_poly/shift_right.c`, FLINT 3.6.0.
#[inline]
fn div_power_of_x(mut self, n: u64) -> Self {
self.div_power_of_x_assign(n);
self
}
}
impl DivPowerOfX for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Divides a [`NaturalPolynomial`] by $x^n$, discarding the remainder, taking it by reference.
/// Every coefficient moves down by $n$ places, and the lowest $n$ are dropped.
///
/// $$
/// f(p, n) = \sum_{i \geq n} p_ix^{i-n}.
/// $$
///
/// The result is zero when $n$ is at least the number of coefficients, and dividing by $x^0$
/// changes nothing. Multiplying the result by $x^n$ and adding back the dropped low part, the
/// truncation to $n$ coefficients, gives the polynomial back.
///
/// # Worst-case complexity
/// $T(m) = O(m)$
///
/// $M(m) = O(m)$
///
/// where $T$ is time, $M$ is additional memory, and $m$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::DivPowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!((&p).div_power_of_x(2).to_string(), "x+3");
/// let p = NaturalPolynomial::from_str("5*x").unwrap();
/// assert_eq!((&p).div_power_of_x(1).to_string(), "5");
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!((&p).div_power_of_x(10), NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_shift_right` from `fmpz_poly/shift_right.c`, FLINT 3.6.0.
fn div_power_of_x(self, n: u64) -> NaturalPolynomial {
if n >= self.len() {
return NaturalPolynomial::ZERO;
}
// The leading coefficient is kept, so the result needs no trimming.
NaturalPolynomial {
coefficients: self.coefficients[usize::exact_from(n)..].to_vec(),
}
}
}
impl DivPowerOfXAssign for NaturalPolynomial {
/// Divides a [`NaturalPolynomial`] by $x^n$ in place, discarding the remainder. Every
/// coefficient moves down by $n$ places, and the lowest $n$ are dropped.
///
/// $$
/// p \gets \sum_{i \geq n} p_ix^{i-n}.
/// $$
///
/// The result is zero when $n$ is at least the number of coefficients, and dividing by $x^0$
/// changes nothing. Multiplying the result by $x^n$ and adding back the dropped low part, the
/// truncation to $n$ coefficients, gives the polynomial back.
///
/// # Worst-case complexity
/// $T(m) = O(m)$
///
/// $M(m) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $m$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::DivPowerOfXAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// p.div_power_of_x_assign(2);
/// assert_eq!(p.to_string(), "x+3");
///
/// let mut p = NaturalPolynomial::from_str("5*x").unwrap();
/// p.div_power_of_x_assign(1);
/// assert_eq!(p.to_string(), "5");
///
/// let mut p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// p.div_power_of_x_assign(10);
/// assert_eq!(p, NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_shift_right` from `fmpz_poly/shift_right.c`, FLINT 3.6.0.
fn div_power_of_x_assign(&mut self, n: u64) {
if n >= self.len() {
*self = Self::ZERO;
} else if n != 0 {
self.coefficients.drain(..usize::exact_from(n));
}
}
}