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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::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use alloc::vec::Vec;
use core::iter::repeat_with;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::polynomial::{MulPowerOfX, MulPowerOfXAssign};
impl MulPowerOfX for NaturalPolynomial {
type Output = Self;
/// Multiplies a [`NaturalPolynomial`] by $x^n$, taking it by value. Every coefficient moves up
/// by $n$ places, and $n$ zeros fill the places below them.
///
/// $$
/// f(p, n) = x^np.
/// $$
///
/// The zero polynomial stays zero, and multiplying by $x^0$ changes nothing.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n, m) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `n`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the polynomial is nonzero and `n` is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::MulPowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^2+3*x+2")
/// .unwrap()
/// .mul_power_of_x(2)
/// .to_string(),
/// "x^4+3*x^3+2*x^2"
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("5")
/// .unwrap()
/// .mul_power_of_x(1)
/// .to_string(),
/// "5*x"
/// );
/// assert_eq!(
/// NaturalPolynomial::ZERO.mul_power_of_x(3),
/// NaturalPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_shift_left` from `fmpz_poly/shift_left.c`, FLINT 3.6.0.
#[inline]
fn mul_power_of_x(mut self, n: u64) -> Self {
self.mul_power_of_x_assign(n);
self
}
}
impl MulPowerOfX for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Multiplies a [`NaturalPolynomial`] by $x^n$, taking it by reference. Every coefficient moves
/// up by $n$ places, and $n$ zeros fill the places below them.
///
/// $$
/// f(p, n) = x^np.
/// $$
///
/// The zero polynomial stays zero, and multiplying by $x^0$ changes nothing.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n, m) = O(n + m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `n`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the polynomial is nonzero and `n` is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::MulPowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+3*x+2").unwrap())
/// .mul_power_of_x(2)
/// .to_string(),
/// "x^4+3*x^3+2*x^2"
/// );
/// assert_eq!(
/// (&NaturalPolynomial::from_str("5").unwrap())
/// .mul_power_of_x(1)
/// .to_string(),
/// "5*x"
/// );
/// assert_eq!(
/// (&NaturalPolynomial::ZERO).mul_power_of_x(3),
/// NaturalPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_shift_left` from `fmpz_poly/shift_left.c`, FLINT 3.6.0.
fn mul_power_of_x(self, n: u64) -> NaturalPolynomial {
if self.coefficients.is_empty() {
return NaturalPolynomial::ZERO;
}
let n = usize::exact_from(n);
let mut coefficients = Vec::with_capacity(n + self.coefficients.len());
coefficients.extend(repeat_with(|| Natural::ZERO).take(n));
coefficients.extend_from_slice(&self.coefficients);
NaturalPolynomial { coefficients }
}
}
impl MulPowerOfXAssign for NaturalPolynomial {
/// Multiplies a [`NaturalPolynomial`] by $x^n$ in place. Every coefficient moves up by $n$
/// places, and $n$ zeros fill the places below them.
///
/// $$
/// p \gets x^np.
/// $$
///
/// The zero polynomial stays zero, and multiplying by $x^0$ changes nothing.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n, m) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `n`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the polynomial is nonzero and `n` is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::MulPowerOfXAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.mul_power_of_x_assign(2);
/// assert_eq!(p.to_string(), "x^4+3*x^3+2*x^2");
///
/// let mut p = NaturalPolynomial::from_str("5").unwrap();
/// p.mul_power_of_x_assign(1);
/// assert_eq!(p.to_string(), "5*x");
///
/// let mut p = NaturalPolynomial::ZERO;
/// p.mul_power_of_x_assign(3);
/// assert_eq!(p, NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_shift_left` from `fmpz_poly/shift_left.c`, FLINT 3.6.0.
fn mul_power_of_x_assign(&mut self, n: u64) {
if n == 0 || self.coefficients.is_empty() {
return;
}
let n = usize::exact_from(n);
self.coefficients
.splice(0..0, repeat_with(|| Natural::ZERO).take(n));
}
}