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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;
use alloc::vec::Vec;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::polynomial::{ComposePowerOfX, ComposePowerOfXAssign, Polynomial};
// The value at 1, the sum of the coefficients.
fn sum_of_coefficients(coefficients: &[Natural]) -> Natural {
coefficients.iter().sum()
}
// Moves the coefficient of x^i to x^(ik), in place, for k at least 2. The vector is first extended
// with zeros to the final length; then the coefficients are moved from the top down, so each lands
// on a place that is already zero. The leading coefficient stays nonzero.
fn spread(coefficients: &mut Vec<Natural>, k: u64) {
let len = coefficients.len();
if len <= 1 {
return;
}
let k = usize::exact_from(k);
let new_len = (len - 1)
.checked_mul(k)
.and_then(|n| n.checked_add(1))
.unwrap();
coefficients.resize(new_len, Natural::ZERO);
for i in (1..len).rev() {
coefficients.swap(i, i * k);
}
}
impl ComposePowerOfX for NaturalPolynomial {
type Output = Self;
/// Composes a [`NaturalPolynomial`] with $x^k$, giving $p(x^k)$, taking it by value. The
/// coefficient of $x^i$ moves to $x^{ik}$, and zeros fill the places in between.
///
/// $$
/// f(p, k) = p(x^k).
/// $$
///
/// When $k$ is 0 the result is the constant $p(1)$, the sum of the coefficients; when $k$ is 1,
/// or the polynomial is constant, nothing changes.
///
/// # Worst-case complexity
/// $T(m, k) = O(mk)$
///
/// $M(m, k) = O(mk)$
///
/// where $T$ is time, $M$ is additional memory, $k$ is `k`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the degree of the result is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ComposePowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!(p.compose_power_of_x(2).to_string(), "x^4+3*x^2+2");
/// // With k = 0, this is p(1).
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!(p.compose_power_of_x(0).to_string(), "6");
/// ```
///
/// This is equivalent to `fmpz_poly_inflate` from `fmpz_poly/inflate.c`, FLINT 3.6.0.
#[inline]
fn compose_power_of_x(mut self, k: u64) -> Self {
self.compose_power_of_x_assign(k);
self
}
}
impl ComposePowerOfX for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Composes a [`NaturalPolynomial`] with $x^k$, giving $p(x^k)$, taking it by reference. The
/// coefficient of $x^i$ moves to $x^{ik}$, and zeros fill the places in between.
///
/// $$
/// f(p, k) = p(x^k).
/// $$
///
/// When $k$ is 0 the result is the constant $p(1)$, the sum of the coefficients; when $k$ is 1,
/// or the polynomial is constant, nothing changes.
///
/// # Worst-case complexity
/// $T(m, k) = O(mk)$
///
/// $M(m, k) = O(mk)$
///
/// where $T$ is time, $M$ is additional memory, $k$ is `k`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the degree of the result is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ComposePowerOfX;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!((&p).compose_power_of_x(2).to_string(), "x^4+3*x^2+2");
/// // With k = 0, this is p(1).
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!((&p).compose_power_of_x(0).to_string(), "6");
/// ```
///
/// This is equivalent to `fmpz_poly_inflate` from `fmpz_poly/inflate.c`, FLINT 3.6.0.
fn compose_power_of_x(self, k: u64) -> NaturalPolynomial {
if k == 0 {
return NaturalPolynomial::from_coefficients_asc(vec![sum_of_coefficients(
&self.coefficients,
)]);
}
let mut coefficients = self.coefficients.clone();
if k != 1 {
spread(&mut coefficients, k);
}
NaturalPolynomial { coefficients }
}
}
impl ComposePowerOfXAssign for NaturalPolynomial {
/// Composes a [`NaturalPolynomial`] with $x^k$ in place, replacing $p$ with $p(x^k)$. The
/// coefficient of $x^i$ moves to $x^{ik}$, and zeros fill the places in between.
///
/// $$
/// p \gets p(x^k).
/// $$
///
/// When $k$ is 0 the result is the constant $p(1)$, the sum of the coefficients; when $k$ is 1,
/// or the polynomial is constant, nothing changes.
///
/// # Worst-case complexity
/// $T(m, k) = O(mk)$
///
/// $M(m, k) = O(mk)$
///
/// where $T$ is time, $M$ is additional memory, $k$ is `k`, and $m$ is the total number of bits
/// of the coefficients.
///
/// # Panics
/// Panics if the degree of the result is greater than `usize::MAX`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ComposePowerOfXAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.compose_power_of_x_assign(2);
/// assert_eq!(p.to_string(), "x^4+3*x^2+2");
///
/// // With k = 0, this is p(1).
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.compose_power_of_x_assign(0);
/// assert_eq!(p.to_string(), "6");
/// ```
///
/// This is equivalent to `fmpz_poly_inflate` from `fmpz_poly/inflate.c`, FLINT 3.6.0.
fn compose_power_of_x_assign(&mut self, k: u64) {
match k {
0 => {
*self = Self::from_coefficients_asc(vec![sum_of_coefficients(&self.coefficients)]);
}
1 => {}
_ => spread(&mut self.coefficients, k),
}
}
}