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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::rational_polynomial::RationalPolynomial;
use alloc::vec;
use malachite_base::polynomial::{ComposePowerOfX, ComposePowerOfXAssign, Polynomial};
use malachite_nz::integer::Integer;
use malachite_nz::integer_polynomial::IntegerPolynomial;
// The constant p(1), the sum of the numerator's coefficients over the denominator, in lowest terms.
fn value_at_one(p: &RationalPolynomial) -> RationalPolynomial {
RationalPolynomial::from_numerator_and_denominator(
IntegerPolynomial::from_coefficients_asc(vec![
p.numerator.coefficients_asc().iter().sum::<Integer>(),
]),
p.denominator.clone(),
)
}
impl ComposePowerOfX for RationalPolynomial {
type Output = Self;
/// Composes a [`RationalPolynomial`] 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.
///
/// $$
/// f(p, k) = p(x^k).
/// $$
///
/// Only the numerator changes when $k$ is positive, so the result stays in lowest terms. 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 numerator's coefficients and the denominator.
///
/// # 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_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("1/2*x^2-1/3").unwrap();
/// assert_eq!(p.compose_power_of_x(2).to_string(), "1/2*x^4-1/3");
/// // With k = 0, this is p(1).
/// let p = RationalPolynomial::from_str("1/2*x^2+1/3*x+1/6").unwrap();
/// assert_eq!(p.compose_power_of_x(0).to_string(), "1");
/// ```
///
/// FLINT has no `fmpq_poly_inflate`; this corresponds to `fmpz_poly_inflate` from
/// `fmpz_poly/inflate.c`, FLINT 3.6.0, applied to the numerator.
#[inline]
fn compose_power_of_x(mut self, k: u64) -> Self {
self.compose_power_of_x_assign(k);
self
}
}
impl ComposePowerOfX for &RationalPolynomial {
type Output = RationalPolynomial;
/// Composes a [`RationalPolynomial`] 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.
///
/// $$
/// f(p, k) = p(x^k).
/// $$
///
/// Only the numerator changes when $k$ is positive, so the result stays in lowest terms. 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 numerator's coefficients and the denominator.
///
/// # 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_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("1/2*x^2-1/3").unwrap();
/// assert_eq!((&p).compose_power_of_x(2).to_string(), "1/2*x^4-1/3");
/// // With k = 0, this is p(1).
/// let p = RationalPolynomial::from_str("1/2*x^2+1/3*x+1/6").unwrap();
/// assert_eq!((&p).compose_power_of_x(0).to_string(), "1");
/// ```
///
/// FLINT has no `fmpq_poly_inflate`; this corresponds to `fmpz_poly_inflate` from
/// `fmpz_poly/inflate.c`, FLINT 3.6.0, applied to the numerator.
fn compose_power_of_x(self, k: u64) -> RationalPolynomial {
if k == 0 {
return value_at_one(self);
}
RationalPolynomial {
numerator: (&self.numerator).compose_power_of_x(k),
denominator: self.denominator.clone(),
}
}
}
impl ComposePowerOfXAssign for RationalPolynomial {
/// Composes a [`RationalPolynomial`] 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.
///
/// $$
/// p \gets p(x^k).
/// $$
///
/// Only the numerator changes when $k$ is positive, so the result stays in lowest terms. 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 numerator's coefficients and the denominator.
///
/// # 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_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("1/2*x^2-1/3").unwrap();
/// p.compose_power_of_x_assign(2);
/// assert_eq!(p.to_string(), "1/2*x^4-1/3");
///
/// // With k = 0, this is p(1).
/// let mut p = RationalPolynomial::from_str("1/2*x^2+1/3*x+1/6").unwrap();
/// p.compose_power_of_x_assign(0);
/// assert_eq!(p.to_string(), "1");
/// ```
///
/// FLINT has no `fmpq_poly_inflate`; this corresponds to `fmpz_poly_inflate` from
/// `fmpz_poly/inflate.c`, FLINT 3.6.0, applied to the numerator.
fn compose_power_of_x_assign(&mut self, k: u64) {
if k == 0 {
*self = value_at_one(self);
} else {
self.numerator.compose_power_of_x_assign(k);
}
}
}