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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 malachite_base::polynomial::{Derivative, DerivativeAssign};
// The coefficients of the derivative of the polynomial whose coefficients `xs` holds in ascending
// order: the coefficient of x^i, for i at least 1, times i. The leading coefficient of a
// nonconstant polynomial, times its degree, is nonzero, so the result is normalized.
fn derivative_ref(xs: &[Natural]) -> Vec<Natural> {
xs.iter()
.enumerate()
.skip(1)
.map(|(i, c)| c * Natural::from(i))
.collect()
}
fn derivative_in_place(xs: &mut Vec<Natural>) {
if xs.is_empty() {
return;
}
xs.remove(0);
for (i, c) in xs.iter_mut().enumerate() {
*c *= Natural::from(i + 1);
}
}
impl Derivative for NaturalPolynomial {
type Output = Self;
/// Computes the derivative of a [`NaturalPolynomial`], taking it by value.
///
/// $$
/// f(p) = p' = \sum_{i=1}^n ia_ix^{i-1}.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$ and moves to $x^{i-1}$. A constant polynomial,
/// including zero, has derivative zero.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m \log m)$
///
/// $M(n, m) = O(n + m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// coefficients, and $m$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Derivative;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!(p.derivative().to_string(), "3*x^2+6*x+2");
///
/// let p = NaturalPolynomial::from_str("7").unwrap();
/// assert_eq!(p.derivative(), NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_derivative` from `fmpz_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn derivative(mut self) -> Self {
self.derivative_assign();
self
}
}
impl Derivative for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Computes the derivative of a [`NaturalPolynomial`], taking it by reference.
///
/// $$
/// f(p) = p' = \sum_{i=1}^n ia_ix^{i-1}.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$ and moves to $x^{i-1}$. A constant polynomial,
/// including zero, has derivative zero.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m \log m)$
///
/// $M(n, m) = O(n + m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// coefficients, and $m$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Derivative;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!((&p).derivative().to_string(), "3*x^2+6*x+2");
///
/// let p = NaturalPolynomial::from_str("7").unwrap();
/// assert_eq!((&p).derivative(), NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_derivative` from `fmpz_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn derivative(self) -> NaturalPolynomial {
NaturalPolynomial {
coefficients: derivative_ref(&self.coefficients),
}
}
}
impl DerivativeAssign for NaturalPolynomial {
/// Replaces a [`NaturalPolynomial`] with its derivative.
///
/// $$
/// p \gets p' = \sum_{i=1}^n ia_ix^{i-1}.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$ and moves to $x^{i-1}$. A constant polynomial,
/// including zero, has derivative zero.
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m \log m)$
///
/// $M(n, m) = O(n + m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// coefficients, and $m$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::DerivativeAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+5").unwrap();
/// p.derivative_assign();
/// assert_eq!(p.to_string(), "3*x^2+6*x+2");
///
/// let mut p = NaturalPolynomial::from_str("7").unwrap();
/// p.derivative_assign();
/// assert_eq!(p, NaturalPolynomial::ZERO);
/// ```
///
/// This is equivalent to `fmpz_poly_derivative` from `fmpz_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn derivative_assign(&mut self) {
derivative_in_place(&mut self.coefficients);
}
}