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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::num::basic::unsigneds::PrimitiveUnsigned;
use crate::polynomial::{Content, ContentAndPrimitivePart, PrimitivePart, PrimitivePartAssign};
use crate::unsigned_polynomial::UnsignedPolynomial;
// The GCD of the coefficients. It stops as soon as it reaches 1, since nothing can lower it
// further.
fn content<T: PrimitiveUnsigned>(coefficients: &[T]) -> T {
let mut gcd = T::ZERO;
for &c in coefficients {
gcd.gcd_assign(c);
if gcd == T::ONE {
break;
}
}
gcd
}
// Divides every coefficient by the content, which divides each of them exactly.
fn divide_by_content<T: PrimitiveUnsigned>(coefficients: &mut [T], content: T) {
if content > T::ONE {
for c in coefficients {
c.div_exact_assign(content);
}
}
}
impl<T: PrimitiveUnsigned> Content for UnsignedPolynomial<T> {
type Output = T;
/// Computes the content of an [`UnsignedPolynomial`], the GCD of its coefficients, taking the
/// polynomial by value.
///
/// The content of the zero polynomial is zero. The GCD is taken coefficient by coefficient,
/// stopping early once it reaches 1.
///
/// $$
/// f(p) = \gcd(c_0, c_1, \ldots, c_{n-1}),
/// $$
///
/// where $c_i$ is the coefficient of $x^i$ in $p$ and $n$ is its length.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Content;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// assert_eq!(p.clone().content(), 2);
/// assert_eq!(UnsignedPolynomial::<u8>::ZERO.content(), 0);
/// ```
///
/// This is equivalent to `fmpz_poly_content` from `fmpz_poly/content.c`, FLINT 3.6.0.
#[inline]
fn content(self) -> T {
content(&self.coefficients)
}
}
impl<T: PrimitiveUnsigned> Content for &UnsignedPolynomial<T> {
type Output = T;
/// Computes the content of an [`UnsignedPolynomial`], the GCD of its coefficients, taking the
/// polynomial by reference.
///
/// The content of the zero polynomial is zero. The GCD is taken coefficient by coefficient,
/// stopping early once it reaches 1.
///
/// $$
/// f(p) = \gcd(c_0, c_1, \ldots, c_{n-1}),
/// $$
///
/// where $c_i$ is the coefficient of $x^i$ in $p$ and $n$ is its length.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Content;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// assert_eq!((&p).content(), 2);
/// assert_eq!((&UnsignedPolynomial::<u8>::ZERO).content(), 0);
/// ```
///
/// This is equivalent to `fmpz_poly_content` from `fmpz_poly/content.c`, FLINT 3.6.0.
#[inline]
fn content(self) -> T {
content(&self.coefficients)
}
}
impl<T: PrimitiveUnsigned> PrimitivePart for UnsignedPolynomial<T> {
type Output = Self;
/// Computes the primitive part of an [`UnsignedPolynomial`], the polynomial divided by its
/// content, taking the polynomial by value.
///
/// The coefficients are non-negative, so no sign needs normalizing and $p =
/// \operatorname{cont}(p) \operatorname{pp}(p)$. The primitive part of the zero polynomial is
/// zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::PrimitivePart;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// assert_eq!(p.clone().primitive_part().to_string(), "3*x^2+2*x+5");
/// assert_eq!(
/// UnsignedPolynomial::<u8>::ZERO.primitive_part(),
/// UnsignedPolynomial::<u8>::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_primitive_part` from `fmpz_poly/primitive_part.c`, FLINT
/// 3.6.0.
#[inline]
fn primitive_part(mut self) -> Self {
let content = content(&self.coefficients);
divide_by_content(&mut self.coefficients, content);
self
}
}
impl<T: PrimitiveUnsigned> PrimitivePart for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Computes the primitive part of an [`UnsignedPolynomial`], the polynomial divided by its
/// content, taking the polynomial by reference.
///
/// The coefficients are non-negative, so no sign needs normalizing and $p =
/// \operatorname{cont}(p) \operatorname{pp}(p)$. The primitive part of the zero polynomial is
/// zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::PrimitivePart;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// assert_eq!((&p).primitive_part().to_string(), "3*x^2+2*x+5");
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::ZERO).primitive_part(),
/// UnsignedPolynomial::<u8>::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_primitive_part` from `fmpz_poly/primitive_part.c`, FLINT
/// 3.6.0.
#[inline]
fn primitive_part(self) -> UnsignedPolynomial<T> {
let content = content(&self.coefficients);
let mut coefficients = self.coefficients.clone();
divide_by_content(&mut coefficients, content);
UnsignedPolynomial { coefficients }
}
}
impl<T: PrimitiveUnsigned> PrimitivePartAssign for UnsignedPolynomial<T> {
/// Replaces an [`UnsignedPolynomial`] with its primitive part, the polynomial divided by its
/// content.
///
/// See [`primitive_part`](PrimitivePart::primitive_part).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::PrimitivePartAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// p.primitive_part_assign();
/// assert_eq!(p.to_string(), "3*x^2+2*x+5");
/// ```
#[inline]
fn primitive_part_assign(&mut self) {
let content = content(&self.coefficients);
divide_by_content(&mut self.coefficients, content);
}
}
impl<T: PrimitiveUnsigned> ContentAndPrimitivePart for UnsignedPolynomial<T> {
type Content = T;
type PrimitivePart = Self;
/// Computes the content and the primitive part of an [`UnsignedPolynomial`] together, taking
/// the polynomial by value.
///
/// See [`content`](Content::content) and [`primitive_part`](PrimitivePart::primitive_part); the
/// content is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ContentAndPrimitivePart;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// let (content, primitive_part) = p.clone().content_and_primitive_part();
/// assert_eq!(content, 2);
/// assert_eq!(primitive_part.to_string(), "3*x^2+2*x+5");
/// ```
#[inline]
fn content_and_primitive_part(mut self) -> (T, Self) {
let content = content(&self.coefficients);
divide_by_content(&mut self.coefficients, content);
(content, self)
}
}
impl<T: PrimitiveUnsigned> ContentAndPrimitivePart for &UnsignedPolynomial<T> {
type Content = T;
type PrimitivePart = UnsignedPolynomial<T>;
/// Computes the content and the primitive part of an [`UnsignedPolynomial`] together, taking
/// the polynomial by reference.
///
/// See [`content`](Content::content) and [`primitive_part`](PrimitivePart::primitive_part); the
/// content is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ContentAndPrimitivePart;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("6*x^2+4*x+10").unwrap();
/// let (content, primitive_part) = (&p).content_and_primitive_part();
/// assert_eq!(content, 2);
/// assert_eq!(primitive_part.to_string(), "3*x^2+2*x+5");
/// ```
#[inline]
fn content_and_primitive_part(self) -> (T, UnsignedPolynomial<T>) {
let content = content(&self.coefficients);
let mut coefficients = self.coefficients.clone();
divide_by_content(&mut coefficients, content);
(content, UnsignedPolynomial { coefficients })
}
}