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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::integer_polynomial::IntegerPolynomial;
use crate::integer_polynomial::arithmetic::content::negate;
use crate::integer_vector::arithmetic::content::{content, normalize_in_place, normalized};
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, CanonicalPrimitivePartAssign, ContentAndCanonicalPrimitivePart,
};
impl CanonicalPrimitivePart for IntegerPolynomial {
type Output = Self;
/// Computes the canonical primitive part of an [`IntegerPolynomial`], taking the polynomial by
/// value.
///
/// This is the polynomial divided by its content, with the sign chosen so that the leading
/// coefficient is non-negative: the [`primitive_part`](
/// malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part), negated if the
/// leading coefficient is negative. The sign matters: when the leading coefficient is negative,
/// the content times the canonical primitive part is the negation of the polynomial, and the
/// identity needs the sign of the leading coefficient $\operatorname{lc}(p)$.
///
/// $$
/// p = \operatorname{sgn}(\operatorname{lc}(p)) \operatorname{cont}(p) \operatorname{cpp}(p).
/// $$
///
/// The canonical primitive part of the zero polynomial is zero.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// let p = IntegerPolynomial::from_str("-6*x^2+4*x-10").unwrap();
/// assert_eq!(
/// p.clone().canonical_primitive_part().to_string(),
/// "3*x^2-2*x+5"
/// );
/// assert_eq!(
/// IntegerPolynomial::ZERO.canonical_primitive_part(),
/// IntegerPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_primitive_part` from `fmpz_poly/primitive_part.c`, FLINT
/// 3.6.0.
#[inline]
fn canonical_primitive_part(mut self) -> Self {
let content = content(&self.coefficients);
let negate = negate(&self.coefficients);
normalize_in_place(&mut self.coefficients, &content, negate);
self
}
}
impl CanonicalPrimitivePart for &IntegerPolynomial {
type Output = IntegerPolynomial;
/// Computes the canonical primitive part of an [`IntegerPolynomial`], taking the polynomial by
/// reference.
///
/// This is the polynomial divided by its content, with the sign chosen so that the leading
/// coefficient is non-negative: the [`primitive_part`](
/// malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part), negated if the
/// leading coefficient is negative. The sign matters: when the leading coefficient is negative,
/// the content times the canonical primitive part is the negation of the polynomial, and the
/// identity needs the sign of the leading coefficient $\operatorname{lc}(p)$.
///
/// $$
/// p = \operatorname{sgn}(\operatorname{lc}(p)) \operatorname{cont}(p) \operatorname{cpp}(p).
/// $$
///
/// The canonical primitive part of the zero polynomial is zero.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// let p = IntegerPolynomial::from_str("-6*x^2+4*x-10").unwrap();
/// assert_eq!((&p).canonical_primitive_part().to_string(), "3*x^2-2*x+5");
/// assert_eq!(
/// (&IntegerPolynomial::ZERO).canonical_primitive_part(),
/// IntegerPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_primitive_part` from `fmpz_poly/primitive_part.c`, FLINT
/// 3.6.0.
#[inline]
fn canonical_primitive_part(self) -> IntegerPolynomial {
let content = content(&self.coefficients);
IntegerPolynomial {
coefficients: normalized(&self.coefficients, &content, negate(&self.coefficients)),
}
}
}
impl CanonicalPrimitivePartAssign for IntegerPolynomial {
/// Replaces an [`IntegerPolynomial`] with its canonical primitive part.
///
/// See [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part).
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePartAssign;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// let mut p = IntegerPolynomial::from_str("-6*x^2+4*x-10").unwrap();
/// p.canonical_primitive_part_assign();
/// assert_eq!(p.to_string(), "3*x^2-2*x+5");
/// ```
#[inline]
fn canonical_primitive_part_assign(&mut self) {
let content = content(&self.coefficients);
let negate = negate(&self.coefficients);
normalize_in_place(&mut self.coefficients, &content, negate);
}
}
impl ContentAndCanonicalPrimitivePart for IntegerPolynomial {
type Content = Natural;
type CanonicalPrimitivePart = Self;
/// Computes the content and the canonical primitive part of an [`IntegerPolynomial`] together,
/// taking the polynomial by value.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// let p = IntegerPolynomial::from_str("-6*x^2+4*x-10").unwrap();
/// let (content, primitive_part) = p.clone().content_and_canonical_primitive_part();
/// assert_eq!(content, 2);
/// assert_eq!(primitive_part.to_string(), "3*x^2-2*x+5");
/// ```
#[inline]
fn content_and_canonical_primitive_part(mut self) -> (Natural, Self) {
let content = content(&self.coefficients);
let negate = negate(&self.coefficients);
normalize_in_place(&mut self.coefficients, &content, negate);
(content, self)
}
}
impl ContentAndCanonicalPrimitivePart for &IntegerPolynomial {
type Content = Natural;
type CanonicalPrimitivePart = IntegerPolynomial;
/// Computes the content and the canonical primitive part of an [`IntegerPolynomial`] together,
/// taking the polynomial by reference.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// let p = IntegerPolynomial::from_str("-6*x^2+4*x-10").unwrap();
/// let (content, primitive_part) = (&p).content_and_canonical_primitive_part();
/// assert_eq!(content, 2);
/// assert_eq!(primitive_part.to_string(), "3*x^2-2*x+5");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Natural, IntegerPolynomial) {
let content = content(&self.coefficients);
let coefficients = normalized(&self.coefficients, &content, negate(&self.coefficients));
(content, IntegerPolynomial { coefficients })
}
}