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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;
use crate::rational_polynomial::RationalPolynomial;
use crate::rational_vector::arithmetic::content::content_over;
use malachite_base::num::arithmetic::traits::{Content, ContentAndPrimitivePart, PrimitivePart};
use malachite_nz::integer_polynomial::IntegerPolynomial;
impl Content for RationalPolynomial {
type Output = Rational;
/// Computes the content of a [`RationalPolynomial`], taking the polynomial by value.
///
/// Over the rationals every nonzero coefficient is a unit, so the GCD of the coefficients says
/// nothing. The content is instead the non-negative [`Rational`] $c$ for which $p/c$ is a
/// primitive polynomial with integer coefficients. For $p = A/d$ it is
/// $\operatorname{cont}(A)/d$, which is already in lowest terms, so no GCD with the denominator
/// is needed. The content 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
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Content;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// assert_eq!(p.clone().content().to_string(), "2/3");
/// assert_eq!(RationalPolynomial::ZERO.content(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_content` from `fmpq_poly/content.c`, FLINT 3.6.0.
#[inline]
fn content(self) -> Rational {
content_over(self.numerator.content(), self.denominator)
}
}
impl Content for &RationalPolynomial {
type Output = Rational;
/// Computes the content of a [`RationalPolynomial`], taking the polynomial by reference.
///
/// Over the rationals every nonzero coefficient is a unit, so the GCD of the coefficients says
/// nothing. The content is instead the non-negative [`Rational`] $c$ for which $p/c$ is a
/// primitive polynomial with integer coefficients. For $p = A/d$ it is
/// $\operatorname{cont}(A)/d$, which is already in lowest terms, so no GCD with the denominator
/// is needed. The content 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
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Content;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// assert_eq!((&p).content().to_string(), "2/3");
/// assert_eq!((&RationalPolynomial::ZERO).content(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_content` from `fmpq_poly/content.c`, FLINT 3.6.0.
#[inline]
fn content(self) -> Rational {
content_over((&self.numerator).content(), self.denominator.clone())
}
}
impl PrimitivePart for RationalPolynomial {
type Output = IntegerPolynomial;
/// Computes the primitive part of a [`RationalPolynomial`], taking the polynomial by value.
///
/// This is the polynomial divided by its content, with every coefficient keeping its sign; for
/// the one with a non-negative leading coefficient, see [`canonical_primitive_part`](
/// malachite_base::num::arithmetic::traits::CanonicalPrimitivePart::canonical_primitive_part).
/// It always has integer coefficients, so it is an [`IntegerPolynomial`]; for $p = A/d$ it is
/// the primitive part of $A$, and the denominator plays no part.
///
/// $$
/// p = \operatorname{cont}(p) \operatorname{pp}(p).
/// $$
///
/// The 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
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::PrimitivePart;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// assert_eq!(p.clone().primitive_part().to_string(), "-x-2");
/// assert_eq!(RationalPolynomial::ZERO.primitive_part(), 0);
/// ```
#[inline]
fn primitive_part(self) -> IntegerPolynomial {
self.numerator.primitive_part()
}
}
impl PrimitivePart for &RationalPolynomial {
type Output = IntegerPolynomial;
/// Computes the primitive part of a [`RationalPolynomial`], taking the polynomial by reference.
///
/// This is the polynomial divided by its content, with every coefficient keeping its sign; for
/// the one with a non-negative leading coefficient, see [`canonical_primitive_part`](
/// malachite_base::num::arithmetic::traits::CanonicalPrimitivePart::canonical_primitive_part).
/// It always has integer coefficients, so it is an [`IntegerPolynomial`]; for $p = A/d$ it is
/// the primitive part of $A$, and the denominator plays no part.
///
/// $$
/// p = \operatorname{cont}(p) \operatorname{pp}(p).
/// $$
///
/// The 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
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::PrimitivePart;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// assert_eq!((&p).primitive_part().to_string(), "-x-2");
/// assert_eq!((&RationalPolynomial::ZERO).primitive_part(), 0);
/// ```
#[inline]
fn primitive_part(self) -> IntegerPolynomial {
(&self.numerator).primitive_part()
}
}
impl ContentAndPrimitivePart for RationalPolynomial {
type Content = Rational;
type PrimitivePart = IntegerPolynomial;
/// Computes the content and the primitive part of a [`RationalPolynomial`] 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
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndPrimitivePart;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// let (content, primitive_part) = p.clone().content_and_primitive_part();
/// assert_eq!(content.to_string(), "2/3");
/// assert_eq!(primitive_part.to_string(), "-x-2");
/// ```
#[inline]
fn content_and_primitive_part(self) -> (Rational, IntegerPolynomial) {
let (content, primitive_part) = self.numerator.content_and_primitive_part();
(content_over(content, self.denominator), primitive_part)
}
}
impl ContentAndPrimitivePart for &RationalPolynomial {
type Content = Rational;
type PrimitivePart = IntegerPolynomial;
/// Computes the content and the primitive part of a [`RationalPolynomial`] 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
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// numerator's coefficients and the denominator.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndPrimitivePart;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// let (content, primitive_part) = (&p).content_and_primitive_part();
/// assert_eq!(content.to_string(), "2/3");
/// assert_eq!(primitive_part.to_string(), "-x-2");
/// ```
#[inline]
fn content_and_primitive_part(self) -> (Rational, IntegerPolynomial) {
let (content, primitive_part) = (&self.numerator).content_and_primitive_part();
(
content_over(content, self.denominator.clone()),
primitive_part,
)
}
}