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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_vector::RationalVector;
use malachite_base::num::arithmetic::traits::{Content, ContentAndPrimitivePart, PrimitivePart};
use malachite_nz::integer_vector::IntegerVector;
use malachite_nz::natural::Natural;
// The content of a vector or polynomial written as integers $A$ over a common denominator $d$ is
// $\operatorname{cont}(A)/d$. It is already in lowest terms when the numerators and denominator
// share no factor, as they do for a canonical `RationalPolynomial` and for
// `to_numerators_and_denominator`.
pub(crate) const fn content_over(numerator_content: Natural, denominator: Natural) -> Rational {
Rational {
sign: true,
numerator: numerator_content,
denominator,
}
}
impl Content for RationalVector {
type Output = Rational;
/// Computes the content of a [`RationalVector`], taking the vector by value.
///
/// The content is the unique non-negative rational $c$ such that the vector is $c$ times a
/// vector of coprime integers. It is the GCD of the numerators that
/// [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives,
/// divided by the denominator, the least common multiple of the elements' denominators; that
/// fraction is already in lowest terms. The content of a vector of zeros, and of the
/// 0-dimensional vector, is zero.
///
/// $$
/// f(v) = \frac{\gcd(a_0, a_1, \ldots, a_{m-1})}{d}, \\quad \text{where} \\quad
/// v_i = \frac{a_i}{d} \text{ and } d = \operatorname{lcm}(\operatorname{den}(v_0), \ldots,
/// \operatorname{den}(v_{m-1})).
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Content;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!(v.content().to_string(), "1/6");
///
/// let v = RationalVector::from_str("(2/3, 4/3)").unwrap();
/// assert_eq!(v.content().to_string(), "2/3");
/// ```
#[inline]
fn content(self) -> Rational {
let (numerators, denominator) = self.to_numerators_and_denominator();
content_over(numerators.content(), denominator)
}
}
impl Content for &RationalVector {
type Output = Rational;
/// Computes the content of a [`RationalVector`], taking the vector by reference.
///
/// The content is the unique non-negative rational $c$ such that the vector is $c$ times a
/// vector of coprime integers. It is the GCD of the numerators that
/// [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives,
/// divided by the denominator, the least common multiple of the elements' denominators; that
/// fraction is already in lowest terms. The content of a vector of zeros, and of the
/// 0-dimensional vector, is zero.
///
/// $$
/// f(v) = \frac{\gcd(a_0, a_1, \ldots, a_{m-1})}{d}, \\quad \text{where} \\quad
/// v_i = \frac{a_i}{d} \text{ and } d = \operatorname{lcm}(\operatorname{den}(v_0), \ldots,
/// \operatorname{den}(v_{m-1})).
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Content;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!((&v).content().to_string(), "1/6");
///
/// let v = RationalVector::from_str("(2/3, 4/3)").unwrap();
/// assert_eq!((&v).content().to_string(), "2/3");
/// ```
#[inline]
fn content(self) -> Rational {
let (numerators, denominator) = self.to_numerators_and_denominator();
content_over(numerators.content(), denominator)
}
}
impl PrimitivePart for RationalVector {
type Output = IntegerVector;
/// Computes the primitive part of a [`RationalVector`], taking the vector by value.
///
/// This is the vector divided by its content, with every element keeping its sign. Its elements
/// are coprime integers, so it is an [`IntegerVector`]: the primitive part of the numerators
/// that [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives,
/// the denominator playing no part. For the one whose first nonzero element is positive, see
/// [`canonical_primitive_part`](
/// malachite_base::num::arithmetic::traits::CanonicalPrimitivePart::canonical_primitive_part).
///
/// $$
/// v = \operatorname{cont}(v) \operatorname{pp}(v).
/// $$
///
/// The primitive part of a vector of zeros is a vector of zeros of the same dimension.
///
/// Taking the vector by value saves nothing, since the numerators are built afresh either way.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::PrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!(v.primitive_part().to_string(), "(-3, 4, -30)");
/// ```
#[inline]
fn primitive_part(self) -> IntegerVector {
self.to_numerators_and_denominator().0.primitive_part()
}
}
impl PrimitivePart for &RationalVector {
type Output = IntegerVector;
/// Computes the primitive part of a [`RationalVector`], taking the vector by reference.
///
/// This is the vector divided by its content, with every element keeping its sign. Its elements
/// are coprime integers, so it is an [`IntegerVector`]: the primitive part of the numerators
/// that [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives,
/// the denominator playing no part. For the one whose first nonzero element is positive, see
/// [`canonical_primitive_part`](
/// malachite_base::num::arithmetic::traits::CanonicalPrimitivePart::canonical_primitive_part).
///
/// $$
/// v = \operatorname{cont}(v) \operatorname{pp}(v).
/// $$
///
/// The primitive part of a vector of zeros is a vector of zeros of the same dimension.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::PrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!((&v).primitive_part().to_string(), "(-3, 4, -30)");
/// ```
#[inline]
fn primitive_part(self) -> IntegerVector {
self.to_numerators_and_denominator().0.primitive_part()
}
}
impl ContentAndPrimitivePart for RationalVector {
type Content = Rational;
type PrimitivePart = IntegerVector;
/// Computes the content and the primitive part of a [`RationalVector`] together, taking the
/// vector by value.
///
/// See [`content`](Content::content) and [`primitive_part`](PrimitivePart::primitive_part); the
/// numerators are cleared and the content found once rather than twice.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// let (content, primitive_part) = v.content_and_primitive_part();
/// assert_eq!(content.to_string(), "1/6");
/// assert_eq!(primitive_part.to_string(), "(-3, 4, -30)");
/// ```
#[inline]
fn content_and_primitive_part(self) -> (Rational, IntegerVector) {
let (numerators, denominator) = self.to_numerators_and_denominator();
let (content, primitive_part) = numerators.content_and_primitive_part();
(content_over(content, denominator), primitive_part)
}
}
impl ContentAndPrimitivePart for &RationalVector {
type Content = Rational;
type PrimitivePart = IntegerVector;
/// Computes the content and the primitive part of a [`RationalVector`] together, taking the
/// vector by reference.
///
/// See [`content`](Content::content) and [`primitive_part`](PrimitivePart::primitive_part); the
/// numerators are cleared and the content found once rather than twice.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n, m) = O(mn)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements' numerators and denominators, and $m$ is the dimension.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// let (content, primitive_part) = (&v).content_and_primitive_part();
/// assert_eq!(content.to_string(), "1/6");
/// assert_eq!(primitive_part.to_string(), "(-3, 4, -30)");
/// ```
#[inline]
fn content_and_primitive_part(self) -> (Rational, IntegerVector) {
let (numerators, denominator) = self.to_numerators_and_denominator();
let (content, primitive_part) = numerators.content_and_primitive_part();
(content_over(content, denominator), primitive_part)
}
}