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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_vector::IntegerVector;
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{ElementLcm, LcmAssign};
use malachite_base::num::basic::traits::One;
impl ElementLcm for IntegerVector {
type Output = Natural;
/// Returns the LCM of the elements of a [`IntegerVector`], taking the vector by reference.
///
/// The LCM of the elements of the 0-dimensional vector is 1. If an element is 0 the LCM is 0,
/// and the elements after it are not examined. The LCM is the LCM of the absolute values, so it
/// is non-negative.
///
/// $$
/// f(v) = \operatorname{lcm}(v_0, v_1, \ldots, v_{n-1}),
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements, and $m$ is the dimension of the vector.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ElementLcm;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(-4, 6, -10)")
/// .unwrap()
/// .to_element_lcm(),
/// 60
/// );
/// assert_eq!(
/// IntegerVector::from_str("(-4, 0, 6)")
/// .unwrap()
/// .to_element_lcm(),
/// 0
/// );
/// assert_eq!(IntegerVector::from_str("()").unwrap().to_element_lcm(), 1);
/// ```
///
/// This is equivalent to `_fmpz_vec_lcm` from `fmpz_vec/lcm.c`, FLINT 3.6.0.
fn to_element_lcm(&self) -> Natural {
let mut lcm = Natural::ONE;
for c in &self.elements {
lcm.lcm_assign(&c.abs);
if lcm == 0u32 {
break;
}
}
lcm
}
/// Returns the LCM of the elements of a [`IntegerVector`], taking the vector by value.
///
/// The LCM of the elements of the 0-dimensional vector is 1. If an element is 0 the LCM is 0,
/// and the elements after it are not examined. The LCM is the LCM of the absolute values, so it
/// is non-negative.
///
/// $$
/// f(v) = \operatorname{lcm}(v_0, v_1, \ldots, v_{n-1}),
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// elements, and $m$ is the dimension of the vector.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ElementLcm;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(-4, 6, -10)")
/// .unwrap()
/// .into_element_lcm(),
/// 60
/// );
/// assert_eq!(
/// IntegerVector::from_str("(-4, 0, 6)")
/// .unwrap()
/// .into_element_lcm(),
/// 0
/// );
/// assert_eq!(IntegerVector::from_str("()").unwrap().into_element_lcm(), 1);
/// ```
///
/// This is equivalent to `_fmpz_vec_lcm` from `fmpz_vec/lcm.c`, FLINT 3.6.0.
fn into_element_lcm(self) -> Natural {
let mut lcm = Natural::ONE;
for c in self.elements {
lcm.lcm_assign(c.abs);
if lcm == 0u32 {
break;
}
}
lcm
}
}