1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
// 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::natural::Natural;
use crate::natural_vector::NaturalVector;
use malachite_base::num::arithmetic::traits::{ElementLcm, LcmAssign};
use malachite_base::num::basic::traits::One;
impl ElementLcm for NaturalVector {
type Output = Natural;
/// Returns the LCM of the elements of a [`NaturalVector`], 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.
///
/// $$
/// f(v) = \operatorname{lcm}(v_0, v_1, \ldots, v_{n-1}),
/// $$
///
/// 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::natural_vector::NaturalVector;
///
/// assert_eq!(
/// NaturalVector::from_str("(4, 6, 10)")
/// .unwrap()
/// .to_element_lcm(),
/// 60
/// );
/// assert_eq!(
/// NaturalVector::from_str("(4, 0, 6)")
/// .unwrap()
/// .to_element_lcm(),
/// 0
/// );
/// assert_eq!(NaturalVector::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);
if lcm == 0u32 {
break;
}
}
lcm
}
/// Returns the LCM of the elements of a [`NaturalVector`], 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.
///
/// $$
/// f(v) = \operatorname{lcm}(v_0, v_1, \ldots, v_{n-1}),
/// $$
///
/// 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::natural_vector::NaturalVector;
///
/// assert_eq!(
/// NaturalVector::from_str("(4, 6, 10)")
/// .unwrap()
/// .into_element_lcm(),
/// 60
/// );
/// assert_eq!(
/// NaturalVector::from_str("(4, 0, 6)")
/// .unwrap()
/// .into_element_lcm(),
/// 0
/// );
/// assert_eq!(NaturalVector::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);
if lcm == 0u32 {
break;
}
}
lcm
}
}