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
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
// 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 crate::rational_vector::arithmetic::content::content_over;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, ContentAndCanonicalPrimitivePart,
};
use malachite_nz::integer_vector::IntegerVector;
impl CanonicalPrimitivePart for RationalVector {
type Output = IntegerVector;
/// Computes the canonical primitive part of a [`RationalVector`], taking the vector by value.
///
/// This is the
/// [`primitive_part`](malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part),
/// negated if its first nonzero element is negative, so that the first nonzero element is
/// positive: the canonical primitive part of the numerators that
/// [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives. A
/// vector and its negation have the same canonical primitive part.
///
/// $$
/// v = \pm \operatorname{cont}(v) \operatorname{cpp}(v).
/// $$
///
/// The canonical 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::CanonicalPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!(v.canonical_primitive_part().to_string(), "(3, -4, 30)");
/// ```
#[inline]
fn canonical_primitive_part(self) -> IntegerVector {
self.to_numerators_and_denominator()
.0
.canonical_primitive_part()
}
}
impl CanonicalPrimitivePart for &RationalVector {
type Output = IntegerVector;
/// Computes the canonical primitive part of a [`RationalVector`], taking the vector by
/// reference.
///
/// This is the
/// [`primitive_part`](malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part),
/// negated if its first nonzero element is negative, so that the first nonzero element is
/// positive: the canonical primitive part of the numerators that
/// [`to_numerators_and_denominator`](RationalVector::to_numerators_and_denominator) gives. A
/// vector and its negation have the same canonical primitive part.
///
/// $$
/// v = \pm \operatorname{cont}(v) \operatorname{cpp}(v).
/// $$
///
/// The canonical 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::CanonicalPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// assert_eq!((&v).canonical_primitive_part().to_string(), "(3, -4, 30)");
/// ```
#[inline]
fn canonical_primitive_part(self) -> IntegerVector {
self.to_numerators_and_denominator()
.0
.canonical_primitive_part()
}
}
impl ContentAndCanonicalPrimitivePart for RationalVector {
type Content = Rational;
type CanonicalPrimitivePart = IntegerVector;
/// Computes the content and the canonical primitive part of a [`RationalVector`] together,
/// taking the vector by value.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_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::ContentAndCanonicalPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// let (content, primitive_part) = v.content_and_canonical_primitive_part();
/// assert_eq!(content.to_string(), "1/6");
/// assert_eq!(primitive_part.to_string(), "(3, -4, 30)");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, IntegerVector) {
let (numerators, denominator) = self.to_numerators_and_denominator();
let (content, primitive_part) = numerators.content_and_canonical_primitive_part();
(content_over(content, denominator), primitive_part)
}
}
impl ContentAndCanonicalPrimitivePart for &RationalVector {
type Content = Rational;
type CanonicalPrimitivePart = IntegerVector;
/// Computes the content and the canonical primitive part of a [`RationalVector`] together,
/// taking the vector by reference.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_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::ContentAndCanonicalPrimitivePart;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(-1/2, 2/3, -5)").unwrap();
/// let (content, primitive_part) = (&v).content_and_canonical_primitive_part();
/// assert_eq!(content.to_string(), "1/6");
/// assert_eq!(primitive_part.to_string(), "(3, -4, 30)");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, IntegerVector) {
let (numerators, denominator) = self.to_numerators_and_denominator();
let (content, primitive_part) = numerators.content_and_canonical_primitive_part();
(content_over(content, denominator), primitive_part)
}
}