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_polynomial::RationalPolynomial;
use crate::rational_vector::arithmetic::content::content_over;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, ContentAndCanonicalPrimitivePart,
};
use malachite_nz::integer_polynomial::IntegerPolynomial;
impl CanonicalPrimitivePart for RationalPolynomial {
type Output = IntegerPolynomial;
/// Computes the canonical primitive part of a [`RationalPolynomial`], taking the polynomial by
/// value.
///
/// This is the polynomial divided by its content, with the sign chosen so that the leading
/// coefficient is non-negative. It always has integer coefficients, so it is an
/// [`IntegerPolynomial`]; for $p = A/d$ it is the canonical primitive part of $A$, and the
/// denominator plays no part.
///
/// $$
/// p = \operatorname{sgn}(\operatorname{lc}(p)) \operatorname{cont}(p) \operatorname{cpp}(p).
/// $$
///
/// The canonical 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::CanonicalPrimitivePart;
/// 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().canonical_primitive_part().to_string(), "x+2");
/// assert_eq!(RationalPolynomial::ZERO.canonical_primitive_part(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_primitive_part` from `fmpq_poly/primitive_part.c`, FLINT
/// 3.6.0, except that the result is an [`IntegerPolynomial`].
#[inline]
fn canonical_primitive_part(self) -> IntegerPolynomial {
self.numerator.canonical_primitive_part()
}
}
impl CanonicalPrimitivePart for &RationalPolynomial {
type Output = IntegerPolynomial;
/// Computes the canonical primitive part of a [`RationalPolynomial`], taking the polynomial by
/// reference.
///
/// This is the polynomial divided by its content, with the sign chosen so that the leading
/// coefficient is non-negative. It always has integer coefficients, so it is an
/// [`IntegerPolynomial`]; for $p = A/d$ it is the canonical primitive part of $A$, and the
/// denominator plays no part.
///
/// $$
/// p = \operatorname{sgn}(\operatorname{lc}(p)) \operatorname{cont}(p) \operatorname{cpp}(p).
/// $$
///
/// The canonical 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::CanonicalPrimitivePart;
/// 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).canonical_primitive_part().to_string(), "x+2");
/// assert_eq!((&RationalPolynomial::ZERO).canonical_primitive_part(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_primitive_part` from `fmpq_poly/primitive_part.c`, FLINT
/// 3.6.0, except that the result is an [`IntegerPolynomial`].
#[inline]
fn canonical_primitive_part(self) -> IntegerPolynomial {
(&self.numerator).canonical_primitive_part()
}
}
impl ContentAndCanonicalPrimitivePart for RationalPolynomial {
type Content = Rational;
type CanonicalPrimitivePart = IntegerPolynomial;
/// Computes the content and the canonical primitive part of a [`RationalPolynomial`] together,
/// taking the polynomial by value.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_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::ContentAndCanonicalPrimitivePart;
/// 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_canonical_primitive_part();
/// assert_eq!(content.to_string(), "2/3");
/// assert_eq!(primitive_part.to_string(), "x+2");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, IntegerPolynomial) {
let (content, primitive_part) = self.numerator.content_and_canonical_primitive_part();
(content_over(content, self.denominator), primitive_part)
}
}
impl ContentAndCanonicalPrimitivePart for &RationalPolynomial {
type Content = Rational;
type CanonicalPrimitivePart = IntegerPolynomial;
/// Computes the content and the canonical primitive part of a [`RationalPolynomial`] together,
/// taking the polynomial by reference.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_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::ContentAndCanonicalPrimitivePart;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("-2/3*x-4/3").unwrap();
/// let (content, primitive_part) = (&p).content_and_canonical_primitive_part();
/// assert_eq!(content.to_string(), "2/3");
/// assert_eq!(primitive_part.to_string(), "x+2");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, IntegerPolynomial) {
let (content, primitive_part) = (&self.numerator).content_and_canonical_primitive_part();
(
content_over(content, self.denominator.clone()),
primitive_part,
)
}
}