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
// 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_polynomial::RationalPolynomial;
use malachite_base::num::arithmetic::traits::{CanonicalPrimitivePart, UnsignedAbs};
use malachite_base::num::basic::traits::Zero;
use malachite_base::polynomial::{MakeMonic, MakeMonicAssign, Polynomial};
use malachite_nz::integer_polynomial::IntegerPolynomial;
// For p = A/d, the monic multiple of p is A/lc(A). Dividing numerator and denominator by cont(A),
// which divides lc(A), gives pp(A)/lc(pp(A)) up to sign, and that pair is already canonical: pp(A)
// has content 1. So the denominator of p plays no part, and no GCD is needed beyond the content.
fn monic_from_primitive_part(primitive_part: IntegerPolynomial) -> RationalPolynomial {
if primitive_part == IntegerPolynomial::ZERO {
return RationalPolynomial::ZERO;
}
let denominator = primitive_part.leading_coefficient().unsigned_abs();
RationalPolynomial {
numerator: primitive_part,
denominator,
}
}
impl MakeMonic for RationalPolynomial {
type Output = Self;
/// Makes a [`RationalPolynomial`] monic, by dividing it by its leading coefficient, taking the
/// polynomial by value.
///
/// The zero polynomial has no leading coefficient, and is returned unchanged. For $p = A/d$ the
/// result is $\operatorname{pp}(A)/\operatorname{lc}(\operatorname{pp}(A))$, which is already
/// in lowest terms, so the denominator of $p$ plays no part.
///
/// # 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.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::MakeMonic;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("6*x+4").unwrap();
/// assert_eq!(p.clone().make_monic().to_string(), "x+2/3");
/// let p = RationalPolynomial::from_str("-1/2*x^2+1/3").unwrap();
/// assert_eq!(p.clone().make_monic().to_string(), "x^2-2/3");
/// assert_eq!(RationalPolynomial::ZERO.make_monic(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_make_monic` from `fmpq_poly/make_monic.c`, FLINT 3.6.0.
#[inline]
fn make_monic(self) -> Self {
monic_from_primitive_part(self.numerator.canonical_primitive_part())
}
}
impl MakeMonic for &RationalPolynomial {
type Output = RationalPolynomial;
/// Makes a [`RationalPolynomial`] monic, by dividing it by its leading coefficient, taking the
/// polynomial by reference.
///
/// The zero polynomial has no leading coefficient, and is returned unchanged. For $p = A/d$ the
/// result is $\operatorname{pp}(A)/\operatorname{lc}(\operatorname{pp}(A))$, which is already
/// in lowest terms, so the denominator of $p$ plays no part.
///
/// # 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.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::MakeMonic;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let p = RationalPolynomial::from_str("6*x+4").unwrap();
/// assert_eq!((&p).make_monic().to_string(), "x+2/3");
/// let p = RationalPolynomial::from_str("-1/2*x^2+1/3").unwrap();
/// assert_eq!((&p).make_monic().to_string(), "x^2-2/3");
/// assert_eq!((&RationalPolynomial::ZERO).make_monic(), 0);
/// ```
///
/// This is equivalent to `fmpq_poly_make_monic` from `fmpq_poly/make_monic.c`, FLINT 3.6.0.
#[inline]
fn make_monic(self) -> RationalPolynomial {
monic_from_primitive_part((&self.numerator).canonical_primitive_part())
}
}
impl MakeMonicAssign for RationalPolynomial {
/// Makes a [`RationalPolynomial`] monic in place, by dividing it by its leading coefficient.
///
/// See [`make_monic`](MakeMonic::make_monic). The zero polynomial is left unchanged.
///
/// # 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.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::MakeMonicAssign;
/// use malachite_q::rational_polynomial::RationalPolynomial;
///
/// let mut p = RationalPolynomial::from_str("6*x+4").unwrap();
/// p.make_monic_assign();
/// assert_eq!(p.to_string(), "x+2/3");
/// ```
#[inline]
fn make_monic_assign(&mut self) {
let numerator = core::mem::take(&mut self.numerator);
*self = monic_from_primitive_part(numerator.canonical_primitive_part());
}
}