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
// 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::num::arithmetic::traits::{ModIsReduced, ModNeg, ModNegAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::unsigned_polynomial::UnsignedPolynomial;
fn assert_reduced<T: PrimitiveUnsigned>(p: &UnsignedPolynomial<T>, m: T) {
assert!(
p.mod_is_reduced(&m),
"self must be reduced mod m, but {p} has a coefficient >= {m}"
);
}
// Negates every coefficient modulo m. The coefficients are reduced, so a nonzero one stays nonzero
// and nothing needs trimming.
fn negate<T: PrimitiveUnsigned>(coefficients: &mut [T], m: T) {
for c in coefficients {
if *c != T::ZERO {
*c = m - *c;
}
}
}
impl<T: PrimitiveUnsigned> ModNeg<T> for UnsignedPolynomial<T> {
type Output = Self;
/// Negates an [`UnsignedPolynomial`] modulo `m`, taking the polynomial by value. The
/// coefficients must already be reduced modulo `m`.
///
/// Each nonzero coefficient $c$ becomes $m - c$, which is also nonzero, so the degree is
/// unchanged. The zero polynomial is its own negation.
///
/// $$
/// f(p, m) = -p \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModNeg;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("5*x^2+x+3").unwrap();
/// assert_eq!(p.clone().mod_neg(7).to_string(), "2*x^2+6*x+4");
/// assert_eq!(
/// UnsignedPolynomial::<u8>::ZERO.mod_neg(7),
/// UnsignedPolynomial::<u8>::ZERO
/// );
/// ```
///
/// This is equivalent to `nmod_poly_neg` from `nmod_poly/neg.c`, FLINT 3.6.0.
#[inline]
fn mod_neg(mut self, m: T) -> Self {
self.mod_neg_assign(m);
self
}
}
impl<T: PrimitiveUnsigned> ModNeg<T> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Negates an [`UnsignedPolynomial`] modulo `m`, taking the polynomial by reference. The
/// coefficients must already be reduced modulo `m`.
///
/// Each nonzero coefficient $c$ becomes $m - c$, which is also nonzero, so the degree is
/// unchanged. The zero polynomial is its own negation.
///
/// $$
/// f(p, m) = -p \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModNeg;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("5*x^2+x+3").unwrap();
/// assert_eq!((&p).mod_neg(7).to_string(), "2*x^2+6*x+4");
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::ZERO).mod_neg(7),
/// UnsignedPolynomial::<u8>::ZERO
/// );
/// ```
///
/// This is equivalent to `nmod_poly_neg` from `nmod_poly/neg.c`, FLINT 3.6.0.
fn mod_neg(self, m: T) -> UnsignedPolynomial<T> {
assert_reduced(self, m);
let mut coefficients = self.coefficients.clone();
negate(&mut coefficients, m);
UnsignedPolynomial { coefficients }
}
}
impl<T: PrimitiveUnsigned> ModNegAssign<T> for UnsignedPolynomial<T> {
/// Negates an [`UnsignedPolynomial`] modulo `m`, in place. The coefficients must already be
/// reduced modulo `m`.
///
/// See [`mod_neg`](ModNeg::mod_neg).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModNegAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("5*x^2+x+3").unwrap();
/// p.mod_neg_assign(7);
/// assert_eq!(p.to_string(), "2*x^2+6*x+4");
/// ```
fn mod_neg_assign(&mut self, m: T) {
assert_reduced(self, m);
negate(&mut self.coefficients, m);
}
}