malachite_nz/integer/arithmetic/
conjugate.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::integer::Integer;
10use malachite_base::num::arithmetic::traits::{Conjugate, ConjugateAssign};
11
12impl Conjugate for Integer {
13    type Output = Self;
14
15    /// Computes the complex conjugate of a [`Integer`], taking it by value. A real number is its
16    /// own conjugate, so this is the identity.
17    ///
18    /// $$
19    /// f(x) = \overline{x} = x.
20    /// $$
21    ///
22    /// # Worst-case complexity
23    /// Constant time and additional memory.
24    ///
25    /// # Examples
26    /// ```
27    /// use malachite_base::num::arithmetic::traits::Conjugate;
28    /// use malachite_nz::integer::Integer;
29    ///
30    /// assert_eq!(Integer::from(-123).conjugate(), Integer::from(-123));
31    /// ```
32    #[inline]
33    fn conjugate(self) -> Self {
34        self
35    }
36}
37
38impl Conjugate for &Integer {
39    type Output = Integer;
40
41    /// Computes the complex conjugate of a [`Integer`], taking it by reference. A real number is
42    /// its own conjugate, so this just clones.
43    ///
44    /// $$
45    /// f(x) = \overline{x} = x.
46    /// $$
47    ///
48    /// # Worst-case complexity
49    /// $T(n) = O(n)$
50    ///
51    /// $M(n) = O(n)$
52    ///
53    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
54    ///
55    /// # Examples
56    /// ```
57    /// use malachite_base::num::arithmetic::traits::Conjugate;
58    /// use malachite_nz::integer::Integer;
59    ///
60    /// assert_eq!((&Integer::from(-123)).conjugate(), Integer::from(-123));
61    /// ```
62    #[inline]
63    fn conjugate(self) -> Integer {
64        self.clone()
65    }
66}
67
68impl ConjugateAssign for Integer {
69    /// Replaces a [`Integer`] with its complex conjugate. A real number is its own conjugate, so
70    /// this does nothing.
71    ///
72    /// $$
73    /// x \gets \overline{x} = x.
74    /// $$
75    ///
76    /// # Worst-case complexity
77    /// Constant time and additional memory.
78    ///
79    /// # Examples
80    /// ```
81    /// use malachite_base::num::arithmetic::traits::ConjugateAssign;
82    /// use malachite_nz::integer::Integer;
83    ///
84    /// let mut x = Integer::from(-123);
85    /// x.conjugate_assign();
86    /// assert_eq!(x, Integer::from(-123));
87    /// ```
88    #[inline]
89    fn conjugate_assign(&mut self) {}
90}
malachite_nz/integer/arithmetic/conjugate.rs

malachite_nz/integer/arithmetic/
conjugate.rs
