malachite_nz/gaussian_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::gaussian_integer::GaussianInteger;
10use malachite_base::num::arithmetic::traits::{Conjugate, ConjugateAssign, NegAssign};
11
12impl Conjugate for GaussianInteger {
13    type Output = Self;
14
15    /// Computes the complex conjugate of a [`GaussianInteger`], taking it by value. The sign of the
16    /// imaginary part is flipped.
17    ///
18    /// $$
19    /// f(x) = \overline{x} = \Re(x) - \Im(x) i.
20    /// $$
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_base::num::basic::traits::I;
29    /// use malachite_nz::gaussian_integer::GaussianInteger;
30    /// use std::str::FromStr;
31    ///
32    /// assert_eq!(GaussianInteger::I.conjugate().to_string(), "-i");
33    /// assert_eq!(
34    ///     GaussianInteger::from_str("2-3i")
35    ///         .unwrap()
36    ///         .conjugate()
37    ///         .to_string(),
38    ///     "2+3i"
39    /// );
40    /// assert_eq!(
41    ///     GaussianInteger::from_str("-123")
42    ///         .unwrap()
43    ///         .conjugate()
44    ///         .to_string(),
45    ///     "-123"
46    /// );
47    /// ```
48    fn conjugate(mut self) -> Self {
49        self.conjugate_assign();
50        self
51    }
52}
53
54impl Conjugate for &GaussianInteger {
55    type Output = GaussianInteger;
56
57    /// Computes the complex conjugate of a [`GaussianInteger`], taking it by reference. The sign of
58    /// the imaginary part is flipped.
59    ///
60    /// $$
61    /// f(x) = \overline{x} = \Re(x) - \Im(x) i.
62    /// $$
63    ///
64    /// # Worst-case complexity
65    /// $T(n) = O(n)$
66    ///
67    /// $M(n) = O(n)$
68    ///
69    /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
70    /// bits of the real and imaginary parts.
71    ///
72    /// # Examples
73    /// ```
74    /// use malachite_base::num::arithmetic::traits::Conjugate;
75    /// use malachite_nz::gaussian_integer::GaussianInteger;
76    /// use std::str::FromStr;
77    ///
78    /// let x = GaussianInteger::from_str("2-3i").unwrap();
79    /// assert_eq!((&x).conjugate().to_string(), "2+3i");
80    /// ```
81    fn conjugate(self) -> GaussianInteger {
82        GaussianInteger {
83            real: self.real.clone(),
84            imaginary: -&self.imaginary,
85        }
86    }
87}
88
89impl ConjugateAssign for GaussianInteger {
90    /// Replaces a [`GaussianInteger`] with its complex conjugate. The sign of the imaginary part is
91    /// flipped.
92    ///
93    /// $$
94    /// x \gets \overline{x} = \Re(x) - \Im(x) i.
95    /// $$
96    ///
97    /// # Worst-case complexity
98    /// Constant time and additional memory.
99    ///
100    /// # Examples
101    /// ```
102    /// use malachite_base::num::arithmetic::traits::ConjugateAssign;
103    /// use malachite_nz::gaussian_integer::GaussianInteger;
104    /// use std::str::FromStr;
105    ///
106    /// let mut x = GaussianInteger::from_str("2-3i").unwrap();
107    /// x.conjugate_assign();
108    /// assert_eq!(x.to_string(), "2+3i");
109    /// ```
110    #[inline]
111    fn conjugate_assign(&mut self) {
112        self.imaginary.neg_assign();
113    }
114}
malachite_nz/gaussian_integer/arithmetic/conjugate.rs

malachite_nz/gaussian_integer/arithmetic/
conjugate.rs
