deep_causality_num 0.3.2

Number utils for for deep_causality crate.
Documentation 
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

/*
 * SPDX-License-Identifier: MIT
 * Copyright (c) 2023 - 2026. The DeepCausality Authors and Contributors. All Rights Reserved.
 */
use crate::{
    AbelianGroup, Associative, Commutative, Complex, ComplexField, Distributive, DivisionAlgebra,
    RealField,
};

// | Type | `Distributive` | `Associative` | `Commutative` | Trait |
// | :--- | :---: | :---: | :---: | :--- |
// | **Complex** | ✅ | ✅ | ✅ | `Field`  `ComplexField` |

// Marker Traits
impl<T: RealField> Associative for Complex<T> {}
impl<T: RealField> Commutative for Complex<T> {}
impl<T: RealField> Distributive for Complex<T> {}
impl<T: RealField> AbelianGroup for Complex<T> {}

// The blanket impls for AssociativeRing, Field, and AssociativeDivisionAlgebra
// will apply automatically as Complex<T> now satisfies their super-traits.

// Implement all methods for DivisionAlgebra, delegating to inherent methods.
impl<T: RealField> DivisionAlgebra<T> for Complex<T> {
    fn conjugate(&self) -> Self {
        self._conjugate_impl()
    }

    fn norm_sqr(&self) -> T {
        self._norm_sqr_impl()
    }

    fn inverse(&self) -> Self {
        self._inverse_impl()
    }
}

// Implement ComplexField for Complex<T>
impl<T: RealField> ComplexField<T> for Complex<T> {
    #[inline]
    fn real(&self) -> T {
        self.re
    }

    #[inline]
    fn imag(&self) -> T {
        self.im
    }

    #[inline]
    fn conjugate(&self) -> Self {
        self._conjugate_impl()
    }

    #[inline]
    fn norm_sqr(&self) -> T {
        self._norm_sqr_impl()
    }

    #[inline]
    fn norm(&self) -> T {
        self._norm_sqr_impl().sqrt()
    }

    #[inline]
    fn arg(&self) -> T {
        self.im.atan2(self.re)
    }

    #[inline]
    fn from_re_im(re: T, im: T) -> Self {
        Self::new(re, im)
    }

    #[inline]
    fn from_polar(r: T, theta: T) -> Self {
        Self::new(r * theta.cos(), r * theta.sin())
    }

    #[inline]
    fn i() -> Self {
        Self::new(T::zero(), T::one())
    }

    #[inline]
    fn is_real(&self) -> bool {
        self.im.is_zero()
    }

    #[inline]
    fn is_imaginary(&self) -> bool {
        self.re.is_zero()
    }
}