alga 0.9.3

Abstract algebra for Rust
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
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

//! Operators traits and structures.
#[cfg(feature = "decimal")]
use decimal::d128;
pub use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, Sub, SubAssign};

use num::Num;
use num_complex::Complex;

/// Trait implemented by types representing abstract operators.
pub trait Operator: Copy {
    /// Returns the structure that identifies the operator.
    fn operator_token() -> Self;
}

/// Trait used to define the two_sided_inverse element relative to the given operator.
///
/// The operator, e.g., `Additive` or `Multiplicative`, is identified by the type parameter `O`.
pub trait TwoSidedInverse<O: Operator>: Sized {
    /// Returns the two_sided_inverse of `self`, relative to the operator `O`.
    ///
    /// The parameter `O` is generally either `Additive` or `Multiplicative`.
    fn two_sided_inverse(&self) -> Self;

    /// In-place inversion of `self`, relative to the operator `O`.
    ///
    /// The parameter `O` is generally either `Additive` or `Multiplicative`.
    #[inline]
    fn two_sided_inverse_mut(&mut self) {
        *self = self.two_sided_inverse()
    }
}

/*
 *
 * Implementations.
 *
 */

#[derive(Clone, Copy)]
/// The addition operator, commonly symbolized by `+`.
pub struct Additive;

#[derive(Clone, Copy)]
/// The multiplication operator, commonly symbolized by `×`.
pub struct Multiplicative;

#[derive(Clone, Copy)]
/// The default abstract operator.
pub struct AbstractOperator;

impl Operator for Additive {
    #[inline]
    fn operator_token() -> Self {
        Additive
    }
}

impl Operator for Multiplicative {
    #[inline]
    fn operator_token() -> Self {
        Multiplicative
    }
}

impl Operator for AbstractOperator {
    #[inline]
    fn operator_token() -> Self {
        AbstractOperator
    }
}

macro_rules! impl_additive_inverse(
    ($($T:ty),* $(,)*) => {$(
        impl TwoSidedInverse<Additive> for $T {
            fn two_sided_inverse(&self) -> Self {
                -*self
            }
        }
    )*}
);

impl_additive_inverse!(i8, i16, i32, i64, i128, isize, f32, f64);
#[cfg(feature = "decimal")]
impl_additive_inverse!(d128);

impl<N: TwoSidedInverse<Additive>> TwoSidedInverse<Additive> for Complex<N> {
    #[inline]
    fn two_sided_inverse(&self) -> Complex<N> {
        Complex {
            re: self.re.two_sided_inverse(),
            im: self.im.two_sided_inverse(),
        }
    }
}

impl TwoSidedInverse<Multiplicative> for f32 {
    #[inline]
    fn two_sided_inverse(&self) -> f32 {
        1.0 / self
    }
}

impl TwoSidedInverse<Multiplicative> for f64 {
    #[inline]
    fn two_sided_inverse(&self) -> f64 {
        1.0 / self
    }
}

#[cfg(feature = "decimal")]
impl TwoSidedInverse<Multiplicative> for d128 {
    #[inline]
    fn two_sided_inverse(&self) -> d128 {
        d128!(1.0) / self
    }
}

impl<N: Num + Clone + ClosedNeg> TwoSidedInverse<Multiplicative> for Complex<N> {
    #[inline]
    fn two_sided_inverse(&self) -> Self {
        self.inv()
    }
}

/// [Alias] Trait alias for `Add` and `AddAssign` with result of type `Self`.
pub trait ClosedAdd<Right = Self>: Sized + Add<Right, Output = Self> + AddAssign<Right> {}

/// [Alias] Trait alias for `Sub` and `SubAssign` with result of type `Self`.
pub trait ClosedSub<Right = Self>: Sized + Sub<Right, Output = Self> + SubAssign<Right> {}

/// [Alias] Trait alias for `Mul` and `MulAssign` with result of type `Self`.
pub trait ClosedMul<Right = Self>: Sized + Mul<Right, Output = Self> + MulAssign<Right> {}

/// [Alias] Trait alias for `Div` and `DivAssign` with result of type `Self`.
pub trait ClosedDiv<Right = Self>: Sized + Div<Right, Output = Self> + DivAssign<Right> {}

/// [Alias] Trait alias for `Neg` with result of type `Self`.
pub trait ClosedNeg: Sized + Neg<Output = Self> {}

impl<T, Right> ClosedAdd<Right> for T where T: Add<Right, Output = T> + AddAssign<Right> {}
impl<T, Right> ClosedSub<Right> for T where T: Sub<Right, Output = T> + SubAssign<Right> {}
impl<T, Right> ClosedMul<Right> for T where T: Mul<Right, Output = T> + MulAssign<Right> {}
impl<T, Right> ClosedDiv<Right> for T where T: Div<Right, Output = T> + DivAssign<Right> {}
impl<T> ClosedNeg for T where T: Neg<Output = T> {}