laddu-compile 0.24.1

Amplitude analysis tools 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

//! Algebraic laws. Each statement is a checked equation over typed CAS terms.

use super::Cas;
use super::pattern::{Call2, Guard, Pattern, Rule, RuleSet};
use laddu_cas_macros::cas_rules;

pub(super) fn standard(cas: &Cas) -> RuleSet {
    let equations = cas_rules! {
        x + 0 => x;
        x * 1 => x;
        x * 0 => 0;
        x - x => 0;
        x - 0 => x;
        0 - x => -x;
        x / 1 => x;
        x / x => 1 if nonzero(x);
        -(-x) => x;
        x ^ 0 => 1;
        x ^ 1 => x;
        sqrt(x) ^ 2 => x;
        conj(conj(x)) => x;
        conj(complex(re, im)) => complex(re, -im) if real(re) && real(im);
        conj(exp(x)) => exp(conj(x));
        conj(-x) => -conj(x);
        conj(x + y) => conj(x) + conj(y);
        conj(x * y) => conj(x) * conj(y);
        real(real(x)) => real(x);
        imag(real(x)) => 0;
        real(complex(re, im)) => re;
        imag(complex(re, im)) => im;
        real(conj(x)) => real(x);
        imag(conj(x)) => -imag(x);
        conj(x) => x if real(x);
        real(x) => x if real(x);
        imag(x) => 0 if real(x);
        norm_sqr(conj(x)) => norm_sqr(x);
        norm_sqr(x) => x ^ 2 if real(x);
        norm_sqr(exp(I * x) * y) => norm_sqr(y) if real(x);
        cos(-x) => cos(x);
        sin(-x) => -sin(x);
        sin(x)^2 + cos(x)^2 => 1;
        1 - sin(x)^2 => cos(x)^2;
        1 - cos(x)^2 => sin(x)^2;
        1 + -sin(x)^2 => cos(x)^2;
        1 + -cos(x)^2 => sin(x)^2;
        sin(0.5 * x) ^ 2 => 0.5 * (1 - cos(x));
        cos(0.5 * x) ^ 2 => 0.5 * (1 + cos(x));
        exp(0) => 1;
        exp(x) * exp(y) <=> exp(x + y);
        cos(x) + I * sin(x) <=> exp(I * x) if real(x);
        cos(x) - I * sin(x) => exp(-(I * x)) if real(x);
        -(x + y) => -x + -y;
        c * cos(x) + (c * I) * sin(x) => c * exp(I * x) if real(x);
        x * a + x * b <=> x * (a + b);
        x^2 - y^2 <=> (x - y) * (x + y);
        matmul(identity, a) => a if identity(identity);
        matmul(a, identity) => a if identity(identity);
        matvec(identity, v) => v if identity(identity);
        dot(zero, v) => 0 if zero(zero);
        solve(identity, rhs) => rhs if identity(identity);
        x + (-x) => 0;
        x + x => 2 * x;
        x - (-y) => x + y;
        -(x - y) => y - x;
        0 / x => 0 if nonzero(x);
        (-x) / y => -(x / y);
        x / (-y) => -(x / y);
        (x * y) / x => y if nonzero(x);
        (x / y) * y => x if nonzero(y);
        sqrt(0) => 0;
        sqrt(1) => 1;
        I^2 => -1;
        conj(I) => -I;
        real(I) => 0;
        imag(I) => 1;
        complex(a, 0) => a if real(a);
        complex(a, b) + complex(c, d) => complex(a + c, b + d) if real(a) && real(b) && real(c) && real(d);
        conj(x / y) => conj(x) / conj(y) if nonzero(y);
        real(x + y) => real(x) + real(y);
        imag(x + y) => imag(x) + imag(y);
        real(-x) => -real(x);
        imag(-x) => -imag(x);
        norm_sqr(0) => 0;
        norm_sqr(1) => 1;
            norm_sqr(-x) => norm_sqr(x);
            norm_sqr(x / y) => norm_sqr(x) / norm_sqr(y) if nonzero(y);
        matmul(zero, m) => zero if zero(zero);
        matvec(zero, v) => zero if zero(zero);
        matvec(a, zero) => zero if zero(zero);
        dot(a, zero) => 0 if zero(zero);
        cos(0) => 1;
        sin(0) => 0;
    };
    RuleSet::new(cas, equations)
}