symplex 0.17.0

Exact symbolic mathematics for Rust: calculus, summation, solving, linear algebra, transforms, compile-time dimensional analysis, and Rust/C code generation
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
145
146
147
148
149
150
151
152
153
154

//! Wave α tests: Gamma half-integers, new macro functions, #[must_use] smoke tests.

use symplex::prelude::*;

// ── Gamma half-integer evaluation ──────────────────────────────────────

#[test]
fn gamma_half_is_sqrt_pi() {
    let ctx = Context::new();
    let half = ctx.rational(1, 2);
    let result = half.gamma().eval();
    let expected = ctx.pi().sqrt();
    assert_eq!(
        format!("{result}"),
        format!("{expected}"),
        "Gamma(1/2) = √π"
    );
}

#[test]
fn gamma_three_halves() {
    let ctx = Context::new();
    // Gamma(3/2) = (1/2) · √π
    let arg = ctx.rational(3, 2);
    let result = arg.gamma().eval();
    let expected = &ctx.rational(1, 2) * &ctx.pi().sqrt();
    assert_eq!(
        format!("{result}"),
        format!("{expected}"),
        "Gamma(3/2) = (1/2)·√π"
    );
}

#[test]
fn gamma_five_halves() {
    let ctx = Context::new();
    // Gamma(5/2) = (3/4) · √π
    let arg = ctx.rational(5, 2);
    let result = arg.gamma().eval();
    let expected = &ctx.rational(3, 4) * &ctx.pi().sqrt();
    assert_eq!(
        format!("{result}"),
        format!("{expected}"),
        "Gamma(5/2) = (3/4)·√π"
    );
}

#[test]
fn gamma_seven_halves() {
    let ctx = Context::new();
    // Gamma(7/2) = (15/8) · √π
    let arg = ctx.rational(7, 2);
    let result = arg.gamma().eval();
    let expected = &ctx.rational(15, 8) * &ctx.pi().sqrt();
    assert_eq!(
        format!("{result}"),
        format!("{expected}"),
        "Gamma(7/2) = (15/8)·√π"
    );
}

// ── expr! macro: floor / ceiling ───────────────────────────────────────

#[test]
fn macro_floor() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let e = expr!(ctx, floor(x));
    let s = format!("{e}");
    assert!(
        s.contains("floor"),
        "floor(x) should display with floor: {s}"
    );
}

#[test]
fn macro_ceiling() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let e = expr!(ctx, ceiling(x));
    let s = format!("{e}");
    assert!(
        s.contains("ceiling") || s.contains("ceil"),
        "ceiling(x) should display with ceiling: {s}"
    );
}

// ── expr! macro: min / max ─────────────────────────────────────────────

#[test]
fn macro_min() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let y = ctx.symbol("y");
    let e = expr!(ctx, min(x, y));
    let s = format!("{e}");
    assert!(
        s.contains("min") || s.contains("Min"),
        "min(x,y) should display with min: {s}"
    );
}

#[test]
fn macro_max() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let y = ctx.symbol("y");
    let e = expr!(ctx, max(x, y));
    let s = format!("{e}");
    assert!(
        s.contains("max") || s.contains("Max"),
        "max(x,y) should display with max: {s}"
    );
}

// ── expr! macro: heaviside / dirac_delta / lambertw ────────────────────

#[test]
fn macro_heaviside_eval_positive() {
    let ctx = Context::new();
    let result = expr!(ctx, heaviside(5)).eval();
    assert_eq!(format!("{result}"), "1", "heaviside(5) should eval to 1");
}

#[test]
fn macro_heaviside_eval_negative() {
    let ctx = Context::new();
    let result = expr!(ctx, heaviside(-3)).eval();
    assert_eq!(format!("{result}"), "0", "heaviside(-3) should eval to 0");
}

#[test]
fn macro_dirac_delta_symbolic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let e = expr!(ctx, dirac_delta(x));
    let s = format!("{e}");
    assert!(
        s.contains("dirac") || s.contains("Dirac") || s.contains("delta") || s.contains("δ"),
        "dirac_delta(x) should display appropriately: {s}"
    );
}

#[test]
fn macro_lambertw_symbolic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let e = expr!(ctx, lambertw(x));
    let s = format!("{e}");
    assert!(
        s.contains("lambert") || s.contains("Lambert") || s.contains("W("),
        "lambertw(x) should display appropriately: {s}"
    );
}