symplex 0.11.1

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

//! Tests for definite integrals, degree(), and coeffs().

use symplex::prelude::*;

// ═══════════════════════════════════════════════════════════════════════════
// Definite integrals
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn definite_integral_x_squared_0_to_1() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // ∫₀¹ x² dx = 1/3
    let result = x.powi(2).integrate_definite(&x, &ctx.int(0), &ctx.int(1));
    assert_eq!(format!("{result}"), "1/3");
}

#[test]
fn definite_integral_constant() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // ∫₀³ 5 dx = 15
    let result = ctx.int(5).integrate_definite(&x, &ctx.int(0), &ctx.int(3));
    assert_eq!(format!("{result}"), "15");
}

#[test]
fn definite_integral_linear() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // ∫₀² x dx = 2
    let result = x.integrate_definite(&x, &ctx.int(0), &ctx.int(2));
    assert_eq!(format!("{result}"), "2");
}

#[test]
fn definite_integral_polynomial() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // ∫₁² (x^2 + x) dx = [x^3/3 + x^2/2]₁² = (8/3 + 2) - (1/3 + 1/2) = 14/3 - 5/6 = 23/6
    let expr = &x.powi(2) + &x;
    let result = expr.integrate_definite(&x, &ctx.int(1), &ctx.int(2));
    assert_eq!(format!("{result}"), "23/6");
}

#[test]
fn definite_integral_sin_0_to_pi() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // ∫₀^π sin(x) dx = [-cos(x)]₀^π = -cos(π) - (-cos(0)) = 1 + 1 = 2
    let result = x.sin().integrate_definite(&x, &ctx.int(0), &ctx.pi());
    let evaled = result.eval();
    assert_eq!(format!("{evaled}"), "2");
}

#[test]
fn definite_integral_same_bounds_is_zero() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let result = x.powi(2).integrate_definite(&x, &ctx.int(3), &ctx.int(3));
    assert_eq!(format!("{result}"), "0");
}

// ═══════════════════════════════════════════════════════════════════════════
// degree()
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn degree_quadratic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x.powi(2) + &x + 1;
    assert_eq!(expr.degree(&x), Some(2));
}

#[test]
fn degree_cubic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x.powi(3) + 1;
    assert_eq!(expr.degree(&x), Some(3));
}

#[test]
fn degree_constant() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert_eq!(ctx.int(5).degree(&x), Some(0));
}

#[test]
fn degree_linear() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert_eq!((&x + 1).degree(&x), Some(1));
}

#[test]
fn degree_non_polynomial() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert_eq!(x.sin().degree(&x), None);
}

#[test]
fn degree_zero_polynomial() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert_eq!(ctx.int(0).degree(&x), None);
}

// ═══════════════════════════════════════════════════════════════════════════
// coeffs()
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn coeffs_quadratic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^2 + 3*x + 5
    let expr = &x.powi(2) + &x * 3 + 5;
    let cs = expr.coeffs(&x).unwrap();
    let strs: Vec<String> = cs.iter().map(|c| format!("{c}")).collect();
    assert_eq!(strs, vec!["5", "3", "1"]);
}

#[test]
fn coeffs_linear() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x * 2 + 7;
    let cs = expr.coeffs(&x).unwrap();
    let strs: Vec<String> = cs.iter().map(|c| format!("{c}")).collect();
    assert_eq!(strs, vec!["7", "2"]);
}

#[test]
fn coeffs_constant() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let cs = ctx.int(42).coeffs(&x).unwrap();
    let strs: Vec<String> = cs.iter().map(|c| format!("{c}")).collect();
    assert_eq!(strs, vec!["42"]);
}

#[test]
fn coeffs_non_polynomial() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert!(x.sin().coeffs(&x).is_none());
}