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
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183

//! Public API tests for Ex::series() and Ex::factor().

use symplex::prelude::*;

// ═══════════════════════════════════════════════════════════════════════════
// series()
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn series_exp_x_order_4() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    // exp(x) around 0, order 4: 1 + x + x^2/2 + x^3/6
    let s = x.exp().series(&x, &zero, 4);
    let result = s.expand().eval();
    let text = format!("{result}");
    assert!(text.contains("1"), "constant term 1: {text}");
    assert!(text.contains("x"), "x term: {text}");
    assert!(text.contains("x^2"), "x^2 term: {text}");
    assert!(text.contains("x^3"), "x^3 term: {text}");
}

#[test]
fn series_sin_x_order_4() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    // sin(x) around 0, order 4: x - x^3/6
    let s = x.sin().series(&x, &zero, 4);
    let result = s.expand().eval();
    let text = format!("{result}");
    assert!(text.contains("x"), "should have x term: {text}");
    assert!(text.contains("x^3"), "should have x^3 term: {text}");
}

#[test]
fn series_cos_x_order_4() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    // cos(x) around 0, order 4: 1 - x^2/2
    let s = x.cos().series(&x, &zero, 4);
    let result = s.expand().eval();
    let text = format!("{result}");
    assert!(text.contains("1"), "constant term 1: {text}");
    assert!(text.contains("x^2"), "should have x^2 term: {text}");
}

#[test]
fn series_polynomial_is_exact() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    // series(x^2, x, 0, 5) should give exactly x^2
    let s = x.powi(2).series(&x, &zero, 5);
    assert_eq!(format!("{s}"), "x^2");
}

#[test]
fn series_constant() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    let s = ctx.int(7).series(&x, &zero, 3);
    assert_eq!(format!("{s}"), "7");
}

#[test]
fn series_order_zero() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    let s = x.series(&x, &zero, 0);
    assert_eq!(format!("{s}"), "0");
}

#[test]
fn series_x_around_zero() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    let s = x.series(&x, &zero, 3);
    assert_eq!(format!("{s}"), "x");
}

// ═══════════════════════════════════════════════════════════════════════════
// factor()
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn factor_x_squared_minus_one() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x.powi(2) - 1;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    // Should be factored — no x^2
    assert!(!s.contains("x^2"), "should be factored (no x^2): {s}");
}

#[test]
fn factor_quadratic_two_roots() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^2 - 5x + 6 = (x-2)(x-3)
    let expr = &x.powi(2) - &x * 5 + 6;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    assert!(!s.contains("x^2"), "should be factored: {s}");
}

#[test]
fn factor_with_content() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // 2*x^2 - 2 = 2*(x-1)*(x+1)
    let expr = &x.powi(2) * 2 - 2;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    assert!(!s.contains("x^2"), "should be factored: {s}");
    assert!(s.contains("2"), "should have content factor 2: {s}");
}

#[test]
fn factor_no_rational_roots() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^2 + 1 — no real rational roots
    let expr = &x.powi(2) + 1;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    assert!(s.contains("x^2"), "should stay unfactored: {s}");
}

#[test]
fn factor_already_linear() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x + 1;
    let factored = expr.factor(&x);
    assert_eq!(format!("{factored}"), "x + 1");
}

#[test]
fn factor_cubic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^3 - 6x^2 + 11x - 6 = (x-1)(x-2)(x-3)
    let expr = &x.powi(3) - &x.powi(2) * 6 + &x * 11 - 6;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    assert!(!s.contains("x^3"), "should be fully factored: {s}");
}

#[test]
fn factor_non_polynomial() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = x.sin();
    let factored = expr.factor(&x);
    assert_eq!(format!("{factored}"), "sin(x)");
}

#[test]
fn factor_constant() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let factored = ctx.int(42).factor(&x);
    assert_eq!(format!("{factored}"), "42");
}

#[test]
fn factor_double_root() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^2 - 2x + 1 = (x-1)^2
    let expr = &x.powi(2) - &x * 2 + 1;
    let factored = expr.factor(&x);
    let s = format!("{factored}");
    // Should show the double root — either as (x-1)^2 or (-1+x)^2 or (-1+x)*(-1+x)
    assert!(!s.contains("x^2"), "should be factored: {s}");
}