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
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232

//! Tests for new math features: partial fractions, nsolve, expand_trig,
//! polynomial GCD/LCM, odd/even trig eval, inverse hyperbolics.

use symplex::prelude::*;

// ═══════════════════════════════════════════════════════════════════════════
// Partial fractions (apart)
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn apart_simple() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // 1/(x^2 - 1) should decompose
    let expr = 1 / (&x.powi(2) - 1);
    let decomposed = expr.partial_fractions(&x);
    let s = format!("{decomposed}");
    // Should NOT contain x^2 in denominator anymore
    assert!(
        s != format!("{expr}") || s.contains("1/"),
        "should decompose: {s}"
    );
}

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

// ═══════════════════════════════════════════════════════════════════════════
// Numerical root finding (nsolve)
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn nsolve_x_minus_cos_x() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x - cos(x) = 0 has a root near 0.739
    let expr = &x - &x.cos();
    let root = expr.solve_numeric(&x, 1.0, 50, 1e-12).unwrap();
    assert!((root - 0.7390851332).abs() < 1e-6, "got: {root}");
}

#[test]
fn nsolve_x_squared_minus_2() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // x^2 - 2 = 0 has root sqrt(2) ≈ 1.4142
    let expr = &x.powi(2) - 2;
    let root = expr.solve_numeric(&x, 1.5, 50, 1e-12).unwrap();
    assert!(
        (root - std::f64::consts::SQRT_2).abs() < 1e-8,
        "got: {root}"
    );
}

#[test]
fn nsolve_exp_minus_2() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // exp(x) - 2 = 0 → x = ln(2) ≈ 0.6931
    let expr = &x.exp() - 2;
    let root = expr.solve_numeric(&x, 1.0, 50, 1e-12).unwrap();
    assert!((root - 2.0_f64.ln()).abs() < 1e-8, "got: {root}");
}

// ═══════════════════════════════════════════════════════════════════════════
// Trig expansion
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn expand_trig_sin_sum() {
    let ctx = Context::new();
    let (x, y) = (ctx.symbol("x"), ctx.symbol("y"));
    let expr = (&x + &y).sin();
    let expanded = expr.expand_trig();
    let s = format!("{expanded}");
    assert!(s.contains("sin(x)"), "should contain sin(x): {s}");
    assert!(s.contains("cos(y)"), "should contain cos(y): {s}");
}

#[test]
fn expand_trig_cos_sum() {
    let ctx = Context::new();
    let (x, y) = (ctx.symbol("x"), ctx.symbol("y"));
    let expr = (&x + &y).cos();
    let expanded = expr.expand_trig();
    let s = format!("{expanded}");
    assert!(s.contains("cos(x)"), "should contain cos(x): {s}");
    assert!(s.contains("sin(x)"), "should contain sin(x): {s}");
}

#[test]
fn expand_trig_bare_sin_unchanged() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = x.sin();
    let expanded = expr.expand_trig();
    assert_eq!(format!("{expanded}"), "sin(x)");
}

// ═══════════════════════════════════════════════════════════════════════════
// Polynomial GCD / LCM
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn poly_gcd_common_factor() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // gcd(x^2 - 1, x - 1) = x - 1 (up to sign/scalar)
    let a = &x.powi(2) - 1;
    let b = &x - 1;
    let g = a.poly_gcd(&b, &x).unwrap();
    let s = format!("{g}");
    assert!(s.contains("x"), "gcd should involve x: {s}");
}

#[test]
fn poly_gcd_coprime() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // gcd(x + 1, x + 2) = 1
    let a = &x + 1;
    let b = &x + 2;
    let g = a.poly_gcd(&b, &x).unwrap();
    assert_eq!(format!("{g}"), "1");
}

#[test]
fn poly_lcm_basic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let a = &x - 1;
    let b = &x + 1;
    let lcm = a.poly_lcm(&b, &x).unwrap();
    let s = format!("{lcm}");
    // lcm(x-1, x+1) should be x^2 - 1 (up to sign)
    assert!(s.contains("x^2"), "lcm should be degree 2: {s}");
}

// ═══════════════════════════════════════════════════════════════════════════
// Odd/even trig in eval
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn eval_sin_neg_x() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = (-&x).sin();
    let evaled = expr.eval();
    // sin(-x) should evaluate to -sin(x)
    assert_eq!(format!("{evaled}"), "-sin(x)");
}

#[test]
fn eval_cos_neg_x() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = (-&x).cos();
    let evaled = expr.eval();
    // cos(-x) should evaluate to cos(x)
    assert_eq!(format!("{evaled}"), "cos(x)");
}

#[test]
fn eval_tan_neg_x() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = (-&x).tan();
    let evaled = expr.eval();
    // tan(-x) should evaluate to -tan(x)
    assert_eq!(format!("{evaled}"), "-tan(x)");
}

// ═══════════════════════════════════════════════════════════════════════════
// Inverse hyperbolic functions
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn display_inverse_hyperbolic() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    assert_eq!(format!("{}", x.asinh()), "asinh(x)");
    assert_eq!(format!("{}", x.acosh()), "acosh(x)");
    assert_eq!(format!("{}", x.atanh()), "atanh(x)");
}

#[test]
fn eval_asinh_zero() {
    let ctx = Context::new();
    let result = ctx.int(0).asinh().eval();
    assert_eq!(format!("{result}"), "0");
}

#[test]
fn eval_acosh_one() {
    let ctx = Context::new();
    let result = ctx.int(1).acosh().eval();
    assert_eq!(format!("{result}"), "0");
}

#[test]
fn eval_atanh_zero() {
    let ctx = Context::new();
    let result = ctx.int(0).atanh().eval();
    assert_eq!(format!("{result}"), "0");
}

#[test]
fn diff_asinh() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let d = x.asinh().diff(&x);
    let s = format!("{d}");
    // d/dx(asinh(x)) = 1/sqrt(x^2+1)
    assert!(s.contains("sqrt"), "should contain sqrt: {s}");
}

#[test]
fn parse_inverse_hyperbolic() {
    let ctx = Context::new();
    let e = symplex::parse::parse(&ctx, "asinh(x) + acosh(x) + atanh(x)").unwrap();
    let s = format!("{e}");
    assert!(
        s.contains("asinh") && s.contains("acosh") && s.contains("atanh"),
        "got: {s}"
    );
}