symplex 0.2.0

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

//! Integration tests for the stripper-collector sub-expression matching
//! optimisation in `apply_rules`.
//!
//! The stripper-collector algorithm replaces O(n²) pairwise enumeration
//! with O(k·n) scanning for k-term patterns inside n-term Add/Mul nodes.

use symplex::expr;
use symplex::prelude::*;

// ═══════════════════════════════════════════════════════════════════════════
// Pythagorean identity inside sums of increasing size
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn stripper_collector_pythagorean_plus_constant() {
    let ctx = Context::new();
    symplex::syms!(ctx; x);
    let expr = expr!(ctx, sin(x) ^ 2 + cos(x) ^ 2 + 5);
    let result = expr.simplify();
    assert_eq!(format!("{result}"), "6");
}

#[test]
fn stripper_collector_pythagorean_in_large_sum() {
    let ctx = Context::new();
    symplex::syms!(ctx; x, a, b, c);
    // a + b + sin²(x) + cos²(x) + c → a + b + c + 1
    let expr = &a + &b + &x.sin().powi(2) + &x.cos().powi(2) + &c;
    let result = expr.simplify();
    let s = format!("{result}");
    assert!(!s.contains("sin"), "should not contain sin: {s}");
    assert!(!s.contains("cos"), "should not contain cos: {s}");
}

#[test]
fn stripper_collector_5_term_add() {
    let ctx = Context::new();
    symplex::syms!(ctx; x);
    // 1 + 2 + sin²(x) + 3 + cos²(x) → 7
    let expr = expr!(ctx, 1 + 2 + sin(x) ^ 2 + 3 + cos(x) ^ 2);
    let result = expr.simplify();
    assert_eq!(format!("{result}"), "7");
}

#[test]
fn stripper_collector_6_term_two_symbols() {
    let ctx = Context::new();
    symplex::syms!(ctx; x, y, z);
    // y + z + sin²(x) + 10 + cos²(x) + y  →  2*y + z + 11
    let expr = &y + &z + &x.sin().powi(2) + 10 + &x.cos().powi(2) + &y;
    let result = expr.simplify();
    let s = format!("{result}");
    assert!(!s.contains("sin"), "sin should have been eliminated: {s}");
    assert!(!s.contains("cos"), "cos should have been eliminated: {s}");
    assert!(s.contains("11"), "constant part should be 11: {s}");
}

// ═══════════════════════════════════════════════════════════════════════════
// Hyperbolic Pythagorean in larger sums
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn stripper_collector_cosh_sinh_in_sum() {
    let ctx = Context::new();
    symplex::syms!(ctx; x);
    // cosh²(x) - sinh²(x) + 3 → 4
    let expr = expr!(ctx, cosh(x) ^ 2 - sinh(x) ^ 2 + 3);
    let result = expr.simplify();
    assert_eq!(format!("{result}"), "4");
}

// ═══════════════════════════════════════════════════════════════════════════
// Mul sub-expression matching (exp combine in larger product)
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn stripper_collector_exp_mul_in_product() {
    let ctx = Context::new();
    symplex::syms!(ctx; a, b, z);
    // z * exp(a) * exp(b) → z * exp(a + b)
    let expr = &z * &a.exp() * &b.exp();
    let result = expr.simplify();
    let s = format!("{result}");
    assert!(s.contains("exp("), "should still contain exp: {s}");
    assert!(s.contains("z"), "should still contain z: {s}");
    // There should be only one exp() call, not two
    let exp_count = s.matches("exp(").count();
    assert_eq!(
        exp_count, 1,
        "should have exactly one exp after combining: {s}"
    );
}

// ═══════════════════════════════════════════════════════════════════════════
// Regression: 2-term sums still work via normal matching
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn regression_exact_2_term_pythagorean() {
    let ctx = Context::new();
    symplex::syms!(ctx; x);
    // sin²(x) + cos²(x) → 1  (exact match, no sub-expression needed)
    let expr = expr!(ctx, sin(x) ^ 2 + cos(x) ^ 2);
    let result = expr.simplify();
    assert_eq!(format!("{result}"), "1");
}

#[test]
fn regression_3_term_add_pythagorean() {
    let ctx = Context::new();
    // The original sub-expression matching handled 3-term sums.
    // Verify it still works.
    symplex::syms!(ctx; x);
    let expr = expr!(ctx, sin(x) ^ 2 + cos(x) ^ 2 + 3);
    let result = expr.simplify();
    assert_eq!(format!("{result}"), "4");
}

// ═══════════════════════════════════════════════════════════════════════════
// Non-matching cases: ensure no false positives
// ═══════════════════════════════════════════════════════════════════════════

#[test]
fn no_false_match_different_args() {
    let ctx = Context::new();
    symplex::syms!(ctx; x, y);
    // sin²(x) + cos²(y) should NOT simplify via Pythagorean (different args)
    let expr = expr!(ctx, sin(x) ^ 2 + cos(y) ^ 2 + 3);
    let result = expr.simplify();
    let s = format!("{result}");
    assert!(s.contains("sin"), "sin should remain (different args): {s}");
    assert!(s.contains("cos"), "cos should remain (different args): {s}");
}

#[test]
fn no_false_match_sin_sin() {
    let ctx = Context::new();
    symplex::syms!(ctx; x);
    // sin²(x) + sin²(x) → 2*sin²(x), not 1
    let expr = expr!(ctx, sin(x) ^ 2 + sin(x) ^ 2);
    let result = expr.simplify();
    let s = format!("{result}");
    assert!(s.contains("sin"), "should still contain sin: {s}");
    assert_ne!(s, "1", "should not reduce to 1");
}