mathhook-core 0.2.0

Core mathematical engine for MathHook - expressions, algebra, and solving
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

//! Associativity property tests
//!
//! Validates that associative operations satisfy (a + b) + c = a + (b + c)
//! and (a * b) * c = a * (b * c).

use mathhook_core::{symbol, Expression, Simplify};

#[test]
fn test_integer_addition_associativity() {
    let test_cases = vec![(1, 2, 3), (0, 5, 10), (-3, 7, 2), (100, -50, 25)];

    for (a, b, c) in test_cases {
        let left = Expression::add(vec![
            Expression::add(vec![Expression::integer(a), Expression::integer(b)]),
            Expression::integer(c),
        ])
        .simplify();

        let right = Expression::add(vec![
            Expression::integer(a),
            Expression::add(vec![Expression::integer(b), Expression::integer(c)]),
        ])
        .simplify();

        assert_eq!(
            left, right,
            "Addition associativity failed: ({} + {}) + {} != {} + ({} + {})",
            a, b, c, a, b, c
        );
    }
}

#[test]
fn test_integer_multiplication_associativity() {
    let test_cases = vec![(2, 3, 4), (1, 5, 10), (-2, 3, 4), (2, -3, -4)];

    for (a, b, c) in test_cases {
        let left = Expression::mul(vec![
            Expression::mul(vec![Expression::integer(a), Expression::integer(b)]),
            Expression::integer(c),
        ])
        .simplify();

        let right = Expression::mul(vec![
            Expression::integer(a),
            Expression::mul(vec![Expression::integer(b), Expression::integer(c)]),
        ])
        .simplify();

        assert_eq!(
            left, right,
            "Multiplication associativity failed: ({} * {}) * {} != {} * ({} * {})",
            a, b, c, a, b, c
        );
    }
}

#[test]
fn test_symbolic_addition_associativity() {
    let x = symbol!(x);
    let y = symbol!(y);
    let z = symbol!(z);

    let left = Expression::add(vec![
        Expression::add(vec![
            Expression::symbol(x.clone()),
            Expression::symbol(y.clone()),
        ]),
        Expression::symbol(z.clone()),
    ])
    .simplify();

    let right = Expression::add(vec![
        Expression::symbol(x.clone()),
        Expression::add(vec![
            Expression::symbol(y.clone()),
            Expression::symbol(z.clone()),
        ]),
    ])
    .simplify();

    assert_eq!(
        left, right,
        "Symbolic addition associativity failed: (x + y) + z != x + (y + z)"
    );
}

#[test]
fn test_symbolic_multiplication_associativity() {
    let x = symbol!(x);
    let y = symbol!(y);
    let z = symbol!(z);

    let left = Expression::mul(vec![
        Expression::mul(vec![
            Expression::symbol(x.clone()),
            Expression::symbol(y.clone()),
        ]),
        Expression::symbol(z.clone()),
    ])
    .simplify();

    let right = Expression::mul(vec![
        Expression::symbol(x.clone()),
        Expression::mul(vec![
            Expression::symbol(y.clone()),
            Expression::symbol(z.clone()),
        ]),
    ])
    .simplify();

    assert_eq!(
        left, right,
        "Symbolic multiplication associativity failed: (x * y) * z != x * (y * z)"
    );
}

#[test]
fn test_mixed_associativity() {
    let x = symbol!(x);

    let left = Expression::add(vec![
        Expression::add(vec![Expression::symbol(x.clone()), Expression::integer(2)]),
        Expression::integer(3),
    ])
    .simplify();

    let right = Expression::add(vec![
        Expression::symbol(x.clone()),
        Expression::add(vec![Expression::integer(2), Expression::integer(3)]),
    ])
    .simplify();

    assert_eq!(
        left, right,
        "Mixed associativity failed: (x + 2) + 3 != x + (2 + 3)"
    );
}

#[test]
fn test_power_associativity_note() {
    // Note: Exponentiation is NOT associative: (2^3)^4 != 2^(3^4)
    // (2^3)^4 = 8^4 = 4096
    // 2^(3^4) = 2^81 = huge number
    // This test documents this mathematical fact

    let left = Expression::pow(
        Expression::pow(Expression::integer(2), Expression::integer(3)),
        Expression::integer(2),
    )
    .simplify();

    let right = Expression::pow(
        Expression::integer(2),
        Expression::pow(Expression::integer(3), Expression::integer(2)),
    )
    .simplify();

    // These should NOT be equal - documenting non-associativity
    assert_ne!(
        left, right,
        "Exponentiation should NOT be associative: (2^3)^2 should != 2^(3^2)"
    );
}