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
165
166
167
168

//! Logarithmic Function Simplification Strategies
//!
//! Implements algebraic rewrite rules for logarithmic functions (log, ln).

use super::strategy::SimplificationStrategy;
use crate::core::commutativity::Commutativity;
use crate::core::{Expression, Number};

/// Logarithm (base 10) simplification strategy
pub struct LogarithmSimplificationStrategy;

impl SimplificationStrategy for LogarithmSimplificationStrategy {
    fn simplify(&self, args: &[Expression]) -> Expression {
        if args.len() == 1 {
            match &args[0] {
                Expression::Number(Number::Integer(n)) if *n == 1 => Expression::integer(0),

                Expression::Number(Number::Integer(n)) if *n == 10 => Expression::integer(1),

                Expression::Pow(base, exp) => Expression::mul(vec![
                    exp.as_ref().clone(),
                    Expression::function("log", vec![base.as_ref().clone()]),
                ]),

                Expression::Mul(factors) => {
                    let commutativity =
                        Commutativity::combine(factors.iter().map(|f| f.commutativity()));

                    if commutativity.can_sort() {
                        let log_terms: Vec<Expression> = factors
                            .iter()
                            .map(|f| Expression::function("log", vec![f.clone()]))
                            .collect();
                        Expression::add(log_terms)
                    } else {
                        Expression::function("log", args.to_vec())
                    }
                }

                _ => Expression::function("log", args.to_vec()),
            }
        } else if args.len() == 2 {
            let x = &args[0];
            let base = &args[1];

            if x == base {
                Expression::integer(1)
            } else if x.is_one() {
                Expression::integer(0)
            } else {
                Expression::function("log", args.to_vec())
            }
        } else {
            Expression::function("log", args.to_vec())
        }
    }

    fn applies_to(&self, args: &[Expression]) -> bool {
        !args.is_empty() && args.len() <= 2
    }

    fn name(&self) -> &str {
        "LogarithmSimplificationStrategy"
    }
}

/// Natural logarithm (ln) simplification strategy
pub struct NaturalLogSimplificationStrategy;

impl SimplificationStrategy for NaturalLogSimplificationStrategy {
    fn simplify(&self, args: &[Expression]) -> Expression {
        if args.len() == 1 {
            match &args[0] {
                Expression::Number(Number::Integer(n)) if *n == 1 => Expression::integer(0),

                Expression::Function {
                    name,
                    args: inner_args,
                } if name.as_ref() == "exp" && inner_args.len() == 1 => inner_args[0].clone(),

                Expression::Pow(base, exp) => Expression::mul(vec![
                    exp.as_ref().clone(),
                    Expression::function("ln", vec![base.as_ref().clone()]),
                ]),

                _ => Expression::function("ln", args.to_vec()),
            }
        } else {
            Expression::function("ln", args.to_vec())
        }
    }

    fn applies_to(&self, args: &[Expression]) -> bool {
        args.len() == 1
    }

    fn name(&self) -> &str {
        "NaturalLogSimplificationStrategy"
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{expr, symbol};

    #[test]
    fn test_log_of_one() {
        let strategy = LogarithmSimplificationStrategy;
        let result = strategy.simplify(&[expr!(1)]);
        assert_eq!(result, expr!(0));
    }

    #[test]
    fn test_log_of_ten() {
        let strategy = LogarithmSimplificationStrategy;
        let result = strategy.simplify(&[expr!(10)]);
        assert_eq!(result, expr!(1));
    }

    #[test]
    fn test_log_power_rule() {
        let strategy = LogarithmSimplificationStrategy;
        let result = strategy.simplify(&[expr!(x ^ 2)]);

        if let Expression::Mul(terms) = result {
            assert_eq!(terms.len(), 2);
        } else {
            panic!("Expected multiplication");
        }
    }

    #[test]
    fn test_log_with_base() {
        let strategy = LogarithmSimplificationStrategy;
        let x = symbol!(x);
        let result = strategy.simplify(&[x.clone().into(), x.into()]);
        assert_eq!(result, expr!(1));
    }

    #[test]
    fn test_ln_of_one() {
        let strategy = NaturalLogSimplificationStrategy;
        let result = strategy.simplify(&[expr!(1)]);
        assert_eq!(result, expr!(0));
    }

    #[test]
    fn test_ln_of_exp() {
        let strategy = NaturalLogSimplificationStrategy;
        let x = symbol!(x);
        let exp_x = Expression::function("exp", vec![x.clone().into()]);
        let result = strategy.simplify(&[exp_x]);
        assert_eq!(result, x.into());
    }

    #[test]
    fn test_ln_power_rule() {
        let strategy = NaturalLogSimplificationStrategy;
        let result = strategy.simplify(&[expr!(x ^ 3)]);

        if let Expression::Mul(terms) = result {
            assert_eq!(terms.len(), 2);
        } else {
            panic!("Expected multiplication");
        }
    }
}