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

//! Integration tests for `Context::compact()` — generational arena GC.

use symplex::prelude::*;

#[test]
fn compact_reduces_node_count() {
    let ctx = Context::new();
    let x = ctx.symbol("x");

    // Create lots of intermediate expressions that we won't keep.
    let _ = x.powi(2).sin().exp().ln().abs();
    let _ = x.powi(3).cos().exp();
    let _ = (&x + 1).powi(10).expand();
    let big_count = ctx.node_count();

    // Keep only x.
    let (new_ctx, new_exprs) = ctx.compact(std::slice::from_ref(&x));
    let small_count = new_ctx.node_count();

    assert!(
        small_count < big_count,
        "compact should reduce node count: {} → {}",
        big_count,
        small_count,
    );
    assert_eq!(format!("{}", new_exprs[0]), "x");
}

#[test]
fn compact_preserves_expression_display() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x.powi(2) + &x.sin() + 1;
    let original_str = format!("{expr}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_preserves_assumptions() {
    let ctx = Context::new();
    let x = ctx.symbol_with("x", &[Assumption::Positive, Assumption::Real]);

    let (_new_ctx, new_exprs) = ctx.compact(std::slice::from_ref(&x));
    assert_eq!(new_exprs[0].is_positive(), Some(true));
    assert_eq!(new_exprs[0].is_real(), Some(true));
}

#[test]
fn compact_multiple_roots() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let y = ctx.symbol("y");
    let expr1 = &x + 1;
    let expr2 = y.sin();

    let orig1 = format!("{expr1}");
    let orig2 = format!("{expr2}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr1, expr2]);
    assert_eq!(new_exprs.len(), 2);
    assert_eq!(format!("{}", new_exprs[0]), orig1);
    assert_eq!(format!("{}", new_exprs[1]), orig2);
}

#[test]
fn compact_empty_roots() {
    let ctx = Context::new();
    let _ = ctx.symbol("x"); // create something to pollute the arena
    let (new_ctx, new_exprs) = ctx.compact(&[]);
    assert!(new_exprs.is_empty());
    // New context should have only pre-interned constants (0, 1, -1, pi, e, ...).
    assert!(new_ctx.node_count() > 0);
}

#[test]
fn compact_shared_subexpressions() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let shared = x.sin(); // sin(x) is shared between expr1 and expr2
    let expr1 = &shared + 1;
    let expr2 = shared.powi(2);

    let (new_ctx, _new_exprs) = ctx.compact(&[expr1, expr2]);
    // sin(x) should be shared in the new arena too, keeping the count small.
    assert!(new_ctx.node_count() <= ctx.node_count());
}

#[test]
fn compact_preserves_rational() {
    let ctx = Context::new();
    let half = ctx.rational(1, 2);
    let x = ctx.symbol("x");
    let expr = &x + &half;
    let original_str = format!("{expr}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_preserves_constants() {
    let ctx = Context::new();
    let pi = ctx.pi();
    let e = ctx.e();
    let expr = &pi + &e;
    let original_str = format!("{expr}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_duplicate_root() {
    // Passing the same expression twice should work — both entries in
    // the result should display identically.
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = x.sin();

    let (_new_ctx, new_exprs) = ctx.compact(&[expr.clone(), expr]);
    assert_eq!(new_exprs.len(), 2);
    assert_eq!(format!("{}", new_exprs[0]), format!("{}", new_exprs[1]));
}

#[test]
fn compact_deep_tree() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    // Build a moderately deep chain: sin(cos(sin(cos(... x ...))))
    let mut expr = x.clone();
    for i in 0..20 {
        expr = if i % 2 == 0 { expr.sin() } else { expr.cos() };
    }
    let original_str = format!("{expr}");

    let (new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
    // Only the chain nodes + x + pre-interned constants should survive.
    assert!(new_ctx.node_count() < ctx.node_count() || new_ctx.node_count() > 0);
}

#[test]
fn compact_neg_and_pow() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = (-&x).powi(3);
    let original_str = format!("{expr}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_old_context_still_works() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x + 1;
    let original_str = format!("{expr}");

    // Compact into a new context.
    let (_new_ctx, _new_exprs) = ctx.compact(std::slice::from_ref(&expr));

    // The original context and expressions should still be usable.
    assert_eq!(format!("{expr}"), original_str);
    let expr2 = &x + 2;
    assert_eq!(format!("{expr2}"), "x + 2");
}

#[test]
fn compact_infinity_and_special_values() {
    let ctx = Context::new();
    let inf = ctx.infinity();
    let x = ctx.symbol("x");
    let expr = &x + &inf;
    let original_str = format!("{expr}");

    let (_new_ctx, new_exprs) = ctx.compact(&[expr]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_piecewise() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    let cond = x.gt(&zero);
    let neg_x = -&x;
    let not_cond = cond.not();
    let pw = Ex::piecewise(&[(&x, &cond), (&neg_x, &not_cond)]);
    let original_str = format!("{pw}");

    let (_new_ctx, new_exprs) = ctx.compact(&[pw]);
    assert_eq!(format!("{}", new_exprs[0]), original_str);
}

#[test]
fn compact_result_can_be_further_operated_on() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let expr = &x + 1;

    let (new_ctx, new_exprs) = ctx.compact(&[expr]);

    // We should be able to do further math in the new context.
    let y = new_ctx.symbol("y");
    let combined = &new_exprs[0] + &y;
    let combined_str = format!("{combined}");
    assert!(combined_str.contains("x"));
    assert!(combined_str.contains("y"));
}

#[test]
fn compact_with_expand_result() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let big = (&x + 1).powi(5).expand();
    let big_str = format!("{big}");

    // The expansion creates many intermediates.
    let before = ctx.node_count();

    let (new_ctx, new_exprs) = ctx.compact(&[big]);
    let after = new_ctx.node_count();

    assert_eq!(format!("{}", new_exprs[0]), big_str);
    assert!(
        after <= before,
        "compacted arena ({after}) should not be larger than original ({before})",
    );
}