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

//! symplex 0.2 base-layer fixes — canonical `Mul` construction.
//!
//! * `0 × (±∞ | zoo | nan)` is `nan` regardless of argument order.
//! * Products of numeric radicals never produce a `Mul` nested inside a
//!   `Mul` (which fires `canon_mul`'s canonical-form `debug_assert`).

use symplex::prelude::*;

fn s<T: std::fmt::Display>(e: &T) -> String {
    format!("{e}")
}

fn specials(ctx: &Context) -> Vec<(&'static str, Ex)> {
    vec![
        ("0", ctx.int(0)),
        ("oo", ctx.infinity()),
        ("-oo", ctx.neg_infinity()),
        ("zoo", ctx.complex_infinity()),
        ("nan", ctx.nan()),
    ]
}

#[test]
fn zero_times_infinity_is_nan_in_every_order() {
    let ctx = Context::new();
    let zero = ctx.int(0);
    for (name, v) in specials(&ctx) {
        if name == "0" {
            continue;
        }
        assert_eq!(s(&(&zero * &v)), "nan", "0 * {name}");
        assert_eq!(s(&(&v * &zero)), "nan", "{name} * 0");
    }
}

#[test]
fn products_of_specials_are_commutative() {
    let ctx = Context::new();
    let sp = specials(&ctx);
    for (na, a) in &sp {
        for (nb, b) in &sp {
            let ab = a * b;
            let ba = b * a;
            assert_eq!(ab, ba, "{na} * {nb} = {ab} but {nb} * {na} = {ba}");
        }
    }
}

#[test]
fn products_of_specials_expected_values() {
    let ctx = Context::new();
    let oo = ctx.infinity();
    let moo = ctx.neg_infinity();
    let zoo = ctx.complex_infinity();
    let nan = ctx.nan();
    assert_eq!(s(&(&oo * &oo)), "oo");
    assert_eq!(s(&(&oo * &moo)), "-oo");
    assert_eq!(s(&(&moo * &moo)), "oo");
    assert_eq!(s(&(&oo * &zoo)), "zoo");
    assert_eq!(s(&(&moo * &zoo)), "zoo");
    assert_eq!(s(&(&zoo * &zoo)), "zoo");
    for (name, v) in specials(&ctx) {
        assert_eq!(s(&(&nan * &v)), "nan", "nan * {name}");
        assert_eq!(s(&(&v * &nan)), "nan", "{name} * nan");
    }
}

#[test]
fn zero_times_infinity_with_symbolic_factors_between() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    for (name, v) in specials(&ctx) {
        if name == "0" {
            continue;
        }
        let a = &(&zero * &x) * &v;
        let b = &(&v * &x) * &zero;
        let c = &(&x * &v) * &zero;
        let d = &zero * &(&x * &v);
        assert_eq!(s(&a), "nan", "(0*x)*{name}");
        assert_eq!(s(&b), "nan", "({name}*x)*0");
        assert_eq!(s(&c), "nan", "(x*{name})*0");
        assert_eq!(s(&d), "nan", "0*(x*{name})");
    }
}

#[test]
fn zero_times_zoo_via_inverse_of_zero() {
    // The shape hit by `proptest_algebraic::mul_commutative`: `0 * 0^(-1)`.
    let ctx = Context::new();
    let zero = ctx.int(0);
    let inv0 = zero.powi(-1);
    assert_eq!(s(&inv0), "zoo");
    assert_eq!(s(&(&zero * &inv0)), s(&(&inv0 * &zero)));
    assert_eq!(s(&(&zero * &inv0)), "nan");
}

#[test]
fn zero_times_finite_is_zero_in_every_order() {
    let ctx = Context::new();
    let x = ctx.symbol("x");
    let zero = ctx.int(0);
    let finite = vec![
        x.clone(),
        x.sin(),
        &x + 1,
        ctx.pi(),
        ctx.rational(3, 7),
        x.powi(-1),
        (&x + 1).exp(),
    ];
    for f in finite {
        assert_eq!(s(&(&zero * &f)), "0", "0 * {f}");
        assert_eq!(s(&(&f * &zero)), "0", "{f} * 0");
    }
}

#[test]
fn zero_times_unknown_finiteness_is_symmetric() {
    // Function applications are never evaluated at construction time, so
    // `Γ(zoo)` has unknown finiteness and `0 · Γ(zoo)` folds to `0` —
    // the same in both orders.
    let ctx = Context::new();
    let zero = ctx.int(0);
    let g = ctx.complex_infinity().gamma();
    assert_eq!(&zero * &g, &g * &zero);
    let e = ctx.neg_infinity().exp();
    assert_eq!(&zero * &e, &e * &zero);
}