karpal_algebra/
vector_space.rs

1use crate::field::Field;
2use crate::module::Module;
3
4/// A `Module` over a `Field` — a vector space.
5pub trait VectorSpace<F: Field>: Module<F> {}
6
7impl VectorSpace<f32> for f32 {}
8impl VectorSpace<f64> for f64 {}
9
10impl<F: Field + crate::abelian::AbelianGroup> VectorSpace<F> for (F, F) {}
11
12#[cfg(test)]
13mod tests {
14    use super::*;
15    use crate::module::Module;
16    use crate::semiring::Semiring;
17    use karpal_core::Semigroup;
18
19    #[test]
20    fn f64_is_vector_space() {
21        fn use_vs<V: VectorSpace<f64>>(v: V, s: f64) -> V {
22            v.scale(s)
23        }
24        assert!((use_vs(3.0f64, 2.0) - 6.0).abs() < 1e-10);
25    }
26
27    #[test]
28    fn tuple_is_vector_space() {
29        fn add_scaled<V: VectorSpace<f64> + Semigroup>(a: V, b: V, s: f64) -> V {
30            a.combine(b.scale(s))
31        }
32        let result = add_scaled((1.0f64, 0.0), (0.0, 1.0f64), 2.0);
33        assert!((result.0 - 1.0).abs() < 1e-10);
34        assert!((result.1 - 2.0).abs() < 1e-10);
35    }
36
37    #[test]
38    fn tuple_linear_combination() {
39        let e1 = (1.0f64, 0.0);
40        let e2 = (0.0f64, 1.0);
41        let v = e1.scale(3.0).combine(e2.scale(4.0));
42        assert!((v.0 - 3.0).abs() < 1e-10);
43        assert!((v.1 - 4.0).abs() < 1e-10);
44    }
45
46    #[test]
47    fn scalar_field_is_one_dimensional() {
48        // Every field is a vector space over itself
49        let v: f64 = 5.0;
50        let scaled = v.scale(f64::one());
51        assert!((scaled - 5.0).abs() < 1e-10);
52    }
53}
karpal_algebra/vector_space.rs

karpal_algebra/
vector_space.rs
