Trait alga::general::Module [−] [src]

pub trait Module: GroupAbelian<Additive> {
    type Ring: RingCommutative;
}

A module combines two sets: one with an additive abelian group structure and another with a commutative ring structure.

In addition, and external multiplicative law ∘ is defined. Let S be the ring with multiplicative operator noted × and multiplicative identity element noted 1. Then:

∀ a, b ∈ S
∀ x, y ∈ Self

a ∘ (x + y) = (a ∘ x) + (a ∘ y)
(a + b) ∘ x = (a ∘ x) + (b ∘ x)
(a × b) ∘ x = a ∘ (b ∘ x)
1 ∘ x       = x

Associated Types

The underlying scalar field.

Implementors