Trait Algebra 

pub trait Algebra<R: Ring>:
    Module<R>
    + Mul<Output = Self>
    + MulAssign
    + One
    + Distributive {
    // Provided method
    fn sqr(&self) -> Self { ... }
}

Represents a Unital Algebra over a Ring.

In abstract algebra, an algebra is a vector space—or, more generally, a module—equipped with a bilinear binary operation. This trait abstracts over this concept.

This trait defines a Unital Algebra because it requires the One trait, which provides a multiplicative identity (1).

Mathematical Definition

An algebra A over a commutative ring R is a module over R that is also a ring itself, where the ring multiplication is R-bilinear. This implementation is slightly more general, as R is only required to be a Ring, not necessarily commutative.

An algebra is unital if it has a multiplicative identity element.

Structure:

1. Self is a Module over a scalar Ring R. This provides vector addition and scalar multiplication.
2. Self has a binary operation * (multiplication) that is compatible with the module structure.
3. Self has a multiplicative identity 1 (from the One trait).

Note:

This trait does not require the algebra to be associative. For that, see the AssociativeAlgebra trait. An Algebra over a Ring R.

Mathematical Definition: A Vector Space (Module) equipped with a bilinear product.

Constraints:

1. It is a Module (AddGroup + Scaling).
2. It is Unital (Has One).
3. It is Distributive (a(b+c) = ab + ac).
4. It is NOT necessarily Associative (Octonions allowed).

Provided Methods

fn sqr(&self) -> Self

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<T, R> Algebra<R> for T

where T: Module<R> + Mul<Output = Self> + MulAssign + One + Distributive, R: Ring,