Trait Algebra 

pub trait Algebra
where
    Self: Copy + Clone + Eq + PartialEq + Ord + PartialOrd + Default + Into<Symbol> + TryFrom<Symbol, Error = Symbol> + Debug + Display + Mul<Output = (i8, Self)> + Not<Output = (i8, Self)>,
{
    const N: u32;

    // Required methods
    fn basis(    ) -> impl ExactSizeIterator<Item = Self> + DoubleEndedIterator<Item = Self>;
    fn scalar() -> Self;
    fn pseudoscalar() -> Self;
    fn grade(&self) -> u32;
    fn blade_len(&self) -> usize;

    // Provided method
    fn rev(self) -> (i8, Self) { ... }
}

A geometric algebra defined by a flavor’s basis (i.e., all its basis blades).

Implementations for this trait (e.g., pga::Pga) define the basis of a particular flavor from which the Cayley table can be constructed. The generators of a basis (i.e., the basis blades of Self::grade() == 1) define the whole algebra whereas the required Mul operator implements the signature-aware anti-commutative multiplication for the chosen storage.

Required Associated Constants

const N: u32

The embedded dimension.

Not to be confused with the embedding dimension, e.g., N + 1 is the embedding dimension for one-up flavors of embedded dimension N.

Required Methods

fn basis() -> impl ExactSizeIterator<Item = Self> + DoubleEndedIterator<Item = Self>

The ordered basis (i.e., all basis blades).

fn scalar() -> Self

The scalar.

fn pseudoscalar() -> Self

The pseudoscalar.

fn grade(&self) -> u32

The grade.

fn blade_len(&self) -> usize

The number $n$ of basis blades with the same grade $g$ of this basis blade.

n = { N + 1  \choose g }

Provided Methods

fn rev(self) -> (i8, Self)

The reverse.

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<const M: i8, const N: u32> Algebra for Pga<M, N>

const N: u32 = N