API reference

project(multivector::T, n::Integer) -> T

Project a given multivector of type T so that only the component of grade n is kept.

The function will always return a multivector of the same type as that passed in. If n is such that multivector does not contain this grade (e.g. because n is odd, and the multivector is an even type), then we will return a zero multivector.

GA41

Code for GA(4,1). implementation is via 2x2 quaternion matrices.

GA20

Module representing the GA(2, 0) geometric algebra. Even and odd elements are stored as complex numbers.

GA24

Module representing the GA(2,4) geometric algebra.

This is the conformal algebra for spacetime. Even and odd elements are stored as complex Static Arrays.

GA30

Module representing the GA(3, 0) geometric algebra. Underlying rep is quaternions, but not used explicitly here to keep this code self-contained.

GA31

Code for GA(3,1). Even and odd elements are stored as complex structs. 2x2 matrix products are unwrapped.

GA33

Module for GA(3,3). Base representation is a pair of 4x4 static arrays.

GA40

Code for GA(4,0). Even and odd elements are stored as quaternion pairs.

GA44

Uses a list-based approach to multivector storage. Not as fast as smaller algebras, but useful for checks.

GA3232

Module representing the GA(32,32) geometric algebra.

Not optimised in any way, but useful for some experimentation. Use with caution. GA(32,32) is very BIG!

PGA

Code for GA(3,0,1). The Euclidean group algebra. C Core representation is a quaternion pair.

STA

Code for GA(1,3). Even and odd elements are stored as complex structs. 2x2 matrix products are unwrapped. Gamma and sigma used for pretty typing.

Quaternions

Quaternion code. This is called by some of the later GA implementations.

The core mirrors much of the GA code structure. For completeness we have defined a division operation for quaternions as they are a division algebra.