Introduction

Geometric algebra is a very powerful mathematical tool that allows us to work with spaces, lines, and many other geometrical constructs, with the same simplicity as we normally work with vectors.

The main elements are multivectors, which can be vectors, products of vectors, and sums of such elements. The main operation is the geometric product, which combines multivectors into new multivectors.

With this library you can create multivectors and perform many operations with them.

Example:

(require '[jordibc.geometric-algebra :as ga])

(ga/def-basis [1 3] 0) ; start with e0, the "space-time algebra"
;; Will print:
;; Defined basis multivectors: e0 e1 e2 e3 e01 e02 e03 e12 e13 e23 e012 e013 e023 e123 e0123

(ga/def-ops)
;; Will print some warnings for replacing +, -, *, /, and then:
;; Defined operators: + - * / · ∧ ∨ × ⌋ ⌊ ∘ •

(ga/infix (2 e1 + 3 e2) ∧ (4 e1 - 0.5 e2)) ; => -13.0 e12