The online tools below allow you to generate code, explore Cayley tables and visualizations for arbitrary geometric algebras.

Click below to download the reference source code for the algebra you selected.
** These implementations are generated to be simple and small, ignoring computational and storage efficiency. Checkout /lib for efficient and mature libraries.

Cayley Table

Instruction counts

Expression Evaluator

e1, 2e3, e13Multivectors a ^ bOuter Product
a * bGeometric Product a & bRegressive Product
a | bInner Product a << bLeft Contraction
a >>> bSandwich Product !aDual
a.Grade(b)Grade Selection ~aReverse
a.NormalizedNormalisation E**(a)Exponentiation

result ..