# Formalizing Geometric Algebra in Lean

@article{Wieser2022FormalizingGA, title={Formalizing Geometric Algebra in Lean}, author={Eric Wieser and Utensil Song}, journal={ArXiv}, year={2022}, volume={abs/2110.03551} }

This paper explores formalizing Geometric (or Clifford) algebras into the Lean 3 theorem prover, building upon the substantial body of work that is the Lean mathematics library, . As we use Lean source code to demonstrate many of our ideas, we include a brief introduction to the Lean language targeted at a reader with no prior experience with Lean or theorem provers in general. We formalize the multivectors as the quotient of the tensor algebra by a suitable relation, which provides the ring…

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