FreeAlgebra

FreeAlgebra supports the differentiable manipulation of freely-generated algebras. It is an offshoot project of the theoretical research on fermionic Gaussian computation and a nice implementation practice for the theory of finitely-generated algebras. Highlights:

• Inference of a finitely-generated algebras based on its commutation, adjoint, and tracial conditions.
  • Supports non-representable algebras e.g., Grassmann algebra with self-adjoint elements.
  • Calculations are not built in representations, making them particularly suited for sparse computations.
• Automatic inference of multiplication rules from commutators, and support for commuting and anti-commuting tensor products.
• Inference of new commutator relations from the base algebra and the specification of an automorphism.
• Fully differentiable using Pytorch.