Tutorials

The first three tutorials introduce Clifford coefficient tensors, layouts, ordinary tensor composition, and reusable operations with autograd. Each page is self-contained; run its Python blocks in order. Python and PyTorch are assumed.

1. First Clifford Product introduces the signature, coefficient lanes, and the scalar and exterior parts of a vector product.
2. Layouts, Storage, and Tensor Composition separates coefficient meaning from physical storage and leading tensor dimensions.

3. Planned Differentiation fixes an operation's contracts and reuses it with changing values and gradients. Three optional application studies use those same contracts and tensor operations for geometric transformations:

4. Bivector Exponentials and Induced Actions compares a materialized rotor with its action on vectors.

5. Fit a Rotation with PyTorch fits a rotation from point correspondences with an ordinary PyTorch parameter.
6. Differentiate a Spatial Deformation composes a coordinate-dependent action with PyTorch to fit a twisted surface from sparse observations.

Explanations develop the mathematical and numerical semantics. The API Reference describes the public API.