cuequivariance: Groups, Irreps, and Segmented Polynomials

Overview

cuequivariance (imported as cue) provides two core abstractions:

1. Group theory: Irrep subclasses define irreducible representations of Lie groups (SO3, O3, SU2, or custom). Irreps manages collections with multiplicities.
2. Segmented polynomials: SegmentedTensorProduct describes tensor contractions over segments of varying shape, linked by Path objects carrying Clebsch-Gordan coefficients. SegmentedPolynomial wraps multiple STPs into a polynomial with named inputs/outputs. Two higher-level wrappers attach group representations:
   • EquivariantPolynomial — dense operands with IrrepsAndLayout metadata
   • IrDictPolynomial — operands already split by irrep, with per-group Irreps metadata for the dict[Irrep, Array] workflow

Defining a custom group

Subclass cue.Irrep (a frozen dataclass) and implement: