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EP-0111: Clifford Geometric Algebra & Multivector Rotors

Field Value
EP 0111
Title Clifford Geometric Algebra & Multivector Rotors
Author Eran Rivlis & Antigravity
Status Final
Type Standards Track
Created 2026-08-01
Updated 2026-08-01

Abstract

This proposal specifies algebrax.clifford, building upon QuotientMonoidAlgebraSemiring (EP-0100). It implements Clifford / Geometric Algebra \(Cl(p, q, r)\) as a quotient algebra semiring, representing multivectors as sparse mappings {blade_tuple: coeff}, geometric products \(A B = A \cdot B + A \wedge B\), outer wedge products \(\wedge\), and rotor spatial rotations in \(3\text{D} / 4\text{D}\).

Deliverables

  1. Core Implementation: src/algebrax/clifford.py (CliffordSemiring, geometric_product, outer_product, rotor_rotation).
  2. Unit Tests: tests/algebrax/test_clifford.py (verifying blade multiplication, rotor rotations, and \(Cl(3,0)\) quaternion isomorphism).
  3. Use Case Recipe: recipes/clifford_rotor_kinematics.py & .ipynb.
  4. Graphical Laboratory View: View 22 (view_clifford_geometric_algebra_group) in recipes/lab.py.