Correct the A.4.33 versor identity test - #27
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Closes #14.
Appendix A.4.33 of arXiv:1205.5935 states
(A B ~A) ∧ (A C ~A) = (A ⊛ A) A (B ∧ C) ~A.For a versor
A,~Ais reversion andA ⊛ Ais the signed scalar product. The commented test used the Clifford conjugateAǂand the unsigned magnitudenorm()^2, so it did not encode the paper's identity.The new test uses small, concrete witnesses in
Cl2andℂ, the one-generator negative-signature algebra. Their values ofA ⊛ Aare+1and-1, respectively. Each case first checks that the left-hand side is nonzero, preventing a vacuous pass, and then checks the identity.PR #19 records the original expression as
@test_broken. This patch addresses the same gap by correcting the expression and adding passing, sign-sensitive coverage.Mutation checks performed during verification:
~AwithAǂfails both witnessesA ⊛ Awith the unsigned norm fails the negative-signature witnessVerification with Julia 1.10.11 and Python
galgebra==0.6.0:No dependency or version changes are included.