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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | import OAI.Combinatorics.PolynomialVacuum.Algebra.PairImage
namespace OAI
namespace PolynomialVacuumAlgebra
abbrev BitTensorFamily := Bool → Bool → Bool → Spin → Spin → Spin → ℂ
noncomputable def bitSwap : Matrix Pair Pair ℂ := Pone-zeta • Ptwo
def BitTensorEquations (W : BitTensorFamily) : Prop :=
(∀ i j k a b c, ¬(allowedSpin i a ∧ allowedSpin j b ∧ allowedSpin k c) → W i j k a b c=0) ∧
(∀ i k c, Pone.mulVec (fun ab => W i i k ab.1 ab.2 c)=fun ab => W i i k ab.1 ab.2 c) ∧
(∀ i k a, Pone.mulVec (fun bc => W i k k a bc.1 bc.2)=fun bc => W i k k a bc.1 bc.2) ∧
(∀ i j k c, ∑ ab : Pair, cup ab*W i j k ab.1 ab.2 c=0) ∧
(∀ i j k a, ∑ bc : Pair, cup bc*W i j k a bc.1 bc.2=0) ∧
(∀ i a, bitSwap.mulVec (fun bc => W i false true a bc.1 bc.2)=fun bc => W i true false a bc.1 bc.2)
end PolynomialVacuumAlgebra
end OAI
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