バシク行列の解析 その２

ユーザーブログ:KurohaKafka/バシク行列の解析_by_Kuroha

(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(Λ_0)\\=Ψ^0_Ω(Ξ(2)^2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(1,1,1)(2,1,1)(3,1,1)(3.1)(2)	\(ψ_Ω(Λ_0^2)\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ξ(2)}(Ξ(2)^2)^2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)	\(ψ_Ω(χ_1(Λ_0+ω))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ψ^0_{Ξ(2)}(Ψ^0_{Ξ(2)}(Ξ(2)^2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(0)+ψ_{χ_0(Λ_0+1)}(ψ_{χ_{Λ_0}(0)}(0)))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))\cdot2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(0)^2)\\ =Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))^2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(1))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(5,3)(6,3)(7,3)(6,3)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(1)+ψ_{Ω_{ψ_{χ_{Λ_0}(0)}(0)+1}}(Ω_{ψ_{χ_{Λ_0}(0)}(0)+1}))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))+1}))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(5,3,1)(6,3,1)(7,3,1)(7,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(1)+ψ_{Ω_{ψ_{χ_{Λ_0}(0)}(0)+1}}(ψ_{χ_{Λ_0}(0)}(1)))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ω))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(Λ_0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ψ_{χ_{Λ_0}(0)}(0)))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ψ_{χ_{Λ_0}(0)}(0))+ψ_{χ_{Λ_0}(0)}(0)^2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(6,3,1)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ψ_{χ_{Λ_0}(0)}(0))+ψ_{Ω_{ψ_{χ_{Λ_0}(0)}(0)+1}}(ψ_{χ_{Λ_0}(0)}(ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(6,3,1)(7,3)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(χ_0(ψ_{χ_{Λ_0}(0)}(0)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,1)(6,3,1)(7,3)(5,3,1)(6,3,1)(7,3,1)(7,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ψ_{χ_{Λ_0}(0)}(1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)	\(ψ_Ω(ψ_{χ_{Λ_0}(0)}(ψ_{χ_{Λ_0}(0)}(ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(4)	\(ψ_Ω(χ_{Λ_0}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)\\+Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1)	\(ψ_Ω(χ_{Λ_0}(ω))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(4)	\(ψ_Ω(ψ_{χ_{Λ_0+1}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)+Ξ(2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1)(5,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0\cdot2}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}\\(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)\cdot2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)	\(ψ_Ω(ψ_{χ_M(0)}(1))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)^2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)(3,2,1)	\(ψ_Ω(ψ_{χ_M(0)}(1)+χ_0(Λ_0+ω))\\=Ψ^0_Ω(Ξ(2)^2+Ω_{Ψ^0_{Ξ(2)}(Ξ(2)^2)+ω})\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)	\(ψ_Ω(ψ_{χ_M(0)}(1)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+1))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(4,2)(5,3,1)(6,3,1)(7,3,1)(7,2)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)	\(ψ_Ω(ψ_{χ_{ψ_{χ_M(0)}(1)}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+1)+1}}\\(Ξ(2)\cdotΨ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)	\(ψ_Ω(ψ_{χ_M(0)}(ω))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+ω))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(2)	\(ψ_Ω(χ_M(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^1_{Ξ(2)}(Ξ(2)^2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(2,1,1)	\(ψ_Ω(χ_M(0)\cdotω)\\=Ψ^0_Ω(Ξ(2)^2+Ψ^1_{Ξ(2)}(Ξ(2)^2)\cdotω)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)	\(ψ_Ω(χ_0(χ_M(0)+ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+ω}))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)	\(ψ_Ω(χ_1(χ_M(0)+ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ψ^0_{Ξ(2)}(Ψ^1_{Ξ(2)}(Ξ(2)^2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(5)	\(ψ_Ω(ψ_{χ_2(χ_M(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{Λ_0}(χ_M(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ξ(2)}(Ξ(2)^2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3,1)(8,2)(3,2,1)(4,2,1)(5,2,1)(5,2)(4)	\(ψ_Ω(ψ_{χ_{ψ_{χ_M(0)}(1)}(χ_M(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)	\(ψ_Ω(ψ_{χ_{ψ_{χ_M(0)}(ω)}(χ_M(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)	\(ψ_Ω(ψ_{χ_{ψ_{χ_M(0)}(χ_1(χ_M(0)+ω))}(χ_M(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ψ^0_{Ξ(2)}(Ψ^1_{Ξ(2)}(Ξ(2)^2)+ω)))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)+ψ_{χ_M(0)}(ψ_{χ_{χ_M(0)}(0)}(0)))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2,1,1)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)\cdotω)\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))\cdotω)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)\cdotψ_{χ_M(0)}(ψ_{χ_{χ_M(0)}(0)}(0)))\\=Ψ^0_Ω(Ξ(2)^2+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\\\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)))\cdotΨ^0_{Ψ^1_{Ξ(2)}(Ξ(2)^2)}(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)\cdotχ_M(0))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)\cdotψ_{χ_0(χ_M(0)+1)}(ψ_{χ_{χ_M(0)}(0)}(0)))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))^2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(4,2,1)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)+χ_0(χ_M(0)+ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+ω}))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2)))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2)(6,3,1)(7,3,1)(8,3,1)(8,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(1))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2)))}\\(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(0)}(ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2)))}\\(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2)(5)	\(ψ_Ω(χ_{χ_M(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^1_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2)))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2)))+1}}\\(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,1)(7,3,1)(8,3,1)(9,3,1)(9,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(1)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdot(Ψ^0_{Ξ(2)}(Ξ(2)^2)+1))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,1)(8,3,1)	\(ψ_Ω(ψ_{χ_{χ_M(0)}(1)}(ω))\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+1)}\\(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2))+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,1)(8,3,1)(9,3)(8)	\(ψ_Ω(χ_{χ_M(0)}(1))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^1_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2))\\+Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+1))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)	\(ψ_Ω(χ_{χ_M(0)}(ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdot(Ψ^1_{Ξ(2)}(Ξ(2)^2))+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)	\(ψ_Ω(χ_{χ_M(0)}(ω^2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(5)	\(ψ_Ω(ψ_{χ_{χ_M(0)+1}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(5,2)(6,3,1)(7,3,1)(8,3,1)(8,1)(7,3,1)(8,3,1)(7,3,1)(8,3)(7)	\(ψ_Ω(ψ_{χ_{χ_M(0)+1}(0)}(1))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2))}\\(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(5,2,1)(6,2)(5)	\(ψ_Ω(χ_{χ_M(0)+1}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)\\+Ψ^1_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2))))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,1)(8,3,1)(9,3,1)(8,3,1)(9,3)(8)	\(ψ_Ω(ψ_{χ_{χ_M(0)+1}(1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(5,2,1)(6,2,1)	\(ψ_Ω(χ_{χ_M(0)+1}(ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)+Ξ(2)+ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,1)(5,2,1)(6,2,1)(6,1)(2)	\(ψ_Ω(ψ_{χ_{χ_M(0)\cdot2}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)\cdot2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)	\(ψ_Ω(ψ_{χ_{χ_0(χ_M(0)+1)}(0)}(0))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(5)	\(ψ_Ω(ψ_{χ_M(1)}(0))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ω_{Ψ^1_{Ξ(2)}(Ξ(2)^2)+1}}(Ξ(2)^2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(5)(4,2,1)(5,2,1)(6,1)(2)	\(Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ξ(2)}(Ξ(2)\cdotΨ^1_{Ξ(2)}(Ξ(2)^2)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(5)(4,2,1)(5,2,1)(6,2)(5)	\(ψ_Ω(ψ_{χ_M(1)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ξ(2)}(Ξ(2)^2+1))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(9,3)(8)(7,3,1)(8,3,1)(9,3,1)(8)	\(ψ_Ω(ψ_{χ_M(2)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ξ(2)}(Ξ(2)^2+2))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1,1)	\(ψ_Ω(χ_M(ω))\\=Ψ^0_Ω(Ξ(2)^2\\+Ψ^0_{Ξ(2)}(Ξ(2)^2+ω))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)	\(ψ_Ω(χ_{M+1}(ω))\\=Ψ^0_Ω(Ξ(2)^2+Ξ(2)\\+Ψ^0_{Ξ(2)}(Ξ(2)^2+Ξ(2)+ω))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2,1,1)(3,1,1)(3,1)(2)	\(ψ_Ω(ψ_{χ_{M\cdot2}(0)}(0))\\=Ψ^0_Ω(Ξ(2)^2\cdot2)\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2)	\(ψ_Ω(ψ_{χ_{φ_1(M+1)}(0)}(0))\\=Ψ^0_Ω(φ_1(Ξ(2)+1))\\=\text{PTO(KPM)}\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5)	\(Ψ^0_Ω(Ψ^0_{Ξ(3)}(4)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5,2)(6,3,1)(7,3,1)(8,3)(7)	\(Ψ^0_Ω(Ψ^0_{Ψ^1_{Ξ(3)}(4)}(5)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3)(8)	\(Ψ^0_Ω(Ψ^0_{Ψ^1_{Ψ^2_{Ξ(3)}(4)}(5)}(6)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3)(8,3,1)	\(Ψ^0_Ω(Ψ^0_{Ψ^1_{Ψ^2_{Ξ(3)}(4)}(5)}(ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3)(8,3,1)(9,3)(8)	\(Ψ^0_Ω(Ψ^1_{Ψ^2_{Ξ(3)}(4)}(5)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)	\(Ψ^0_Ω(Ψ^0_{Ψ^2_{Ξ(3)}(4)}(ω)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(5)	\(Ψ^0_Ω(Ψ^2_{Ξ(3)}(4)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(7,3)	\(Ψ^0_Ω(φ_1(Ψ^2_{Ξ(3)}(4)+1)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(6,2)(7,3,1)(8,3,1)(9,3)(8)	\(Ψ^0_Ω(Ψ^0_{Ξ(3)}(5)))\)
(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)	\(Ψ^0_Ω(Ψ^0_{Ξ(3)}(ω))\)