SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\OneCo-1606"];
<<VdVAlgebraAt1.m

(Subscript[t, 2])UU[(Subscript[c, 2]),(Subscript[u, 1])]

(Subscript[t, 2])UU[(Subscript[c, 2]),(Subscript[u, 1])]//m[1,2]

(BLBasis[4] // m[1,2]//m[1,3])-(BLBasis[4] // m[2,3]//m[1,2])

U[] /. a_.*x_U :> {a,x}

U[] /. a_.+x_U :> {a,x}

(LBasis[2] // Δ[2,2,3] // Δ[3,3,4])-(LBasis[2] // Δ[2,2,4] // Δ[2,2,3])

(LBasis[3] // m[2,3,2] // Δ[2,2,3])-(LBasis[3] // Δ[2,2,4]//Δ[3,3,5]//m[2,3,2]//m[4,5,3])

(Subscript[t, 1])U[]//S[1]

U[(Subscript[u, 2])]// S[1]

U[]**U[]

U[(Subscript[u, 1])]// S[1]

U[(Subscript[u, 1])]// S[1] // S[1]

Simp[(# // S[3] // S[2]) - (# // S[2]//S[3])]& /@ LBasis[3]

tt=U[(Subscript[u, 3]),(Subscript[w, 2])]

tt// m[2,3,2]

tt// m[2,3,2] // S[2]

tt//S[2]//S[3]

tt//S[2]//S[3]//m[3,2,2]

Simp[(# // m[2,3,2] // S[2]) - (# // S[2]//S[3]//m[3,2,2])]& /@ LBasis[3]

Simp[(# // S[2] // Δ[2,2,3]) - (# // Δ[2,3,2] // S[2]//S[3])]& /@ LBasis[2]

Simp[(# //Δ[2,2,3] // S[2] // m[2,3,2])]& /@ LBasis[2]

Simp[(# //Δ[2,2,3] // S[3] // m[2,3,2])]& /@ LBasis[2]

R[1,2,1]

R[1,2,1]//S[1]//S[2] // ToDegree[1]

With[{d=4}, (R[1,2,d]//S[1]//S[2] // ToDegree[d])-R[1,2,d]]

With[{d=4}, (R[1,2,d]//S[1])**R[1,2,d] // ToDegree[d]]

With[{d=4}, (R[1,2,d]//S[2])**R[1,2,d] // ToDegree[d]]

LBasis[2]//CoUnit[2]

Simp[(# //Δ[2,2,3] // S[3] // m[2,3,2])-#//CoUnit[2]]& /@ LBasis[2]

{R[1,2,5]//CoUnit[1],R[1,2,5]//CoUnit[2]}

With[{d=4}, ToDegree[d][(R[1,3,d]//Δ[1,1,2])-(R[1,3,d]**R[2,3,d])]]

With[{d=4}, ToDegree[d][(R[1,2,d]//Δ[2,2,3])-(R[1,3,d]**R[1,2,d])]]

With[{d=4}, ToDegree[d][R[1,2,d]**Δ[1,1,2][#]-Δ[1,2,1][#]**R[1,2,d]]& /@ LBasis[1]]

With[{d=3},
Dru=R[1,2,d]//S[2]//m[2,1,1];
{Dru, Dru//S[1]} // ToDegree[d]
]

ToDegree[3][{((Subscript[t, 1])^(-1))Dru, Dru//S[1]} /. ϵ->0] // Column

With[{d=3},
Dru=ToDegree[d][R[1,2,d]//S[2]//m[2,1,1]];
Drv2=ToDegree[d][(Dru//S[1])**Dru];
ToDegree[d][Drv2-Dru**(Dru//S[1])]
]

With[{d=3},
Dru=ToDegree[d][R[1,2,d]//S[2]//m[2,1,1]];
Drv2=ToDegree[d][(Dru//S[1])**Dru];
ToDegree[d][Drv2**#-#**Drv2]&  /@ LBasis[1]
]