using Oscar, PBWDeformations

] status

L = general_linear_lie_algebra(QQ, 3)

V = direct_sum(standard_module(L), dual(standard_module(L)))

sp = smash_product(L, V)

sp isa NCRing

some_elem = gen(sp, 4)*gen(sp, 10) - gen(sp, 10)*gen(sp, 4) # just a formal commutator

simplify(some_elem)

symmetric_deformation(sp)

kappa = zero_matrix(underlying_algebra(sp), dim(base_module(sp)), dim(base_module(sp)))
deform(sp, kappa)

is_pbwdeformation(symmetric_deformation(sp))

kappa2 = zero_matrix(underlying_algebra(sp), dim(base_module(sp)), dim(base_module(sp)))
kappa2[1,2] = gen(underlying_algebra(sp), 4)
kappa2[2,1] = -kappa2[1,2]
deform2 = deform(sp, kappa)
is_pbwdeformation(deform2)

kappas = all_pbwdeformations(sp, 0:2)

for kappa in kappas
    d = deform(sp, kappa)
    println(is_pbwdeformation(d))
end

PBWDeformations.pbw_arc_diagrams(PBWDeformations.GL(), tensor_product(standard_module(L), dual(standard_module(L))), 2) |> collect

PBWDeformations.arcdiag_to_deformationmap(PBWDeformations.GL(), arc_diagram(Directed, "aB,AdDb"), sp, tensor_product(standard_module(L), dual(standard_module(L))))

all_pbwdeformations(sp, ArcDiagDeformBasis{QQFieldElem}(sp, 0:0))

all_pbwdeformations(sp, ArcDiagDeformBasis{QQFieldElem}(sp, 0:1))

all_pbwdeformations(sp, ArcDiagDeformBasis{QQFieldElem}(sp, 0:2))

all_pbwdeformations(sp, ArcDiagDeformBasis{QQFieldElem}(sp, 0:3))