using Oscar

Oscar.example("BinomIdeal2.jl")

Qab = QabField()

R, x = PolynomialRing(Qab, :x => 1:6)

I = ideal([x[5]*(x[1]-x[2]),x[6]*(x[3]-x[4]),x[5]^2,x[6]^2,x[5]*x[6]])

iscellular(I)

Cellular.witness_monomials(I)

Cellular.minimal_associated_primes(I)

Cellular.associated_primes(I)

R, (x, y, z) = PolynomialRing(Qab, ["x", "y", "z"])

I = ideal([x-y,x^3-1,z*y^2-z])

iscellular(I)

bcd = Cellular.decomposition(I)

bcd[1] ∩ bcd[2] == I

Binomial.primary_decomposition(I)[1]