If cellularBinomialIsPrimary does not return true it can either return 'false' or two associated primes. If this option is set then two associated primes are returned. If ReturnPChars is set too, then partial characters will be returned.
i1 : R = QQ[x,y,z]
o1 = R
o1 : PolynomialRing
i2 : I = ideal (x^2-1)
2
o2 = ideal(x - 1)
o2 : Ideal of R
i3 : cellularBinomialIsPrimary (I,ReturnPrimes=>true)
The radical is not prime, as the character is not saturated
o3 = {ideal (x - 1, x - 1), ideal(x + 1)}
o3 : List