If the input is a cellular binomial ideal then a very fast algorithm is used. If one knows this and also the cellular variables then cellularBinomialRadical should be used.
i1 : R = QQ[x,y]
o1 = R
o1 : PolynomialRing
i2 : I = ideal (y^2, x*y-y, x^2-1)
2 2
o2 = ideal (y , x*y - y, x - 1)
o2 : Ideal of R
i3 : binomialRadical I
2 2
o3 = ideal (y , x*y - y, x - 1, y)
o3 : Ideal of R