The cellular variables of a binomial ideal are the variables which are non-zerodivisors module that ideal. If this option is set to 'true' then binomialCellularDecomposition will return the set of variables for each of its outputs
i1 : R = QQ[x,y,z]
o1 = R
o1 : PolynomialRing
i2 : I = ideal (x*y-z, x*z-y^2)
2
o2 = ideal (x*y - z, - y + x*z)
o2 : Ideal of R
i3 : bcd = binomialCellularDecomposition (I,ReturnCellVars=>true)
2 2
o3 = {{ideal (y - x*z, x*y - z, x - y), {x, y, z}}, {ideal (z, y), {x}}}
o3 : List
Functions with optional argument named ReturnCellVars :
binomialCellularDecomposition(...,ReturnCellVars=>...) -- see binomialCellularDecomposition -- Binomial Cellular Decomposition