The Saturate command computes the saturation of an ideal J with respect to a polynomial f, denoted J:.  Saturation removes all the solutions of f from J, and is equivalent to a repeated application of Quotient. This functionality is also available through the Simplify command.

If the second argument is a list or set of polynomials, then the Saturate command removes the solutions of each polynomial, or equivalently their product.

If the optional third argument s is given, it is assigned a positive integer exponent with the property that J:f^infinity = J:f^s. This value is not guaranteed to be minimal.

Becker, T., and Weispfenning, V. Groebner Bases. New York: Springer-Verlag, 1993.