saturate an ideal
Saturate(J, f, s)
polynomial, or list or set of polynomials
The Saturate command computes the saturation of an ideal J with respect to a polynomial f, denoted J:f∞. 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.
J ≔ x2,y−12⁢y+1
K ≔ x3⁢y2+x⁢y2,x3⁢y+x3⁢y3
q1 ≔ Quotient⁡K,x
q2 ≔ Quotient⁡q1,x
q3 ≔ Quotient⁡q2,x
Becker, T., and Weispfenning, V. Groebner Bases. New York: Springer-Verlag, 1993.
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