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Saturation

saturation of ideals
Syntax

Saturation(I:IDEAL,J:IDEAL):IDEAL


Description
This function returns the saturation of I with respect to J: the ideal of polynomials F such that F*G is in I for all G in J^d for some positive integer d.

The coefficient ring must be a field.

Example
Use R ::= Q[x,y,z];
I := Ideal(x-z, y-2z);
J := Ideal(x-2z, y-z);
K := Intersection(I, J); -- ideal of two points in the
                         -- projective plane
L := Intersection(K, Ideal(x,y,z)^3); -- add an irrelevant component
Hilbert(R/L);
H(0) = 1
H(1) = 3
H(2) = 6
H(t) = 2   for t >= 3
-------------------------------
Saturation(L, Ideal(x,y,z)) = K; -- saturating gets rid of the
                                 -- irrelevant component
TRUE
-------------------------------


See Also