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saturate

saturation of ideals

Syntax 
saturate(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 ::= QQ[x,y,z];
/**/  I := ideal(x-z, y-2*z);
/**/  J := ideal(x-2*z, 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
/**/  HilbertFn(R/L);
H(0) = 1
H(1) = 3
H(2) = 6
H(t) = 2   for t >= 3

/**/  saturate(L, ideal(x,y,z)) = K; -- saturating gets rid of the
                                     -- irrelevant component
true

See Also