CoCoA:Saturation
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Saturation
saturation of ideals
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 <formula>J^d</formula>
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 -------------------------------
Syntax
Saturation(I:IDEAL,J:IDEAL):IDEAL
<type>groebner</type> <type>groebner-basic</type> <type>ideal</type> <type>cocoaserver</type>