CoCoA:Saturation

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 <command>
   <title>Saturation</title>
   <short_description>saturation of ideals</short_description>
   <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. <par/> 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


</example>

   </description>
   <syntax>

Saturation(I:IDEAL,J:IDEAL):IDEAL </syntax>

   <see>Colon</see>
   <see>HColon</see>
   <see>HSaturation</see>
   <see>GBasis5, and more</see>
   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>cocoaserver</type>
   <key>saturation</key>
 </command>