up previous next
Intersection

intersect lists, ideals, or modules
Syntax

Intersection(E_1:LIST,....,E_n:LIST):LIST
Intersection(E_1:IDEAL,...,E_n:IDEAL):IDEAL
Intersection(E_1:MODULE,....,E_n:MODULE):MODULE


Description
The function Intersection returns the intersection of E_1,...,E_n. In the case where the E_i's are lists, it returns the elements common to all of the lists.

The coefficient ring must be a field.

NOTE: In order to compute the intersection of inhomogeneous ideals, it may be faster to use the function HIntersection. To compute the intersection of ideals corresponding to zero-dimensional schemes, see the commands GBM and HGBM .

Example
Use R ::= Q[x,y,z];
Points := [[0,0],[1,0],[0,1],[1,1]]; -- a list of points in the plane
I := Ideal(x,y); -- the ideal for the first point
Foreach P In Points Do
  I := Intersection(I,Ideal(x-P[1]z,y-P[2]z));
EndForeach;
I;  -- the ideal for (the projective closure of) Points
Ideal(y^2 - yz, x^2 - xz)
-------------------------------
Intersection(["a","b","c"],["b","c","d"]);
["b", "c"]
-------------------------------
It = Intersection(Ideal(x,y),Ideal(y^2,z));
TRUE
-------------------------------


See Also