Intersection

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 ::= QQ[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"]
-------------------------------

See Also