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intersect

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 intersect 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 := intersect(I, ideal(x-P[1]*z,y-P[2]*z));
      EndForeach;
/**/  I;  -- the ideal for (the projective closure of) Points
ideal(y^2 -y*z, x^2 -x*z)

  Intersection(["a","b","c"], ["b","c","d"]);
["b", "c"]
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See Also