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IntersectionList

intersect lists, ideals, or modules

Syntax
IntersectionList(L:LIST of LIST):LIST
IntersectionList(L:LIST of IDEAL):IDEAL
IntersectionList(L:LIST of MODULE):MODULE

Description
The function IntersectionList applies the function Intersection to the elements of a list, i.e., IntersectionList([X_1,...,X_n]) is the same as Intersection(X_1,...,X_n) .

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 HIntersectionList .

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
/**/  IntersectionList([ Ideal(x-P[1]*z, y-P[2]*z)  |  P In Points]);
ideal(y^2 - y*z, x^2 - x*z)

/**/  Intersection(["a","b","c"],["b","c","d"]);
["b", "c"]

/**/  IntersectionList([Ideal(x,y), Ideal(y^2,z)]);
ideal(y*z, x*z, y^2)

/**/  It = intersect(ideal(x,y), ideal(y^2,z));
true

See Also