Intersection(E_1:IDEAL,...,E_n:IDEAL):IDEAL
Intersection(E_1:LIST,....,E_n:LIST):LIST
Intersection(E_1:MODULE,....,E_n:MODULE):MODULE
IntersectionList(L:LIST):OBJECT
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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 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 'HIntersection'. To compute the
intersection of ideals corresponding to zero-dimensional schemes, see
the commands 'GBM' and 'HGBM'.
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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)
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Intersection(['a','b','c'],['b','c','d']);
["b", "c"]
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IntersectionList([Ideal(x,y),Ideal(y^2,z)]);
Ideal(yz, xz, y^2)
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It = Intersection(Ideal(x,y),Ideal(y^2,z));
TRUE
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