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Intersection, IntersectionList
Syntax
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
Summary
intersect lists, ideals, or modules
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 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
.
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"]
-------------------------------
IntersectionList([Ideal(x,y),Ideal(y^2,z)]);
Ideal(yz, xz, y^2)
-------------------------------
It = Intersection(Ideal(x,y),Ideal(y^2,z));
TRUE
-------------------------------
See Also