# CoCoA:IntersectionList

## IntersectionList

intersect lists, ideals, or modules

### 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 <ttref>GBM</ttref> and <ttref>HGBM</ttref>.

#### Example

```  Use R ::= Q[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 - yz, x^2 - xz)
-------------------------------
Intersection([<quotes>a</quotes>,<quotes>b</quotes>,<quotes>c</quotes>],[<quotes>b</quotes>,<quotes>c</quotes>,<quotes>d</quotes>]);
[<quotes>b</quotes>, <quotes>c</quotes>]
-------------------------------
IntersectionList([Ideal(x,y),Ideal(y^2,z)]);
Ideal(yz, xz, y^2)
-------------------------------
It = Intersection(Ideal(x,y),Ideal(y^2,z));
TRUE
-------------------------------
```

### Syntax

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

```   <type>groebner</type>
<type>groebner-basic</type>
<type>ideal</type>
<type>list</type>
<type>module</type>
```