# CASA Function: implIntersect

Computes the intersection of algebraic sets.

### Calling Sequence:

### Parameters:

- As : exprseq(algset("impl"))
- algebraic sets in implicit representation

### Result:

- I : algset("impl")
- the intersection of the given sequence of algebraic sets.

### Description:

- The function computes the intersection of algebraic sets in implicit form by computing the union of the corresponding ideals. These ideals are given by a finite basis. A basis of the union is obtained by putting all basis elements into one new basis.

### Examples:

`> ` **a1 := mkImplAlgSet([x^3+x^2*y-x,z],[x,y,z]);**

`> ` **a2 := mkImplAlgSet([x,y^2+z^2-1],[x,y,z]);**

`> ` **a3 := implIntersect(a1,a2);**

`> ` **tsolve(a3);**

### See Also:

[CASA]
[implUnion]
[implUnionLCM]
[implSubSet]
[implEqual]
[implEmpty]
[implIdealQuo]