# CASA Function: computeRadical

Computes a radical of an algebraic set.

### Calling Sequence:

### Parameters:

- A : algset("impl")
- An algebraic set in implicit representation.

### Result:

- R : exprseq(algset("impl"))
- The intersection of radical ideals.

### Description:

- The function splits the ideal of an algebraic set in implicit representation into the intersection of radical ideals. The ideal of an algebraic set is the set of all polynomials vanishing on the algebraic set.
- First the ideal generated by the given basis and whose zeros form the given algebraic set is split at least into an intersection of unmixed-dimensional ideals. For each of the ideals a set of independent variables is computed along the splitting (that is why it is sometimes necessary to split unmixed-dimensional ideals, compare [27]). For each of the unmixed-dimensional ideals the radical is computed by reducing the problem to the zero-dimensional case.

### Examples:

`> ` **a1:=mkImplAlgSet([z*x^2+z*y^2-z,x^4+2*x^2*y^2-2*x^2+y^4-2*y^2+1],**

`> ` ** [x,y,z]);**

`> ` **[computeRadical(a1)];**

### See Also:

[CASA]
[mkImplAlgSet]
[toProj]