# ApCoCoA-1:BB.HomNDgens

## BB.HomNDgens

Compute the generators of the vanishing ideal of a homogeneous border basis scheme.

### Syntax

BB.HomNDgens(K:INT,OO:LIST):LIST

### Description

Computes the generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of NDneighbors(OO). The inputs are an integer K in the range 1..Len(NDneighbors(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.

@param

*K*The generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of the list returned by NDneighbors(OO) will be computed.@param

*OO*A list of terms representing an order ideal.@return A list of generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of the list returned by NDneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].