# Difference between revisions of "ApCoCoA-1:BB.NDgens"

## BB.NDgens

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

### Syntax

`BB.NDgens(K:INT,OO:LIST):LIST`

### Description

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

• @param K The generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.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 border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.NDneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

```Use QQ[x,y,z];
BB.NDgens(1, [1,x]);
[BBS :: c[1,5]c[2,1] - c[1,3], BBS :: c[2,1]c[2,5] + c[1,1] - c[2,3]]
-------------------------------
```