# ApCoCoA-1:BB.LiftND

## BB.LiftND

Compute the border basis scheme ideal generators obtained from lifting of ND neighbors.

### Syntax

`BB.LiftND(OO:LIST):LIST`

### Description

Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbors. The input is a list of terms OO (2nd element of type POLY). The output is a list of poly in the ring BBS=K[c_{ij}].

• @param OO A list of terms representing an order ideal.

• @return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of next-door neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

```Use QQ[x,y], DegRevLex;
BB.LiftND([Poly(1), x, y, xy]);

[BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3],
BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3],
BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3],
BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3],
BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4],
BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4],
BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4],
BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]]
-------------------------------
```