# ApCoCoA-1:BB.LiftNDViaServer

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## BB.LiftNDViaServer

BBS generators from lifting of ND neighbors

### Syntax

```BB.LiftNDViaServer(OO:LIST,Border:LIST):LIST
```

### Description

Compute the equations defining the border basis scheme and coming from the lifting of next-door neighbors by using the ApCoCoAServer. The input is a list of terms OO representing an order ideal and a list of terms Border representing the border of the order ideal. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.

#### Example

```Use Q[x,y], DegRevLex;
BB.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y]);

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