# ApCoCoA-1:BB.LiftASViaServer

## BB.LiftASViaServer

Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.

### Syntax

```BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

If HomogeneousLift is set to FALSE, the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street neighbors will be computed by using the ApCoCoAServer. If HomogeneousLift is set to TRUE, generators of I(B^hom_O) will be computed instead.

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

• @param Border A list of terms representing the border of order ideal.

• @param Homogeneous Set to TRUE if you want to compute the generators of the homogeneous border basis scheme.

• @return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

```Use QQ[x,y], DegRevLex;
BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False);

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