# ApCoCoA-1:BB.LiftASViaServer

## BB.LiftASViaServer

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

### 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 computed 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. If `HomogeneousLift` is set to `True`, generators of I(B^hom_O) will be computed instead. The output is a list of polynomials in the ring BBS=K[c_{ij}].

@param

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

*Border*A list of terms representing the border of OO@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 I(B_O) that results from the lifting of across-the-street neighbors. 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]] -------------------------------