# ApCoCoA-1:BB.LiftHomND

From ApCoCoAWiki

## BB.LiftHomND

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

### Syntax

BB.LiftHomND(OO:LIST):LIST

### Description

Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> 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 <formula>BBS=K[c_{ij}]</formula>.

@param

*OO*A list of terms representing an order ideal.@return A list of generators of the homogeneous 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,z], DegRevLex; BB.LiftHomND([Poly(1), x, y, xy]); [BBS :: c[3,1]c[4,4] + c[2,1] - c[4,2], BBS :: c[2,1]c[4,5] + c[3,1] - c[4,3]] -------------------------------