# ApCoCoA-1:BB.LiftHomND

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## BB.LiftHomND

Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.

### Syntax

BB.LiftHomND(OO:LIST):LIST

### Description

This command computes the generators of the border basis scheme ideal `I(B^hom_O)` that result from the lifting of next-door (ND) neighbors.

@param

*OO*A list of terms representing an order ideal. The second element is of type`POLY`.@return A list of generators of the homogeneous border basis scheme ideal. 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]] -------------------------------