# Difference between revisions of "ApCoCoA-1:BB.LiftHomND"

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<description> | <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>. | 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>. | ||

+ | <itemize> | ||

+ | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||

+ | <item>@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}].</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

Use Q[x,y,z], DegRevLex; | Use Q[x,y,z], DegRevLex; |

## Revision as of 16:34, 22 April 2009

## 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 Q[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]] -------------------------------