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

From ApCoCoAWiki

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<title>BB.LiftND</title> | <title>BB.LiftND</title> | ||

− | <short_description> | + | <short_description>Compute the border basis scheme ideal generators obtained from lifting of ND neighbors.</short_description> |

<syntax> | <syntax> | ||

BB.LiftND(OO:LIST):LIST | BB.LiftND(OO:LIST):LIST |

## Revision as of 16:15, 21 April 2009

## BB.LiftND

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

### Syntax

BB.LiftND(OO:LIST):LIST

### Description

Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\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>.

#### Example

Use Q[x,y], DegRevLex; BB.LiftND([Poly(1), x, y, xy]); [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3], BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3], BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4], BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] -------------------------------