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

From ApCoCoAWiki

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</syntax> | </syntax> | ||

<description> | <description> | ||

− | + | This command computes the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of across-the-street neighbours. | |

<itemize> | <itemize> | ||

− | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | + | <item>@param <em>OO</em> A list of terms representing an order ideal with second element of type <tt>POLY</tt>.</item> |

− | <item>@return A list of generators of the border basis scheme ideal | + | <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].</item> |

</itemize> | </itemize> | ||

<example> | <example> |

## Revision as of 15:33, 8 July 2009

## BB.LiftAS

Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.

### Syntax

BB.LiftAS(OO:LIST):LIST

### Description

This command computes the generators of the border basis scheme ideal `I(B_O)` that result from the lifting of across-the-street neighbours.

@param

*OO*A list of terms representing an order ideal with second element of type`POLY`.@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

Use QQ[x,y], DegRevLex; BB.LiftAS([Poly(1), x, y, xy]); [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], 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[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]] -------------------------------