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

m (fixed links to namespace ApCoCoA) |
m (insert version info) |
||

Line 1: | Line 1: | ||

+ | {{Version|1}} | ||

<command> | <command> | ||

<title>BB.LiftNDViaServer</title> | <title>BB.LiftNDViaServer</title> |

## Latest revision as of 09:42, 7 October 2020

This article is about a function from ApCoCoA-1. |

## BB.LiftNDViaServer

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

### Syntax

BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

If `HomogeneousLift` is set to `FALSE`, the generators of the border basis scheme ideal `I(B_O)` that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. If `HomogeneousLift` is set to `TRUE`, generators of `I(B^hom_O)` will be computed instead.

@param

*OO*A list of terms representing an order ideal.@param

*Border*A list of terms representing the border of the order ideal.@param

*Homogeneous*Set to`TRUE`if you want to compute the generators of the homogeneous border basis scheme.@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.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); ------------------------------- [BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], 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[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4], 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[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] -------------------------------

#### Example

Use QQ[x,y,z], DegRevLex; BB.LiftNDViaServer([Poly(1), x, y, xy], [z, yz, xz, y^2, x^2, xyz, xy^2, x^2y], True); ------------------------------- [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]] -------------------------------