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

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If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. The input is a list of terms <tt>OO</tt> representing an order ideal and a list of terms <tt>Border</tt> representing the border of the order ideal. If <tt>HomogeneousLift</tt> is set to <tt>True</tt>, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>. | If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. The input is a list of terms <tt>OO</tt> representing an order ideal and a list of terms <tt>Border</tt> representing the border of the order ideal. If <tt>HomogeneousLift</tt> is set to <tt>True</tt>, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials 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>@param <em>Border</em> A list of terms representing the border of OO</item> | ||

+ | <item>@param <em>Homogeneous</em> Set to <em>TRUE</em> if you want to compute the generators of the homogeneous border basis scheme.</item> | ||

+ | <item>@return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of next-door neighbors. The polynomials will belong to the ring BBS=K[c_{ij}].</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

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

## Revision as of 16:38, 22 April 2009

## BB.LiftNDViaServer

Compute the border basis scheme ideal generators obtained from lifting of ND 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 <formula>I(\mathbb{B}_\mathcal{O})</formula> that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. The input is a list of terms `OO` representing an order ideal and a list of terms `Border` representing the border of the order ideal. If `HomogeneousLift` is set to `True`, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.

@param

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

*Border*A list of terms representing the border of OO@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 I(B_O) that results from the lifting of next-door neighbors. The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

Use Q[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]] ------------------------------- Use Q[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]] -------------------------------