ApCoCoA-1:BB.LiftND
From ApCoCoAWiki
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>.
@param OO A list of terms representing an order ideal.
@return A list of generators of the 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], 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]] -------------------------------
