ApCoCoA-1:BB.LiftND

This article is about a function from ApCoCoA-1.

BB.LiftND

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

Syntax

BB.LiftND(OO:LIST):LIST

Description

This command computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door (ND) neighbours.

• @param OO A list of terms representing an order ideal. The second element is 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.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]]
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BB.LiftAS

BB.LiftASViaServer

BB.LiftHomAS

BB.LiftNDViaServer

BB.LiftHomND