ApCoCoA-1:BB.LiftND

BB.LiftND

BBS generators from lifting of ND neighbors

Syntax

BB.LiftND(OO:LIST):LIST

Description

Compute the equations defining the border basis scheme and coming 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>.

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]]
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BB.LiftAS

BB.LiftASViaServer

BB.LiftHomAS

BB.LiftNDViaServer

BB.LiftHomND