ApCoCoA-1:BB.BBscheme

BB.BBscheme

Compute the defining equations of a border basis scheme.

Syntax

BB.BBscheme(OO:LIST):IDEAL

Description

Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is an ideal in the ring <formula>BBS = K[c_{ij}]</formula>.

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

• @return A list of polynomials representing the defining equations of the border basis scheme. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[x,y,z];
BB.BBscheme([1,x]);
BBS :: Ideal(c[1,5]c[2,2] - c[1,4], c[1,2]c[1,5] - c[1,5]c[2,4] + c[1,4]c[2,5],
c[2,2]c[2,5] + c[1,2] - c[2,4], c[1,5]c[2,2] - c[1,4], c[1,5]c[2,1] - c[1,3],
c[1,1]c[1,5] - c[1,5]c[2,3] + c[1,3]c[2,5], c[2,1]c[2,5] + c[1,1] - c[2,3],
c[1,5]c[2,1] - c[1,3], c[1,4]c[2,1] - c[1,3]c[2,2],
c[1,2]c[1,3] - c[1,1]c[1,4] + c[1,4]c[2,3] - c[1,3]c[2,4],
c[1,2]c[2,1] - c[1,1]c[2,2] + c[2,2]c[2,3] - c[2,1]c[2,4], c[1,4]c[2,1] - c[1,3]c[2,2])
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BB.HomBBscheme