ApCoCoA-1:BB.ASneighbors

BB.ASneighbors

Computes a list of across-the-street neighbors.

Syntax

BB.ASneighbors(OO:LIST):LIST

Description

This command computes the list of across-the-street neighbors in the border of the order ideal OO. The input is a list OO of terms that specify an order ideal. The output is a list of quadruples [i,j,k,l] such that x_k * b_i = x_l * b_j where the border terms b_i and b_j correspond to the i-th and j-th element of the list returned by the command BB.Border.

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

• @return A list of across-the-street neighbors of OO.

Example

Use QQ[x,y,z];
BB.Border([1,x]);
BB.ASneighbors([1,x]);

[z, y, xz, xy, x^2]
-------------------------------
[[1, 2, 2, 3], [3, 4, 2, 3], [3, 5, 1, 3], [4, 5, 1, 2]]

-- E.g. the first quadruple of the result can be interpreted
-- as that y*z = z*y

BB.NDneighbors