ApCoCoA-1:BB.NDneighbors

This article is about a function from ApCoCoA-1.

BB.NDneighbors

Computes a list of next-door neighbors.

Syntax

BB.NDneighbors(OO:LIST):LIST

Description

This command computes the list of next-door 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 triples [i,j,k] such that b_i = x_k * 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(OO).

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

• @return A list of next-door neighbors of OO.

Example

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

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

-- E.g. the first triple of the result can be interpreted
-- as x*z = xz

BB.ASneighbors