# ApCoCoA-1:BBF.Explanation of BBF variables and structures

## BBF.BBFOverview

Explanation of the variables and structures used in the Border Basis Framework.

### Description

To be able to use all the features of the Border Basis Framework you should be familiar with the notion of the Border Basis Algorithm as it is described in [1]. During a border basis computation you can query the ApCoCoABBFServer for information about certain variables and structures. The following list provides an overview of all available objects and explains their meaning.

*U*Order ideal; so called computing universe; named "L" in [1].*V*Set of polynomials with pairwise different leading terms; represents a linear basis.*W'*Set of polynomials with pairwise different leading terms; represents a linear basis extension of V.*O*Order ideal consisting of elements U \ { LT(v) : v in V }.

Please see [1] for additional information regarding the Border Basis Algorithm.

References: [1] A. Kehrein und M. Kreuzer, Computing border bases, J. Pure Appl. Alg. 205 (2006), S. 279 - 295

BBF.RetrieveVPolysWithTermInSupport