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

From ApCoCoAWiki

## BBF.BBFOverview

An overview of the Border Basis Framework.

### Syntax

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### Description

The naming convention for the structures used during a computation is as follows.

STRUCTURE 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 A. Kehrein und M. Kreuzer: Computing border bases 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

#### Example

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