Difference between revisions of "ApCoCoA-1:BBF.Explanation of BBF variables and structures"

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   <title>BBF.BBFOverview</title>
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   <title>BBF.Explanation of BBF variables and structures</title>
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   <short_description>An overview of the Border Basis Framework.</short_description>
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   <short_description>Explanation of the variables and structures used in the Border Basis Framework.</short_description>
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  <syntax>...</syntax>
 
 
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   <description>
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The naming convention for the structures used during a computation is as follows.
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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.
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   STRUCTURE    MEANING
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   <item><em>U</em> Order ideal; so called computing universe; named "L" in [1].</item>
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  --------------------------------------------------------------------------
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  <item><em>V</em> Set of polynomials with pairwise different leading terms; represents a linear basis.</item>
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    U           Order ideal; so called computing universe; named "L" in [1].
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  <item><em>W'</em> Set of polynomials with pairwise different leading terms; represents a linear basis extension of V.</item>
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    V           Set of polynomials with pairwise different leading terms;
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  <item><em>O</em> Order ideal consisting of elements U \ { LT(v) : v in V }.</item>
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                represents a linear basis.
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    W'         Set of polynomials with pairwise different leading terms;
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Please see [1] for additional information regarding the Border Basis Algorithm.
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                represents a linear basis extension of V.
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<par/>
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    O           Order ideal consisting of elements U \ { LT(v) : v in V }.
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References: [1] A. Kehrein und M. Kreuzer, Computing border bases, J. Pure Appl. Alg. 205 (2006), S. 279 - 295
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Please see [http://staff.fim.uni-passau.de/kreuzer/papers/algbb.pdf A. Kehrein und M. Kreuzer: Computing border bases] for additional information regarding the Border Basis Algorithm.
 
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   <see>BB.BBasis</see>
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   <see>ApCoCoA-1:BBF.RetrieveOGenerators|BBF.RetrieveOGenerators</see>
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   <wiki-category>Package_bbf</wiki-category>
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  <see>ApCoCoA-1:BBF.RetrieveUGenerators|BBF.RetrieveUGenerators</see>
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  <see>ApCoCoA-1:BBF.RetrieveV|BBF.RetrieveV</see>
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  <see>ApCoCoA-1:BBF.RetrieveVLTs|BBF.RetrieveVLTs</see>
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  <see>ApCoCoA-1:BBF.RetrieveVPolysWithTermInSupport|BBF.RetrieveVPolysWithTermInSupport</see>
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  <see>ApCoCoA-1:BBF.RetrieveWPrime|BBF.RetrieveWPrime</see>
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  <see>ApCoCoA-1:BBF.RetrieveWPrimeLTs|BBF.RetrieveWPrimeLTs</see>
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   <wiki-category>ApCoCoA-1:Package_bbf</wiki-category>
 
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Latest revision as of 13:27, 29 October 2020

This article is about a function from ApCoCoA-1.

BBF.Explanation of BBF variables and structures

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.RetrieveOGenerators

BBF.RetrieveUGenerators

BBF.RetrieveV

BBF.RetrieveVLTs

BBF.RetrieveVPolysWithTermInSupport

BBF.RetrieveWPrime

BBF.RetrieveWPrimeLTs


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