Difference between revisions of "ApCoCoA-1:BBF.RetrieveBorderBasisLTs"

From ApCoCoAWiki
(Updated parameter and return value list.)
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{{Version|1}}
 
<command>
 
<command>
    <title>BBF.RetrieveBorderBasisLTs</title>
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  <title>BBF.RetrieveBorderBasisLTs</title>
    <short_description>Retrieve leading terms of computed border basis.</short_description>
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  <short_description>Retrieves leading terms of a computed border basis.</short_description>
 +
 
 
<syntax>
 
<syntax>
 
BBF.RetrieveBorderBasisLTs():LIST
 
BBF.RetrieveBorderBasisLTs():LIST
 
BBF.RetrieveBorderBasisLTs(Degree:INT):LIST
 
BBF.RetrieveBorderBasisLTs(Degree:INT):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
The first function without parameter retrieves the leading terms of the computed border basis polynomials from the ApCoCoABBFServer.
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoABBFServer</em>. You will have to start the ApCoCoABBFServer in order to use it/them.
The second function with parameter <tt>Degree</tt> >= 0 retrieves the leading terms of degree <tt>Degree</tt> of the computed border basis polynomials.
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<par/>
Please note that in order to use this function you have to start the ApCoCoABBFServer.
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The first variant of this command without parameter retrieves the leading terms of the computed border basis polynomials from the ApCoCoABBFServer.
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The second variant with the parameter <tt>Degree</tt> >= 0 retrieves the leading terms of degree <tt>Degree</tt> of the computed border basis polynomials.
 
<itemize>
 
<itemize>
   <item>@return A list of border basis polynomial leading terms.</item>
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   <item>@return List of border basis leading terms.</item>
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</itemize>
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The following parameter is optional.
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<itemize>
 +
  <item>@param <em>Degree</em> Retrieve the border basis leading terms of degree <tt>Degree</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
Use Z/(32003)[x, y, z],DegLex;
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Use ZZ/(32003)[x, y, z],DegLex;
 
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
 
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
 
BBF.Init(I);
 
BBF.Init(I);
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</example>
 
</example>
 
<example>
 
<example>
Use Z/(32003)[x, y, z],DegLex;
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Use ZZ/(32003)[x, y, z],DegLex;
 
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
 
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
 
BBF.Init(I);
 
BBF.Init(I);
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[z^2, y^2, x^2]
 
[z^2, y^2, x^2]
 
</example>
 
</example>
    </description>
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  </description>
     <see>Border Basis Framework overview</see>
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  <types>
    <see>BBF.RetrieveBorderBasis</see>
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     <type>borderbasis</type>
    <see>BBF.RetrieveBorderBasisPolyByLT</see>
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  </types>
    <see>BBasis</see>
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  <see>ApCoCoA-1:BBF.RetrieveBorderBasis|BBF.RetrieveBorderBasis</see>
    <key>bbf.retrieveborderbasislts</key>
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  <see>ApCoCoA-1:BBF.RetrieveBorderBasisPolyByLT|BBF.RetrieveBorderBasisPolyByLT</see>
    <wiki-category>Package_bbf</wiki-category>
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  <see>ApCoCoA-1:BB.BBasis|BB.BBasis</see>
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  <key>RetrieveBorderBasisLTs</key>
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  <key>BBF.RetrieveBorderBasisLTs</key>
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  <wiki-category>ApCoCoA-1:Package_bbf</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:47, 7 October 2020

This article is about a function from ApCoCoA-1.

BBF.RetrieveBorderBasisLTs

Retrieves leading terms of a computed border basis.

Syntax

BBF.RetrieveBorderBasisLTs():LIST
BBF.RetrieveBorderBasisLTs(Degree:INT):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoABBFServer. You will have to start the ApCoCoABBFServer in order to use it/them.

The first variant of this command without parameter retrieves the leading terms of the computed border basis polynomials from the ApCoCoABBFServer.

The second variant with the parameter Degree >= 0 retrieves the leading terms of degree Degree of the computed border basis polynomials.

  • @return List of border basis leading terms.

The following parameter is optional.

  • @param Degree Retrieve the border basis leading terms of degree Degree.

Example

Use ZZ/(32003)[x, y, z],DegLex;
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
BBF.Init(I);
BBF.Finish();
-- After computation has finished:
BBF.RetrieveBorderBasisLTs();

Output:
[z^2, y^2, x^2, yz^2, y^2z, xz^2, xy^2, x^2z, x^2y, xyz^2, xy^2z, x^2yz]

Example

Use ZZ/(32003)[x, y, z],DegLex;
I:=Ideal(-4*x^2 + 1, -4*y^2 - 1, 5*z^2);
BBF.Init(I);
BBF.Finish();
-- After computation has finished:
BBF.RetrieveBorderBasisLTs(2);

Output:
[z^2, y^2, x^2]

BBF.RetrieveBorderBasis

BBF.RetrieveBorderBasisPolyByLT

BB.BBasis