Difference between revisions of "ApCoCoA-1:Num.IsAppBB"

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(New page: <command> <title>Numerical.IsAppBB</title> <short_description>Checks if a given set of polynomials is an approximate border basis.</short_description> <syntax> Num.IsAppBB(Polys:...)
 
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   <command>
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   {{Version|1}}
     <title>Numerical.IsAppBB</title>
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<command>
 +
     <title>Num.IsAppBB</title>
 
     <short_description>Checks if a given set of polynomials is an approximate border basis.</short_description>
 
     <short_description>Checks if a given set of polynomials is an approximate border basis.</short_description>
 
<syntax>
 
<syntax>
Num.IsAppBB(Polys:PolyList, OI:PolyList, Epsilon:Number):A:Number;
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Num.IsAppBB(Polys:LIST, OI:LIST, Epsilon:RAT):RAT
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
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<par/>
Checks if a set of polynomials is an approximate border basis with respect to an order ideal. The function returns the distance to an exact border basis.
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This command checks if a set of polynomials is an approximate border basis with respect to an order ideal and a threshold number <tt>Epsilon</tt>.
 +
<itemize>
 +
<item>@param <em>Polys</em> A list of polynomials.</item>
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<item>@param <em>OI</em> A list containing the order ideal.</item>
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<item>@param <em>Epsilon</em> Rational number</item>
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<item>@return A number which specifies how close the given polynomials are to an exact border basis</item>
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</itemize>
  
 
<example>
 
<example>
Res := Num.AVI([[1,0],[0,1]],0);
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Use P::=QQ[x,y];
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Res := Num.AVI([[1,1],[0,1]],0);
 
Num.IsAppBB(Res[1],Res[2],0.1);
 
Num.IsAppBB(Res[1],Res[2],0.1);
 
-- CoCoAServer: computing Cpu Time = 0.031
 
-- CoCoAServer: computing Cpu Time = 0.031
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     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
       <see>Introduction to CoCoAServer</see>
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       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
 
     </seealso>
 
     </seealso>
 
     <types>
 
     <types>
       <type>cocoaserver</type>
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       <type>apcocoaserver</type>
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      <type>polynomial</type>
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      <type>borderbasis</type>
 
     </types>
 
     </types>
    <key>numerical.IsAppBB</key>
 
 
     <key>Num.IsAppBB</key>
 
     <key>Num.IsAppBB</key>
 
     <key>IsAppBB</key>
 
     <key>IsAppBB</key>
     <wiki-category>Package_Numerical</wiki-category>
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    <key>numerical.isappbb</key>
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     <wiki-category>ApCoCoA-1:Package_numerical</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 10:29, 7 October 2020

This article is about a function from ApCoCoA-1.

Num.IsAppBB

Checks if a given set of polynomials is an approximate border basis.

Syntax

Num.IsAppBB(Polys:LIST, OI:LIST, Epsilon:RAT):RAT

Description

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

This command checks if a set of polynomials is an approximate border basis with respect to an order ideal and a threshold number Epsilon.

  • @param Polys A list of polynomials.

  • @param OI A list containing the order ideal.

  • @param Epsilon Rational number

  • @return A number which specifies how close the given polynomials are to an exact border basis

Example

Use P::=QQ[x,y];
Res := Num.AVI([[1,1],[0,1]],0);
Num.IsAppBB(Res[1],Res[2],0.1);
-- CoCoAServer: computing Cpu Time = 0.031
-------------------------------
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
0
-------------------------------

See also

Introduction to CoCoAServer