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

From ApCoCoAWiki
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m (replaced <quotes> tag by real quotes)
 
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   <command>
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   {{Version|1}}
     <title>Numerical.IsAVI</title>
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<command>
     <short_description>Checks if a given set of polynomials vanishes at a given set of points</short_description>
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     <title>Num.IsAVI</title>
 +
     <short_description>Checks if a given set of polynomials vanishes at a given set of points.</short_description>
 
<syntax>
 
<syntax>
Num.IsAVI(Polys:PolyList, Points:Matrix, Epsilon:Number):[A:Number,B:Number];
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Num.IsAVI(Polys:LIST, Points:MAT, Epsilon:RAT):[A:INT or RAT,B:INT or 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 vanishes at a set of points epsilon approximately. The polynomials are preprocessed first to have norm 1.
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This command checks if a set of polynomials vanishes at a set of points <tt>Epsilon</tt> approximately. The polynomials are preprocessed first to have norm 1.
The function returns a number A which specifies how well the points vanish on average and the number B contains the maximal evaluation value.
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<itemize>
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<item>@param <em>Polys</em> A list of polynomials.</item>
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<item>@param <em>Points</em> A matrix containing the points to check.</item>
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<item>@param <em>Epsilon</em> Rational number</item>
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<item>@return A number <tt>A</tt> which specifies how well the points vanish on average and a number <tt>B</tt> which contains the maximal evaluation value</item>
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</itemize>
  
 
<example>
 
<example>
Num.IsAVI([x[1]+1,x[1]^2],[[0]],0.1);
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Use P::=Q[x,y,z];
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Dec(Num.IsAVI([x+1,x^2],[[0]],0.1),3);
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
[1/2, 1]
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["0.353", "0.707"]
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
     </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>points</type>
 
     </types>
 
     </types>
    <key>numerical.IsAvi</key>
 
 
     <key>Num.IsAvi</key>
 
     <key>Num.IsAvi</key>
 
     <key>IsAvi</key>
 
     <key>IsAvi</key>
     <wiki-category>Package_Numerical</wiki-category>
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    <key>numerical.isavi</key>
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     <wiki-category>ApCoCoA-1:Package_numerical</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 13:47, 29 October 2020

This article is about a function from ApCoCoA-1.

Num.IsAVI

Checks if a given set of polynomials vanishes at a given set of points.

Syntax

Num.IsAVI(Polys:LIST, Points:MAT, Epsilon:RAT):[A:INT or RAT,B:INT or 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 vanishes at a set of points Epsilon approximately. The polynomials are preprocessed first to have norm 1.

  • @param Polys A list of polynomials.

  • @param Points A matrix containing the points to check.

  • @param Epsilon Rational number

  • @return A number A which specifies how well the points vanish on average and a number B which contains the maximal evaluation value

Example

Use P::=Q[x,y,z];
Dec(Num.IsAVI([x+1,x^2],[[0]],0.1),3);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
["0.353", "0.707"]
-------------------------------

See also

Introduction to CoCoAServer