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

From ApCoCoAWiki
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     <short_description>Checks if a given set of polynomials vanishes at a given set of points</short_description>
 
     <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];
+
Num.IsAVI(Polys:PolyList, Points:Matrix, Epsilon:Rat):[A:Number,B:Number];
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
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Checks if a set of polynomials vanishes at a set of points epsilon approximately. The polynomials are preprocessed first to have norm 1.
 
Checks if a set of polynomials vanishes at a set of points epsilon 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.
+
<itemize>
 +
<item>@param <em>Polys</em> A list of polynomials.</item>
 +
<item>@param <em>Points</em> A matrix containing the points to check.</item>
 +
<item>@param <em>Epsilon</em> Rational number</item>
 +
<item>@return A number A which specifies how well the points vanish on average and a number B which contains the maximal evaluation value</item>
 +
</itemize>
  
 
<example>
 
<example>

Revision as of 16:23, 22 April 2009

Numerical.IsAVI

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

Syntax

Num.IsAVI(Polys:PolyList, Points:Matrix, Epsilon:Rat):[A:Number,B:Number];

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. Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.

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

Num.IsAVI([x[1]+1,x[1]^2],[[0]],0.1);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[1/2, 1]
-------------------------------

See also

Introduction to CoCoAServer