ApCoCoA-1:Num.IsAVI: Difference between revisions
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<command> | {{Version|1}} | ||
<title> | <command> | ||
<short_description>Checks if a given set of polynomials vanishes at a given set of points</short_description> | <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:LIST, Points:MAT, Epsilon:RAT):[A:INT,B:INT]; | Num.IsAVI(Polys:LIST, Points:MAT, Epsilon:RAT):[A:INT or RAT,B:INT or RAT]; | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
<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. | <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. | ||
<par/> | <par/> | ||
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. | |||
<itemize> | <itemize> | ||
<item>@param <em>Polys</em> A list of polynomials.</item> | <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>Points</em> A matrix containing the points to check.</item> | ||
<item>@param <em>Epsilon</em> Rational number</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> | <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> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
Num.IsAVI([x | Use P::=Q[x,y,z]; | ||
Dec(Num.IsAVI([x+1,x^2],[[0]],0.1),3); | |||
-- CoCoAServer: computing Cpu Time = 0 | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
[ | ["0.353", "0.707"] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>Introduction to CoCoAServer</see> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 34: | Line 36: | ||
<key>Num.IsAvi</key> | <key>Num.IsAvi</key> | ||
<key>IsAvi</key> | <key>IsAvi</key> | ||
<wiki-category>Package_numerical</wiki-category> | <key>numerical.isavi</key> | ||
<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
