Difference between revisions of "ApCoCoA-1:Num.IsAVI"
From ApCoCoAWiki
m (replaced <quotes> tag by real quotes) |
|||
| (9 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| − | <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
