# Difference between revisions of "ApCoCoA-1:Num.RatPoints"

From ApCoCoAWiki

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<command> | <command> | ||

<title>Num.RatPoints</title> | <title>Num.RatPoints</title> | ||

− | <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.RatPoints(AppBB: | + | Num.RatPoints(AppBB:LIST, OrderIdeal:LIST)):[MAT]; |

</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. | |

− | + | <par/> | |

Calculates a set of points which are the zeros of an exact border basis which is close to AppBB. Uses the eigenvalue methode. | Calculates a set of points which are the zeros of an exact border basis which is close to AppBB. Uses the eigenvalue methode. | ||

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<types> | <types> | ||

<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||

+ | <type>polynomial</type> | ||

+ | <type>points</type> | ||

</types> | </types> | ||

− | |||

<key>Num.RatPoints</key> | <key>Num.RatPoints</key> | ||

<key>RatPoints</key> | <key>RatPoints</key> | ||

<wiki-category>Package_numerical</wiki-category> | <wiki-category>Package_numerical</wiki-category> | ||

</command> | </command> |

## Revision as of 16:51, 23 April 2009

## Num.RatPoints

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

### Syntax

Num.RatPoints(AppBB:LIST, OrderIdeal:LIST)):[MAT];

### 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.

Calculates a set of points which are the zeros of an exact border basis which is close to AppBB. Uses the eigenvalue methode.

@param

*AppBB*An approximate border basis.@param

*Points*The asscoiated order ideal@return A set of points in matrix form.

#### Example

Use P::=QQ[x,y,z]; Points := Mat([[2/3,0,0],[0,1,0],[0,0,1/3]]); R:=Num.SubAVI(Points, 0.001, [1]); Dec(Num.RatPoints(R[1],R[2]),2); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [Mat([ ["0.66", "0.00", "-0.00"], ["0", "0", "1.00"], ["0", "0.33", "0"] ]), Mat([ ["0", "0", "0"], ["0", "0", "0"], ["0", "0", "0"] ])] -------------------------------

### See also