Difference between revisions of "ApCoCoA-1:Num.RatPoints"
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| − | <command> | + | {{Version|1}} |
| + | <command> | ||
<title>Num.RatPoints</title> | <title>Num.RatPoints</title> | ||
| − | <short_description> | + | <short_description>Computes the zero set of an exact zero dimensional border basis. The zeros are computed approximately using the eigenvalues of the transposed multiplication matrices.</short_description> |
<syntax> | <syntax> | ||
| − | Num.RatPoints( | + | Num.RatPoints(BB:LIST, OrderIdeal:LIST)):LIST of 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. | <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 computes a set of points, which are the zeros of an exact border basis. This border basis is close to the approximate border basis <tt>AppBB</tt>. The set of (complex) points is represented as two matrices. The <tt>j</tt>-th column of the first matrix gives the real part of a point and the <tt>j</tt>-th column of the second matrix gives the imaginary part. For computation the function is using the <ref>ApCoCoA-1:Num.EigenValues|Num.EigenValues</ref> command. | |
<itemize> | <itemize> | ||
<item>@param <em>AppBB</em> An approximate border basis.</item> | <item>@param <em>AppBB</em> An approximate border basis.</item> | ||
| − | <item>@param <em> | + | <item>@param <em>OrderIdeal</em> The associated order ideal</item> |
| − | <item>@return A set of points in matrix form.</item> | + | <item>@return A set of points in matrix form described above.</item> |
</itemize> | </itemize> | ||
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Use P::=QQ[x,y,z]; | Use P::=QQ[x,y,z]; | ||
| − | Points := Mat([[2/3,0,0],[0, | + | Points := Mat([[2/3,0,0],[0,10,0],[0,0,1/3]]); |
| − | R:=Num. | + | R:=Num.ABM(Points, 0); |
Dec(Num.RatPoints(R[1],R[2]),2); | Dec(Num.RatPoints(R[1],R[2]),2); | ||
-- CoCoAServer: computing Cpu Time = 0 | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | -- CoCoAServer: computing Cpu Time = 0 | + | -- CoCoAServer: computing Cpu Time = 0.016 |
------------------------------- | ------------------------------- | ||
[Mat([ | [Mat([ | ||
| − | ["0.66", "0.00", " | + | ["0.66", "0.00", "0"], |
| − | ["0", "0", " | + | ["0", "0", "10"], |
["0", "0.33", "0"] | ["0", "0.33", "0"] | ||
]), Mat([ | ]), Mat([ | ||
| Line 41: | Line 42: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 51: | Line 52: | ||
<key>RatPoints</key> | <key>RatPoints</key> | ||
<key>numerical.RatPoints</key> | <key>numerical.RatPoints</key> | ||
| − | <wiki-category>Package_numerical</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_numerical</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:48, 29 October 2020
| This article is about a function from ApCoCoA-1. |
Num.RatPoints
Computes the zero set of an exact zero dimensional border basis. The zeros are computed approximately using the eigenvalues of the transposed multiplication matrices.
Syntax
Num.RatPoints(BB:LIST, OrderIdeal:LIST)):LIST of 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.
This command computes a set of points, which are the zeros of an exact border basis. This border basis is close to the approximate border basis AppBB. The set of (complex) points is represented as two matrices. The j-th column of the first matrix gives the real part of a point and the j-th column of the second matrix gives the imaginary part. For computation the function is using the Num.EigenValues command.
@param AppBB An approximate border basis.
@param OrderIdeal The associated order ideal
@return A set of points in matrix form described above.
Example
Use P::=QQ[x,y,z]; Points := Mat([[2/3,0,0],[0,10,0],[0,0,1/3]]); R:=Num.ABM(Points, 0); Dec(Num.RatPoints(R[1],R[2]),2); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- [Mat([ ["0.66", "0.00", "0"], ["0", "0", "10"], ["0", "0.33", "0"] ]), Mat([ ["0", "0", "0"], ["0", "0", "0"], ["0", "0", "0"] ])] -------------------------------
See also
