Difference between revisions of "ApCoCoA-1:Num.RatPoints"
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<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 points is represented as | + | 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>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>OrderIdeal</em> The associated order ideal</item> | <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> | ||
Revision as of 13:47, 8 July 2009
Num.RatPoints
Computes a set of points, which are the zeros of an exact border basis. This border basis is close to an approximate border basis.
Syntax
Num.RatPoints(AppBB: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],[0,1,0],[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([ [<quotes>0.66</quotes>, <quotes>0.00</quotes>, <quotes>-0.00</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>1.00</quotes>], [<quotes>0</quotes>, <quotes>0.33</quotes>, <quotes>0</quotes>] ]), Mat([ [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>] ])] -------------------------------
See also
