Difference between revisions of "ApCoCoA-1:Num.RatPoints"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Num.RatPoints</title> | <title>Num.RatPoints</title> | ||
| − | <short_description>Computes a set of points which are the zeros of an exact border basis | + | <short_description>Computes a set of points, which are the zeros of an exact border basis. This border basis is close to an approximate border basis.</short_description> |
<syntax> | <syntax> | ||
| − | Num.RatPoints(AppBB:LIST, OrderIdeal:LIST)): | + | Num.RatPoints(AppBB: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 points is represented as one matrix, in which each column represents one point. For computation the function is using the <ref>Num.EigenValue</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.</item> | ||
</itemize> | </itemize> | ||
Revision as of 11:49, 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 points is represented as one matrix, in which each column represents one point. For computation the function is using the Num.EigenValue command.
@param AppBB An approximate border basis.
@param OrderIdeal The associated 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([ [<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
