Difference between revisions of "ApCoCoA-1:Bertini.BPMCSolve"

From ApCoCoAWiki
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<command>
 
<command>
 
<title>Bertini.BPMCSolve</title>
 
<title>Bertini.BPMCSolve</title>
<short_description> Memnership testing for Positive dimensional Homogeneous or Non-Homogeneous polynomial system with Default and User Configurations.</short_description>
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<short_description>Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.</short_description>
 
<syntax>
 
<syntax>
Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST)
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Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST
 
</syntax>
 
</syntax>
 
<description>
 
<description>
 
<em>Please note:</em>  
 
<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.
 
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>
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<par/>
You need to write(or generate by using the function BPCSolve ) the witness date file and save it with the name "witness_data" in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.  
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<em>Please note:</em> You need to write (or generate by using the function <ref>Bertini.BPCSolve</ref>) the witness date file and save it with the name <quotes>witness_data</quotes> in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.  
  
 
<itemize>
 
<itemize>
 
<item>@param <em>M</em>: List of polynomials in the system.</item>
 
<item>@param <em>M</em>: List of polynomials in the system.</item>
  
<item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or nonhomogeneous (<tt>Nhom</tt>).</item>
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<item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or non-homogeneous (<tt>Nhom</tt>).</item>
  
<item>@param <em>MPoints</em>: List of lists containg member points.</item>
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<item>@param <em>MPoints</em>: List of lists containig member points.</item>
  
<item>@param <em>ConfigSet</em>: List of strings representing Configurations to be used by bertini. For detials about configuraion settings see Bertini mannul <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
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<item>@param <em>ConfigSet</em>: List of strings representing configurations to be used by Bertini. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
 
</itemize>
 
</itemize>
 
   
 
   

Revision as of 09:13, 7 July 2009

Bertini.BPMCSolve

Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.

Syntax

Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST

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.

Please note: You need to write (or generate by using the function Bertini.BPCSolve) the witness date file and save it with the name "witness_data" in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.

  • @param M: List of polynomials in the system.

  • @param SysTyp: Type of polynomials in the system. Homogeneous (hom) or non-homogeneous (Nhom).

  • @param MPoints: List of lists containig member points.

  • @param ConfigSet: List of strings representing configurations to be used by Bertini. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

Example

-- Membership testing.
-- We want to test membership for the points [[[1.0, 0.0],[0.0, 0.0],[0.0, 0.0 ]],[[1.3650269, -0.31430820],
-- [1.7645087, -0.85807828],[2.1389007, -1.7258994]]], where the polynomial system is
--  x^2+y^2+z^2-1=0, x^3+y^2+z^3-1=0, (y-x^2)*(z-x^3)(z-5)=0.

Use S ::= QQ[x,y,z];             --  Define appropriate ring 
M := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)];
SysTyp := <quotes>Nhom</quotes>;
MPoints :=[[["1.0", "0.0"],["0.0", "0.0"],["0.0", "0.0" ]],[["1.3650269", "-0.31430820"],
          ["1.7645087", "-0.85807828"],["2.1389007", "-1.7258994"]]];
ConfigSet := ["TRACKTYPE: 3"];

-- Then we compute the witness point super sets with
$Bertini.BPMCSolve(M,SysTyp,MPoints,ConfigSet);

-- And we achieve a list of lists containing witness point supersets:
----------------------------------------



--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).



See also

Introduction to CoCoAServer

Bertini.BSolve

Bertini.BPCSolve