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

From ApCoCoAWiki
Line 1: Line 1:
 
<command>
 
<command>
 
<title>Bertini.BPMCSolve</title>
 
<title>Bertini.BPMCSolve</title>
−
<short_description>Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.</short_description>
+
<short_description>Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
−
Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST
+
Bertini.BPMCSolve(P:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST
 
</syntax>
 
</syntax>
 
<description>
 
<description>
−
<em>Please note:</em>
 
−
Due to a Bug in Bertini.exe. This command is not working at the moment. Sorry for inconvienience.
 
  
 
<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.
 
<par/>
 
<par/>
−
<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.  
+
<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 ApCoCoA directory/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>P</em>: List of polynomials of the given system.</item>
  
−
<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>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt><quotes>hom</quotes></tt>) or non-homogeneous (<tt><quotes>Nhom</quotes></tt>).</item>
  
 
<item>@param <em>MPoints</em>: List of lists containig member points.</item>
 
<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 details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
+
<item>@param <em>ConfigSet</em>: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then set ConfigSet := ["TRACKTYPE: 3"]. If you want to provide specific configurations then simply add them to ConfigSet. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
 
</itemize>
 
</itemize>
 
   
 
   
 
<example>
 
<example>
−
-- Membership testing.
+
-- An example of 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],
+
-- 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
+
-- [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.
 
--  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
+
Use S ::= QQ[x,y,z];          
−
M := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)];
+
P := [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>;
 
SysTyp := <quotes>Nhom</quotes>;
−
MPoints :=[[[<quotes>1.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes> ]],[[<quotes>1.3650269</quotes>, <quotes>-0.31430820</quotes>],
+
MPoints :=[ [ [<quotes>1.0</quotes>, <quotes>0.0</quotes>], [<quotes>0.0</quotes>, <quotes>0.0</quotes>], [<quotes>0.0</quotes>, <quotes>0.0</quotes> ] ], [ [<quotes>1.3650269</quotes>, <quotes>-0.31430820</quotes>],
−
           [<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>],[<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>]]];
+
           [<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>], [<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>] ] ];
 
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
 
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
−
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/). In this example we can use the following file.
+
-- Save the file named witness_data in ApCoCoA directory/Bertini. In this example we can use the following file.
  
 
4
 
4
Line 44: Line 42:
 
2
 
2
 
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−
-- 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:
+
-- Then we test sampling with
 +
Bertini.BPMCSolve(P,SysTyp,MPoints,ConfigSet);
 +
 
 +
-- And we can see the related information in ApCoCoAServer. Please note that
 +
-- you will get only the following message in ApCoCoA GUI.
 
----------------------------------------
 
----------------------------------------
−
 
  
  

Revision as of 13:44, 12 May 2010

Bertini.BPMCSolve

Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems.

Syntax

Bertini.BPMCSolve(P: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 ApCoCoA directory/Bertini, Otherwise you will get an error message.

  • @param P: List of polynomials of the given 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. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then set ConfigSet := ["TRACKTYPE: 3"]. If you want to provide specific configurations then simply add them to ConfigSet. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

Example

-- An example of 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];            
P := [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 :=[ [ [<quotes>1.0</quotes>, <quotes>0.0</quotes>], [<quotes>0.0</quotes>, <quotes>0.0</quotes>], [<quotes>0.0</quotes>, <quotes>0.0</quotes> ] ],  [ [<quotes>1.3650269</quotes>, <quotes>-0.31430820</quotes>],
          [<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>], [<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>] ] ];
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
-- Save the file named witness_data in ApCoCoA directory/Bertini. In this example we can use the following file.

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10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464

2 1
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4
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11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
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3 0

4
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4
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11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808
10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464


-- Then we test sampling with
Bertini.BPMCSolve(P,SysTyp,MPoints,ConfigSet);

-- And we can see the related information in ApCoCoAServer. Please note that
-- you will get only the following message in ApCoCoA GUI.
----------------------------------------


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



See also

Introduction to CoCoAServer

Bertini.BSolve

Bertini.BPCSolve




Retrieved from "http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Bertini.BPMCSolve&oldid=10358"