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

From ApCoCoAWiki
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<item>@param <em>SSys</em>: List of polynomials in the start system for homotopy.</item>
 
<item>@param <em>SSys</em>: List of polynomials in the start system for homotopy.</item>
  
<item>@param <em>Gamma</em>: Complex number in the form  "a+b*I" ( e.g. "0.8 - 1.2*I" ).</item>
+
<item>@param <em>Gamma</em>: Complex number in the form  <quotes>a+b*I</quotes> ( e.g. <quotes>0.8 - 1.2*I</quotes> ).</item>
  
 
<item>@param <em>SSol</em>: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings.</item>
 
<item>@param <em>SSol</em>: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings.</item>
  
<item>@param <em>ConfigSet</em>: List of strings representing Configurations to be used by bertini. Note that if you want to use default configraions then the ConfigSet := ["USERHOMOTOPY: 1"], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini mannual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>. </item>
+
<item>@param <em>ConfigSet</em>: List of strings representing Configurations to be used by bertini. Note that if you want to use default configraions then the ConfigSet := [<quotes>USERHOMOTOPY: 1</quotes>], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini mannual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>. </item>
 
</itemize>
 
</itemize>
 
   
 
   
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M := [x^2-1, y^2-1];
 
M := [x^2-1, y^2-1];
 
SSys := [x^2,y^2];
 
SSys := [x^2,y^2];
Gamma := "0.8 - 1.2*I";
+
Gamma := <quotes>0.8 - 1.2*I</quotes>;
SSol := [[["-1.0", "0.0"], ["-1.0","0.0"]],[["1.0", "0.0"],["1.0","0.0"]]];
+
SSol := [[[<quotes>-1.0</quotes>, <quotes>0.0</quotes>], [<quotes>-1.0</quotes>,<quotes>0.0</quotes>]],[[<quotes>1.0</quotes>, <quotes>0.0</quotes>],[<quotes>1.0</quotes>,<quotes>0.0</quotes>]]];
ConfigSet := ["USERHOMOTOPY: 1"];
+
ConfigSet := [<quotes>USERHOMOTOPY: 1</quotes>];
  
  

Revision as of 12:45, 27 April 2009

Bertini.BUHSolve

Solves zero dimensional non-homogeneous polynomial system by user definged homotopy.

Syntax

Bertini.BUHSolve(M:LIST, SSys:LIST, Gamma:STRING, SSol:LIST OF LIST, ConfigSet: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.

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

  • @param SSys: List of polynomials in the start system for homotopy.

  • @param Gamma: Complex number in the form "a+b*I" ( e.g. "0.8 - 1.2*I" ).

  • @param SSol: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings.

  • @param ConfigSet: List of strings representing Configurations to be used by bertini. Note that if you want to use default configraions then the ConfigSet := ["USERHOMOTOPY: 1"], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini mannual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

Example

-- We want to solve the system x^2-1=0, y^2-1=0, where Gamma=0.8-1.2I. 
-- The two start solutions for the homotopy are [[-1.0, 0.0 ],[-1.0,0.0]] and [[1.0, 0.0],[1.0,0.0]].
-- The start system for the homotopy is x^2=0, y^2=0. 

Use S ::= QQ[x,y];             --  Define appropriate ring 
M := [x^2-1, y^2-1];
SSys := [x^2,y^2];
Gamma := <quotes>0.8 - 1.2*I</quotes>;
SSol := [[[<quotes>-1.0</quotes>, <quotes>0.0</quotes>], [<quotes>-1.0</quotes>,<quotes>0.0</quotes>]],[[<quotes>1.0</quotes>, <quotes>0.0</quotes>],[<quotes>1.0</quotes>,<quotes>0.0</quotes>]]];
ConfigSet := [<quotes>USERHOMOTOPY: 1</quotes>];


-- Then we compute the solution with
$Bertini.BUHSolve(M, SSys, Gamma, SSol, ConfigSet);

-- And we achieve:
----------------------------------------
The number of real finite solutions are:
2       
The real finite solutions are:
                                         
-1.000000000000043e+00 2.460120586181259e-14
-1.000000000000043e+00 2.460120586181259e-14

1.000000000000043e+00 -2.460120586181259e-14
1.000000000000043e+00 -2.460120586181259e-14

For summary of all solutions refer to ApCoCoAServer



See also

Introduction to CoCoAServer

Bertini.BCMSolve

Bertini.BCSolve

Bertini.BMSolve

Bertini.BSolve