Difference between revisions of "ApCoCoA-1:Bertini.BUHSolve"
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<item>@param <em>M</em>: List of polynomials in the system to be solved.</item> | <item>@param <em>M</em>: List of polynomials in the system to be solved.</item> | ||
| − | <item><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><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 "a+b*I" ( e.g. "0.8 - 1.2*I" ).</item> |
| − | <item><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><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 := ["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> |
</itemize> | </itemize> | ||
Revision as of 10:41, 23 April 2009
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 := "0.8 - 1.2*I";
SSol := [[["-1.0", "0.0"], ["-1.0","0.0"]],[["1.0", "0.0"],["1.0","0.0"]]];
ConfigSet := ["USERHOMOTOPY: 12"];
-- 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
