Difference between revisions of "ApCoCoA-1:Bertini.BUHSolve"
From ApCoCoAWiki
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<command> | <command> | ||
<title>Bertini.BUHSolve</title> | <title>Bertini.BUHSolve</title> | ||
| − | <short_description>Solves zero dimensional non-homogeneous polynomial system by user defined homotopy.</short_description> | + | <short_description>Solves a zero dimensional non-homogeneous polynomial system of equations by user defined homotopy.</short_description> |
<syntax> | <syntax> | ||
| − | Bertini.BUHSolve( | + | Bertini.BUHSolve(P:LIST, SSys:LIST, Gamma:STRING, SSol:LIST, ConfigSet:LIST) |
</syntax> | </syntax> | ||
| Line 11: | Line 11: | ||
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>P</em>: List of polynomials of the given system.</item> |
| − | <item>@param <em>SSys</em>: List of polynomials | + | <item>@param <em>SSys</em>: List of polynomials of the start system for homotopy.</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>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. | + | <item>@param <em>SSol</em>: List of lists containing the start solution for the homotopy. The elements of Lists are strings.</item> |
| − | <item>@param <em>ConfigSet</em>: List of strings representing configurations to be used by | + | <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 the ConfigSet := [<quotes>USERHOMOTOPY: 1</quotes>]. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>. </item> |
| − | <item>@return A list of lists containing real solutions.</item> | + | <item>@return A list of lists containing real solutions of system P.</item> |
</itemize> | </itemize> | ||
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-- The start system for the homotopy is x^2=0, y^2=0. | -- The start system for the homotopy is x^2=0, y^2=0. | ||
| − | Use S ::= QQ[x,y]; | + | Use S ::= QQ[x,y]; |
| − | + | P := [x^2-1, y^2-1]; | |
SSys := [x^2,y^2]; | SSys := [x^2,y^2]; | ||
Gamma := <quotes>0.8 - 1.2*I</quotes>; | Gamma := <quotes>0.8 - 1.2*I</quotes>; | ||
| Line 38: | Line 38: | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | Bertini.BUHSolve( | + | Bertini.BUHSolve(P, SSys, Gamma, SSol, ConfigSet); |
| − | -- And we achieve a list of lists containing real solutions | + | -- And we achieve a list of lists containing real solutions. |
---------------------------------------- | ---------------------------------------- | ||
[[-1000000000000043/1000000000000000, -1000000000000043/1000000000000000], | [[-1000000000000043/1000000000000000, -1000000000000043/1000000000000000], | ||
[1000000000000043/1000000000000000, 1000000000000043/1000000000000000]] | [1000000000000043/1000000000000000, 1000000000000043/1000000000000000]] | ||
| − | For | + | For Bertini output files please refer to ApCoCoA directory/Bertini. |
</example> | </example> | ||
Revision as of 10:47, 12 May 2010
Bertini.BUHSolve
Solves a zero dimensional non-homogeneous polynomial system of equations by user defined homotopy.
Syntax
Bertini.BUHSolve(P:LIST, SSys:LIST, Gamma:STRING, SSol: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 P: List of polynomials of the given system.
@param SSys: List of polynomials of 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. The elements of Lists are strings.
@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 the ConfigSet := ["USERHOMOTOPY: 1"]. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
@return A list of lists containing real solutions of system P.
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]; P := [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(P, SSys, Gamma, SSol, ConfigSet); -- And we achieve a list of lists containing real solutions. ---------------------------------------- [[-1000000000000043/1000000000000000, -1000000000000043/1000000000000000], [1000000000000043/1000000000000000, 1000000000000043/1000000000000000]] For Bertini output files please refer to ApCoCoA directory/Bertini.
See also
