ApCoCoA-1:Bertini.BUHSolve
Bertini.BUHSolve
Solves zero dimensional non-homogeneous polynomial system by user defined homotopy.
Syntax
Bertini.BUHSolve(M: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 M: List of polynomials in the system.
@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 configrations then the ConfigSet := ["USERHOMOTOPY: 1"], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
@return A list of lists containing real solutions.
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 a list of lists containing real solutions: ---------------------------------------- [[-1000000000000043/1000000000000000, -1000000000000043/1000000000000000], [1000000000000043/1000000000000000, 1000000000000043/1000000000000000]] For other Bertini output files please refer to Bertini directory(.../ApCoCoA-1.2/Bertini/).
See also
