ApCoCoA-1:Bertini.BUHSolve
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.
This function solves a zero dimensional non-homogeneous polynomial system of equaiton by user defined homotopy. Please note that user defined homotopy as implemented in Bertini is quite sensitive. The purpose of user defined homotopy is to solve parameterized systems of polynomial equations. If F is a polynomial system having solution S and G is a polynomial system having the same monomials but differs only in coefficients then we can use user defined homotopy to solve the system G, considering the system F as start system for the homotopy and S the start solution. User defined homotopy works well for square systems.
@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 in the form of 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 set 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
