ApCoCoA-1:Bertini.BUHSolve
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
