# ApCoCoA-1:Bertini.BUHSolve

## 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