# 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
```