# ApCoCoA-1:Bertini.BSolve

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## BSolve

Solves zero dimensional Homogenous or Non-Homogenous polynomial system with Default Configurations.

### Syntax

```Bertini.BSolve(M:LIST, SysTyp:STRING)
```

### 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.

M: List of polynomials in the system to be solved.

SysTyp: Type of the system to be solved. Homogeneous ("hom") or nonhomogeneous ("Nhom").

Zero Dimensional Non-Homogenous Solving

#### Example

```-- We want to solve zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0.

Use S ::= QQ[x,y];             --  Define appropriate ring
M := [x^2+y^2-5, xy-2];
SysTyp := "Nhom";

-- Then we compute the solution with
\$Bertini.BSolve(M,SysTyp);

-- And we achieve:
----------------------------------------
The number of real finite solutions are:
4
The real finite solutions are:

2.000000000000052e+00 -1.207721921243940e-14
9.999999999999164e-01 1.727395183148409e-14

-9.999999999999680e-01 -1.380221440309691e-14
-2.000000000000005e+00 -8.389594590085023e-15

9.999999999999293e-01 2.686603221243866e-14
2.000000000000473e+00 4.530296702485832e-13

-2.000000000000031e+00 -1.809322618557695e-15
-9.999999999999383e-01 -2.558999563654189e-15

For summary of all solutions refer to ApCoCoAServer.

```