# ApCoCoA-1:Bertini.BSolve

## Bertini.BSolve

Solves zero dimensional homogeneous or non-homogeneous 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.

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

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

#### Example

```-- Zero Dimensional Non-Homogeneous Solving
-- We want to solve zero dimensional non-homogeneous 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 := <quotes>Nhom</quotes>;

-- 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.

```

#### Example

```-- Zero Dimensional Homogeneous Solving
-- We want to solve zero dimensional homogeneous system x^2-z^2=0, xy-z^2=0.

Use S ::= QQ[x,y,z];             --  Define appropriate ring
M := [x^2-z^2, xy-z^2];
SysTyp := <quotes>hom</quotes>;

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

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

4.750270171019972e-01 7.277175694441498e-01
4.750270171019972e-01 7.277175694441498e-01
4.750270171019972e-01 7.277175694441498e-01

-1.161874166440340e+00 -1.121939725361908e+00
-1.161874166440340e+00 -1.121939725361908e+00
1.161874166440340e+00 1.121939725361908e+00

-1.213218743783253e-14 9.540042296620362e-14
1.297490331797821e+00 -3.349764345312171e-01
-9.696352192508132e-14 -3.162549982974766e-13

-2.845295858183006e-14 1.079961801218032e-13
1.297490331797885e+00 -3.349764345312022e-01
-9.799048563439788e-14 -3.558617333271439e-13

For summary of all solutions refer to ApCoCoAServer

------------------------------------
```