# Difference between revisions of "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.

• @param SysTyp: Type of polynomials in the system. 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 a list of lists containing all finite solutions:
----------------------------------------
[[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000),
Vector(9999999999999927/10000  000000000000, 8966048861359829/1000000000000000000000000000000)],
[Vector(2499999999999963/2500000000000000, 5007041073746  771/100000000000000000000000000000),
Vector(249999999999999/125000000000000, -1089183184148021/250000000000000000000000000  00)],
[Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000),
Vector(-19999999999999  99/1000000000000000, 2443331461729629/2500000000000000000000000000000)],
[Vector(-250000000000001/125000000000000, 4347064  850996171/1000000000000000000000000000000),
Vector(-9999999999999943/10000000000000000, -2154842536286333/5000000000000000  00000000000000)]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
```

#### 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 a list of lists containing all real solutions:
----------------------------------------
[[2190685167348543/5000000000000000, 2190685167348543/5000000000000000, 2190685167348543/5000000000000000],
[1237092982347  763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000],
[3235177805819999/1000000000  00000000000000000000, 9932123317905381/10000000000000000,
621807549382663/5000000000000000000000000000], [30067693529  85381/100000000000000000000000000000,
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
------------------------------------
```