# Difference between revisions of "ApCoCoA-1:Bertini.BMSolve"

## Bertini.BMSolve

Solves zero dimensional non-homogeneous polynomial system using mult-homogenization with default configurations.

### Syntax

```Bertini.BMSolve(M: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.

#### Example

```-- We want to solve the non-homogenous system x[1]^2+x[2]^2-5=0, x[1]x[2]-2=0, using multi-homogenization.

Use S ::= QQ[x[1..2]];             --  Define appropriate ring
M := [x[1]^2+x[2]^2-5, x[1]x[2]-2];

-- Then we compute the solution with
Bertini.BMSolve(M);

-- And we achieve a list of lists containing finite solutions:
----------------------------------------
[[Vector(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000),
Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000)],
[Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000),
Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)],
[Vector(-2, 1724810333092189/1000000000000000000000000000000),
Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)],
[Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000),
Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]]
--For other Bertini output files refer to Bertini directory (../ApCoCoA-1.2/Bertini)
------------------------------------------
```