# ApCoCoA-1:Bertini.BPMCSolve

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## Bertini.BPMCSolve

Solves(By finding witness point supersets) Positive dimensional Homogeneous or Non-Homogeneous polynomial system with User Configurations.

### Syntax

```Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints: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.

• @param SysTyp: Type of polynomials in the system. Homogeneous (hom) or nonhomogeneous (Nhom).

• @param MPoints: List of lists containg member points.

• @param ConfigSet: List of strings representing Configurations to be used by bertini. For detials about configuraion settings see Bertini mannul http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

#### Example

```-- Membership testing.
-- We want to test membership for the points [[[1.0, 0.0],[0.0, 0.0],[0.0, 0.0 ]],[[1.3650269, -0.31430820],[1.7645087, -0.85807828],[2.1389007, -1.7258994]]], where the polynomial system is x^2+y^2+z^2-1=0, x^3+y^2+z^3-1=0, (y-x^2)*(z-x^3)(z-5)=0.

Use S ::= QQ[x,y,z];             --  Define appropriate ring
M := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)];
SysTyp := <quotes>Nhom</quotes>;
MPoints :=[[["1.0", "0.0"],["0.0", "0.0"],["0.0", "0.0" ]],[["1.3650269", "-0.31430820"],
["1.7645087", "-0.85807828"],["2.1389007", "-1.7258994"]]];
ConfigSet := ["TRACKTYPE: 3"];

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

-- And we achieve a list of lists containing witness point supersets:
----------------------------------------

```