# ApCoCoA-1:Bertini.BPMCSolve

## Bertini.BPMCSolve

Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.

### Syntax

Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST

### Description

Please note: Due to a Bug in Bertini.exe. This command is not working at the moment.

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.

Please note: You need to write (or generate by using the function Bertini.BPCSolve) the witness date file and save it with the name "witness_data" in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.

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

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

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

• @param ConfigSet: List of strings representing configurations to be used by Bertini. For details about configuration settings see Bertini manual 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 :=[[[<quotes>1.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes> ]],[[<quotes>1.3650269</quotes>, <quotes>-0.31430820</quotes>],
[<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>],[<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>]]];
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/).

-- Then we compute the witness point super sets with
\$Bertini.BPMCSolve(M,SysTyp,MPoints,ConfigSet);

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

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