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Memnership testing for Positive dimensional Homogeneous or Non-Homogeneous polynomial system with Default and User Configurations.


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


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.

Please note:

You need to write(or generate by using the function 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 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.


-- 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 witness point super sets with

-- 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/).

See also

Introduction to CoCoAServer