ApCoCoA-1:Bertini.BSolve

Bertini.BSolve

Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.

Syntax

Bertini.BSolve(P: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.

This function uses total degree homotopy to find all isolated solutions of a zero dimensional system of polynomial equaions.

• @param P: List of polynomials of the given system.

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

• @return A list of lists containing the finite (or real) solutions of the system P.

Example

-- An example of 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];              
P := [x^2+y^2-5, xy-2];
SysTyp := <quotes>Nhom</quotes>;

-- Then we compute the solution with
Bertini.BSolve(P,SysTyp);

-- And we achieve a list of lists containing all finite solutions.
----------------------------------------
[[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000), 
Vector(9999999999999927/10000000000000000, 8966048861359829/1000000000000000000000000000000)],
[Vector(2499999999999963/2500000000000000, 5007041073746771/100000000000000000000000000000),
Vector(249999999999999/125000000000000, -1089183184148021/25000000000000000000000000000)],
[Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000),
Vector(-1999999999999999/1000000000000000, 2443331461729629/2500000000000000000000000000000)],
[Vector(-250000000000001/125000000000000, 4347064  850996171/1000000000000000000000000000000),
Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]]

--The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000)
--represents the complex number 5000/1000-4150/1000i.
--For Bertini output files please refer to ApCoCoA directory/Bertini.

Example

-- An example of 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];            
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],
[1237092982347763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000],
[3235177805819999/100000000000000000000000000000, 9932123317905381/10000000000000000, 
621807549382663/5000000000000000000000000000], [3006769352985381/100000000000000000000000000000,
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]

--For Bertini output files please refer to ApCoCoA directory/Bertini.
------------------------------------

See also

Introduction to CoCoAServer

Bertini.BPCSolve

Bertini.BZCSolve

Bertini.BMSolve

Bertini.BUHSolve