ApCoCoA-1:Bertini.BZCSolve

Bertini.BZCSolve

Solves zero dimensional Homogeneous or Non-Homogeneous polynomial system with User Configurations.

Syntax

Bertini.BZCSolve(M:LIST, SysTyp:STRING ,  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 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

-- Zero dimensional Non-homogenous solving with fixed higher precision
-- We want to solve zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. 

Use S ::= QQ[x,y];             --  Define appropriate ring 
M := [x^2+y^2-5,xy-2];
SysTyp := <quotes>Nhom</quotes>;
ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>];

-- Then we compute the solution with
Bertini.BZCSolve(M,SysTyp,ConfigSet);

-- And we achieve a list of lists containing all real finite solutions:
----------------------------------------
[[Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, 
41243336046164965623860294533917  3594181/200000000000000000000000000000000000000000000000000000),
 Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000,
 -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000)],
 [Vector(999999999999996907691691548150283767063/500000000000000000000000000000000000000, 
4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000),
 Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000,
 -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000)],
 [Vector(-1999999999999981470621955122058645854307/1000000000000000000000000000000000000000, 
 -2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), 
Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000,
 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000)],
 [Vector(-9999999999999986714415752390569533003343/10000000000000000000000000000000000000000,
 2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), 
Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000,
 -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]]

See also

Introduction to CoCoAServer

Bertini.BCMSolve

Bertini.BMSolve

Bertini.BSolve

Bertini.BUHSolve