# Difference between revisions of "ApCoCoA-1:Bertini.BZCSolve"

## Bertini.BZCSolve

Solves zero dimensional homogeneous or non-homogeneous polynomial systems with user defined configurations.

### Syntax

```Bertini.BZCSolve(M:LIST, SysTyp:STRING ,  ConfigSet:LIST):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 non-homogeneous (Nhom).

• @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.

• @return A list of lists containing the finite solutions of the polynomial system.

#### 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 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)]]

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

#### Example

```-- Zero dimensional homogenous solving with fixed higher precision
-- We want to solve zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision.

Use S ::= QQ[x,y];             --  Define appropriate ring
M := [x^2-z^2, xy-z^2];
SysTyp := <quotes>hom</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 solutions:
----------------------------------------
[[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000,
-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000,
-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000],
[-666269356331265789905402745641735631587/1250000000000000000000000000000000000000,
-666269356331265789905402745641735631587/1250000000000000000000000000000000000000,
666269356331265789905402745641735631587/1250000000000000000000000000000000000000],
[-1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000,
1604689603443950100804972123829819895459/2500000000000000000000000000000000000000,
-9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000],
[-1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000,
3209379206887735502321156763919697536571/5000000000000000000000000000000000000000,
-4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]]

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