ApCoCoA-1:Bertini.BCMSolve: Difference between revisions

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New page: <command> <title>BSolve</title> <short_description>Solves zero dimensional Homogeneous or Non-Homogeneous polynomial system with Default Configurations.</short_description> <syntax> Bertin...
 
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<command>
<command>
<title>BSolve</title>
<title>BCMSolve</title>
<short_description>Solves zero dimensional Homogeneous or Non-Homogeneous polynomial system with Default Configurations.</short_description>
<short_description>Solves zero dimensional non-homogeneous polynomial system using multi-homogenization with User Configurations.</short_description>
<syntax>
<syntax>
Bertini.BSolve(M:LIST, SysTyp:STRING)
Bertini.BCMSolve(M:LIST, ConfigSet:LIST)
</syntax>
</syntax>
<description>
<description>
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<em>M</em>: List of polynomials in the system to be solved.
<em>M</em>: List of polynomials in the system to be solved.


<em>SysTyp</em>: Type of the system to be solved. Homogeneous ("hom") or nonhomogeneous ("Nhom").
<em>ConfigSet</em>: List of strings representing Configurations to be used by bertini.


   
   
<example>
<example>
-- Zero Dimensional Non-Homogeneous Solving
-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision.  
-- We want to solve zero dimensional non-homogeneous system x^2+y^2-5=0, xy-2=0.  


Use S ::= QQ[x,y];            --  Define appropriate ring  
Use S ::= QQ[x,y];            --  Define appropriate ring  
M := [x^2+y^2-5, xy-2];
M := [x^2+y^2-5,xy-2];
SysTyp := "Nhom";
ConfigSet := ["MPTYPE: 2"];


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


-- And we achieve:
-- And we achieve:
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The real finite solutions are:
The real finite solutions are:
                                          
                                          
2.000000000000052e+00 -1.207721921243940e-14
9.999999999999164e-01 1.727395183148409e-14


-9.999999999999680e-01 -1.380221440309691e-14
1.999999999999915e+00 3.462532971773811e-13
-2.000000000000005e+00 -8.389594590085023e-15
1.000000000000124e+00 -6.955132704987047e-14


9.999999999999293e-01 2.686603221243866e-14
-1.999999999999993e+00 1.957928785100847e-14
2.000000000000473e+00 4.530296702485832e-13
-1.000000000000000e+00 -9.165547572809745e-17


-2.000000000000031e+00 -1.809322618557695e-15
-1.000000000000005e+00 3.596111848160151e-16
-9.999999999999383e-01 -2.558999563654189e-15
-1.999999999999997e+00 2.776127010762429e-15
 
1.000000000000007e+00 -2.243821806115299e-15
1.999999999999988e+00 1.140511608347484e-15


For summary of all solutions refer to ApCoCoAServer.
For summary of all solutions refer to ApCoCoAServer.
</example>
<example>
-- 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];            --  Define appropriate ring
M := [x^2-z^2, xy-z^2];
SysTyp := "hom";
-- Then we compute the solution with
$Bertini.BSolve(M,SysTyp);
-- And we achieve:
----------------------------------------
The number of real solutions are:
4     
The real solutions are:
                                       
4.750270171019972e-01 7.277175694441498e-01
4.750270171019972e-01 7.277175694441498e-01
4.750270171019972e-01 7.277175694441498e-01
-1.161874166440340e+00 -1.121939725361908e+00
-1.161874166440340e+00 -1.121939725361908e+00
1.161874166440340e+00 1.121939725361908e+00
-1.213218743783253e-14 9.540042296620362e-14
1.297490331797821e+00 -3.349764345312171e-01
-9.696352192508132e-14 -3.162549982974766e-13
-2.845295858183006e-14 1.079961801218032e-13
1.297490331797885e+00 -3.349764345312022e-01
-9.799048563439788e-14 -3.558617333271439e-13
For summary of all solutions refer to ApCoCoAServer
------------------------------------
</example>
</example>


Revision as of 10:44, 20 April 2009

BCMSolve

Solves zero dimensional non-homogeneous polynomial system using multi-homogenization with User Configurations.

Syntax

Bertini.BCMSolve(M:LIST, 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.

M: List of polynomials in the system to be solved.

ConfigSet: List of strings representing Configurations to be used by bertini.


Example

-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. 

Use S ::= QQ[x,y];             --  Define appropriate ring 
M := [x^2+y^2-5,xy-2];
ConfigSet := ["MPTYPE: 2"];

-- Then we compute the solution with
$Bertini.BSolve(M,ConfigSet);

-- And we achieve:
----------------------------------------
The number of real finite solutions are:
4       
The real finite solutions are:
                                         

1.999999999999915e+00 3.462532971773811e-13
1.000000000000124e+00 -6.955132704987047e-14

-1.999999999999993e+00 1.957928785100847e-14
-1.000000000000000e+00 -9.165547572809745e-17

-1.000000000000005e+00 3.596111848160151e-16
-1.999999999999997e+00 2.776127010762429e-15

1.000000000000007e+00 -2.243821806115299e-15
1.999999999999988e+00 1.140511608347484e-15

For summary of all solutions refer to ApCoCoAServer.





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