Difference between revisions of "ApCoCoA-1:Bertini.BSolve"

From ApCoCoAWiki
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For summary of all solutions refer to ApCoCoAServer.
 
For summary of all solutions refer to ApCoCoAServer.
  
 +
</example>
 +
<example>
 +
-- Zero Dimensional Homogenous Solving
 +
-- We want to solve zero dimensional homogenous 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 08:46, 20 April 2009

BSolve

Solves zero dimensional Homogenous or Non-Homogenous polynomial system with Default Configurations.

Syntax

Bertini.BSolve(M: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.

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

SysTyp: Type of the system to be solved. Homogeneous ("hom") or nonhomogeneous ("Nhom").


Example

-- Zero Dimensional Non-Homogenous Solving
-- We want to solve zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0. 

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

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

-- And we achieve:
----------------------------------------
The number of real finite solutions are:
4       
The real finite solutions are:
                                         
2.000000000000052e+00 -1.207721921243940e-14
9.999999999999164e-01 1.727395183148409e-14

-9.999999999999680e-01 -1.380221440309691e-14
-2.000000000000005e+00 -8.389594590085023e-15

9.999999999999293e-01 2.686603221243866e-14
2.000000000000473e+00 4.530296702485832e-13

-2.000000000000031e+00 -1.809322618557695e-15
-9.999999999999383e-01 -2.558999563654189e-15

For summary of all solutions refer to ApCoCoAServer.

Example

-- Zero Dimensional Homogenous Solving
-- We want to solve zero dimensional homogenous 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

------------------------------------