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

From ApCoCoAWiki
(New page: <command> <title>BSolve</title> <short_description>Solves zero dimensional Homogeneous or Non-Homogeneous polynomial system with Default Configurations.</short_description> <syntax> Bertin...)
 
Line 1: Line 1:
 
<command>
 
<command>
−
<title>BSolve</title>
+
<title>BMSolve</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 Mult-homogenization with Default Configurations.</short_description>
 
<syntax>
 
<syntax>
−
Bertini.BSolve(M:LIST, SysTyp:STRING)
+
Bertini.BMSolve(M:LIST)
 
</syntax>
 
</syntax>
 
<description>
 
<description>
Line 9: Line 9:
  
 
<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").
 
−
 
 
   
 
   
 
<example>
 
<example>
−
-- Zero Dimensional Non-Homogeneous Solving
+
-- We want to solve the non-homogenous system x[1]^2+x[2]^2-5=0, x[1]x[2]-2=0, using multi-homogenization.  
−
-- 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[1..2]];            --  Define appropriate ring  
−
M := [x^2+y^2-5, xy-2];
+
M := [x[1]^2+x[2]^2-5, x[1]x[2]-2];
−
SysTyp := "Nhom";
 
  
 
-- Then we compute the solution with
 
-- Then we compute the solution with
−
$Bertini.BSolve(M,SysTyp);
+
$Bertini.BSolve(M);
  
 
-- And we achieve:
 
-- And we achieve:
Line 30: Line 25:
 
The real finite solutions are:
 
The real finite solutions are:
 
                                          
 
                                          
−
2.000000000000052e+00 -1.207721921243940e-14
+
-2.000000000000035e+00 2.454024452036439e-14
−
9.999999999999164e-01 1.727395183148409e-14
+
-9.999999999999871e-01 -1.788069996029196e-15
−
 
 
−
-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>
 
−
<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
+
-9.999999999999907e-01 -1.089397896007851e-14
−
4.750270171019972e-01 7.277175694441498e-01
+
-2.000000000000040e+00 2.607382514440176e-14
−
4.750270171019972e-01 7.277175694441498e-01
 
  
−
-1.161874166440340e+00 -1.121939725361908e+00
+
1.999999999999310e+00 2.357507317170427e-13
−
-1.161874166440340e+00 -1.121939725361908e+00
+
1.000000000000226e+00 -9.624182470906783e-14
−
1.161874166440340e+00 1.121939725361908e+00
 
  
−
-1.213218743783253e-14 9.540042296620362e-14
+
1.000000000000282e+00 7.742365792116463e-14
−
1.297490331797821e+00 -3.349764345312171e-01
+
1.999999999999288e+00 -1.777128279159746e-14
−
-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
 
For summary of all solutions refer to ApCoCoAServer
−
 
+
------------------------------------------
−
------------------------------------
 
 
</example>
 
</example>
  
Line 89: Line 45:
 
   <type>cocoaserver</type>
 
   <type>cocoaserver</type>
 
</types>
 
</types>
−
<key>bsolve</key>
+
<key>bmsolve</key>
−
<key>solve zero dimensional polynomial system</key>
+
<key>solve zero dimensional Non-homogeneous polynomial system using mult-homogenization</key>
−
<key>solve b</key>
+
<key>solve bm</key>
 
<key>eullah</key>
 
<key>eullah</key>
 
<wiki-category>Package_bertini</wiki-category>
 
<wiki-category>Package_bertini</wiki-category>
 
</command>
 
</command>

Revision as of 10:12, 20 April 2009

BMSolve

Solves zero dimensional Non-Homogeneous polynomial system using Mult-homogenization with Default Configurations.

Syntax

Bertini.BMSolve(M: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.

Example

-- We want to solve the non-homogenous system x[1]^2+x[2]^2-5=0, x[1]x[2]-2=0, using multi-homogenization. 

Use S ::= QQ[x[1..2]];             --  Define appropriate ring 
M := [x[1]^2+x[2]^2-5, x[1]x[2]-2];

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

-- And we achieve:
----------------------------------------
The number of real finite solutions are:
4       
The real finite solutions are:
                                         
-2.000000000000035e+00 2.454024452036439e-14
-9.999999999999871e-01 -1.788069996029196e-15

-9.999999999999907e-01 -1.089397896007851e-14
-2.000000000000040e+00 2.607382514440176e-14

1.999999999999310e+00 2.357507317170427e-13
1.000000000000226e+00 -9.624182470906783e-14

1.000000000000282e+00 7.742365792116463e-14
1.999999999999288e+00 -1.777128279159746e-14

For summary of all solutions refer to ApCoCoAServer
------------------------------------------





Retrieved from "http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Bertini.BMSolve&oldid=8315"