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

From ApCoCoAWiki
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<itemize>
 
<itemize>
<item>@param <em>M</em>: List of polynomials in the system to be solved.</item>
+
<item>@param <em>M</em>: List of polynomials in the system.</item>
 
</itemize>
 
</itemize>
 
   
 
   
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Bertini.BMSolve(M);
 
Bertini.BMSolve(M);
  
-- And we achieve:
+
-- And we achieve a list of lists containing finite solutions:
 
----------------------------------------
 
----------------------------------------
The number of real finite solutions are:
+
[[Vector(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000),
4     
+
Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000)],
The real finite solutions are:
+
[Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000),
                                       
+
Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)],
-2.000000000000035e+00 2.454024452036439e-14
+
[Vector(-2, 1724810333092189/1000000000000000000000000000000),
-9.999999999999871e-01 -1.788069996029196e-15
+
Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)],
 
+
[Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000),
-9.999999999999907e-01 -1.089397896007851e-14
+
Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]]
-2.000000000000040e+00 2.607382514440176e-14
+
--For other Bertini output files refer to Bertini directory (../ApCoCoA-1.2/Bertini)
 
 
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
 
 
------------------------------------------
 
------------------------------------------
 
</example>
 
</example>

Revision as of 10:51, 1 July 2009

Bertini.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.

  • @param M: List of polynomials in the system.

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.BMSolve(M);

-- And we achieve a list of lists containing finite solutions:
----------------------------------------
[[Vector(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000),
 Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000)],
 [Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000),
 Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)],
 [Vector(-2, 1724810333092189/1000000000000000000000000000000),
 Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)],
 [Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000),
 Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]]
--For other Bertini output files refer to Bertini directory (../ApCoCoA-1.2/Bertini)
------------------------------------------



See also

Bertini.BCMSolve

Bertini.BCSolve

Bertini.BSolve

Bertini.BUHSolve



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