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

From ApCoCoAWiki
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This function solves a polynomial system of equations using multihomogeneous homotopy. The system of polynomials must be square. If the system has N variables then multihomogeneous homotopy will introduce N homogeneous variables to solve the system.
+
This function solves a polynomial system of equations using multihomogeneous homotopy. The system of polynomials must be square. If the system has N variables then multihomogeneous homotopy will introduce N homogeneous variables to solve the system. It uses total degree homotopy to find all isolated solutions and default configurations provided by Bertini. The system of polynomials should be non-homogeneous. The output will be the list of all finite solutions.  
 
<itemize>
 
<itemize>
 
<item>@param <em>P</em>: List of polynomials of the given system.</item>
 
<item>@param <em>P</em>: List of polynomials of the given system.</item>
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-- And we achieve a list of lists containing finite solutions.
 
-- 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(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000),
  Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)],
+
  Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000)
  [Vector(-2, 1724810333092189/1000000000000000000000000000000),
+
],
  Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)],
+
[
  [Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000),
+
  Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000),
  Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]]
+
  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 Bertini output files refer to ApCoCoA directory/Bertini.
 
--For Bertini output files refer to ApCoCoA directory/Bertini.
 
------------------------------------------
 
------------------------------------------

Revision as of 10:10, 13 May 2010

Bertini.BMSolve

Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations.

Syntax

Bertini.BMSolve(P: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.


This function solves a polynomial system of equations using multihomogeneous homotopy. The system of polynomials must be square. If the system has N variables then multihomogeneous homotopy will introduce N homogeneous variables to solve the system. It uses total degree homotopy to find all isolated solutions and default configurations provided by Bertini. The system of polynomials should be non-homogeneous. The output will be the list of all finite solutions.

  • @param P: List of polynomials of the given system.

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

Example

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

Use S ::= QQ[x[1..2]];             
P := [x[1]^2+x[2]^2-5, x[1]x[2]-2];

-- Then we compute the solution with
Bertini.BMSolve(P);

-- 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 Bertini output files refer to ApCoCoA directory/Bertini.
------------------------------------------




See also

Bertini.BCMSolve

Bertini.BSolve

Bertini.BUHSolve



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