Difference between revisions of "ApCoCoA-1:Bertini.BMSolve"
From ApCoCoAWiki
| Line 9: | Line 9: | ||
| − | 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> | ||
| Line 26: | Line 26: | ||
-- 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(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000), | |
| − | Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)], | + | Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000) |
| − | + | ], | |
| − | Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)], | + | [ |
| − | + | 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
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