Difference between revisions of "ApCoCoA-1:Bertini.BMSolve"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Bertini.BMSolve</title> | <title>Bertini.BMSolve</title> | ||
| − | <short_description>Solves zero dimensional non-homogeneous polynomial system using multi-homogenization | + | <short_description>Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations.</short_description> |
<syntax> | <syntax> | ||
| − | Bertini.BMSolve( | + | Bertini.BMSolve(P:LIST):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| Line 9: | Line 9: | ||
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>P</em>: List of polynomials of the given system.</item> |
| − | <item>@return A list of lists containing the finite solutions of the polynomial system.</item> | + | <item>@return A list of lists containing the finite solutions of the polynomial system P.</item> |
</itemize> | </itemize> | ||
<example> | <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. | + | -- 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]]; | + | 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 | -- Then we compute the solution with | ||
| − | Bertini.BMSolve( | + | Bertini.BMSolve(P); |
| − | -- 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(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000), | ||
| Line 32: | Line 32: | ||
[Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000), | [Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000), | ||
Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]] | Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]] | ||
| − | --For | + | --For Bertini output files refer to ApCoCoA directory/Bertini. |
------------------------------------------ | ------------------------------------------ | ||
</example> | </example> | ||
Revision as of 09:35, 12 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.
@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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