Difference between revisions of "ApCoCoA-1:Bertini.BCMSolve"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Bertini.BCMSolve</title> | <title>Bertini.BCMSolve</title> | ||
| − | <short_description>Solves zero dimensional non-homogeneous polynomial system using multi-homogenization | + | <short_description>Solves a zero dimensional non-homogeneous polynomial system of equations using multi-homogenization and user configurations.</short_description> |
<syntax> | <syntax> | ||
| − | Bertini.BCMSolve( | + | Bertini.BCMSolve(P:LIST, ConfigSet:LIST) |
</syntax> | </syntax> | ||
<description> | <description> | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. 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. | ||
<itemize> | <itemize> | ||
| − | <item>@param <em>M</em>: List of polynomials | + | <item>@param <em>M</em>: List of polynomials of the given system.</item> |
| − | <item>@param <em>ConfigSet</em>: List of strings representing | + | <item>@param <em>ConfigSet</em>: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then leave this list empty. For details about configuration settings see Bertini mannual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</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> | ||
| Line 18: | Line 20: | ||
-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. | -- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. | ||
| − | Use S ::= QQ[x,y]; | + | Use S ::= QQ[x,y]; |
| − | + | P := [x^2+y^2-5,xy-2]; | |
ConfigSet := [<quotes>MPTYPE: 2</quotes>]; | ConfigSet := [<quotes>MPTYPE: 2</quotes>]; | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | Bertini.BCMSolve( | + | Bertini.BCMSolve(P,ConfigSet); |
| − | -- And we achieve a list of lists containing finite solutions | + | -- And we achieve a list of lists containing finite solutions. |
---------------------------------------- | ---------------------------------------- | ||
[[Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000), | [[Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000), | ||
| Line 36: | Line 38: | ||
Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000)]] | Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000)]] | ||
| − | --For | + | --For Bertini output files please refer to ApCoCoA directory/Bertini. |
</example> | </example> | ||
Revision as of 10:33, 12 May 2010
Bertini.BCMSolve
Solves a zero dimensional non-homogeneous polynomial system of equations using multi-homogenization and user configurations.
Syntax
Bertini.BCMSolve(P:LIST, ConfigSet: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.
@param M: List of polynomials of the given system.
@param ConfigSet: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then leave this list empty. For details about configuration settings see Bertini mannual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
@return A list of lists containing the finite solutions of the polynomial system P.
Example
-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. Use S ::= QQ[x,y]; P := [x^2+y^2-5,xy-2]; ConfigSet := [<quotes>MPTYPE: 2</quotes>]; -- Then we compute the solution with Bertini.BCMSolve(P,ConfigSet); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [[Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000), Vector(49999999999999/25000000000000, -3537662353156057/100000000000000000000000000000)], [Vector(-62500000000003/62500000000000, 4415730565392687/100000000000000000000000000000), Vector(-499999999999983/250000000000000, -66866973306543/400000000000000000000000000)], [Vector(999999999999983/500000000000000, -1787591178181031/50000000000000000000000000000), Vector(1000000000000013/1000000000000000, 281412486737749/25000000000000000000000000000)], [Vector(-499999999999999/250000000000000, -3956938527452181/1000000000000000000000000000000), Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000)]] --For Bertini output files please refer to ApCoCoA directory/Bertini.
See also
