ApCoCoA-1:Bertini.BPCSSolve

From ApCoCoAWiki
Revision as of 12:51, 12 May 2010 by 132.231.10.53 (talk) (New page: <command> <title>Bertini.BPCSolve</title> <short_description>Solves, by finding witness point supersets, a positive dimensional homogeneous or non-homogeneous polynomial systems with user ...)
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Bertini.BPCSolve

Solves, by finding witness point supersets, a positive dimensional homogeneous or non-homogeneous polynomial systems with user defined configurations. You can also use this function for sampling.

Syntax

Bertini.BPCSolve(M:LIST, SysTyp:STRING ,  ConfigSet:LIST):LIST

Description

Please note:

Due to a Bug in Bertini.exe. Use of this function for doing sampling is not working at the moment. Sorry for inconvienience.

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.

Please note: For sampling you need to write (or generate by a positive dimensional run) the witness data file and save it with the name "witness_data" in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.

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

  • @param SysTyp: Type of polynomials in the system. Homogeneous (hom) or nonhomogeneous (Nhom).

  • @param ConfigSet: List of strings representing Configurations to be used by Bertini. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

  • @return A list of lists containing witness point supersets.


Example

-- Sampling example
-- We want to solve positive dimensional homogenous system (y-x^2)*(x^2+y^2+z^2-1)*(x-5), (z-x^3)*(x^2+y^2+z^2-1)*(y-5),
-- (y-x^2)*(z-x^3)*(x^2+y^2+z^2-1)*(z-5).

Use S ::= QQ[x,y,z];             --  Define appropriate ring 
M := [(y-x^2)*(x^2+y^2+z^2-1)*(x-5), (z-x^3)*(x^2+y^2+z^2-1)*(y-5),(y-x^2)*(z-x^3)*(x^2+y^2+z^2-1)*(z-5)];
SysTyp := <quotes>Nhom</quotes>;
ConfigSet := [<quotes>TRACKTYPE: 2</quotes>];
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/). In this exammple we can use the following file.

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10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464

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4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232
11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808
10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464

3 0

4
1 0
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0 0
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4
4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232
11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808
10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464



-- Then we compute the solution with
$Bertini.BPCSolve(M,SysTyp,ConfigSet);



--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).



See also

Introduction to CoCoAServer

Bertini.BSolve

Bertini.BPMCSolve