Difference between revisions of "ApCoCoA-1:Bertini.BPMCSolve"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Bertini.BPMCSolve</title> | <title>Bertini.BPMCSolve</title> | ||
| − | <short_description> | + | <short_description>Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.</short_description> |
<syntax> | <syntax> | ||
| − | Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST) | + | Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
<em>Please note:</em> | <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. | 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> | + | <par/> |
| − | You need to write(or generate by using the function BPCSolve ) the witness date file and save it with the name | + | <em>Please note:</em> You need to write (or generate by using the function <ref>Bertini.BPCSolve</ref>) the witness date file and save it with the name <quotes>witness_data</quotes> in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message. |
<itemize> | <itemize> | ||
<item>@param <em>M</em>: List of polynomials in the system.</item> | <item>@param <em>M</em>: List of polynomials in the system.</item> | ||
| − | <item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or | + | <item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or non-homogeneous (<tt>Nhom</tt>).</item> |
| − | <item>@param <em>MPoints</em>: List of lists | + | <item>@param <em>MPoints</em>: List of lists containig member points.</item> |
| − | <item>@param <em>ConfigSet</em>: List of strings representing | + | <item>@param <em>ConfigSet</em>: List of strings representing configurations to be used by Bertini. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item> |
</itemize> | </itemize> | ||
Revision as of 09:13, 7 July 2009
Bertini.BPMCSolve
Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.
Syntax
Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet: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.
Please note: You need to write (or generate by using the function Bertini.BPCSolve) the witness date 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 non-homogeneous (Nhom).
@param MPoints: List of lists containig member points.
@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.
Example
-- Membership testing.
-- We want to test membership for the points [[[1.0, 0.0],[0.0, 0.0],[0.0, 0.0 ]],[[1.3650269, -0.31430820],
-- [1.7645087, -0.85807828],[2.1389007, -1.7258994]]], where the polynomial system is
-- x^2+y^2+z^2-1=0, x^3+y^2+z^3-1=0, (y-x^2)*(z-x^3)(z-5)=0.
Use S ::= QQ[x,y,z]; -- Define appropriate ring
M := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)];
SysTyp := <quotes>Nhom</quotes>;
MPoints :=[[["1.0", "0.0"],["0.0", "0.0"],["0.0", "0.0" ]],[["1.3650269", "-0.31430820"],
["1.7645087", "-0.85807828"],["2.1389007", "-1.7258994"]]];
ConfigSet := ["TRACKTYPE: 3"];
-- Then we compute the witness point super sets with
$Bertini.BPMCSolve(M,SysTyp,MPoints,ConfigSet);
-- And we achieve a list of lists containing witness point supersets:
----------------------------------------
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
See also
