Difference between revisions of "ApCoCoA-1:Bertini.BSolve"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Bertini.BSolve</title> | <title>Bertini.BSolve</title> | ||
| − | <short_description>Solves zero dimensional homogeneous or non-homogeneous polynomial | + | <short_description>Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.</short_description> |
<syntax> | <syntax> | ||
Bertini.BSolve(M:LIST, SysTyp:STRING) | Bertini.BSolve(M:LIST, SysTyp:STRING) | ||
| Line 9: | Line 9: | ||
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>P</em>: List of polynomials of the given system.</item> |
| − | <item>@param <em>SysTyp</em>: Type of polynomials in the | + | <item>@param <em>SysTyp</em>: Type of polynomials in the list P. Homogeneous (<tt><quotes>hom</quotes></tt>) or nonhomogeneous (<tt><quotes>Nhom</quotes></tt>).</item> |
<item>@return A list of lists containing the finite (or real) solutions of the polynomial system.</item> | <item>@return A list of lists containing the finite (or real) solutions of the polynomial system.</item> | ||
| Line 20: | Line 20: | ||
Use S ::= QQ[x,y]; -- Define appropriate ring | Use S ::= QQ[x,y]; -- Define appropriate ring | ||
| − | + | P := [x^2+y^2-5, xy-2]; | |
SysTyp := <quotes>Nhom</quotes>; | SysTyp := <quotes>Nhom</quotes>; | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | Bertini.BSolve( | + | Bertini.BSolve(P,SysTyp); |
-- And we achieve a list of lists containing all finite solutions: | -- And we achieve a list of lists containing all finite solutions: | ||
| Line 37: | Line 37: | ||
Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]] | Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]] | ||
| − | --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1. | + | --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/). |
</example> | </example> | ||
<example> | <example> | ||
| Line 48: | Line 48: | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | + | Bertini.BSolve(M,SysTyp); | |
-- And we achieve a list of lists containing all real solutions: | -- And we achieve a list of lists containing all real solutions: | ||
| Line 58: | Line 58: | ||
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]] | 1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]] | ||
| − | --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1. | + | --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/). |
------------------------------------ | ------------------------------------ | ||
</example> | </example> | ||
Revision as of 08:17, 12 May 2010
Bertini.BSolve
Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.
Syntax
Bertini.BSolve(M:LIST, SysTyp:STRING)
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.
@param SysTyp: Type of polynomials in the list P. Homogeneous ("hom") or nonhomogeneous ("Nhom").
@return A list of lists containing the finite (or real) solutions of the polynomial system.
Example
-- Zero Dimensional Non-Homogeneous Solving -- We want to solve zero dimensional non-homogeneous system x^2+y^2-5=0, xy-2=0. Use S ::= QQ[x,y]; -- Define appropriate ring P := [x^2+y^2-5, xy-2]; SysTyp := <quotes>Nhom</quotes>; -- Then we compute the solution with Bertini.BSolve(P,SysTyp); -- And we achieve a list of lists containing all finite solutions: ---------------------------------------- [[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000), Vector(9999999999999927/10000000000000000, 8966048861359829/1000000000000000000000000000000)], [Vector(2499999999999963/2500000000000000, 5007041073746771/100000000000000000000000000000), Vector(249999999999999/125000000000000, -1089183184148021/25000000000000000000000000000)], [Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000), Vector(-1999999999999999/1000000000000000, 2443331461729629/2500000000000000000000000000000)], [Vector(-250000000000001/125000000000000, 4347064 850996171/1000000000000000000000000000000), Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]] --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/).
Example
-- Zero Dimensional Homogeneous Solving -- We want to solve zero dimensional homogeneous system x^2-z^2=0, xy-z^2=0. Use S ::= QQ[x,y,z]; -- Define appropriate ring M := [x^2-z^2, xy-z^2]; SysTyp := <quotes>hom</quotes>; -- Then we compute the solution with Bertini.BSolve(M,SysTyp); -- And we achieve a list of lists containing all real solutions: ---------------------------------------- [[2190685167348543/5000000000000000, 2190685167348543/5000000000000000, 2190685167348543/5000000000000000], [1237092982347763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000], [3235177805819999/100000000000000000000000000000, 9932123317905381/10000000000000000, 621807549382663/5000000000000000000000000000], [3006769352985381/100000000000000000000000000000, 1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]] --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/). ------------------------------------
See also
