Difference between revisions of "ApCoCoA-1:Bertini.BSolve"
From ApCoCoAWiki
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<example> | <example> | ||
| − | -- | + | -- An example of zero dimensional Non-Homogeneous Solving. |
-- We want to solve zero dimensional non-homogeneous system x^2+y^2-5=0, xy-2=0. | -- We want to solve zero dimensional non-homogeneous system x^2+y^2-5=0, xy-2=0. | ||
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</example> | </example> | ||
<example> | <example> | ||
| − | -- | + | -- An example of zero dimensional Homogeneous Solving |
-- We want to solve zero dimensional homogeneous system x^2-z^2=0, xy-z^2=0. | -- We want to solve zero dimensional homogeneous system x^2-z^2=0, xy-z^2=0. | ||
Revision as of 08:50, 12 May 2010
Bertini.BSolve
Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.
Syntax
Bertini.BSolve(P: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 system P.
Example
-- An example of 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]; 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 ApCoCoA directory/Bertini.
Example
-- An example of 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]; 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 ApCoCoA directory/Bertini. ------------------------------------
See also
