ApCoCoA-1:Bertini.BSolve
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Revision as of 07:56, 8 July 2009 by 132.231.54.1 (talk)
Bertini.BSolve
Solves zero dimensional homogeneous or non-homogeneous polynomial systems 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 M: List of polynomials in the system.
@param SysTyp: Type of polynomials in the system. Homogeneous (hom) or nonhomogeneous (Nhom).
@return A list of lists containing the finite 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 M := [x^2+y^2-5, xy-2]; SysTyp := <quotes>Nhom</quotes>; -- Then we compute the solution with Bertini.BSolve(M,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-1.2/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-1.2/Bertini/). ------------------------------------
See also
