Bertini.BZCSolve |
Syntax |
Bertini.BZCSolve(P:LIST, SysTyp:STRING , ConfigSet:LIST):LIST |
Description |
Example |
-- An example of zero dimensional Non-homogenous solving with fixed higher precision. -- We want to solve the zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [x^2+y^2-5,xy-2]; SysTyp := "Nhom"; ConfigSet := ["MPTYPE: 1", "PRECISION: 128"]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all finite solutions. ---------------------------------------- [ [ Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, 41243336046164965623860294533917 3594181/200000000000000000000000000000000000000000000000000000), Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000, -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000) ], [ Vector(999999999999996907691691548150283767063/500000000000000000000000000000000000000, 4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000), Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000, -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000) ], [ Vector(-1999999999999981470621955122058645854307/1000000000000000000000000000000000000000, -2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000, 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000) ], [ Vector(-9999999999999986714415752390569533003343/10000000000000000000000000000000000000000, 2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000, -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000) ] ] --The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) --represents the complex number 5000/1000-4150/1000i. --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of regeneration -- Regeneration is an equation-by-equation method for finding the non-singular isolated solutions. Use S ::= QQ[x,y,z]; P := [ (x^2-y)(x^2+y^2+z^2-1)(x-1/2), (x^3-z)(x^2+y^2+z^2-1)(y-1/2), (x^2-y)(x^3-z)(x^2+y^2+z^2-1)(z-1/2) ]; SysTyp := "Nhom"; ConfigSet := ["USEREGENERATION: 1"]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all finite solutions. ---------------------------------------- [ [ Vector(1/2, -1400610179539509/5000000000000000000000000000000), Vector(5000000000000001/10000000000000000, -7779179774559159/10000000000000000000000000000000), Vector(1/2, -4045284236617077/10000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of zero dimensional homogenous solving with fixed higher precision -- We want to solve the zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [x^2-z^2, xy-z^2]; SysTyp := "hom"; ConfigSet := ["MPTYPE: 1", "PRECISION: 128"]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all real solutions. ---------------------------------------- [ [-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000 ], [ -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, 666269356331265789905402745641735631587/1250000000000000000000000000000000000000 ], [ -1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000, 1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000 ], [ -1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000, 3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000 ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of zero dimensional Non-homogenous solving. -- We want to solve the zero dimensional homogenous system x^2-1=0, xy-1=0. -- In addition we want Bertini to solve the polynomial system using secure path tracking (SECURITYLEVEL: 1), tighter tracking -- tolerances all along the paths ( TRACKTOLBEFOREEG: 1e-7 and TRACKTOLDURINGEG: 1e-7 ), tighter convergence tolearance for the -- endgame ( FINALTOL: 1e-12 ), and sets the adaptive precision settings appropriately for the system -- (COEFFBOUND: 2 and DEGREEBOUND: 2). Bertini now computes the solutions at infinity using the settings requested. Use S ::= QQ[x,y]; P := [x^2-1, xy-1]; SysTyp := "Nhom"; ConfigSet := ["SECURITYLEVEL: 1", "TRACKTOLBEFOREEG: 1e-7" , "TRACKTOLDURINGEG: 1e-7", "FINALTOL: 1e-12", "COEFFBOUND: 2" , "DEGREEBOUND: 2"]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all finite solutions. ---------------------------------------- [ [Vector(1, 0), Vector(1, 0)], [Vector(-1, 0), Vector(-1, 0)] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
See Also |