Bertini.BCMSolve |
Syntax |
Bertini.BCMSolve(P:LIST, ConfigSet:LIST) |
Description |
Example |
-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. Use S ::= QQ[x,y]; P := [x^2+y^2-5,xy-2]; ConfigSet := ["MPTYPE: 2"]; -- Then we compute the solution with Bertini.BCMSolve(P,ConfigSet); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [ [ Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000), Vector(49999999999999/25000000000000, -3537662353156057/100000000000000000000000000000) ], [ Vector(-62500000000003/62500000000000, 4415730565392687/100000000000000000000000000000), Vector(-499999999999983/250000000000000, -66866973306543/400000000000000000000000000) ], [ Vector(999999999999983/500000000000000, -1787591178181031/50000000000000000000000000000), Vector(1000000000000013/1000000000000000, 281412486737749/25000000000000000000000000000) ], [ Vector(-499999999999999/250000000000000, -3956938527452181/1000000000000000000000000000000), Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
--The same example as above but this time using regeneration. --Regeneration is an equation-by-equation method for finding the non-singular isolated solutions. -- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. Use S ::= QQ[x,y]; P := [x^2+y^2-5,xy-2]; ConfigSet := ["USEREGENERATION: 1"]; -- Then we compute the solution with Bertini.BCMSolve(P,ConfigSet); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [ [ Vector(9999999999999999/10000000000000000, -643977180168769/1250000000000000000000000000000), Vector(2, 1660674691787513/5000000000000000000000000000000) ], [ Vector(-2000000000000001/1000000000000000, 584020313856301/500000000000000000000000000000), Vector(-9999999999999999/10000000000000000, 45486167963413/125000000000000000000000000000) ], [ Vector(2, 2989952880295369/1000000000000000000000000000000), Vector(9999999999999993/10000000000000000, 732258034227497/5000000000000000000000000000000) ], [ Vector(-1, -879366755419571/5000000000000000000000000000000), Vector(-2, 4460430333228999/10000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- We want to solve the non-homogenous polynomial system (29/16)z[1]^3 - 2z[1]z[2]=0, z[2] - z[1]^2=0, using multi-homogenization. -- In addition suppose we want Bertini to follow the paths very closely (correct to 8 digits before the endgame and correct to 11 -- digits when running the endgame) and that you want the endgame to compute approximations of each solution until successive -- approximations agree to at least 14 digits. Use S ::= QQ[z[1..2]]; P := [(29/16)z[1]^3 - 2z[1]z[2], z[2] - z[1]^2]; ConfigSet := ["TRACKTOLBEFOREEG: 1e-8", "TRACKTOLDURINGEG: 1e-11", "FINALTOL: 1e-14"]; -- Then we compute the solution with Bertini.BCMSolve(P,ConfigSet); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [ [ Vector(-6272142330887219272991421734532181259967888828557/2500000000000000000000000000000000000000000000000000000000000000, -16866585769960937068249054027382922938807741513177/100000000000000000000000000000000000000000000000000000000000000000), Vector(8805522460698904717783577526969974058842568093851/20000000000000000000000000000000000000000000000000000000000000000000000000, 371666764789855282623508352529304991388858172316/6250000000000000000000000000000000000000000000000000000000000000000000000000000) ], [ Vector(2800994767392818954296004874687536350261142130669/2000000000000000000000000000000000000000000000000000000000000000, -10442004545151043511524382737808469250701933034019/5000000000000000000000000000000000000000000000000000000000000000), Vector(-16863840390941893071858292951853672304120979133893/100000000000000000000000000000000000000000000000000000000000000000000000, -5137795605139651161672232162161044043786444504329/1250000000000000000000000000000000000000000000000000000000000000000000000000000) ], [ Vector(1745556907758497619927983789627389730399846491963/1250000000000000000000000000000000000000000000000000000000000000, 28437259304210599902269601024330245142947311467321/10000000000000000000000000000000000000000000000000000000000000000), Vector(-43119800109410418470261587328237339500316468515037/100000000000000000000000000000000000000000000000000000000000000000000000, 11161237954525426581510768500892187905929449123739/2000000000000000000000000000000000000000000000000000000000000000000000000000000) ] ] --For Bertini output files refer to ApCoCoA directory/Bertini. ------------------------------------------ |
See Also |