Bertini.BPCSolve |
Syntax |
Bertini.BPCSolve(P:LIST, SysTyp:STRING , ConfigSet:LIST):LIST |
Description |
Example |
-- An example of homogeneous positive dimensional solving with default configurations. -- We want to solve a positive dimensional homogeneous system x^2-wy=0, x^3-zw^2=0. Use S ::= QQ[x,y,z,w]; P := [x^2-wy, x^3-zw^2]; SysTyp := "hom"; ConfigSet := ["TRACKTYPE: 1"]; -- Then we compute the solution with Bertini.BPCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing witness point supersets. ---------------------------------------- [ [ Vector(-755572432434347/12500000000000000, 1212469385646449/500000000000000000), Vector(1298004943638751/5000000000000000, -1142577751598529/10000000000000000), Vector(-2342040006871913/2500000000000000, 1179799639878209/1250000000000000), Vector(609385691937087/50000000000000000, 211745411898973/50000000000000000) ], [ Vector(1261061851901631/2500000000000000, 2488819338268271/5000000000000000), Vector(2282600091308383/5000000000000000, -1003166917277761/5000000000000000), Vector(-1266611634699783/100000000000000000, -3506599942546397/10000000000000000), Vector(-245572945934717/625000000000000, 2318280651577719/2500000000000000) ], [ Vector(-5499850009487371/10000000000000000, -1238476107570149/1000000000000000), Vector(1731610073705601/2000000000000000, -4674149620192353/10000000000000000), Vector(966993267243377/2500000000000000, 1501592012502773/2500000000000000), Vector(-1758972965024007/1000000000000000, 6238313035434359/10000000000000000) ], [ Vector(-1674674005500441/50000000000000000000000000000000, -139223041258509/4000000000000000000000000000000), Vector(2733406006983317/10000000000000000, -210607026124287/2000000000000000), Vector(-918496799516071/1000000000000000, 1142768401415781/1250000000000000), Vector(13944005158723/1250000000000000000000000000000, -3407948311604289/100000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of homogenous positive dimensional solving with user configurations. -- We want to solve a positive dimensional homogenous polynomial system x^2-wy=0, x^3-zw^2=0, for fixed higher precision. Use S ::= QQ[x,y,z,w]; P := [x^2-wy, x^3-zw^2]; SysTyp := "hom"; ConfigSet := ["TRACKTYPE: 1", "MPTYPE: 1", "PRECISION: 128"]; -- Then we compute the solution with Bertini.BPCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing witness point supersets. ---------------------------------------- [ [ Vector(-3789467495454911613823851164626681463651/10000000000000000000000000000000000000000, 1200734725407166211921788902942849185503/1000000000000000000000000000000000000000), Vector(-246001393466366309986866914393676541221/125000000000000000000000000000000000000, -279722792064708736248520972068122497257/500000000000000000000000000000000000000), Vector(4083988954899604873030242779673433634501/5000000000000000000000000000000000000000, -1611351492565067582850937617799756261201/500000000000000000000000000000000000000), Vector(7319342772891341731507480575523588267957/10000000000000000000000000000000000000000, 19870617690036348352514491511362841819/78125000000000000000000000000000000000) ], [ Vector(3048866987455758258878751406208402973051/10000000000000000000000000000000000000000, -2898035102105205140344370335032912017083/5000000000000000000000000000000000000000), Vector(-5539460172405722710678127397246600460333/10000000000000000000000000000000000000000, 626442207647239461619975960511872586713/5000000000000000000000000000000000000000), Vector(986380263365471019267174885767305829617/2500000000000000000000000000000000000000, 736987741407866469670001545005869554379/2500000000000000000000000000000000000000), Vector(1400107689781321399920833229898425820819/5000000000000000000000000000000000000000, 2191732091470400698700321524968735909/3125000000000000000000000000000000000) ], [ Vector(354996962262331142136973979259558150991/400000000000000000000000000000000000000, 1816598489416934847206968307485748462499/1000000000000000000000000000000000000000), Vector(1967511413109990263685197237623604100867/1000000000000000000000000000000000000000, 1727412577136936817572423873769337954923/1000000000000000000000000000000000000000), Vector(803360350133974614907008034061208613233/250000000000000000000000000000000000000, 1081558694105850161535777129438751374871/1000000000000000000000000000000000000000), Vector(9143301947447558293770285751969676840889/100000000000000000000000000000000000000000, 155856385824660750993297595625859090071/100000000000000000000000000000000000000) ], [ Vector(-825065032224960020386592540685453030181/50000000000000000000000000000000000000000000000000000000000000000000000000, -870815934189224420445215323683468742119/50000000000000000000000000000000000000000000000000000000000000000000000000), Vector(-2670487187708557160891411850766573823343/1000000000000000000000000000000000000000, 2412331000084757896737353053811227631099/2500000000000000000000000000000000000000), Vector(-2260897026243730139776564722393608088003/1000000000000000000000000000000000000000, -5881973549623185468407939053314195499303/10000000000000000000000000000000000000000), Vector(-6276316819449156764984023481918376370437/1000000000000000000000000000000000000000000000000000000000000000000000000000, -457717591175786069863350181676761297761/25000000000000000000000000000000000000000000000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of homogeneous positive dimensional solving with user configurations. -- We want to find the numerical irreducible decomposition of the twisted cubic, x^2-wy=0, xy-wz=0, xz-y^2=0. -- In addition we want to instruct Bertini to use dimension by dimension slicing for witness superset generation to compute the -- numerical irreducible decomposition of the twisted cubic. Use S ::= QQ[x,y,z,w]; P := [x^2-wy, xy-wz, xz-y^2]; SysTyp := "hom"; ConfigSet := ["TRACKTYPE: 1", "WITNESSGENTYPE: 1"]; -- Then we compute the solution with Bertini.BPCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing witness point supersets. ---------------------------------------- [ [ Vector(-6942026116799083/100000000000000000, 4612445857279657/10000000000000000), Vector(-660130555588941/2500000000000000, -3406132801364543/10000000000000000), Vector(1980599587423497/5000000000000000, 4074862446889013/100000000000000000), Vector(258142996733279/625000000000000, -580518904347863/2000000000000000) ], [ Vector(333984658654543/400000000000000, 2114142485709457/10000000000000000), Vector(2502940254499371/5000000000000000, 166534572523981/400000000000000), Vector(2057347374261689/10000000000000000, 223561664132829/500000000000000), Vector(1117184759814529/1000000000000000, -2238949523369569/10000000000000000) ], [ Vector(2522626882012411/10000000000000000, -449777889912661/2500000000000000), Vector(-3124384466089009/10000000000000000, -3468473241908347/10000000000000000), Vector(-465770235043267/1000000000000000, 2634944111403243/5000000000000000), Vector(9964067241416377/100000000000000000, 224882867669343/1250000000000000) ], [ Vector(-8958209355386233/10000000000000000, 5991364293445607/10000000000000000), Vector(4479104677693117/5000000000000000, 748920536680701/1250000000000000), Vector(4479104677693117/5000000000000000, 748920536680701/1250000000000000), Vector(4479104677693117/5000000000000000, 748920536680701/1250000000000000) ], [ Vector(838951317127217/5000000000000000, 1225282193168769/2000000000000000), Vector(2669420883548849/10000000000000000, -542051267199167/1250000000000000), Vector(-4000931691247049/10000000000000000, 2026256168319313/25000000000000000), Vector(-1753050275159781/2500000000000000, -3689466057646187/10000000000000000) ], [ Vector(1994140751299623/5000000000000000, -571186186780739/12500000000000000), Vector(417774557591413/2500000000000000, -4720503734495957/10000000000000000), Vector(-4376288560752593/10000000000000000, -4457205772193031/10000000000000000), Vector(866134273205727/5000000000000000, 2712167348922953/10000000000000000) ], [ Vector(-3041727474132977/5000000000000000, -1407307897083329/10000000000000000), Vector(129825645247897/312500000000000, -349049200579/1250000000000), Vector(-6388578727727609/100000000000000000, 3961667379950517/10000000000000000), Vector(3899466643358429/10000000000000000, 3371280434832643/5000000000000000) ], [ Vector(-3521791211952947/10000000000000000, 1053118768909601/5000000000000000), Vector(3521791211952947/10000000000000000, -1053118768909601/5000000000000000), Vector(-3521791211952947/10000000000000000, 1053118768909601/5000000000000000), Vector(3521791211952947/10000000000000000, -2106237537819201/10000000000000000) ], [ Vector(7754466790293177/10000000000000000, 9327014277087599/1000000000000000000), Vector(4140435604899347/10000000000000000, 8742834549314157/10000000000000000), Vector(-3766519251579417/5000000000000000, 9426940170746841/10000000000000000), Vector(559053891116487/2000000000000000, -5553052894825133/10000000000000000) ], [ Vector(0, 0), Vector(0, 0), Vector(-9187908867396413/10000000000000000, 3764804692184237/10000000000000000), Vector(9038104431042463/100000000000000000000000000000000, 1369503460549361/10000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- Deflation Example -- An example of Non-homogeneous positive dimensional solving with user configurations. -- We want to find the numerical irreducible decomposition of the curve, (29/16)x^3-2xy=0, y-x^2=0. -- In addition we want to instruct Bertini to sharpen the witness points for each component to 30 digits. Bertini automatically -- deates the components that are generically nonreduced. In this case the isolated solution at the origin is correct to at least -- 30 digits. Use S ::= QQ[x,y]; P := [(29/16)x^3-2xy, y-x^2]; SysTyp := "Nhom"; ConfigSet := ["TRACKTYPE: 1", "SHARPENDIGITS: 30"]; -- Then we compute the solution with Bertini.BPCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing witness point supersets. ---------------------------------------- [ [ Vector(-144037547051541/25000000000000000000000000000000000000, 1194673810665003/1250000000000000000000000000000000000000), Vector(3960923778190771/10000000000000000000000000000000000000000, 2427766741188941/1000000000000000000000000000000000000000) ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini. |
See Also |