Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_03_PD.dat at {9.4002284322997349923473005467386795415424329150000e-1 ,0 ,7.4077518339434003212979996565337404848312284398669e-2 ,0 ,1.0753858702167459588650180961091416844057472100581e-1 ,0 }
Validate the existence of a branch of period-1 points:
proveBranchHaloOrbits(this->cr3bpFixPointsSolver.pm,this->cr3bpFixPointsSolver.pm,c,s,this->fp,0,4,2,3,5,&(this->Dfp)): true
############################

y0[i][3]=[-9.0636024933824934672735602650239963070485066257867e-34 ,9.0635911846411211688812278732206002466242547973176e-34 ]
D0[i][3][0]=[1.3959816040640292857944703728962633773058280363818 ,1.3959816040640292857944703728988737432985580749101 ]
D0[i][3][2]=[-2.6350040264045923547623677653903772707416949389972e-30 ,2.6350043015969649437618160231609407594882882871866e-30 ]
dy0=[-2.6425140872324720488391180373536231211276621955979e-32 ,9.5343758095470065150882098227274847264188413359045e-33 ]
Ddy=[6.0238598939714176557128055665660965022237412495225 ,6.0238598939714578995028131184514118022378165852388 ]
dy=[-1.5827685200794355908464383462123284726766016963090e-33 ,4.3867455979131549106661657635707155437521670584971e-33 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-8.3066081966751539588930727349531521652200849254944e-32 ,8.3066079402463851348118675830132863142280266912565e-32 ]
D0[i][3][0]=[-7.1514927716662268123687374173445491056939712617560e-29 ,7.1514928022375838746546753386597286624828087753554e-29 ]
D0[i][3][2]=[-2.5337695592433762797087332862151236371807789704246e-28 ,2.5337695723104852046382393373598991719373794631881e-28 ]
dy0=[-1.5741782331923790210076891253669860446713773709959e-31 ,8.3066079402466387779218810294352323929460912011945e-32 ]
Ddy=[3.9208420989228926374097812546216011791094633676729e1 ,3.9208420989229299733243617312470999878942055411619e1 ]
dy=[-2.1185775225502129314717520911993679056369164064513e-33 ,4.0148983138719783548537836070529050753303475223482e-33 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

Intersection of two enclosures of dy(x,z) along fixed point curve:
intersection(r[4],fp[4],fp[4]): true
############################

DBif[i][3][4]=[6.0238598939714377776078093424958682071361346363027 ,6.0238598939714377776078093425216400973254231984586 ]
D0[i][5][0]=[-1.3525842050350906391063179527079758025274182421199 ,-1.3525842050350906391063179527023494963392708958039 ]
D0[i][3][0]=[1.3959816040640292857944703728962633773058280363818 ,1.3959816040640292857944703728988737432985580749101 ]
DBif[i][5][0]=[-1.3525842050350906391063179527080254898329300131411 ,-1.3525842050350906391063179527022998090337591247827 ]
DBif[i][3][0]=[1.3959816040640292857944703728958339461689947483700 ,1.3959816040640292857944703728993031744353913629219 ]
D[k][3][4]=[6.0238598939714303166803616799380278580041968054381 ,6.0238598939714452385352570050794804464573610293233 ]
_H(5,0,0)=[4.9857106567954933419717674876300324751004538558511e1 ,4.9857106568877083261300891219368422906580215478681e1 ]
_H(5,0,2)=[-1.3059705713189705875727148793879757714157379331045e2 ,-1.3059705713029489301101740765544353094525636967814e2 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[3.9208420989229113053670714928171097344196771884330e1 ,3.9208420989229113053670714930515914325839917204018e1 ]
D0[i][5][0]=[-4.9372335230876399868156727672368278903040883413557e-29 ,4.9372334976778472965668136651571043309937104823058e-29 ]
D0[i][3][0]=[-7.1514927716662268123687374173445491056939712617560e-29 ,7.1514928022375838746546753386597286624828087753554e-29 ]
DBif[i][5][0]=[-4.9615070298576998806058024729538184513620664738095e-29 ,4.9615070044479071903569433708740948920516886147596e-29 ]
DBif[i][3][0]=[-7.1716005645368743296769264301752154986373826292241e-29 ,7.1716005951082313919628643514903950554262201428234e-29 ]
D[k][3][4]=[3.9208420989229061316578996684819737507418935757467e1 ,3.9208420989229164790762433173867274162617753330881e1 ]
_H(5,0,0)=[-5.8273753000077999300576054679487064443483210306550e-9 ,5.8273753000073635947928469659909719131677095430893e-9 ]
_H(5,0,2)=[-1.2226690155630171987698572214622889897985860242209e2 ,-1.2226690148501884085528303214621337364470586290071e2 ]
g=[-9.9920098495825061546784093433682703433080768987005e-29 ,9.9920098456797369825076656809730273547104645534448e-29 ]
Dg=[-1.2226690155630171987698572923580674107877601994760e2 ,-1.2226690148501884085528302505663553154579052613977e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-8.1722933420430306938161717692096169202680244472072e-31 ,8.1722933388510227793529566790873416522350274595425e-31 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-1.2165988077152720798937722496021948256404695686518e-15 ,1.2165988077152724369609697999063539387889943294311e-15 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.7926414516186018197363946774229527488895220330129e-16 ,3.7926414516186030674091343123674132088936391929685e-16 ],[0 ,0 ]}
DH[2]=[-4.0437655423458325679031767274670485541365249066528e-1 ,-4.0437655423458325679031767271100132184088707991966e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-4.0437655423458326713229591872028362264602531853022e-1 ,-4.0437655423458324644833942673741915238753027477643e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[3.9208420989229113053670714923942990444260713537595e1 ,3.9208420989229113053670714934744021227427427613009e1 ]
_H(5,0,0)=[-4.2768829992107719053456548548470897752285868359998e-16 ,4.2768829901967516959433559785241534803242967330835e-16 ]
_H(5,0,2)=[-1.2226690152066028254925488896255693621774904406340e2 ,-1.2226690152066027818301284197825101428635175068999e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.4979891908752407598217495111592540056072244082943e-18 ,3.4979891835028283593331855921798692417393226645467e-18 ],[0 ,0 ],[-5.7324960618437180236003507873082013112263509638302e-20 ,5.7324960739256093131861649400584688066491608156629e-20 ],[0 ,0 ]}
DH*T2=[-1.4160679805731257977380549521513360018502230605601e-18 ,1.4160679835576510755994704886746607826325346667759e-18 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[8.0967284188985178702436092780673534149146250991405 ,8.0967284189788926878215075846094158975737165392859 ],[0 ,0 ],[-4.3217389130848734013742095101102038897530684068267e-1 ,-4.3217389130848196143513557807904603802464143594651e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-4.9661667710470932368066460801075302000755471037470 ,-4.9661667710145913714985952297489652867778831226230 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0090943496211074826379101851939367616810141910138 ,3.0090943496211074826379101851985718437097666467247 ]
dat/JupiterL1_03_PD.dat at {9.4002284322997349923473005467386795415424329150000e-1 ,0 ,7.4077518339434003212979996565337404848312284398669e-2 ,0 ,1.0753858702167459588650180961091416844057472100581e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:34:08 2018
elapsed time: 0hours 58minutes 12seconds