Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_10_PQ.dat at {-8.5111596196950856804454383279062837983993352840917e-1 ,0 ,6.9134536648007998139971500301223139275938183541152e-2 ,0 ,2.0222014945535467047482268710519235625508381098033 ,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]=[-3.0767280007775054646988074907494693218716003357970e-33 ,3.0767279922838803947608662580734562573502954002689e-33 ]
D0[i][3][0]=[3.5393781710921384662694464688925239531216608569369e-1 ,3.5393781710921384662694464689271849748585738050947e-1 ]
D0[i][3][2]=[-6.8614327979093001685960310856968047031255199368646e-31 ,6.8614328058950580256406133458236155118663818918534e-31 ]
dy0=[-5.4115560056009318435124737871763050207392140256882e-33 ,6.4362360170667757011821188356553393369583174254243e-33 ]
Ddy=[9.8283099592879743438268207108383938059256655552804 ,9.8283099592879848968825769329574017101874149180736 ]
dy=[-6.5486701617345591103836084091672328752356904476090e-34 ,5.5060900887511077075876414794730872329491228483906e-34 ]
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]=[-3.1847466600378057617611041656001713045402490493838e-31 ,3.1847466600095497943532571880500082484397083008483e-31 ]
D0[i][3][0]=[9.5507693570152487111551004478671203822398248638718e-3 ,9.5507693570152487111551006128596721271320185524512e-3 ]
D0[i][3][2]=[-3.3310532071800966622626870292697077348111571295887e-29 ,3.3310532072248599372310715934830743670687690299826e-29 ]
dy0=[-3.1853766973687871447262883863837648684778658037519e-31 ,3.1897790192693207779188272967375610668898591766641e-31 ]
Ddy=[4.6159100614984690949775091138021050553520011459330 ,4.6159100614984974088218334079199719923554407230362 ]
dy=[-6.9104011490072632012036690714171477135499418463969e-32 ,6.9008638706767046948065906826206921645293276451984e-32 ]
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]=[-1.8246063892107235758804161062357853973327818851036e-29 ,1.8246063892166800651659529189614587416998312594716e-29 ]
D0[i][3][0]=[3.5393781710921384662694464096751998478182154682257e-1 ,3.5393781710921384662694465281445090803458828412182e-1 ]
D0[i][3][2]=[-5.1651753873878468977065061857466029970308921819495e-27 ,5.1651753873835695548032919507688730590108433359157e-27 ]
dy0=[-1.8255837806649817035574402422043270673188187431951e-29 ,1.8248398720171675728721711034703005027677972982950e-29 ]
Ddy=[-7.9422593871255552960910756429855559694760741183268e1 ,-7.9422593871255305917151181934550178498825352691646e1 ]
dy=[-2.2985698296687066139454922894809492602877553855579e-31 ,2.2976331835437764550621783930020413429645309157811e-31 ]
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]=[-5.0734584465871998555735344714412257322957180399112e-28 ,5.0734584465874101088426091538046898223581439866849e-28 ]
D0[i][3][0]=[-2.2936203708793801820830461953947882188170486890168e-25 ,2.2936203708795811458362355478079700225933821151883e-25 ]
D0[i][3][2]=[-2.3587073274133931603312789050011196752368958973305e-25 ,2.3587073274132448752010795786894371886256951799812e-25 ]
dy0=[-5.0734847695789130096654004402331843950345446806627e-28 ,5.0734584465874336959393538735528470746401665220522e-28 ]
Ddy=[-2.7757744065835446261298120654991060145582834447411e1 ,-2.7757744065835169475377071836549848056048010372950e1 ]
dy=[-1.8277727316548997117950501683946366106639220435169e-29 ,1.8277632485386144396672911520995878988209878848332e-29 ]
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]=[9.8283099592879796203546988141487034870291354271780 ,9.8283099592879796203546988296470920290839450461760 ]
D0[i][5][0]=[4.8587160457378561040000218054234808012292908629121e-1 ,4.8587160457378561040000218054376708523672679728236e-1 ]
D0[i][3][0]=[3.5393781710921384662694464688925239531216608569369e-1 ,3.5393781710921384662694464689271849748585738050947e-1 ]
DBif[i][5][0]=[4.8587160457378561040000217990747823824242787399248e-1 ,4.8587160457378561040000218117863692711722800958109e-1 ]
DBif[i][3][0]=[3.5393781710921384662694464575933372686552101572668e-1 ,3.5393781710921384662694464802263716593250245047648e-1 ]
D[k][3][4]=[9.8283099592879785816877513741509565426742460838328 ,9.8283099592879806590216462696448389734388343895212 ]
_H(5,0,0)=[-9.5742058102303200593750811290628120671328803042501 ,-9.5742058101396642288993936973017892846145708898511 ]
_H(5,0,2)=[1.7320535876573147829148343209518900460700798423050e1 ,1.7320535876645629590106420345097336323787613787402e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[4.6159100614984832518996712350630057253753591766915 ,4.6159100614984832518996712866590713223320826922777 ]
D0[i][5][0]=[-9.8165705116752380450660596572885236165607635847637e-2 ,-9.8165705116752380450660596564275125839540880362013e-2 ]
D0[i][3][0]=[9.5507693570152487111551004478671203822398248638718e-3 ,9.5507693570152487111551006128596721271320185524512e-3 ]
DBif[i][5][0]=[-9.8165705116752380450660596576255336581556796063859e-2 ,-9.8165705116752380450660596560905025423591720145791e-2 ]
DBif[i][3][0]=[9.5507693570152487111551002363021322611281796687709e-3 ,9.5507693570152487111551008244246602482436637475521e-3 ]
D[k][3][4]=[4.6159100614984830626670726857529508568563836485282 ,4.6159100614984834411322698359691261908510582204410 ]
_H(5,0,0)=[-3.6602229963364238054964468253564154550200510695255e-1 ,-3.6602229205773378255960760048173167872243282198027e-1 ]
_H(5,0,2)=[1.2248246880614942580112037278482982332497653254640 ,1.2248246942781979886340378167042256345254979015881 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-7.9422593871255429439030969630809593321161876379770e1 ,-7.9422593871255429439030968733596144872424217495144e1 ]
D0[i][5][0]=[4.8587160457378561040000217787736316988559496571989e-1 ,4.8587160457378561040000218320875199546371086846159e-1 ]
D0[i][3][0]=[3.5393781710921384662694464096751998478182154682257e-1 ,3.5393781710921384662694465281445090803458828412182e-1 ]
DBif[i][5][0]=[4.8587160457378561040000217045191400092952501848611e-1 ,4.8587160457378561040000219063420116441978081569538e-1 ]
DBif[i][3][0]=[3.5393781710921384662694463800802748981594152914610e-1 ,3.5393781710921384662694465577394340300046830179829e-1 ]
D[k][3][4]=[-7.9422593871255433506362580073995210170577914723148e1 ,-7.9422593871255425371699358290410528023008179151766e1 ]
_H(5,0,0)=[8.2556686404961477832739506161441516333682869356107 ,8.2556687919378424177051583557049314129834226784661 ]
_H(5,0,2)=[-1.6805068573798539373827458918370944947390241289621e1 ,-1.6805068433822141032876644084904561154395027326564e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-2.7757744065835307868337608853260016739229060440940e1 ,-2.7757744065835307868337583638280891462401784379421e1 ]
D0[i][5][0]=[-1.2384874628325282309461971794389472145909123178437e-26 ,1.2384874628331364652356778374570185819457085823650e-26 ]
D0[i][3][0]=[-2.2936203708793801820830461953947882188170486890168e-25 ,2.2936203708795811458362355478079700225933821151883e-25 ]
DBif[i][5][0]=[-1.7303852202289974651189698678097001697849675218486e-26 ,1.7303852202296056994084505258277715371397637863698e-26 ]
DBif[i][3][0]=[-2.3054526655083926442560927745781283141374068771209e-25 ,2.3054526655085936080092821269913101179137403032925e-25 ]
D[k][3][4]=[-2.7757744065835310721082929516519881653058186935183e1 ,-2.7757744065835305015592262975021026548572657885178e1 ]
_H(5,0,0)=[-3.3777446832089343185211180334456720995405265064693e-6 ,3.3777446832089894025264124772050370473901122721901e-6 ]
_H(5,0,2)=[4.7195356735166311321331108160896064801029822066872 ,4.7195439304530479696091725517061069737224125106469 ]
g=[-1.7901932434017710011419936273497506402676961719457e-25 ,1.7901932434016893970251654373044223358510974539683e-25 ]
Dg=[4.7195356735166311321316228621552491287365371795197 ,4.7195439304530479696106605056404643250124498318593 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-3.7931554441832972619999536799605658556047690148878e-26 ,3.7931554441834701690875854278536697186904699240205e-26 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

Check intersection of two enclosures of hessian at bif point:intersection(H1,H[3],H[3]): true
############################

Check intersection of two enclosures of derivative at bif point:intersection(D1,D[3],D[3]): true
############################

T1={[-4.4051699400315153514093394841870691555368973618398e-16 ,4.4051699400315151252000989371608292353581739707902e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.8966231580731594816588369022086242353183617005265e-17 ,1.8966231580731594468196921584630446665268074758469e-17 ],[0 ,0 ]}
DH[2]=[3.1184920359313461549576987373891571107988345365415e-1 ,3.1184920359313461549577019234874184612536707481752e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[3.1184920359313453710897799598191121632654472629587e-1 ,3.1184920359313469388256207010574778076874226122397e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-2.7757744065835307868337619674164099779952886524422e1 ,-2.7757744065835307868337572817376808422171218074310e1 ]
_H(5,0,0)=[-6.1681299262750449943499750015037742203345354460970e-15 ,6.1681299277355852140439424783038948833957418710902e-15 ]
_H(5,0,2)=[4.7195398019848345634045949979719209129069943140921 ,4.7195398019848445384779957898565735812216035958887 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.3069346136548178321861019343781427188104970772392e-15 ,1.3069346133453511720935803386015582392753829369433e-15 ],[0 ,0 ],[-2.2561905612711618344450235257200259994397807370789e-16 ,2.2561905618054010765793440625270206252941202157493e-16 ],[0 ,0 ]}
DH*T2=[-1.3400424258820628300372329437747194704862597996688e-15 ,1.3400424255647566316629804980469069976368118148733e-15 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[5.2347338286314848966377818983273185967990610306367 ,5.2347641244434048647842293589539366417648853981404 ],[0 ,0 ],[-3.2577535786539328835151798217151560722214922456199e-1 ,-3.2577535786539041057390445807232290107063897496488e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[4.3126867766067932884422574298494672156614103740668 ,4.3126962243316438669836626611119619457830166819894 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [-1.0047273496488781433698792059213144031398220378240 ,-1.0047273496488781433698790845762951519728582132829 ]
dat/MoonL1_10_PQ.dat at {-8.5111596196950856804454383279062837983993352840917e-1 ,0 ,6.9134536648007998139971500301223139275938183541152e-2 ,0 ,2.0222014945535467047482268710519235625508381098033 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 12:52:00 2018
elapsed time: 2hours 16minutes 4seconds