Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_04_PT.dat at {8.6009876172029402511948949465424144912924691632082e-1 ,0 ,1.8413333604715407806236388704686274304284045697056e-1 ,0 ,2.5384160379384825610152616245786241881482345497742e-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]=[-1.1278517595881532735912531252358502660908529434917e-33 ,1.1278501943732074351646157897526143337031589223688e-33 ]
D0[i][3][0]=[1.9589938015965040117913508862228793960074184493566 ,1.9589938015965040117913508862239390285974736625248 ]
D0[i][3][2]=[-1.0823162027043121725797102210086428767607191896752e-30 ,1.0823161360291107036625916883502388044532520108470e-30 ]
dy0=[-1.0305622921737210269624129120270996924088214358498e-32 ,6.1004019186574506748461026636958701456742764674877e-33 ]
Ddy=[2.9821240800250230386351501993941846400898153552337 ,2.9821240800250236422348327832177298639171223214093 ]
dy=[-2.0456566376695707878685737117683847947240552683931e-33 ,3.4557995057169907112239407219219134089803411592215e-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]=[-3.3898032485225602168990281323993061430688198519417e-32 ,3.3898030899052239747725739341652279372571484569987e-32 ]
D0[i][3][0]=[3.2774282629511605066897132846041999312908707358701e-1 ,3.2774282629511605066897132854716590804717723433441e-1 ]
D0[i][3][2]=[-1.5541645167557040172363864190731379931527561759126e-28 ,1.5541645178456819903477600229477835249438021317941e-28 ]
dy0=[-4.4218780542189108204483632162865321497959509131139e-32 ,3.4729946831961499539494702525399650453216754691782e-32 ]
Ddy=[1.1491876675234039247175870463456668058769826854760e1 ,1.1491876675234049811923322339294692501658834846496e1 ]
dy=[-3.0221301370913121530989925656341766017079892642827e-33 ,3.8478293660672759626867506399954022480416368683978e-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]=[-6.3170142269831222195160205849322167409751529216217e-31 ,6.3170141893014491848508964773946897773892482272896e-31 ]
D0[i][3][0]=[-1.1840269087715481593308074492277576656299978447509e-27 ,1.1840269087004600892051513901171274114306418008748e-27 ]
D0[i][3][2]=[-7.9189193562867685027716963378442684871735847040300e-27 ,7.9189193571194206618952328062698188136329851180102e-27 ]
dy0=[-6.5109769391767845702196568354482697889898906267797e-31 ,6.3170141893022411041224830634330107982854645295899e-31 ]
Ddy=[2.4270391726176400310956528011650864960186797421959e1 ,2.4270391726177315438178065278714463020184877197474e1 ]
dy=[-2.6027656498387446905291991812112904045597711989728e-32 ,2.6826830867152778303493532556198749060315374765743e-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
############################

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

DBif[i][3][4]=[2.9821240800250233404349914913039718607736953479132 ,2.9821240800250233404349914913079426432332423287298 ]
D0[i][5][0]=[-1.0592739317952313522608754584151632433983396124352 ,-1.0592739317952313522608754584126732173785571837766 ]
D0[i][3][0]=[1.9589938015965040117913508862228793960074184493566 ,1.9589938015965040117913508862239390285974736625248 ]
DBif[i][5][0]=[-1.0592739317952313522608754584153966202614115967582 ,-1.0592739317952313522608754584124398405154851994537 ]
DBif[i][3][0]=[1.9589938015965040117913508862224607066945137375612 ,1.9589938015965040117913508862243577179103783743202 ]
D[k][3][4]=[2.9821240800250233309232922796327050069490314060783 ,2.9821240800250233499466907029792094970579062705647 ]
_H(5,0,0)=[9.7870646253162409047925440550018683564199734993146 ,9.7870646255177459518648613751366103978986472553172 ]
_H(5,0,2)=[-3.9340421784580285168234182524904137081886520088963 ,-3.9340421780724170705684810905425802824665676793994 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[1.1491876675234044529549596401185130887231727213790e1 ,1.1491876675234044529549596401566229673196934487466e1 ]
D0[i][5][0]=[-1.5983709742167860924940343162225073356450851093480 ,-1.5983709742167860924940343161757079468715362561668 ]
D0[i][3][0]=[3.2774282629511605066897132846041999312908707358701e-1 ,3.2774282629511605066897132854716590804717723433441e-1 ]
DBif[i][5][0]=[-1.5983709742167860924940343162237109210306491754429 ,-1.5983709742167860924940343161745043614859721900719 ]
DBif[i][3][0]=[3.2774282629511605066897132845949446551430896035541e-1 ,3.2774282629511605066897132854809143566195534756601e-1 ]
D[k][3][4]=[1.1491876675234042268503750271166458385807356737624e1 ,1.1491876675234046790595442531584902174621304963632e1 ]
_H(5,0,0)=[4.0271877897450520784433562454713579394214667124836 ,4.0271877915865980449833745988560139162838704289762 ]
_H(5,0,2)=[-2.5554413689043647184398287310562465901432249760941e1 ,-2.5554413677665882798124905218047725694963821594917e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[2.4270391726176857874567296617700550570308036525643e1 ,2.4270391726176857874567296672664777410063638093789e1 ]
D0[i][5][0]=[-4.0125549074058715058346222583657616341235196678311e-27 ,4.0125549074486551169879010566277405677778570324852e-27 ]
D0[i][3][0]=[-1.1840269087715481593308074492277576656299978447509e-27 ,1.1840269087004600892051513901171274114306418008748e-27 ]
DBif[i][5][0]=[-4.0258190102540865837776856422478965347779979722003e-27 ,4.0258190102968701949309644405098754684323353368543e-27 ]
DBif[i][3][0]=[-1.1863348402480567525722270630375037070747967854022e-27 ,1.1863348401769686824465710039268734528754407415261e-27 ]
D[k][3][4]=[2.4270391726176834504374328165214576221890525449885e1 ,2.4270391726176881244760265125150751758481149169547e1 ]
_H(5,0,0)=[-1.2506104132351657078249408707951121429170553914552e-7 ,1.2506104132355749790994967578210477872686777363161e-7 ]
_H(5,0,2)=[-1.0605405970797233240487651678821330961277632067668e2 ,-1.0605405737985203936612879964211504030785093728341e2 ]
g=[-5.0789938033741970364206079746243869447846585312989e-27 ,5.0789938034800957573924038767408294652942039816673e-27 ]
Dg=[-1.0605405970797233240487655532438600820856625139403e2 ,-1.0605405737985203936612876110594234171206056004598e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-4.7890612852112296638043897628002787170608461641098e-29 ,4.7890612853110831947188178912394382239775163515221e-29 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[1.8280973001972336258455013285442943827754716314712e-1 ,1.8280973001972336342938342084255059099136176923765e-1 ],[-3.7019576665450946279109511900164975303035425181711 ,-3.7019576665450946251681068118177376629343480386979 ],[4.3038175121337765383486941206066611835905472615887e-1 ,4.3038175121337765650526464969235110024023642661761e-1 ],[4.7925138992296375829168489035868901168529970425336 ,4.7925138992296375861207158046168018346724879452373 ],[1.0914017026868283775397752135086695131585865491868e1 ,1.0914017026868283778459232607981771113187988147879e1 ],[9.8269555424191135833709597825168776373461969536847e-1 ,9.8269555424191135941383249658492296672533679845323e-1 ]},
{[-6.4090648064782943402574721066528102985065833527747e-21 ,6.4090648064782943402575600055509930316448877364673e-21 ],[-4.5924133723708615735418943575454534666844884788290e-20 ,4.5924133723708615735418057979364908527783593678295e-20 ],[-9.3606717413406915813494454285472543776503485073753e-21 ,9.3606717413406915813495418716093560075920520548481e-21 ],[-6.9084985739854853386529464592887645658506146115451e-20 ,6.9084985739854853386530747252235688159123537408762e-20 ],[-1.4114795286323944215275296558701936393416777857285e-19 ,1.4114795286323944215275588327725988674850941766479e-19 ],[-1.8311971980165556591094648888029468713967199524344e-20 ,1.8311971980165556591094970513213306335311978056773e-20 ]},
{[-2.0700130494090591583622711655443522559876666865041e-1 ,-2.0700130494090591453044227955680382495745688516560e-1 ],[-6.8463047233153346611775089748137587036910913469741 ,-6.8463047233153346568105912715057218523601026552753 ],[6.7562620817714052709189371637276117860571091429226e-1 ,6.7562620817714053133792197716343273057315352276819e-1 ],[8.8631512027720209721864883444682885133728252420906 ,8.8631512027720209773027755037376823617638403476491 ],[2.0558606406094452476414308710025466786000370866081e1 ,2.0558606406094452481285308115809254988585675053822e1 ],[1.8173717315536527315619782780864166469380560753163 ,1.8173717315536527332399228446814711537492681000076 ]},
{[-1.8194605498467846103007900764773829952303843718790e-18 ,1.8194606077257825371037710354021488990619499989131e-18 ],[-5.5435641762720247941009659874079406807627666262387 ,-5.5435641762720247821500155151744150757606710162807 ],[-5.7250123027305356235235910479839338113049792158881e-18 ,5.7250124054890018537669553559852847161099507896563e-18 ],[1.0023871303762607491412812721756407065165013692067e1 ,1.0023871303762607505490086216592540338894420849068e1 ],[2.4270391726176857867716292350646625072600043150009e1 ,2.4270391726176857881418302284128164865539034900921e1 ],[3.2809940856689361070894180953305847672500824311623 ,3.2809940856689361116973419151251658339662829483659 ]},
{[1.0425724548854243583252206509830052450020703245718 ,1.0425724548854243659578424549650128817229278789366 ],[3.8961812293078570949904529283576365801660199663345e1 ,3.8961812293078570975410700341428100938550705994640e1 ],[-4.0910842036882526398973664563173336217586008712916 ,-4.0910842036882526152649318341397544908117032597388 ],[-5.0439535989621143691214443105479188109743171034194e1 ,-5.0439535989621143661274975161213902647629055246820e1 ],[-1.1606970180740788138964860536048248556976554448949e2 ,-1.1606970180740788136074348777594773444218747621649e2 ],[-1.0342527704091391237333426188050278749524744233202e1 ,-1.0342527704091391227478322099067678652082730080775e1 ]},
{[-1.1458170369269570189890373163359784985412115568577e-18 ,1.1458170394642786829522630674973114849611229975824e-18 ],[-7.3139626952378919146405051185132103517627096452603 ,-7.3139626952378919066286968159485334745070267804654 ],[-3.6453616696122550103217841314364325605713719014946e-18 ,3.6453617098375643557928203401286591284953248648827e-18 ],[7.9290099692889378152821355436138212760972255239320 ,7.9290099692889378248775993540111908498475067945034 ],[2.1548319379445867486821865076293871044293029290481e1 ,2.1548319379445867497010185183443711937158280925770e1 ],[9.6310695707921948973517413660388648421046634050893e-1 ,9.6310695707921949278204613060236938685058330002624e-1 ]}
}
D[2]={
{[1.8280973001972336232400185967447747740329636049451e-1 ,1.8280973001972336368993169445219455099055987302562e-1 ],[-3.7019576665450946311204286186021925227900788645879 ,-3.7019576665450946219586293561602121847727215639612 ],[4.3038175121337765188507286062193024433318778257112e-1 ,4.3038175121337765845506119437790029336687261470027e-1 ],[4.7925138992296375788882599819801564232130299542022 ,4.7925138992296375901493046914411059500307550596615 ],[1.0914017026868283770239287599327840933955956321726e1 ,1.0914017026868283783617697073399497257909395178796e1 ],[9.8269555424191135735224096481075715705625041294239e-1 ,9.8269555424191136039868750401688549246311583905970e-1 ]},
{[-4.3872412896509868610809487105868181372767369094022e-18 ,4.3872412896509868610717198403339626372878863154584e-18 ],[-2.2849255662516864368757444738692116664391459996453e-17 ,2.2849255662516864368709379724264686505759091095133e-17 ],[-1.7134251070037930934750199857977039912671521298058e-17 ,1.7134251070037930934786242958769841326304080223106e-17 ],[-2.7821220719550318277034341397240818675414476226607e-17 ,2.7821220719550318277092865289442154752031070965689e-17 ],[-3.0461950372118066225290103867839597397344469103716e-17 ,3.0461950372118066225354182720374185325441781261155e-17 ],[-7.6867441957370344810394077897361582224178271581290e-18 ,7.6867441957370344810555773961393179167405697379302e-18 ]},
{[-2.0700130494090591597669935701435980786111405914218e-1 ,-2.0700130494090591438997004605630432226801247247176e-1 ],[-6.8463047233153346659773510963223008387595074613787 ,-6.8463047233153346520107492164901037948152447135925 ],[6.7562620817714052484894441328455787651318489246137e-1 ,6.7562620817714053358087131775243816409606903003754e-1 ],[8.8631512027720209661922019625111034539403363015546 ,8.8631512027720209832970619693935617864089956928059 ],[2.0558606406094452468901300457290557743572316638533e1 ,2.0558606406094452488798316486946955368108564495181e1 ],[1.8173717315536527300506434594640631356596020499476 ,1.8173717315536527347512576708942577872273282194509 ]},
{[-8.3144282883280920849583747237373741005644995771806e-18 ,8.3144283034458158758372851787543346603093870111586e-18 ],[-5.5435641762720248461270026200858710355268018676541 ,-5.5435641762720247301239791965796511424878593892223 ],[-3.7714576381183156151692297029591502816530816164901e-17 ,3.7714576685558997514535983273618389096552300156527e-17 ],[1.0023871303762607426994827365872587793178357378519e1 ,1.0023871303762607569908071962408398011695596043309e1 ],[2.4270391726176857788887326766336301349857715410512e1 ,2.4270391726176857960247268358060656961906797729268e1 ],[3.2809940856689360906762333468952938762737962683574 ,3.2809940856689361281105266886666067285689787281479 ]},
{[1.0425724548854243563162259518294975246023083421529 ,1.0425724548854243679668371954149010928463429812017 ],[3.8961812293078570901039709434724208824332125260541e1 ,3.8961812293078571024275520654917355276854212129930e1 ],[-4.0910842036882526578010121452347834772037775105509 ,-4.0910842036882525973612863601156120420794876624782 ],[-5.0439535989621143755824576230272588367281841640750e1 ,-5.0439535989621143596664842625142900963781420399846e1 ],[-1.1606970180740788150556543143666369490911215444481e2 ,-1.1606970180740788124482666265198586038278063466660e2 ],[-1.0342527704091391249567265933997799496786879180692e1 ,-1.0342527704091391215244482421499202337814275304198e1 ]},
{[-2.5656315987319957102462099104077303112587692446081e-17 ,2.5656315988509200463040338103173676161007718390069e-17 ],[-7.3139626952378920589396579690759928957280289344750 ,-7.3139626952378917623295439825132300277347216004172 ],[-1.0754602308754123733727446521206234702296416830536e-16 ,1.0754602312761625468674889793736358420383262206611e-16 ],[7.9290099692889376388179915621326305018163427419500 ,7.9290099692889380013417433609223559792327778613011 ],[2.1548319379445867284917502098276648789994498685614e1 ,2.1548319379445867698914548224996491749965034034182e1 ],[9.6310695707921944139716076136125518385722050253529e-1 ,9.6310695707921954112005951263587591855361404132837e-1 ]}
}
Check intersection of two enclosures of hessian at bif point:intersection(H1,H[2],H[2]): true
############################

Check intersection of two enclosures of derivative at bif point:intersection(D1,D[2],D[2]): true
############################

T1={[-3.0813890793452723515005265524413650085475451857081e-16 ,3.0813890793452723872046975423036807158181113818161e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.5983484197128862553304341519884832302159660060842e-16 ,1.5983484197128861713557082049333460739664952173900e-16 ],[0 ,0 ]}
DH[2]=[-2.5076223941341908858783561500054475687511236229018e-1 ,-2.5076223941341908858783561356738479209794596056739e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-2.5076223941341924338168957328836325461732121218338e-1 ,-2.5076223941341893379398165527957442229283632752192e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[2.4270391726176857874567296505779264471293333222777e1 ,2.4270391726176857874567296784586063506744745116361e1 ]
_H(5,0,0)=[-7.5119892186367772420063597109964937243022726890737e-16 ,7.5119890619765131241485345495041465686013968300521e-16 ]
_H(5,0,2)=[-1.0605405854391218996376065569132232290400489662477e2 ,-1.0605405854391218180846684877171819308321117819257e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-7.0831699623512312547058010033021324736209792982228e-18 ,7.0831698146338630853472413888378935671254529842033e-18 ],[0 ,0 ],[-2.8977844140951426427333937557676801276528937611786e-17 ,2.8977844745275617955397136333907035428158981712949e-17 ],[0 ,0 ]}
DH*T2=[2.3734696641839077964804301085906434442523423600959e-4 ,2.3734696641845043335230196030778907487226818559314e-4 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [2.9999869116424563261043537683800237105744005121270 ,2.9999869116424563261043537687011366370174463187477 ]
dat/MoonL1_04_PT.dat at {8.6009876172029402511948949465424144912924691632082e-1 ,0 ,1.8413333604715407806236388704686274304284045697056e-1 ,0 ,2.5384160379384825610152616245786241881482345497742e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:53:56 2018
elapsed time: 0hours 18minutes 0seconds