Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_09_PT.dat at {-8.5502867081045788192915324982879185959098362620299e-1 ,0 ,9.0974601222155564506375764195089378490447772353696e-2 ,0 ,2.0177948221206802642312930655088947337858020935123 ,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]=[-3.2751493717710577576624731256136089008564887383524e-33 ,3.2751493718585834307321167614455910660796900193705e-33 ]
D0[i][3][0]=[7.4726520061791686887121470683787183549499287543799e-1 ,7.4726520061791686887121470684228937172460800202492e-1 ]
D0[i][3][2]=[-8.8828685374917559118106311730437837754705079104648e-31 ,8.8828685389041783962528018100264326071574340416906e-31 ]
dy0=[-6.4717259434020354448505186712549409199971223020556e-33 ,7.1830158694809826767814087087369782540713061325039e-33 ]
Ddy=[7.2044937571367864328417302913981835949103995589096 ,7.2044937571367941572164780432134647860275125564786 ]
dy=[-9.9701882069999329014919818767722057619142861860378e-34 ,8.9829017298975800006796630954612600398531601394175e-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]=[-3.0431939382047321136347245967357291969809670125232e-31 ,3.0431939378408393219658187253676890741578303854148e-31 ]
D0[i][3][0]=[1.8223434659568633650502484330569093280235925941120e-2 ,1.8223434659568633650502484527907135879245142290098e-2 ]
D0[i][3][2]=[-4.1366265901128332322799207735440716096130171631801e-29 ,4.1366265817916989519197338980468614676290727115269e-29 ]
dy0=[-3.0439734821235385121238524098638140140867926803735e-31 ,3.0480752369081200835872284527273593319285805259284e-31 ]
Ddy=[5.0347376184950070492750842866609530941529874201277 ,5.0347376184950365579848751647204040368688585002510 ]
dy=[-6.0540895432387125908467841435259527943018737371283e-32 ,6.0459426345110087716278684280333453844967312448669e-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]=[-1.1573487589850273065280325219089721601331018393624e-29 ,1.1573487590106884994128028708342625998941934084655e-29 ]
D0[i][3][0]=[-3.5065553551278062329564405029115452393745945868361e-27 ,3.5065553544895909914541296458951458748980637411704e-27 ]
D0[i][3][2]=[-4.8258017182665946473226989872268434095401031736077e-27 ,4.8258017184893125018478004154710895379094059628806e-27 ]
dy0=[-1.1580263236458293185778051359724745871170631171081e-29 ,1.1573487590106933252178073984665698214214681385361e-29 ]
Ddy=[-8.3810317115432540861425984786935596598217827095067e1 ,-8.3810317115431847030553466527423301766818325006481e1 ]
dy=[-1.3817228755391547826973179517224802661543458850560e-31 ,1.3809144253883185981514866381455414244962408867951e-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
############################

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

DBif[i][3][4]=[7.2044937571367902950291041672674031150819910210065 ,7.2044937571367902950291041673442452658559210943818 ]
D0[i][5][0]=[7.9690585460390389149992836162732098773445419434325e-1 ,7.9690585460390389149992836162975082986448266368055e-1 ]
D0[i][3][0]=[7.4726520061791686887121470683787183549499287543799e-1 ,7.4726520061791686887121470684228937172460800202492e-1 ]
DBif[i][5][0]=[7.9690585460390389149992836162489403199428825542506e-1 ,7.9690585460390389149992836163217778560464860259874e-1 ]
DBif[i][3][0]=[7.4726520061791686887121470683747549997109853438313e-1 ,7.4726520061791686887121470684268570724850234307978e-1 ]
D[k][3][4]=[7.2044937571367889975717946520767008343907831128158 ,7.2044937571367915924864136825349475465471290025724 ]
_H(5,0,0)=[4.8266651340651885471588050266342846802453543335423 ,4.8266651343600807068008848517105588675117981219534 ]
_H(5,0,2)=[5.5510375475061816807748507809549724838532592101351e1 ,5.5510375475268444090374719137635497191797156783789e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[5.0347376184950218036299797252475674794687567389788 ,5.0347376184950218036299797261337896515530891813998 ]
D0[i][5][0]=[-8.2135072928549539669360546010583250765163352813227e-2 ,-8.2135072928549539669360545997214733496725648903889e-2 ]
D0[i][3][0]=[1.8223434659568633650502484330569093280235925941120e-2 ,1.8223434659568633650502484527907135879245142290098e-2 ]
DBif[i][5][0]=[-8.2135072928549539669360546010929867955338274401516e-2 ,-8.2135072928549539669360545996868116306550727315601e-2 ]
DBif[i][3][0]=[1.8223434659568633650502484327631604815636052370789e-2 ,1.8223434659568633650502484530844624343845015860429e-2 ]
D[k][3][4]=[5.0347376184950216305536028907302698510339939867922 ,5.0347376184950219767063565606510872799878519335864 ]
_H(5,0,0)=[4.1939458138200179736792062394079547168659424928958e-1 ,4.1939459544872995032715390359778095410825848955689e-1 ]
_H(5,0,2)=[3.2950037934117367732498555469588340952890421741622 ,3.2950038044117578059211298457253725555464980891451 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-8.3810317115432193945989725782397155071949066050450e1 ,-8.3810317115432193945989725531961743293087086051097e1 ]
D0[i][5][0]=[-2.0019951753823948710713258379663724997959143853758e-27 ,2.0019951781976477068336479338671357532683985547055e-27 ]
D0[i][3][0]=[-3.5065553551278062329564405029115452393745945868361e-27 ,3.5065553544895909914541296458951458748980637411704e-27 ]
DBif[i][5][0]=[-2.1294284219970574163269955592418993044906812484600e-27 ,2.1294284248123102520893176551426625579631654177897e-27 ]
DBif[i][3][0]=[-3.5107957708001748774297182761284869209338078688668e-27 ,3.5107957701619596359274074191120875564572770232010e-27 ]
D[k][3][4]=[-8.3810317115432194586984717460455406406988520507073e1 ,-8.3810317115432193304994733853903491958047631594474e1 ]
_H(5,0,0)=[-2.5805022288160089125709545031031921131597545027859e-7 ,2.5805022288164279975411065160946813955512267235911e-7 ]
_H(5,0,2)=[-4.3800392458358715864433899638181429838033242153960e1 ,-4.3800391995093363551704211738968468811835544219173e1 ]
g=[-3.2163347051025042769906417117123133329466087331774e-27 ,3.2163347077201335351489174862098476124825339234221e-27 ]
Dg=[-4.3800392458358715864433951519643960175707970865175e1 ,-4.3800391995093363551704159857505938474163576308300e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-7.3431642015048784224577082970490666229555516969897e-29 ,7.3431642074811474440945684615913877724137356235189e-29 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-5.6757664625280541256420900751716825027303596023044e-2 ,-5.6757664625280538104711902974042549000563951663031e-2 ],[-8.4727997858217583462886333289827226800468366463571 ,-8.4727997858217583364323539902440118046379442218653 ],[-1.0574992699426869961771742862083824424366986361530e-1 ,-1.0574992699426869832075032173376237367581752236887e-1 ],[3.7841560400578574208854758740244851893360051381777 ,3.7841560400578574260969249147673230256094080013833 ],[-5.8943169236378804082107718437141859197692171150226 ,-5.8943169236378804013322706791627855655037964229072 ],[8.3959650705607708716775770178313006717900356078955e-1 ,8.3959650705607708893707857483507207403368844419331e-1 ]},
{[-1.8890954244776929314139570113815927450068792428611e-21 ,1.8890954244776929314139449563306351068880024514937e-21 ],[-4.5117621587746785587021203525367752768842082879743e-20 ,4.5117621587746785587021207325091445365276418758088e-20 ],[-1.5640481679655668756879527686388786890172462609152e-21 ,1.5640481679655668756879456654859488645982389891887e-21 ],[-2.0463414254952907557707901902236024566540712405297e-20 ,2.0463414254952907557707906617379579784678750382722e-20 ],[-5.3132164939682372589818068355615775685477604008546e-20 ,5.3132164939682372589817935141769962191857990345722e-20 ],[-2.6877999452809316590335322633079599660713648183556e-20 ,2.6877999452809316590335519858048733622555012558087e-20 ]},
{[-1.1985072602802649229296301226878475019910352953501e-1 ,-1.1985072602802649205625309247518070622819879144488e-1 ],[7.9450143265599781318553282812410050689282001191019 ,7.9450143265599781326492706112285648411701323713794 ],[-1.1675340244592409152180680121825490938974783439521e-1 ,-1.1675340244592409142328642938047759116638178482460e-1 ],[-3.5484343678825872540251257880572569119652563829243 ,-3.5484343678825872536097494852846476858977027086262 ],[8.9319122400774118466687378893974292828119273426269 ,8.9319122400774118472522592099727225126381700191037 ],[-7.8729657795676104299958698916582234483254004681767e-1 ,-7.8729657795676104283903208065793378769015286542774e-1 ]},
{[-4.4698194682675865990464413586073036076621880661242e-18 ,4.4698194685843059562251507750640544062115282031700e-18 ],[-8.0621998465725722190767144316116770931806874785185e1 ,-8.0621998465725722160466548516776683515341864410900e1 ],[-1.8665396096659597442980376765019944173043590451607e-18 ,1.8665396095734252958612603912957387571159705050544e-18 ],[3.6305094664643102459753037330137311086283715134546e1 ,3.6305094664643102475583911191496785724783466123115e1 ],[-8.3810317115432193957182906854119900568775857776323e1 ,-8.3810317115432193934796544459803498032264687220976e1 ],[1.7153070799292880243522800542890076253769295945627e1 ,1.7153070799292880250056672319689311566560977876965e1 ]},
{[1.2898998186265784904506547414561020028521838326303e-1 ,1.2898998186265786912521598524537611230702225336910e-1 ],[-8.3031587057981006406416815572638404492793043594093e1 ,-8.3031587057981006342219546996956560876457167698611e1 ],[-1.2456511315581434112146496877117010498363229610098e-1 ,-1.2456511315581433282977589363610732927291318796659e-1 ],[3.7083902561563319505346739968329856766621028985230e1 ,3.7083902561563319539163690876194672019254492986451e1 ],[-7.1686367958918676951355152054122643923397887476979e1 ,-7.1686367958918676905804043115356605495392579390380e1 ],[8.2278623632603770375479289943088173080172872957706 ,8.2278623632603770496984330330986027551467919137219 ]},
{[-1.0254703013422098108155040890810523705370253387507e-17 ,1.0254703009181354375990684229222600329096143753170e-17 ],[4.6312701780024056491729268966849834427832868826994e1 ,4.6312701780024056556839265995338449006085199407974e1 ],[-4.2303848019978909447306957952734231584284980046425e-18 ,4.2303848034376654687601004009309495157298779756026e-18 ],[-2.0367239147897515538789183405246810021111770254770e1 ,-2.0367239147897515504445282070338991117099593252922e1 ],[2.5951894645282260444552777187451980861707185630009e1 ,2.5951894645282260490503030198277827256166195183151e1 ],[5.1834714162456104582798353394149637120173269432707 ,5.1834714162456104703831937604958753876868547020572 ]}
}
D[2]={
{[-5.6757664625280540033760850749400788406710281376855e-2 ,-5.6757664625280539327371952985170543956456459471665e-2 ],[-8.4727997858217583447485823280984075101087726378923 ,-8.4727997858217583379724049910878587651127186991209 ],[-1.0574992699426869921360877723485616793459301004372e-1 ,-1.0574992699426869872485897313151298460097404988677e-1 ],[3.7841560400578574218049697962390973819646922180450 ,3.7841560400578574251774309925404380946759629779914 ],[-5.8943169236378804085148057546593581120109886934282 ,-5.8943169236378804010282367682191443454217549225284 ],[8.3959650705607708598547520419018830358676090292902e-1 ,8.3959650705607709011936107258114750512005102276669e-1 ]},
{[-1.7052592425906096371852599073037455898893712639053e-18 ,1.7052592425906096371813556260925434072643547088555e-18 ],[-9.8823615754462730424073857014681950277529688933555e-18 ,9.8823615754462730423847595120550793655046078209065e-18 ],[-8.7891458728235994354861824648708958727102406339377e-19 ,8.7891458728235994354660592506189390883533256181181e-19 ],[-5.0057272278828323655188715781896217855759713900302e-18 ,5.0057272278828323655303324553841857451733513148368e-18 ],[-9.7233724887173322854680720452484489596297674015352e-18 ,9.7233724887173322854458098697568523385009239077534e-18 ],[-4.6557800259073335296400601531933836439523307847519e-18 ,4.6557800259073335296507198077635740447358867526383e-18 ]},
{[-1.1985072602802649229124255309199400947366836776777e-1 ,-1.1985072602802649205797355165078123171285783969881e-1 ],[7.9450143265599781312261945367361857332721205757392 ,7.9450143265599781332784043555871445240152759171460 ],[-1.1675340244592409155549739635438766592110636776685e-1 ,-1.1675340244592409138959583424321461287971789602524e-1 ],[-3.5484343678825872543321157644973774924280817094199 ,-3.5484343678825872533027595087780378457556924975333 ],[8.9319122400774118458531195320179193686067703498857 ,8.9319122400774118480678775671791824834707029447240 ],[-7.8729657795676104352255226437374983597580573134930e-1 ,-7.8729657795676104231606680541243269566991954734895e-1 ]},
{[-1.6474483996722520238763034358526141711609942678122e-17 ,1.6474483997030729446119647490398516724463599739954e-17 ],[-8.0621998465725722309053480522330394343285599242089e1 ,-8.0621998465725722042180212319338749609040220393713e1 ],[-1.0094938322360441131181702638172419357819591657920e-17 ,1.0094938322223456529474938621578950748860727246638e-17 ],[3.6305094664643102401029986803976340993561470853371e1 ,3.6305094664643102534306961721583251439824625972493e1 ],[-8.3810317115432194091451778391299856739475367526686e1 ,-8.3810317115432193800527672930168008513343637468261e1 ],[1.7153070799292880167599969867317214743243645945680e1 ,1.7153070799292880325979502996393212051690795294729e1 ]},
{[1.2898998186265785285198327906156164963545547305211e-1 ,1.2898998186265786531829818021010796854369753065939e-1 ],[-8.3031587057981006470094172830225272781167194866887e1 ,-8.3031587057981006278542189744480783778290305531757e1 ],[-1.2456511315581434354504970296419409376889936470600e-1 ,-1.2456511315581433040619115945811695333889248713152e-1 ],[3.7083902561563319474553429642724647495605446505396e1 ,3.7083902561563319569957001204010279280865436641176e1 ],[-7.1686367958918677047295586895561350367547708997917e1 ,-7.1686367958918676809863608276735551780609419916169e1 ],[8.2278623632603769683791180680508319399252449674375 ,8.2278623632603771188672439589362848656181328521507 ]},
{[-9.2504714619066524806188224235979998084471344381566e-18 ,9.2504714578493687587961244747352506532824812502682e-18 ],[4.6312701780024056443608753066586706328143853693779e1 ,4.6312701780024056604959781893559562166228291755270e1 ],[-5.8646713514821219683586923178729261606390657156531e-18 ,5.8646713531324722649336786525333180667732030898834e-18 ],[-2.0367239147897515561778267904631902588279011761086e1 ,-2.0367239147897515481456197570070923617452942657328e1 ],[2.5951894645282260378103848978487104504450311914564e1 ,2.5951894645282260556951958403232242257396244602388e1 ],[5.1834714162456104155450415044768725078919376966031 ,5.1834714162456105131179875948000157014587572024705 ]}
}
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={[-2.0105180282728762926020629352739124536910123416957e-16 ,2.0105180282728761856151240597384219256930440242443e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.6169003613858041320916435215067909940025292292952e-17 ,1.6169003613858041154807164437862137599071200030525e-17 ],[0 ,0 ]}
DH[2]=[3.8650042794705927590377811610324263087552302630862e-1 ,3.8650042794705927590377811679211690402518951309883e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[3.8650042794705918771395093215654542347618265610733e-1 ,3.8650042794705936409360530073881362484283794130545e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-8.3810317115432193945989725787104086480751351642044e1 ,-8.3810317115432193945989725527254811880454042001790e1 ]
_H(5,0,0)=[-1.0779748739197721282842493829693987436742542768246e-14 ,1.0779748737969115148431425618214661317106295250477e-14 ]
_H(5,0,2)=[-4.3800392226726048701374762363501400171763193432190e1 ,-4.3800392226726030714792169985531901337366777271377e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.4611078100392345323542893504484148108255845521338e-16 ,2.4611078097587333605722248240442286414569308135443e-16 ],[0 ,0 ],[-3.0656817281168064391448849178441973081590826753050e-17 ,3.0656817284662130411777824853655759417293707085964e-17 ],[0 ,0 ]}
DH*T2=[1.0910105480646527848370274900678939489368454384073e-1 ,1.0910105480646571996915612230881863698282290316839e-1 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [-9.9679533512816265894207872144350159210963073510756e-1 ,-9.9679533512816265894207872114587420989636109617880e-1 ]
dat/MoonL1_09_PT.dat at {-8.5502867081045788192915324982879185959098362620299e-1 ,0 ,9.0974601222155564506375764195089378490447772353696e-2 ,0 ,2.0177948221206802642312930655088947337858020935123 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:08:22 2018
elapsed time: 0hours 32minutes 26seconds