Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_05_PT.dat at {8.7462689562844476292584461155075681818465355282895e-1 ,0 ,1.9125416820532551511710507597324600631311267684418e-1 ,0 ,2.3295646058503593099440948172348432177760592977843e-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]=[-1.4585019070102992122608016169942659796799767942241e-33 ,1.4585013111392039082743507425168358753950035339575e-33 ]
D0[i][3][0]=[-5.4913313951062188355583128858557238229156328727494 ,-5.4913313951062188355583128858510515349712740958366 ]
D0[i][3][2]=[-1.1468756080582597625302518129334886099270432228408e-30 ,1.1468760860555324269718768819474879649693474516117e-30 ]
dy0=[-1.2563294648594615989489752280438602091431662009592e-32 ,1.0538900766481810577190639172872753173729046138623e-32 ]
Ddy=[-7.0435430397354711878020127508948470959186923877028 ,-7.0435430397354680542220595363291323785061464574968 ]
dy=[-1.7836612309628836122686687451898746511908470250794e-33 ,1.4962499280585948520064814860338271567561007567648e-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]=[-1.9115796119497216287785022651345331871055208001691e-31 ,1.9115796127338103320527099890768114059618681698154e-31 ]
D0[i][3][0]=[-2.5263018574270769292637984153537738001862943854152 ,-2.5263018574270769292637984142465613984557546257226 ]
D0[i][3][2]=[-2.5699935420092883094863536411207054938335950950528e-28 ,2.5699935458987265133284406351411782651928223117873e-28 ]
dy0=[-1.9772318229031767736183932640729458341206102971309e-31 ,1.9533542359712086820484160596973131328899977973614e-31 ]
Ddy=[-1.0006019355282484860629683497009872821537544634115e1 ,-1.0006019355282481640956829663290247712668813756556e1 ]
dy=[-1.9760423727936684611896745460561718834768371771904e-32 ,1.9521791499833284152941917924964314475538380131421e-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]=[-7.9601630658135414954063224001843724221035423880209e-30 ,7.9601630648250989514335404011837470296463662746260e-30 ]
D0[i][3][0]=[-4.6840192323439678796668040054971674702940008131377e-26 ,4.6840192325224897208901158315904050248055828869405e-26 ]
D0[i][3][2]=[-2.8216123401648398326811178099592732276560678443304e-26 ,2.8216123402934248594125385265514664200096934771963e-26 ]
dy0=[-7.9601630658138236618721453543738810453657139922494e-30 ,7.9634002617980895519769957310082406901062781572840e-30 ]
Ddy=[1.5037880450349394788718845636963617591577869731327e1 ,1.5037880450350111930380356263469508844301849140640e1 ]
dy=[-5.2955602939462558601281271090207492623648970732337e-31 ,5.2934075996254344201045695271142863751129481461487e-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]=[-7.0435430397354696210120361436459289554735945676172 ,-7.0435430397354696210120361435780505189512442775825 ]
D0[i][5][0]=[1.2139384401061840576719646048118944629546821725010 ,1.2139384401061840576719646048257952117491824980339 ]
D0[i][3][0]=[-5.4913313951062188355583128858557238229156328727494 ,-5.4913313951062188355583128858510515349712740958366 ]
DBif[i][5][0]=[1.2139384401061840576719646047288212494378972570791 ,1.2139384401061840576719646049088684252659674134558 ]
DBif[i][3][0]=[-5.4913313951062188355583128859570201833651964825532 ,-5.4913313951062188355583128857497551745217104860328 ]
D[k][3][4]=[-7.0435430397354705773842043936921507023676303590191 ,-7.0435430397354686646398678935318287720572084861806 ]
_H(5,0,0)=[5.1247966617349349916017039052644435894310445957540 ,5.1247966643371655266388691355596270776500342577895 ]
_H(5,0,2)=[-9.5457654007742342599307637885926392922500203199789e-1 ,-9.5457653813026768392402940278890031485270819421734e-1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-1.0006019355282483250793256580434648048076989969294e1 ,-1.0006019355282483250793256579865472486129368421377e1 ]
D0[i][5][0]=[4.9914528274234637863262908780506861148671037785567 ,4.9914528274234637863262908788289011771179807427468 ]
D0[i][3][0]=[-2.5263018574270769292637984153537738001862943854152 ,-2.5263018574270769292637984142465613984557546257226 ]
DBif[i][5][0]=[4.9914528274234637863262908779692178842955607658718 ,4.9914528274234637863262908789103694076895237554317 ]
DBif[i][3][0]=[-2.5263018574270769292637984154286209433443364298338 ,-2.5263018574270769292637984141717142552977125813040 ]
D[k][3][4]=[-1.0006019355282483691397482379113580853607249237146e1 ,-1.0006019355282482810189030781186539680599109153525e1 ]
_H(5,0,0)=[3.1179420674365252968260111975152493462389375805673e1 ,3.1179420943760986354734866588497104784605247239977e1 ]
_H(5,0,2)=[1.7777447266555243796405992253896041391729979382088e1 ,1.7777447495190779185963477040630958237629070116352e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[1.5037880450349753359549600808578811839993082588237e1 ,1.5037880450349753359549601091854314595886636283730e1 ]
D0[i][5][0]=[-1.4261130037472374682524862726884907886388038188400e-25 ,1.4261130037514267471285044765202640387818987114925e-25 ]
D0[i][3][0]=[-4.6840192323439678796668040054971674702940008131377e-26 ,4.6840192325224897208901158315904050248055828869405e-26 ]
DBif[i][5][0]=[-1.4343903075582500937658928570650135982469132257884e-25 ,1.4343903075624393726419110608967868483900081184409e-25 ]
DBif[i][3][0]=[-4.7815321234678731858159558576209907102996488133470e-26 ,4.7815321236463950270392676837142282648112308871498e-26 ]
D[k][3][4]=[1.5037880450349741363882213628757109089245872834637e1 ,1.5037880450349765355216988271676017346633846037330e1 ]
_H(5,0,0)=[-2.7395110831641939652131061909095467199901054445906e-5 ,2.7395110831699482965435439792149336335689394984068e-5 ]
_H(5,0,2)=[1.9278711235757223380088272499166150439486932846644e2 ,1.9278717142980848853274286826651008125876537022673e2 ]
g=[-1.8148661277754100710910905061487626394796768007674e-25 ,1.8148661277938051605728038110040536717859272954091e-25 ]
Dg=[1.9278711235757223380088101982099280636113007985624e2 ,1.9278717142980848853274457343717877929248860492357e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-9.4138353212515525214115546722610634777702765042000e-28 ,9.4138353211561359281716757509520628882372957297797e-28 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-7.1203211862975016419667740231523154904769547556685e-1 ,-7.1203211862975016100692527011633431175703100202726e-1 ],[-9.1705261159318055470759472844650106460760000024805e-2 ,-9.1705261159318053621063354503469785872166609150497e-2 ],[1.1989609258703231876187937156982536831689058020592e-1 ,1.1989609258703232029540293571624919525194505612642e-1 ],[3.7322869077231192355416908012916423917699860657542e-1 ,3.7322869077231192551116908578062251469063170215143e-1 ],[-4.5585962800712502144918766514112171217742343263693 ,-4.5585962800712502132029672400043032101434014779181 ],[1.8890058012025266911839591126709265756318447099588e-1 ,1.8890058012025266999030419499300029171715714292134e-1 ]},
{[-1.6499332026991402448898040752405273557347678810611e-20 ,1.6499332026991402448897724170381448394501998256087e-20 ],[-5.9709274768238958714268907151319736963994919724230e-21 ,5.9709274768238958714269140682734805566887606623431e-21 ],[-6.5543969635050909437065627577320993851128175909057e-21 ,6.5543969635050909437066139177133948199103544360415e-21 ],[-1.8559941211898819098573226844541069913397934543535e-20 ,1.8559941211898819098573329426019220737692843343638e-20 ],[-8.0956527768399201427643432889562536253908135983028e-20 ,8.0956527768399201427641910355958553069409853455690e-20 ],[-9.4793786604490562824257539702762319801608285710153e-21 ,9.4793786604490562824258302300289905047060138519884e-21 ]},
{[-6.0084845698136282192440162782415598242125789785511e-1 ,-6.0084845698136281439788943754139739168080978430840e-1 ],[-4.1483485740556111725074895116982407701362792510105e-1 ,-4.1483485740556111288491792699877164696049049516923e-1 ],[4.9711586686749416747010962429004702777371868239132e-1 ,4.9711586686749417108649660121408103034255015026301e-1 ],[1.6883248437318732566607956939410609602702498423452 ,1.6883248437318732612830123712567784982013745878893 ],[-1.2550384152098902058609040776201336622912661685960e1 ,-1.2550384152098902055596240520584965263557321131247e1 ],[8.5450435697331276382596950157077826061150121816050e-1 ,8.5450435697331276586930381793504296103611080870094e-1 ]},
{[-1.8519985690298541697017960150296717313077917231448e-17 ,1.8519985342641518687457775892757644205542828244926e-17 ],[2.6037115411849919809387972111220770975905389052585 ,2.6037115411849920023896234916241282284646408564329 ],[-8.9121226626335246781516165897400068241999683443287e-18 ,8.9121227043039501864040585363538462021496830693552e-18 ],[-1.6644957843651305764326929350786704379451571152229 ,-1.6644957843651305536516738868124346753639575431674 ],[1.5037880450349753351946346073232475465104439304476e1 ,1.5037880450349753367152854371938674490718691607571e1 ],[2.5770304716052608334406310039079406943163629140809e-1 ,2.5770304716052609339011926614689914331941702616890e-1 ]},
{[4.7973173463365479442285214279677815225405005061393 ,4.7973173463365480042499770837091747126312135334891 ],[3.3542699237847513225822978438406385857383603270579 ,3.3542699237847513573695971196849720870153880860440 ],[-3.9976774368416541436983195602374208170401657965380 ,-3.9976774368416541148687099676292323743322737094945 ],[-1.3651449833136648696543662349744892138950258166202e1 ,-1.3651449833136648659619584560524373977468211822656e1 ],[1.0043832281718502455195851422440727714999705662124e2 ,1.0043832281718502457664649687368854242668167649250e2 ],[-6.9093476914271189347439173590923919847503240960375 ,-6.9093476914271189183878351233225143785498288588491 ]},
{[-5.8790754616416259958712728017756898220240765194090e-18 ,5.8790753632456412033414403398640688302190102501540e-18 ],[-6.9098953448391067723864092175595587120687504950732e-1 ,-6.9098953448391067050461986659252241000714226442064e-1 ],[-2.8094762725364722568431141646298937929077170071758e-18 ,2.8094762684976581704818779560270666019790731162576e-18 ],[8.3762963155903144368521871263239095905354245969225e-1 ,8.3762963155903145111627135341478924476234408300142e-1 ],[-1.1966338691383484774939636458579842968289170595082e1 ,-1.1966338691383484768523607582972356151323137786273e1 ],[1.8074233797838861976237338902149572437388098745625e-1 ,1.8074233797838862301481808437187880979592128906483e-1 ]}
}
D[2]={
{[-7.1203211862975016642860647570060508680284736169283e-1 ,-7.1203211862975015877499621245152148769630817075016e-1 ],[-9.1705261159318057904170369101129005134521515460545e-2 ,-9.1705261159318051187652450308935498438357383667291e-2 ],[1.1989609258703231653649761546755325772275324542661e-1 ,1.1989609258703232252078468669282336187195104340592e-1 ],[3.7322869077231191952082341773707894512421940486271e-1 ,3.7322869077231192954451473749188046901743887790981e-1 ],[-4.5585962800712502181614632803681732582423755387138 ,-4.5585962800712502095333805991727842845443622224128 ],[1.8890058012025266809197875775793011597252561446436e-1 ,1.8890058012025267101672134722101162505977203233751e-1 ]},
{[-3.6934405014490349535265540863737772924753380491774e-17 ,3.6934405014490349535318172234892200103788729659454e-17 ],[-2.2410498639751535301919474306279927773180354407962e-17 ,2.2410498639751535301887539440368271659630295434698e-17 ],[-1.8540666723133186858981153037218500860164752280474e-17 ,1.8540666723133186859007573408993081213567225062565e-17 ],[-2.5666312620362099251659885183702338432563679735279e-17 ,2.5666312620362099251696459570785543384731748846941e-17 ],[-2.1962293971447577750912610900991035671403202168765e-17 ,2.1962293971447577750881314724838735304218469919404e-17 ],[-1.0294119091048427718590445440439045611638343321402e-17 ,1.0294119091048427718605114516666922690156515342853e-17 ]},
{[-6.0084845698136282422996115406893683848521916975022e-1 ,-6.0084845698136281209232981689777094213059078491883e-1 ],[-4.1483485740556111951891360034339339848592400595348e-1 ,-4.1483485740556111061675331525306085420718010234753e-1 ],[4.9711586686749416543637330937442494187309110031786e-1 ,4.9711586686749417312023293799175414950071620448691e-1 ],[1.6883248437318732527194041541465966189016615369223 ,1.6883248437318732652244039525871679948049195628631 ],[-1.2550384152098902064411223542566762622446923990529e1 ,-1.2550384152098902049794057691734992432252638094851e1 ],[8.5450435697331276287728826807578461467026122741136e-1 ,8.5450435697331276681798505137427469952202216299244e-1 ]},
{[-1.0605759015513084617613223591472312267893018901670e-16 ,1.0605759040374859991880138925333573857712478026889e-16 ],[2.6037115411849919227853515223005054061632081434573 ,2.6037115411849920605430689386699100015224748626565 ],[-5.7207282935554248083843015815507983732017620994117e-17 ,5.7207283122191876532774305594283402916998186092127e-17 ],[-1.6644957843651306454430627139010875571033831133077 ,-1.6644957843651304846413038376965301677805289777237 ],[1.5037880450349753285893333705972896521322419676204e1 ,1.5037880450349753433205867092133843254634116543975e1 ],[2.5770304716052605686521188703615066971952542280977e-1 ,2.5770304716052611986897047932955645871601098485439e-1 ]},
{[4.7973173463365479109363049922033289115214064423619 ,4.7973173463365480375421927196982736495675919712433 ],[3.3542699237847512891317987421449325302318249876320 ,3.3542699237847513908200965475756022407435736733337 ],[-3.9976774368416541737977493026182835165256846021844 ,-3.9976774368416540847692804196095850883655830707938 ],[-1.3651449833136648756518624540265125139344859390272e1 ,-1.3651449833136648599644622750707877015907178447950e1 ],[1.0043832281718502442602557263356530456766868592578e2 ,1.0043832281718502470257943811612407597847293991304e2 ],[-6.9093476914271189490602407351024577913305165664686 ,-6.9093476914271189040715117598505256476823124571912 ]},
{[-3.2804451932595213527393843435581940987425723621248e-16 ,3.2804451933321461399491230569397955438084690019907e-16 ],[-6.9098953448391087661677338436787867508334304742713e-1 ,-6.9098953448391047112648743862641673409601765356087e-1 ],[-1.6871464969428689938365266631200799450250666267725e-16 ,1.6871464970895471789493340496706746352934960716997e-16 ],[8.3762963155903120952083612218330295342535879993767e-1 ,8.3762963155903168528065397901972428716098459736592e-1 ],[-1.1966338691383484994578290741068307885001354158994e1 ,-1.1966338691383484548884953167110783713794061164349e1 ],[1.8074233797838852867705869565493349998203677702799e-1 ,1.8074233797838871410013277554186490457646341220673e-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={[-6.2243612707890321747035244099053418820400060960358e-17 ,6.2243612707890321162481545029612922360530161519233e-17 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.3053896706078964854405599144721958723895562244079e-17 ,4.3053896706078970066191427532172280239263596770729e-17 ],[0 ,0 ]}
DH[2]=[2.8143626687355647369839959324522778074034118025404e-2 ,2.8143626687355647369839976775924992714976969585338e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[2.8143626687355598710392905088510904015885062487743e-2 ,2.8143626687355696029287031011931142385654472199051e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[1.5037880450349753359549599679326449019463394965692e1 ,1.5037880450349753359549602221106677404970466857336e1 ]
_H(5,0,0)=[-3.2506737982382727746777707745961897580741359339654e-14 ,3.2506738534177437502094617721920870126094557533392e-14 ]
_H(5,0,2)=[1.9278714189369033164679878085168238872284341669563e2 ,1.9278714189369039067948112944028413778092298982568e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.6861466078532771739346771573011005230932178438733e-16 ,1.6861465792313107743499950247348838009856361517748e-16 ],[0 ,0 ],[-6.7406701352306091034193261675139469616272659019593e-16 ,6.7406702496519983770797866966693335251473212061266e-16 ],[0 ,0 ]}
DH*T2=[2.3879144811603003491115326634232788342239239540094e-2 ,2.3879144811604490100128675000632440503668256793722e-2 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [2.9979195016002165129225206984793744050192387728487 ,2.9979195016002165129225207037235847829426897247990 ]
dat/MoonL1_05_PT.dat at {8.7462689562844476292584461155075681818465355282895e-1 ,0 ,1.9125416820532551511710507597324600631311267684418e-1 ,0 ,2.3295646058503593099440948172348432177760592977843e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:55:34 2018
elapsed time: 0hours 19minutes 38seconds