Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL2_01_PQ.dat at {1.0538331100220000205460218440856744185261965743092 ,0 ,7.4871016628357675794089449244933306178314973889213e-2 ,0 ,3.6200688312371891820950612454167478278116939821477e-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]=[-1.5745685279176759570856247186637600735811948977118e-43 ,1.5745670191223958059061345297864897639244443553242e-43 ]
D0[i][3][0]=[1.6521914906715555457930080002346256239712883253424e-1 ,1.6521914906715555457930080002346256239721373723011e-1 ]
D0[i][3][2]=[-3.8415338405245585987900122127201216870034111111012e-41 ,3.8415332768736956460115589718342903709950143897609e-41 ]
dy0=[-1.8978801679398268639061602373388696036485577808635e-43 ,1.8978799906269554019895523795146432401475696666740e-43 ]
Ddy=[-4.4164188477709530733829563095265342368995738884240e1 ,-4.4164188477709530733828103370438443336503574123499e1 ]
dy=[-4.2973282955209773794117655239621510556096863888842e-45 ,4.2973278940353448484084179016156751157518476368008e-45 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-5.8208299468309746085136104071268506867903141405288e-42 ,5.8208234173154544443261136520974007599152775742287e-42 ]
D0[i][3][0]=[8.6797647883707970248582210449658733837810078231327e-1 ,8.6797647883707970248582210449658733838594478319673e-1 ]
D0[i][3][2]=[-3.9562086552157237576309495887073665424128141292639e-39 ,3.9562085105052983337910283931535691152226618541329e-39 ]
dy0=[-5.9906812627697847063360084685673050695949976547122e-42 ,5.9906779325441043165527146492329238565901838844742e-42 ]
Ddy=[-1.0464618007969042499538927950826902833560247436974e3 ,-1.0464618007969042499534405738809937126220182257316e3 ]
dy=[-5.7247013299556141340087770642378790520438078532554e-45 ,5.7246981475884432982062943859628385486860577262982e-45 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-2.1692666835019985802736513936609498651786717160157e-40 ,2.1692661522937120324816427923175581997270567431919e-40 ]
D0[i][3][0]=[1.6521914906715555457930080002346256216244790932115e-1 ,1.6521914906715555457930080002346256263189464612238e-1 ]
D0[i][3][2]=[-2.6953412733488282911103029611575094882145124607216e-37 ,2.6953412655123596139232093987443806906921317353325e-37 ]
dy0=[-2.1695899951420207311807428961716698932609125777698e-40 ,2.1695897455370503254221335229566766286367761267698e-40 ]
Ddy=[-9.1755534514846210018497511671047287322981385634884e3 ,-9.1755534514846210018078876087309684245477315415804e3 ]
dy=[-2.3645331113961056807051373056298260894501451710012e-44 ,2.3645328393635010803013572191120480013573528978624e-44 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-5.1505924765549574158865645831320227541402679942385e-39 ,5.1505912109095623817307784035476354251946841001813e-39 ]
D0[i][3][0]=[-1.0786238007575202785581842531711820269510853800844e-35 ,1.0786237665496627787299668752075577933306164783804e-35 ]
D0[i][3][2]=[-1.4924381497275124459103182770909527627081026799218e-35 ,1.4924381483712683268248649579103694506646748685852e-35 ]
dy0=[-5.1505924765549574158880605381339519203033388375977e-39 ,5.1505918810458633099980055874952649478781611389912e-39 ]
Ddy=[-2.1833358498911907307009603683962179610072706120171e5 ,-2.1833358498911907304916995108435484648487061239025e5 ]
dy=[-2.3590472701722200119102382636683253987568570620239e-44 ,2.3590469974202775493852929754956276731320993032367e-44 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
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]=[-4.4164188477709530733828833232851892852750192162723e1 ,-4.4164188477709530733828833232851892852749120845017e1 ]
D0[i][5][0]=[8.3843902975958571892393035126201273653571886251799e-1 ,8.3843902975958571892393035126201273653577496528852e-1 ]
D0[i][3][0]=[1.6521914906715555457930080002346256239712883253424e-1 ,1.6521914906715555457930080002346256239721373723011e-1 ]
DBif[i][5][0]=[8.3843902975958571892393035126201273653571517206603e-1 ,8.3843902975958571892393035126201273653577865574047e-1 ]
DBif[i][3][0]=[1.6521914906715555457930080002346256239712097664040e-1 ,1.6521914906715555457930080002346256239722159312395e-1 ]
D[k][3][4]=[-4.4164188477709530733828844088010396113323523728611e1 ,-4.4164188477709530733828822377693389592175789279128e1 ]
_H(5,0,0)=[-3.3475190091851110496920942501928123568507867994964 ,-3.3475190091851110494848109102853482406537486517549 ]
_H(5,0,2)=[4.2210318700765150976661905861922940119202534728954 ,4.2210318700765150980275272118581197467183050836259 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-1.0464618007969042499536666844818419979900875360558e3 ,-1.0464618007969042499536666844818419979879554333731e3 ]
D0[i][5][0]=[-1.5665780697367971553095867716118506010263175113529 ,-1.5665780697367971553095867716118506010131341821968 ]
D0[i][3][0]=[8.6797647883707970248582210449658733837810078231327e-1 ,8.6797647883707970248582210449658733838594478319673e-1 ]
DBif[i][5][0]=[-1.5665780697367971553095867716118506010263666684763 ,-1.5665780697367971553095867716118506010130850250734 ]
DBif[i][3][0]=[8.6797647883707970248582210449658733837802194506477e-1 ,8.6797647883707970248582210449658733838602362044523e-1 ]
D[k][3][4]=[-1.0464618007969042499536673948725069659546435614023e3 ,-1.0464618007969042499536659740911770300233994080266e3 ]
_H(5,0,0)=[-2.7670495039967994195925709682526225789174870801204 ,-2.7670495039967993639961520584869070864678176164687 ]
_H(5,0,2)=[-2.9709435322516531054078603724885559727612985319445e-1 ,-2.9709435322516517450377405298117854661047755582947e-1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-9.1755534514846210018288193879178485787305087128397e3 ,-9.1755534514846210018288193879178485781153613922291e3 ]
D0[i][5][0]=[8.3843902975958571892393035126201273637951246389638e-1 ,8.3843902975958571892393035126201273669198137556893e-1 ]
D0[i][3][0]=[1.6521914906715555457930080002346256216244790932115e-1 ,1.6521914906715555457930080002346256263189464612238e-1 ]
DBif[i][5][0]=[8.3843902975958571892393035126201273637770489366020e-1 ,8.3843902975958571892393035126201273669378894580511e-1 ]
DBif[i][3][0]=[1.6521914906715555457930080002346256216131594367658e-1 ,1.6521914906715555457930080002346256263302661176694e-1 ]
D[k][3][4]=[-9.1755534514846210018288317776279187363416238592881e3 ,-9.1755534514846210018288069982077784205042462457808e3 ]
_H(5,0,0)=[4.9324203229310899907022159846201276362990751434903 ,4.9324203229310958442991226832027736085786371794940 ]
_H(5,0,2)=[-1.1866004838294760959960215463652343914357977036532e1 ,-1.1866004838294735604781135940950281595700000691644e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-2.1833358498911907305963299396198832159532937381185e5 ,-2.1833358498911907305963299396198832099026829978010e5 ]
D0[i][5][0]=[-2.4731725143146335385133261395613323976858589288231e-35 ,2.4731725121236218596110492945159286466067318746498e-35 ]
D0[i][3][0]=[-1.0786238007575202785581842531711820269510853800844e-35 ,1.0786237665496627787299668752075577933306164783804e-35 ]
DBif[i][5][0]=[-2.4739386406037598450388706326465394789406178166286e-35 ,2.4739386384127481661365937876011357278614907624552e-35 ]
DBif[i][3][0]=[-1.0807449632497326959936771539266192969756395721243e-35 ,1.0807449290418751961654597759629950633551706704203e-35 ]
D[k][3][4]=[-2.1833358498911907305963338242382055762327156453863e5 ,-2.1833358498911907305963260550015608496232610905332e5 ]
_H(5,0,0)=[-3.2948227621320340014418019484162042059280345097638e-13 ,3.2948227621320340023795654505646919440587608486737e-13 ]
_H(5,0,2)=[2.7304264840855949874219703615660895934401728161709e1 ,2.7304264840860599977283029242183022187427589175790e1 ]
g=[-2.5502546994513225870037099968875385982753380175873e-35 ,2.5502546996776500422963372417888371890720523340683e-35 ]
Dg=[2.7304264840855949874219703615660895932973452637935e1 ,2.7304264840860599977283029242183022188855864699564e1 ]
r[2]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
Dg!=0.: true
############################

-g/Dg=[-9.3401331789810722627714445688405931244835534367047e-37 ,9.3401331781521634581880350232456975251919316593906e-37 ]
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={[-4.3349085121944871728192045257664980881079437833416e-24 ,4.3349085121944871728192069833073241762339721695115e-24 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-6.1386460627361824747851166134366415946159539205843e-26 ,6.1386460627361824747851024558280558836964359433540e-26 ],[0 ,0 ]}
DH[2]=[-3.7728783962117398783974856407364060781446245985443e-1 ,-3.7728783962117398783974856407364058324234536233145e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-3.7728783962117398783974870563316627966673156937061e-1 ,-3.7728783962117398783974842251411491139007625281560e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-2.1833358498911907305963299396198832522361462184735e5 ,-2.1833358498911907305963299396198831736198305206660e5 ]
_H(5,0,0)=[-1.4161688697033125943582804703404636267073254119657e-23 ,1.4161688686286125581144534343910115902116058984385e-23 ]
_H(5,0,2)=[2.7304264840858274925751354870047673494317491416379e1 ,2.7304264840858274925751377987793302156131658405269e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-5.1866214925862002675694652041350995592197757106446e-25 ,5.1866214965222155476279822593299385527005961881652e-25 ],[0 ,0 ],[-4.9030723729228234632833602747064383551718568114326e-25 ,4.9030723766436594268515003733664938880875577310043e-25 ],[0 ,0 ]}
DH*T2=[-1.3263521608654968328597371840377823422577880893451e-24 ,1.3263521615750347646463754902047772434155703719593e-24 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[2.2654841090120839009303332026514171105278470383446 ,2.2654842010361013915195123351641227827648870465082 ],[0 ,0 ],[-9.2860787303957221515575573815887680582728449974988e-2 ,-9.2860787303957221515561300427553712341645635401435e-2 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-1.4817989708392884360934265963443817483251825389065 ,-1.4817989361197456838078334173849268634418137656507 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0718699461469360570969464883995709445469271050179 ,3.0718699461469360570969464883995709492788336031243 ]
dat/MoonL2_01_PQ.dat at {1.0538331100220000205460218440856744185261965743092 ,0 ,7.4871016628357675794089449244933306178314973889213e-2 ,0 ,3.6200688312371891820950612454167478278116939821477e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 15:19:19 2018
elapsed time: 4hours 43minutes 23seconds