Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL2_04_PQ.dat at {9.9011234298616825691201751869050771278989133347734e-1 ,0 ,3.8893395834689105529370100146358399199678618074882e-2 ,0 ,7.4695384574560705105765751945180413416934712887773e-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]=[-1.1909683193400541491996144190187919440550519740589e-43 ,1.1909682238586772212635424284309697923389249674435e-43 ]
D0[i][3][0]=[-6.0459640137549064893551725466623152334160555679223e-2 ,-6.0459640137549064893551725466623152334133062533545e-2 ]
D0[i][3][2]=[-1.4271751449244470051789685457271529144777060056585e-41 ,1.4271759510888191976142158714969340011985878426239e-41 ]
dy0=[-2.9848594273982870261367245597790805994600872059489e-43 ,2.9848585738765627890277501182187905330634955617651e-43 ]
Ddy=[-5.2310521220635626611054901476265975720917636721305e1 ,-5.2310521220635626611053979518368280318395025531150e1 ]
dy=[-5.7060403103397292348499718565404234735089507674338e-45 ,5.7060386786952639902388839942502569740638888549025e-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]=[-2.0467790467613020969686006292790629155687280288749e-41 ,2.0467790470095421351914565318331001094705178538411e-41 ]
D0[i][3][0]=[1.5965869072076670382252300442934928469113145313864e-1 ,1.5965869072076670382252300442934928469960586187053e-1 ]
D0[i][3][2]=[-6.9826964435906746966298857456530539894613243931435e-39 ,6.9826964332580139926170190597884406770522436253563e-39 ]
dy0=[-2.0941511753298602826042991823789948723976234083012e-41 ,2.0941511864426638444311337526734854912736243844010e-41 ]
Ddy=[5.8513738080710781499635299234546872348412052960030e1 ,5.8513738080710781499953793838325454600435217453684e1 ]
dy=[-3.5789051513921423505909498148982185817013197633350e-43 ,3.5789051324003569573924907475413704405743804504480e-43 ]
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]=[-3.2042783134722491958580624051983165932881164289807e-39 ,3.2042783134674497265814190205423257971984806674126e-39 ]
D0[i][3][0]=[-6.0459640137549064893551725466623153480171768941894e-2 ,-6.0459640137549064893551725466623151188121849263454e-2 ]
D0[i][3][2]=[-2.2571541976903307053964382437473626170958541425994e-36 ,2.2571541977133821652058890942180988032789503940586e-36 ]
dy0=[-3.2044577025632342832258232060041317083349550779728e-39 ,3.2044577025024515151384211545564014566191201765659e-39 ]
Ddy=[-3.5068467111550958549243870394994316520484735887121e1 ,-3.5068467111550958548966066002215502603282938017974e1 ]
dy=[-9.1377182024239098872459989982156872528821861154592e-41 ,9.1377182022505838964233740820178984993213894893395e-41 ]
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]=[-3.5051157228319567857931922465731377966512326799821e-37 ,3.5051157228317166405635238462546368282755410004442e-37 ]
D0[i][3][0]=[-1.1225979344829407167724091869841696614647916411855e-34 ,1.1225979344828341762318948637659786303105286954741e-34 ]
D0[i][3][2]=[-4.4178398374343414266018289314750958913139405857288e-34 ,4.4178398374341233339398622232483574234036768359691e-34 ]
dy0=[-3.5051157228319567857936340306004327634278358003372e-37 ,3.5051157228324600552279793659257182957348128956390e-37 ]
Ddy=[6.4669626365218048684814863307399835879733423743651e1 ,6.4669626365218048685250684908377084141912893300156e1 ]
dy=[-5.4200339786061507770412335588156279562804217066587e-39 ,5.4200339786053725609564472485841792608894968872512e-39 ]
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]=[-5.2310521220635626611054440497317128043936302360907e1 ,-5.2310521220635626611054440497317127995376359891547e1 ]
D0[i][5][0]=[-1.9205686653170177069914712241839893563747680566613e-2 ,-1.9205686653170177069914712241839893563718389583253e-2 ]
D0[i][3][0]=[-6.0459640137549064893551725466623152334160555679223e-2 ,-6.0459640137549064893551725466623152334133062533545e-2 ]
DBif[i][5][0]=[-1.9205686653170177069914712241839893983874353410136e-2 ,-1.9205686653170177069914712241839893143591716739730e-2 ]
DBif[i][3][0]=[-6.0459640137549064893551725466623153130849139601409e-2 ,-6.0459640137549064893551725466623151537444478611360e-2 ]
D[k][3][4]=[-5.2310521220635626611054453523207020534601914848349e1 ,-5.2310521220635626611054427471427235504710747404106e1 ]
_H(5,0,0)=[-1.3986537849663082834208465796984015441364818190133 ,-1.3986537849663082832352153039697094268694510629312 ]
_H(5,0,2)=[-3.0072249857411058061047853336724323245430284803207 ,-3.0072249857411058057283474166117117636466463966482 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[5.8513738080710781499794546536436154852861179269938e1 ,5.8513738080710781499794546536436172095986091143777e1 ]
D0[i][5][0]=[-1.6144580484649959132301143419529234508172514331138e-1 ,-1.6144580484649959132301143419529234504866977607243e-1 ]
D0[i][3][0]=[1.5965869072076670382252300442934928469113145313864e-1 ,1.5965869072076670382252300442934928469960586187053e-1 ]
DBif[i][5][0]=[-1.6144580484649959132301143419529234659552961344907e-1 ,-1.6144580484649959132301143419529234353486530593474e-1 ]
DBif[i][3][0]=[1.5965869072076670382252300442934928466010052594990e-1 ,1.5965869072076670382252300442934928473063678905928e-1 ]
D[k][3][4]=[5.8513738080710781499794330343585991748039183394993e1 ,5.8513738080710781499794762729286335200808087018721e1 ]
_H(5,0,0)=[1.0014072178347068105981232057551293141290340925127e1 ,1.0014072178347069402374192291294722065472864799473e1 ]
_H(5,0,2)=[9.7785206791269088589867748384800429747461184854885 ,9.7785206791269107924006203357345735697409629889402 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-3.5068467111550958549104968198604917942195962621569e1 ,-3.5068467111550958549104968198604901181571711283525e1 ]
D0[i][5][0]=[-1.9205686653170177069914712241839894569376374619309e-2 ,-1.9205686653170177069914712241839892558089695533574e-2 ]
D0[i][3][0]=[-6.0459640137549064893551725466623153480171768941894e-2 ,-6.0459640137549064893551725466623151188121849263454e-2 ]
DBif[i][5][0]=[-1.9205686653170177069914712241839897901597774019166e-2 ,-1.9205686653170177069914712241839889225868296133717e-2 ]
DBif[i][3][0]=[-6.0459640137549064893551725466623155159732830019884e-2 ,-6.0459640137549064893551725466623149508560788185463e-2 ]
D[k][3][4]=[-3.5068467111550958549105105006568434459993057890637e1 ,-3.5068467111550958549104831390641384663774616014458e1 ]
_H(5,0,0)=[-1.3558628960574075822274029290077637807041769270318 ,-1.3558628960573019185067396095687712568693647292581 ]
_H(5,0,2)=[-9.5831251471507706045194095582061163247711789965746e-2 ,-9.5831251471317777700174965805690435812418037368601e-2 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[6.4669626365218048685032774107888199748654970946210e1 ,6.4669626365218048685032774107888720272991346097597e1 ]
D0[i][5][0]=[-4.0916353724042863242944593917099530051445085008106e-34 ,4.0916353724044817688295372762842999585088372321490e-34 ]
D0[i][3][0]=[-1.1225979344829407167724091869841696614647916411855e-34 ,1.1225979344828341762318948637659786303105286954741e-34 ]
DBif[i][5][0]=[-4.0975858875750424091226285546770924308108137102570e-34 ,4.0975858875752378536577064392514393841751424415954e-34 ]
DBif[i][3][0]=[-1.3260981228551926934298531530190078976017351988476e-34 ,1.3260981228550861528893388298008168664474722531361e-34 ]
D[k][3][4]=[6.4669626365218048685032754410642763476328004866052e1 ,6.4669626365218048685032793805134156545318312177755e1 ]
_H(5,0,0)=[-4.4368761530115524546368165300435640830091488813027e-12 ,4.4368761530115524494978845660123265317572044540959e-12 ]
_H(5,0,2)=[-1.6201200678419482049106533222930150291639562275625 ,-1.6201200678081312605859608049555945159095242837972 ]
g=[-4.4441105434138280286047313023140662577267312144491e-34 ,4.4441105434139956328491411985309030637069176216354e-34 ]
Dg=[-1.6201200678419482049106533222930151594671619087435 ,-1.6201200678081312605859608049555943856063186026162 ]
r[2]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
Dg!=0.: true
############################

-g/Dg=[-2.7430748076753891144763081956710062855894955996341e-34 ,2.7430748076754925662190155425762976594342745573286e-34 ]
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={[-2.9368231428487595059561730813612949701436397377399e-23 ,2.9368231428487595059561765623803535799315706428026e-23 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.2991153832089544693188782701816318962874621299255e-26 ,2.2991153832089544693188983214431531068815466763480e-26 ],[0 ,0 ]}
DH[2]=[-2.1621635243384306592687741450325958649873209233098e-2 ,-2.1621635243384306592687741450312813347605949136425e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-2.1621635243384306592688103451089715718728165827114e-2 ,-2.1621635243384306592687379449549056278750992539251e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[6.4669626365218048685032774107888145717637235138330e1 ,6.4669626365218048685032774107888774304009081907515e1 ]
_H(5,0,0)=[-4.2878070366144966417869665262349898845966899221969e-23 ,4.2878070366174466800580244504800644899832076397194e-23 ]
_H(5,0,2)=[-1.6201200678250397327483973198003187319945835178559 ,-1.6201200678250397327482168073941723044083964900300 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.6465983119206361128468654187851783069271717521131e-23 ,2.6465983119224569891693334553042383604494947506669e-23 ],[0 ,0 ],[-2.6341393516667109614142604977633233047284472227452e-23 ,2.6341393516648986569349925393139525179032957075845e-23 ],[0 ,0 ]}
DH*T2=[-4.1532326082458755154389744485460790763501187014236e-22 ,4.1532326082430180652230295344592223192499027646015e-22 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[6.4044503270211884279724164643913114324534808991323e1 ,6.4044503446313818634417733216807734476879423193201e1 ],[0 ,0 ],[-3.0943387241769097416848518540479355091592948571838e-1 ,-3.0943387241769097416845682906235985648446221229120e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-1.3615635789458483991493407284137821307837627703882 ,-1.3615635751382366088682515641989924437828403183854 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0158978159595140970471858000274980469913165535332 ,3.0158978159595140970471858000274997550951843627673 ]
dat/MoonL2_04_PQ.dat at {9.9011234298616825691201751869050771278989133347734e-1 ,0 ,3.8893395834689105529370100146358399199678618074882e-2 ,0 ,7.4695384574560705105765751945180413416934712887773e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 17:51:19 2018
elapsed time: 7hours 15minutes 23seconds