Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL2_02_PT.dat at {1.0352452449582038316391331458182477850665293611531 ,0 ,7.5021753557565546955064888352908642209894948240001e-2 ,0 ,4.1978964451292388650258250150626740330451527892493e-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]=[-6.3743977125947261068645739325994916649580107048284e-34 ,6.3743953905681746340640620862897428083232377803832e-34 ]
D0[i][3][0]=[1.8321882388320227731598335410047938199944294532606e-1 ,1.8321882388320227731598335410083258138029098086795e-1 ]
D0[i][3][2]=[-1.5041840122553003426027423226141613624005607723619e-31 ,1.5041839987844812554794557369347872856238034948660e-31 ]
dy0=[-8.8994812858519127334075131253369517221846569404451e-34 ,1.5489462420592150187692535649072335270622092230120e-33 ]
Ddy=[3.8942177438689512095749654367822790649806522411213e1 ,3.8942177438689594437385600834420351087062595886792e1 ]
dy=[-3.9775542713241265185400203367572524428250822799816e-35 ,2.2853065419526780810335782017312334620350561084716e-35 ]
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]=[-4.5374264008901132156445656551052979091446706346483e-32 ,4.5373996316620013736752717933785993527590782876287e-32 ]
D0[i][3][0]=[9.0445726189454421273559134909902643690924284156327e-1 ,9.0445726189454421273559134913472212783379100091209e-1 ]
D0[i][3][2]=[-1.9996552317867090304737745612609059513511841210848e-29 ,1.9996568337359678159425643996799394349009863011743e-29 ]
dy0=[-4.6620768121480382412119243753775960215464784012423e-32 ,5.8729968272314259912029966685603571741131864814101e-32 ]
Ddy=[6.9223203142304630566513114024442902033787176170961e2 ,6.9223203142306754174052068201984216877979409446474e2 ]
dy=[-8.4841448540861291839788133478155144941843739597319e-35 ,6.7348469884643146533653568829221042951024055744668e-35 ]
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]=[-1.4735411708164629088248420803651250550222427503025e-30 ,1.4735400085723834870445447073502806896763725326092e-30 ]
D0[i][3][0]=[-1.1075168766721844932160344649707108324442470969946e-27 ,1.1075168848831606494421471172384718300846206530997e-27 ]
D0[i][3][2]=[-1.6329992016484723572489967596728790183402313059889e-27 ,1.6329992588552220908653315693847074384176453674614e-27 ]
dy0=[-1.4735411708164792845515652194760361744110435863506e-30 ,1.5449605738601749797163065262305041653456147396355e-30 ]
Ddy=[4.0321311441840208396219670637180265308811087064176e3 ,4.0321311441841444985129020336641129343903571339173e3 ]
dy=[-3.8316228282620192839619584461777353441632904452372e-34 ,3.6544971334623557607728042838878805770714958602182e-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
############################

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

DBif[i][3][4]=[3.8942177438689553266567627601118436705052208641438e1 ,3.8942177438689553266567627601124705031816909656567e1 ]
D0[i][5][0]=[9.7998578403124291295269321448662192293003873355397e-1 ,9.7998578403124291295269321448684946876432479609374e-1 ]
D0[i][3][0]=[1.8321882388320227731598335410047938199944294532606e-1 ,1.8321882388320227731598335410083258138029098086795e-1 ]
DBif[i][5][0]=[9.7998578403124291295269321448653000892113320489487e-1 ,9.7998578403124291295269321448694138277323032475284e-1 ]
DBif[i][3][0]=[1.8321882388320227731598335410036260181710739175558e-1 ,1.8321882388320227731598335410094936156262653443843e-1 ]
D[k][3][4]=[3.8942177438689552653845694327712106242827522180629e1 ,3.8942177438689553879289560874531035494041596117375e1 ]
_H(5,0,0)=[-1.7024414507178526548524408232677537345561516713475 ,-1.7024414506919771248310487263057953294316639173295 ]
_H(5,0,2)=[-2.5773336522433046820806999299325541554106674398215 ,-2.5773336522014045140375053494218961063392344835562 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[6.9223203142305692370282591112693202950822573365023e2 ,6.9223203142305692370282591113733915960944012252412e2 ]
D0[i][5][0]=[-1.2402280142297818162690173194238169869513735755049 ,-1.2402280142297818162690173193559110273103355057531 ]
D0[i][3][0]=[9.0445726189454421273559134909902643690924284156327e-1 ,9.0445726189454421273559134913472212783379100091209e-1 ]
DBif[i][5][0]=[-1.2402280142297818162690173194240528797620106677548 ,-1.2402280142297818162690173193556751344996984135031 ]
DBif[i][3][0]=[9.0445726189454421273559134909823511765397821527349e-1 ,9.0445726189454421273559134913551344708905562720186e-1 ]
D[k][3][4]=[6.9223203142305687714128792506640441650744171395660e2 ,6.9223203142305697026436389719786677261022414221775e2 ]
_H(5,0,0)=[-1.3440448290192773174025229572090598488627912765156 ,-1.3440448209192938771707416104630892520055854682753 ]
_H(5,0,2)=[-6.6656259836028058761406322444444179876696008966090 ,-6.6656259669841570200126130143777014743104023004984 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[4.0321311441840826690674345473424528837329624117587e3 ,4.0321311441840826690674345500396865815385034285762e3 ]
D0[i][5][0]=[-7.9816569839532118283599393860188230122914025413590e-28 ,7.9816569491442467053020301707081201349636435418744e-28 ]
D0[i][3][0]=[-1.1075168766721844932160344649707108324442470969946e-27 ,1.1075168848831606494421471172384718300846206530997e-27 ]
DBif[i][5][0]=[-8.0761443847887431711872591227563072004887859959776e-28 ,8.0761443499797780481293499074456043231610269964931e-28 ]
DBif[i][3][0]=[-1.1130736563062502178402967027538703726796833315216e-27 ,1.1130736645172263740664093550216313703200568876268e-27 ]
D[k][3][4]=[4.0321311441840821273960861101139231464184229843500e3 ,4.0321311441840832107387829872682163188530428559849e3 ]
_H(5,0,0)=[-2.6039097858812740972937746913409156040773916689262e-7 ,2.6039097858912569309971988188744804009044721831404e-7 ]
_H(5,0,2)=[1.7391626246526915432281715278904791240078489808891e1 ,1.7391627885684403241279032230067039890036677232638e1 ]
g=[-1.8027547933067046334586056563619660446154813529318e-27 ,1.8027547972408440619904669571061261488061505124513e-27 ]
Dg=[1.7391626246526915432281658693467428198055629569669e1 ,1.7391627885684403241279088815504402932059696969344e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-1.0365648224534791798557395122805714174177841082638e-28 ,1.0365648201913908778388400299798474656574654286734e-28 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-3.3652552758573349629508203817754733568141106177379e-1 ,-3.3652552758573348940152440118468214481157267644078e-1 ],[3.9932109893041649757554525984506942071991614366392e2 ,3.9932109893041649780057084599366378202633631650129e2 ],[2.2250053526741290849687495084166394144527599908557e-1 ,2.2250053526741291586935917377094721040492680942692e-1 ],[1.9935226488719076657197878382642301652722040993204e2 ,1.9935226488719076667568715110667612142612296117738e2 ],[2.8869994045461903100957102176985057856310008551616e3 ,2.8869994045461903116044846442754872074848338847967e3 ],[1.4538101186524120604843435471664872304236774822206e2 ,1.4538101186524120612876492056071889424975634634362e2 ]},
{[-3.4611450469451040197305877873829325349704850789903e-21 ,3.4611450469451040197305867373874725950696362577594e-21 ],[-5.0787248902756196950239124456187284513719244390412e-19 ,5.0787248902756196950239539113616977047027374763153e-19 ],[-3.9480863878511317083958450924824152035929979073281e-21 ,3.9480863878511317083958205013822692188063893631612e-21 ],[-2.5742310625864892000789252683868005276245069417666e-19 ,2.5742310625864892000789463584788244970185427724533e-19 ],[-3.6958241470378258881159760531584001698097099038981e-18 ,3.6958241470378258881160068276127045237722540988940e-18 ],[-1.8534670949749868195774576750318971754681349944681e-19 ,1.8534670949749868195774728161716062411026887227290e-19 ]},
{[-3.7264820744558716968158728472338745497975017489550e-1 ,-3.7264820744558716829649900039593183231447988029001e-1 ],[-7.4657350433000016340832353988009961676236957217992e1 ,-7.4657350433000016290245530063763503925714847113134e1 ],[3.0419343218949796649264777389885488948564302335141e-1 ,3.0419343218949796802161907740752282180001453261819e-1 ],[-3.7271038117343994640699496366726548934260373155650e1 ,-3.7271038117343994617307335697498067658243419211051e1 ],[-5.4496553507230674815455902183427469883651003276719e2 ,-5.4496553507230674781412013051838857747290587657292e2 ],[-2.7180535108711505620157079484625551100074179895991e1 ,-2.7180535108711505602070189932506494981569713596380e1 ]},
{[-4.8119564173594569177080390823257360155683844520117e-18 ,4.8119568555751860045296257713825890696369583902477e-18 ],[5.5746750277742433071119070025925775834121094717853e2 ,5.5746750277742433103226291223828199221378163462405e2 ],[-5.1749571040848907618336082945321697485444339913302e-18 ,5.1749574835032555999008084117165994779108958830486e-18 ],[2.7806295053407226515093536486514988690656303788759e2 ,2.7806295053407226529903824556973146829556247539071e2 ],[4.0321311441840826679900957373990536929054921545158e3 ,4.0321311441840826701447737903410075998282043796234e3 ],[2.0292984097327340819934815663193460877628645590350e2 ,2.0292984097327340831400442806118853833924524416313e2 ]},
{[8.5443117815022695768095406534173487044142874074317e-1 ,8.5443117815022696485199087975596686246493305340202e-1 ],[-3.5249111073738090781722044519930618393190867989377e2 ,-3.5249111073738090758360312812586099247701185538349e2 ],[5.2954906295897006835068815916855649777041429399364e-2 ,5.2954906295897014489303107794259517654754924300828e-2 ],[-1.7597342456062733454485111895760265639466267399636e2 ,-1.7597342456062733443716650943768791024404503884699e2 ],[-2.5486282856981206943900546488518383283745836536782e3 ,-2.5486282856981206928234552905622772671475438878052e3 ],[-1.2833159702746632889190971558692054337248703747447e2 ,-1.2833159702746632880850919866343532478455592215499e2 ]},
{[-4.1710501224151565706629727586982287453405426321395e-18 ,4.1710497303853441469300747380270969125821946815674e-18 ],[-5.0065037122342988729370825070089617119912746387175e2 ,-5.0065037122342988702638223424930078467420927061338e2 ],[-4.4363069803678970830422190803763555752866302596788e-18 ,4.4363066391161978481872239339048456414741681078003e-18 ],[-2.5122463174940814690047479723164651128946401207276e2 ,-2.5122463174940814677729311912150978612023814452976e2 ],[-3.6412719734455505736229000620606569243884094036834e3 ,-3.6412719734455505718309880727813254973583024705365e3 ],[-1.8241964717190052972384228658418500717645172298639e2 ,-1.8241964717190052962842718445403979663758778286944e2 ]}
}
D[2]={
{[-3.3652552758573349739577591930060111846886586604868e-1 ,-3.3652552758573348830083052866009215821729034759874e-1 ],[3.9932109893041649727793261037438103324200054645636e2 ,3.9932109893041649809818350224657669558823493689578e2 ],[2.2250053526741290583578644170228883874531943096813e-1 ,2.2250053526741291853044765597884253402836231293807e-1 ],[1.9935226488719076642496778929672036909062081243042e2 ,1.9935226488719076682269814911505326494984739584833e2 ],[2.8869994045461903079578749797256585318934654714869e3 ,2.8869994045461903137423199328144425717979433448982e3 ],[1.4538101186524120593950509719821399248036628981856e2 ,1.4538101186524120623769418055877989531566535544388e2 ]},
{[-1.6186077315504848127488955852225492197107107218693e-18 ,1.6186077315504848127389097264994070901651435669547e-18 ],[-1.8672966325677945580894622339949412306068110019573e-16 ,1.8672966325677945581009823571251818474882559092645e-16 ],[-2.2442177565625941650308837481679192418845657725219e-18 ,2.2442177565625941650170382431550809578112331489363e-18 ],[-9.2123617468332081552348504669936956149352548409347e-17 ,9.2123617468332081552916853264331928374504427599282e-17 ],[-1.3387276339679291102851535606480575422928971327159e-15 ,1.3387276339679291102934127236070558673685953850407e-15 ],[-6.8248362578352069736707426587929481387141912479629e-17 ,6.8248362578352069737128478887080659109555030190455e-17 ]},
{[-3.7264820744558717012220438488369459786158250433321e-1 ,-3.7264820744558716785588188738227690598283566204301e-1 ],[-7.4657350433000016450340157618696522655082958925299e1 ,-7.4657350433000016180737738663606047704752831387346e1 ],[3.0419343218949796564821232875792665090398124905374e-1 ,3.0419343218949796886605452814455528030734833911715e-1 ],[-3.7271038117343994695359480615573194216175802496708e1 ,-3.7271038117343994562647357610300249226070539776508e1 ],[-5.4496553507230674894879244316912174753203534517587e2 ,-5.4496553507230674701988679846494825904525694416137e2 ],[-2.7180535108711505660352290301133812601292971936556e1 ,-2.7180535108711505561874983575070746747205757492554e1 ]},
{[-6.9580216620740363955561869207465112239017964249296e-18 ,6.9580220986153980231845101681464816104598062581548e-18 ],[5.5746750277742433012615015401128649859990224276013e2 ,5.5746750277742433161730346729784489178471733250655e2 ],[-9.7166106603763515520072652022577288950731400494032e-18 ,9.7166109832609705005337126457971954985266733969824e-18 ],[2.7806295053407226485763859448462181716170315180526e2 ,2.7806295053407226559233502048464609590397482123040e2 ],[4.0321311441840826637251448958939516829363705391499e3 ,4.0321311441840826744097246979818079759285483934277e3 ],[2.0292984097327340798405999505782144138485478261002e2 ,2.0292984097327340852929259285820578095558714719854e2 ]},
{[8.5443117815022695666446918442065213167739620570135e-1 ,8.5443117815022696586847577581440709607173053004392e-1 ],[-3.5249111073738090818982288324197944455130719581116e2 ,-3.5249111073738090721100069729926471525485877213135e2 ],[5.2954906295897004225587150946765786317824519517492e-2 ,5.2954906295897017098784793155371116687516550182041e-2 ],[-1.7597342456062733473207306267576460301273052304873e2 ,-1.7597342456062733424994456942363210705811154575696e2 ],[-2.5486282856981206971128658323165835165529413543124e3 ,-2.5486282856981206901006441608438292724192098945576e3 ],[-1.2833159702746632902917512340593382918143075551353e2 ,-1.2833159702746632867124379348336463151917477542855e2 ]},
{[-5.0817745615999814245880524688459747178201465439959e-18 ,5.0817742057709081699083906323261897157401429474542e-18 ],[-5.0065037122342988767764372332065619778668448356516e2 ,-5.0065037122342988664244678957180931826028566009453e2 ],[-7.0950658571962660607250303040584545046987951183384e-18 ,7.0950655545835051614963867898549837023155766672396e-18 ],[-2.5122463174940814709206763352517954991623341677617e2 ,-2.5122463174940814658570029691123264791497228417722e2 ],[-3.6412719734455505764082152063684502260830890922816e3 ,-3.6412719734455505690456731327620098050705038287045e3 ],[-1.8241964717190052986485659068630391831895154991172e2 ,-1.8241964717190052948741289053998514418534359785316e2 ]}
}
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={[-2.1730951536661690330421820965200761638861536525871e-16 ,2.1730951536661690391674896570905033791034797935901e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.5425715440819830306336616507634790701446582559110e-18 ,3.5425715440819829180904979889516199642037072550831e-18 ],[0 ,0 ]}
DH[2]=[3.1071677661662347623466640830341163825488449049749e-1 ,3.1071677661662347623466641071872047480951773527754e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[3.1071677661662346531040400461244504884131988835285e-1 ,3.1071677661662348715892881440968741125879712848297e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[4.0321311441840826690674345417276782479530404957493e3 ,4.0321311441840826690674345556544612050653411698315e3 ]
_H(5,0,0)=[-6.4673160573268265805130551586313765822267623826669e-15 ,6.4673160548138845160748774388340749563413593951230e-15 ]
_H(5,0,2)=[1.7391627066105647166931777334490549493315338691443e1 ,1.7391627066105671505495690582598545938160010417434e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.7186377273567269821543396911586691575610628829396e-16 ,3.7186377288016418569308481972199900978723750408447e-16 ],[0 ,0 ],[-1.9692011240141876127624647695691650470424683404639e-17 ,1.9692011247793409307742558970458124207276390196440e-17 ],[0 ,0 ]}
DH*T2=[2.3423579463330704415142883006174860144834394480532e-6 ,2.3423579466856023023168686164814633678679140371499e-6 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [3.0508350386522086394609997887756339364669273868380 ,3.0508350386522086394609997892897960685452197128656 ]
dat/MoonL2_02_PT.dat at {1.0352452449582038316391331458182477850665293611531 ,0 ,7.5021753557565546955064888352908642209894948240001e-2 ,0 ,4.1978964451292388650258250150626740330451527892493e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:50:18 2018
elapsed time: 0hours 14minutes 22seconds