Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_10_PQ.dat at {-9.3084175443043082342670095581828258078038838193837e-1 ,0 ,3.4806811691777132879783846612212866821903779912453e-2 ,0 ,2.0042392150557617949049976895812483504447148040514 ,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]=[-6.7736540562251538123600949327260071128459744487863e-33 ,6.7736538432347054317175027999099841992152710126156e-33 ]
D0[i][3][0]=[3.2458694747454044330864918585981947563761840049842e-1 ,3.2458694747454044330864918587969316195821387118233e-1 ]
D0[i][3][2]=[-4.8529244119760893529510265642585494811648537353022e-30 ,4.8529244126596364976483315507249600869628469945040e-30 ]
dy0=[-1.2463231559725358658287554635965087702231799155642e-32 ,1.4302701111277822679834314273923603117502820272503e-32 ]
Ddy=[1.8747578559912800903307569401547384291522737030501e1 ,1.8747578559912870483161941985979450691895687368976e1 ]
dy=[-7.6290925068375057804543673373648893674782743916824e-34 ,6.6479153667210064912906462639056955629216961362877e-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]=[-7.8798718679659391896312648730378265182810174051906e-31 ,7.8798718676547726551165089971600320066662123561221e-31 ]
D0[i][3][0]=[9.3667109317846398334283012995277984929627114288489e-3 ,9.3667109317846398334283021163706974198544723311660e-3 ]
D0[i][3][2]=[-2.0000716044018856001507095528028123319179915399819e-28 ,2.0000716040296459754190012191332072679498570779935e-28 ]
dy0=[-7.8815137278193487429331386714776762552965995528261e-31 ,7.8852661785311233307580556575598158652713043491331e-31 ]
Ddy=[4.4134880101152238948485820215010649110966968211542 ,4.4134880101153457929929998520364269319801791854149 ]
dy=[-1.7866291152165746940486025975873303173121782604776e-31 ,1.7857788918324453188392868579048964221925595095462e-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
############################

y0[i][3]=[-1.4640601836158974513162269670740669945059920726185e-28 ,1.4640601836294546544492362630985171231344186207500e-28 ]
D0[i][3][0]=[3.2458694747454044330864903821778131100339738826620e-1 ,3.2458694747454044330864933352173132529805625979338e-1 ]
D0[i][3][2]=[-1.8124957772010793387920188760725079217011136653135e-25 ,1.8124957772074312657794347799434147205201852596330e-25 ]
dy0=[-1.4642726169479871466161575627649963534770798588997e-28 ,1.4641170794045077813031045126987532620318560593673e-28 ]
Ddy=[-1.9032356213735523893795871549884310315466363221822e2 ,-1.9032356213734995854532597025276437319154472763647e2 ]
dy=[-7.6935961081438358120794339358285079181127345078956e-31 ,7.6927788811976150429144079886715577035175186486486e-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
############################

y0[i][3]=[-7.0281429310632357793503323904770880045462481531203e-27 ,7.0281429310630449042988899698608444005215976284802e-27 ]
D0[i][3][0]=[-5.1663251605536914879045561119749006710456834732537e-24 ,5.1663251605532577616272608128917996808867801351109e-24 ]
D0[i][3][2]=[-6.8540889883999383991690870358995064122070199405592e-24 ,6.8540889884002375743275914056311816465587017225618e-24 ]
dy0=[-7.0281456822208521637234025861643513888942766882788e-27 ,7.0281429310631134451953300628865611340124824396886e-27 ]
Ddy=[-3.3069497978952450953631544647683524443161822145765e1 ,-3.3069497978950103679781367208447604396404810800356e1 ]
dy=[-2.1252653084405797763505724738151658504890383986710e-28 ,2.1252644765084650312956131854577898510299310286651e-28 ]
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]=[1.8747578559912835693234755068253669564686507527563e1 ,1.8747578559912835693234756319273165418731916871914e1 ]
D0[i][5][0]=[4.3875063415900251383377084979690527538595012281862e-1 ,4.3875063415900251383377084980578559309633477297363e-1 ]
D0[i][3][0]=[3.2458694747454044330864918585981947563761840049842e-1 ,3.2458694747454044330864918587969316195821387118233e-1 ]
DBif[i][5][0]=[4.3875063415900251383377081503559463094785962934408e-1 ,4.3875063415900251383377088456709623753442526644817e-1 ]
DBif[i][3][0]=[3.2458694747454044330864911688747812705407234669638e-1 ,3.2458694747454044330864925485203451054175992498437e-1 ]
D[k][3][4]=[1.8747578559912830334017094123886484398514363280486e1 ,1.8747578559912841052452417263640350584904061118991e1 ]
_H(5,0,0)=[-2.0803265611279891485179082885454593512612703551978e1 ,-2.0803265608408924060770575628568326723938006656452e1 ]
_H(5,0,2)=[3.6066697898236518845045097458672144591521502255189e1 ,3.6066697900932919389313908226988502240074160712094e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[4.4134880101152848439207896431634650761545427234142 ,4.4134880101152848439207922303740267669223332831549 ]
D0[i][5][0]=[-3.7107154209315168335241903726198420719467587107209e-2 ,-3.7107154209315168335241903707854849148857925599923e-2 ]
D0[i][3][0]=[9.3667109317846398334283012995277984929627114288489e-3 ,9.3667109317846398334283021163706974198544723311660e-3 ]
DBif[i][5][0]=[-3.7107154209315168335241904125589704967219581810256e-2 ,-3.7107154209315168335241903308463564901105930896876e-2 ]
DBif[i][3][0]=[9.3667109317846398334282945039254722077183446956420e-3 ,9.3667109317846398334283089119730237050988390643729e-3 ]
D[k][3][4]=[4.4134880101152846983611306152406175502148206703356 ,4.4134880101152849894804512582968742928620553362335 ]
_H(5,0,0)=[-3.2398058102340109555298056935377851095939840030945e-1 ,-3.2398036419379721571238184897108285179937877151244e-1 ]
_H(5,0,2)=[1.1774625807572087553554450319107534047562377661738 ,1.1774627867190610567253004725226061998346329301899 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-1.9032356213735259874164241331904830930488201272378e2 ,-1.9032356213735259874164227243255916704132634713090e2 ]
D0[i][5][0]=[4.3875063415900251383377077755986596155047983741275e-1 ,4.3875063415900251383377092204282490882747045995713e-1 ]
D0[i][3][0]=[3.2458694747454044330864903821778131100339738826620e-1 ,3.2458694747454044330864933352173132529805625979338e-1 ]
DBif[i][5][0]=[4.3875063415900251383377028395321181553180092853212e-1 ,4.3875063415900251383377141564947905484614936883776e-1 ]
DBif[i][3][0]=[3.2458694747454044330864884500808169917168463180442e-1 ,3.2458694747454044330864952673143093712976901625516e-1 ]
D[k][3][4]=[-1.9032356213735261089244222579030766845338117586750e2 ,-1.9032356213735258659084245996129980789282718398718e2 ]
_H(5,0,0)=[1.7833581392139304743369061758269089318272109072067e1 ,1.7833592431096484436524670982049764358149348525685e1 ]
_H(5,0,2)=[-3.3113624174065892704941407659832105836082277422337e1 ,-3.3113612757980207606800830923053721439335424966282e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-3.3069497978951277316707085782878259158141785127407e1 ,-3.3069497978951277316705826073252869681424847818715e1 ]
D0[i][5][0]=[-1.1484405397601001886890088742212056366102911000850e-25 ,1.1484405397565481739283933126283991188696937840627e-25 ]
D0[i][3][0]=[-5.1663251605536914879045561119749006710456834732537e-24 ,5.1663251605532577616272608128917996808867801351109e-24 ]
DBif[i][5][0]=[-2.5224705894835616726735780921559205907378874419242e-25 ,2.5224705894800096579129625305631140729972901259018e-25 ]
DBif[i][3][0]=[-5.2042786922329521421870001013538586045052410510251e-24 ,5.2042786922325184159097048022707576143463377128823e-24 ]
D[k][3][4]=[-3.3069497978951282510207526604278324333453477919453e1 ,-3.3069497978951272123205385251852804506113155026668e1 ]
_H(5,0,0)=[-2.2536484352920015783761429812108896005157833206328e-4 ,2.2536484352920927071475956782214549942627759140942e-4 ]
_H(5,0,2)=[3.8683349454788578948957905389762584965449202513825 ,3.8689078584844637300540673383197055830621340127171 ]
g=[-3.9906789668120418652638776699379205463023657749347e-24 ,3.9906789668120028372195754896060096106531028140585e-24 ]
Dg=[3.8683349454788578946881883270006800705865519970912 ,3.8689078584844637302616695502952839853935255174608 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-1.0316270496369853723013174900599695314226091443840e-24 ,1.0316270496369954614080913992369272928093046871472e-24 ]
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={[-9.2118277511492758142759232678855185649177208864734e-16 ,9.2118277511492747658880567511095906028098153522101e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.6638571156411905393476276087950988931057704377676e-17 ,1.6638571156411904297990118720729470403608356842663e-17 ],[0 ,0 ]}
DH[2]=[1.2594261051047022661034791551958214711592595755673e-1 ,1.2594261051047022661035528391234415474764399914475e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[1.2594261051047015972740679510360176589873819672704e-1 ,1.2594261051047029349329640432832893954825684195789e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-3.3069497978951277316707621552714356887962004728022e1 ,-3.3069497978951277316705290303416771956844350624856e1 ]
_H(5,0,0)=[-1.7420022327981583392636003413596766654940719820338e-13 ,1.7420022332640546345603523868222439024875428473002e-13 ]
_H(5,0,2)=[3.8686214019814959310008587169445523741558053227416 ,3.8686214019818257084112249046661589667375947661759 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.5029018150284917312994717281509510351556144496845e-14 ,4.5029018138241963327936334409607658763153987858200e-14 ],[0 ,0 ],[-3.5728361113266856613237201902352561653801458714408e-15 ,3.5728361122822361629317788107382332346751186564654e-15 ],[0 ,0 ]}
DH*T2=[-2.0032989663422161526773814187624828856201826865590e-14 ,2.0032989658064363766856528578264118904094357981337e-14 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[2.5608251940848550837099702732667787203744713301479 ,2.1041895461438870470146584232718441357180154162434e1 ],[0 ,0 ],[-3.9182288298685643500443382460636342425855470584604e-1 ,-3.9182288298683792168213640913688070770316736994144e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[2.9403373185193878747485844073542184492097593251807 ,5.2678915530180058983659553154392752307713125936739 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [-1.0022784586182533648812736926707598955200170946062 ,-1.0022784586182533648812707608773394832696276961313 ]
dat/JupiterL1_10_PQ.dat at {-9.3084175443043082342670095581828258078038838193837e-1 ,0 ,3.4806811691777132879783846612212866821903779912453e-2 ,0 ,2.0042392150557617949049976895812483504447148040514 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 13:18:29 2018
elapsed time: 2hours 42minutes 33seconds