Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL2_05_PD.dat at {9.8898097866095133255830060643019829971109116498313e-1 ,0 ,3.4886155332975552497395589007678477358050781252444e-2 ,0 ,7.9336441942459750951338573417434034513436770592672e-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]=[-3.3907868981689613684237650823578673168295846162869e-34 ,3.3907871164423888971271765446139343359434380230119e-34 ]
D0[i][3][0]=[-1.6245120640758717656885414854027234018848206723312e-1 ,-1.6245120640758717656885414854014836902847642905339e-1 ]
D0[i][3][2]=[-6.0217937869621625720426356163434528972646319667237e-32 ,6.0217934564009303705102256499240200933369687842820e-32 ]
dy0=[-1.6305745660491899994686530499757359858023707268381e-33 ,9.0221026820113905119622247001054980609035366279799e-34 ]
Ddy=[5.8959994200059439824650267163428684808198326018010e1 ,5.8959994200059637961938952506657294100409428837658e1 ]
dy=[-1.5302075253600169087641519536036170419263240403346e-35 ,2.7655609335991864037515889071714101850372635007687e-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]=[-6.3906060965645990748180463441126469457197149489800e-32 ,6.3906062882997434436588529821932682076583421870342e-32 ]
D0[i][3][0]=[-9.3048736607027196887671001252221837000720226015562e-30 ,9.3048737029931822594288664909220038525351565964976e-30 ]
D0[i][3][2]=[-2.4463954570800431160756110279393039124097451651085e-29 ,2.4463954600402428081657049389161574603467530869624e-29 ]
dy0=[-6.3906060965646236742338466149351415071203451342158e-32 ,6.6233311942164718918672453269182479875172457445036e-32 ]
Ddy=[-1.7565578996164808288351835448581316532745206591611e2 ,-1.7565578996160240175981658049875483255593538722765e2 ]
dy=[-3.6381414458137603149927563789483534300600956612569e-34 ,3.7706307293737960647087655236184726022927375303996e-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]=[5.8959994200059538893294609835037603290747790445450e1 ,5.8959994200059538893294609835048375617859964410218e1 ]
D0[i][5][0]=[3.8056640113539258650248614600804532096631624303649e-1 ,3.8056640113539258650248614600817148689646251278796e-1 ]
D0[i][3][0]=[-1.6245120640758717656885414854027234018848206723312e-1 ,-1.6245120640758717656885414854014836902847642905339e-1 ]
DBif[i][5][0]=[3.8056640113539258650248614600800805083252672878728e-1 ,3.8056640113539258650248614600820875703025202703717e-1 ]
DBif[i][3][0]=[-1.6245120640758717656885414854034213925320954369386e-1 ,-1.6245120640758717656885414854007856996374895259266e-1 ]
D[k][3][4]=[5.8959994200059537569865227465508459738750842900425e1 ,5.8959994200059540216723992204577519169856911955242e1 ]
_H(5,0,0)=[-1.6593591774405502639659382210040739301591625451958 ,-1.6593591774121269316999064636635255405530760536463 ]
_H(5,0,2)=[-2.7254389405367970453998010522434666632352169607268 ,-2.7254389404869009565581345377341211891639539782363 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-1.7565578996162524232166746750142243240212178490299e2 ,-1.7565578996162524232166746748314556548126566824077e2 ]
D0[i][5][0]=[-3.7918569141173577068758543302457745420162013516815e-29 ,3.7918569149403173697810753258254813347252953441271e-29 ]
D0[i][3][0]=[-9.3048736607027196887671001252221837000720226015562e-30 ,9.3048737029931822594288664909220038525351565964976e-30 ]
DBif[i][5][0]=[-3.8464236530841261722522911721974011707527530606301e-29 ,3.8464236539070858351575121677771079634618470530758e-29 ]
DBif[i][3][0]=[-1.0123926178558627631424483026211968191227609165342e-29 ,1.0123926220849090202086249391911788343690743160284e-29 ]
D[k][3][4]=[-1.7565578996162526856581463529276201343436758258091e2 ,-1.7565578996162521607752029969180598444901987056285e2 ]
_H(5,0,0)=[-1.2173823030411347946837531105207443230585193820499e-8 ,1.2173823030410589552956204086466250392542466192926e-8 ]
_H(5,0,2)=[-3.8232501317628751140461739337764994496056693988504 ,-3.8232500450989424535669688289482468151146119279677 ]
g=[-4.3921195560054119149042998561251091107454313378754e-29 ,4.3921195591672360756848252446124309083729618188403e-29 ]
Dg=[-3.8232501317628751140461810335041737736647235554799 ,-3.8232500450989424535669617292205724910556157177102 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-1.1487921282145038471059104280444824154154312545310e-29 ,1.1487921290415028985631111754882966268618233978564e-29 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-5.8319622821756777460971262299034816651182382683308e-16 ,5.8319622821756777936962837301766430743874500334962e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.0775749394685377793280775155759056948683774226365e-18 ,4.0775749394685378944389728327012327234127687328637e-18 ],[0 ,0 ]}
DH[2]=[-3.1036541563870198273824575596042739750801274591041e-2 ,-3.1036541563870198273824575034438994139216173738053e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-3.1036541563870279964351043068087432103030937285456e-2 ,-3.1036541563870116583298107562396607929676760081176e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-1.7565578996162524232166746753157150202296654607483e2 ,-1.7565578996162524232166746745299649583871702229562e2 ]
_H(5,0,0)=[-1.7977574557441806636452870151769179738762062895806e-16 ,1.7977574474997555024443215986606586860392107153955e-16 ]
_H(5,0,2)=[-3.8232500884309092259093532045328266617745173298256 ,-3.8232500884309083417001802461062364976695277272897 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.7021707033609050311951375544455487648246273878185e-17 ,4.7021706817969869758514396207162749277063530301034e-17 ],[0 ,0 ],[-4.6862093369674625344514133071258446845579401088494e-17 ,4.6862093584581826658460660334717590785803355465637e-17 ],[0 ,0 ]}
DH*T2=[-9.4029905765663008400334010005685125704699608741914e-16 ,9.4029905335785134559236856525614363227044217502746e-16 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[4.8642974334836923857897667039253366631320133833993 ,4.8673346088558966842766653490023347807528717882551 ],[0 ,0 ],[2.1091919035869496009338972514891552268089045075062e-1 ,2.1091919035869548027464345328640332206502570598718e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-1.6173839988446360023933052821999065932937257362689e-1 ,-1.6164413646475780728146851093640494277201114633661e-1 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0171436625421554797811944118574791003196564145240 ,3.0171436625421554797811944119326690735316497701077 ]
dat/MoonL2_05_PD.dat at {9.8898097866095133255830060643019829971109116498313e-1 ,0 ,3.4886155332975552497395589007678477358050781252444e-2 ,0 ,7.9336441942459750951338573417434034513436770592672e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:59:38 2018
elapsed time: 1hours 23minutes 42seconds