Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_03_PD.dat at {8.4264057255485370306651522626245079736076422343115e-1 ,0 ,1.6385429425076094220846750362849715664492221996940e-1 ,0 ,2.6346538151927592200694736604355290698611701256528e-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]=[-5.9064068116178638376227882898977587552412226988264e-34 ,5.9063968719963008352686935547488237179210083496877e-34 ]
D0[i][3][0]=[1.3038192924793859081375725937835860554790821504564 ,1.3038192924793859081375725937844031021523488076075 ]
D0[i][3][2]=[-7.2075200214019198508492132374344593928454554691402e-31 ,7.2075191746409804473550127231977094504251331093830e-31 ]
dy0=[-1.0618885091776631343352113980696034425300378354296e-32 ,4.0494907710688840398933652451062845809712136732390e-33 ]
Ddy=[7.0788440742610411727319763659220726308069986095554 ,7.0788440742610630794061355944543075420388196650015 ]
dy=[-5.7205537070564863455653752081305153962803084393770e-34 ,1.5000874408842144470412570598454014626686168550718e-33 ]
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]=[-6.0557699111407501108215417731917082999298397717382e-32 ,6.0557696095663021746669948473583319513968600858483e-32 ]
D0[i][3][0]=[-1.7902357167902173133778646358620794075142847617503e-29 ,1.7902357013237621763738664080218865195572287953122e-29 ]
D0[i][3][2]=[-5.6465082317874379213834302336252806468348054504765e-29 ,5.6465082199592994616068747645334685268683276314153e-29 ]
dy0=[-9.5363362990401113001808714618798858538053139356090e-32 ,6.0557696095663586785120764446957022184888460394670e-32 ]
Ddy=[5.3664190902300782196882415566186074131786245878837e1 ,5.3664190902301022330215597825628887675587579655993e1 ]
dy=[-1.1284563333101003586263270459665545895093690344194e-33 ,1.7770390531745170350663015702222736327601002811513e-33 ]
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]=[7.0788440742610521260690559801845803262971589614013 ,7.0788440742610521260690559801917998465486593131556 ]
D0[i][5][0]=[-1.3633140514728064865584610322933676964012156687459 ,-1.3633140514728064865584610322918809788544976847361 ]
D0[i][3][0]=[1.3038192924793859081375725937835860554790821504564 ,1.3038192924793859081375725937844031021523488076075 ]
DBif[i][5][0]=[-1.3633140514728064865584610322933768423480135794772 ,-1.3633140514728064865584610322918718329076997740048 ]
DBif[i][3][0]=[1.3038192924793859081375725937834996669378754478066 ,1.3038192924793859081375725937844894906935555102572 ]
D[k][3][4]=[7.0788440742610484259126579210344796843387658012521 ,7.0788440742610558262254540393419004885070524733048 ]
_H(5,0,0)=[1.6354648469792444977795287811997631815326846905384e1 ,1.6354648469885150524900586888964275152222744601151e1 ]
_H(5,0,2)=[-4.6732524291243722738620580840735482822818986783007e1 ,-4.6732524291086567194620925835707818829929717597828e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[5.3664190902300902263549006695563395596210650480446e1 ,5.3664190902300902263549006696251566211163175054384e1 ]
D0[i][5][0]=[-1.0648991911493386596007390696946560421748708796108e-29 ,1.0648992034902407460872900158039512248714431234908e-29 ]
D0[i][3][0]=[-1.7902357167902173133778646358620794075142847617503e-29 ,1.7902357013237621763738664080218865195572287953122e-29 ]
DBif[i][5][0]=[-1.0711223909089738876415935741884362131723489107330e-29 ,1.0711224032498759741281445202977313958689211546130e-29 ]
DBif[i][3][0]=[-1.7980310301121630575355302854677110453819254160387e-29 ,1.7980310146457079205315320576275181574248694496005e-29 ]
D[k][3][4]=[5.3664190902300871682754258284641307269001341090079e1 ,5.3664190902300932844343755107173654538372484444751e1 ]
_H(5,0,0)=[-6.0058531817884791643687539607225695670486069819248e-10 ,6.0058531817882829847727702325579477462151361494377e-10 ]
_H(5,0,2)=[-5.4234405292577812942705284577379024251071788796740e1 ,-5.4234405286123118495133734479834123338090247196253e1 ]
g=[-2.1128971002903158914887990244570606788954169402525e-29 ,2.1128971036280948703519589148954833360562560209766e-29 ]
Dg=[-5.4234405292577812942705284844375686675619091079521e1 ,-5.4234405286123118495133734212837460913542981654669e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-3.8958611035621329481495972973124013393787210312929e-31 ,3.8958611097164900601232999650787667282675655666324e-31 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-4.4456075488851444217317404435769929224467303540962e-16 ,4.4456075488851450334882372455877854154052125803010e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.2971653273209029483582945993258914006400996628999e-16 ,1.2971653273209031368391260191687295115445196913062e-16 ],[0 ,0 ]}
DH[2]=[-1.1067225468173008327000967679569001775346758477158 ,-1.1067225468173008327000967679406790780161149935350 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-1.1067225468173008495030927691771994994712669559550 ,-1.1067225468173008158971007667203821975899389033564 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[5.3664190902300902263549006694372010306580325833134e1 ,5.3664190902300902263549006697442951498911448385222e1 ]
_H(5,0,0)=[-5.0750874140622890148290291311803383650759589985566e-17 ,5.0750874039248413117043626011793992680481480979257e-17 ]
_H(5,0,2)=[-5.4234405289350465950448705034421462253697328759684e1 ,-5.4234405289350465487390283658742887294026910764179e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-9.3576898040750516353444043413669726179057366972654e-19 ,9.3576897853831389112359162805201811001945602443486e-19 ],[0 ,0 ],[-2.0018253685416188671108594189100265457003923436064e-19 ,2.0018253645429882370354971735735458167362151975784e-19 ],[0 ,0 ]}
DH*T2=[-1.0615675265551001139789636558783407169636342639459e-18 ,1.0615675286755730097603505536350319470667250375003e-18 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[3.2851641182172668505419276943276620208165818076695 ,3.2851641182237243550013653279519677977263038928001 ],[0 ,0 ],[-2.9387491175547306264107015902538689607096653840049e-1 ,-2.9387491175547257501785978451795367479800628316937e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-5.2306246620734833417258889743441175712285305959124 ,-5.2306246620663366037867681261938054510252355461540 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0216192479264201986830801047688126078536906357860 ,3.0216192479264201986830801047710125958753566865968 ]
dat/MoonL1_03_PD.dat at {8.4264057255485370306651522626245079736076422343115e-1 ,0 ,1.6385429425076094220846750362849715664492221996940e-1 ,0 ,2.6346538151927592200694736604355290698611701256528e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:35:43 2018
elapsed time: 0hours 59minutes 47seconds