Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL2_03_PD.dat at {1.0067204379362731808239714106837744086477401280057 ,0 ,6.3160415719473519936206726271288802234254612262007e-2 ,0 ,5.4271169521876553806391099080223890093959220775978e-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]=[-1.3531726011638026334855025038229068534813264413060e-33 ,1.3531724810812660456600147177483062493967429451221e-33 ]
D0[i][3][0]=[1.2354936218990201110314040244229728175731536533406e-1 ,1.2354936218990201110314040244275687853223252730207e-1 ]
D0[i][3][2]=[-2.0315195893357495404858113125216296602770924475806e-31 ,2.0315202151193732003249760135861600412056574621295e-31 ]
dy0=[-1.9735284373006994418845962708396828247247752586669e-33 ,1.5997900146727640619512811316792563951110459332675e-33 ]
Ddy=[3.6916716099647562061029065703056635352555773483415e1 ,3.6916716099647587338010877975380475940777768909304e1 ]
dy=[-4.3335111670131379843760737904932107425513363648877e-35 ,5.3458938004497653566062350138859724646237462120727e-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]=[-5.6565239472183903351778752091839662540777927367268e-32 ,5.6565239785057987707218891655491128503316056983503e-32 ]
D0[i][3][0]=[-3.0345932227248812444961926895614649275614178059808e-29 ,3.0345931427801136610707613639609958107371068589028e-29 ]
D0[i][3][2]=[-5.5616521494636141103039264102605819163856276669101e-29 ,5.5616521897992085903594282156305816232582337848569e-29 ]
dy0=[-5.9444254032595060055040857274492653872183293019165e-32 ,5.6565239785058548695605656584307761887513216286839e-32 ]
Ddy=[3.0646485429800432172051243674537675668712443721137e2 ,3.0646485429801613642637475594042552288749987721736e2 ]
dy=[-1.8457333358707063228952444931512375256385493950116e-34 ,1.9396760574311035114588860616805205877647063410223e-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]=[3.6916716099647574699519971839215586799605517748266e1 ,3.6916716099647574699519971839221524493728024644453e1 ]
D0[i][5][0]=[1.0355687338437939292402750241059027999086399195790 ,1.0355687338437939292402750241062989715772211447610 ]
D0[i][3][0]=[1.2354936218990201110314040244229728175731536533406e-1 ,1.2354936218990201110314040244275687853223252730207e-1 ]
DBif[i][5][0]=[1.0355687338437939292402750241058127644950081528880 ,1.0355687338437939292402750241063890069908529114520 ]
DBif[i][3][0]=[1.2354936218990201110314040244221319611491468205339e-1 ,1.2354936218990201110314040244284096417463321058274e-1 ]
D[k][3][4]=[3.6916716099647574416112809095338515342385729688651e1 ,3.6916716099647574982927134583098595950947812704068e1 ]
_H(5,0,0)=[1.5284410403533251938771203395123916231780552567921 ,1.5284410403787891136904369365107295221128341403226 ]
_H(5,0,2)=[3.1063103609814227411423107958227338622111427058847e-1 ,3.1063103614159573795157883921822742416825754882186e-1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[3.0646485429801022907344359633275269222869695724878e2 ,3.0646485429801022907344359635304958734592735717995e2 ]
D0[i][5][0]=[-6.7081388522338528978286392257359036764486272994280e-29 ,6.7081388266547612507772724055570133757101830293624e-29 ]
D0[i][3][0]=[-3.0345932227248812444961926895614649275614178059808e-29 ,3.0345931427801136610707613639609958107371068589028e-29 ]
DBif[i][5][0]=[-6.7320376532504161767399319558213503810161976712199e-29 ,6.7320376276713245296885651356424600802777534011543e-29 ]
DBif[i][3][0]=[-3.1024186474727836019477500804338755783059808217087e-29 ,3.1024185675280160185223187548334064614816698746306e-29 ]
D[k][3][4]=[3.0646485429801020946071696059901814654075811089432e2 ,3.0646485429801024868617023208678413303386620353441e2 ]
_H(5,0,0)=[-4.3194210370025634589888140599673992899461585834085e-9 ,4.3194210370021144011552624438459173562401662649769e-9 ]
_H(5,0,2)=[-1.1193010178665497495261128322232824600657874447091e1 ,-1.1193010154343607198405854504103132420822299559722e1 ]
g=[-7.6756520168267708835831212024912590033222529682515e-29 ,7.6756520160796494992714835858856345433344796145524e-29 ]
Dg=[-1.1193010178665497495261128580410402782842973525444e1 ,-1.1193010154343607198405854245925554238637201285909e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-6.8575404748008065253230320055601709990303984562400e-30 ,6.8575404741333172851549557622268497514578244154253e-30 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-5.9771338790660216182606086758217248799872396913902e-17 ,5.9771338790660216368867214024302319531145380680008e-17 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.8788546351904092819796251234793774513679269828774e-18 ,1.8788546351904091196721723052248235585375688106303e-18 ],[0 ,0 ]}
DH[2]=[1.2832825451654747867737843632383036798528249694122e-1 ,1.2832825451654747867737843656775742105947608663903e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[1.2832825451654746787437567183234524395554136430793e-1 ,1.2832825451654748948038120105924347832153261629573e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[3.0646485429801022907344359631930318556185305934000e2 ,3.0646485429801022907344359636649909401146212668931e2 ]
_H(5,0,0)=[-2.7504651838429874844742024491037345115200369208103e-16 ,2.7504651944830811575824033030775352452416582478688e-16 ]
_H(5,0,2)=[-1.1193010166504552842392310217706719087398272845219e1 ,-1.1193010166504551851275925886956832500492827404413e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.4573060713139029339919409849310881708853700498354e-17 ,2.4573060808199192020277088382166680923760788725735e-17 ],[0 ,0 ],[-2.4056927379844025416131011075094421404894030996536e-17 ,2.4056927286780509716292853493511105278631296000237e-17 ],[0 ,0 ]}
DH*T2=[-1.4147548246262129339933605904155127814233390866681e-16 ,1.4147548300991503654183638178976028866301440053488e-16 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[4.3377875625324634636827345665120541179126372651642 ,4.3377885265284217310331291285079672174364604309315 ],[0 ,0 ],[5.2734364056363974269307736834245809092701204421763e-1 ,5.2734364056363993287435989962738411858996433600697e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-2.3049944574489441894326357908526277275247825627480e-2 ,-2.3049820866565391566982522527186323867520098290941e-2 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0229911591596336379776897124123329683345467858792 ,3.0229911591596336379776897124485131040423556462526 ]
dat/MoonL2_03_PD.dat at {1.0067204379362731808239714106837744086477401280057 ,0 ,6.3160415719473519936206726271288802234254612262007e-2 ,0 ,5.4271169521876553806391099080223890093959220775978e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:45:07 2018
elapsed time: 1hours 9minutes 11seconds