6
(b-d)*(B-D) - 2*F + 2;
(b-d)*(B+D-2*F) + 2*(B-D);
(b-d)*(b-d) - 2*(b+d) + f + 1;
B**2*b**3 - 1;
D**2*d**3 - 1;
F**2*f**3 - 1;
TITLE : problem of Kotsireas in celestial mechanics
REFERENCES :
Karin Gatermann: "Computer Algebra Methods for Equivariant
Dynamical Systems", Lecture Notes in Mathematics, Volume 1728, 2000.
The system occurs as example 4.1.2 (page 112),
listing Kotsireas as the source.
ROOT COUNTS :
total degree : 1000
3-homogeneous Bezout number : 194
with partition : {b d }{B D F }{f }
generalized Bezout number : 266
based on the set structure :
{b d F }{B D }
{b d }{B D F }
{b d f }{b d }
{b }{b }{b }{B }{B }
{d }{d }{d }{D }{D }
{F }{F }{f }{f }{f }
mixed volume : 126
THE SOLUTIONS :
84 6
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.58305124891592E+00 -1.56862898127658E-01
d : 5.43082125635435E+00 -7.54370815285868E-01
B : 4.92937026998804E-01 7.35675521976243E-02
D : 7.62258175706496E-02 1.60107048555827E-02
F : 1.81100217312709E-01 1.37613679382378E-02
f : -1.42057330853540E+00 2.77567865886967E+00
== err : 3.707E-15 = rco : 1.174E-02 = res : 4.505E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.00000000000000E+00 7.48459293687628E-39
d : 3.00000000000000E+00 2.63567873973435E-38
B : 9.99999999999999E-01 -1.04922054360505E-38
D : 1.92450089729875E-01 -2.37624346308802E-39
F : 1.92450089729875E-01 9.81491865188531E-40
f : 3.00000000000000E+00 -9.84935696294456E-39
== err : 1.003E-14 = rco : 2.611E-03 = res : 1.665E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 7.99517929433542E-02 6.12261423815786E-01
d : 2.17174736526174E-01 -4.75284022572311E-01
B : -1.14775226725523E+00 -1.71188952476226E+00
D : 3.75933472295638E-01 -2.62049345787906E+00
F : 6.10468286122422E-01 -8.90879397014122E-01
f : 7.58178020653008E-01 5.72427177353884E-01
== err : 1.095E-15 = rco : 2.516E-02 = res : 1.547E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.56720815918841E+00 -9.04044681920535E-01
d : 3.85305098438349E-02 -3.91739061131995E+00
B : 2.90393896575461E-01 2.90720746957022E-01
D : 8.98370511564239E-02 -9.25277032669839E-02
F : 2.61548980270193E-01 -5.52485130736170E-03
f : 2.44450171831346E+00 3.44215775341237E-02
== err : 1.278E-15 = rco : 1.282E-02 = res : 5.649E-15 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.41671143686089E+00 -1.07040744115274E+00
d : 8.79417321617750E-01 -3.42289733392807E+00
B : 3.48768626168584E-01 2.38719829177824E-01
D : 5.97457431642707E-02 -1.38152556644316E-01
F : 2.24888883981342E-01 -9.27120561571201E-02
f : -1.81258681038885E+00 1.81662984350187E+00
== err : 8.689E-16 = rco : 1.642E-02 = res : 9.432E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.58941048938941E+00 -4.10711064583680E-01
d : 1.16714285673913E-02 2.10363222055945E+00
B : -1.43501290514998E-01 -2.47646612321211E-02
D : 2.29813585063566E-01 2.33670910152986E-01
F : 7.29052205119302E-03 7.01335610232604E-03
f : -2.76130795873650E-01 2.13771706790958E+01
== err : 1.005E-14 = rco : 9.202E-05 = res : 1.872E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.56720815918841E+00 9.04044681920535E-01
d : 3.85305098438343E-02 3.91739061131995E+00
B : 2.90393896575461E-01 -2.90720746957022E-01
D : 8.98370511564239E-02 9.25277032669839E-02
F : 2.61548980270193E-01 5.52485130736167E-03
f : 2.44450171831346E+00 -3.44215775341235E-02
== err : 8.454E-16 = rco : 1.282E-02 = res : 5.443E-15 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.15986447922862E+00 1.10740971802266E-33
d : 1.04511556474012E+00 3.06945084886716E-34
B : 1.78031690051563E-01 -1.00058079141993E-34
D : 9.35951891911779E-01 -4.45371299639548E-34
F : 1.98594537923601E-01 4.17535593412077E-35
f : 2.93779711660717E+00 -4.18287909796603E-34
== err : 4.403E-15 = rco : 2.366E-03 = res : 9.992E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 8.79417321617749E-01 -3.42289733392807E+00
d : -1.41671143686089E+00 -1.07040744115274E+00
B : 5.97457431642707E-02 -1.38152556644316E-01
D : 3.48768626168584E-01 2.38719829177824E-01
F : 2.24888883981342E-01 -9.27120561571201E-02
f : -1.81258681038885E+00 1.81662984350187E+00
== err : 3.222E-15 = rco : 1.452E-02 = res : 6.496E-15 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -3.49232221807114E-02 -3.07044156676641E+00
d : -1.39080409143159E+00 -8.54192308761247E-01
B : 1.33636719336615E-01 -1.29153019379636E-01
D : 3.52644728040142E-01 3.25005803339010E-01
F : 3.48261038459728E-01 -6.52044612696676E-02
f : -7.78106785216693E-01 -1.83932781021399E+00
== err : 9.449E-16 = rco : 2.095E-02 = res : 2.845E-15 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.00402472589652E+00 -2.58170838218446E-01
d : 6.53580793020367E+00 -1.14500224595691E+00
B : 3.41754447182115E-01 6.64993390392727E-02
D : -5.65380021479991E-02 -1.50490261790126E-02
F : 6.13526580990657E-02 -8.17062915195228E-03
f : -3.67092375288857E+00 5.23150918893175E+00
== err : 5.793E-15 = rco : 3.031E-03 = res : 9.827E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.17657268556030E-01 4.08082521659275E-01
d : -2.68987353577069E-01 2.19821137365878E-01
B : 1.00541010611548E+00 -1.20582134728877E+00
D : 4.18141866611332E+00 -2.52394245339684E+00
F : -5.32071106836510E-01 2.85392611008994E-01
f : -1.05335650718356E+00 9.21965430172160E-01
== err : 2.626E-15 = rco : 7.304E-03 = res : 2.117E-15 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.29998158436125E+00 -1.71980752392422E+00
d : 1.48692882940621E+00 -4.81527483960937E-01
B : -8.44366903159331E-02 -5.42051540319783E-02
D : 4.56336342854246E-01 2.31673545446093E-01
F : 6.23895209104366E-02 -6.72817050123577E-02
f : 4.19389248274622E+00 2.56402413987881E+00
== err : 1.117E-14 = rco : 5.746E-03 = res : 1.787E-15 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.17174736526174E-01 -4.75284022572311E-01
d : 7.99517929433543E-02 6.12261423815786E-01
B : 3.75933472295638E-01 -2.62049345787906E+00
D : -1.14775226725523E+00 -1.71188952476226E+00
F : 6.10468286122422E-01 -8.90879397014122E-01
f : 7.58178020653008E-01 5.72427177353884E-01
== err : 2.332E-15 = rco : 2.305E-02 = res : 2.941E-15 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.92510925800308E+00 -3.36623119563892E-01
d : 1.37413491296265E-01 1.80161979940941E+00
B : -1.95009455990649E-01 -3.38491839133529E-02
D : 2.56071178902394E-01 3.22415562220693E-01
F : -9.62807351785094E-03 -1.43188755893648E-02
f : 1.92588059142304E+00 1.48515348265164E+01
== err : 9.040E-15 = rco : 2.121E-04 = res : 2.180E-15 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.04511556474011E+00 -1.92610116068084E-46
d : 3.15986447922862E+00 -6.81490854720468E-46
B : 9.35951891911780E-01 2.72322650781874E-46
D : 1.78031690051563E-01 6.16660273912471E-47
F : 1.98594537923600E-01 -2.53591915693548E-47
f : 2.93779711660717E+00 2.52480045574149E-46
== err : 1.290E-14 = rco : 2.366E-03 = res : 1.776E-15 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.16367873719349E-01 3.22058737546843E-01
d : -8.19113737030566E-02 -4.25905515717239E-01
B : 1.44205685980580E+00 -2.18555722441885E+00
D : 3.07180960951395E+00 -1.67970815220434E+00
F : 7.83142524977039E-01 -7.35525446726455E-01
f : -1.99186842183576E-02 -9.53083686771368E-01
== err : 2.277E-15 = rco : 1.419E-02 = res : 2.739E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.39080409143159E+00 -8.54192308761247E-01
d : -3.49232221807111E-02 -3.07044156676641E+00
B : 3.52644728040142E-01 3.25005803339010E-01
D : 1.33636719336615E-01 -1.29153019379636E-01
F : 3.48261038459728E-01 -6.52044612696676E-02
f : -7.78106785216692E-01 -1.83932781021399E+00
== err : 3.077E-15 = rco : 2.071E-02 = res : 1.854E-15 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.85305098438339E-02 3.91739061131995E+00
d : -1.56720815918841E+00 9.04044681920534E-01
B : 8.98370511564240E-02 9.25277032669839E-02
D : 2.90393896575460E-01 -2.90720746957022E-01
F : 2.61548980270193E-01 5.52485130736159E-03
f : 2.44450171831346E+00 -3.44215775341231E-02
== err : 1.529E-15 = rco : 1.435E-02 = res : 1.011E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.16714285673911E-02 2.10363222055945E+00
d : 3.58941048938941E+00 -4.10711064583680E-01
B : 2.29813585063566E-01 2.33670910152986E-01
D : -1.43501290514998E-01 -2.47646612321211E-02
F : 7.29052205119303E-03 7.01335610232604E-03
f : -2.76130795873656E-01 2.13771706790958E+01
== err : 4.169E-15 = rco : 9.107E-05 = res : 6.099E-15 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.43082125635435E+00 -7.54370815285868E-01
d : 1.58305124891592E+00 -1.56862898127658E-01
B : 7.62258175706496E-02 1.60107048555827E-02
D : 4.92937026998804E-01 7.35675521976243E-02
F : 1.81100217312709E-01 1.37613679382378E-02
f : -1.42057330853540E+00 2.77567865886967E+00
== err : 1.507E-15 = rco : 1.187E-02 = res : 2.070E-15 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.30213979330224E+00 -2.11788583292615E-01
d : -4.29698734234514E-01 -2.90227478214610E+00
B : 1.58058073367248E-01 6.40739850980841E-01
D : -1.68072891185853E-01 1.06527832266064E-01
F : 1.39089946138373E-01 2.05691179887331E-01
f : 2.01388552960032E+00 -1.53354547340774E+00
== err : 1.403E-15 = rco : 1.668E-02 = res : 2.183E-15 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.25000000000000E-01 -2.16506350946110E-01
d : 1.25000000000000E-01 -2.16506350946110E-01
B : 3.54904813880920E-16 8.00000000000000E+00
D : 2.63459027411672E-16 8.00000000000000E+00
F : 1.00000000000000E+00 6.18704994634400E-33
f : -5.00000000000000E-01 -8.66025403784439E-01
== err : 7.320E-16 = rco : 1.234E-03 = res : 1.323E-15 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.25000000000000E-01 2.16506350946110E-01
d : 1.25000000000000E-01 2.16506350946110E-01
B : -8.27010080394767E-16 8.00000000000000E+00
D : -1.00019849287248E-15 8.00000000000000E+00
F : 1.00000000000000E+00 -6.16297582212884E-33
f : -5.00000000000000E-01 8.66025403784439E-01
== err : 5.581E-15 = rco : 1.246E-03 = res : 1.401E-15 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -7.80797735595231E-02 -2.29393535938812E-01
d : 2.54182375635127E-01 1.41285368911490E-01
B : -8.02546083219746E+00 2.42365329033086E+00
D : -4.61767202534470E+00 4.39746476213804E+00
F : 1.20031447910796E+00 9.59509132306502E-01
f : -6.20790081135221E-01 -4.22541473228005E-01
== err : 5.056E-15 = rco : 1.366E-03 = res : 2.106E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -6.39055311560109E-01 7.56548801495828E-01
d : -3.46046354899180E-01 -8.27870111148479E-01
B : 9.78802229066274E-01 -2.67431671717294E-01
D : 1.15502716778482E+00 -2.23947740406620E-01
F : 1.06026612429816E+00 -1.33236472220197E-01
f : -5.45674290857136E-01 7.85855245710202E-01
== err : 1.176E-15 = rco : 9.384E-02 = res : 1.423E-15 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.00402472589652E+00 2.58170838218446E-01
d : 6.53580793020367E+00 1.14500224595691E+00
B : 3.41754447182115E-01 -6.64993390392727E-02
D : -5.65380021479991E-02 1.50490261790126E-02
F : 6.13526580990657E-02 8.17062915195227E-03
f : -3.67092375288857E+00 -5.23150918893175E+00
== err : 1.959E-15 = rco : 3.031E-03 = res : 5.526E-15 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.53580793020367E+00 1.14500224595691E+00
d : 2.00402472589652E+00 2.58170838218446E-01
B : -5.65380021479991E-02 1.50490261790126E-02
D : 3.41754447182115E-01 -6.64993390392727E-02
F : 6.13526580990656E-02 8.17062915195226E-03
f : -3.67092375288857E+00 -5.23150918893175E+00
== err : 1.411E-15 = rco : 2.898E-03 = res : 1.958E-15 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.53580793020367E+00 -1.14500224595691E+00
d : 2.00402472589652E+00 -2.58170838218446E-01
B : -5.65380021479991E-02 -1.50490261790126E-02
D : 3.41754447182115E-01 6.64993390392726E-02
F : 6.13526580990657E-02 -8.17062915195226E-03
f : -3.67092375288857E+00 5.23150918893175E+00
== err : 2.670E-15 = rco : 2.898E-03 = res : 1.825E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.58305124891592E+00 1.56862898127658E-01
d : 5.43082125635435E+00 7.54370815285868E-01
B : 4.92937026998804E-01 -7.35675521976243E-02
D : 7.62258175706496E-02 -1.60107048555827E-02
F : 1.81100217312709E-01 -1.37613679382378E-02
f : -1.42057330853540E+00 -2.77567865886967E+00
== err : 1.419E-15 = rco : 1.174E-02 = res : 5.219E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.07538807867492E-01 2.69049305150365E-43
d : 1.68104296116274E+00 1.43492962746861E-42
B : 2.76564298827501E+00 7.17464813734306E-43
D : 4.58808844471358E-01 -1.79366203433577E-43
F : -3.53539724358438E-01 -3.58732406867153E-43
f : 2.00005154025927E+00 7.17464813734306E-43
== err : 2.901E-15 = rco : 2.528E-02 = res : 1.443E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.00000000000000E+00 3.18029065536218E-45
d : 1.00000000000000E+00 8.97706828708086E-46
B : 1.92450089729875E-01 -2.83270295034411E-46
D : 9.99999999999999E-01 -1.25624217797869E-45
F : 1.92450089729875E-01 1.19055631246347E-46
f : 3.00000000000000E+00 -1.20971468990541E-45
== err : 1.197E-14 = rco : 2.611E-03 = res : 2.331E-15 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.68104296116274E+00 -1.39902984916624E-47
d : 5.07538807867493E-01 -2.56585412168851E-48
B : 4.58808844471358E-01 5.64487906771472E-48
D : 2.76564298827501E+00 3.83167548838817E-47
F : -3.53539724358438E-01 -1.36845553156720E-47
f : 2.00005154025927E+00 -1.36845553156720E-48
== err : 2.755E-15 = rco : 2.544E-02 = res : 1.887E-15 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.99358726797465E-01 1.45242337721204E+00
d : -9.54681283106095E-01 -1.74001585259444E-02
B : -5.03635705156045E-01 -1.49563560982546E-01
D : -2.92946346804868E-02 -1.07137600761025E+00
F : 2.14560090819637E-01 -1.38737834858243E-01
f : -1.95501742388122E+00 1.53155881814258E+00
== err : 1.737E-15 = rco : 1.991E-02 = res : 1.765E-15 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -3.49232221807112E-02 3.07044156676641E+00
d : -1.39080409143159E+00 8.54192308761247E-01
B : 1.33636719336615E-01 1.29153019379636E-01
D : 3.52644728040142E-01 -3.25005803339010E-01
F : 3.48261038459729E-01 6.52044612696677E-02
f : -7.78106785216692E-01 1.83932781021399E+00
== err : 7.612E-16 = rco : 2.095E-02 = res : 3.265E-15 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.00000000000000E-01 0.00000000000000E+00
d : 5.00000000000000E-01 -6.56858655152258E-47
B : -2.82842712474619E+00 4.20389539297445E-45
D : -2.82842712474619E+00 2.80259692864963E-45
F : 1.00000000000000E+00 0.00000000000000E+00
f : 1.00000000000000E+00 0.00000000000000E+00
== err : 8.764E-16 = rco : 1.843E-02 = res : 7.772E-16 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.85305098438347E-02 -3.91739061131995E+00
d : -1.56720815918841E+00 -9.04044681920534E-01
B : 8.98370511564239E-02 -9.25277032669839E-02
D : 2.90393896575461E-01 2.90720746957022E-01
F : 2.61548980270193E-01 -5.52485130736166E-03
f : 2.44450171831346E+00 3.44215775341235E-02
== err : 1.272E-15 = rco : 1.435E-02 = res : 3.249E-15 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.29998158436125E+00 1.71980752392422E+00
d : 1.48692882940621E+00 4.81527483960937E-01
B : -8.44366903159331E-02 5.42051540319783E-02
D : 4.56336342854246E-01 -2.31673545446092E-01
F : 6.23895209104365E-02 6.72817050123577E-02
f : 4.19389248274622E+00 -2.56402413987882E+00
== err : 2.611E-15 = rco : 5.746E-03 = res : 4.122E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.00000000000000E+00 1.36845553156720E-48
d : 1.00000000000000E+00 -5.13170824337702E-49
B : -1.92450089729875E-01 1.28292706084425E-49
D : 1.00000000000000E+00 0.00000000000000E+00
F : -1.92450089729875E-01 1.71056941445901E-49
f : 3.00000000000000E+00 -8.21073318940323E-48
== err : 2.611E-15 = rco : 2.173E-02 = res : 2.887E-15 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -5.22166501862045E-01 1.02282260587624E+00
d : -5.22166501862046E-01 -1.02282260587624E+00
B : 8.10137988950260E-01 6.27989318296639E-02
D : 8.10137988950260E-01 -6.27989318296638E-02
F : 8.71535665799477E-01 2.71749897171044E-17
f : 1.09599832491768E+00 -2.27825774498706E-17
== err : 6.242E-16 = rco : 1.134E-01 = res : 1.074E-15 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -7.31358242550330E-01 5.04470146102484E-01
d : 8.71371770145311E-01 1.44915211509366E+00
B : 9.39610574640192E-01 -7.36875557139666E-01
D : 1.21236933679971E-02 -4.54618751535578E-01
F : 1.23423012062172E-01 -2.11899339792217E-01
f : -2.39629241586836E+00 8.79104234083145E-01
== err : 2.034E-15 = rco : 1.923E-02 = res : 1.107E-15 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -8.19113737030566E-02 -4.25905515717239E-01
d : 4.16367873719349E-01 3.22058737546843E-01
B : 3.07180960951395E+00 -1.67970815220434E+00
D : 1.44205685980580E+00 -2.18555722441885E+00
F : 7.83142524977039E-01 -7.35525446726455E-01
f : -1.99186842183577E-02 -9.53083686771368E-01
== err : 1.024E-15 = rco : 1.516E-02 = res : 3.330E-15 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -7.31358242550331E-01 -5.04470146102485E-01
d : 8.71371770145311E-01 -1.44915211509366E+00
B : 9.39610574640192E-01 7.36875557139666E-01
D : 1.21236933679970E-02 4.54618751535578E-01
F : 1.23423012062172E-01 2.11899339792217E-01
f : -2.39629241586836E+00 -8.79104234083144E-01
== err : 2.019E-15 = rco : 1.923E-02 = res : 2.360E-15 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -2.68987353577069E-01 -2.19821137365878E-01
d : 6.17657268556029E-01 -4.08082521659275E-01
B : 4.18141866611332E+00 2.52394245339685E+00
D : 1.00541010611548E+00 1.20582134728877E+00
F : -5.32071106836510E-01 -2.85392611008994E-01
f : -1.05335650718356E+00 -9.21965430172160E-01
== err : 6.507E-15 = rco : 7.436E-03 = res : 2.803E-15 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.48692882940621E+00 4.81527483960937E-01
d : 4.29998158436125E+00 1.71980752392422E+00
B : 4.56336342854246E-01 -2.31673545446092E-01
D : -8.44366903159330E-02 5.42051540319783E-02
F : 6.23895209104365E-02 6.72817050123576E-02
f : 4.19389248274622E+00 -2.56402413987882E+00
== err : 4.385E-15 = rco : 5.139E-03 = res : 4.438E-15 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -3.46046354899180E-01 8.27870111148479E-01
d : -6.39055311560109E-01 -7.56548801495828E-01
B : 1.15502716778482E+00 2.23947740406619E-01
D : 9.78802229066274E-01 2.67431671717294E-01
F : 1.06026612429816E+00 1.33236472220197E-01
f : -5.45674290857136E-01 -7.85855245710202E-01
== err : 5.310E-16 = rco : 1.023E-01 = res : 1.289E-15 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.17657268556029E-01 -4.08082521659275E-01
d : -2.68987353577069E-01 -2.19821137365878E-01
B : 1.00541010611548E+00 1.20582134728877E+00
D : 4.18141866611332E+00 2.52394245339685E+00
F : -5.32071106836510E-01 -2.85392611008994E-01
f : -1.05335650718356E+00 -9.21965430172160E-01
== err : 3.848E-15 = rco : 7.304E-03 = res : 2.256E-15 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 8.71371770145310E-01 -1.44915211509366E+00
d : -7.31358242550331E-01 -5.04470146102484E-01
B : 1.21236933679969E-02 4.54618751535578E-01
D : 9.39610574640192E-01 7.36875557139666E-01
F : 1.23423012062172E-01 2.11899339792217E-01
f : -2.39629241586836E+00 -8.79104234083144E-01
== err : 2.822E-15 = rco : 2.467E-02 = res : 1.382E-15 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -6.39055311560109E-01 -7.56548801495827E-01
d : -3.46046354899180E-01 8.27870111148479E-01
B : 9.78802229066274E-01 2.67431671717294E-01
D : 1.15502716778482E+00 2.23947740406620E-01
F : 1.06026612429816E+00 1.33236472220197E-01
f : -5.45674290857136E-01 -7.85855245710202E-01
== err : 9.398E-16 = rco : 9.384E-02 = res : 1.933E-15 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.17174736526174E-01 4.75284022572311E-01
d : 7.99517929433543E-02 -6.12261423815786E-01
B : 3.75933472295638E-01 2.62049345787906E+00
D : -1.14775226725523E+00 1.71188952476226E+00
F : 6.10468286122422E-01 8.90879397014122E-01
f : 7.58178020653008E-01 -5.72427177353884E-01
== err : 1.827E-15 = rco : 2.305E-02 = res : 1.542E-15 ==
solution 51 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -8.19113737030566E-02 4.25905515717239E-01
d : 4.16367873719349E-01 -3.22058737546843E-01
B : 3.07180960951395E+00 1.67970815220434E+00
D : 1.44205685980580E+00 2.18555722441885E+00
F : 7.83142524977039E-01 7.35525446726455E-01
f : -1.99186842183578E-02 9.53083686771368E-01
== err : 2.589E-15 = rco : 1.516E-02 = res : 2.864E-15 ==
solution 52 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.54182375635127E-01 -1.41285368911490E-01
d : -7.80797735595231E-02 2.29393535938812E-01
B : -4.61767202534470E+00 -4.39746476213804E+00
D : -8.02546083219746E+00 -2.42365329033086E+00
F : 1.20031447910796E+00 -9.59509132306502E-01
f : -6.20790081135221E-01 4.22541473228005E-01
== err : 3.069E-15 = rco : 1.032E-03 = res : 3.155E-15 ==
solution 53 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -7.80797735595231E-02 2.29393535938812E-01
d : 2.54182375635127E-01 -1.41285368911490E-01
B : -8.02546083219746E+00 -2.42365329033086E+00
D : -4.61767202534470E+00 -4.39746476213804E+00
F : 1.20031447910796E+00 -9.59509132306502E-01
f : -6.20790081135221E-01 4.22541473228005E-01
== err : 4.900E-15 = rco : 1.366E-03 = res : 3.464E-15 ==
solution 54 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -9.54681283106095E-01 1.74001585259443E-02
d : -4.99358726797464E-01 -1.45242337721204E+00
B : -2.92946346804867E-02 1.07137600761025E+00
D : -5.03635705156045E-01 1.49563560982547E-01
F : 2.14560090819637E-01 1.38737834858243E-01
f : -1.95501742388122E+00 -1.53155881814258E+00
== err : 2.539E-15 = rco : 2.101E-02 = res : 1.259E-15 ==
solution 55 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.00000000000000E+00 -1.25556342403504E-42
d : 3.00000000000000E+00 -2.86985925493723E-42
B : 1.00000000000000E+00 2.51112684807007E-42
D : -1.92450089729875E-01 -2.69049305150365E-43
F : -1.92450089729875E-01 -8.96831017167883E-43
f : 3.00000000000000E+00 -3.58732406867153E-42
== err : 1.950E-15 = rco : 2.173E-02 = res : 3.775E-15 ==
solution 56 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -2.68987353577069E-01 2.19821137365878E-01
d : 6.17657268556029E-01 4.08082521659275E-01
B : 4.18141866611332E+00 -2.52394245339685E+00
D : 1.00541010611548E+00 -1.20582134728877E+00
F : -5.32071106836510E-01 2.85392611008994E-01
f : -1.05335650718356E+00 9.21965430172160E-01
== err : 6.523E-15 = rco : 7.436E-03 = res : 2.194E-15 ==
solution 57 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.00000000000000E-01 2.13821176807376E-50
d : 5.00000000000000E-01 -2.13821176807376E-50
B : 2.82842712474619E+00 -5.13170824337702E-49
D : 2.82842712474619E+00 0.00000000000000E+00
F : 1.00000000000000E+00 1.98234086353841E-65
f : 1.00000000000000E+00 -1.32156057569228E-65
== err : 1.629E-15 = rco : 2.343E-02 = res : 6.661E-16 ==
solution 58 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.25000000000000E-01 2.16506350946110E-01
d : 1.25000000000000E-01 2.16506350946110E-01
B : 3.11651425797081E-17 -8.00000000000000E+00
D : -2.72680435826189E-16 -8.00000000000000E+00
F : 1.00000000000000E+00 2.16667118743564E-32
f : -5.00000000000000E-01 8.66025403784439E-01
== err : 1.874E-15 = rco : 1.247E-03 = res : 7.548E-16 ==
solution 59 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -5.22166501862045E-01 -1.02282260587624E+00
d : -5.22166501862045E-01 1.02282260587624E+00
B : 8.10137988950260E-01 -6.27989318296639E-02
D : 8.10137988950260E-01 6.27989318296640E-02
F : 8.71535665799477E-01 4.10087328799130E-17
f : 1.09599832491768E+00 -3.43803122902238E-17
== err : 7.497E-16 = rco : 1.134E-01 = res : 1.178E-15 ==
solution 60 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.54182375635127E-01 1.41285368911490E-01
d : -7.80797735595231E-02 -2.29393535938812E-01
B : -4.61767202534470E+00 4.39746476213804E+00
D : -8.02546083219746E+00 2.42365329033086E+00
F : 1.20031447910796E+00 9.59509132306502E-01
f : -6.20790081135221E-01 -4.22541473228005E-01
== err : 6.856E-15 = rco : 1.032E-03 = res : 2.636E-15 ==
solution 61 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.26173933609854E+00 5.11187331216359E-01
d : 6.99214897031286E-01 2.99443105767239E+00
B : 3.43647008519854E-01 -5.27503076801445E-01
D : -7.92111917862769E-02 -1.67686424981561E-01
F : 1.38640989394945E-01 -1.72237993276942E-01
f : 1.96109022418931E-01 -2.72781781679659E+00
== err : 1.059E-15 = rco : 3.563E-02 = res : 3.276E-15 ==
solution 62 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.30213979330224E+00 2.11788583292615E-01
d : -4.29698734234515E-01 2.90227478214610E+00
B : 1.58058073367248E-01 -6.40739850980842E-01
D : -1.68072891185853E-01 -1.06527832266064E-01
F : 1.39089946138373E-01 -2.05691179887331E-01
f : 2.01388552960031E+00 1.53354547340775E+00
== err : 1.696E-15 = rco : 1.668E-02 = res : 2.732E-15 ==
solution 63 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.25000000000000E-01 -2.16506350946110E-01
d : 1.25000000000000E-01 -2.16506350946110E-01
B : -6.23277328964428E-17 -8.00000000000000E+00
D : -1.30498747924064E-16 -8.00000000000000E+00
F : 1.00000000000000E+00 4.25614444661042E-33
f : -5.00000000000000E-01 -8.66025403784439E-01
== err : 2.400E-15 = rco : 1.241E-03 = res : 2.150E-15 ==
solution 64 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 3.58941048938941E+00 4.10711064583680E-01
d : 1.16714285673911E-02 -2.10363222055945E+00
B : -1.43501290514998E-01 2.47646612321211E-02
D : 2.29813585063566E-01 -2.33670910152986E-01
F : 7.29052205119302E-03 -7.01335610232604E-03
f : -2.76130795873655E-01 -2.13771706790958E+01
== err : 1.653E-14 = rco : 9.202E-05 = res : 1.548E-15 ==
solution 65 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.26173933609854E+00 -5.11187331216359E-01
d : 6.99214897031285E-01 -2.99443105767239E+00
B : 3.43647008519854E-01 5.27503076801445E-01
D : -7.92111917862769E-02 1.67686424981561E-01
F : 1.38640989394945E-01 1.72237993276942E-01
f : 1.96109022418932E-01 2.72781781679659E+00
== err : 1.169E-15 = rco : 3.563E-02 = res : 3.894E-15 ==
solution 66 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 8.79417321617749E-01 3.42289733392807E+00
d : -1.41671143686089E+00 1.07040744115274E+00
B : 5.97457431642707E-02 1.38152556644316E-01
D : 3.48768626168584E-01 -2.38719829177824E-01
F : 2.24888883981342E-01 9.27120561571201E-02
f : -1.81258681038885E+00 -1.81662984350187E+00
== err : 3.275E-15 = rco : 1.452E-02 = res : 3.347E-15 ==
solution 67 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -3.46046354899180E-01 -8.27870111148479E-01
d : -6.39055311560109E-01 7.56548801495828E-01
B : 1.15502716778482E+00 -2.23947740406619E-01
D : 9.78802229066274E-01 -2.67431671717294E-01
F : 1.06026612429816E+00 -1.33236472220197E-01
f : -5.45674290857136E-01 7.85855245710202E-01
== err : 8.908E-16 = rco : 1.023E-01 = res : 1.712E-15 ==
solution 68 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.41671143686089E+00 1.07040744115274E+00
d : 8.79417321617749E-01 3.42289733392807E+00
B : 3.48768626168584E-01 -2.38719829177824E-01
D : 5.97457431642707E-02 1.38152556644316E-01
F : 2.24888883981342E-01 9.27120561571199E-02
f : -1.81258681038885E+00 -1.81662984350187E+00
== err : 1.853E-15 = rco : 1.642E-02 = res : 1.473E-15 ==
solution 69 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 2.92510925800308E+00 3.36623119563892E-01
d : 1.37413491296264E-01 -1.80161979940941E+00
B : -1.95009455990649E-01 3.38491839133528E-02
D : 2.56071178902394E-01 -3.22415562220693E-01
F : -9.62807351785094E-03 1.43188755893648E-02
f : 1.92588059142304E+00 -1.48515348265164E+01
== err : 7.896E-15 = rco : 2.121E-04 = res : 1.288E-15 ==
solution 70 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.16367873719349E-01 -3.22058737546843E-01
d : -8.19113737030566E-02 4.25905515717239E-01
B : 1.44205685980580E+00 2.18555722441885E+00
D : 3.07180960951395E+00 1.67970815220434E+00
F : 7.83142524977039E-01 7.35525446726455E-01
f : -1.99186842183576E-02 9.53083686771368E-01
== err : 1.251E-15 = rco : 1.419E-02 = res : 1.264E-15 ==
solution 71 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.48692882940621E+00 -4.81527483960937E-01
d : 4.29998158436125E+00 -1.71980752392422E+00
B : 4.56336342854246E-01 2.31673545446092E-01
D : -8.44366903159330E-02 -5.42051540319783E-02
F : 6.23895209104365E-02 -6.72817050123576E-02
f : 4.19389248274623E+00 2.56402413987882E+00
== err : 2.337E-15 = rco : 5.139E-03 = res : 3.258E-15 ==
solution 72 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -9.54681283106095E-01 -1.74001585259444E-02
d : -4.99358726797464E-01 1.45242337721204E+00
B : -2.92946346804868E-02 -1.07137600761025E+00
D : -5.03635705156045E-01 -1.49563560982547E-01
F : 2.14560090819637E-01 -1.38737834858243E-01
f : -1.95501742388122E+00 1.53155881814258E+00
== err : 3.891E-15 = rco : 2.101E-02 = res : 1.541E-15 ==
solution 73 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -1.39080409143159E+00 8.54192308761247E-01
d : -3.49232221807116E-02 3.07044156676641E+00
B : 3.52644728040142E-01 -3.25005803339010E-01
D : 1.33636719336615E-01 1.29153019379636E-01
F : 3.48261038459728E-01 6.52044612696675E-02
f : -7.78106785216693E-01 1.83932781021399E+00
== err : 2.895E-15 = rco : 2.071E-02 = res : 2.287E-15 ==
solution 74 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.43082125635435E+00 7.54370815285868E-01
d : 1.58305124891592E+00 1.56862898127658E-01
B : 7.62258175706496E-02 -1.60107048555827E-02
D : 4.92937026998804E-01 -7.35675521976243E-02
F : 1.81100217312709E-01 -1.37613679382378E-02
f : -1.42057330853540E+00 -2.77567865886967E+00
== err : 4.245E-16 = rco : 1.187E-02 = res : 9.024E-16 ==
solution 75 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.99358726797464E-01 -1.45242337721204E+00
d : -9.54681283106095E-01 1.74001585259442E-02
B : -5.03635705156045E-01 1.49563560982547E-01
D : -2.92946346804866E-02 1.07137600761025E+00
F : 2.14560090819637E-01 1.38737834858243E-01
f : -1.95501742388122E+00 -1.53155881814258E+00
== err : 2.656E-15 = rco : 1.991E-02 = res : 1.697E-15 ==
solution 76 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.29698734234515E-01 -2.90227478214610E+00
d : -1.30213979330224E+00 -2.11788583292615E-01
B : -1.68072891185853E-01 1.06527832266064E-01
D : 1.58058073367248E-01 6.40739850980841E-01
F : 1.39089946138373E-01 2.05691179887331E-01
f : 2.01388552960032E+00 -1.53354547340775E+00
== err : 2.765E-15 = rco : 2.246E-02 = res : 2.216E-15 ==
solution 77 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.99214897031285E-01 -2.99443105767239E+00
d : -1.26173933609854E+00 -5.11187331216359E-01
B : -7.92111917862769E-02 1.67686424981561E-01
D : 3.43647008519854E-01 5.27503076801445E-01
F : 1.38640989394945E-01 1.72237993276942E-01
f : 1.96109022418931E-01 2.72781781679659E+00
== err : 1.784E-15 = rco : 3.205E-02 = res : 1.049E-15 ==
solution 78 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.99214897031285E-01 2.99443105767239E+00
d : -1.26173933609854E+00 5.11187331216359E-01
B : -7.92111917862769E-02 -1.67686424981561E-01
D : 3.43647008519854E-01 -5.27503076801445E-01
F : 1.38640989394945E-01 -1.72237993276942E-01
f : 1.96109022418931E-01 -2.72781781679659E+00
== err : 1.591E-15 = rco : 3.205E-02 = res : 2.159E-15 ==
solution 79 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.29698734234515E-01 2.90227478214610E+00
d : -1.30213979330224E+00 2.11788583292615E-01
B : -1.68072891185853E-01 -1.06527832266064E-01
D : 1.58058073367247E-01 -6.40739850980841E-01
F : 1.39089946138373E-01 -2.05691179887331E-01
f : 2.01388552960032E+00 1.53354547340775E+00
== err : 9.888E-16 = rco : 2.246E-02 = res : 4.007E-15 ==
solution 80 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 8.71371770145310E-01 1.44915211509366E+00
d : -7.31358242550331E-01 5.04470146102484E-01
B : 1.21236933679968E-02 -4.54618751535578E-01
D : 9.39610574640192E-01 -7.36875557139666E-01
F : 1.23423012062172E-01 -2.11899339792217E-01
f : -2.39629241586836E+00 8.79104234083145E-01
== err : 2.112E-15 = rco : 2.467E-02 = res : 2.171E-15 ==
solution 81 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 7.99517929433542E-02 -6.12261423815786E-01
d : 2.17174736526174E-01 4.75284022572311E-01
B : -1.14775226725523E+00 1.71188952476226E+00
D : 3.75933472295638E-01 2.62049345787906E+00
F : 6.10468286122422E-01 8.90879397014122E-01
f : 7.58178020653008E-01 -5.72427177353884E-01
== err : 1.337E-15 = rco : 2.516E-02 = res : 1.253E-15 ==
solution 82 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.37413491296264E-01 1.80161979940941E+00
d : 2.92510925800308E+00 -3.36623119563892E-01
B : 2.56071178902394E-01 3.22415562220693E-01
D : -1.95009455990649E-01 -3.38491839133528E-02
F : -9.62807351785094E-03 -1.43188755893648E-02
f : 1.92588059142304E+00 1.48515348265164E+01
== err : 5.655E-15 = rco : 2.127E-04 = res : 6.617E-15 ==
solution 83 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.37413491296264E-01 -1.80161979940941E+00
d : 2.92510925800308E+00 3.36623119563892E-01
B : 2.56071178902394E-01 -3.22415562220693E-01
D : -1.95009455990649E-01 3.38491839133528E-02
F : -9.62807351785094E-03 1.43188755893648E-02
f : 1.92588059142303E+00 -1.48515348265165E+01
== err : 1.612E-14 = rco : 2.127E-04 = res : 4.829E-15 ==
solution 84 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 1.16714285673910E-02 -2.10363222055945E+00
d : 3.58941048938941E+00 4.10711064583680E-01
B : 2.29813585063566E-01 -2.33670910152986E-01
D : -1.43501290514998E-01 2.47646612321211E-02
F : 7.29052205119303E-03 -7.01335610232604E-03
f : -2.76130795873657E-01 -2.13771706790958E+01
== err : 1.913E-14 = rco : 9.107E-05 = res : 6.559E-15 ==