```
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 ==
```