6
1 + y1 + y2 + y3 + y4 + y5 + y6;
y1 + y1*y2 + y2*y3 + y3*y4 + y4*y5 + y5*y6 + y6;
y1*y2 + y1*y2*y3 + y2*y3*y4 + y3*y4*y5 + y4*y5*y6 + y5*y6 + y6*y1;
y1*y2*y3 + y1*y2*y3*y4 + y2*y3*y4*y5 + y3*y4*y5*y6 + y4*y5*y6
+ y5*y6*y1 + y6*y1*y2;
y1*y2*y3*y4 + y1*y2*y3*y4*y5 + y2*y3*y4*y5*y6 + y3*y4*y5*y6
+ y4*y5*y6*y1 + y5*y6*y1*y2 + y6*y1*y2*y3;
y1*y2*y3*y4*y5 + y1*y2*y3*y4*y5*y6 + y2*y3*y4*y5*y6 + y3*y4*y5*y6*y1
+ y4*y5*y6*y1*y2 + y5*y6*y1*y2*y3 + y6*y1*y2*y3*y4;
z0**7*y1*y2*y3*y4*y5*y6 - 1;
TITLE : reduced cyclic 7-roots problem
ROOT COUNTS :
total degree : 6! = 720
generalized Bezout number : 504
based on
{ y1 y2 y3 y4 y5 y6 }
{ y1 y3 y5 }{ y2 y4 y6 }
{ y1 y4 }{ y2 y5 }{ y3 y6 }
{ y1 }{ y2 }{ y3 }{ y4 }{ y5 }{ y6 }
{ y1 }{ y2 }{ y3 }{ y4 }{ y5 }{ y6 }
{ y1 }{ y2 }{ y3 }{ y4 }{ y5 }{ y6 }
mixed volume : 132
REFERENCES :
Ioannis Z. Emiris:
`Sparse Elimination and Application in Kinematics'
PhD Thesis, Computer Science, University of California at Berkeley, 1994,
page 25.
yi = zi/z0
This reduces the dimension of the problem by 1
and the mixed volume drops with 7.
THE SYMMETRY GROUP :
y1 y2 y3 y4 y5 y6
y6 y5 y4 y3 y2 y1
THE GENERATING SOLUTIONS :
66 6
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.24950255955781E+01 1.72585317139373E-92
y2 : -8.18237007073836E-01 -7.49068216750752E-95
y3 : 5.93181127710669E+01 -1.34233024441735E-92
y4 : 3.43668012576714E+00 -5.76782526898079E-94
y5 : -7.70182528827205E+00 1.28839733281129E-93
y6 : 1.72602949940899E+01 -3.35582561104337E-93
== err : 3.171E-14 = rco : 1.776E-07 = res : 3.311E-10 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -8.09905111428176E-01 -5.86560917963781E-01
y2 : -8.78150166608380E-01 4.78385080124447E-01
y3 : 8.17281792388163E-01 -5.76238207541631E-01
y4 : -7.45559757800135E-01 6.66438780045852E-01
y5 : 2.80434187110110E-01 9.59873255539445E-01
y6 : 3.35899056338419E-01 -9.41897990204332E-01
== err : 1.832E-15 = rco : 2.703E-02 = res : 5.722E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -1.29839351396707E-01 3.97954647018752E-74
y2 : 1.68582571711176E-02 8.84343660041671E-75
y3 : -4.46216318487560E-01 -4.06798083619169E-73
y4 : -3.55616391515110E-01 4.77545576422502E-73
y5 : -4.74057371182826E-02 -7.51692111035421E-74
y6 : -3.77804586534582E-02 -3.53737464016668E-74
== err : 3.666E-16 = rco : 1.509E-04 = res : 8.327E-17 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 6.61437827766148E-01
y2 : 1.00000000000000E+00 -2.99058358315246E-16
y3 : -7.50000000000001E-01 -6.61437827766148E-01
y4 : -7.50000000000000E-01 6.61437827766148E-01
y5 : -7.50000000000000E-01 -6.61437827766147E-01
y6 : 1.00000000000000E+00 -7.69397955004172E-16
== err : 1.132E-15 = rco : 4.646E-02 = res : 1.196E-15 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 5.45338715592088E-01 -2.63554948580763E-82
y2 : -3.55616391515110E-01 2.63554948580763E-81
y3 : -1.22213978511701E+00 2.89910443438839E-81
y4 : -4.20010351042094E+00 1.00150880460690E-80
y5 : 2.73889531709513E+00 -7.11598361168060E-81
y6 : 1.49362565436584E+00 -7.05009487453541E-81
== err : 4.485E-15 = rco : 1.417E-02 = res : 1.776E-15 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.70182528827206E+00 2.63554948580763E-82
y2 : 2.90978491859721E-01 -1.23541382147233E-83
y3 : 3.65110704946766E-01 1.72957935006126E-82
y4 : 2.73889531709513E+00 -9.22442320032671E-82
y5 : 3.43668012576715E+00 4.61221160016335E-82
y6 : -1.29839351396707E-01 -3.91214376799570E-83
== err : 4.673E-15 = rco : 3.954E-03 = res : 3.109E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.00968867902419E-01 4.33883739117558E-01
y2 : 6.23489801858733E-01 -7.81831482468030E-01
y3 : -2.22520933956314E-01 9.74927912181824E-01
y4 : -2.22520933956314E-01 -9.74927912181824E-01
y5 : 6.23489801858733E-01 7.81831482468030E-01
y6 : -9.00968867902419E-01 -4.33883739117558E-01
== err : 8.607E-16 = rco : 8.694E-02 = res : 6.661E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 2.12925716127124E-01 9.77068390345195E-01
y2 : -9.09325278823503E-01 4.16085973438854E-01
y3 : -3.23921889150932E-01 -9.46083828066462E-01
y4 : -8.78150166608381E-01 4.78385080124447E-01
y5 : 9.97573466842276E-01 6.96216794704273E-02
y6 : -9.91018483865845E-02 -9.95077295312461E-01
== err : 1.201E-15 = rco : 4.276E-02 = res : 6.408E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 8.55417302803806E-01 5.17939415437617E-01
y2 : 2.12925716127123E-01 -9.77068390345195E-01
y3 : -9.93359903237232E-01 1.15048262222934E-01
y4 : -9.09325278823503E-01 -4.16085973438854E-01
y5 : 8.17281792388164E-01 5.76238207541630E-01
y6 : -9.82939629258358E-01 1.83928478581868E-01
== err : 9.952E-16 = rco : 2.435E-02 = res : 9.226E-16 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 1.47154785030934E-71
y2 : -2.08712152522080E-01 1.69793982728001E-72
y3 : -4.79128784747792E+00 -1.81233024129781E-71
y4 : 1.00000000000000E+00 1.13195988485334E-72
y5 : 1.00000000000000E+00 4.52783953941336E-72
y6 : 1.00000000000000E+00 5.09381948184003E-72
== err : 1.603E-16 = rco : 1.088E-02 = res : 8.882E-16 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -8.09905111428176E-01 5.86560917963783E-01
y2 : 2.80434187110109E-01 9.59873255539446E-01
y3 : -7.90149219457783E-01 -6.12914521764868E-01
y4 : 2.12925716127124E-01 -9.77068390345196E-01
y5 : -3.23921889150932E-01 9.46083828066463E-01
y6 : 4.30616316799658E-01 -9.02535089459628E-01
== err : 7.042E-16 = rco : 1.450E-02 = res : 6.727E-16 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.91018483865844E-02 9.95077295312461E-01
y2 : -9.93359903237232E-01 1.15048262222934E-01
y3 : -3.23921889150932E-01 -9.46083828066463E-01
y4 : 9.73527794718966E-01 -2.28568661258770E-01
y5 : -3.89003826976192E-01 -9.21236138347751E-01
y6 : -1.68140326968026E-01 9.85763070137589E-01
== err : 7.174E-16 = rco : 3.506E-02 = res : 2.483E-16 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.24106550694846E+00 1.10542957505209E-75
y2 : -1.29839351396707E-01 -6.15327009550479E-77
y3 : 9.41270710281754E+00 -4.14536090644533E-75
y4 : 1.06239362287250E-01 -1.20906359771322E-76
y5 : -7.70182528827206E+00 3.31628872515627E-75
y6 : -4.46216318487560E-01 8.63616855509445E-78
== err : 5.980E-15 = rco : 1.778E-03 = res : 8.882E-16 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 4.35607626104000E-02 -6.58887371451908E-83
y2 : -2.08712152522080E-01 -1.33397312537137E-82
y3 : -2.08712152522080E-01 6.58887371451908E-83
y4 : -2.08712152522080E-01 1.64721842862977E-82
y5 : -2.08712152522080E-01 -1.11858525611451E-82
y6 : -2.08712152522080E-01 6.58887371451908E-83
== err : 2.491E-17 = rco : 6.097E-04 = res : 1.596E-16 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.25476870339538E+00 2.15133956739870E-66
y2 : -4.74057371182826E-02 -7.18658691695688E-68
y3 : 3.65110704946766E-01 1.02003169143904E-67
y4 : -2.81201886037784E+00 -2.81899667452244E-66
y5 : 1.06239362287250E-01 2.96736492054994E-67
y6 : 1.33305826866725E-01 4.05191874250745E-67
== err : 3.236E-15 = rco : 3.355E-03 = res : 2.220E-16 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.64687099003354E+01 4.98932682851293E-83
y2 : -2.10944932151332E+01 -7.24776108597098E-82
y3 : -2.81201886037784E+00 1.02951151789361E-82
y4 : -2.24106550694846E+00 9.78035941998925E-83
y5 : 5.93181127710669E+01 1.77899590292015E-81
y6 : -7.70182528827206E+00 -6.58887371451908E-83
== err : 3.032E-14 = rco : 1.146E-06 = res : 1.892E-10 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -4.46216318487560E-01 5.06025501275065E-80
y2 : 1.99109002884591E-01 4.21687917729221E-81
y3 : 3.43668012576714E+00 -2.02410200510026E-79
y4 : -4.74057371182826E-02 2.10843958864611E-80
y5 : -4.20010351042094E+00 6.74700668366754E-80
y6 : 5.79364373750512E-02 -2.21386156807841E-80
== err : 5.866E-15 = rco : 5.188E-04 = res : 5.551E-16 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.25000000000000E-01 9.92156741649222E-01
y2 : -7.50000000000000E-01 -6.61437827766147E-01
y3 : -7.50000000000000E-01 -6.61437827766148E-01
y4 : 1.00000000000000E+00 -2.50055086786988E-16
y5 : -7.50000000000000E-01 -6.61437827766148E-01
y6 : 1.25000000000001E-01 9.92156741649221E-01
== err : 8.460E-16 = rco : 5.276E-02 = res : 6.280E-16 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 1.81113581576534E-71
y2 : 1.00000000000000E+00 1.24515587333867E-71
y3 : 1.00000000000000E+00 -4.52783953941336E-72
y4 : 1.00000000000000E+00 5.43340744729603E-71
y5 : -2.08712152522080E-01 9.05567907882671E-72
y6 : -4.79128784747792E+00 -7.24454326306137E-71
== err : 9.691E-17 = rco : 9.068E-03 = res : 2.220E-16 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 2.29564392373896E+01 -9.22442320032671E-82
y2 : -4.79128784747792E+00 -3.04735409296507E-82
y3 : -4.79128784747792E+00 4.87988459481569E-82
y4 : -4.79128784747792E+00 -4.11804607157442E-83
y5 : -4.79128784747792E+00 -1.81194027149275E-82
y6 : -4.79128784747792E+00 1.15305290004084E-82
== err : 2.773E-15 = rco : 1.628E-04 = res : 9.095E-13 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -3.23921889150932E-01 9.46083828066462E-01
y2 : 2.12925716127123E-01 9.77068390345196E-01
y3 : -3.89003826976192E-01 -9.21236138347751E-01
y4 : -3.89003826976192E-01 9.21236138347751E-01
y5 : 2.12925716127124E-01 -9.77068390345195E-01
y6 : -3.23921889150931E-01 -9.46083828066463E-01
== err : 7.838E-16 = rco : 1.818E-02 = res : 3.331E-16 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -8.42713333399786E-01 5.38362552291875E-01
y2 : -3.89003826976192E-01 -9.21236138347751E-01
y3 : -8.78150166608381E-01 4.78385080124447E-01
y4 : 2.80434187110109E-01 9.59873255539445E-01
y5 : 9.97573466842276E-01 -6.96216794704271E-02
y6 : -1.68140326968026E-01 -9.85763070137589E-01
== err : 4.945E-16 = rco : 3.837E-02 = res : 7.357E-16 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 -6.61437827766148E-01
y2 : 1.25000000000000E-01 9.92156741649222E-01
y3 : -7.50000000000000E-01 -6.61437827766148E-01
y4 : -7.50000000000001E-01 -6.61437827766148E-01
y5 : 1.00000000000000E+00 -2.68094822200953E-16
y6 : 1.25000000000000E-01 9.92156741649222E-01
== err : 8.008E-16 = rco : 3.593E-02 = res : 8.006E-16 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 6.61437827766148E-01
y2 : -7.50000000000000E-01 -6.61437827766148E-01
y3 : -7.50000000000000E-01 6.61437827766148E-01
y4 : 1.00000000000000E+00 8.52372025906106E-17
y5 : 1.00000000000000E+00 -5.31597386831047E-17
y6 : -7.50000000000000E-01 -6.61437827766148E-01
== err : 4.059E-16 = rco : 3.843E-02 = res : 6.661E-16 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 7.50154755800563E+00 -1.32651549006251E-73
y2 : 9.41270710281753E+00 -6.19040562029170E-74
y3 : -3.55616391515110E-01 1.79632305945964E-75
y4 : 2.73889531709513E+00 -1.21597253255730E-74
y5 : -2.10944932151332E+01 2.65303098012501E-73
y6 : 7.96959628729993E-01 -8.84343660041671E-75
== err : 1.954E-14 = rco : 4.409E-05 = res : 4.263E-13 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 6.61437827766148E-01
y2 : 1.25000000000000E-01 -9.92156741649222E-01
y3 : -7.50000000000000E-01 6.61437827766148E-01
y4 : -7.50000000000000E-01 6.61437827766148E-01
y5 : 1.00000000000000E+00 -2.96670668116775E-16
y6 : 1.25000000000000E-01 -9.92156741649221E-01
== err : 1.204E-15 = rco : 3.593E-02 = res : 7.109E-16 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.83372273306192E+00 4.08510170300183E-81
y2 : 2.73889531709513E+00 3.88743549156626E-81
y3 : 5.02237460643417E+00 2.63554948580763E-81
y4 : -7.70182528827206E+00 -2.63554948580763E-82
y5 : -2.24106550694846E+00 7.90664845742289E-82
y6 : -6.52101861370705E-01 -2.67672994652338E-82
== err : 4.851E-15 = rco : 8.487E-04 = res : 5.684E-14 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 3.43668012576714E+00 2.80675478040570E-77
y2 : 1.18107702868429E+01 5.18170113305667E-77
y3 : -7.70182528827206E+00 -8.63616855509445E-78
y4 : -4.20010351042095E+00 -2.37494635265097E-77
y5 : -2.81201886037784E+00 -1.51132949714153E-77
y6 : -1.53350275353918E+00 6.20724614897413E-78
== err : 2.410E-14 = rco : 3.030E-04 = res : 6.821E-13 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 6.61437827766148E-01
y2 : -7.50000000000000E-01 6.61437827766148E-01
y3 : 1.25000000000001E-01 -9.92156741649221E-01
y4 : 1.00000000000000E+00 2.28301836609090E-16
y5 : 1.25000000000000E-01 -9.92156741649222E-01
y6 : -7.50000000000000E-01 6.61437827766147E-01
== err : 7.067E-16 = rco : 4.407E-02 = res : 6.280E-16 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.93359903237232E-01 -1.15048262222933E-01
y2 : -3.23921889150931E-01 -9.46083828066462E-01
y3 : 8.17281792388164E-01 5.76238207541630E-01
y4 : 8.17281792388164E-01 -5.76238207541630E-01
y5 : -3.23921889150932E-01 9.46083828066462E-01
y6 : -9.93359903237232E-01 1.15048262222934E-01
== err : 5.017E-16 = rco : 2.296E-02 = res : 4.003E-16 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 4.30616316799658E-01 -9.02535089459626E-01
y2 : -8.78150166608381E-01 4.78385080124447E-01
y3 : -7.45559757800135E-01 -6.66438780045852E-01
y4 : 2.12925716127123E-01 9.77068390345195E-01
y5 : 9.73527794718966E-01 2.28568661258770E-01
y6 : -9.93359903237232E-01 -1.15048262222934E-01
== err : 8.864E-16 = rco : 2.401E-02 = res : 4.441E-16 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 8.55417302803806E-01 -5.17939415437618E-01
y2 : -7.45559757800135E-01 6.66438780045852E-01
y3 : 9.97573466842276E-01 6.96216794704271E-02
y4 : -9.93359903237232E-01 1.15048262222933E-01
y5 : -7.90149219457783E-01 6.12914521764868E-01
y6 : -3.23921889150932E-01 -9.46083828066463E-01
== err : 1.217E-15 = rco : 4.787E-02 = res : 4.302E-16 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 0.00000000000000E+00
y2 : 1.00000000000000E+00 0.00000000000000E+00
y3 : -4.79128784747792E+00 -3.16265938296916E-81
y4 : -2.08712152522080E-01 1.05421979432305E-81
y5 : 1.00000000000000E+00 2.63329036414247E-81
y6 : 1.00000000000000E+00 2.40752670980074E-81
== err : 3.841E-16 = rco : 1.216E-02 = res : 4.441E-16 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -8.42713333399786E-01 -5.38362552291875E-01
y2 : -3.89003826976192E-01 9.21236138347751E-01
y3 : -8.78150166608381E-01 -4.78385080124447E-01
y4 : 2.80434187110108E-01 -9.59873255539445E-01
y5 : 9.97573466842276E-01 6.96216794704271E-02
y6 : -1.68140326968026E-01 9.85763070137589E-01
== err : 7.803E-16 = rco : 3.837E-02 = res : 6.480E-16 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.08712152522080E-01 1.10542957505209E-75
y2 : -4.79128784747792E+00 4.42171830020836E-74
y3 : 1.00000000000000E+00 -1.32651549006251E-74
y4 : 1.00000000000000E+00 -6.63257745031253E-75
y5 : 1.00000000000000E+00 -1.10542957505209E-74
y6 : 1.00000000000000E+00 -8.84343660041671E-75
== err : 2.871E-16 = rco : 1.022E-02 = res : 4.441E-16 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 6.23489801858734E-01 7.81831482468030E-01
y2 : -2.22520933956314E-01 9.74927912181824E-01
y3 : -9.00968867902419E-01 4.33883739117558E-01
y4 : -9.00968867902419E-01 -4.33883739117558E-01
y5 : -2.22520933956315E-01 -9.74927912181824E-01
y6 : 6.23489801858734E-01 -7.81831482468030E-01
== err : 6.967E-16 = rco : 1.094E-01 = res : 7.850E-16 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 4.30616316799658E-01 9.02535089459627E-01
y2 : -8.78150166608381E-01 -4.78385080124447E-01
y3 : -7.45559757800135E-01 6.66438780045852E-01
y4 : 2.12925716127124E-01 -9.77068390345195E-01
y5 : 9.73527794718966E-01 -2.28568661258770E-01
y6 : -9.93359903237232E-01 1.15048262222934E-01
== err : 7.816E-16 = rco : 2.401E-02 = res : 8.196E-16 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 -6.61437827766148E-01
y2 : -7.50000000000001E-01 -6.61437827766148E-01
y3 : 1.25000000000000E-01 9.92156741649222E-01
y4 : -7.50000000000000E-01 -6.61437827766148E-01
y5 : 1.00000000000000E+00 -3.72188726845367E-16
y6 : 1.25000000000000E-01 9.92156741649222E-01
== err : 8.844E-16 = rco : 3.546E-02 = res : 1.223E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.91018483865846E-02 9.95077295312461E-01
y2 : 9.97573466842276E-01 -6.96216794704274E-02
y3 : -8.78150166608381E-01 -4.78385080124447E-01
y4 : -3.23921889150932E-01 9.46083828066462E-01
y5 : -9.09325278823503E-01 -4.16085973438853E-01
y6 : 2.12925716127124E-01 -9.77068390345196E-01
== err : 6.711E-16 = rco : 3.422E-02 = res : 6.753E-16 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.82939629258358E-01 -1.83928478581868E-01
y2 : -7.45559757800135E-01 -6.66438780045852E-01
y3 : -3.89003826976192E-01 9.21236138347751E-01
y4 : 9.97573466842276E-01 6.96216794704270E-02
y5 : 8.17281792388164E-01 5.76238207541630E-01
y6 : -6.97352045195754E-01 -7.16728766732088E-01
== err : 8.022E-16 = rco : 3.842E-02 = res : 5.901E-16 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 1.10910203972226E-16
y2 : -7.50000000000000E-01 6.61437827766148E-01
y3 : -7.50000000000000E-01 -6.61437827766148E-01
y4 : -7.50000000000000E-01 6.61437827766148E-01
y5 : 1.00000000000000E+00 -1.84847045638262E-16
y6 : -7.50000000000000E-01 -6.61437827766148E-01
== err : 4.975E-16 = rco : 3.452E-02 = res : 6.329E-16 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -9.82939629258359E-01 1.83928478581869E-01
y2 : -7.45559757800135E-01 6.66438780045852E-01
y3 : -3.89003826976192E-01 -9.21236138347751E-01
y4 : 9.97573466842276E-01 -6.96216794704272E-02
y5 : 8.17281792388164E-01 -5.76238207541630E-01
y6 : -6.97352045195754E-01 7.16728766732088E-01
== err : 1.205E-15 = rco : 3.842E-02 = res : 6.661E-16 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 4.30616316799658E-01 9.02535089459627E-01
y2 : -3.23921889150932E-01 -9.46083828066463E-01
y3 : 2.12925716127123E-01 9.77068390345196E-01
y4 : -7.90149219457783E-01 6.12914521764867E-01
y5 : 2.80434187110109E-01 -9.59873255539445E-01
y6 : -8.09905111428175E-01 -5.86560917963783E-01
== err : 8.901E-16 = rco : 1.570E-02 = res : 4.965E-16 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -1.37940498921763E-02 5.39760534693403E-79
y2 : -1.22213978511701E+00 6.90893484407556E-77
y3 : 1.68582571711176E-02 -1.48434147040686E-78
y4 : 2.90978491859721E-01 -5.82941377468875E-77
y5 : -1.29839351396707E-01 2.15904213877361E-78
y6 : 5.79364373750512E-02 -1.32410006166975E-77
== err : 3.476E-15 = rco : 3.015E-05 = res : 1.908E-17 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.24106550694846E+00 2.88263225010210E-83
y2 : 5.02237460643417E+00 -1.40013566433530E-82
y3 : 2.90978491859721E-01 -1.31262718531435E-83
y4 : -2.10944932151332E+01 1.82841245577904E-81
y5 : -2.38089370302157E-01 -2.26492533936593E-83
y6 : 1.72602949940899E+01 -2.10843958864610E-81
== err : 1.345E-14 = rco : 1.150E-04 = res : 3.126E-13 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.25000000000000E-01 -9.92156741649222E-01
y2 : 1.00000000000000E+00 4.78787153068146E-16
y3 : -7.50000000000000E-01 6.61437827766148E-01
y4 : 1.25000000000000E-01 -9.92156741649221E-01
y5 : -7.50000000000000E-01 6.61437827766148E-01
y6 : -7.50000000000000E-01 6.61437827766147E-01
== err : 5.450E-16 = rco : 4.370E-02 = res : 4.441E-16 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 -4.42171830020836E-74
y2 : -4.79128784747792E+00 2.12242478410001E-73
y3 : -2.08712152522080E-01 0.00000000000000E+00
y4 : 1.00000000000000E+00 0.00000000000000E+00
y5 : 1.00000000000000E+00 -1.76868732008334E-73
y6 : 1.00000000000000E+00 -1.76868732008334E-74
== err : 2.639E-16 = rco : 1.069E-02 = res : 4.441E-16 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 8.55417302803806E-01 -5.17939415437618E-01
y2 : 2.12925716127124E-01 9.77068390345195E-01
y3 : -9.93359903237232E-01 -1.15048262222933E-01
y4 : -9.09325278823503E-01 4.16085973438854E-01
y5 : 8.17281792388163E-01 -5.76238207541630E-01
y6 : -9.82939629258358E-01 -1.83928478581868E-01
== err : 6.237E-16 = rco : 2.435E-02 = res : 2.776E-16 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 7.96959628729993E-01 1.48249658576679E-82
y2 : 1.06239362287250E-01 1.02951151789361E-82
y3 : 8.46684827249577E-02 3.25583017533853E-83
y4 : -2.24106550694846E+00 -2.14138395721870E-82
y5 : 2.90978491859721E-01 -7.41248292883396E-83
y6 : -3.77804586534582E-02 2.05902303578721E-84
== err : 3.545E-15 = rco : 2.364E-03 = res : 1.110E-16 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.12868020992015E-02 -2.57326176703940E-67
y2 : -8.18237007073836E-01 -2.67062842849494E-66
y3 : -4.74057371182826E-02 4.35831722705772E-67
y4 : 1.06239362287250E-01 -5.56380922603113E-67
y5 : -2.38089370302157E-01 3.04154904356369E-66
y6 : -1.37940498921763E-02 -1.73869038313473E-69
== err : 4.305E-16 = rco : 1.876E-05 = res : 6.418E-17 ==
solution 51 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.25000000000000E-01 -9.92156741649221E-01
y2 : -7.50000000000000E-01 6.61437827766148E-01
y3 : -7.50000000000000E-01 6.61437827766148E-01
y4 : 1.00000000000000E+00 6.65131445978868E-17
y5 : -7.50000000000000E-01 6.61437827766148E-01
y6 : 1.25000000000000E-01 -9.92156741649222E-01
== err : 5.927E-16 = rco : 5.276E-02 = res : 6.497E-16 ==
solution 52 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.22520933956315E-01 9.74927912181824E-01
y2 : -9.00968867902419E-01 -4.33883739117558E-01
y3 : 6.23489801858734E-01 -7.81831482468030E-01
y4 : 6.23489801858734E-01 7.81831482468030E-01
y5 : -9.00968867902419E-01 4.33883739117558E-01
y6 : -2.22520933956314E-01 -9.74927912181824E-01
== err : 5.829E-16 = rco : 7.167E-02 = res : 4.441E-16 ==
solution 53 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -1.53350275353918E+00 -1.13195988485334E-72
y2 : -4.46216318487560E-01 -4.95232449623336E-73
y3 : -1.29839351396707E-01 1.41494985606667E-72
y4 : 1.99109002884591E-01 -3.80267773817919E-73
y5 : 3.65110704946766E-01 -3.53737464016669E-73
y6 : 5.45338715592088E-01 8.48969913640004E-73
== err : 1.967E-15 = rco : 9.462E-03 = res : 2.220E-16 ==
solution 54 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 5.65952697791819E-17
y2 : -7.50000000000000E-01 6.61437827766148E-01
y3 : 1.00000000000000E+00 -6.50306153512137E-17
y4 : -7.50000000000000E-01 -6.61437827766148E-01
y5 : -7.50000000000000E-01 6.61437827766148E-01
y6 : -7.50000000000000E-01 -6.61437827766148E-01
== err : 6.180E-16 = rco : 2.144E-02 = res : 6.280E-16 ==
solution 55 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 -6.61437827766148E-01
y2 : 1.25000000000000E-01 9.92156741649222E-01
y3 : 1.00000000000000E+00 3.22472976548807E-17
y4 : 1.25000000000000E-01 9.92156741649221E-01
y5 : -7.50000000000000E-01 -6.61437827766148E-01
y6 : -7.50000000000000E-01 -6.61437827766148E-01
== err : 8.485E-16 = rco : 4.900E-02 = res : 4.003E-16 ==
solution 56 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -1.68140326968026E-01 -9.85763070137589E-01
y2 : -3.89003826976192E-01 9.21236138347751E-01
y3 : 9.73527794718966E-01 2.28568661258770E-01
y4 : -3.23921889150932E-01 9.46083828066462E-01
y5 : -9.93359903237232E-01 -1.15048262222933E-01
y6 : -9.91018483865842E-02 -9.95077295312461E-01
== err : 7.793E-16 = rco : 3.261E-02 = res : 3.511E-16 ==
solution 57 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 8.85990550034317E+01 -3.96386642665468E-79
y2 : -1.22213978511701E+00 -3.36032559440473E-81
y3 : -2.10944932151332E+01 3.32079235211762E-80
y4 : 9.41270710281754E+00 -5.53465392019602E-81
y5 : -4.20010351042094E+00 -3.29443685725954E-82
y6 : -7.24950255955781E+01 7.37953856026137E-80
== err : 1.289E-14 = rco : 1.191E-07 = res : 9.022E-10 ==
solution 58 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -6.52101861370705E-01 1.58132969148458E-80
y2 : -3.55616391515110E-01 1.31777474290382E-81
y3 : -2.38089370302157E-01 9.35620067461709E-81
y4 : -1.29839351396707E-01 -1.79217365034919E-80
y5 : 8.46684827249577E-02 -4.21687917729221E-81
y6 : 2.90978491859721E-01 -4.74398907445374E-81
== err : 4.600E-16 = rco : 2.344E-03 = res : 1.110E-16 ==
solution 59 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 2.12925716127123E-01 -9.77068390345196E-01
y2 : -9.93359903237232E-01 -1.15048262222933E-01
y3 : 2.80434187110108E-01 -9.59873255539445E-01
y4 : 2.80434187110109E-01 9.59873255539445E-01
y5 : -9.93359903237232E-01 1.15048262222934E-01
y6 : 2.12925716127124E-01 9.77068390345196E-01
== err : 1.114E-15 = rco : 1.399E-02 = res : 7.022E-16 ==
solution 60 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 2.90978491859721E-01 -1.69793982728001E-72
y2 : -4.46216318487560E-01 3.11288968334668E-72
y3 : -8.18237007073836E-01 6.93325429472670E-72
y4 : -1.22213978511701E+00 -6.79175930912004E-72
y5 : -2.24106550694846E+00 -5.65979942426670E-73
y6 : 3.43668012576715E+00 -7.92371919397337E-72
== err : 4.669E-15 = rco : 2.954E-02 = res : 1.332E-15 ==
solution 61 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 6.69511799745148E-01 7.93130781703919E-81
y2 : 3.65110704946766E-01 -8.43375835458442E-81
y3 : -2.38089370302157E-01 -2.53012750637533E-80
y4 : -8.18237007073836E-01 -8.43375835458442E-81
y5 : -2.81201886037784E+00 2.95181542410455E-80
y6 : 1.83372273306192E+00 1.68675167091688E-80
== err : 8.796E-16 = rco : 7.507E-02 = res : 6.661E-16 ==
solution 62 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 8.55417302803806E-01 5.17939415437618E-01
y2 : -7.45559757800135E-01 -6.66438780045852E-01
y3 : 9.97573466842276E-01 -6.96216794704269E-02
y4 : -9.93359903237232E-01 -1.15048262222934E-01
y5 : -7.90149219457783E-01 -6.12914521764868E-01
y6 : -3.23921889150932E-01 9.46083828066462E-01
== err : 8.270E-16 = rco : 4.787E-02 = res : 5.341E-16 ==
solution 63 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -2.64687099003354E+01 6.01353688828336E-73
y2 : 3.43668012576714E+00 -1.95108319996694E-73
y3 : -4.46216318487560E-01 1.35415122943881E-74
y4 : 1.18107702868429E+01 -3.97954647018752E-73
y5 : 9.41270710281753E+00 -4.24484956820002E-73
y6 : 1.25476870339538E+00 3.92427499143492E-74
== err : 2.471E-14 = rco : 1.409E-05 = res : 1.023E-12 ==
solution 64 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -7.50000000000000E-01 -6.61437827766148E-01
y2 : -7.50000000000000E-01 6.61437827766148E-01
y3 : -7.50000000000000E-01 -6.61437827766148E-01
y4 : 1.00000000000000E+00 2.99480296410678E-16
y5 : 1.00000000000000E+00 -1.69797198414960E-16
y6 : -7.50000000000000E-01 6.61437827766148E-01
== err : 7.679E-16 = rco : 3.843E-02 = res : 5.661E-16 ==
solution 65 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : 1.00000000000000E+00 3.36681559313763E-16
y2 : -7.50000000000000E-01 -6.61437827766148E-01
y3 : 1.00000000000000E+00 3.69824496452142E-16
y4 : -7.50000000000000E-01 6.61437827766148E-01
y5 : -7.50000000000000E-01 -6.61437827766148E-01
y6 : -7.50000000000001E-01 6.61437827766148E-01
== err : 1.043E-15 = rco : 2.144E-02 = res : 8.882E-16 ==
solution 66 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 2
the solution for t :
y1 : -8.09905111428176E-01 5.86560917963781E-01
y2 : -8.78150166608380E-01 -4.78385080124447E-01
y3 : 8.17281792388163E-01 5.76238207541631E-01
y4 : -7.45559757800135E-01 -6.66438780045852E-01
y5 : 2.80434187110110E-01 -9.59873255539445E-01
y6 : 3.35899056338419E-01 9.41897990204332E-01
== err : 1.832E-15 = rco : 2.703E-02 = res : 5.722E-16 ==