9
n1^2 + n2^2 + n3^2 - 1;
h11^2 + h12^2 + h13^2 - 1;
h21^2 + h22^2 + h23^2 - 1;
h11*h21 + h12*h22 + h13*h23;
n1^2 + 1.085610*n1*h11 - 2.215830*n1 + 0.2946372680*h11^2 - 1.202763603*h11
+ 0.8110958214+n2^2 + 1.085610*n2*h12 + 0.2946372680*h12^2 + n3^2
+ 1.085610*n3*h13 + 0.2946372680*h13^2;
- 1.050876963*h11 - 1.446982100*h12 + 0.5808481060*h21 + 0.7997861232*h22
- 1.098188*n1 - 1.512126*n2 - 1.012257626*h12*h22 + 0.9156939726*h11^2
+ 0.9156939726*h12^2 + 0.2797510772*h23^2 + 0.9156939726*h13^2 + n2^2 + n3^2
- 1.012257626*h11*h21 + n1^2 - 1.012257626*h13*h23 + 0.2797510772*h22^2
+ 0.2797510772*h21^2 - 1.057830*n3*h23 - 0.3068774482 + 1.913838*n1*h11
+ 1.913838*n2*h12 + 1.913838*n3*h13 - 1.057830*n1*h21 - 1.057830*n2*h22;
2.805076*n1*h12*h23 - 0.9789534962*h11 + 0.2982299150*h12 - 0.7004990340*h13
+ 0.5196729762*h21 - 0.1583139833*h22 + 0.3718567014*h23 - 1.470154*n1
+ 0.447870*n2 - 1.051982*n3 + 2.805076*n3*h11*h22 - 0.4707567232*h12*h22
- 2.061946850*h12*h23 - 0.6281546940*h11*h23 - 1.475444730*h11*h22
+ 1.475444730*h12*h21 - 2.805076*n1*h13*h22 + 2.805076*n2*h13*h21
- 2.805076*n2*h11*h23 + 0.4434028332*h11^2 + 0.4434028332*h12^2
+ 0.1249495243*h23^2 + 0.4434028332*h13^2 + 0.6281546940*h13*h21
+ 2.061946850*h13*h22 + n2^2 + n3^2 - 2.805076*n3*h12*h21
- 0.4707567232*h11*h21 + n1^2 - 0.4707567232*h13*h23 - 1.393177215
+ 0.1249495243*h22^2 + 0.1249495243*h21^2 - 3.934225682*h11*h22*h12*h21
+ 1.967112841*h11^2*h22^2 + 1.967112841*h12^2*h21^2 - 0.706964*n3*h23
+ 1.967112841*h12^2*h23^2 + 1.967112841*h13^2*h22^2 + 1.331770*n1*h11
+ 1.331770*n2*h12 + 1.331770*n3*h13 - 3.934225682*h12*h23*h13*h22
+ 1.967112841*h13^2*h21^2 + 1.967112841*h11^2*h23^2
- 3.934225682*h13*h21*h11*h23 - 0.706964*n1*h21 - 0.706964*n2*h22;
0.215344*n1*h12*h23 - 0.4919329150*h11 + 0.5032939412*h12 + 0.3524721322*h13
- 1.191622463*h21 + 1.219142585*h22 + 0.8538028204*h23 - 1.028376*n1
+ 1.052126*n2 + 0.736836*n3 + 0.215344*n3*h11*h22 + 1.108589329*h12*h22
- 0.1107273007*h12*h23 - 0.1132845107*h11*h23 + 0.7933660580E-1*h11*h22
- 0.7933660580E-1*h12*h21 - 0.215344*n1*h13*h22 + 0.215344*n2*h13*h21
- 0.215344*n2*h11*h23 + 0.2288273329*h11^2 + 0.2288273329*h12^2
+ 1.342683023*h23^2 + 0.2288273329*h13^2 + 0.1132845107*h13*h21
+ 0.1107273007*h13*h22 + n2^2 + n3^2 - 0.215344*n3*h12*h21
+ 1.108589329*h11*h21 + n1^2 + 1.108589329*h13*h23 + 1.342683023*h22^2
+ 1.342683023*h21^2 - 0.2318651916E-1*h11*h22*h12*h21
+ 0.1159325958E-1*h11^2*h22^2 + 0.1159325958E-1*h12^2*h21^2
+ 2.317484*n3*h23 + 0.1159325958E-1*h12^2*h23^2 + 0.1159325958E-1*h13^2*h22^2
+ 0.956718*n1*h11 + 0.956718*n2*h12 + 0.956718*n3*h13
- 0.2318651916E-1*h12*h23*h13*h22 + 0.1159325958E-1*h13^2*h21^2
+ 0.1159325958E-1*h11^2*h23^2 - 0.2318651916E-1*h13*h21*h11*h23
+ 2.317484*n1*h21 + 2.317484*n2*h22 - 0.9664888140;
0.707826*n1*h12*h23 + 0.1618923443*h11 + 0.2597332554E-1*h12
- 0.5621060514E-1*h13 + 0.2776652044*h21 + 0.4454743538E-1*h22
- 0.9640807436E-1*h23 - 1.180946*n1 - 0.189466*n2 + 0.410036*n3
+ 0.707826*n3*h11*h22 + 0.6446406506E-1*h12*h22 - 0.4179521416*h12*h23
+ 0.6705448046E-1*h11*h23 + 0.1451170709*h11*h22 - 0.1451170709*h12*h21
- 0.707826*n1*h13*h22 + 0.707826*n2*h13*h21 - 0.707826*n2*h11*h23
+ 0.1879284557E-1*h11^2 + 0.1879284557E-1*h12^2 + 0.5528188464E-1*h23^2
+ 0.1879284557E-1*h13^2 - 0.6705448046E-1*h13*h21 + 0.4179521416*h13*h22
+ n2^2 + n3^2 - 0.707826*n3*h12*h21 + 0.6446406506E-1*h11*h21 + n1^2
+ 0.6446406506E-1*h13*h23 + 0.5528188464E-1*h22^2 + 0.5528188464E-1*h21^2
- 0.2505088232*h11*h22*h12*h21 + 0.1252544116*h11^2*h22^2
+ 0.1252544116*h12^2*h21^2 - 0.470242*n3*h23 + 0.1252544116*h12^2*h23^2
+ 0.1252544116*h13^2*h22^2 - 0.274174*n1*h11 - 0.274174*n2*h12
- 0.274174*n3*h13 - 0.2505088232*h12*h23*h13*h22 + 0.1252544116*h13^2*h21^2
+ 0.1252544116*h11^2*h23^2 - 0.2505088232*h13*h21*h11*h23 - 0.470242*n1*h21
- 0.470242*n2*h22 - 0.1948854017;
TITLE : Stewart-Gough platform with 40 real postures
ROOT COUNTS :
total degree : 4096
2-homogeneous Bezout number : 2560
with partition : {n1 n2 n3 h11 h12 h13 }{h21 h22 h23 }
mixed volume : 1536
REFERENCES :
Peter Dietmaier:
"The Stewart-Gough platform of general geometry can have 40 real postures",
pages 7-16, in Proceedings of the Sixth International Workshop on Advances
in Robot Kinematics: Analysis and Control,
edited by Jadran Lenarcic and Manfred L. Husty,
Kluwer Academic Publishers, Dordrecht, 1998
NOTE :
# Maple program to generate the equations of the Stewart-Gough platform
# that has all 40 solutions real. The equations and coefficients are
# taken from a paper by Peter Dietmaier:
# "The Stewart-Gough platform of general geometry can have 40 real postures",
# pages 1-10, in Advances in Robot Kinematics: Analysis and Control,
# edited by Jadran Lenarcic and Manfred L. Husty,
# Kluwer Academic Publishers, Dordrecht, 1998
with(linalg);
E1 := [1,0,0]; # (E1,E2,E3) are unit vectors attached to the base
E2 := [0,1,0];
E3 := [0,0,1];
h1 := [h11,h12,h13]; # (h1,h2,e3) are unit vectors attached to platform
h2 := [h21,h22,h23];
e3 := crossprod(h1,h2);
n := [n1,n2,n3]; # unit vector connecting A1 to B1, so L1 = 1
a21 := 1.107915; # coordinates of the 6 base points (zeros omitted)
a31 := 0.549094; a32 := 0.756063;
a41 := 0.735077; a42 := -0.223935; a43 := 0.525991;
a51 := 0.514188; a52 := -0.526063; a53 := -0.368418;
a61 := 0.590473; a62 := 0.094733; a63 := -0.205018;
b21 := 0.542805; # coordinates of the 6 points on the platform
b31 := 0.956919; b32 := -0.528915;
b41 := 0.665885; b42 := -0.353482; b43 := 1.402538;
b51 := 0.478359; b52 := 1.158742; b53 := 0.107672;
b61 := -0.137087; b62 := -0.235121; b63 := 0.353913;
L2 := 0.645275; # lengths of the connecting rods
L3 := 1.086284;
L4 := 1.503439;
L5 := 1.281933;
L6 := 0.771071;
s1 := dotprod(n,n) - 1; # eq 1
s2 := dotprod(h1,h1) - 1; # eq 2
s3 := dotprod(h2,h2) - 1; # eq 3
s4 := dotprod(h1,h2); # eq 4
for i from 1 to 3 do
p.i := n[i] + b21*h1[i] - a21*E1[i];
od:
s5 := p1^2 + p2^2 + p3^2 - L2^2; # eq 5
for i from 1 to 3 do
p.i := n[i] + b31*h1[i] + b32*h2[i] - a31*E1[i] - a32*E2[i];
od:
s6 := p1^2 + p2^2 + p3^2 - L3^2; # eq 6
for i from 1 to 3 do
p.i := n[i] + b41*h1[i]+b42*h2[i]+b43*e3[i]-a41*E1[i]-a42*E2[i]-a43*E3[i];
od:
s7 := p1^2 + p2^2 + p3^2 - L4^2; # eq 7
for i from 1 to 3 do
p.i := n[i] + b51*h1[i]+b52*h2[i]+b53*e3[i]-a51*E1[i]-a52*E2[i]-a53*E3[i];
od:
s8 := p1^2 + p2^2 + p3^2 - L5^2; # eq 8
for i from 1 to 3 do
p.i := n[i] + b61*h1[i]+b62*h2[i]+b63*e3[i]-a61*E1[i]-a62*E2[i]-a63*E3[i];
od:
s9 := p1^2 + p2^2 + p3^2 - L6^2; # eq 9
lprint([expand(s1),expand(s2),expand(s3),expand(s4),expand(s5),expand(s6),expand(s7),expand(s8),expand(s9)]);
THE SOLUTIONS :
40 9
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 5.34003548614846E-01 1.05854328139471E-36
n2 : 6.17464537788932E-03 3.89866935952116E-36
n3 : -8.45459687874714E-01 5.71091229760302E-37
h11 : 6.36859679827326E-02 -3.40926078133970E-36
h12 : -2.73293377921528E-01 -3.23745378718363E-36
h13 : 9.59820205593914E-01 -5.45030755331031E-37
h21 : 9.92514435679251E-01 3.22059192913124E-37
h22 : -8.30827232386822E-02 -2.26314948449908E-37
h23 : -8.95117649671954E-02 3.08198203190666E-36
== err : 1.255E-11 = rco : 4.124E-06 = res : 1.246E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.63325713770891E-01 -9.85287982728387E-47
n2 : 5.64402867997359E-03 2.40848173555828E-46
n3 : -5.04615553547690E-01 0.00000000000000E+00
h11 : 1.91288333012351E-01 3.06534039071054E-46
h12 : 9.43756501770663E-01 -2.40848173555828E-46
h13 : 2.69689523376340E-01 3.50324616081204E-46
h21 : -7.27039337601767E-01 -2.18952885050753E-47
h22 : -4.83533608080227E-02 -9.85287982728387E-47
h23 : 6.84891052707037E-01 -2.18952885050753E-47
== err : 1.416E-15 = rco : 7.863E-03 = res : 9.368E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.58734196042698E-01 -1.39752196496346E-40
n2 : -3.73482566386209E-01 -1.17712994638985E-39
n3 : -8.06271486527107E-01 4.78499985314531E-40
h11 : 3.68860267183001E-01 8.86192359226729E-40
h12 : 4.07073379420521E-02 9.77601860651565E-40
h13 : 9.28593030305180E-01 -4.07995755029724E-40
h21 : 9.24342754384125E-01 -3.46712769289407E-40
h22 : -1.21006255697330E-01 -3.43313919864187E-40
h23 : -3.61867321679759E-01 -7.56653526587614E-40
== err : 1.696E-12 = rco : 5.552E-06 = res : 1.416E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.32284652705197E-01 6.06061585820484E-44
n2 : -2.82751760714109E-01 -3.64337600724452E-44
n3 : 4.76816210593203E-01 -1.28218809485721E-43
h11 : -3.82981891941851E-01 -3.48923317616879E-43
h12 : -2.66292049783987E-01 3.62936302260128E-43
h13 : -8.84541358369682E-01 8.46033947836108E-44
h21 : -4.75822014065617E-01 -4.54721351673403E-43
h22 : -7.63878999533626E-01 4.62428493227190E-43
h23 : 4.35984271507638E-01 1.08600630985173E-43
== err : 2.572E-14 = rco : 1.480E-03 = res : 1.998E-15 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.25080174807858E-01 -8.36575354258857E-49
n2 : -3.18925637259120E-01 -5.86939130336246E-48
n3 : 4.66400196224120E-01 -2.11682965039302E-48
h11 : -2.60309875080715E-01 1.70201656738671E-47
h12 : -3.06586498174506E-01 -4.21227718310530E-48
h13 : -9.15556381700525E-01 -4.34056988918973E-48
h21 : -2.26750206541050E-01 3.54943153500244E-47
h22 : -9.02315220510292E-01 -1.89017920297720E-47
h23 : 3.66621857871369E-01 -1.00068310745852E-47
== err : 2.269E-14 = rco : 3.203E-03 = res : 1.374E-15 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.58098206425925E-01 -1.29620107950046E-44
n2 : -2.84038680295125E-01 1.47136338754106E-44
n3 : -3.70115514350629E-02 -2.52233723578467E-44
h11 : -2.51037203502158E-01 -3.50324616081204E-45
h12 : -4.94976885688591E-02 -4.37905770101505E-44
h13 : 9.66711074356840E-01 -1.25241050249031E-44
h21 : -3.11210657578553E-03 5.74532370373175E-44
h22 : -9.98645308796313E-01 1.44508904133497E-44
h23 : -5.19409473515592E-02 -9.98425155831432E-45
== err : 9.637E-15 = rco : 3.619E-03 = res : 7.529E-16 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 5.35059805089595E-01 -1.71056941445901E-48
n2 : -7.49596111150599E-01 -2.39479718024261E-48
n3 : -3.89636593668234E-01 2.39479718024261E-48
h11 : 2.75453499517998E-01 1.43687830814556E-47
h12 : 4.90427569122504E-01 -6.84227765783602E-49
h13 : 8.26804795007794E-01 -6.15804989205242E-48
h21 : 9.58346562586592E-01 -5.98699295060652E-48
h22 : -2.07623649715259E-01 -2.05268329735081E-48
h23 : -1.96123140035486E-01 -1.40266691985638E-47
== err : 2.427E-15 = rco : 1.749E-02 = res : 8.049E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 5.39848418396206E-01 1.82168800362226E-43
n2 : 6.78840402335085E-01 0.00000000000000E+00
n3 : 4.97734259733700E-01 7.62306364592701E-43
h11 : 8.72889092300304E-01 6.05360936588321E-43
h12 : -4.87412172424983E-01 3.58732406867153E-43
h13 : -2.22262618339058E-02 -1.07619722060146E-42
h21 : -4.26919121596827E-01 1.03135566974307E-42
h22 : -7.85022713166514E-01 -6.27781712017518E-43
h23 : 4.48864571366107E-01 3.62936302260128E-43
== err : 4.775E-15 = rco : 5.738E-03 = res : 1.096E-15 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.55765578596128E-01 2.72751423589234E-38
n2 : -3.34679158802413E-01 -3.71933759439864E-39
n3 : 3.94531538857596E-01 -5.80400335718505E-38
h11 : -2.62159355550805E-01 -1.79308806248478E-38
h12 : -3.05118645203351E-01 1.57268287170560E-39
h13 : -9.15519024732123E-01 4.49419959323170E-39
h21 : 7.53301863744732E-02 2.18935822840651E-37
h22 : -9.52275693659966E-01 -2.53465969396056E-38
h23 : 2.95797846992195E-01 -4.99585099099472E-38
== err : 6.957E-15 = rco : 8.044E-03 = res : 2.236E-15 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.93577279882540E-01 1.31457259501175E-46
n2 : 7.96654869549876E-02 9.32739290316206E-45
n3 : -8.03591879590493E-02 2.21470843228836E-44
h11 : 8.58684284463838E-02 2.10194769648723E-44
h12 : 9.58900432623298E-01 1.13616020508367E-45
h13 : -2.70437743872780E-01 1.37502411811873E-44
h21 : -9.70578427677462E-01 2.78727022669608E-44
h22 : 1.92225092956508E-02 2.21416105007574E-45
h23 : -2.40016688718775E-01 -7.40498657241646E-44
== err : 8.236E-14 = rco : 8.967E-04 = res : 1.658E-15 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 6.89418318569635E-01 -2.30995293728544E-45
n2 : 5.93656300371125E-01 -2.55080111084127E-45
n3 : -4.15059729497196E-01 -8.01367559285755E-45
h11 : -2.10582457802054E-01 1.11665971375884E-44
h12 : -9.71898937276348E-01 -2.81354457290217E-45
h13 : 1.05202111134483E-01 1.81183512379498E-45
h21 : -2.51238756720206E-01 1.12103877145985E-44
h22 : -5.01948080335288E-02 -8.53916251697936E-45
h23 : -9.66622764250958E-01 -3.30618856426637E-45
== err : 6.253E-15 = rco : 2.057E-03 = res : 1.533E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 6.36111780656805E-01 8.77000920499002E-52
n2 : 7.71451960369755E-01 6.26429228927858E-52
n3 : 1.49557798623220E-02 6.68191177523049E-52
h11 : 4.03995111057654E-01 1.00228676628457E-51
h12 : -5.70369249047288E-01 7.51715074713430E-52
h13 : -7.15169119847010E-01 -6.68191177523049E-52
h21 : 5.46802941037561E-01 -8.35238971903811E-52
h22 : -4.76187161523352E-01 -1.41990625223648E-51
h23 : 6.88659807795552E-01 -2.92333640166334E-52
== err : 1.281E-15 = rco : 3.902E-02 = res : 1.166E-15 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.98901201703156E-01 4.92643991364194E-47
n2 : -4.15643212288688E-02 1.02469950203752E-44
n3 : -2.16517074794277E-02 1.55456548386034E-45
h11 : -7.68309996521777E-01 -1.89175292683850E-44
h12 : -3.80464598421854E-02 2.09100005223469E-45
h13 : -6.38946176245061E-01 2.84638750565979E-44
h21 : 6.37073346346389E-01 -3.18795400633896E-44
h22 : 5.11533959452041E-02 3.04782415990648E-44
h23 : -7.69103947108769E-01 -1.47136338754106E-44
== err : 1.773E-14 = rco : 2.089E-03 = res : 1.638E-15 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.03267816614331E-01 -8.75811540203011E-47
n2 : -2.96007114309009E-01 -7.99178030435247E-46
n3 : 5.16856462734190E-01 9.85287982728387E-47
h11 : 3.47483676895208E-01 -3.50324616081204E-46
h12 : 9.24976155378647E-01 -6.56858655152258E-46
h13 : 1.53864246244288E-01 5.25486924121806E-46
h21 : 6.61165323640850E-01 4.37905770101505E-46
h22 : -1.25334288273277E-01 -1.75162308040602E-46
h23 : -7.39697053527944E-01 7.88230386182710E-46
== err : 2.521E-15 = rco : 1.126E-02 = res : 1.804E-15 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.91374858482066E-01 -9.54260525400104E-51
n2 : -7.98270407205689E-02 1.26956323729379E-50
n3 : -4.46182143564569E-01 -2.47230735683528E-50
h11 : -7.72754070399605E-01 1.47002059055071E-50
h12 : 1.24475148333286E-01 -2.45560257739721E-50
h13 : 6.22380176522556E-01 2.43889779795913E-50
h21 : -5.30468237908900E-01 -3.74187059412907E-50
h22 : 4.11756423596472E-01 -4.34324265389982E-51
h23 : -7.40985894735433E-01 1.82082095875031E-50
== err : 6.299E-15 = rco : 2.000E-02 = res : 1.971E-15 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.54376241567566E-01 -9.18354961579912E-39
n2 : -2.94202949023025E-01 5.55604751755847E-39
n3 : 4.28352498102948E-01 1.69895667892284E-38
h11 : -5.12684519571621E-01 4.84891419714194E-38
h12 : -1.28566989770228E-01 -4.88564839560513E-38
h13 : -8.48896408599447E-01 -8.99987862348314E-39
h21 : -6.51892330670189E-01 5.96012370065363E-38
h22 : -5.85147000776723E-01 -6.29991503643820E-38
h23 : 4.82327043296761E-01 -1.24178809961134E-38
== err : 5.403E-14 = rco : 1.908E-03 = res : 1.471E-15 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.55868038053903E-01 -2.15239444120292E-42
n2 : -4.69956294144925E-02 -7.71274674764379E-42
n3 : -2.90013283562870E-01 -6.81591573047591E-42
h11 : -4.04503572788201E-02 -1.23762680369168E-41
h12 : 9.83337493668175E-01 5.38098610300730E-43
h13 : -1.77231888051804E-01 -3.40795786523796E-42
h21 : -9.32229494182938E-01 -1.25556342403504E-42
h22 : 2.66955230935295E-02 1.97302823776934E-42
h23 : 3.60881586150066E-01 3.01335221768409E-41
== err : 6.512E-15 = rco : 3.075E-03 = res : 1.970E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.93725753949452E-01 9.34518008903719E-37
n2 : 1.11785841717458E-01 7.10072056293588E-37
n3 : 3.61269001070998E-03 -1.28363983109794E-35
h11 : 1.60649572104603E-01 -4.07014918972217E-36
h12 : 9.63663368265282E-01 -1.62254954611939E-36
h13 : -2.13411873255029E-01 -1.66332450641354E-35
h21 : -8.57007169860833E-01 -3.17971221897429E-35
h22 : 2.89304252424857E-02 -3.60656360511663E-36
h23 : -5.14491731034051E-01 3.08332168220686E-35
== err : 2.946E-13 = rco : 4.913E-04 = res : 1.429E-15 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.98523184555461E-01 -2.61731164050275E-39
n2 : 3.11963433241766E-02 -4.70197740328915E-38
n3 : 4.44773882823691E-02 1.15345383174437E-37
h11 : -9.67647453552388E-01 -5.43666137255308E-38
h12 : 9.45970104164593E-02 2.58608757180903E-37
h13 : -2.33901285276178E-01 3.20322210599073E-37
h21 : 2.51917037750896E-01 -1.91017832008622E-37
h22 : 4.13708197898153E-01 2.05711511393900E-37
h23 : -8.74861893719618E-01 4.88564839560513E-38
== err : 1.240E-15 = rco : 1.565E-03 = res : 1.915E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.85480868222368E-01 -4.14385268551873E-33
n2 : -2.00817523650534E-01 -2.95934934599174E-32
n3 : -8.50870524101595E-01 8.98033015242896E-33
h11 : 2.36223483879496E-01 2.21391665638389E-32
h12 : -1.02020949277161E-01 2.44728519886394E-32
h13 : 9.66328200753978E-01 -7.65014074503846E-33
h21 : 9.65580988216924E-01 -7.56407104867126E-33
h22 : -8.67721144732894E-02 -6.62861264428688E-33
h23 : -2.45201866517901E-01 -1.94962791049981E-32
== err : 6.032E-12 = rco : 3.484E-06 = res : 1.402E-15 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.42198664294286E-01 -7.29726175297149E-43
n2 : -7.13494517208498E-01 3.39562643875190E-41
n3 : -5.43494172194847E-01 -3.97408244482518E-41
h11 : 6.35108872193352E-01 -2.83790964995062E-41
h12 : 3.28441911591642E-01 -2.93263742613898E-41
h13 : 6.99115606442394E-01 3.50100408326912E-41
h21 : 7.72001416124780E-01 2.10026613833004E-41
h22 : -2.99793875619531E-01 2.65461981081693E-41
h23 : -5.60479656760489E-01 1.76311372781348E-41
== err : 2.305E-13 = rco : 1.597E-04 = res : 1.568E-15 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.17778090378591E-01 -3.15684518043095E-41
n2 : -1.11176182195232E-01 -8.60957776481168E-41
n3 : 3.81212845184314E-01 1.54972399766610E-40
h11 : 9.95042737783780E-02 5.16574665888701E-41
h12 : 9.81800859405347E-01 2.08064795982949E-41
h13 : 1.61758993477207E-01 1.49232681256736E-40
h21 : 2.79494636423541E-01 3.67341984631965E-40
h22 : 1.28443119283290E-01 -3.15684518043095E-41
h23 : -9.51517269059922E-01 -5.88321147262131E-41
== err : 9.906E-15 = rco : 7.172E-03 = res : 3.849E-15 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.43037558993735E-01 -5.63712104151045E-39
n2 : -5.58620406851917E-01 -1.00657443507668E-37
n3 : -7.01185398000751E-01 7.14853241812314E-38
h11 : 5.08689536806823E-01 7.66654201363930E-38
h12 : 1.95638330781374E-01 8.48416491537092E-38
h13 : 8.38427455819726E-01 -6.15857446813254E-38
h21 : 8.58129045381476E-01 -4.17098169464439E-38
h22 : -1.93982996160302E-01 -4.88263504338745E-38
h23 : -4.75378942185442E-01 -5.91693231886683E-38
== err : 1.100E-12 = rco : 2.425E-05 = res : 1.027E-15 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 5.21847667572176E-01 -1.23314264860584E-43
n2 : 8.10720215374404E-01 3.13890856008759E-43
n3 : 2.65344576414820E-01 0.00000000000000E+00
h11 : 7.44610461306344E-01 1.87773994219526E-43
h12 : -6.20756202696880E-01 -6.72623262875912E-44
h13 : 2.45391519263612E-01 -1.34524652575182E-43
h21 : -6.54481004425527E-01 0.00000000000000E+00
h22 : -6.06710821818961E-01 -7.84727140021898E-44
h23 : 4.51172465398670E-01 3.36311631437956E-43
== err : 4.028E-15 = rco : 7.285E-03 = res : 1.346E-15 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.89132291307142E-01 1.17030317059627E-44
n2 : 1.16671335896421E-01 -2.43475608176437E-44
n3 : 8.94712784843688E-02 -2.38220738935219E-43
h11 : 2.00591802337382E-01 -1.29007039871903E-43
h12 : 9.72716506813502E-01 -2.50372624055536E-44
h13 : -1.16556965504332E-01 -2.69224467458405E-43
h21 : -6.70069414937762E-01 -5.02715824076528E-43
h22 : 4.94310791152468E-02 -5.53950799178404E-44
h23 : -7.40650759523318E-01 6.63164498241720E-43
== err : 9.542E-14 = rco : 8.763E-04 = res : 1.728E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.77891495744216E-01 4.67733824266134E-51
n2 : -7.81098769166185E-01 -7.26631607609439E-51
n3 : -4.01876139006070E-01 2.60594559233989E-50
h11 : 8.26711558940246E-01 -1.33638235504610E-51
h12 : 5.62537417927839E-01 -4.00914706513829E-51
h13 : 9.98257209683472E-03 8.01829413027659E-51
h21 : 1.68452377741072E-01 1.60365882605532E-50
h22 : -2.30552752606781E-01 -2.47230735683528E-50
h23 : -9.58368000665097E-01 2.67276471009220E-50
== err : 2.298E-15 = rco : 2.301E-02 = res : 9.125E-16 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 6.79796319226422E-01 4.23627099269421E-39
n2 : 3.48060722634918E-01 6.96801827098758E-39
n3 : -6.45546820707117E-01 7.52190110719047E-39
h11 : -3.16630836891232E-01 -9.91392879618065E-39
h12 : -5.70962406372255E-01 -6.51099318463883E-39
h13 : 7.57460786865672E-01 -8.04923774528518E-39
h21 : 9.48521087940044E-01 -2.79542228051229E-39
h22 : -1.96693912816955E-01 -4.43895480257415E-39
h23 : 2.48232250913921E-01 8.70858790910701E-39
== err : 3.889E-13 = rco : 7.793E-05 = res : 2.345E-15 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 7.81100385565255E-01 1.02634164867540E-48
n2 : 6.87982308185337E-02 6.84227765783602E-49
n3 : -6.20603731140935E-01 -2.39479718024261E-48
h11 : -5.41606685574368E-01 -1.36845553156720E-48
h12 : -1.73803010414417E-01 -2.39479718024261E-48
h13 : 8.22468669137028E-01 -2.05268329735081E-48
h21 : -8.31931660393735E-01 0.00000000000000E+00
h22 : 2.51219864599270E-01 -1.71056941445901E-48
h23 : -4.94750737306422E-01 -6.84227765783602E-49
== err : 1.166E-15 = rco : 1.569E-02 = res : 8.604E-16 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.95367590043985E-01 -5.84667280332668E-52
n2 : -5.11993233294401E-02 3.20731765211064E-50
n3 : 8.13756104778135E-02 -1.77070662043608E-50
h11 : -9.44300925088411E-01 3.84209927075753E-51
h12 : 3.27693285372367E-01 -8.68648530779964E-50
h13 : 3.02137981564153E-02 -9.48831472082730E-50
h21 : 1.48424585882925E-01 4.14278530064290E-50
h22 : 5.06047270810245E-01 -4.20960441839521E-50
h23 : -8.49638924491448E-01 -1.50343014942686E-50
== err : 6.976E-15 = rco : 4.263E-03 = res : 1.429E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.91613476781441E-01 1.52040883379243E-43
n2 : -1.27016034010182E-01 7.73516752307299E-43
n3 : 2.38671273878463E-02 2.71851902079015E-43
h11 : -3.57494436822097E-01 -5.36697311836405E-43
h12 : -1.63558833763925E-01 -6.15170025838595E-43
h13 : 9.19481503641610E-01 -2.52233723578467E-43
h21 : 2.16483051632442E-01 1.15186733767500E-42
h22 : -9.72241757701029E-01 1.41531144896807E-43
h23 : -8.87752946394405E-02 -1.89175292683850E-43
== err : 1.769E-14 = rco : 4.592E-03 = res : 1.568E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 5.85910442911322E-01 -2.76918997326013E-39
n2 : 1.61497863147955E-01 -8.90759471181656E-39
n3 : -7.94120515467333E-01 -2.40713929162946E-39
h11 : -8.56103454963281E-02 8.18941243326852E-39
h12 : -4.04087038763322E-01 7.42262191358998E-39
h13 : 9.10705514339015E-01 2.20454516485123E-39
h21 : 9.92920002672369E-01 -3.21491498879257E-40
h22 : -1.10148655080763E-01 1.21724631882654E-39
h23 : 4.44650658045476E-02 -7.38567247568267E-39
== err : 8.391E-12 = rco : 8.322E-06 = res : 1.301E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 6.67532055667499E-01 2.09921078542409E-45
n2 : 7.38317082958943E-01 -2.56448566615694E-45
n3 : -9.63786266104705E-02 -3.31439929745577E-45
h11 : -2.74641413158143E-01 -6.27847397883033E-45
h12 : -9.02131529759339E-01 3.43824452306260E-46
h13 : 3.32762373462766E-01 -6.37700277710317E-45
h21 : -8.48377924744068E-01 8.70337718076742E-45
h22 : 6.44572818041603E-02 3.29797783107696E-45
h23 : -5.25452334307659E-01 -1.05644767036988E-44
== err : 5.407E-14 = rco : 1.130E-03 = res : 1.096E-15 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 7.19131226940004E-01 2.27711000452783E-45
n2 : 6.33882537501859E-01 1.19110369467609E-44
n3 : -2.84680886414891E-01 3.22298646794708E-44
h11 : -3.68747962290968E-01 -1.68155815718978E-44
h12 : -9.23636047965730E-01 1.08600630985173E-44
h13 : 1.04505460165994E-01 2.38220738935219E-44
h21 : -4.43454701750678E-01 -5.88545355016423E-44
h22 : 7.59957467835468E-02 2.10194769648723E-44
h23 : -8.93069187670266E-01 3.85357077689325E-44
== err : 2.885E-15 = rco : 9.494E-04 = res : 1.665E-15 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.68094275400576E-01 3.26265223399926E-55
n2 : 2.36773416581551E-01 1.95759134039956E-54
n3 : -8.20476881876155E-02 -3.26265223399926E-54
h11 : 1.08313821993718E-01 -1.95759134039956E-54
h12 : 5.12433497755402E-01 2.61012178719941E-54
h13 : 8.51868549920279E-01 -3.91518268079912E-54
h21 : -7.56895695744459E-01 -1.95759134039956E-54
h22 : -5.13035561502901E-01 6.52530446799852E-54
h23 : 4.04849871430034E-01 1.30506089359970E-54
== err : 1.385E-15 = rco : 4.238E-02 = res : 1.468E-15 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 8.70077503803752E-01 -8.96314442501994E-38
n2 : -4.51122000544921E-01 -1.58691737361009E-37
n3 : -1.98630506214379E-01 -1.68977312930704E-37
h11 : -1.02377480196255E-01 1.49875529729842E-37
h12 : -2.08924583158680E-02 1.61630473238065E-38
h13 : 9.94526197108043E-01 2.58976099165535E-38
h21 : -1.41893697316575E-01 -1.11671963328117E-37
h22 : -9.89249133803585E-01 1.08365885466430E-38
h23 : -3.53882739150989E-02 1.32243114467507E-38
== err : 5.018E-15 = rco : 1.167E-02 = res : 9.576E-16 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.99627516123705E-01 5.65003540815766E-42
n2 : 2.61758190800336E-02 1.75061414551171E-40
n3 : -7.72369754979942E-03 -6.96837700339445E-41
h11 : -9.01448309891712E-01 -2.92725644003597E-40
h12 : -1.15885888359757E-02 -6.74416924910248E-41
h13 : -4.32731613361176E-01 2.35328458904853E-40
h21 : 4.13965587164152E-01 -3.09944799533220E-40
h22 : 2.69235414070789E-01 4.07520014201086E-40
h23 : -8.69565859756447E-01 -3.81691280906651E-40
== err : 1.367E-14 = rco : 1.078E-03 = res : 7.286E-16 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 9.03174122860764E-01 3.67505147637677E-51
n2 : -4.18445409132979E-01 -2.67276471009220E-50
n3 : 9.58120210110546E-02 -5.88008236220283E-50
h11 : -6.81556061565631E-01 -2.53912647458759E-50
h12 : 4.27412220174900E-01 1.01565058983503E-49
h13 : -5.93969804778247E-01 6.94918824623971E-50
h21 : -7.02125371338306E-01 4.00914706513829E-50
h22 : -1.53284563866731E-01 6.94918824623971E-50
h23 : 6.95358760211757E-01 5.88008236220283E-50
== err : 8.896E-16 = rco : 8.132E-03 = res : 1.998E-15 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 7.07962981557702E-01 -8.95376177880886E-49
n2 : 6.85868420834270E-01 1.02366888396531E-48
n3 : -1.68442649130896E-01 1.22412623722223E-48
h11 : -3.89440329781405E-01 2.80105741617662E-48
h12 : -8.97709193093757E-01 -2.05802882677099E-49
h13 : 2.06044738284446E-01 2.69414682777293E-48
h21 : -6.67548527805184E-01 -3.44252094659875E-48
h22 : 1.20968632530243E-01 -1.56089459069384E-48
h23 : -7.34673773159825E-01 4.38333412455120E-48
== err : 4.563E-14 = rco : 7.161E-04 = res : 1.110E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.89122174358057E-01 -3.13214614463929E-53
n2 : 6.96229957966802E-01 -3.13214614463929E-53
n3 : -5.25379238437142E-01 -1.98369255827155E-52
h11 : 7.77174054077347E-01 -3.13214614463929E-53
h12 : -2.15031454973226E-01 0.00000000000000E+00
h13 : 5.91406766144148E-01 1.87928768678358E-52
h21 : -6.28581348446903E-01 -8.48289580839808E-53
h22 : -2.20815627982680E-01 1.14845358636774E-52
h23 : 7.45738524432853E-01 -1.56607307231965E-53
== err : 3.017E-15 = rco : 3.818E-02 = res : 9.159E-16 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
n1 : 4.84611616103657E-01 1.80487242205036E-42
n2 : -8.73934747204850E-01 -6.55807681304014E-42
n3 : -3.72778642815946E-02 1.94612330725431E-41
h11 : 8.53425304892223E-01 8.47505311223649E-42
h12 : 4.69308241247517E-01 6.52444564989635E-42
h13 : 2.26748811831019E-01 -1.71294724279066E-41
h21 : 5.05719394616724E-01 -9.14767637511241E-42
h22 : -6.40298096731891E-01 -1.29592081980759E-41
h23 : -5.78157626629634E-01 -1.73200490190547E-42
== err : 4.751E-14 = rco : 1.062E-03 = res : 2.165E-15 ==