4
y**2*z+2*x*y*t-2*x-z;
-x**3*z+4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2;
2*y*z*t+x*t**2-x-2*z;
-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t-10*t**2+2;
TITLE : the system caprasse of the PoSSo test suite
The system has 24 regular roots and 8 quadruple roots.
For each of the 8 quadruple roots, one deflation suffices
to restore quadratic convergence. After the deflation,
by simple grouping of the roots, we get the multiplicities
of all the roots.
ROOT COUNTS :
total degree : 144
2-homogeneous Bezout number : 62
with partition : {y x }{z t }
generalized Bezout number : 94
based on the set structure :
{y }{y x }{z t }
{y x }{y x }{y z t }{x t }
{y x }{z t }{t }
{y z }{z t }{z t }{x t }
mixed volume : 48
REFERENCES :
Shuichi Moritsugu and Kazuko Kuriyama:
"On Multiple Zeros of Systems of Algebraic Equations"
in Proceedings of the 1999 International Symposium on
Symbolic and Algebraic Computation (ISSAC 1999),
edited by Sam Dooley, pages 23-30, ACM 1999.
NOTE :
The solutions below are obtained as the end points of
a 2-homogeneous homotopy, 6 of the 62 paths diverged.
THE SOLUTIONS :
56 4
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -4.60171935497768E-09 -1.73205076792811E+00
z : 2.00000005272859E+00 1.53445880621687E-08
x : 1.99999998406877E+00 7.37417618966893E-09
t : -4.60171952530211E-09 1.73205084720964E+00
== err : 1.751E-07 = rco : 1.530E-09 = res : 1.461E-13 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 3.14626436994197E+00 -4.05694422731437E-69
z : 1.01423605682859E-69 -1.50541613844488E-109
x : -1.01423605682859E-69 -1.50541613844488E-109
t : 3.14626436994197E+00 4.05694422731437E-69
== err : 4.790E-15 = rco : 8.090E-02 = res : 3.952E-14 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 3.06035300517854E-68
z : 3.86370330515627E+00 -5.63799334904488E-66
x : 3.86370330515627E+00 3.25377935212361E-67
t : 1.00000000000000E+00 -1.11276184520623E-67
== err : 5.972E-15 = rco : 1.227E-02 = res : 7.105E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.06566887284394E-08 1.73205085190235E+00
z : 1.99999999237423E+00 -6.40742625050165E-09
x : 2.00000006916205E+00 -2.48653524382443E-08
t : 1.06566885779115E-08 -1.73205076323541E+00
== err : 2.154E-07 = rco : 7.094E-10 = res : 2.248E-13 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 8.06789982260275E-122
z : -1.45222196806849E-121 -2.00000000000000E+00
x : -9.68147978712330E-122 2.00000000000000E+00
t : 1.00000000000000E+00 0.00000000000000E+00
== err : 1.454E-105 = rco : 5.880E-02 = res : 4.453E-120 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -8.39386613494274E-09 5.77350289878091E-01
z : 6.65771221045258E-08 1.15470059312383E+00
x : -5.81832559691208E-08 -1.15470061381229E+00
t : -8.39386613586737E-09 -5.77350248501160E-01
== err : 3.131E-07 = rco : 1.515E-08 = res : 1.262E-13 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.17837245195782E-01 0.00000000000000E+00
z : 0.00000000000000E+00 0.00000000000000E+00
x : 0.00000000000000E+00 0.00000000000000E+00
t : -3.17837245195782E-01 0.00000000000000E+00
== err : 4.991E-16 = rco : 8.090E-02 = res : 1.110E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -5.75009405580655E-08 -5.77350279103889E-01
z : 6.70945295064009E-08 1.15470051755719E+00
x : -1.24595470156539E-07 -1.15470052747145E+00
t : -5.75009407422120E-08 5.77350259275363E-01
== err : 3.671E-07 = rco : 5.098E-09 = res : 2.392E-13 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 0.00000000000000E+00
z : -1.70920219423676E-64 -2.00000000000000E+00
x : 0.00000000000000E+00 2.00000000000000E+00
t : -1.00000000000000E+00 1.65733171735930E-99
== err : 1.625E-48 = rco : 5.880E-02 = res : 5.469E-63 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 0.00000000000000E+00
z : 0.00000000000000E+00 0.00000000000000E+00
x : 0.00000000000000E+00 0.00000000000000E+00
t : 1.00000000000000E+00 0.00000000000000E+00
== err : 4.273E-65 = rco : 2.000E-01 = res : 0.000E+00 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.98806786326294E-08 1.73205086644976E+00
z : 1.99999994075241E+00 1.90667956243172E-08
x : 2.00000004273709E+00 -3.26880579465170E-08
t : 2.98806786493531E-08 -1.73205074868799E+00
== err : 3.298E-07 = rco : 3.846E-09 = res : 1.511E-13 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 1.84798661691364E-56
z : 1.03527618041008E+00 3.58445680004802E-56
x : 1.03527618041008E+00 -5.22534146851444E-56
t : -1.00000000000000E+00 -1.78426294046835E-56
== err : 5.944E-15 = rco : 5.099E-02 = res : 6.217E-15 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.33126171288310E-08 -5.77350288722030E-01
z : 2.84956075182080E-08 -1.15470053214938E+00
x : -1.51829903744763E-08 1.15470055168179E+00
t : -1.33126171586323E-08 5.77350249657221E-01
== err : 1.327E-07 = rco : 7.343E-09 = res : 2.718E-14 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 3.04270817048578E-69
z : 1.03527618041008E+00 5.94052547571032E-69
x : 1.03527618041008E+00 8.69345191567364E-69
t : 1.00000000000000E+00 3.18759903574700E-69
== err : 5.944E-15 = rco : 5.099E-02 = res : 6.217E-15 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -2.25248020988057E-08 -1.73205082824059E+00
z : 2.00000000279144E+00 3.68122801056416E-08
x : 2.00000003859590E+00 -2.20182126730501E-09
t : -2.25248017609183E-08 1.73205078689717E+00
== err : 1.321E-07 = rco : 1.991E-09 = res : 6.112E-14 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 1.18694596821997E-65
z : 3.86370330515627E+00 5.45995145381188E-65
x : 3.86370330515627E+00 -1.13946812949118E-64
t : -1.00000000000000E+00 0.00000000000000E+00
== err : 5.972E-15 = rco : 1.227E-02 = res : 7.105E-15 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 0.00000000000000E+00
z : 0.00000000000000E+00 2.00000000000000E+00
x : -1.27447352890596E-57 -2.00000000000000E+00
t : -1.00000000000000E+00 1.27447352890596E-57
== err : 3.964E-41 = rco : 5.880E-02 = res : 4.588E-56 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.38054364628294E-08 -1.73205081323691E+00
z : -2.00000002047618E+00 4.55002281757761E-09
x : -2.00000003029349E+00 -3.66822029547455E-08
t : 2.38054368350468E-08 1.73205080190085E+00
== err : 1.638E-07 = rco : 1.285E-09 = res : 1.284E-13 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.68677232827175E-08 5.77350296730679E-01
z : 9.23443057057155E-09 -1.15470043951446E+00
x : 7.63329269752966E-09 1.15470046705552E+00
t : 1.68677232534847E-08 -5.77350241648573E-01
== err : 2.754E-07 = rco : 1.091E-08 = res : 1.358E-13 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 0.00000000000000E+00 1.00000000000000E+00
z : 0.00000000000000E+00 0.00000000000000E+00
x : 0.00000000000000E+00 0.00000000000000E+00
t : 0.00000000000000E+00 -1.00000000000000E+00
== err : 0.000E+00 = rco : 1.471E-01 = res : 0.000E+00 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.39617652878053E-08 1.73205082623122E+00
z : 1.99999997175830E+00 3.48705123119496E-09
x : 2.00000000408242E+00 -3.80159433087679E-08
t : 2.39617648518409E-08 -1.73205078890654E+00
== err : 1.064E-07 = rco : 1.612E-09 = res : 4.111E-14 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 3.17837245195782E-01 9.60663906400559E-62
z : 0.00000000000000E+00 0.00000000000000E+00
x : 0.00000000000000E+00 0.00000000000000E+00
t : 3.17837245195782E-01 -2.17805534725140E-60
== err : 4.991E-16 = rco : 8.090E-02 = res : 1.110E-16 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 -1.47390610006945E-75
z : 2.00000000000000E+00 -7.36953050034726E-75
x : -2.00000000000000E+00 3.53737464016668E-74
t : -1.00000000000000E+00 3.45928932213039E-125
== err : 3.186E-58 = rco : 3.999E-02 = res : 1.421E-72 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -4.25906066984997E-08 -5.77350283257430E-01
z : -5.30612558220945E-08 -1.15470047957764E+00
x : 9.56518625109948E-08 1.15470049364545E+00
t : -4.25906066793009E-08 5.77350255121822E-01
== err : 3.650E-07 = rco : 1.126E-08 = res : 1.445E-13 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.08861780139229E-08 5.77350250969379E-01
z : -6.53434323727941E-08 -1.15470057998366E+00
x : 5.44572543372087E-08 1.15470056176341E+00
t : -1.08861780572477E-08 -5.77350287409873E-01
== err : 2.440E-07 = rco : 9.060E-09 = res : 7.797E-14 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.73157499486634E-08 1.73205076817542E+00
z : -2.00000004837654E+00 1.27175095159757E-08
x : -1.99999998014507E+00 -1.72742505727262E-08
t : -1.73157515727019E-08 -1.73205084696234E+00
== err : 1.768E-07 = rco : 2.766E-09 = res : 1.387E-13 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.54533105528812E-08 -5.77350262307923E-01
z : -4.21765506114800E-08 -1.15470057260865E+00
x : 1.67232400820255E-08 1.15470056572695E+00
t : 2.54533105060277E-08 5.77350276071329E-01
== err : 1.832E-07 = rco : 4.579E-09 = res : 5.931E-14 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -8.10288447638169E-64 -1.00000000000000E+00
z : 0.00000000000000E+00 1.33061245000255E-110
x : -1.19850914680120E-94 0.00000000000000E+00
t : 1.21543267145725E-63 1.00000000000000E+00
== err : 2.737E-47 = rco : 1.471E-01 = res : 1.621E-62 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 5.56380922603113E-68
z : -3.86370330515627E+00 -3.15282522808431E-67
x : -3.86370330515627E+00 1.66914276780934E-67
t : -1.00000000000000E+00 6.40008796006211E-69
== err : 5.972E-15 = rco : 1.227E-02 = res : 7.105E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.18932404394616E-08 5.77350293106722E-01
z : 1.19718647557991E-08 -1.15470048260149E+00
x : -4.38651052023211E-08 1.15470050651858E+00
t : -3.18932404535823E-08 -5.77350245272529E-01
== err : 2.567E-07 = rco : 1.779E-08 = res : 8.710E-14 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 3.32834605600984E-08 -1.73205083687285E+00
z : 1.99999998957706E+00 -3.53475049384000E-08
x : 2.00000004033303E+00 2.23011396558213E-08
t : 3.32834603896828E-08 1.73205077826490E+00
== err : 2.270E-07 = rco : 2.334E-09 = res : 7.462E-14 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -4.98400174481321E-08 -5.77350281402745E-01
z : 3.86801972274918E-08 1.15470049696002E+00
x : -8.85202147016844E-08 -1.15470050917314E+00
t : -4.98400175002534E-08 5.77350256976507E-01
== err : 3.259E-07 = rco : 8.512E-09 = res : 1.508E-13 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.35058720427563E-09 -5.77350252460954E-01
z : -8.93250755103654E-08 -1.15470053119123E+00
x : 8.79744883135889E-08 1.15470051446256E+00
t : 1.35058718927740E-09 5.77350285918298E-01
== err : 2.468E-07 = rco : 1.465E-08 = res : 1.115E-13 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.87142063956118E-08 -1.73205081082533E+00
z : -1.99999994833323E+00 -6.14256140585905E-08
x : -1.99999995397358E+00 5.62935843211920E-09
t : -3.87142064404160E-08 1.73205080431242E+00
== err : 2.520E-07 = rco : 3.363E-09 = res : 3.279E-13 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 0.00000000000000E+00
z : 2.00000000000000E+00 0.00000000000000E+00
x : -2.00000000000000E+00 0.00000000000000E+00
t : 1.00000000000000E+00 0.00000000000000E+00
== err : 0.000E+00 = rco : 3.999E-02 = res : 0.000E+00 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.14392436135769E-09 -1.73205086263339E+00
z : -1.99999996024015E+00 -1.05081392061185E-08
x : -2.00000005561469E+00 -5.06270254245053E-09
t : -3.14392428588982E-09 1.73205075250436E+00
== err : 2.271E-07 = rco : 2.542E-09 = res : 9.531E-14 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.78213428278964E-09 5.77350289871061E-01
z : -3.90502937409495E-08 1.15470062516665E+00
x : 4.28324280292502E-08 -1.15470064584809E+00
t : -3.78213429381152E-09 -5.77350248508191E-01
== err : 3.251E-07 = rco : 1.361E-08 = res : 1.957E-13 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 3.70920615068742E-68
z : 2.96736492054994E-67 2.00000000000000E+00
x : 2.96736492054994E-67 -2.00000000000000E+00
t : 1.00000000000000E+00 -6.43281888066017E-154
== err : 1.670E-51 = rco : 5.880E-02 = res : 9.050E-66 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 9.64233343141263E-09 -5.77350315217004E-01
z : -1.46934575544676E-08 1.15470052491166E+00
x : 2.43357909867404E-08 -1.15470057093904E+00
t : 9.64233343313282E-09 5.77350223162247E-01
== err : 1.969E-07 = rco : 9.114E-09 = res : 1.156E-13 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 4.16773854583357E-08 1.73205085903630E+00
z : -1.99999994278260E+00 -5.89359996177214E-08
x : -2.00000003192679E+00 1.32513495088170E-08
t : 4.16773854422501E-08 -1.73205075610146E+00
== err : 3.462E-07 = rco : 2.802E-09 = res : 2.270E-13 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.18839723860942E-08 1.73205079419071E+00
z : -2.00000004525866E+00 -3.79302840832436E-08
x : -2.00000002208699E+00 -2.61325563473865E-11
t : 2.18839717888218E-08 -1.73205082094705E+00
== err : 1.886E-07 = rco : 1.711E-09 = res : 1.121E-13 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 1.30081843910250E-71
z : -1.03527618041008E+00 -1.91980396471126E-69
x : -1.03527618041008E+00 6.63236919002100E-73
t : -1.00000000000000E+00 -9.41790624197978E-70
== err : 5.944E-15 = rco : 5.099E-02 = res : 6.217E-15 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 1.75022304689845E-61
z : -1.03527618041008E+00 -3.88938454866321E-61
x : -1.03527618041008E+00 -3.88938454866321E-62
t : 1.00000000000000E+00 -1.60437112632358E-61
== err : 5.944E-15 = rco : 5.099E-02 = res : 6.217E-15 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 3.24273527548971E-08 5.77350281098515E-01
z : -2.49171088247116E-08 -1.15470049380517E+00
x : 5.73444615868158E-08 1.15470050571406E+00
t : 3.24273527693113E-08 -5.77350257280737E-01
== err : 2.499E-07 = rco : 8.782E-09 = res : 6.777E-14 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.14626436994197E+00 -2.14071725558423E-58
z : 9.95682444457783E-60 -1.39395542224090E-58
x : -5.78093340722365E-61 2.78791084448179E-58
t : -3.14626436994197E+00 1.11516433779272E-57
== err : 4.790E-15 = rco : 8.090E-02 = res : 3.952E-14 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 0.00000000000000E+00
z : 0.00000000000000E+00 0.00000000000000E+00
x : 0.00000000000000E+00 0.00000000000000E+00
t : -1.00000000000000E+00 0.00000000000000E+00
== err : 0.000E+00 = rco : 2.000E-01 = res : 0.000E+00 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 4.06784154255769E-08 -1.73205081158037E+00
z : 1.99999998471609E+00 -3.52869616199396E-08
x : 1.99999999166421E+00 3.51701205834500E-08
t : 4.06784153273083E-08 1.73205080355738E+00
== err : 1.476E-07 = rco : 2.349E-09 = res : 6.698E-14 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 9.10211139072809E-10 5.77350251404726E-01
z : -2.34826864098760E-08 1.15470051673298E+00
x : 2.25724752415740E-08 -1.15470049894808E+00
t : 9.10211197531205E-10 -5.77350286974525E-01
== err : 1.409E-07 = rco : 3.769E-09 = res : 3.418E-14 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.24131153155437E-08 1.73205075640360E+00
z : 2.00000004334035E+00 1.27146629138961E-08
x : 1.99999995471949E+00 3.42148095113567E-08
t : -1.24131155357771E-08 -1.73205085873415E+00
== err : 2.665E-07 = rco : 2.864E-09 = res : 1.982E-13 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -3.29589702380518E-08 -1.73205086013895E+00
z : -1.99999994452023E+00 -2.40123871318052E-08
x : -2.00000003557426E+00 3.30742238912672E-08
t : -3.29589702445372E-08 1.73205075499881E+00
== err : 3.136E-07 = rco : 3.658E-09 = res : 1.316E-13 ==
solution 51 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 2.48715801613858E-08 -5.77350238803341E-01
z : -4.87077204988733E-08 1.15470059940281E+00
x : 7.35793006624899E-08 -1.15470056901652E+00
t : 2.48715801658473E-08 5.77350299575910E-01
== err : 3.239E-07 = rco : 2.142E-08 = res : 9.917E-14 ==
solution 52 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -1.00000000000000E+00 1.38919150070441E-123
z : -2.00000000000000E+00 3.15152336820420E-124
x : 2.00000000000000E+00 -1.51273121673801E-123
t : -1.00000000000000E+00 -2.63821394040205E-249
== err : 1.325E-107 = rco : 3.999E-02 = res : 1.959E-122 ==
solution 53 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -4.82255511629817E-09 1.73205077791628E+00
z : -1.99999999143074E+00 -2.59293773042211E-08
x : -1.99999994007094E+00 -3.42822879761728E-08
t : -4.82255533363793E-09 -1.73205083722148E+00
== err : 1.957E-07 = rco : 1.764E-09 = res : 1.922E-13 ==
solution 54 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : -7.36774589044883E-08 5.77350261676437E-01
z : 4.05398028847714E-08 1.15470049304051E+00
x : 3.31376560062273E-08 -1.15470048552732E+00
t : -7.36774588775104E-08 -5.77350276702815E-01
== err : 3.352E-07 = rco : 2.183E-08 = res : 2.805E-13 ==
solution 55 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 -9.79312961657133E-67
z : -3.86370330515627E+00 -6.40950822838786E-65
x : -3.86370330515627E+00 3.56083790465992E-65
t : 1.00000000000000E+00 2.96736492054994E-66
== err : 5.972E-15 = rco : 1.227E-02 = res : 7.105E-15 ==
solution 56 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
y : 1.00000000000000E+00 5.63536292589461E-133
z : -2.00000000000000E+00 0.00000000000000E+00
x : 2.00000000000000E+00 3.52210182868413E-133
t : 1.00000000000000E+00 0.00000000000000E+00
== err : 4.223E-116 = rco : 3.999E-02 = res : 1.240E-131 ==