7
z0 + z1 + z2 + z3 + z4 + z5 + z6 - 1;
z0*z1 + z1*z2 + z2*z3 + z3*z4 + z4*z5 + z5*z6 + z6*z0
- 0.62348980185873 - 0.78183148246803*i;
z0*z1*z2 + z1*z2*z3 + z2*z3*z4 + z3*z4*z5 + z4*z5*z6 + z5*z6*z0 + z6*z0*z1
+ 0.22252093395631 - 0.97492791218182*i;
z0*z1*z2*z3 + z1*z2*z3*z4 + z2*z3*z4*z5 + z3*z4*z5*z6 + z4*z5*z6*z0
+ z5*z6*z0*z1 + z6*z0*z1*z2
+ 0.90096886790242 - 0.43388373911756*i;
z0*z1*z2*z3*z4 + z1*z2*z3*z4*z5 + z2*z3*z4*z5*z6 + z3*z4*z5*z6*z0
+ z4*z5*z6*z0*z1 + z5*z6*z0*z1*z2 + z6*z0*z1*z2*z3
+ 0.90096886790242 + 0.43388373911756*i;
z0*z1*z2*z3*z4*z5 + z1*z2*z3*z4*z5*z6 + z2*z3*z4*z5*z6*z0 + z3*z4*z5*z6*z0*z1
+ z4*z5*z6*z0*z1*z2 + z5*z6*z0*z1*z2*z3 + z6*z0*z1*z2*z3*z4
+ 0.22252093395631 + 0.97492791218182*i;
z0*z1*z2*z3*z4*z5*z6 - 1;
TITLE : extended cyclic 7-roots problem, to exploit the symmetry
ROOT COUNTS :
total degree : 7! = 5040
mixed volume : 924 = 132*7 = 66*14
REFERENCES :
This is the modified Arnborg's system or Davenport's problem.
Modified to exploit all the symmetry of it. For the original problem:
G\"oran Bj\"orck and Ralf Fr\"oberg:
`A faster way to count the solutions of inhomogeneous systems
of algebraic equations, with applications to cyclic n-roots',
J. Symbolic Computation 12, pp 329--336, 1991.
Backelin, J. and Fr\"oberg, R.:
"How we proved that there are exactly 924 cyclic 7-roots" ,
Proceedings of ISSAC-91, pp 103-111, ACM, New York, 1991.
SYMMETRY GROUP GENERATORS :
z1 z2 z3 z4 z5 z6 z0
z6 z5 z4 z3 z2 z1 z0
CHOICE OF CONSTANTS :
The seventh root of unity w :
w = 0.62348980185873 + 0.78183148246803*i
w^2 = -0.22252093395631 + 0.97492791218182*i
w^3 = -0.90096886790242 + 0.43388373911756*i
w^4 = -0.90096886790242 - 0.43388373911756*i
w^5 = -0.22252093395631 - 0.97492791218182*i
w^6 = 0.62348980185873 - 0.78183148246803*i
w^7 = 1.0
Note however that :
1 + w + w^2 + w^3 + w^4 + w^5 + w^6 = 0
When (w,w^2,w^3,w^4,1) is the vector of the right hand sides, then
(w,w,w,w,w) is a solution of all subsystems of a certain type.
Therefore, (1,w,w^3,w^5,w^3,w,1) seems to be a better choice.
THE GENERATING SOLUTIONS :
66 7
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 4.67863048025800E-01 -4.36446266485858E-01
z1 : -5.34794460209315E-01 5.30787178057164E-03
z2 : -8.01876299168934E-02 8.90354574461262E-01
z3 : -1.25431127166961E+00 1.29480657724513E+00
z4 : 8.23246503393685E-01 -8.52855597667153E-01
z5 : 4.34623556399096E-02 6.90506938096954E-01
z6 : 1.53472145473642E+00 -1.59167409743090E+00
== err : 4.788E-15 = rco : 7.355E-02 = res : 1.351E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 3.46892002616732E-02 -1.33019733117621E+00
z1 : -3.82845405600500E-01 3.19065670655243E-01
z2 : 5.98849385307387E-01 6.39891306885450E-01
z3 : 4.74826244622835E-01 1.49755297426934E+00
z4 : 2.28152473467675E-01 -1.00386193728648E+00
z5 : 7.74176425899374E-01 6.43619137902656E-01
z6 : -7.27848323958444E-01 -7.66069821250006E-01
== err : 3.495E-15 = rco : 4.768E-02 = res : 6.804E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.26401749127306E+00 -4.71182602611984E-01
z1 : 5.07185664997880E-02 3.83572479940344E-01
z2 : 8.50601364596769E-01 -9.25804764466126E-02
z3 : 2.09770941907816E+00 1.55644659263867E+00
z4 : -4.67104244312624E-01 -2.25386687811526E-01
z5 : 1.02122580031828E+00 -2.52695954938842E-01
z6 : -1.28913341490732E+00 -8.98173350770052E-01
== err : 4.923E-15 = rco : 4.827E-02 = res : 9.155E-16 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.55242681068925E-01 4.78605308984734E-01
z1 : 6.23489801858739E-01 7.81831482468026E-01
z2 : 1.09826106499869E+00 -8.09185516785669E-01
z3 : 9.30880848229321E-01 -4.82369528438923E-01
z4 : -9.41197210797834E-01 2.27684170346159E-01
z5 : 4.60078160543901E-01 -9.24540986650787E-01
z6 : -6.16269983763892E-01 7.27975070076461E-01
== err : 2.067E-15 = rco : 1.958E-02 = res : 6.684E-16 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -3.81830703565615E-01 1.10460420454320E+00
z1 : 2.42263888049884E+00 9.00465291919754E-01
z2 : -9.78697068017798E-02 -7.34810566647013E-01
z3 : -2.38515672808567E-01 -5.90085930849034E-01
z4 : -4.27920759161000E-01 8.48778073406815E-01
z5 : -4.30488950533236E-01 -1.87945505563447E+00
z6 : 1.53986912371355E-01 3.50503983260745E-01
== err : 5.087E-15 = rco : 3.172E-02 = res : 8.882E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.38723091113944E-01 9.45504115998003E-01
z1 : 1.59540826432331E+00 -1.21690869876273E+00
z2 : -7.36781172250304E-01 -1.48070199591316E-01
z3 : -5.23811269011459E-01 -7.88147596248678E-01
z4 : 4.49106320460620E-01 8.85940809400818E-01
z5 : -9.71380604472070E-01 -8.94591511173872E-04
z6 : 5.48735369835961E-01 3.22576160715073E-01
== err : 5.068E-15 = rco : 3.968E-02 = res : 1.295E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.10850578699723E+00 1.50089061123433E-01
z1 : 4.34137424726305E-01 -1.81868668949105E+00
z2 : -1.29369155645173E+00 8.76968301120378E-01
z3 : -3.87268155700624E-01 2.33608006773371E-01
z4 : 1.38612641984087E+00 4.09503855466848E-01
z5 : -7.22129478913178E-01 4.36146090350962E-01
z6 : 4.74319559501131E-01 -2.87628625343947E-01
== err : 4.698E-15 = rco : 4.172E-02 = res : 1.734E-15 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.05350039860519E+00 -6.55202117516695E-01
z1 : 2.84160313695804E-01 7.08934794853607E-01
z2 : 1.61811322289881E+00 -4.02820294168558E-01
z3 : -4.06439479135850E-01 4.38961134414078E-01
z4 : -1.35118636521717E-01 1.09967198990319E+00
z5 : -1.37215414570243E+00 -5.44002397357613E-01
z6 : -4.20616738398063E-02 -6.45543110128014E-01
== err : 4.905E-15 = rco : 7.836E-02 = res : 1.256E-15 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.74860679147443E-01 -2.31718942149937E-01
z1 : 4.90817463785468E-01 8.40991270723348E-01
z2 : -1.00462635877409E+00 -1.14766868410966E+00
z3 : -8.90684747276168E-01 1.48040272783550E-01
z4 : 7.05585015794184E-01 -2.05679470773444E-02
z5 : 2.67086813831974E-01 7.90679529552565E-01
z6 : 2.00668249178607E+00 -3.79755499722519E-01
== err : 4.502E-15 = rco : 1.906E-02 = res : 6.661E-16 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -8.01501557819646E-01 -4.15113043434405E-02
z1 : 1.27210975988947E+00 6.11008632726523E-02
z2 : -6.62537789821261E-01 1.88150016367237E-02
z3 : 5.27453423750090E-01 7.95981927041361E-01
z4 : 9.14615819819112E-01 -2.47630020766892E-01
z5 : 3.83528743357508E-01 9.20874790223254E-01
z6 : -6.33668399175276E-01 -1.50763125706366E+00
== err : 2.788E-15 = rco : 7.965E-02 = res : 7.216E-16 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -2.13258815235692E-01 7.14569350072586E-01
z1 : 5.17508027577857E-01 -7.92601696428050E-01
z2 : -1.00627138749158E+00 2.13549571018691E-01
z3 : 5.71122238950643E-01 -5.76220889216237E-01
z4 : 1.54909958454730E+00 -1.06524427570406E+00
z5 : 2.77004043521328E-01 1.05041073799170E+00
z6 : -6.95203691869856E-01 4.55537202265374E-01
== err : 3.620E-15 = rco : 2.410E-02 = res : 7.022E-16 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -9.66961690810054E-01 8.16887864004266E-01
z1 : -8.06613722593504E-01 -1.24708026664746E+00
z2 : -2.93947075652946E-01 5.65513071470415E-01
z3 : 1.68256462961309E+00 2.72230729173175E-01
z4 : -5.21314631821642E-01 -3.04101726359510E-01
z5 : 1.34675240452565E+00 -2.87811599721737E-01
z6 : 5.59520086739407E-01 1.84361928080848E-01
== err : 2.727E-15 = rco : 2.113E-02 = res : 7.777E-16 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.23489801858734E-01 7.81831482468028E-01
z1 : -7.87508457310214E-01 4.50783971674645E-02
z2 : 6.23489801858737E-01 7.81831482468028E-01
z3 : 3.52273754522118E-01 -1.21782562086950E+00
z4 : -7.87508457310214E-01 4.50783971674668E-02
z5 : 3.52273754522109E-01 -1.21782562086952E+00
z6 : 6.23489801858731E-01 7.81831482468032E-01
== err : 4.807E-15 = rco : 3.980E-02 = res : 8.006E-16 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.24294792885181E+00 4.21654661065155E-01
z1 : -5.39143813058367E-01 6.49525816982366E-01
z2 : 8.90747234175513E-01 -1.58799502123764E-01
z3 : -1.94203241663141E-01 -1.61977784446423E+00
z4 : -7.13701839266941E-01 7.31712360291996E-01
z5 : -6.31775087966256E-01 -3.76949486060659E-02
z6 : 9.45128818927384E-01 1.33794568545407E-02
== err : 2.196E-15 = rco : 6.397E-02 = res : 8.968E-16 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 5.78317965428931E-01 3.50767072200667E-01
z1 : 2.94179227359358E+00 -1.42548378160504E+00
z2 : -4.70847259813300E-01 -2.87085694245581E-01
z3 : -1.06836844497333E+00 4.52467393784862E-01
z4 : -8.98962153244924E-01 -4.85454556067693E-01
z5 : 4.83666638302028E-01 2.00243767643539E-01
z6 : -5.65599019292986E-01 1.19454579828925E+00
== err : 3.020E-15 = rco : 6.021E-02 = res : 9.930E-16 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 7.35070990383596E-02 1.09273805064784E+00
z1 : 5.79576422622113E-01 -4.33111371432045E-02
z2 : 6.12432236314391E-01 -1.50870352708843E+00
z3 : -6.98399329230505E-01 5.74895665813042E-02
z4 : 6.92638311248353E-01 -1.23665789407859E+00
z5 : 3.70184227248846E-01 1.36637185163905E+00
z6 : -6.29938967241558E-01 2.72073089442036E-01
== err : 5.507E-15 = rco : 3.944E-02 = res : 7.022E-16 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -6.16269983763888E-01 7.27975070076458E-01
z1 : 6.23489801858748E-01 7.81831482468027E-01
z2 : 9.30880848229317E-01 -4.82369528438918E-01
z3 : -5.50506181511654E-01 -4.31041295074381E-01
z4 : 1.38495990530489E+00 -5.58769175473648E-03
z5 : -1.63507003826049E-01 7.03279771287152E-01
z6 : -6.09047386291363E-01 -1.29408780856360E+00
== err : 2.698E-15 = rco : 1.335E-02 = res : 5.237E-16 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -6.06185900122194E-01 9.85792435739806E-02
z1 : -5.06811384137132E-01 1.64426518681742E+00
z2 : 8.74532451148284E-01 2.62464803239072E-01
z3 : 8.61057561480876E-01 -1.17576044626285E+00
z4 : 6.23620298791294E-01 3.31809625481679E-01
z5 : -6.76819838040741E-01 1.99141910517700E-01
z6 : 4.30606810879613E-01 -1.36050032336700E+00
== err : 3.810E-15 = rco : 3.691E-02 = res : 9.930E-16 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.75816023304665E-01 -1.71949470343037E+00
z1 : -1.91308852691457E-01 2.38704905066217E-01
z2 : 4.66207184356929E-01 1.40303056724897E+00
z3 : 7.38735229667846E-01 -1.63498953108958E-01
z4 : 3.19661978084269E-01 1.88335833233347E+00
z5 : -2.61779593773422E-01 -9.43138498810604E-01
z6 : 5.04300077660500E-01 -6.98961649298726E-01
== err : 2.323E-15 = rco : 9.231E-02 = res : 1.798E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 4.77745512393795E-01 -7.11800427292068E-01
z1 : -4.44005255369307E-01 4.79007002021830E-02
z2 : -8.29179970557220E-01 1.15916042605638E+00
z3 : 6.72401280403119E-01 4.69426152212664E-01
z4 : -7.94420881971855E-01 8.44085973212209E-01
z5 : 1.06579873581600E+00 -1.95853425558663E+00
z6 : 8.51660579285468E-01 1.49761431195266E-01
== err : 3.260E-15 = rco : 7.148E-02 = res : 6.280E-16 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.47209889768618E-01 -2.71000058598525E-01
z1 : 7.29561455012859E-01 -2.11705018415682E+00
z2 : -1.08893972482604E+00 4.18256468290236E-01
z3 : -5.81818282168547E-02 1.15496869289218E+00
z4 : -4.31754982203219E-01 1.21337157918106E-01
z5 : 7.44052482897529E-01 -4.36649710381845E-01
z6 : 4.58052707567111E-01 1.13013763403666E+00
== err : 3.857E-15 = rco : 5.009E-02 = res : 8.882E-16 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 4.22028897675802E-01 -7.07268439077348E-01
z1 : 5.84020481793840E-01 -1.17309534030753E+00
z2 : 8.11601168407088E-01 -6.64869852025852E-01
z3 : -1.09086342644784E-01 1.46339185038839E-01
z4 : -2.23803198842245E+00 3.85599585643257E+00
z5 : 8.39761488146389E-01 -9.52078907054601E-01
z6 : 6.89706295044111E-01 -5.05022503006081E-01
== err : 4.538E-15 = rco : 1.258E-02 = res : 1.110E-15 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -7.84532737705770E-01 -2.16163710683431E-01
z1 : -7.83635786195115E-01 -7.50745456324567E-01
z2 : -1.07364355527362E+00 -1.10236053932901E-01
z3 : 1.55025192368076E-01 1.12421563072172E-01
z4 : 5.31474350094088E+00 1.94656925306319E+00
z5 : -5.89237414794941E-01 -3.85342667533282E-01
z6 : -1.23871919933950E+00 -5.96502927661182E-01
== err : 4.337E-15 = rco : 1.014E-02 = res : 6.661E-16 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.31927070735419E-01 9.13131844138841E-01
z1 : -2.15952333564669E-01 8.26014758586175E-01
z2 : -3.51647989085233E-01 8.21720016952399E-01
z3 : 4.78250051263873E-02 -2.46345536954982E-01
z4 : 1.84957035111052E+00 -4.47089321963393E+00
z5 : -1.00839120875165E-01 1.12785280339627E+00
z6 : -9.70288419764263E-02 1.02851933351523E+00
== err : 4.550E-15 = rco : 1.056E-02 = res : 9.155E-16 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.08033197181971E+00 8.76060801140527E-02
z1 : 9.59763137005627E-01 1.25808260461912E-01
z2 : 8.75055434379027E-01 1.19059076532097E-01
z3 : -2.03776512133031E-01 3.45295791140129E-02
z4 : -3.98281473249811E+00 -1.30072577539723E-01
z5 : 1.10074944356221E+00 -2.00257254252280E-01
z6 : 1.17069125786457E+00 -3.66731644300718E-02
== err : 2.893E-15 = rco : 2.259E-02 = res : 1.986E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.46180527005271E-02 -1.22763706974964E+00
z1 : -1.61834602640436E-01 -7.09113977064605E-01
z2 : -4.93380559004291E-01 -1.33190342595466E+00
z3 : 2.23227388597881E-02 1.75262485368918E-01
z4 : 2.04809557534881E+00 4.80359220914124E+00
z5 : 1.12833887242863E-01 -9.19640666412560E-01
z6 : -4.73418987106209E-01 -7.90559555328691E-01
== err : 2.745E-15 = rco : 1.121E-02 = res : 9.486E-16 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.15495095543561E+00 3.74542012621634E-01
z1 : -8.83806021480559E-01 7.66392864383034E-01
z2 : -6.91881189720677E-01 3.76538373960064E-01
z3 : 2.14178283847358E-01 -6.66019690065468E-02
z4 : 5.01108254485358E+00 -2.21485266210044E+00
z5 : -7.52940857557690E-01 5.84425274502945E-01
z6 : -7.41681804506395E-01 1.79556105639304E-01
== err : 5.907E-15 = rco : 1.397E-02 = res : 1.337E-15 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.23489801858733E-01 7.81831482468030E-01
z1 : 6.23489801858733E-01 7.81831482468029E-01
z2 : 6.23489801858735E-01 7.81831482468029E-01
z3 : -1.80910775475469E-01 -1.52492040374220E-01
z4 : -1.93653823381820E+00 -3.75666537196593E+00
z5 : 6.23489801858734E-01 7.81831482468030E-01
z6 : 6.23489801858734E-01 7.81831482468031E-01
== err : 1.775E-15 = rco : 2.335E-02 = res : 1.490E-15 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 7.42360581030826E-01 2.15572102408905E+00
z1 : 3.10893044360025E-01 1.16495387628399E+00
z2 : 1.72058244640168E-01 7.70284957753373E-01
z3 : 6.24079355536530E-02 4.07233556158862E-01
z4 : -1.27377838913827E-01 -3.48259448613686E-01
z5 : -2.61382241235116E-01 -8.86139354558679E-01
z6 : 1.01040274564271E-01 -3.26379461111291E+00
== err : 3.328E-15 = rco : 1.962E-02 = res : 2.533E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 2.25727591331644E+00 8.92345088427880E-01
z1 : 1.14406261094357E+00 5.44430128529116E-01
z2 : 7.33654125912246E-01 3.86804068248463E-01
z3 : 3.72526984387254E-01 2.31509679109147E-01
z4 : -3.00532585020673E-01 -5.88747338438658E-02
z5 : -9.43994027450510E-01 -5.29560284338798E-01
z6 : -2.26299302208833E+00 -1.46665394613194E+00
== err : 4.165E-15 = rco : 2.236E-02 = res : 1.024E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 2.32115086375199E+00 -1.28671008474272E+00
z1 : 1.25372717889568E+00 -5.27913819122359E-01
z2 : 7.95361098625522E-01 -2.87419952718011E-01
z3 : 4.03789650992859E-01 -1.33460060815518E-01
z4 : -2.25646305586467E-01 1.26305298456633E-01
z5 : -8.08914726731873E-01 4.62468966848685E-01
z6 : -2.73946775994770E+00 1.64672965209329E+00
== err : 4.882E-15 = rco : 2.625E-02 = res : 1.914E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 9.69868799737995E-01 -2.18006125476477E+00
z1 : 3.02222494926693E-01 -1.04962255787411E+00
z2 : 7.65319692895014E-02 -8.45600338140982E-01
z3 : 1.42550578965942E-01 -5.28159684689508E-01
z4 : -6.33566349180896E-02 2.42107763016608E-01
z5 : -1.82351490887766E-01 9.46825190639554E-01
z6 : -2.45465717114276E-01 3.41451088181321E+00
== err : 3.735E-15 = rco : 2.276E-02 = res : 1.590E-15 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -7.94802663291713E-01 -1.67541598633899E+00
z1 : -8.68209591527186E-01 -9.39241083189283E-01
z2 : -4.41634749716923E-01 -6.45151144320355E-01
z3 : -4.23571951938178E-01 -3.33754156586703E-01
z4 : 1.32438663257292E-01 2.28249944002999E-01
z5 : 6.23489801858734E-01 7.81831482468030E-01
z6 : 2.77229049135797E+00 2.58348094396430E+00
== err : 4.329E-15 = rco : 2.526E-02 = res : 9.155E-16 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.82655141623458E+00 7.16734522462485E-02
z1 : -1.16719760367488E+00 -1.57512948835744E-01
z2 : -9.14094851384861E-01 5.11984924730513E-02
z3 : -4.11222579590838E-01 8.08743402742766E-02
z4 : 2.88717756497342E-01 4.44135713907982E-02
z5 : 1.03649803945942E+00 3.53961549502134E-02
z6 : 3.99385065492840E+00 -1.26043062498843E-01
== err : 3.990E-15 = rco : 3.036E-02 = res : 8.882E-16 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.21623588655017E+00 2.01245622516262E+00
z1 : -6.39250771714909E-01 9.94761356782284E-01
z2 : -4.28882900306355E-01 5.97031567094317E-01
z3 : -2.51435846661879E-01 2.80637886484987E-01
z4 : 2.16811318950750E-01 -2.25554136241400E-01
z5 : 7.26629129749011E-01 -7.89804497497309E-01
z6 : 2.59236495653356E+00 -2.86952840178550E+00
== err : 4.841E-15 = rco : 2.493E-02 = res : 1.337E-15 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.37931008073561E+00 -8.49145629200446E+00
z1 : -3.54604800900208E-02 -1.06326053384280E-01
z2 : 1.95499291231091E+00 7.31860941685797E+00
z3 : 1.50877287394944E-01 4.25980036079339E-01
z4 : -8.36762721137356E-02 -1.20765178383852E+00
z5 : 3.63406194188864E-01 1.93727391899176E+00
z6 : 2.91704390446400E-02 1.23570757298188E-01
== err : 5.751E-15 = rco : 2.566E-03 = res : 3.202E-15 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.14823522299322E+01 -1.14689114851150E+00
z1 : 9.16608259234471E-02 1.57451597339053E-02
z2 : -7.71297657908521E+00 1.72779359541418E+00
z3 : -4.69944391226512E-01 -1.36087247381999E-01
z4 : 7.50827010523433E-01 -1.71450882537869E-01
z5 : -3.03944938634341E+00 -2.89363395041718E-01
z6 : -1.02469709723921E-01 2.53918325001679E-04
== err : 3.637E-14 = rco : 1.858E-03 = res : 5.335E-15 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.83385003983611E-01 1.07364666676451E+01
z1 : -2.75849070548782E-02 8.21513752198878E-02
z2 : 2.19514048943661E+00 -9.50886392096554E+00
z3 : 4.22906407360795E-02 -3.24784245462074E-01
z4 : -5.63490730196338E-01 1.16979932378224E+00
z5 : -1.17404387285190E-01 -2.04056201156660E+00
z6 : 5.44338983473294E-02 -1.14207188653016E-01
== err : 5.858E-15 = rco : 1.957E-03 = res : 2.809E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -7.62333945441633E+00 -4.63525349819841E+00
z1 : -1.07714097912325E-01 -4.37018177192465E-02
z2 : 7.07053197655670E+00 3.46984566062804E+00
z3 : 4.65326396790895E-01 2.02151809834683E-01
z4 : -7.90729014616703E-01 -2.39047541696182E-01
z5 : 1.86916542890302E+00 1.18441124191003E+00
z6 : 1.16758764694744E-01 6.15941452410842E-02
== err : 3.404E-15 = rco : 1.874E-03 = res : 1.309E-15 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.34419646691814E+00 -6.35048404735868E+00
z1 : 7.04461408670266E-02 -9.78615016323432E-02
z2 : -4.73288853218600E+00 4.99097184892771E+00
z3 : -2.56681129923913E-01 2.96359118623530E-01
z4 : 7.54221834478220E-01 -8.26226417069500E-01
z5 : -1.10469617701046E+00 1.86741911643772E+00
z6 : -7.45986031430107E-02 1.19821882071560E-01
== err : 2.799E-15 = rco : 2.416E-03 = res : 3.361E-15 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 5.53416321863105E+00 7.08215467979429E+00
z1 : 7.02259322960728E-02 8.62961532324321E-02
z2 : -3.91187913824552E+00 -5.83757274951762E+00
z3 : -4.23571951938178E-01 -3.33754156586703E-01
z4 : 6.23489801858734E-01 7.81831482468030E-01
z5 : -7.94802663291712E-01 -1.67541598633899E+00
z6 : -9.76251993104462E-02 -1.03539423051448E-01
== err : 4.573E-15 = rco : 1.900E-03 = res : 1.776E-15 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -7.64011169724659E+00 3.22594120917718E+00
z1 : -9.43561527605506E-02 5.92227354977115E-02
z2 : 6.69691167034164E+00 -2.31225980791917E+00
z3 : 4.38952676862833E-01 -1.40508580935541E-01
z4 : -7.77739371454065E-01 4.40638394036102E-01
z5 : 2.25123189760680E+00 -1.19897715613580E+00
z6 : 1.25110976649938E-01 -7.40567937204814E-02
== err : 5.780E-15 = rco : 2.645E-03 = res : 4.096E-15 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -4.13891092159968E+00 6.01839524713840E+00
z1 : 2.29583722814674E-01 -1.97664346511378E-01
z2 : 1.57526973996041E-01 -3.49869943594115E-01
z3 : 1.49581722428840E+00 -1.54842721889950E+00
z4 : 2.59217552601449E+00 -3.23328602785338E+00
z5 : -7.22883698419373E-02 9.88040507817362E-02
z6 : 7.36095844328017E-01 -7.87951761061763E-01
== err : 5.984E-15 = rco : 5.202E-03 = res : 5.355E-15 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 8.44215252236127E+00 3.37889053892540E+00
z1 : -2.74862636533005E-01 -1.92844369851578E-01
z2 : -2.48697131025830E-01 -1.21953368580537E-01
z3 : -2.71513041815408E+00 -5.99134443926035E-01
z4 : -3.46954950612640E+00 -2.27740917189017E+00
z5 : 9.73877349311911E-02 6.64278200403241E-02
z6 : -8.31300565453142E-01 -2.53977004717410E-01
== err : 5.211E-15 = rco : 2.789E-03 = res : 2.809E-15 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 2.70952068832967E+00 -6.93433378277982E+00
z1 : -1.22362261023688E-02 3.42379325735827E-01
z2 : -9.65196369784528E-02 3.10513299690975E-01
z3 : -2.21758806791608E-01 2.74004886689960E+00
z4 : -1.22273226368323E+00 2.75791642453123E+00
z5 : 2.59207680088901E-02 -1.50559569284040E-01
z6 : -1.82194522782900E-01 9.34035435206237E-01
== err : 5.457E-15 = rco : 3.187E-03 = res : 3.511E-15 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -6.53608319432967E+00 -3.52688560692628E-01
z1 : 3.25326401643580E-01 -6.35502047858643E-02
z2 : 3.60021170151626E-01 5.20731840104803E-02
z3 : 3.06622314032348E+00 -2.36478793390547E-01
z4 : 2.86707366687298E+00 5.47459376857740E-01
z5 : -1.32849851768639E-01 1.98199988863595E-02
z6 : 1.05028866710665E+00 3.33649991144594E-02
== err : 3.435E-15 = rco : 4.518E-03 = res : 1.790E-15 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 3.10077318555285E+00 7.89576130474084E+00
z1 : -8.40821860391077E-02 -2.25804061628294E-01
z2 : 2.59484357613763E-03 -3.59644813308365E-01
z3 : -8.28376349709442E-01 -3.51393127165406E+00
z4 : -1.12514144109802E+00 -2.75756184812832E+00
z5 : 1.71202458145361E-02 1.08631119035800E-01
z6 : -8.28882980969493E-02 -1.14745042905760E+00
== err : 4.597E-15 = rco : 4.046E-03 = res : 1.650E-15 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 7.50024259822409E+00 -3.23528614828260E+00
z1 : -2.17138696385429E-01 1.05261544333782E-01
z2 : -3.97501055691805E-01 2.40287684999973E-01
z3 : -2.55496200157187E+00 5.14346836934741E-01
z4 : -2.65630848475303E+00 1.95950490694689E+00
z5 : 1.27240562050349E-01 -5.05311475062986E-02
z6 : -8.01572921872302E-01 4.66416322573514E-01
== err : 4.844E-15 = rco : 2.817E-03 = res : 2.324E-15 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -3.91187913824552E+00 -5.83757274951761E+00
z1 : 1.32438663257292E-01 2.28249944002999E-01
z2 : 3.11270984741351E-01 2.84373388189967E-01
z3 : 1.17001439634061E+00 2.06317641394376E+00
z4 : 2.77229049135798E+00 2.58348094396430E+00
z5 : -9.76251993104462E-02 -1.03539423051448E-01
z6 : 6.23489801858734E-01 7.81831482468029E-01
== err : 4.893E-15 = rco : 3.592E-03 = res : 2.802E-15 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 8.50851665207130E-02 1.40352782692055E+00
z1 : 2.01605701018787E-02 -1.03624007145795E+00
z2 : 5.18519413161343E-01 1.27548367346265E+00
z3 : 6.63150277855744E-01 2.97728188699021E-03
z4 : -8.73847591736364E-01 -6.06792200559673E-01
z5 : 8.99320215391229E-01 -1.34421835495523E+00
z6 : -3.12388051294543E-01 3.05261844702665E-01
== err : 5.318E-15 = rco : 3.338E-02 = res : 7.109E-16 ==
solution 51 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 2.11462201566830E+00 1.43460241823758E-01
z1 : -4.20597795950823E-01 3.47561820764584E-01
z2 : 2.08558642560309E+00 -8.03330651593098E-01
z3 : -3.25035393833958E-01 -4.08374163306048E-01
z4 : -1.42476914354590E+00 8.37945336835597E-01
z5 : -1.33026010404358E+00 -2.56266193505825E-01
z6 : 3.00453996102872E-01 1.39003608981032E-01
== err : 5.292E-15 = rco : 4.398E-02 = res : 8.083E-16 ==
solution 52 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -5.50506181511648E-01 -4.31041295074380E-01
z1 : 6.23489801858736E-01 7.81831482468031E-01
z2 : -6.09047386291353E-01 -1.29408780856359E+00
z3 : -5.55242681068930E-01 4.78605308984744E-01
z4 : 9.50172694473942E-01 2.59534900476816E-01
z5 : 4.28726875405535E-02 1.01434292849407E+00
z6 : 1.09826106499870E+00 -8.09185516785684E-01
== err : 5.290E-15 = rco : 1.040E-02 = res : 8.951E-16 ==
solution 53 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -2.49704384148864E-01 3.71278177232070E-01
z1 : 1.45259331076867E+00 -1.11760437355114E+00
z2 : -7.36128730803234E-02 4.66035265618767E-01
z3 : 6.26501579711058E-01 2.95500124173979E+00
z4 : 2.51569518349973E-02 -7.37731504903220E-01
z5 : 4.15054048070996E-01 -4.40166261956803E-01
z6 : -1.19598863315653E+00 -1.49681254417947E+00
== err : 5.176E-15 = rco : 3.368E-02 = res : 1.132E-15 ==
solution 54 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 5.95089267228571E-01 4.16380297629766E-01
z1 : -9.44652374189596E-01 -1.96360099506940E-01
z2 : 6.82507133082846E-01 1.99919204766950E-01
z3 : 1.92440676881714E+00 -1.24038019498083E+00
z4 : -5.77525581491433E-01 2.20841722098335E-01
z5 : -3.50880923713048E-01 -8.72024036632548E-01
z6 : -3.28944289734478E-01 1.47162310662526E+00
== err : 4.947E-15 = rco : 2.067E-02 = res : 6.280E-16 ==
solution 55 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.61119332259871E-01 -5.99233513720669E-01
z1 : -4.93987623493215E-01 1.11477988398373E+00
z2 : -3.17170150296700E-01 -6.31710402463307E-01
z3 : -1.05500650918378E+00 -1.80600891163652E+00
z4 : 1.88787721197165E-01 4.28198738876400E-01
z5 : -2.65160006826006E-01 5.97496330065728E-01
z6 : 2.78141723634267E+00 8.96477874894644E-01
== err : 3.994E-15 = rco : 3.779E-02 = res : 6.680E-16 ==
solution 56 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.09134337625268E+00 -9.00194890586300E-01
z1 : 8.04941115397386E-01 -1.57080350306513E-01
z2 : -1.61038206705506E+00 6.16500054235794E-02
z3 : 2.98687474319621E-02 3.40887813798477E-01
z4 : 1.50129170694199E+00 -2.93828725751230E-01
z5 : 1.71443980351605E+00 1.27554349885528E+00
z6 : -3.48815929979647E-01 -3.26977351433297E-01
== err : 2.908E-15 = rco : 3.916E-02 = res : 9.930E-16 ==
solution 57 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -3.96254245219613E-02 8.22757319505159E-01
z1 : 5.32408763436041E-01 -6.96061964928411E-01
z2 : -1.03791985506087E+00 4.74205902999320E-01
z3 : 1.19520534101604E+00 2.12894386686205E-01
z4 : -6.15540778016679E-01 -7.56707814351714E-03
z5 : 6.23489801858733E-01 7.81831482468029E-01
z6 : 3.41982151288695E-01 -1.58806004858678E+00
== err : 6.102E-15 = rco : 4.846E-02 = res : 9.486E-16 ==
solution 58 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -4.69810740137208E-01 -4.82307947659017E-01
z1 : 1.51828852432890E+00 -3.95703563819911E-01
z2 : -3.75199707002580E-02 5.85500243988043E-01
z3 : -4.95471311686349E-01 -1.58110703330191E+00
z4 : -3.05959628719871E-01 6.58524298163079E-01
z5 : 1.59153814769026E-01 1.68999474807055E+00
z6 : 6.31319312145765E-01 -4.74900745440836E-01
== err : 5.151E-15 = rco : 1.841E-02 = res : 9.421E-16 ==
solution 59 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 3.52273754522113E-01 -1.21782562086951E+00
z1 : 6.23489801858731E-01 7.81831482468028E-01
z2 : -7.87508457310216E-01 4.50783971674661E-02
z3 : 3.52273754522114E-01 -1.21782562086951E+00
z4 : -7.87508457310212E-01 4.50783971674653E-02
z5 : 6.23489801858737E-01 7.81831482468030E-01
z6 : 6.23489801858733E-01 7.81831482468031E-01
== err : 2.245E-15 = rco : 4.327E-02 = res : 1.110E-15 ==
solution 60 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.05705036015054E+00 -5.34822818011864E-01
z1 : -4.31232971060346E-01 1.01762688257698E+00
z2 : -5.77122993940732E-01 -2.06571593358607E-01
z3 : 8.34803501332767E-01 -5.10145626380297E-01
z4 : 2.59219969949732E-01 -1.55862302009499E+00
z5 : -2.20792987649285E-01 1.03465472944064E+00
z6 : 7.80751212173217E-02 7.57881445828149E-01
== err : 4.514E-15 = rco : 5.818E-02 = res : 9.155E-16 ==
solution 61 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 1.07644496874022E+00 7.45349047311069E-01
z1 : -2.70731895098249E-01 5.35111881111971E-01
z2 : 1.44852145827454E+00 -8.34277443607197E-01
z3 : 8.97870256525968E-01 9.20291960241974E-02
z4 : -1.03284246966771E-01 -6.69561096397303E-01
z5 : -1.48149501945311E+00 -4.41233265123636E-01
z6 : -5.67325522022599E-01 5.72581680680898E-01
== err : 4.251E-15 = rco : 7.118E-02 = res : 4.996E-16 ==
solution 62 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 7.49538719077001E-01 7.02037759030335E-01
z1 : -3.84859479089472E-01 -5.30781156189028E-01
z2 : 4.20154304543547E-01 -1.02474883185914E+00
z3 : -3.55346590730028E-01 1.37137147282026E+00
z4 : 1.02141198568599E+00 6.26456849215854E-01
z5 : -1.95820014306654E-01 4.48782599379519E-01
z6 : -2.55078925180383E-01 -1.59311869239780E+00
== err : 5.471E-15 = rco : 1.896E-02 = res : 8.006E-16 ==
solution 63 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -1.37794444679667E-01 7.73005052481766E-01
z1 : 3.77345552247393E-01 -1.46078936155443E+00
z2 : 7.22372950964257E-01 7.58232064904036E-01
z3 : -4.95568514578313E-01 9.31768565728423E-01
z4 : 8.16440101059308E-01 5.81674279314788E-01
z5 : -4.96853036911004E-01 -3.56427342537111E-01
z6 : 2.14057391898025E-01 -1.22746325833747E+00
== err : 3.687E-15 = rco : 9.219E-02 = res : 8.951E-16 ==
solution 64 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : -9.90908671787996E-01 3.66239764056363E-01
z1 : 4.08351726939132E-01 -8.82192008144182E-01
z2 : -1.04656463000504E+00 6.51131202912576E-01
z3 : -3.91359773193377E-01 3.60231297983222E-01
z4 : 8.15558407212566E-01 4.26912915360504E-01
z5 : 8.66812340311791E-01 -8.34377968026784E-01
z6 : 1.33811060052293E+00 -8.79452041416986E-02
== err : 4.015E-15 = rco : 3.765E-02 = res : 8.882E-16 ==
solution 65 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 7.07952956937574E-01 -1.40940479922186E-01
z1 : 3.41982151288698E-01 -1.58806004858678E+00
z2 : -5.67221826264204E-01 4.86587738536703E-01
z3 : 6.23489801858734E-01 7.81831482468029E-01
z4 : 1.07537663548917E+00 -7.96271945349232E-01
z5 : -6.15540778016679E-01 -7.56707814351634E-03
z6 : -5.66038941293288E-01 1.26442033099699E+00
== err : 4.750E-15 = rco : 4.252E-02 = res : 5.049E-16 ==
solution 66 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 14
the solution for t :
z0 : 6.23489801858735E-01 7.81831482468030E-01
z1 : 1.19520534101604E+00 2.12894386686208E-01
z2 : 1.07537663548916E+00 -7.96271945349236E-01
z3 : -3.81950554427645E-01 -7.62479263920682E-01
z4 : -9.05273973150130E-01 -7.45319717926181E-01
z5 : -5.67221826264204E-01 4.86587738536703E-01
z6 : -3.96254245219610E-02 8.22757319505158E-01
== err : 3.928E-15 = rco : 1.430E-01 = res : 9.550E-16 ==