11 + 1*z0*z1*z2*z3*z4*z5*z6*z7*z8 +( 8.09814453125000E-01 - 8.36517333984375E-01*i)*zz1 +( 9.01000976562500E-01 + 9.64630126953125E-01*i)*zz2 -1; + 1*z0 + 1*z1 + 1*z2 + 1*z3 + 1*z4 + 1*z5 + 1*z6 + 1*z7 + 1*z8 +( 3.57177734375000E-01 - 6.44622802734375E-01*i)*zz1 +( 6.20239257812500E-01 + 2.03399658203125E-01*i)*zz2; + 1*z0*z1 + 1*z0*z8 + 1*z1*z2 + 1*z2*z3 + 1*z3*z4 + 1*z4*z5 + 1*z5*z6 + 1*z6*z7 + 1*z7*z8 +( 9.49401855468750E-01 + 2.92816162109375E-01*i)*zz1 +(-5.12145996093750E-01 - 5.68145751953125E-01*i)*zz2; + 1*z0*z1*z2 + 1*z0*z1*z8 + 1*z0*z7*z8 + 1*z1*z2*z3 + 1*z2*z3*z4 + 1*z3*z4*z5 + 1*z4*z5*z6 + 1*z5*z6*z7 + 1*z6*z7*z8 +( 4.01977539062500E-01 + 4.66918945312500E-03*i)*zz1 +(-9.40429687500000E-01 - 9.71527099609375E-01*i)*zz2; + 1*z0*z1*z2*z3 + 1*z0*z1*z2*z8 + 1*z0*z1*z7*z8 + 1*z0*z6*z7*z8 + 1*z1*z2*z3*z4 + 1*z2*z3*z4*z5 + 1*z3*z4*z5*z6 + 1*z4*z5*z6*z7 + 1*z5*z6*z7*z8 +( 5.74279785156250E-01 + 7.25311279296875E-01*i)*zz1 +(-3.05236816406250E-01 - 2.72369384765625E-01*i)*zz2; + 1*z0*z1*z2*z3*z4 + 1*z0*z1*z2*z3*z8 + 1*z0*z1*z2*z7*z8 + 1*z0*z1*z6*z7*z8 + 1*z0*z5*z6*z7*z8 + 1*z1*z2*z3*z4*z5 + 1*z2*z3*z4*z5*z6 + 1*z3*z4*z5*z6*z7 + 1*z4*z5*z6*z7*z8 +(-4.24316406250000E-01 + 9.39117431640625E-01*i)*zz1 +( 2.80761718750000E-03 + 5.13702392578125E-01*i)*zz2; + 1*z0*z1*z2*z3*z4*z5 + 1*z0*z1*z2*z3*z4*z8 + 1*z0*z1*z2*z3*z7*z8 + 1*z0*z1*z2*z6*z7*z8 + 1*z0*z1*z5*z6*z7*z8 + 1*z0*z4*z5*z6*z7*z8 + 1*z1*z2*z3*z4*z5*z6 + 1*z2*z3*z4*z5*z6*z7 + 1*z3*z4*z5*z6*z7*z8 +(-2.34436035156250E-01 - 6.19537353515625E-01*i)*zz1 +( 8.43078613281250E-01 + 6.21063232421875E-01*i)*zz2; + 1*z0*z1*z2*z3*z4*z5*z6 + 1*z0*z1*z2*z3*z4*z5*z8 + 1*z0*z1*z2*z3*z4*z7*z8 + 1*z0*z1*z2*z3*z6*z7*z8 + 1*z0*z1*z2*z5*z6*z7*z8 + 1*z0*z1*z4*z5*z6*z7*z8 + 1*z0*z3*z4*z5*z6*z7*z8 + 1*z1*z2*z3*z4*z5*z6*z7 + 1*z2*z3*z4*z5*z6*z7*z8 +(-2.46704101562500E-01 - 9.66278076171875E-01*i)*zz1 +(-6.75048828125000E-01 - 4.65911865234375E-01*i)*zz2; + 1*z0*z1*z2*z3*z4*z5*z6*z7 + 1*z0*z1*z2*z3*z4*z5*z6*z8 + 1*z0*z1*z2*z3*z4*z5*z7*z8 + 1*z0*z1*z2*z3*z4*z6*z7*z8 + 1*z0*z1*z2*z3*z5*z6*z7*z8 + 1*z0*z1*z2*z4*z5*z6*z7*z8 + 1*z0*z1*z3*z4*z5*z6*z7*z8 + 1*z0*z2*z3*z4*z5*z6*z7*z8 + 1*z1*z2*z3*z4*z5*z6*z7*z8 +( 3.98254394531250E-01 - 8.66729736328125E-01*i)*zz1 +( 8.07800292968750E-01 + 9.87152099609375E-01*i)*zz2; +( 2.93814126877713E-01 + 1.92096677720035E-01*i)*z0 +(-1.33379543011714E-01 + 1.78361504432095E-01*i)*z1 +(-1.94140987554216E-01 + 1.94664546378996E-01*i)*z2 +(-2.95401059232047E-01 - 5.14158221596368E-02*i)*z3 +(-1.86538211186990E-01 - 2.59379181252348E-01*i)*z4 +( 3.83069103439169E-01 - 1.28725110967683E-01*i)*z5 +(-2.43984412828121E-01 + 1.12755116662622E-01*i)*z6 +( 2.63192775134840E-02 + 4.33791685409140E-02*i)*z7 +( 1.94127276329902E-01 + 2.82778182872871E-02*i)*z8 +( 3.47351074218750E-01 + 8.58734130859375E-01*i)*zz1 +(-5.36071777343750E-01 - 2.99102783203125E-01*i)*zz2 -4.13655969736451E-01; +( 4.00055227354677E-02 - 1.78212168127364E-02*i)*z0 +(-5.67824735956847E-02 - 1.50308926563653E-01*i)*z1 +(-1.20729956099808E-01 + 1.76605995309073E-01*i)*z2 +(-1.82210059338039E-01 + 1.38012495099721E-01*i)*z3 +(-4.15664590028213E-03 - 2.46700553101298E-02*i)*z4 +(-2.91758849749721E-01 + 1.90546837675407E-01*i)*z5 +( 3.37332357998628E-01 - 7.81789304912989E-02*i)*z6 +(-1.10719165850518E-01 - 2.98797965629384E-01*i)*z7 +( 1.38748795590589E-02 - 2.66821946699176E-01*i)*z8 +( 3.39898284836732E-01 - 2.05749730862605E-01*i)*zz1 +( 6.05957031250000E-01 - 3.19671630859375E-01*i)*zz2 +(-1.98377408987400E-01 + 2.15444748723150E-01*i); TITLE : cyclic 9-roots, sliced and embedded twice ROOT COUNTS : total degree : 362,880 (= 9!) Mixed volume : 20,376 NOTE : original last equation is moved up to the front REFERENCES : J.C. Faug\`ere: "A new efficient algorithm for computing Gr\"obner bases (F_4)", Journal of Pure and Applied Algebra vol. 139, Nos 1-3, pages 61-88, 1999. Proceedings of MEGA'98, 22-27 June 1998, Saint-Malo, France. TIMING (on 800 Mhz Pentium III Linux machine) : mixed volume calculation : 13m 4s 540ms polyhedral continuation : 4h 4m 29s 730ms solving target system : 4h 54m 53s 550ms The mixed volume computation was done with the fabulous program of TY Li (http://www.math.msu.edu/~li) and Xing Li (http://www.math.msu.edu/~xing). monodromy factorization : 6 3 : 1 10 15 3 : 2 6 18 3 : 3 4 9 3 : 5 13 14 3 : 7 8 16 3 : 11 12 17 Drop in #factors : 9 -> 6 count : 0 calculated sum at samples : -1.44635386266859E-01 1.92130191656687E+00 value at the linear trace : -1.44635386266863E-01 1.92130191656687E+00 The witness points 1 10 15 define a factor. calculated sum at samples : -1.44635386266881E-01 1.92130191656685E+00 value at the linear trace : -1.44635386266863E-01 1.92130191656686E+00 The witness points 2 6 18 define a factor. calculated sum at samples : -1.53848314776488E+00 -2.16427213936603E-01 value at the linear trace : -1.53848314776473E+00 -2.16427213936923E-01 The witness points 3 4 9 define a factor. calculated sum at samples : -1.53848314776461E+00 -2.16427213936896E-01 value at the linear trace : -1.53848314776473E+00 -2.16427213936917E-01 The witness points 5 13 14 define a factor. calculated sum at samples : -1.44635386266869E-01 1.92130191656687E+00 value at the linear trace : -1.44635386266865E-01 1.92130191656686E+00 The witness points 7 8 16 define a factor. calculated sum at samples : -1.53848314776481E+00 -2.16427213936907E-01 value at the linear trace : -1.53848314776472E+00 -2.16427213936904E-01 The witness points 11 12 17 define a factor. The factorization is certified. Number of monodromy loops : 3 TIMING INFORMATION for Monodromy Factorization The elapsed time in seconds was 16.470000000 = 0h 0m16s470ms User time in seconds was 16.470000000 = 0h 0m16s470ms The labels of the generic points refer to the solution list below. An older verification with 32 decimal places took about 2.5 minutes. THE SOLUTIONS with zz1 = 0 = zz2 : 18 11 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 1.94777894754863E-01 3.03980869930257E-01 z1 : -1.75205569745961E+00 7.38019746148818E-01 z2 : -1.14504250637622E-01 -1.45242797165602E+00 z3 : 1.65866208246664E-01 -3.20673039918491E-01 z4 : 1.51517169738923E+00 1.14831486977088E+00 z5 : -1.20058739530241E+00 8.25377575721490E-01 z6 : -3.60644103001527E-01 1.66921699882347E-02 z7 : 2.36884000070388E-01 -1.88633461591970E+00 z8 : 1.31509164594003E+00 6.27050395934529E-01 zz1 : 3.03056941271789E-16 7.72065916513053E-17 zz2 : 1.77123029769856E-16 3.52712221967583E-17 == err : 3.240E-14 = rco : 1.149E-03 = res : 8.065E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 6.96134794996519E-01 -3.81765630552550E-01 z1 : 4.19870265222308E-01 1.05890553195944E+00 z2 : -1.03657206997467E+00 -3.84873632169384E-01 z3 : -6.78686131848552E-01 -4.11987601648983E-01 z4 : 7.07103958273594E-01 -8.93071081955948E-01 z5 : 1.84975692281861E-01 1.09013456153618E+00 z6 : -1.74486631479666E-02 7.93753232201533E-01 z7 : -1.12697422349590E+00 -1.65834450003490E-01 z8 : 8.51596377692809E-01 -7.05260929366793E-01 zz1 : -6.98104655000615E-16 3.60615461130046E-17 zz2 : -2.43066814426445E-16 -7.24956832500021E-17 == err : 1.256E-14 = rco : 6.213E-03 = res : 3.856E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -2.06112760332844E-01 -9.61078642544502E-02 z1 : 4.51764436091336E-01 2.63534164408104E+00 z2 : -1.59051675824592E+00 -4.18105097364720E-01 z3 : 1.86288232114242E-01 -1.30444954365151E-01 z4 : -2.50815502947090E+00 -9.26431343859074E-01 z5 : 1.15734801489257E+00 -1.16837536910348E+00 z6 : 1.98245282186015E-02 2.26552818619601E-01 z7 : 2.05639059337957E+00 -1.70891030022197E+00 z8 : 4.33168743353350E-01 1.58648046646820E+00 zz1 : -9.65192080773141E-17 -2.59890032017615E-16 zz2 : -6.61393537829865E-17 8.29064848659207E-17 == err : 1.186E-13 = rco : 1.476E-04 = res : 8.695E-15 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 4.47843464214542E-01 6.26516284437912E-01 z1 : 1.17677553670748E+00 -1.20139074685270E+00 z2 : -2.78602804862677E-01 7.20114913529667E-01 z3 : -7.66500750315139E-01 7.45856747096647E-02 z4 : 4.52047138292262E-01 1.61981288276709E+00 z5 : -4.84336406329388E-01 -6.01334563341511E-01 z6 : 3.18657286100597E-01 -7.01101959147576E-01 z7 : -1.62882267499974E+00 -4.18422135914392E-01 z8 : 7.62939211192065E-01 -1.18780350188156E-01 zz1 : -3.94901288356343E-18 3.82617038167079E-16 zz2 : 4.64375384070048E-17 1.72104852511891E-16 == err : 2.655E-14 = rco : 4.480E-03 = res : 7.085E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -1.92184149839757E-01 2.12806797245316E-01 z1 : 1.40446168485247E+00 1.84336840303556E+00 z2 : -1.49963421888538E+00 1.25431835283928E-01 z3 : -8.82040175925694E-02 -2.72839754588603E-01 z4 : -2.29863470798858E+00 2.94615296206350E-01 z5 : 6.41189953643502E-01 -1.36143724758114E+00 z6 : 2.80388167432326E-01 6.00329573432866E-02 z7 : 8.94173023136108E-01 -2.13798369924191E+00 z8 : 8.58444265241879E-01 1.23600541229721E+00 zz1 : -2.69694578969180E-16 4.06319303028357E-16 zz2 : -1.10178254985569E-16 2.48439847053124E-16 == err : 7.264E-14 = rco : 2.525E-04 = res : 7.750E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -1.85038777085167E-01 2.68531654821430E-01 z1 : -2.12831064369090E+00 -1.73279877544696E-01 z2 : 5.09374417678794E-01 -1.34265735168901E+00 z3 : 3.25074623338216E-01 2.59824542302457E-02 z4 : 9.14090545927086E-01 1.92981102335348E+00 z5 : -1.41746258398002E+00 2.30197490096766E-01 z6 : -1.40035846253049E-01 -2.94514109051676E-01 z7 : 1.21422009776381E+00 -1.75653114580878E+00 z8 : 9.08088166301223E-01 1.11245986159225E+00 zz1 : 2.01523006191032E-16 -2.58269088124487E-16 zz2 : 1.19376980179133E-16 -2.19780485301289E-16 == err : 3.098E-14 = rco : 6.045E-04 = res : 6.224E-15 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 1.93243706560192E-01 -9.70807989598383E-01 z1 : 1.16145738574929E+00 -8.00421070840451E-01 z2 : -2.83464525987396E-01 6.57725566680197E-01 z3 : -9.37366234469194E-01 3.18050035796601E-01 z4 : -1.27391367394682E+00 -6.05641066051723E-01 z5 : 7.11339312457264E-01 -8.33753027633003E-02 z6 : 7.44122527909003E-01 6.52757953801783E-01 z7 : 1.12456288197528E-01 1.40606213689217E+00 z8 : -4.27874786469869E-01 -5.74350263916897E-01 zz1 : 4.83657441345604E-16 6.07616449753450E-16 zz2 : 4.54097585502138E-17 6.72479715158070E-17 == err : 1.278E-14 = rco : 7.001E-03 = res : 5.623E-15 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 5.45943598887387E-01 3.83857867828646E-02 z1 : -7.21829459608911E-01 1.22131869639108E+00 z2 : -7.31461724390237E-01 -1.06007529474556E+00 z3 : -2.39728732945480E-01 -4.91993919061411E-01 z4 : 1.41860774699602E+00 1.44633010257721E-02 z5 : -5.52321272978810E-01 1.16350208259069E+00 z6 : -3.06214865941907E-01 4.53608132278547E-01 z7 : -6.96778287387110E-01 -1.23578199741685E+00 z8 : 1.28378299736905E+00 -1.03426787845138E-01 zz1 : 1.19195718174989E-16 3.85094396130255E-16 zz2 : 1.39962710386250E-16 1.55333050142353E-17 == err : 2.465E-14 = rco : 2.454E-03 = res : 4.112E-15 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 7.96177224979220E-01 -7.49191407260689E-02 z1 : -1.90587283271681E+00 -6.16360362675215E-01 z2 : 1.87251624620590E-01 -5.95539090395260E-01 z3 : -3.33206733391133E-01 7.26969273109638E-01 z4 : 1.48672014832093E+00 -1.34235410817776E+00 z5 : 4.22126168918677E-01 4.59934209018970E-01 z6 : -4.62970491588087E-01 -6.52050132383568E-01 z7 : 4.19152684395879E-01 1.95871447085297E+00 z8 : -6.09377793539268E-01 1.35604881376291E-01 zz1 : -2.46956292680576E-16 -8.88834886960506E-17 zz2 : -2.34695128092660E-17 -2.00326040102526E-17 == err : 1.592E-14 = rco : 4.032E-03 = res : 9.338E-15 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 5.52774027869717E-01 -7.73376118820404E-01 z1 : 1.14284224731358E+00 2.59523071516570E-01 z2 : -8.51974745252514E-01 2.82581007736281E-01 z3 : -9.46150379513541E-01 -9.20282912772205E-02 z4 : -3.46667550855275E-01 -1.11949195444994E+00 z5 : 6.70709703952884E-01 5.96541268903312E-01 z6 : 3.93376351643823E-01 8.65404410097625E-01 z7 : -7.96174696458305E-01 8.59968882933374E-01 z8 : 1.81265041299630E-01 -8.79122276639593E-01 zz1 : -1.10051371462021E-16 6.41271852090500E-16 zz2 : -1.00541921886301E-16 2.03947746557514E-17 == err : 1.184E-14 = rco : 1.209E-02 = res : 3.969E-15 == solution 11 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 4.05687846341250E-02 -2.84124455231732E-01 z1 : -7.45503479959813E-01 2.30261221569105E+00 z2 : -1.19441060242073E+00 -8.03634866104804E-01 z3 : 2.25774603750032E-01 1.77195825709678E-01 z4 : -1.62136893387291E+00 -1.79693106010042E+00 z5 : 1.29317351062403E+00 -6.32572491193425E-01 z6 : -2.66343388384157E-01 1.06928629522054E-01 z7 : 2.36687241383272E+00 -5.05681155590625E-01 z8 : -9.87629082033027E-02 1.43620735729823E+00 zz1 : -6.05741985763463E-16 -5.19033432124912E-16 zz2 : -9.28090149268392E-17 -8.48307517897459E-17 == err : 8.557E-14 = rco : 2.100E-04 = res : 7.083E-15 == solution 12 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 9.24298094925836E-01 2.32885928443073E-01 z1 : -1.23303583935353E+00 -1.77027805764844E+00 z2 : 4.79922155660824E-01 -7.84514060547976E-02 z3 : -6.63834177678543E-01 6.84022666653798E-01 z4 : 2.14962368936249E+00 -1.82701331832603E-01 z5 : -1.72020167224349E-01 4.54850481668662E-01 z6 : -2.60463917247292E-01 -9.16908595096871E-01 z7 : -9.16587850008959E-01 1.95297938948105E+00 z8 : -3.07901988436475E-01 -3.76399075613864E-01 zz1 : -4.65135445905829E-16 -2.08218303580685E-17 zz2 : -1.22274873369727E-16 3.18610865935046E-17 == err : 1.596E-14 = rco : 4.280E-03 = res : 5.612E-15 == solution 13 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 7.84155191193138E-01 5.12740994760677E-01 z1 : -3.14127291818504E-04 -1.99996564889732E+00 z2 : 2.91994218795347E-01 4.46711535309179E-01 z3 : -8.36124322621019E-01 4.22727818702362E-01 z4 : 1.73217812228722E+00 9.99710782233925E-01 z5 : -5.32860647138971E-01 2.95186435803730E-02 z6 : 5.19691314278816E-02 -9.35468813463040E-01 z7 : -1.73186399499540E+00 1.00025486666340E+00 z8 : 2.40866428343624E-01 -4.76230178889551E-01 zz1 : 1.31314186516337E-17 3.85451463706670E-16 zz2 : -1.21446648329924E-16 6.84575408465178E-17 == err : 1.408E-14 = rco : 6.668E-03 = res : 6.135E-15 == solution 14 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 4.45936887507539E-01 -2.70058512548602E-01 z1 : -1.68148041747863E+00 9.74187780414907E-01 z2 : -4.74227938397982E-01 -8.65672644823417E-01 z3 : 1.09090886215586E-02 5.21221929340393E-01 z4 : -2.93115715636793E-03 -1.94329864771001E+00 z5 : 9.86808470977334E-01 2.21428805747345E-02 z6 : -4.56845976129097E-01 -2.51163416791791E-01 z7 : 1.68441157463500E+00 9.69110867295107E-01 z8 : -5.12580532579352E-01 8.43529764248682E-01 zz1 : 2.45289674316459E-16 8.62179578576891E-17 zz2 : -8.79542777985422E-19 1.04268115608854E-16 == err : 1.772E-14 = rco : 4.613E-03 = res : 4.120E-15 == solution 15 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -4.34438371978545E-01 -5.21695823767205E-01 z1 : -6.21405113054966E-01 -1.69512822071102E+00 z2 : 8.15853637264480E-01 -1.17235338698019E-03 z3 : -2.34582650441377E-01 6.37082578395776E-01 z4 : -1.15732154528017E+00 1.38571672430265E+00 z5 : -4.08942106447577E-01 -7.05963798947484E-01 z6 : 6.69021022419921E-01 -1.15386754628571E-01 z7 : 1.77872665833514E+00 3.09411496408367E-01 z8 : -4.06911530816902E-01 7.07136152334464E-01 zz1 : -1.20220844837185E-16 2.48995482476794E-16 zz2 : 6.54593217365234E-17 2.08406667546686E-16 == err : 1.370E-14 = rco : 6.067E-03 = res : 5.094E-15 == solution 16 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -4.26073754801543E-01 -5.86688698418328E-02 z1 : -1.67024648934138E+00 -1.11848302859626E+00 z2 : 8.64300891751977E-01 -7.68669589241359E-01 z3 : 1.62228145706422E-01 3.98325130464874E-01 z4 : -1.33511471795426E-01 2.00571740464954E+00 z5 : -1.09783783727555E+00 -3.64171734150078E-01 z6 : 2.63845609095121E-01 -3.39656260623042E-01 z7 : 1.80375796113680E+00 -8.87234376053278E-01 z8 : 2.33536945523579E-01 1.13284132339143E+00 zz1 : -4.79484852526130E-16 -2.82254292151564E-16 zz2 : -2.54175648815729E-16 8.74064936487334E-18 == err : 3.067E-14 = rco : 1.779E-03 = res : 6.147E-15 == solution 17 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : 7.30410493009578E-02 5.06727806246054E-01 z1 : 1.70120645939535E+00 2.85256376510535E-01 z2 : -9.67379491728109E-01 5.88556997929289E-01 z3 : -4.75359677663520E-01 -1.90108498909326E-01 z4 : -1.09764249834730E+00 1.33065982266328E+00 z5 : -2.60155659178145E-02 -1.13205371390126E+00 z6 : 4.02318628362563E-01 -3.16619307336728E-01 z7 : -6.03563961048051E-01 -1.61591619917382E+00 z8 : 9.93395057645923E-01 5.43496715971976E-01 zz1 : -1.06313604887849E-16 -2.24208133955173E-16 zz2 : -1.31000694300005E-16 1.10220314581333E-16 == err : 3.015E-14 = rco : 2.769E-03 = res : 3.465E-15 == solution 18 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : z0 : -1.97982467265316E-01 -8.77857096926233E-01 z1 : 4.77821815267592E-01 -1.58321105746037E+00 z2 : 3.76572293670222E-01 5.56511666551676E-01 z3 : -6.61255313197918E-01 6.10386394618801E-01 z4 : -1.61001190294690E+00 3.77799698226055E-01 z5 : 2.93667093901055E-01 -6.04377005955624E-01 z6 : 8.59237780463233E-01 2.67470702307432E-01 z7 : 1.13219008767931E+00 1.20541135923431E+00 z8 : -6.70239387571277E-01 4.78653394039482E-02 zz1 : 3.55740528279679E-16 -4.47108512460978E-16 zz2 : 1.99268167352691E-16 -6.20718779211461E-17 == err : 1.248E-14 = rco : 5.931E-03 = res : 6.578E-15 ==