8
(x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7)*x8 - 1;
(x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6 + x5*x7)*x8 - 2;
(x3 + x1*x4 + x2*x5 + x3*x6 + x4*x7)*x8 - 3;
(x4 + x1*x5 + x2*x6 + x3*x7)*x8 - 4;
(x5 + x1*x6 + x2*x7)*x8 - 5;
(x6 + x1*x7)*x8 - 6;
x7*x8 - 7;
x1 + x2 + x3 + x4 + x5 + x6 + x7 + 1;
TITLE : 8-dimensional economics problem
ROOT COUNTS :
total degree : 1458
3-homogeneous Bezout number : 256
with partition : {x1 x2 x3 x4 x5 x6 }{x7 }{x8 }
generalized Bezout number : 176
based on the set structure :
{x1 x3 x5 x7 }{x2 x4 x6 }{x8 }
{x1 x2 x5 x6 }{x3 x4 x7 }{x8 }
{x1 x2 x3 x7 }{x4 x5 x6 }{x8 }
{x1 x2 x3 x4 }{x5 x6 x7 }{x8 }
{x1 x2 x5 }{x6 x7 }{x8 }
{x1 x6 }{x7 }{x8 }
{x7 }{x8 }
{x1 x2 x3 x4 x5 x6 x7 }
mixed volume : 64
REFERENCE :
Alexander Morgan:
`Solving polynomial systems using continuation for engineering
and scientific problems', Prentice-Hall, Englewood Cliffs, New Jersey, 1987,
(p 148).
NOTE :
Transform u = 1/x8 and the total degree equals the number of solutions.
See the reduced economics problem, in the file redeco8.
THE SOLUTIONS :
64 8
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.78209839580825E-02 -1.74673471603347E+00
x2 : -2.25061288175077E-01 -9.65541438387309E-01
x3 : -2.59969119095552E+00 -1.46033094051729E+00
x4 : -1.84772040826661E+00 2.29707362139904E+00
x5 : 1.45480800105432E+00 2.83093730324484E+00
x6 : 1.86925177577862E+00 -9.05476876953008E-02
x7 : 3.96234094522347E-01 -8.64856142010510E-01
x8 : 3.06486994737651E+00 6.68966056958662E+00
== err : 6.921E-15 = rco : 5.396E-03 = res : 3.198E-14 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.31206034840825E-01 -8.65785019824411E-01
x2 : -7.80875281985146E-01 -2.20760439208593E+00
x3 : -1.22835309328094E+00 9.21433110771690E-01
x4 : -8.06469247698946E-01 8.07711688026660E-01
x5 : 6.64340626635413E-01 1.15785993336426E+00
x6 : 4.31688773993016E-01 3.31850703822340E-01
x7 : 4.88462187495779E-01 -1.45466024074603E-01
x8 : 1.31632748419528E+01 3.92007673076368E+00
== err : 4.285E-14 = rco : 3.735E-03 = res : 7.550E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.31206034840825E-01 -2.62768441224252E+00
x2 : -3.85844611688014E+00 -6.98250845583434E-01
x3 : -4.40272194011276E-01 2.88988515225427E+00
x4 : 8.61326214993982E-01 9.51587434171054E-01
x5 : 1.32403203819477E+00 7.89090697380827E-01
x6 : 1.09096648052896E+00 -8.39705419198962E-01
x7 : -2.08812457667120E-01 -4.64922606781227E-01
x8 : -5.62716181735090E+00 1.25289207843777E+01
== err : 4.290E-15 = rco : 1.405E-03 = res : 2.930E-14 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 9.04963841100940E-01 -1.74673471603347E+00
x2 : -2.06845890440780E+00 -2.62980376922778E+00
x3 : -3.00423794013733E+00 7.60055778523489E-01
x4 : 2.57343272529547E-01 3.12382515229320E+00
x5 : 8.24194415747985E-01 6.37834651815017E-01
x6 : 1.64835675125572E+00 8.10488698284776E-01
x7 : 4.37838563910929E-01 -9.55665795655231E-01
x8 : 2.77363866165643E+00 6.05399299407358E+00
== err : 5.108E-15 = rco : 5.857E-03 = res : 4.977E-14 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688686E-01 -2.78729129753649E-01
x2 : 6.84268653947781E-01 1.79772241022417E+00
x3 : 1.50893398799752E-01 1.70641722701536E-01
x4 : -1.21425244899783E+00 -4.90968316930757E-01
x5 : -6.64940564102784E-01 -2.11960393271642E-01
x6 : 2.15174448159515E-01 -5.07550037830726E-01
x7 : 7.40428898822547E-02 -4.79156255138937E-01
x8 : 2.20484735727226E+00 1.42683032029623E+01
== err : 6.734E-15 = rco : 4.602E-03 = res : 7.444E-15 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688686E-01 2.78729129753649E-01
x2 : 6.84268653947781E-01 -1.79772241022417E+00
x3 : 1.50893398799752E-01 -1.70641722701536E-01
x4 : -1.21425244899783E+00 4.90968316930757E-01
x5 : -6.64940564102784E-01 2.11960393271641E-01
x6 : 2.15174448159515E-01 5.07550037830726E-01
x7 : 7.40428898822546E-02 4.79156255138937E-01
x8 : 2.20484735727226E+00 -1.42683032029623E+01
== err : 5.351E-15 = rco : 4.602E-03 = res : 6.217E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 7.28266057133575E-01 2.90641354199617E+00
x2 : -4.02480045349249E+00 4.77974857901422E-01
x3 : 1.18159160926567E+00 -4.31989607068968E+00
x4 : 2.35266437155773E+00 2.26130810108664E+00
x5 : -2.31317226244749E+00 1.20777100078736E-01
x6 : 5.18093612620539E-01 -1.60012182512894E+00
x7 : 5.57357065362468E-01 1.53544294755645E-01
x8 : 1.16733509971869E+01 -3.21584951135863E+00
== err : 3.191E-14 = rco : 2.489E-03 = res : 7.105E-14 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571429E-01 -6.02220566455407E-01
x2 : 8.39713171180437E-02 -1.02911869361847E+00
x3 : -3.70029864242782E-01 -2.29937976125475E+00
x4 : -1.54493207432736E+00 1.74277200821394E+00
x5 : -4.80758765975095E-01 9.13787435124618E-01
x6 : 3.89841694187333E-02 7.38121476848058E-01
x7 : 8.44193789437036E-01 5.36038101142015E-01
x8 : 5.90935652605925E+00 -3.75226670799410E+00
== err : 7.927E-15 = rco : 1.109E-02 = res : 3.662E-15 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571428E-01 -1.15967882596271E+00
x2 : -4.07121367244140E-01 2.19073427282266E+00
x3 : 3.00074302117930E+00 8.43795237846107E-01
x4 : -2.57574776919183E+00 -1.75555475906375E+00
x5 : -1.41599518322812E+00 1.72047147691013E+00
x6 : 6.12565476144802E-01 -1.07391432908286E+00
x7 : -6.43015606231446E-01 -7.65853073469583E-01
x8 : -4.50110924362012E+00 5.36097151428708E+00
== err : 4.431E-15 = rco : 8.358E-03 = res : 2.197E-14 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.42551771419289E-01 -1.74673471603347E+00
x2 : -1.34084054571022E+00 -2.76051468441591E-01
x3 : -7.68678942106033E-01 9.02740445142473E-01
x4 : 2.20595282770167E-01 1.02073155184390E+00
x5 : 7.02375877262567E-01 4.36162532263085E-01
x6 : 5.26176045404461E-01 -1.12197055754395E-01
x7 : 1.02924053798346E-01 -2.24651289020004E-01
x8 : 1.17990491397357E+01 2.57536649658722E+01
== err : 4.505E-14 = rco : 8.560E-04 = res : 1.005E-14 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.47515612520230E-01 -1.13195988485334E-71
x2 : 1.59955565082714E+00 1.81113581576534E-71
x3 : -7.14195108063652E-01 -4.52783953941336E-71
x4 : 1.32209704041973E+00 8.60289512488538E-71
x5 : 7.67848816841054E-01 2.71670372364801E-71
x6 : -1.98227932283785E+00 -4.11977234100445E-71
x7 : -1.64551146466620E+00 1.35835186182401E-71
x8 : -4.25399649307213E+00 1.35835186182401E-70
== err : 4.725E-15 = rco : 2.914E-02 = res : 3.997E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.26242193739885E-01 8.80949696209057E-01
x2 : 6.84766851039934E-01 -6.70954697940247E-01
x3 : 1.13659996275851E+00 1.57144488632821E+00
x4 : -7.84742698629243E-01 -1.09325148997073E+00
x5 : 3.30907349288984E+00 1.25190184527914E+00
x6 : -3.43647190317998E+00 6.13586232733104E-01
x7 : -2.23546789861895E+00 -2.55367647263853E+00
x8 : -1.35852465730005E+00 1.55190439414930E+00
== err : 4.245E-15 = rco : 3.791E-02 = res : 8.538E-15 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.42857142857143E-01 2.82989971213335E-73
x2 : -1.42857142857143E-01 2.82989971213335E-73
x3 : -1.42857142857143E-01 0.00000000000000E+00
x4 : -1.42857142857143E-01 2.24834569700406E-73
x5 : -1.42857142857143E-01 4.24484956820002E-73
x6 : -1.42857142857143E-01 2.82989971213335E-73
x7 : -1.42857142857143E-01 0.00000000000000E+00
x8 : -4.90000000000000E+01 1.08668148945921E-70
== err : 2.040E-15 = rco : 1.407E-03 = res : 1.332E-15 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.02634606269397E-01 2.02546384578712E+00
x2 : -1.83542167444223E+00 9.45397563054455E-01
x3 : 6.75509155081997E-01 -2.15925850374478E+00
x4 : 3.83025063947650E+00 2.45922649501808E+00
x5 : -3.63602971348939E+00 4.83285613744496E+00
x6 : -3.81540389155297E+00 -6.13981213018347E+00
x7 : 2.97846087865670E+00 -1.96387340737636E+00
x8 : 1.63805628071163E+00 1.08006628273266E+00
== err : 6.418E-15 = rco : 1.241E-02 = res : 1.531E-14 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.59938925712429E+00 -3.86900351268231E-74
x2 : 1.29935154253298E+00 -5.30606196025003E-74
x3 : -1.63719724641073E-01 2.98465985264064E-74
x4 : -1.72340091727033E+00 -1.32651549006251E-74
x5 : -1.40859034083628E+00 2.65303098012501E-74
x6 : 1.73652942442072E+00 -3.53737464016668E-74
x7 : -2.33955924133030E+00 3.53737464016668E-74
x8 : -2.99201656292307E+00 -3.53737464016668E-74
== err : 4.008E-15 = rco : 2.988E-02 = res : 3.553E-15 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 7.28266057133575E-01 -2.90641354199617E+00
x2 : -4.02480045349249E+00 -4.77974857901420E-01
x3 : 1.18159160926567E+00 4.31989607068968E+00
x4 : 2.35266437155772E+00 -2.26130810108664E+00
x5 : -2.31317226244749E+00 -1.20777100078734E-01
x6 : 5.18093612620540E-01 1.60012182512894E+00
x7 : 5.57357065362469E-01 -1.53544294755646E-01
x8 : 1.16733509971869E+01 3.21584951135863E+00
== err : 2.205E-14 = rco : 2.489E-03 = res : 4.494E-14 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.51873644604064E-01 -3.09520281014585E-74
x2 : 1.09122081140823E+00 7.07474928033337E-74
x3 : -1.11424211179408E+00 1.76868732008334E-74
x4 : -6.37151941736669E-01 -6.19040562029170E-74
x5 : 2.91145276196003E-01 6.48940927413164E-74
x6 : -3.32878313838290E-01 2.54248802261980E-74
x7 : -5.49967364839252E-01 -3.09520281014585E-74
x8 : -1.27280279658885E+01 -1.41494985606667E-73
== err : 1.220E-14 = rco : 9.507E-03 = res : 3.553E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688685E-01 -3.77219856182059E+00
x2 : -6.39162737706626E+00 5.56129503395270E-01
x3 : 1.27333920068981E-02 6.84707775070628E+00
x4 : 5.80177107600900E+00 1.00206172064427E+00
x5 : 1.65565900260799E+00 -3.62174951858025E+00
x6 : -1.42211604046533E+00 -1.26814754910442E+00
x7 : -4.11233675403618E-01 2.56826654759426E-01
x8 : -1.22457062910011E+01 -7.64777782071831E+00
== err : 3.487E-14 = rco : 5.158E-04 = res : 1.271E-13 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.44881006250832E-01 2.02546384578712E+00
x2 : -9.69913074191903E-01 -1.78394659173895E+00
x3 : 2.39780453489541E+00 5.10525969081904E-01
x4 : -4.74509572712672E-01 2.52319895744740E+00
x5 : -2.15522917066727E+00 -7.48198344852689E-01
x6 : 4.65723570859314E-02 -2.06539009186894E+00
x7 : 7.00155931841337E-01 -4.61653743855839E-01
x8 : 6.96828567360206E+00 4.59459817903020E+00
== err : 6.674E-15 = rco : 4.446E-03 = res : 1.123E-14 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.28876800009282E-01 2.90641354199617E+00
x2 : -3.80201010831929E+00 -1.26409819593165E+00
x3 : 4.96221479138290E+00 -2.69017551530026E+00
x4 : -1.41431539654813E-02 7.74678341483025E+00
x5 : -6.49225902486156E+00 -2.64610297939910E+00
x6 : 2.54969912472745E+00 -4.51222733924665E+00
x7 : 1.66762157102670E+00 4.59407073051234E-01
x8 : 3.90149945753728E+00 -1.07481006328952E+00
== err : 7.826E-15 = rco : 4.981E-03 = res : 3.102E-14 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571429E-01 -4.65314825802964E+00
x2 : -1.05605882331532E+01 -1.40461093479243E+00
x3 : -1.72418225308741E+00 1.52950278479316E+01
x4 : 1.53737752985508E+01 7.46802772179348E-01
x5 : 3.04264868472084E-01 -1.06492430997778E+01
x6 : -4.66174043546157E+00 -3.21929018534654E-01
x7 : -1.60100673892119E-01 9.87100691023611E-01
x8 : -1.12070471724483E+00 -6.90970483716527E+00
== err : 8.183E-14 = rco : 7.215E-04 = res : 2.913E-13 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.25936822302032E-01 8.65785019824411E-01
x2 : 6.00856924973186E-01 2.54935639473334E+00
x3 : -1.96886687892048E+00 1.06724423008164E+00
x4 : -2.82589112375875E+00 1.04483412963302E+00
x5 : -2.32128192272876E-01 -4.58862776826684E+00
x6 : 9.19624613112195E-01 -1.49860296754324E+00
x7 : 1.88046783456469E+00 5.60010961537670E-01
x8 : 3.41923531247045E+00 -1.01826216852222E+00
== err : 3.807E-15 = rco : 1.002E-02 = res : 7.944E-15 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.78209839580827E-02 1.74673471603347E+00
x2 : -2.25061288175077E-01 9.65541438387308E-01
x3 : -2.59969119095552E+00 1.46033094051729E+00
x4 : -1.84772040826661E+00 -2.29707362139904E+00
x5 : 1.45480800105432E+00 -2.83093730324484E+00
x6 : 1.86925177577862E+00 9.05476876953006E-02
x7 : 3.96234094522347E-01 8.64856142010510E-01
x8 : 3.06486994737651E+00 -6.68966056958662E+00
== err : 7.780E-15 = rco : 5.396E-03 = res : 3.517E-14 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571428E-01 2.89124886561153E+00
x2 : -3.91435387900099E+00 2.56622651399662E+00
x3 : -5.45630497792309E+00 -4.28359545348285E+00
x4 : 3.98380022342191E+00 -5.67888983878634E+00
x5 : 4.48936566690324E+00 1.32411507053572E+00
x6 : 4.26163040031263E-01 2.89160483738685E+00
x7 : -9.57241502003758E-01 2.89290004738477E-01
x8 : -6.70069051402631E+00 -2.02503003316934E+00
== err : 1.110E-14 = rco : 1.779E-03 = res : 5.684E-14 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.40202386339369E+00 2.02546384578712E+00
x2 : -1.65436882863949E+00 2.15943883291291E+00
x3 : -2.12851479896278E+00 -2.20031290401576E+00
x4 : 2.05184647153120E+00 -2.08206273515086E+00
x5 : 2.05412340337162E-01 2.41248718888364E+00
x6 : -1.87186842960293E+00 -1.65864305998415E+00
x7 : 9.95469381943151E-01 -6.56371168432885E-01
x8 : 4.90109152288936E+00 3.23157620699087E+00
== err : 6.684E-15 = rco : 5.778E-03 = res : 3.553E-14 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.00000000000000E+00 4.95232449623336E-73
x2 : 1.00000000000000E+00 1.13195988485334E-72
x3 : 1.00000000000000E+00 1.91018230569001E-72
x4 : 1.00000000000000E+00 1.58474383879468E-72
x5 : 1.00000000000000E+00 8.48969913640004E-73
x6 : 1.00000000000000E+00 1.98092979849334E-72
x7 : -7.00000000000000E+00 6.79175930912004E-72
x8 : -1.00000000000000E+00 -5.65979942426670E-73
== err : 1.020E-56 = rco : 3.878E-02 = res : 1.474E-71 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.02634606269397E-01 -2.02546384578712E+00
x2 : -1.83542167444223E+00 -9.45397563054455E-01
x3 : 6.75509155081998E-01 2.15925850374478E+00
x4 : 3.83025063947650E+00 -2.45922649501808E+00
x5 : -3.63602971348939E+00 -4.83285613744496E+00
x6 : -3.81540389155297E+00 6.13981213018347E+00
x7 : 2.97846087865670E+00 1.96387340737636E+00
x8 : 1.63805628071163E+00 -1.08006628273266E+00
== err : 6.403E-15 = rco : 1.241E-02 = res : 1.776E-14 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.29969462856215E+00 1.74673471603347E+00
x2 : -4.20773748026272E-01 3.31929373917350E+00
x3 : -3.38353768926908E+00 2.53211410631423E+00
x4 : -4.61693651227582E+00 -1.30640300980813E+00
x5 : -1.24447235082903E+00 -5.39838614687383E+00
x6 : 5.68044722330437E+00 -4.57244839996384E+00
x7 : 1.68557844853368E+00 3.67909499512461E+00
x8 : 7.20468376588420E-01 -1.57255902314003E+00
== err : 5.834E-15 = rco : 7.502E-03 = res : 2.844E-14 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.25936822302032E-01 2.62768441224253E+00
x2 : -2.47671390992181E+00 1.73547878282747E+00
x3 : -2.39559793877656E+00 7.76678777389885E-01
x4 : -4.81852275273735E+00 -3.11114097537515E+00
x5 : 4.35149002787906E+00 -6.34471360742584E+00
x6 : 4.51728801087618E+00 2.52616678400144E+00
x7 : -8.03880259621560E-01 1.78984582633967E+00
x8 : -1.46168720366984E+00 -3.25445824746859E+00
== err : 1.520E-14 = rco : 4.822E-03 = res : 3.202E-14 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 9.25631450864178E-01 8.80949696209057E-01
x2 : 5.80275202596967E-01 -1.42922913965630E-01
x3 : -1.39143724803457E-02 9.04963714845271E-01
x4 : -2.34592954474775E+00 -1.23892478112758E+00
x5 : 1.30179835264017E+00 -2.67220218142479E-01
x6 : -7.00716863028764E-01 7.16651272314106E-01
x7 : -7.47144225844456E-01 -8.53496770132749E-01
x8 : -4.06472827578114E+00 4.64332365136781E+00
== err : 4.887E-15 = rco : 1.699E-02 = res : 4.190E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 7.28266057133575E-01 1.14451414957806E+00
x2 : -4.56136934235313E-01 1.11155865313099E+00
x3 : -1.30034690799614E+00 -1.53824981660552E+00
x4 : 8.57247746941892E-01 -8.17101815054367E-02
x5 : -2.62049660027996E-01 1.00268202683989E-01
x6 : -6.45434621422677E-01 -1.63609090637662E-01
x7 : 7.84543196066627E-02 -5.72771916644424E-01
x8 : 1.64315636587197E+00 1.19962014296412E+01
== err : 2.544E-14 = rco : 6.407E-03 = res : 7.324E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.25936822302032E-01 -2.62768441224252E+00
x2 : -2.47671390992181E+00 -1.73547878282746E+00
x3 : -2.39559793877655E+00 -7.76678777389886E-01
x4 : -4.81852275273735E+00 3.11114097537514E+00
x5 : 4.35149002787906E+00 6.34471360742585E+00
x6 : 4.51728801087618E+00 -2.52616678400144E+00
x7 : -8.03880259621558E-01 -1.78984582633967E+00
x8 : -1.46168720366984E+00 3.25445824746859E+00
== err : 6.722E-15 = rco : 4.822E-03 = res : 3.408E-14 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571429E-01 -2.89124886561153E+00
x2 : -3.91435387900099E+00 -2.56622651399662E+00
x3 : -5.45630497792309E+00 4.28359545348285E+00
x4 : 3.98380022342191E+00 5.67888983878634E+00
x5 : 4.48936566690324E+00 -1.32411507053572E+00
x6 : 4.26163040031264E-01 -2.89160483738685E+00
x7 : -9.57241502003759E-01 -2.89290004738477E-01
x8 : -6.70069051402631E+00 2.02503003316934E+00
== err : 8.043E-15 = rco : 1.779E-03 = res : 1.241E-13 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.31206034840825E-01 2.62768441224252E+00
x2 : -3.85844611688014E+00 6.98250845583435E-01
x3 : -4.40272194011275E-01 -2.88988515225427E+00
x4 : 8.61326214993982E-01 -9.51587434171054E-01
x5 : 1.32403203819477E+00 -7.89090697380827E-01
x6 : 1.09096648052896E+00 8.39705419198962E-01
x7 : -2.08812457667120E-01 4.64922606781227E-01
x8 : -5.62716181735090E+00 -1.25289207843777E+01
== err : 1.637E-14 = rco : 1.405E-03 = res : 2.842E-14 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.28876800009282E-01 1.14451414957806E+00
x2 : -2.33346589062116E-01 4.25549167247156E-01
x3 : 3.41257698386961E-01 -1.44992200607483E+00
x4 : 2.33092590705609E+00 2.58954405931279E+00
x5 : -2.01199797300258E+00 5.20777980807650E-01
x6 : -1.79045246708362E+00 -1.51672028949352E+00
x7 : 2.34736623695995E-01 -1.71374306137731E+00
x8 : 5.49180237246639E-01 4.00940341651097E+00
== err : 6.130E-15 = rco : 1.864E-02 = res : 6.405E-15 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 9.04963841100940E-01 1.74673471603347E+00
x2 : -2.06845890440779E+00 2.62980376922778E+00
x3 : -3.00423794013733E+00 -7.60055778523487E-01
x4 : 2.57343272529545E-01 -3.12382515229319E+00
x5 : 8.24194415747984E-01 -6.37834651815019E-01
x6 : 1.64835675125572E+00 -8.10488698284777E-01
x7 : 4.37838563910930E-01 9.55665795655231E-01
x8 : 2.77363866165643E+00 -6.05399299407357E+00
== err : 5.986E-15 = rco : 5.857E-03 = res : 3.449E-14 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571428E-01 4.65314825802964E+00
x2 : -1.05605882331532E+01 1.40461093479243E+00
x3 : -1.72418225308742E+00 -1.52950278479316E+01
x4 : 1.53737752985507E+01 -7.46802772179369E-01
x5 : 3.04264868472107E-01 1.06492430997778E+01
x6 : -4.66174043546156E+00 3.21929018534666E-01
x7 : -1.60100673892122E-01 -9.87100691023610E-01
x8 : -1.12070471724485E+00 6.90970483716527E+00
== err : 5.301E-14 = rco : 7.215E-04 = res : 1.907E-13 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571429E-01 6.02220566455408E-01
x2 : 8.39713171180437E-02 1.02911869361847E+00
x3 : -3.70029864242782E-01 2.29937976125475E+00
x4 : -1.54493207432736E+00 -1.74277200821394E+00
x5 : -4.80758765975095E-01 -9.13787435124618E-01
x6 : 3.89841694187331E-02 -7.38121476848058E-01
x7 : 8.44193789437036E-01 -5.36038101142015E-01
x8 : 5.90935652605925E+00 3.75226670799411E+00
== err : 6.327E-15 = rco : 1.109E-02 = res : 1.081E-14 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 5.30900663402972E-01 -8.80949696209057E-01
x2 : -9.19755701091595E-01 4.90660881263941E-01
x3 : 3.94673442417123E-01 3.81947804965646E-02
x4 : -5.68975899878565E-01 -5.29931641528690E-02
x5 : 1.58549846241613E-02 2.82028740882827E-01
x6 : -2.58622538431232E-01 -9.86421700170221E-02
x7 : -1.94074951042864E-01 2.21700627735615E-01
x8 : -1.56482752903326E+01 -1.78757353084697E+01
== err : 4.749E-14 = rco : 2.230E-03 = res : 3.972E-15 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.25936822302032E-01 -8.65785019824411E-01
x2 : 6.00856924973186E-01 -2.54935639473334E+00
x3 : -1.96886687892048E+00 -1.06724423008164E+00
x4 : -2.82589112375875E+00 -1.04483412963302E+00
x5 : -2.32128192272875E-01 4.58862776826684E+00
x6 : 9.19624613112195E-01 1.49860296754324E+00
x7 : 1.88046783456469E+00 -5.60010961537670E-01
x8 : 3.41923531247045E+00 1.01826216852222E+00
== err : 3.867E-15 = rco : 1.002E-02 = res : 9.607E-15 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.28876800009282E-01 -2.90641354199617E+00
x2 : -3.80201010831929E+00 1.26409819593165E+00
x3 : 4.96221479138290E+00 2.69017551530026E+00
x4 : -1.41431539654798E-02 -7.74678341483024E+00
x5 : -6.49225902486155E+00 2.64610297939909E+00
x6 : 2.54969912472744E+00 4.51222733924664E+00
x7 : 1.66762157102670E+00 -4.59407073051233E-01
x8 : 3.90149945753728E+00 1.07481006328952E+00
== err : 1.637E-14 = rco : 4.981E-03 = res : 4.394E-14 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.05269212538794E-01 -5.14755758946803E-85
x2 : -5.29386459651293E-01 -9.00822578156905E-85
x3 : 1.15852681899207E+00 9.00822578156905E-85
x4 : 2.02601496566939E+00 4.81756572951960E-85
x5 : -1.98415557208050E+00 -1.26276022116638E-84
x6 : -4.57979256055826E-01 -3.86066819210102E-85
x7 : -1.81828970941264E+00 1.60861174670876E-84
x8 : -3.84977155387477E+00 -1.80164515631381E-84
== err : 4.191E-15 = rco : 5.193E-02 = res : 1.776E-15 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -6.84885937213211E-02 -8.80949696209057E-01
x2 : -5.78666659188168E-01 1.01869266523856E+00
x3 : 2.18404212742885E+00 -8.36716792879222E-01
x4 : -5.92211611072873E-01 -5.34720076445635E-01
x5 : -2.42146239570215E-01 4.67906911739125E-01
x6 : -1.12185355590753E+00 1.02455038360827E-01
x7 : -5.80675467968734E-01 6.63331950195402E-01
x8 : -5.23000958091119E+00 -5.97447739092924E+00
== err : 5.007E-15 = rco : 1.331E-02 = res : 6.040E-15 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -6.84885937213211E-02 8.80949696209056E-01
x2 : -5.78666659188168E-01 -1.01869266523856E+00
x3 : 2.18404212742885E+00 8.36716792879222E-01
x4 : -5.92211611072873E-01 5.34720076445635E-01
x5 : -2.42146239570215E-01 -4.67906911739125E-01
x6 : -1.12185355590753E+00 -1.02455038360827E-01
x7 : -5.80675467968734E-01 -6.63331950195402E-01
x8 : -5.23000958091119E+00 5.97447739092924E+00
== err : 5.105E-15 = rco : 1.331E-02 = res : 5.687E-15 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 5.45082508734604E-02 2.02546384578712E+00
x2 : -1.59654661034104E+00 -5.69905321880497E-01
x3 : 5.16862642546052E-01 -1.16646799656723E+00
x4 : 4.91237759965541E-01 4.01056041665406E-01
x5 : -5.75373719029586E-01 6.19660927472800E-02
x6 : -1.24696364116086E-01 -5.97817478504557E-01
x7 : 2.34008040101661E-01 -1.54295183247523E-01
x8 : 2.08492261505969E+01 1.37471138516345E+01
== err : 4.026E-14 = rco : 1.131E-03 = res : 1.589E-14 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.10232923483154E+00 -3.77219856182058E+00
x2 : -6.85329278634063E+00 -4.52696695218433E+00
x3 : -9.05474845175678E+00 8.09165852463592E+00
x4 : 7.45842856856864E+00 1.19920978913958E+01
x5 : 1.17890209232269E+01 -6.01022107632634E+00
x6 : -3.69235087552955E+00 -6.86690951437450E+00
x7 : -1.74938661300016E+00 1.09253968867405E+00
x8 : -2.87863572782532E+00 -1.79778658331597E+00
== err : 5.392E-14 = rco : 1.241E-03 = res : 1.990E-13 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.28876800009282E-01 -1.14451414957806E+00
x2 : -2.33346589062116E-01 -4.25549167247156E-01
x3 : 3.41257698386961E-01 1.44992200607483E+00
x4 : 2.33092590705609E+00 -2.58954405931280E+00
x5 : -2.01199797300258E+00 -5.20777980807649E-01
x6 : -1.79045246708362E+00 1.51672028949352E+00
x7 : 2.34736623695995E-01 1.71374306137731E+00
x8 : 5.49180237246639E-01 -4.00940341651097E+00
== err : 6.266E-15 = rco : 1.864E-02 = res : 4.684E-15 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.42551771419289E-01 1.74673471603347E+00
x2 : -1.34084054571022E+00 2.76051468441591E-01
x3 : -7.68678942106032E-01 -9.02740445142472E-01
x4 : 2.20595282770167E-01 -1.02073155184390E+00
x5 : 7.02375877262567E-01 -4.36162532263085E-01
x6 : 5.26176045404461E-01 1.12197055754395E-01
x7 : 1.02924053798346E-01 2.24651289020004E-01
x8 : 1.17990491397357E+01 -2.57536649658722E+01
== err : 5.099E-14 = rco : 8.560E-04 = res : 2.132E-14 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 5.45082508734605E-02 -2.02546384578712E+00
x2 : -1.59654661034104E+00 5.69905321880497E-01
x3 : 5.16862642546052E-01 1.16646799656723E+00
x4 : 4.91237759965541E-01 -4.01056041665406E-01
x5 : -5.75373719029586E-01 -6.19660927472800E-02
x6 : -1.24696364116086E-01 5.97817478504557E-01
x7 : 2.34008040101661E-01 1.54295183247523E-01
x8 : 2.08492261505969E+01 -1.37471138516345E+01
== err : 3.630E-14 = rco : 1.131E-03 = res : 1.465E-14 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.10232923483154E+00 2.78729129753649E-01
x2 : 2.22603244673394E-01 -1.42213055621695E+00
x3 : 6.18291929397411E-01 -2.62969032904711E+00
x4 : -3.00295846715410E-01 3.61318816677034E-01
x5 : -3.44882007007395E+00 1.96100801887167E+00
x6 : 4.90913313990975E-01 -5.87564109032905E-01
x7 : 3.14978193896038E-01 2.03832902899461E+00
x8 : 5.18300229175783E-01 -3.35409378597256E+00
== err : 4.567E-15 = rco : 1.854E-02 = res : 1.137E-14 ==
solution 51 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.28571428571428E-01 1.15967882596271E+00
x2 : -4.07121367244140E-01 -2.19073427282266E+00
x3 : 3.00074302117930E+00 -8.43795237846107E-01
x4 : -2.57574776919183E+00 1.75555475906375E+00
x5 : -1.41599518322812E+00 -1.72047147691013E+00
x6 : 6.12565476144802E-01 1.07391432908286E+00
x7 : -6.43015606231446E-01 7.65853073469583E-01
x8 : -4.50110924362012E+00 -5.36097151428708E+00
== err : 4.431E-15 = rco : 8.358E-03 = res : 2.197E-14 ==
solution 52 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688687E-01 3.77219856182058E+00
x2 : -6.39162737706625E+00 -5.56129503395277E-01
x3 : 1.27333920069084E-02 -6.84707775070628E+00
x4 : 5.80177107600899E+00 -1.00206172064426E+00
x5 : 1.65565900260799E+00 3.62174951858024E+00
x6 : -1.42211604046533E+00 1.26814754910442E+00
x7 : -4.11233675403618E-01 -2.56826654759426E-01
x8 : -1.22457062910011E+01 7.64777782071832E+00
== err : 1.077E-14 = rco : 5.158E-04 = res : 1.172E-13 ==
solution 53 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.40202386339369E+00 -2.02546384578712E+00
x2 : -1.65436882863949E+00 -2.15943883291291E+00
x3 : -2.12851479896278E+00 2.20031290401576E+00
x4 : 2.05184647153120E+00 2.08206273515086E+00
x5 : 2.05412340337162E-01 -2.41248718888364E+00
x6 : -1.87186842960293E+00 1.65864305998415E+00
x7 : 9.95469381943151E-01 6.56371168432885E-01
x8 : 4.90109152288936E+00 -3.23157620699087E+00
== err : 7.401E-15 = rco : 5.778E-03 = res : 4.550E-14 ==
solution 54 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 7.28266057133575E-01 -1.14451414957806E+00
x2 : -4.56136934235313E-01 -1.11155865313099E+00
x3 : -1.30034690799614E+00 1.53824981660552E+00
x4 : 8.57247746941892E-01 8.17101815054367E-02
x5 : -2.62049660027996E-01 -1.00268202683989E-01
x6 : -6.45434621422677E-01 1.63609090637662E-01
x7 : 7.84543196066627E-02 5.72771916644424E-01
x8 : 1.64315636587197E+00 -1.19962014296412E+01
== err : 2.544E-14 = rco : 6.407E-03 = res : 7.324E-15 ==
solution 55 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.29969462856215E+00 -1.74673471603347E+00
x2 : -4.20773748026273E-01 -3.31929373917350E+00
x3 : -3.38353768926908E+00 -2.53211410631423E+00
x4 : -4.61693651227582E+00 1.30640300980813E+00
x5 : -1.24447235082902E+00 5.39838614687383E+00
x6 : 5.68044722330437E+00 4.57244839996384E+00
x7 : 1.68557844853368E+00 -3.67909499512460E+00
x8 : 7.20468376588420E-01 1.57255902314003E+00
== err : 7.598E-15 = rco : 7.502E-03 = res : 2.623E-14 ==
solution 56 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.26242193739885E-01 -8.80949696209057E-01
x2 : 6.84766851039934E-01 6.70954697940248E-01
x3 : 1.13659996275851E+00 -1.57144488632821E+00
x4 : -7.84742698629243E-01 1.09325148997073E+00
x5 : 3.30907349288984E+00 -1.25190184527914E+00
x6 : -3.43647190317998E+00 -6.13586232733104E-01
x7 : -2.23546789861895E+00 2.55367647263853E+00
x8 : -1.35852465730005E+00 -1.55190439414930E+00
== err : 4.252E-15 = rco : 3.791E-02 = res : 5.366E-15 ==
solution 57 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.10232923483155E+00 3.77219856182059E+00
x2 : -6.85329278634064E+00 4.52696695218433E+00
x3 : -9.05474845175679E+00 -8.09165852463592E+00
x4 : 7.45842856856864E+00 -1.19920978913958E+01
x5 : 1.17890209232269E+01 6.01022107632634E+00
x6 : -3.69235087552956E+00 6.86690951437450E+00
x7 : -1.74938661300016E+00 -1.09253968867405E+00
x8 : -2.87863572782532E+00 1.79778658331598E+00
== err : 4.882E-14 = rco : 1.241E-03 = res : 2.099E-13 ==
solution 58 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 5.30900663402972E-01 8.80949696209057E-01
x2 : -9.19755701091595E-01 -4.90660881263941E-01
x3 : 3.94673442417123E-01 -3.81947804965646E-02
x4 : -5.68975899878565E-01 5.29931641528690E-02
x5 : 1.58549846241612E-02 -2.82028740882827E-01
x6 : -2.58622538431232E-01 9.86421700170220E-02
x7 : -1.94074951042864E-01 -2.21700627735615E-01
x8 : -1.56482752903326E+01 1.78757353084697E+01
== err : 4.793E-14 = rco : 2.230E-03 = res : 5.467E-15 ==
solution 59 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.20465846966309E+00 -3.53737464016669E-73
x2 : -4.66632310578776E-01 9.90464899246672E-73
x3 : -8.03456596206655E-01 -2.47616224811668E-73
x4 : 4.34026212153150E-01 -1.37957610966501E-72
x5 : -9.72072018441767E-01 1.06121239205001E-72
x6 : 2.11190028135553E-01 -4.95232449623336E-73
x7 : -6.07713784724591E-01 -1.23808112405834E-73
x8 : -1.15185802526634E+01 1.65359972306943E-72
== err : 9.523E-15 = rco : 1.151E-02 = res : 3.553E-15 ==
solution 60 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.10232923483154E+00 -2.78729129753649E-01
x2 : 2.22603244673394E-01 1.42213055621695E+00
x3 : 6.18291929397411E-01 2.62969032904711E+00
x4 : -3.00295846715410E-01 -3.61318816677034E-01
x5 : -3.44882007007395E+00 -1.96100801887167E+00
x6 : 4.90913313990975E-01 5.87564109032905E-01
x7 : 3.14978193896038E-01 -2.03832902899461E+00
x8 : 5.18300229175783E-01 3.35409378597256E+00
== err : 4.436E-15 = rco : 1.854E-02 = res : 9.058E-15 ==
solution 61 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.42246399981436E-01 3.28268366607468E-71
x2 : 6.02075090022228E-01 -2.03752779273601E-71
x3 : 7.36634869861379E-01 -9.05567907882671E-72
x4 : 6.99788754004708E-02 1.13195988485334E-71
x5 : -5.55383048045472E-01 1.35835186182401E-71
x6 : -6.83628449696730E-01 1.47154785030934E-71
x7 : -4.27430937560439E-01 -1.13195988485334E-71
x8 : -1.63769146893121E+01 -1.44890865261227E-70
== err : 1.555E-14 = rco : 6.738E-03 = res : 3.553E-15 ==
solution 62 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 9.25631450864178E-01 -8.80949696209057E-01
x2 : 5.80275202596967E-01 1.42922913965630E-01
x3 : -1.39143724803458E-02 -9.04963714845271E-01
x4 : -2.34592954474775E+00 1.23892478112758E+00
x5 : 1.30179835264017E+00 2.67220218142479E-01
x6 : -7.00716863028764E-01 -7.16651272314106E-01
x7 : -7.47144225844456E-01 8.53496770132749E-01
x8 : -4.06472827578114E+00 -4.64332365136781E+00
== err : 4.766E-15 = rco : 1.699E-02 = res : 7.119E-15 ==
solution 63 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.44881006250832E-01 -2.02546384578712E+00
x2 : -9.69913074191903E-01 1.78394659173895E+00
x3 : 2.39780453489541E+00 -5.10525969081903E-01
x4 : -4.74509572712671E-01 -2.52319895744740E+00
x5 : -2.15522917066727E+00 7.48198344852689E-01
x6 : 4.65723570859317E-02 2.06539009186894E+00
x7 : 7.00155931841337E-01 4.61653743855839E-01
x8 : 6.96828567360206E+00 -4.59459817903020E+00
== err : 5.891E-15 = rco : 4.446E-03 = res : 2.275E-14 ==
solution 64 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.31206034840825E-01 8.65785019824411E-01
x2 : -7.80875281985147E-01 2.20760439208593E+00
x3 : -1.22835309328094E+00 -9.21433110771690E-01
x4 : -8.06469247698946E-01 -8.07711688026660E-01
x5 : 6.64340626635413E-01 -1.15785993336426E+00
x6 : 4.31688773993016E-01 -3.31850703822340E-01
x7 : 4.88462187495779E-01 1.45466024074603E-01
x8 : 1.31632748419528E+01 -3.92007673076369E+00
== err : 4.142E-14 = rco : 3.735E-03 = res : 1.845E-14 ==