```8
x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 - 1*u8;
x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6 + x5*x7 - 2*u8;
x3 + x1*x4 + x2*x5 + x3*x6 + x4*x7 - 3*u8;
x4 + x1*x5 + x2*x6 + x3*x7 - 4*u8;
x5 + x1*x6 + x2*x7 - 5*u8;
x6 + x1*x7 - 6*u8;
x7 - 7*u8;
x1 + x2 + x3 + x4 + x5 + x6 + x7 + 1;

TITLE : reduced 8-dimensional economics problem

ROOT COUNTS :

total degree : 64
2-homogeneous Bezout number : 144
with partition : {x1 x2 x3 x4 x5 x6 }{x7 u8 }
generalized Bezout number : 64
based on the set structure :
{x1 x3 x5 x7 u8 }{x2 x4 x6 }
{x1 x2 x5 x6 u8 }{x3 x4 x7 }
{x1 x2 x3 x7 u8 }{x4 x5 x6 }
{x1 x2 x3 x4 u8 }{x5 x6 x7 }
{x1 x2 x5 u8 }{x6 x7 }
{x1 x6 u8 }{x7 }
{x7 u8 }
{x1 x2 x3 x4 x5 x6 x7 }
mixed volume : 64

REFERENCE :

This is the reduced economics problem (u8 = 1/x8).

Alexander Morgan:
`Solving polynomial systems using continuation for engineering
and scientific problems', Prentice-Hall, Englewood Cliffs, New Jersey, 1987,
(p 148).

THE SOLUTIONS :

64 8
===========================================================
solution 1 :
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
u8 :  4.49968848422911E-02   2.91189861284945E-01
== err :  4.433E-15 = rco :  1.581E-02 = res :  1.404E-15 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.59938925712429E+00  -9.49556774575980E-66
x2 :  1.29935154253298E+00   8.54601097118382E-65
x3 : -1.63719724641073E-01  -7.59645419660784E-65
x4 : -1.72340091727033E+00   9.06436552777519E-65
x5 : -1.40859034083628E+00  -1.70920219423676E-64
x6 :  1.73652942442072E+00   1.75668003296556E-64
x7 : -2.33955924133030E+00  -5.22256226016789E-65
u8 : -3.34222748761472E-01  -8.30862177753982E-66
== err :  4.024E-15 = rco :  2.462E-02 = res :  8.882E-16 ==
solution 3 :
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  -9.02740445142473E-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
u8 :  1.47034362569065E-02   3.20930412885720E-02
== err :  2.370E-15 = rco :  1.139E-02 = res :  3.886E-16 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  8.02634606269397E-01  -2.02546384578712E+00
x2 : -1.83542167444223E+00  -9.45397563054456E-01
x3 :  6.75509155081996E-01   2.15925850374478E+00
x4 :  3.83025063947650E+00  -2.45922649501807E+00
x5 : -3.63602971348938E+00  -4.83285613744496E+00
x6 : -3.81540389155297E+00   6.13981213018346E+00
x7 :  2.97846087865670E+00   1.96387340737636E+00
u8 :  4.25494411236671E-01   2.80553343910909E-01
== err :  9.967E-15 = rco :  1.225E-02 = res :  6.866E-15 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  6.05269212538794E-01  -5.62420859578400E-58
x2 : -5.29386459651293E-01  -1.75240110224570E-57
x3 :  1.15852681899207E+00   2.70825624892517E-57
x4 :  2.02601496566939E+00   2.23032867558543E-57
x5 : -1.98415557208050E+00  -3.18618382226491E-58
x6 : -4.57979256055826E-01  -1.75240110224570E-57
x7 : -1.81828970941264E+00   2.38963786669868E-58
u8 : -2.59755672773234E-01   3.98272977783113E-59
== err :  4.352E-15 = rco :  2.181E-02 = res :  1.665E-15 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.44881006250833E-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  -7.48198344852690E-01
x6 :  4.65723570859319E-02  -2.06539009186894E+00
x7 :  7.00155931841337E-01  -4.61653743855839E-01
u8 :  1.00022275977334E-01  -6.59505348365484E-02
== err :  3.259E-15 = rco :  1.310E-02 = res :  1.256E-15 ==
solution 7 :
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 : -1.24447235082902E+00   5.39838614687383E+00
x6 :  5.68044722330437E+00   4.57244839996384E+00
x7 :  1.68557844853368E+00  -3.67909499512461E+00
u8 :  2.40796921219097E-01  -5.25584999303515E-01
== err :  8.113E-15 = rco :  8.102E-03 = res :  1.648E-14 ==
solution 8 :
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 : -2.39559793877656E+00   7.76678777389887E-01
x4 : -4.81852275273735E+00  -3.11114097537514E+00
x5 :  4.35149002787906E+00  -6.34471360742584E+00
x6 :  4.51728801087618E+00   2.52616678400144E+00
x7 : -8.03880259621558E-01   1.78984582633967E+00
u8 : -1.14840037088794E-01   2.55692260905667E-01
== err :  9.115E-15 = rco :  7.030E-03 = res :  7.589E-15 ==
solution 9 :
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   9.21433110771691E-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
u8 :  6.97803124993970E-02  -2.07808605820862E-02
== err :  4.851E-15 = rco :  1.240E-02 = res :  7.109E-16 ==
solution 10 :
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   8.17101815054366E-02
x5 : -2.62049660027996E-01  -1.00268202683989E-01
x6 : -6.45434621422677E-01   1.63609090637662E-01
x7 :  7.84543196066627E-02   5.72771916644424E-01
u8 :  1.12077599438090E-02   8.18245595206320E-02
== err :  4.304E-15 = rco :  1.681E-02 = res :  4.965E-16 ==
solution 11 :
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   6.13586232733105E-01
x7 : -2.23546789861895E+00  -2.55367647263853E+00
u8 : -3.19352556945564E-01  -3.64810924662647E-01
== err :  3.664E-15 = rco :  3.115E-02 = res :  1.332E-15 ==
solution 12 :
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 : -1.39143724803459E-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
u8 : -1.06734889406351E-01  -1.21928110018964E-01
== err :  4.787E-15 = rco :  1.768E-02 = res :  8.083E-16 ==
solution 13 :
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  -5.20777980807649E-01
x6 : -1.79045246708362E+00   1.51672028949352E+00
x7 :  2.34736623695995E-01   1.71374306137731E+00
u8 :  3.35338033851422E-02   2.44820437339616E-01
== err :  6.468E-15 = rco :  2.466E-02 = res :  2.558E-15 ==
solution 14 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.28571428571429E-01   2.89124886561153E+00
x2 : -3.91435387900100E+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
u8 : -1.36748786000537E-01   4.13271435340681E-02
== err :  6.086E-15 = rco :  6.062E-03 = res :  9.566E-15 ==
solution 15 :
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   5.20777980807650E-01
x6 : -1.79045246708362E+00  -1.51672028949352E+00
x7 :  2.34736623695995E-01  -1.71374306137731E+00
u8 :  3.35338033851422E-02  -2.44820437339616E-01
== err :  6.499E-15 = rco :  2.466E-02 = res :  1.601E-15 ==
solution 16 :
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  -7.46802772179367E-01
x5 :  3.04264868472102E-01   1.06492430997778E+01
x6 : -4.66174043546156E+00   3.21929018534662E-01
x7 : -1.60100673892121E-01  -9.87100691023610E-01
u8 : -2.28715248417316E-02  -1.41014384431944E-01
== err :  4.217E-14 = rco :  1.685E-03 = res :  3.623E-14 ==
solution 17 :
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 :  3.89841694187333E-02   7.38121476848058E-01
x7 :  8.44193789437036E-01   5.36038101142015E-01
u8 :  1.20599112776719E-01   7.65768715917164E-02
== err :  4.254E-15 = rco :  1.976E-02 = res :  4.996E-16 ==
solution 18 :
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 : -1.39143724803459E-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
u8 : -1.06734889406351E-01   1.21928110018964E-01
== err :  4.835E-15 = rco :  1.768E-02 = res :  1.790E-15 ==
solution 19 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  3.26242193739885E-01  -8.80949696209057E-01
x2 :  6.84766851039935E-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
u8 : -3.19352556945564E-01   3.64810924662647E-01
== err :  3.549E-15 = rco :  3.115E-02 = res :  1.144E-15 ==
solution 20 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.29969462856215E+00   1.74673471603347E+00
x2 : -4.20773748026274E-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
u8 :  2.40796921219097E-01   5.25584999303515E-01
== err :  6.897E-15 = rco :  8.102E-03 = res :  6.169E-15 ==
solution 21 :
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
u8 : -8.29536382812477E-02   9.47617071707717E-02
== err :  5.026E-15 = rco :  2.188E-02 = res :  4.965E-16 ==
solution 22 :
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 : -4.40272194011276E-01   2.88988515225427E+00
x4 :  8.61326214993982E-01   9.51587434171055E-01
x5 :  1.32403203819477E+00   7.89090697380827E-01
x6 :  1.09096648052896E+00  -8.39705419198962E-01
x7 : -2.08812457667120E-01  -4.64922606781227E-01
u8 : -2.98303510953029E-02  -6.64175152544610E-02
== err :  4.229E-15 = rco :  7.496E-03 = res :  9.930E-16 ==
solution 23 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.78209839580828E-02  -1.74673471603347E+00
x2 : -2.25061288175076E-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  -9.05476876953007E-02
x7 :  3.96234094522347E-01  -8.64856142010510E-01
u8 :  5.66048706460496E-02  -1.23550877430073E-01
== err :  7.552E-15 = rco :  1.297E-02 = res :  1.986E-15 ==
solution 24 :
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 : -4.40272194011275E-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
u8 : -2.98303510953029E-02   6.64175152544610E-02
== err :  4.120E-15 = rco :  7.496E-03 = res :  1.422E-15 ==
solution 25 :
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  -4.01056041665407E-01
x5 : -5.75373719029586E-01  -6.19660927472803E-02
x6 : -1.24696364116086E-01   5.97817478504557E-01
x7 :  2.34008040101661E-01   1.54295183247523E-01
u8 :  3.34297200145231E-02   2.20421690353605E-02
== err :  3.726E-15 = rco :  1.100E-02 = res :  1.351E-15 ==
solution 26 :
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 :  2.05412340337164E-01   2.41248718888364E+00
x6 : -1.87186842960293E+00  -1.65864305998415E+00
x7 :  9.95469381943151E-01  -6.56371168432886E-01
u8 :  1.42209911706164E-01  -9.37673097761265E-02
== err :  5.628E-15 = rco :  8.538E-03 = res :  2.512E-15 ==
solution 27 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.20465846966309E+00   5.34125685698989E-66
x2 : -4.66632310578776E-01   3.56083790465993E-66
x3 : -8.03456596206656E-01  -1.36498786345297E-65
x4 :  4.34026212153150E-01   5.34125685698989E-66
x5 : -9.72072018441767E-01  -1.78041895232996E-66
x6 :  2.11190028135553E-01   5.04452036493489E-66
x7 : -6.07713784724591E-01  -6.08309808712737E-66
u8 : -8.68162549606558E-02  -8.53117414658107E-67
== err :  3.422E-15 = rco :  1.354E-02 = res :  1.110E-16 ==
solution 28 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  7.28266057133575E-01  -2.90641354199617E+00
x2 : -4.02480045349249E+00  -4.77974857901421E-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 :  5.57357065362469E-01  -1.53544294755645E-01
u8 :  7.96224379089241E-02  -2.19348992508065E-02
== err :  5.657E-15 = rco :  7.312E-03 = res :  1.986E-15 ==
solution 29 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688687E-01   3.77219856182058E+00
x2 : -6.39162737706625E+00  -5.56129503395274E-01
x3 :  1.27333920069005E-02  -6.84707775070627E+00
x4 :  5.80177107600898E+00  -1.00206172064427E+00
x5 :  1.65565900260799E+00   3.62174951858024E+00
x6 : -1.42211604046533E+00   1.26814754910442E+00
x7 : -4.11233675403619E-01  -2.56826654759425E-01
u8 : -5.87476679148026E-02  -3.66895221084893E-02
== err :  5.730E-15 = rco :  7.937E-03 = res :  4.190E-15 ==
solution 30 :
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  -9.86421700170221E-02
x7 : -1.94074951042864E-01   2.21700627735615E-01
u8 : -2.77249930061235E-02   3.16715182479450E-02
== err :  6.031E-16 = rco :  1.322E-02 = res :  1.570E-16 ==
solution 31 :
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   9.02740445142472E-01
x4 :  2.20595282770167E-01   1.02073155184390E+00
x5 :  7.02375877262567E-01   4.36162532263086E-01
x6 :  5.26176045404461E-01  -1.12197055754395E-01
x7 :  1.02924053798346E-01  -2.24651289020004E-01
u8 :  1.47034362569065E-02  -3.20930412885720E-02
== err :  2.550E-15 = rco :  1.139E-02 = res :  7.448E-16 ==
solution 32 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.10232923483154E+00   3.77219856182058E+00
x2 : -6.85329278634063E+00   4.52696695218432E+00
x3 : -9.05474845175677E+00  -8.09165852463591E+00
x4 :  7.45842856856864E+00  -1.19920978913958E+01
x5 :  1.17890209232269E+01   6.01022107632633E+00
x6 : -3.69235087552954E+00   6.86690951437449E+00
x7 : -1.74938661300016E+00  -1.09253968867404E+00
u8 : -2.49912373285737E-01  -1.56077098382006E-01
== err :  3.985E-14 = rco :  1.746E-03 = res :  3.370E-14 ==
solution 33 :
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   9.86421700170221E-02
x7 : -1.94074951042864E-01  -2.21700627735615E-01
u8 : -2.77249930061235E-02  -3.16715182479450E-02
== err :  6.031E-16 = rco :  1.322E-02 = res :  1.570E-16 ==
solution 34 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.42246399981436E-01  -7.59645419660784E-65
x2 :  6.02075090022228E-01  -2.30743190993074E-64
x3 :  7.36634869861379E-01   0.00000000000000E+00
x4 :  6.99788754004707E-02  -7.59645419660784E-65
x5 : -5.55383048045472E-01  -5.73712372484625E-66
x6 : -6.83628449696730E-01   2.37389193643995E-65
x7 : -4.27430937560439E-01   8.22262865703340E-65
u8 : -6.10615625086341E-02   1.30564056504197E-65
== err :  4.129E-16 = rco :  1.874E-02 = res :  1.110E-16 ==
solution 35 :
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 : -1.72418225308742E+00   1.52950278479316E+01
x4 :  1.53737752985507E+01   7.46802772179362E-01
x5 :  3.04264868472096E-01  -1.06492430997778E+01
x6 : -4.66174043546156E+00  -3.21929018534659E-01
x7 : -1.60100673892121E-01   9.87100691023611E-01
u8 : -2.28715248417315E-02   1.41014384431944E-01
== err :  4.252E-14 = rco :  1.685E-03 = res :  2.848E-14 ==
solution 36 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.28571428571429E-01  -1.15967882596271E+00
x2 : -4.07121367244140E-01   2.19073427282266E+00
x3 :  3.00074302117930E+00   8.43795237846108E-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
u8 : -9.18593723187780E-02  -1.09407581924226E-01
== err :  4.551E-15 = rco :  1.926E-02 = res :  2.716E-15 ==
solution 37 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.44881006250832E-01  -2.02546384578712E+00
x2 : -9.69913074191904E-01   1.78394659173895E+00
x3 :  2.39780453489541E+00  -5.10525969081903E-01
x4 : -4.74509572712672E-01  -2.52319895744740E+00
x5 : -2.15522917066727E+00   7.48198344852689E-01
x6 :  4.65723570859318E-02   2.06539009186894E+00
x7 :  7.00155931841337E-01   4.61653743855839E-01
u8 :  1.00022275977334E-01   6.59505348365485E-02
== err :  3.284E-15 = rco :  1.310E-02 = res :  2.220E-15 ==
solution 38 :
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   7.60055778523488E-01
x4 :  2.57343272529546E-01   3.12382515229319E+00
x5 :  8.24194415747985E-01   6.37834651815019E-01
x6 :  1.64835675125572E+00   8.10488698284777E-01
x7 :  4.37838563910930E-01  -9.55665795655232E-01
u8 :  6.25483662729900E-02  -1.36523685093605E-01
== err :  4.829E-15 = rco :  9.352E-03 = res :  1.986E-15 ==
solution 39 :
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 :  2.05412340337164E-01  -2.41248718888364E+00
x6 : -1.87186842960293E+00   1.65864305998415E+00
x7 :  9.95469381943151E-01   6.56371168432886E-01
u8 :  1.42209911706164E-01   9.37673097761265E-02
== err :  5.353E-15 = rco :  8.538E-03 = res :  1.422E-15 ==
solution 40 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.00000000000000E+00   0.00000000000000E+00
x2 :  1.00000000000000E+00   6.22301527786114E-61
x3 :  1.00000000000000E+00   6.22301527786114E-61
x4 :  1.00000000000000E+00   0.00000000000000E+00
x5 :  1.00000000000000E+00   3.11150763893057E-61
x6 :  1.00000000000000E+00   1.24460305557223E-60
x7 : -7.00000000000000E+00   7.46761833343337E-60
u8 : -1.00000000000000E+00   1.24460305557223E-60
== err :  1.682E-44 = rco :  3.878E-02 = res :  1.027E-59 ==
solution 41 :
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   4.01056041665407E-01
x5 : -5.75373719029586E-01   6.19660927472802E-02
x6 : -1.24696364116086E-01  -5.97817478504557E-01
x7 :  2.34008040101661E-01  -1.54295183247523E-01
u8 :  3.34297200145230E-02  -2.20421690353604E-02
== err :  3.708E-15 = rco :  1.100E-02 = res :  4.965E-16 ==
solution 42 :
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 :  4.26163040031265E-01  -2.89160483738685E+00
x7 : -9.57241502003759E-01  -2.89290004738477E-01
u8 : -1.36748786000537E-01  -4.13271435340682E-02
== err :  5.207E-15 = rco :  6.062E-03 = res :  7.589E-15 ==
solution 43 :
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   4.90968316930756E-01
x5 : -6.64940564102784E-01   2.11960393271641E-01
x6 :  2.15174448159515E-01   5.07550037830726E-01
x7 :  7.40428898822547E-02   4.79156255138937E-01
u8 :  1.05775556974650E-02   6.84508935912767E-02
== err :  3.429E-15 = rco :  1.750E-02 = res :  3.414E-16 ==
solution 44 :
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 : -1.41431539654746E-02  -7.74678341483025E+00
x5 : -6.49225902486156E+00   2.64610297939909E+00
x6 :  2.54969912472744E+00   4.51222733924665E+00
x7 :  1.66762157102670E+00  -4.59407073051232E-01
u8 :  2.38231653003815E-01  -6.56295818644618E-02
== err :  1.053E-14 = rco :  7.991E-03 = res :  1.353E-14 ==
solution 45 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.28571428571429E-01   6.02220566455408E-01
x2 :  8.39713171180438E-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 :  3.89841694187332E-02  -7.38121476848058E-01
x7 :  8.44193789437036E-01  -5.36038101142015E-01
u8 :  1.20599112776719E-01  -7.65768715917164E-02
== err :  4.267E-15 = rco :  1.976E-02 = res :  1.404E-15 ==
solution 46 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.28571428571429E-01   1.15967882596271E+00
x2 : -4.07121367244140E-01  -2.19073427282266E+00
x3 :  3.00074302117930E+00  -8.43795237846108E-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
u8 : -9.18593723187780E-02   1.09407581924226E-01
== err :  4.624E-15 = rco :  1.926E-02 = res :  2.036E-15 ==
solution 47 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.78209839580827E-02   1.74673471603347E+00
x2 : -2.25061288175076E-01   9.65541438387309E-01
x3 : -2.59969119095552E+00   1.46033094051729E+00
x4 : -1.84772040826661E+00  -2.29707362139904E+00
x5 :  1.45480800105433E+00  -2.83093730324484E+00
x6 :  1.86925177577862E+00   9.05476876953012E-02
x7 :  3.96234094522347E-01   8.64856142010510E-01
u8 :  5.66048706460496E-02   1.23550877430073E-01
== err :  6.110E-15 = rco :  1.297E-02 = res :  1.570E-15 ==
solution 48 :
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   1.20777100078736E-01
x6 :  5.18093612620539E-01  -1.60012182512894E+00
x7 :  5.57357065362469E-01   1.53544294755645E-01
u8 :  7.96224379089241E-02   2.19348992508065E-02
== err :  4.840E-15 = rco :  7.312E-03 = res :  4.832E-15 ==
solution 49 :
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  -9.21433110771691E-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
u8 :  6.97803124993970E-02   2.07808605820862E-02
== err :  5.056E-15 = rco :  1.240E-02 = res :  8.083E-16 ==
solution 50 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.47515612520229E-01  -8.50802870020078E-63
x2 :  1.59955565082714E+00  -5.34790375441192E-62
x3 : -7.14195108063651E-01   4.37555761724612E-62
x4 :  1.32209704041973E+00  -5.83407682299482E-62
x5 :  7.67848816841054E-01  -4.86173068582902E-62
x6 : -1.98227932283785E+00   6.32024989157772E-62
x7 : -1.64551146466620E+00   5.96029807057353E-62
u8 : -2.35073066380886E-01   8.51471152939075E-63
== err :  3.010E-15 = rco :  2.503E-02 = res :  6.661E-16 ==
solution 51 :
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 :  9.19624613112194E-01  -1.49860296754324E+00
x7 :  1.88046783456469E+00   5.60010961537670E-01
u8 :  2.68638262080670E-01   8.00015659339528E-02
== err :  3.866E-15 = rco :  1.425E-02 = res :  1.422E-15 ==
solution 52 :
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
u8 :  4.49968848422911E-02  -2.91189861284945E-01
== err :  4.469E-15 = rco :  1.581E-02 = res :  1.831E-15 ==
solution 53 :
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  -8.17101815054366E-02
x5 : -2.62049660027996E-01   1.00268202683989E-01
x6 : -6.45434621422677E-01  -1.63609090637662E-01
x7 :  7.84543196066627E-02  -5.72771916644424E-01
u8 :  1.12077599438090E-02  -8.18245595206320E-02
== err :  4.300E-15 = rco :  1.681E-02 = res :  4.578E-16 ==
solution 54 :
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  -3.12382515229319E+00
x5 :  8.24194415747984E-01  -6.37834651815019E-01
x6 :  1.64835675125572E+00  -8.10488698284777E-01
x7 :  4.37838563910930E-01   9.55665795655231E-01
u8 :  6.25483662729900E-02   1.36523685093604E-01
== err :  4.319E-15 = rco :  9.352E-03 = res :  1.422E-15 ==
solution 55 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  2.51873644604064E-01   0.00000000000000E+00
x2 :  1.09122081140823E+00   1.02389830887948E-57
x3 : -1.11424211179409E+00  -1.14702617601537E-56
x4 : -6.37151941736669E-01  -4.26735858928732E-57
x5 :  2.91145276196003E-01  -3.18618382226490E-57
x6 : -3.32878313838290E-01   7.64684117343577E-57
x7 : -5.49967364839252E-01   9.55855146679471E-57
u8 : -7.85667664056075E-02   1.47361001779752E-57
== err :  5.036E-15 = rco :  1.868E-02 = res :  4.441E-16 ==
solution 56 :
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 :  9.19624613112194E-01   1.49860296754324E+00
x7 :  1.88046783456469E+00  -5.60010961537670E-01
u8 :  2.68638262080670E-01  -8.00015659339528E-02
== err :  3.866E-15 = rco :  1.425E-02 = res :  1.422E-15 ==
solution 57 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.42857142857143E-01   6.37236764452981E-58
x2 : -1.42857142857143E-01   4.46065735117087E-57
x3 : -1.42857142857143E-01  -7.64684117343577E-57
x4 : -1.42857142857143E-01  -1.59309191113245E-58
x5 : -1.42857142857143E-01  -6.07399628701094E-58
x6 : -1.42857142857143E-01   6.37236764452981E-58
x7 : -1.42857142857143E-01   1.11516433779272E-57
u8 : -2.04081632653061E-02   1.59309191113245E-58
== err :  1.683E-16 = rco :  3.636E-02 = res :  5.551E-17 ==
solution 58 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.10232923483154E+00  -3.77219856182058E+00
x2 : -6.85329278634064E+00  -4.52696695218432E+00
x3 : -9.05474845175676E+00   8.09165852463593E+00
x4 :  7.45842856856866E+00   1.19920978913958E+01
x5 :  1.17890209232269E+01  -6.01022107632635E+00
x6 : -3.69235087552956E+00  -6.86690951437448E+00
x7 : -1.74938661300015E+00   1.09253968867404E+00
u8 : -2.49912373285736E-01   1.56077098382006E-01
== err :  4.490E-14 = rco :  1.746E-03 = res :  3.843E-14 ==
solution 59 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.45186377688685E-01  -3.77219856182058E+00
x2 : -6.39162737706625E+00   5.56129503395272E-01
x3 :  1.27333920069007E-02   6.84707775070628E+00
x4 :  5.80177107600899E+00   1.00206172064427E+00
x5 :  1.65565900260799E+00  -3.62174951858024E+00
x6 : -1.42211604046533E+00  -1.26814754910442E+00
x7 : -4.11233675403618E-01   2.56826654759426E-01
u8 : -5.87476679148026E-02   3.66895221084894E-02
== err :  1.124E-14 = rco :  7.937E-03 = res :  7.192E-15 ==
solution 60 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  8.02634606269397E-01   2.02546384578712E+00
x2 : -1.83542167444223E+00   9.45397563054456E-01
x3 :  6.75509155081997E-01  -2.15925850374478E+00
x4 :  3.83025063947650E+00   2.45922649501808E+00
x5 : -3.63602971348939E+00   4.83285613744497E+00
x6 : -3.81540389155297E+00  -6.13981213018347E+00
x7 :  2.97846087865670E+00  -1.96387340737636E+00
u8 :  4.25494411236672E-01  -2.80553343910909E-01
== err :  1.273E-14 = rco :  1.225E-02 = res :  4.023E-15 ==
solution 61 :
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  -4.90968316930756E-01
x5 : -6.64940564102784E-01  -2.11960393271642E-01
x6 :  2.15174448159515E-01  -5.07550037830726E-01
x7 :  7.40428898822547E-02  -4.79156255138937E-01
u8 :  1.05775556974650E-02  -6.84508935912767E-02
== err :  3.473E-15 = rco :  1.750E-02 = res :  3.511E-16 ==
solution 62 :
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   6.34471360742584E+00
x6 :  4.51728801087618E+00  -2.52616678400144E+00
x7 : -8.03880259621558E-01  -1.78984582633967E+00
u8 : -1.14840037088794E-01  -2.55692260905667E-01
== err :  8.496E-15 = rco :  7.030E-03 = res :  1.070E-14 ==
solution 63 :
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 : -1.41431539654805E-02   7.74678341483025E+00
x5 : -6.49225902486156E+00  -2.64610297939909E+00
x6 :  2.54969912472744E+00  -4.51222733924664E+00
x7 :  1.66762157102670E+00   4.59407073051233E-01
u8 :  2.38231653003815E-01   6.56295818644619E-02
== err :  7.782E-15 = rco :  7.991E-03 = res :  1.638E-14 ==
solution 64 :
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 : -1.12185355590754E+00  -1.02455038360827E-01
x7 : -5.80675467968734E-01  -6.63331950195402E-01
u8 : -8.29536382812477E-02  -9.47617071707717E-02
== err :  4.976E-15 = rco :  2.188E-02 = res :  2.776E-16 ==
```