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 ==