3
1.25623491196412E-02*x2**6+ 5.62718762857620E-01*x2**5+
4.79909553837465E+00*x2**4+ 1.48399354804415E+01*x2**3-1.45832692729029E-01*x1**2*x3+
1.32206878780498E+01*x2**2+ 3.64174153281780E+00*x2+ 2.82896953297879E-01;
-1.00037203701072E-01*x2**5-1.70631629738197E+00*x2**4
-7.91449875082614E+00*x2**3+ 5.38347462575619E+00*x2*x1**2+ 7.77761241586725E-02*x1**2*x3
-9.40121946251430E+00*x2**2+ 1.92514482107687E-01*x2*x1-3.23704898069416E+00*x2
-3.01751660098453E-01;
-3.97516381945663E+00*x1**2+ 8.81655270550827E+01*x1*x3+
3.27346103274571E+02*x2+ 8.71643679865540E-06;
TITLE : problem pb 601, obtained after variable scaling
ROOT COUNTS :
total degree : 60
3-homogeneous Bezout number : 48
with partition : {x2 }{x1 }{x3 }
generalized Bezout number : 34
based on the set structure :
{x2 x1 }{x2 x1 }{x2 x3 }{x2 }{x2 }{x2 }
{x2 x3 }{x2 x1 }{x2 x1 }{x2 }{x2 }
{x2 x1 }{x1 x3 }
mixed volume : 18
REFERENCES :
L.T. Watson.
`Globally convergent homotopy methods: a tutorial.
Appl. Math. Comput., 31(Spec. Issue):369--396, 1989.
SCALING COEFFICIENTS :
2
-5.58284669093836E+00 -0.00000000000000E+00
-1.67520041104278E+01 0.00000000000000E+00
-1.32808756630858E+01 0.00000000000000E+00
-1.82165145539501E+00 0.00000000000000E+00
-4.31352888756371E+00 0.00000000000000E+00
-1.68078300746298E+01 0.00000000000000E+00
THE SOLUTIONS :
18 3
===========================================================================
== 1 = #step : 114 #fail : 23 #iter : 394 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 1.51417056266106E+02
the solution for t :
x2 : -3.47876021004140E+01 4.17619485951906E-53
x1 : 1.25014277263060E+02 -3.34095588761525E-52
x3 : 6.66975557480272E+00 1.04404871487976E-53
== err : 1.025E-14 = rco : 1.559E-02 = res : 4.329E-10 ==
== 2 = #step : 2256 #fail : 408 #iter : 6008 = regular solution ==
t : 8.18837546585981E-01 0.00000000000000E+00
m : 1 Length of path : 3.59940345549310E+03
the solution for t :
x2 : 4.07793127917372E+02 -2.51414162526606E+02
x1 : -4.88332596829551E+05 1.01622917239244E+05
x3 : -2.20634619238498E+04 4.85863401586538E+03
== err : 1.553E-10 = rco : 7.740E-08 = res : 2.519E-01 ==
== 3 = #step : 34 #fail : 1 #iter : 108 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 3.88580115711918E+01
the solution for t :
x2 : -1.18880069085656E-03 1.97619646321882E-03
x1 : -1.75072552725694E+00 3.00444343606573E+00
x3 : -8.13980201652647E-02 1.35428527182017E-01
== err : 5.787E-16 = rco : 5.508E-04 = res : 4.002E-15 ==
== 4 = #step : 31 #fail : 0 #iter : 98 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 3.44567006862109E+01
the solution for t :
x2 : -1.18880069085656E-03 -1.97619646321882E-03
x1 : -1.75072552725694E+00 -3.00444343606573E+00
x3 : -8.13980201652647E-02 -1.35428527182017E-01
== err : 6.153E-17 = rco : 5.508E-04 = res : 2.397E-15 ==
== 5 = #step : 2257 #fail : 409 #iter : 6007 = regular solution ==
t : 8.19658881053935E-01 0.00000000000000E+00
m : 1 Length of path : 3.59691763617562E+03
the solution for t :
x2 : -4.27334623518065E+02 -2.27353236579361E+02
x1 : 3.38890720668619E+05 3.70587721432870E+05
x3 : 1.55399332079013E+04 1.66074574940813E+04
== err : 5.570E-10 = rco : 8.152E-08 = res : 2.253E-01 ==
== 6 = #step : 52 #fail : 8 #iter : 179 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 6.54738725451108E+01
the solution for t :
x2 : -1.34084837788082E-01 1.45083281976863E-02
x1 : -6.75378871328467E-02 1.62498762938185E-01
x3 : -1.37146978805544E+00 -2.48756854009304E+00
== err : 7.053E-15 = rco : 3.199E-05 = res : 1.776E-15 ==
== 7 = #step : 44 #fail : 5 #iter : 151 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 5.57039072442433E+01
the solution for t :
x2 : -8.12251666196718E-01 -5.08868644921481E-02
x1 : -3.67815066454638E-03 -2.82474779594114E-01
x3 : -8.07904973435950E-01 1.06530097501544E+01
== err : 7.324E-15 = rco : 7.128E-05 = res : 7.105E-15 ==
== 8 = #step : 2256 #fail : 410 #iter : 6006 = regular solution ==
t : 8.18800817136328E-01 0.00000000000000E+00
m : 1 Length of path : 3.60102551350054E+03
the solution for t :
x2 : 1.29286768096253E+01 4.80362125722100E+02
x1 : 1.53436050424424E+05 -4.75748078260604E+05
x3 : 6.69957235456581E+03 -2.16273574298210E+04
== err : 3.312E-10 = rco : 9.523E-08 = res : 1.250E-01 ==
== 9 = #step : 58 #fail : 8 #iter : 189 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 7.80037872308306E+01
the solution for t :
x2 : -4.37182877824838E+00 -1.57749037776311E+00
x1 : -1.72688322695659E+00 3.96081790054435E-01
x3 : -8.26863225772740E+00 -5.25245374362730E+00
== err : 5.205E-15 = rco : 1.465E-02 = res : 3.216E-13 ==
== 10 = #step : 31 #fail : 0 #iter : 106 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 4.10343141813164E+01
the solution for t :
x2 : -2.35913424673580E-01 2.13238963442555E-30
x1 : -1.62836982216020E-01 -3.74708929979981E-30
x3 : -5.38642098420832E+00 5.04870979341448E-28
== err : 4.885E-14 = rco : 2.276E-05 = res : 1.421E-14 ==
== 11 = #step : 113 #fail : 21 #iter : 361 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 1.59798310617040E+02
the solution for t :
x2 : -3.47235200857174E+01 2.73691106313441E-48
x1 : -1.24172498368731E+02 1.91583774419409E-47
x3 : -6.63688975440234E+00 8.55284707229503E-49
== err : 5.768E-15 = rco : 1.563E-02 = res : 5.002E-10 ==
== 12 = #step : 127 #fail : 24 #iter : 314 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 1.93118414758458E+02
the solution for t :
x2 : -8.12251666196717E-01 5.08868644921481E-02
x1 : -3.67815066454634E-03 2.82474779594114E-01
x3 : -8.07904973435948E-01 -1.06530097501544E+01
== err : 3.222E-15 = rco : 7.128E-05 = res : 3.553E-15 ==
== 13 = #step : 54 #fail : 6 #iter : 179 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 6.51956233418061E+01
the solution for t :
x2 : -4.45034660791591E+00 -1.62904049389287E+00
x1 : 1.76739501810143E+00 -4.52350992973645E-01
x3 : 8.03194887050077E+00 5.43713373782053E+00
== err : 1.833E-14 = rco : 1.579E-02 = res : 1.019E-13 ==
== 14 = #step : 31 #fail : 0 #iter : 111 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 4.33745778684609E+01
the solution for t :
x2 : -3.04202065274022E-01 8.66668474974256E-34
x1 : 1.23706734580432E-01 1.30150734523044E-33
x3 : 9.13571147655490E+00 -4.19082355898663E-31
== err : 1.529E-14 = rco : 8.890E-06 = res : 1.110E-16 ==
== 15 = #step : 108 #fail : 18 #iter : 352 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 1.36394843947802E+02
the solution for t :
x2 : -4.37182877824838E+00 1.57749037776311E+00
x1 : -1.72688322695660E+00 -3.96081790054435E-01
x3 : -8.26863225772739E+00 5.25245374362729E+00
== err : 8.617E-15 = rco : 1.465E-02 = res : 1.922E-13 ==
== 16 = #step : 39 #fail : 3 #iter : 125 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 5.39353043865107E+01
the solution for t :
x2 : -1.34084837788082E-01 -1.45083281976863E-02
x1 : -6.75378871328466E-02 -1.62498762938185E-01
x3 : -1.37146978805544E+00 2.48756854009303E+00
== err : 1.546E-14 = rco : 3.199E-05 = res : 2.139E-14 ==
== 17 = #step : 90 #fail : 13 #iter : 306 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 1.15672043218905E+02
the solution for t :
x2 : -4.45034660791591E+00 1.62904049389287E+00
x1 : 1.76739501810143E+00 4.52350992973644E-01
x3 : 8.03194887050078E+00 -5.43713373782052E+00
== err : 1.114E-14 = rco : 1.579E-02 = res : 4.547E-13 ==
== 18 = #step : 52 #fail : 8 #iter : 161 = regular solution ==
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1 Length of path : 5.94247475902365E+01
the solution for t :
x2 : 2.23778697913352E-03 -6.35033028702915E-29
x1 : 3.55502844589014E+00 -1.96268593218988E-27
x3 : 1.57950205937646E-01 3.90486148084401E-29
== err : 6.120E-14 = rco : 6.899E-04 = res : 3.442E-15 ==
== #regu : 18 = #sing : 0 = #clus : 0 = #infi : 0 = #fail : 0 ==