3
6.89081434496698E-05*x2**6+ 6.44001340651120E-05*x2**5+
1.14590985880982E-05*x2**4+ 7.39296683103111E-07*x2**3-7.99985447950654E+00*x1**2*x3+
1.37415740353738E-08*x2**2+ 7.89745634216885E-11*x2+ 1.27997671672105E-13;
-1.81128150008056E-05*x2**5-6.44584163729738E-06*x2**4
-6.23791126190069E-07*x2**3+ 2.24999351824589E+00*x2*x1**2+ 6.74998055473766E+00*x1**2*x3
-1.54595074644379E-08*x2**2+ 7.28997899911668E-07*x2*x1-1.11059680060617E-10*x2
-2.15999377751605E-13;
-1.33333318933335E+00*x1**2+ 2.66666637866670E+00*x1*x3+
4.31999953344005E-07*x2+ 2.39999974080003E-16;
TITLE : problem pb 601 with every equation divided by average coefficient.
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.
NOTE :
---------------------------------------------------------------------
| TIMING INFORMATION SUMMARY on juno, Wed 5 Nov 1997 |
---------------------------------------------------------------------
| root counts | start system | continuation | total time |
---------------------------------------------------------------------
| 0h 0m 0s 34ms | 0h 0m 0s787ms | 0h 0m20s178ms | 0h 0m21s325ms |
---------------------------------------------------------------------
THE SOLUTIONS :
18 3
===========================================================================
solution : 1 : start residual : 7.213E-22
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -7.25805372901499E-01 2.49212288249311E-68
x1 : 1.13267128276082E-03 -8.71609111337071E-71
x3 : 6.70143755976064E-04 -1.58474383879467E-71
== err : 2.006E-15 = rco : 2.094E-03 = res : 7.213E-22 = real regular ==
solution : 2 : start residual : 3.078E+02
t : 8.18837546585981E-01 0.00000000000000E+00
m : 1
the solution for t :
x2 : 8.50815880957819E+00 -5.24548226861460E+00
x1 : -4.42445711781346E+00 9.20737715301611E-01
x3 : -2.21682655048735E+00 4.88171299800807E-01
== err : 1.553E-10 = rco : 7.740E-08 = res : 3.078E+02 = no solution ==
solution : 3 : start residual : 1.497E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.48030297185225E-05 4.12311836490762E-05
x1 : -1.58621604838585E-05 2.72212652443695E-05
x3 : -8.17846686445923E-06 1.36071825802625E-05
== err : 1.051E-19 = rco : 1.715E-05 = res : 1.497E-25 = complex regular ==
solution : 4 : start residual : 1.483E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.48030297185225E-05 -4.12311836490762E-05
x1 : -1.58621604838585E-05 -2.72212652443695E-05
x3 : -8.17846686445923E-06 -1.36071825802625E-05
== err : 9.233E-20 = rco : 1.715E-05 = res : 1.483E-25 = complex regular ==
solution : 5 : start residual : 3.211E+02
t : 8.19658881053935E-01 0.00000000000000E+00
m : 1
the solution for t :
x2 : -8.91587080020560E+00 -4.74347729342008E+00
x1 : 3.07046359583193E+00 3.35764905417576E+00
x3 : 1.56137493957089E+00 1.66863445256399E+00
== err : 5.570E-10 = rco : 8.152E-08 = res : 3.211E+02 = no solution ==
solution : 6 : start residual : 2.602E-29
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.79753388607537E-03 3.02700442741163E-04
x1 : -6.11915910154367E-07 1.47229329556450E-06
x3 : -1.37798440237791E-04 -2.49938473158386E-04
== err : 3.392E-17 = rco : 1.173E-08 = res : 2.602E-29 = complex regular ==
solution : 7 : start residual : 8.416E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -1.69467450435956E-02 -1.06169892227416E-03
x1 : -3.33252787010257E-08 -2.55931624735300E-06
x3 : -8.11742600306795E-05 1.07036125782306E-03
== err : 1.813E-16 = rco : 2.088E-08 = res : 8.416E-25 = complex regular ==
solution : 8 : start residual : 3.095E+02
t : 8.18800817136328E-01 0.00000000000000E+00
m : 1
the solution for t :
x2 : 2.69742739549773E-01 1.00222317934163E+01
x1 : 1.39018208048578E+00 -4.31043715863374E+00
x3 : 6.73139597211546E-01 -2.17300894722606E+00
== err : 3.312E-10 = rco : 9.523E-08 = res : 3.095E+02 = no solution ==
solution : 9 : start residual : 1.654E-24
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.12134388423492E-02 -3.29126160686788E-02
x1 : -1.56461412462451E-05 3.58863386679535E-06
x3 : -8.30790906178327E-04 -5.27740340761897E-04
== err : 2.532E-16 = rco : 7.540E-07 = res : 1.654E-24 = complex regular ==
solution : 10 : start residual : 2.524E-29
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -4.92207628089560E-03 -4.56516765330819E-45
x1 : -1.47535767566305E-06 -5.29207412598255E-49
x3 : -5.41200700556774E-04 -1.25897908904183E-45
== err : 1.034E-16 = rco : 6.382E-09 = res : 2.524E-29 = real singular ==
solution : 11 : start residual : 6.899E-22
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -7.24468371562951E-01 1.73768889747404E-63
x1 : -1.12504448363903E-03 5.74926953356550E-66
x3 : -6.66841562353025E-04 2.46662209020714E-66
== err : 2.081E-15 = rco : 2.076E-03 = res : 6.899E-22 = real regular ==
solution : 12 : start residual : 8.336E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -1.69467450435956E-02 1.06169892227416E-03
x1 : -3.33252787010254E-08 2.55931624735300E-06
x3 : -8.11742600306793E-05 -1.07036125782306E-03
== err : 1.755E-16 = rco : 2.088E-08 = res : 8.336E-25 = complex regular ==
solution : 13 : start residual : 1.654E-24
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.28516277142570E-02 -3.39881530129233E-02
x1 : 1.60131916619861E-05 -4.09845171837017E-06
x3 : 8.07010140554413E-04 5.46296064967122E-04
== err : 2.193E-16 = rco : 8.445E-07 = res : 1.654E-24 = complex regular ==
solution : 14 : start residual : 4.136E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -6.34684428050861E-03 -7.43028589405630E-49
x1 : 1.12082450749626E-06 4.69821921695894E-53
x3 : 9.17910699087857E-04 -2.24512235647744E-49
== err : 1.097E-16 = rco : 5.530E-09 = res : 4.136E-25 = real singular ==
solution : 15 : start residual : 6.617E-24
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.12134388423492E-02 3.29126160686787E-02
x1 : -1.56461412462451E-05 -3.58863386679535E-06
x3 : -8.30790906178328E-04 5.27740340761897E-04
== err : 2.260E-16 = rco : 7.540E-07 = res : 6.617E-24 = complex regular ==
solution : 16 : start residual : 2.132E-25
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.79753388607537E-03 -3.02700442741164E-04
x1 : -6.11915910154367E-07 -1.47229329556450E-06
x3 : -1.37798440237790E-04 2.49938473158385E-04
== err : 3.252E-17 = rco : 1.173E-08 = res : 2.132E-25 = complex regular ==
solution : 17 : start residual : 6.821E-24
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.28516277142570E-02 3.39881530129233E-02
x1 : 1.60131916619861E-05 4.09845171837017E-06
x3 : 8.07010140554413E-04 -5.46296064967122E-04
== err : 2.610E-16 = rco : 8.445E-07 = res : 6.821E-24 = complex regular ==
solution : 18 : start residual : 4.201E-26
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 4.66889844311746E-05 -3.50324616081204E-46
x1 : 3.22097501038582E-05 -2.73691106313441E-48
x3 : 1.58700484713607E-05 -2.05268329735081E-48
== err : 7.222E-20 = rco : 1.957E-05 = res : 4.201E-26 = real regular ==
===========================================================================
A list of 18 solutions has been refined :
Number of regular solutions : 13.
Number of singular solutions : 2.
Number of real solutions : 5.
Number of complex solutions : 10.
Number of clustered solutions : 0.
Number of failures : 3.
===========================================================================