10
x2 + 2*x6 + x9 + 2*x10 - 1.0E-5;
x3 + x8 - 3.0E-5;
x1 + x3 + 2*x5 + 2*x8 + x9 + x10 - 5.0E-5;
x4 + 2*x7 - 1.0E-5;
0.5140437E-7 * x5 - x1**2;
0.1006932E-6 * x6 - x2**2;
0.7816278E-15 * x7 - x4**2;
0.1496236E-6 * x8 - x1*x3;
0.6194411E-7 * x9 - x1*x2;
0.2089296E-14 * x10 - x1*x2**2;
TITLE : Model A combustion chemistry example for a temparature of 3000 degrees
ROOT COUNTS :
total degree : 96
5-homogeneous Bezout number : 44
with partition : {x2 x6 x9 x10 }{x3 x8 }{x1 }{x5 }{x4 x7 }
mixed volume : 16
REFERENCES :
A.P. Morgan:
`Solving Polynomial Systems Using Continuation for Engineering and
Scientific Problems', Prentice-Hall, Englewood Cliffs, N.J., 1987.
Chapter 9.
NOTE :
The system should be scaled properly. See the file comb3000s.
THE SOLUTIONS :
16 10
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 2.44157718332959E-07 -2.69135029358109E-68
x6 : 5.92025990052519E-07 -1.39548002247951E-67
x9 : 5.53814405529183E-07 1.66914276780934E-67
x10 : 4.00898794801641E-06 6.95476153253892E-68
x3 : 1.54714076656939E-05 9.27301537671856E-67
x8 : 1.45285923343061E-05 -9.08755506918418E-67
x1 : 1.40505656302463E-07 5.30735744001309E-68
x5 : 3.84049827922917E-07 2.90136321227487E-67
x4 : 6.25149147668167E-11 -8.25298368527951E-67
x7 : 4.99996874254262E-06 4.12163150278652E-67
== err : 4.098E-19 = rco : 1.302E-15 = res : 2.753E-21 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -8.91664127240689E-08 -9.91828751827260E-08
x6 : -1.87360573646801E-08 1.75657962676780E-07
x9 : -7.91642740880272E-07 1.14477345706777E-06
x10 : 5.45914063416685E-06 -6.98453253619300E-07
x3 : 4.73669630616887E-10 7.13749004225551E-06
x8 : 2.99995263303694E-05 -7.13749004225551E-06
x1 : -1.49581864476755E-07 -6.28891662707340E-07
x5 : -7.25872117958961E-06 3.66003075075719E-06
x4 : 6.25149147668167E-11 -1.65059673705590E-66
x7 : 4.99996874254262E-06 8.24326300557305E-67
== err : 8.070E-19 = rco : 1.843E-15 = res : 1.388E-20 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 2.44157718332959E-07 6.52530446799852E-55
x6 : 5.92025990052519E-07 4.24144790419904E-54
x9 : 5.53814405529183E-07 -3.75205006909915E-54
x10 : 4.00898794801641E-06 -2.61012178719941E-54
x3 : 1.54714076656939E-05 -2.54486874251943E-53
x8 : 1.45285923343061E-05 2.54486874251943E-53
x1 : 1.40505656302463E-07 -8.97229364349797E-55
x5 : 3.84049827922917E-07 -8.93151049057298E-54
x4 : -6.25153055807167E-11 1.14702617601537E-55
x7 : 5.00003125765279E-06 -5.70326904185418E-56
== err : 4.098E-19 = rco : 1.302E-15 = res : 2.753E-21 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -8.91664127240689E-08 -9.91828751827260E-08
x6 : -1.87360573646801E-08 1.75657962676780E-07
x9 : -7.91642740880272E-07 1.14477345706777E-06
x10 : 5.45914063416685E-06 -6.98453253619300E-07
x3 : 4.73669630616975E-10 7.13749004225551E-06
x8 : 2.99995263303694E-05 -7.13749004225551E-06
x1 : -1.49581864476755E-07 -6.28891662707340E-07
x5 : -7.25872117958961E-06 3.66003075075719E-06
x4 : -6.25153055807167E-11 -4.63650768835928E-69
x7 : 5.00003125765279E-06 2.31825384417964E-69
== err : 8.068E-19 = rco : 1.843E-15 = res : 1.395E-20 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 7.04569390653156E-08 -9.69102131998154E-08
x6 : -4.39692964369002E-08 -1.35619823110719E-07
x9 : 8.31555564214474E-07 9.93970971497191E-07
x10 : 4.59296304479701E-06 -3.12910556037969E-07
x3 : -1.40318385913825E-07 -6.90383625579641E-06
x8 : 3.01403183859138E-05 6.90383625579641E-06
x1 : -1.62832772240636E-07 6.49907434653423E-07
x5 : -7.70100211134234E-06 -4.11740205295453E-06
x4 : 6.25149147668167E-11 0.00000000000000E+00
x7 : 4.99996874254262E-06 0.00000000000000E+00
== err : 8.466E-19 = rco : 2.446E-15 = res : 8.375E-21 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -8.91664127240689E-08 9.91828751827260E-08
x6 : -1.87360573646801E-08 -1.75657962676780E-07
x9 : -7.91642740880272E-07 -1.14477345706777E-06
x10 : 5.45914063416685E-06 6.98453253619300E-07
x3 : 4.73669630616939E-10 -7.13749004225551E-06
x8 : 2.99995263303694E-05 7.13749004225551E-06
x1 : -1.49581864476755E-07 6.28891662707340E-07
x5 : -7.25872117958961E-06 -3.66003075075719E-06
x4 : 6.25149147668167E-11 -1.42581726046354E-56
x7 : 4.99996874254262E-06 7.09033777052028E-57
== err : 8.069E-19 = rco : 1.843E-15 = res : 1.388E-20 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 7.04569390653156E-08 -9.69102131998154E-08
x6 : -4.39692964369002E-08 -1.35619823110719E-07
x9 : 8.31555564214474E-07 9.93970971497191E-07
x10 : 4.59296304479701E-06 -3.12910556037969E-07
x3 : -1.40318385913825E-07 -6.90383625579641E-06
x8 : 3.01403183859138E-05 6.90383625579641E-06
x1 : -1.62832772240636E-07 6.49907434653423E-07
x5 : -7.70100211134234E-06 -4.11740205295453E-06
x4 : -6.25153055807167E-11 0.00000000000000E+00
x7 : 5.00003125765279E-06 0.00000000000000E+00
== err : 8.468E-19 = rco : 2.446E-15 = res : 8.565E-21 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -8.91664127240689E-08 9.91828751827260E-08
x6 : -1.87360573646801E-08 -1.75657962676780E-07
x9 : -7.91642740880272E-07 -1.14477345706777E-06
x10 : 5.45914063416685E-06 6.98453253619300E-07
x3 : 4.73669630616637E-10 -7.13749004225551E-06
x8 : 2.99995263303694E-05 7.13749004225551E-06
x1 : -1.49581864476755E-07 6.28891662707340E-07
x5 : -7.25872117958961E-06 -3.66003075075719E-06
x4 : -6.25153055807167E-11 -4.63650768835928E-69
x7 : 5.00003125765279E-06 2.31825384417964E-69
== err : 9.068E-19 = rco : 1.843E-15 = res : 1.474E-20 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 7.04569390653156E-08 9.69102131998154E-08
x6 : -4.39692964369002E-08 1.35619823110719E-07
x9 : 8.31555564214474E-07 -9.93970971497191E-07
x10 : 4.59296304479701E-06 3.12910556037969E-07
x3 : -1.40318385913825E-07 6.90383625579641E-06
x8 : 3.01403183859138E-05 -6.90383625579641E-06
x1 : -1.62832772240636E-07 -6.49907434653423E-07
x5 : -7.70100211134234E-06 4.11740205295453E-06
x4 : -6.25153055807167E-11 0.00000000000000E+00
x7 : 5.00003125765279E-06 0.00000000000000E+00
== err : 8.467E-19 = rco : 2.446E-15 = res : 1.525E-20 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.60313982923272E-07 -1.28338532813785E-65
x6 : 6.72968678176653E-07 4.36944484550978E-65
x9 : -6.17521153048185E-07 -8.60535826959482E-66
x10 : 4.76594888980908E-06 -3.29377506181043E-65
x3 : 1.51354874557977E-05 -1.54302975868597E-65
x8 : 1.48645125442023E-05 1.54302975868597E-65
x1 : 1.46944846381988E-07 8.25298368527951E-67
x5 : 4.20057436327419E-07 1.28338532813785E-65
x4 : -6.25153055807167E-11 -1.66914276780934E-66
x7 : 5.00003125765279E-06 8.34571383904670E-67
== err : 3.791E-19 = rco : 1.325E-15 = res : 1.482E-21 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 7.04569390653156E-08 9.69102131998154E-08
x6 : -4.39692964369002E-08 1.35619823110719E-07
x9 : 8.31555564214474E-07 -9.93970971497191E-07
x10 : 4.59296304479701E-06 3.12910556037969E-07
x3 : -1.40318385913825E-07 6.90383625579641E-06
x8 : 3.01403183859138E-05 -6.90383625579641E-06
x1 : -1.62832772240636E-07 -6.49907434653423E-07
x5 : -7.70100211134234E-06 4.11740205295453E-06
x4 : 6.25149147668167E-11 -3.56454315115886E-57
x7 : 4.99996874254262E-06 1.75240110224570E-57
== err : 8.468E-19 = rco : 2.446E-15 = res : 8.565E-21 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.60313982923272E-07 -1.03487250547164E-54
x6 : 6.72968678176653E-07 3.54813430447420E-54
x9 : -6.17521153048185E-07 -3.97635741018660E-55
x10 : 4.76594888980908E-06 -2.85482070474935E-54
x3 : 1.51354874557977E-05 -3.28304381046176E-54
x8 : 1.48645125442023E-05 3.28304381046176E-54
x1 : 1.46944846381988E-07 3.13839106493093E-56
x5 : 4.20057436327419E-07 -4.39693367472557E-56
x4 : 6.25149147668167E-11 3.54462950226971E-57
x7 : 4.99996874254262E-06 -1.77231475113485E-57
== err : 3.791E-19 = rco : 1.325E-15 = res : 1.482E-21 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.94190576551449E-08 -1.46096250884933E-06
x6 : -2.11885804732594E-05 8.53685060755712E-07
x9 : -2.35403168406488E-09 6.04925907316275E-07
x10 : 2.62044670179290E-05 -4.25666759989186E-07
x3 : 3.62020323688239E-05 1.79872021664988E-07
x8 : -6.20203236882388E-06 -1.79872021664988E-07
x1 : -2.56361634369072E-08 -6.16039194939472E-10
x5 : 1.27777730079002E-08 6.14456766419239E-10
x4 : -6.25153055807167E-11 1.53683970830301E-50
x7 : 5.00003125765279E-06 -7.68419854151506E-51
== err : 4.634E-19 = rco : 6.286E-16 = res : 1.211E-20 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.94190576551449E-08 1.46096250884933E-06
x6 : -2.11885804732594E-05 -8.53685060755712E-07
x9 : -2.35403168406488E-09 -6.04925907316275E-07
x10 : 2.62044670179290E-05 4.25666759989186E-07
x3 : 3.62020323688239E-05 -1.79872021664988E-07
x8 : -6.20203236882388E-06 1.79872021664988E-07
x1 : -2.56361634369072E-08 6.16039194939473E-10
x5 : 1.27777730079003E-08 -6.14456766419239E-10
x4 : -6.25153055807167E-11 1.05638191171578E-64
x7 : 5.00003125765279E-06 -5.28669782977005E-65
== err : 4.619E-19 = rco : 6.286E-16 = res : 6.776E-21 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.94190576551449E-08 -1.46096250884933E-06
x6 : -2.11885804732594E-05 8.53685060755713E-07
x9 : -2.35403168406489E-09 6.04925907316275E-07
x10 : 2.62044670179290E-05 -4.25666759989186E-07
x3 : 3.62020323688239E-05 1.79872021664988E-07
x8 : -6.20203236882388E-06 -1.79872021664988E-07
x1 : -2.56361634369072E-08 -6.16039194939473E-10
x5 : 1.27777730079002E-08 6.14456766419239E-10
x4 : 6.25149147668167E-11 1.48368246027497E-67
x7 : 4.99996874254262E-06 -7.41841230137484E-68
== err : 4.523E-19 = rco : 6.286E-16 = res : 2.131E-21 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.94190576551449E-08 1.46096250884933E-06
x6 : -2.11885804732594E-05 -8.53685060755712E-07
x9 : -2.35403168406488E-09 -6.04925907316275E-07
x10 : 2.62044670179290E-05 4.25666759989186E-07
x3 : 3.62020323688239E-05 -1.79872021664988E-07
x8 : -6.20203236882388E-06 1.79872021664988E-07
x1 : -2.56361634369072E-08 6.16039194939473E-10
x5 : 1.27777730079003E-08 -6.14456766419239E-10
x4 : 6.25149147668167E-11 -3.13214614463929E-51
x7 : 4.99996874254262E-06 1.56607307231965E-51
== err : 4.619E-19 = rco : 6.286E-16 = res : 6.776E-21 ==