4
 y**2*z+2*x*y*t-2*x-z;
-x**3*z+4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2;
2*y*z*t+x*t**2-x-2*z;
-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t-10*t**2+2;

TITLE : the system caprasse of the PoSSo test suite

ROOT COUNTS :

total degree : 144
2-homogeneous Bezout number : 62
  with partition : {y x }{z t }
generalized Bezout number : 94
  based on the set structure :
     {y }{y x }{z t }
     {y x }{y x }{y z t }{x t }
     {y x }{z t }{t }
     {y z }{z t }{z t }{x t }
mixed volume : 48

NOTE :
 
There are 54 isolated solutions, so 6 ones with zero
components which are not counted by the mixed volume.

REFERENCES :

The PoSSo test suite.

THE SOLUTIONS :

48 4
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.06079387292675E-07   5.77350327054609E-01
 z :  1.45317416603335E-07   1.15470048989962E+00
 x : -3.92380293112556E-08  -1.15470054776460E+00
 t : -1.06079387291484E-07  -5.77350211324643E-01
== err :  1.533E-07 = rco :  2.130E-08 = res :  4.384E-13 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.06079387292675E-07   5.77350327054609E-01
 z : -1.45317416603335E-07  -1.15470048989962E+00
 x :  3.92380293112556E-08   1.15470054776460E+00
 t : -1.06079387291484E-07  -5.77350211324643E-01
== err :  1.533E-07 = rco :  2.130E-08 = res :  4.384E-13 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.05994025912692E-07  -5.77350327116111E-01
 z :  1.45274862525765E-07   1.15470048990682E+00
 x : -3.92808366117427E-08  -1.15470054783331E+00
 t :  1.05994025915353E-07   5.77350211263141E-01
== err :  1.534E-07 = rco :  2.130E-08 = res :  4.378E-13 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.05994025912692E-07  -5.77350327116111E-01
 z : -1.45274862525765E-07  -1.15470048990682E+00
 x :  3.92808366117427E-08   1.15470054783331E+00
 t :  1.05994025915353E-07   5.77350211263141E-01
== err :  1.534E-07 = rco :  2.130E-08 = res :  4.378E-13 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -8.77313232090609E-08   5.77350349491674E-01
 z :  9.35035689166768E-08  -1.15470051672660E+00
 x : -1.81234892107680E-07   1.15470059702865E+00
 t : -8.77313231729429E-08  -5.77350188887578E-01
== err :  1.906E-07 = rco :  1.434E-08 = res :  4.983E-13 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   4.07831529249908E-56
 z : -2.00000000000000E+00   1.01957882312477E-56
 x :  2.00000000000000E+00   0.00000000000000E+00
 t : -1.00000000000000E+00   4.07831529249908E-56
== err :  2.755E-40 = rco :  3.999E-02 = res :  1.387E-54 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   3.25541656235428E-150
 z : -4.74778387287990E-66  -2.00000000000000E+00
 x : -4.74778387287990E-66   2.00000000000000E+00
 t : -1.00000000000000E+00  -1.18694596821997E-66
== err :  3.207E-50 = rco :  5.880E-02 = res :  1.045E-64 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   0.00000000000000E+00
 z : -3.56083790465993E-66   2.00000000000000E+00
 x :  4.74778387287990E-66  -2.00000000000000E+00
 t : -1.00000000000000E+00  -4.74778387287990E-66
== err :  3.207E-50 = rco :  5.880E-02 = res :  1.045E-64 ==
solution 9 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -8.77513880611068E-08   5.77350349703671E-01
 z : -9.34852953226433E-08   1.15470051629058E+00
 x :  1.81236683363123E-07  -1.15470059680462E+00
 t : -8.77513880198494E-08  -5.77350188675580E-01
== err :  1.905E-07 = rco :  1.442E-08 = res :  4.985E-13 ==
solution 10 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00  -3.39859607708257E-57
 z :  2.00000000000000E+00  -1.69929803854128E-56
 x : -2.00000000000000E+00   0.00000000000000E+00
 t : -1.00000000000000E+00   1.01957882312477E-56
== err :  3.673E-40 = rco :  3.999E-02 = res :  2.447E-55 ==
solution 11 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  8.76784229248577E-08  -5.77350349659721E-01
 z :  9.34252745994218E-08  -1.15470051648474E+00
 x : -1.81103697507645E-07   1.15470059695484E+00
 t :  8.76784228915865E-08   5.77350188719531E-01
== err :  1.906E-07 = rco :  1.439E-08 = res :  4.984E-13 ==
solution 12 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00   4.07831529249908E-56
 z : -2.00000000000000E+00  -1.01957882312477E-56
 x :  2.00000000000000E+00  -3.05873646937431E-56
 t :  1.00000000000000E+00   5.09789411562385E-57
== err :  3.214E-40 = rco :  3.999E-02 = res :  2.896E-54 ==
solution 13 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00   0.00000000000000E+00
 z :  0.00000000000000E+00  -2.00000000000000E+00
 x :  0.00000000000000E+00   2.00000000000000E+00
 t :  1.00000000000000E+00   5.93472984109987E-67
== err :  2.138E-50 = rco :  5.880E-02 = res :  1.424E-65 ==
solution 14 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00   4.74778387287990E-66
 z : -4.74778387287990E-66   2.00000000000000E+00
 x :  3.56083790465993E-66  -2.00000000000000E+00
 t :  1.00000000000000E+00   0.00000000000000E+00
== err :  3.207E-50 = rco :  5.880E-02 = res :  1.045E-64 ==
solution 15 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  8.77405950783069E-08  -5.77350349472713E-01
 z : -9.35144851768356E-08   1.15470051674896E+00
 x :  1.81255080253416E-07  -1.15470059703204E+00
 t :  8.77405950748513E-08   5.77350188906539E-01
== err :  1.904E-07 = rco :  1.433E-08 = res :  4.989E-13 ==
solution 16 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00   4.07831529249908E-56
 z :  2.00000000000000E+00   1.01957882312477E-56
 x : -2.00000000000000E+00   0.00000000000000E+00
 t :  1.00000000000000E+00  -3.21909202921851E-120
== err :  2.755E-40 = rco :  3.999E-02 = res :  1.713E-54 ==
solution 17 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  4.98607301189714E-08   5.77350213814064E-01
 z :  1.50798591339040E-07  -1.15470064822190E+00
 x : -1.00937861254465E-07   1.15470059284634E+00
 t :  4.98607300501771E-08  -5.77350324565188E-01
== err :  1.860E-07 = rco :  8.075E-09 = res :  3.479E-13 ==
solution 18 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -5.01523750950706E-08  -5.77350213905358E-01
 z :  1.50859133388934E-07  -1.15470064802726E+00
 x : -1.00706758298574E-07   1.15470059274299E+00
 t : -5.01523750856486E-08   5.77350324473893E-01
== err :  1.863E-07 = rco :  7.978E-09 = res :  3.478E-13 ==
solution 19 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  5.00878414230803E-08   5.77350213853182E-01
 z : -1.50738519457209E-07   1.15470064813160E+00
 x :  1.00650678045970E-07  -1.15470059279515E+00
 t :  5.00878413993948E-08  -5.77350324526070E-01
== err :  1.862E-07 = rco :  7.980E-09 = res :  3.479E-13 ==
solution 20 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -4.99744070211252E-08  -5.77350213733803E-01
 z : -1.50410208193325E-07   1.15470064837104E+00
 x :  1.00435801156692E-07  -1.15470059291522E+00
 t : -4.99744070521402E-08   5.77350324645449E-01
== err :  1.868E-07 = rco :  7.962E-09 = res :  3.474E-13 ==
solution 21 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  4.35129158956362E-08   5.77350358962175E-01
 z : -1.21675118777727E-07  -1.15470065364167E+00
 x :  1.65188034697681E-07   1.15470074341422E+00
 t :  4.35129159442658E-08  -5.77350179417076E-01
== err :  2.632E-07 = rco :  1.337E-08 = res :  6.667E-13 ==
solution 22 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -4.37472610290454E-08  -5.77350358904876E-01
 z :  1.21150500984062E-07   1.15470065383538E+00
 x : -1.64897762006051E-07  -1.15470074355063E+00
 t : -4.37472610149285E-08   5.77350179474376E-01
== err :  2.632E-07 = rco :  1.330E-08 = res :  6.671E-13 ==
solution 23 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -4.38381107605702E-08  -5.77350358852071E-01
 z : -1.21029587513588E-07  -1.15470065385332E+00
 x :  1.64867698259043E-07   1.15470074351576E+00
 t : -4.38381107303348E-08   5.77350179527181E-01
== err :  2.633E-07 = rco :  1.328E-08 = res :  6.674E-13 ==
solution 24 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  4.39494246527390E-08   5.77350358863699E-01
 z :  1.20674859668386E-07   1.15470065401861E+00
 x : -1.64624284280550E-07  -1.15470074369268E+00
 t :  4.39494245715835E-08  -5.77350179515552E-01
== err :  2.634E-07 = rco :  1.324E-08 = res :  6.669E-13 ==
solution 25 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -8.03633037684401E-08  -1.73205070031825E+00
 z : -2.00000002853558E+00  -1.49454216126415E-07
 x : -1.99999984277204E+00  -1.02608911068846E-08
 t : -8.03633035704206E-08   1.73205091481951E+00
== err :  1.600E-07 = rco :  1.797E-08 = res :  7.452E-13 ==
solution 26 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  8.09400644530456E-08   1.73205069904967E+00
 z :  2.00000002839131E+00   1.50295919644092E-07
 x :  1.99999984043052E+00   1.01036152794788E-08
 t :  8.09400648734116E-08  -1.73205091608809E+00
== err :  1.567E-07 = rco :  1.793E-08 = res :  7.383E-13 ==
solution 27 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -9.61047376416230E-08  -1.73205074565506E+00
 z :  2.00000008738129E+00   1.40899654114353E-07
 x :  1.99999998014341E+00  -2.55586339770353E-08
 t : -9.61047372351930E-08   1.73205086948269E+00
== err :  1.643E-07 = rco :  2.723E-09 = res :  3.708E-13 ==
solution 28 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  9.13950441969567E-08   1.73205074015760E+00
 z : -2.00000008801649E+00  -1.39894670756851E-07
 x : -1.99999997125673E+00   1.84061895395854E-08
 t :  9.13950444132389E-08  -1.73205087498016E+00
== err :  1.646E-07 = rco :  2.862E-09 = res :  3.744E-13 ==
solution 29 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -8.09400644530456E-08  -1.73205069904967E+00
 z :  2.00000002839131E+00   1.50295919644092E-07
 x :  1.99999984043052E+00   1.01036152794788E-08
 t : -8.09400648734116E-08   1.73205091608809E+00
== err :  1.567E-07 = rco :  1.793E-08 = res :  7.383E-13 ==
solution 30 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  8.03072751517330E-08   1.73205070036440E+00
 z : -2.00000002852399E+00  -1.49379363774783E-07
 x : -1.99999984284040E+00  -1.02830832993386E-08
 t :  8.03072747998243E-08  -1.73205091477335E+00
== err :  1.598E-07 = rco :  1.796E-08 = res :  7.441E-13 ==
solution 31 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -9.13950441969567E-08  -1.73205074015760E+00
 z : -2.00000008801649E+00  -1.39894670756851E-07
 x : -1.99999997125673E+00   1.84061895395854E-08
 t : -9.13950444132389E-08   1.73205087498016E+00
== err :  1.646E-07 = rco :  2.862E-09 = res :  3.744E-13 ==
solution 32 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  9.34115735173893E-08   1.73205074298615E+00
 z :  2.00000008817823E+00   1.39641870549700E-07
 x :  1.99999997631766E+00  -2.21517205363262E-08
 t :  9.34115732159578E-08  -1.73205087215160E+00
== err :  1.649E-07 = rco :  2.748E-09 = res :  3.760E-13 ==
solution 33 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   1.38662719944969E-54
 z : -1.03527618041008E+00  -2.61012178719941E-54
 x : -1.03527618041008E+00   2.73922305764310E-54
 t : -1.00000000000000E+00  -5.70964140949871E-55
== err :  2.972E-15 = rco :  5.099E-02 = res :  3.553E-15 ==
solution 34 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00  -4.89397835099889E-55
 z :  1.03527618041008E+00   1.79445872869959E-54
 x :  1.03527618041008E+00  -9.45130671136214E-55
 t :  1.00000000000000E+00   5.70964140949871E-55
== err :  2.972E-15 = rco :  5.099E-02 = res :  3.553E-15 ==
solution 35 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -6.87146778792226E-08   1.73205075848417E+00
 z : -2.00000012423210E+00   6.72451725057925E-08
 x : -2.00000003921490E+00  -5.17721413751262E-08
 t : -6.87146785355248E-08  -1.73205085665358E+00
== err :  1.394E-07 = rco :  6.697E-09 = res :  4.134E-13 ==
solution 36 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  6.64123385764048E-08  -1.73205075991201E+00
 z :  2.00000012220410E+00  -6.55381358439691E-08
 x :  2.00000003965998E+00   4.94914088517632E-08
 t :  6.64123386132757E-08   1.73205085522575E+00
== err :  1.387E-07 = rco :  6.542E-09 = res :  3.937E-13 ==
solution 37 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   1.38662719944969E-54
 z :  1.03527618041008E+00   2.61012178719941E-54
 x :  1.03527618041008E+00  -2.73922305764310E-54
 t : -1.00000000000000E+00  -5.70964140949871E-55
== err :  2.972E-15 = rco :  5.099E-02 = res :  3.553E-15 ==
solution 38 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00  -1.06036197604976E-54
 z : -1.03527618041008E+00  -1.71289242284961E-54
 x : -1.03527618041008E+00   1.80792937639691E-54
 t :  1.00000000000000E+00   5.30180988024880E-55
== err :  2.972E-15 = rco :  5.099E-02 = res :  3.553E-15 ==
solution 39 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -6.70676624484987E-08   1.73205075948725E+00
 z :  2.00000012231556E+00  -6.59142382481208E-08
 x :  2.00000003903574E+00   5.02503608947312E-08
 t : -6.70676627223605E-08  -1.73205085565051E+00
== err :  1.383E-07 = rco :  6.559E-09 = res :  3.800E-13 ==
solution 40 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  6.71985300364174E-08  -1.73205075841178E+00
 z : -2.00000012262647E+00   6.46883747124073E-08
 x : -2.00000003748388E+00  -5.17028939308009E-08
 t :  6.71985305285384E-08   1.73205085672598E+00
== err :  1.380E-07 = rco :  6.569E-09 = res :  3.831E-13 ==
solution 41 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   9.27301537671855E-69
 z : -3.86370330515627E+00   8.90209476164981E-67
 x : -3.86370330515627E+00   1.48368246027497E-67
 t : -1.00000000000000E+00  -1.39095230650778E-68
== err :  3.119E-15 = rco :  1.227E-02 = res :  7.105E-15 ==
solution 42 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00  -5.56380922603113E-68
 z :  3.86370330515627E+00  -5.93472984109987E-67
 x :  3.86370330515627E+00   2.78190461301557E-68
 t :  1.00000000000000E+00   2.78190461301557E-68
== err :  3.119E-15 = rco :  1.227E-02 = res :  7.105E-15 ==
solution 43 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.00000000000000E+00   1.04321422988084E-68
 z :  3.86370330515627E+00  -7.41841230137484E-67
 x :  3.86370330515627E+00  -1.03857772219248E-66
 t : -1.00000000000000E+00  -1.28001759201242E-68
== err :  3.119E-15 = rco :  1.227E-02 = res :  7.105E-15 ==
solution 44 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.00000000000000E+00   5.21607114940419E-69
 z : -3.86370330515627E+00   5.37834891849676E-67
 x : -3.86370330515627E+00  -4.82196799589365E-67
 t :  1.00000000000000E+00  -4.34672595783682E-70
== err :  3.119E-15 = rco :  1.227E-02 = res :  7.105E-15 ==
solution 45 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.47770838224294E-07   1.73205083400279E+00
 z : -1.99999988873008E+00   1.92142362285763E-07
 x : -1.99999993451496E+00  -6.38042375209335E-08
 t : -1.47770838368828E-07  -1.73205078113496E+00
== err :  2.221E-07 = rco :  7.753E-09 = res :  8.620E-13 ==
solution 46 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.47452975307093E-07  -1.73205083375888E+00
 z :  1.99999988868296E+00  -1.92059110471295E-07
 x :  1.99999993404537E+00   6.33369348504009E-08
 t :  1.47452975725790E-07   1.73205078137888E+00
== err :  2.214E-07 = rco :  7.754E-09 = res :  8.582E-13 ==
solution 47 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y : -1.47770838224294E-07   1.73205083400279E+00
 z :  1.99999988873008E+00  -1.92142362285763E-07
 x :  1.99999993451496E+00   6.38042375209335E-08
 t : -1.47770838368828E-07  -1.73205078113496E+00
== err :  2.221E-07 = rco :  7.753E-09 = res :  8.620E-13 ==
solution 48 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 y :  1.47452975307093E-07  -1.73205083375888E+00
 z : -1.99999988868296E+00   1.92059110471295E-07
 x : -1.99999993404537E+00  -6.33369348504009E-08
 t :  1.47452975725790E-07   1.73205078137888E+00
== err :  2.214E-07 = rco :  7.754E-09 = res :  8.582E-13 ==