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 ==