8 y1 + y2 + y3 + y4 + y5 + y6 + y7 +( 9.80163574218750E-01 + 8.04046630859375E-01*i)*zz + 1; y1*y2 + y2*y3 + y3*y4 + y4*y5 + y5*y6 + y6*y7 + y1 + y7 +( 1.28051757812500E-01 + 2.37121582031250E-02*i)*zz; y1*y2*y3 + y2*y3*y4 + y3*y4*y5 + y4*y5*y6 + y5*y6*y7 + y1*y2 + y1*y7 + y6*y7 +(-1.29333496093750E-01 - 8.72833251953125E-01*i)*zz; y1*y2*y3*y4 + y2*y3*y4*y5 + y3*y4*y5*y6 + y4*y5*y6*y7 + y1*y2*y3 + y1*y2*y7 + y1*y6*y7 + y5*y6*y7 +( 3.17382812500000E-01 + 5.98785400390625E-01*i)*zz; y1*y2*y3*y4*y5 + y2*y3*y4*y5*y6 + y3*y4*y5*y6*y7 + y1*y2*y3*y4 + y1*y2*y3*y7 + y1*y2*y6*y7 + y1*y5*y6*y7 + y4*y5*y6*y7 +(-1.72424316406250E-01 - 8.27056884765625E-01*i)*zz; y1*y2*y3*y4*y5*y6 + y2*y3*y4*y5*y6*y7 + y1*y2*y3*y4*y5 + y1*y2*y3*y4*y7 + y1*y2*y3*y6*y7 + y1*y2*y5*y6*y7 + y1*y4*y5*y6*y7 + y3*y4*y5*y6*y7 +(-9.89379882812500E-01 - 1.65985107421875E-01*i)*zz; y1*y2*y3*y4*y5*y6*y7 + y1*y2*y3*y4*y5*y6 + y1*y2*y3*y4*y5*y7 + y1*y2*y3*y4*y6*y7 + y1*y2*y3*y5*y6*y7 + y1*y2*y4*y5*y6*y7 + y1*y3*y4*y5*y6*y7 + y2*y3*y4*y5*y6*y7 +( 7.25891113281250E-01 - 1.83624267578125E-01*i)*zz; +( 9.09790039062500E-01 + 8.24981689453125E-01*i)*y1 +(-4.29077148437500E-02 - 5.79376220703125E-01*i)*y2 +(-1.66503906250000E-01 - 4.90570068359375E-01*i)*y3 +( 8.98376464843750E-01 - 1.74224853515625E-01*i)*y4 +(-2.38891601562500E-01 - 6.45965576171875E-01*i)*y5 +(-7.18933105468750E-01 - 6.71417236328125E-01*i)*y6 +( 5.67626953125000E-01 - 7.66204833984375E-01*i)*y7 +( 8.27636718750000E-02 + 6.04400634765625E-01*i)*zz +( 5.82214355468750E-01 - 7.61871337890625E-01*i); TITLE : embedding and slicing of the system redcyc8, zz added ROOT COUNTS : total degree : 5040 mixed volume : 775 REFERENCES : Andrew J. Sommese and Jan Verschelde : "Numerical Homotopies to compute generic Points on positive dimensional Algebraic Sets", Journal of Complexity 16(3):572-602, 2000. THE SOLUTIONS with zz = 0 : 18 8 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -9.66882369948171E-02 4.29790450139676E-01 y2 : -5.08618438050409E-01 9.76578100446502E-01 y3 : -1.00000000000000E+00 -2.00988957288253E-16 y4 : -4.12636739267664E-01 -5.96452940771173E-01 y5 : 5.08618438050409E-01 -9.76578100446502E-01 y6 : 9.66882369948170E-02 -4.29790450139676E-01 y7 : 4.12636739267664E-01 5.96452940771173E-01 zz : -1.40222303476852E-16 3.96032212603570E-17 == err : 3.303E-15 = rco : 3.128E-02 = res : 2.155E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 4.50688359346362E-01 1.89472529719516E-01 y2 : -2.58473855962195E-16 -1.00000000000000E+00 y3 : 1.89472529719517E-01 -4.50688359346362E-01 y4 : -1.00000000000000E+00 3.88542003221364E-16 y5 : -4.50688359346362E-01 -1.89472529719517E-01 y6 : 3.05623743113666E-16 1.00000000000000E+00 y7 : -1.89472529719517E-01 4.50688359346362E-01 zz : 6.03287432152353E-18 -4.85687672360627E-17 == err : 5.296E-15 = rco : 9.939E-03 = res : 1.389E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 5.11531032767470E-01 8.30684118526793E-04 y2 : -7.87891606701390E+00 3.06924282703220E-01 y3 : -1.00000000000000E+00 -2.74156202138925E-17 y4 : -5.14534904975061E-02 -1.65384284470976E-03 y5 : 7.87891606701390E+00 -3.06924282703220E-01 y6 : -5.11531032767469E-01 -8.30684118526812E-04 y7 : 5.14534904975061E-02 1.65384284470977E-03 zz : 8.09664920752157E-17 1.05632778783361E-16 == err : 1.388E-14 = rco : 3.067E-04 = res : 3.737E-15 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.37419963358425E-02 -6.12955547733521E-01 y2 : 2.36840440853007E+00 1.02386018138798E+00 y3 : 5.04179780418724E-01 4.12848936026186E-01 y4 : 1.37419963358423E-02 6.12955547733521E-01 y5 : -9.99999999999999E-01 6.74683801298582E-17 y6 : -5.04179780418724E-01 -4.12848936026186E-01 y7 : -2.36840440853007E+00 -1.02386018138799E+00 zz : 1.76707930017902E-15 4.06161657137751E-16 == err : 2.496E-14 = rco : 3.205E-03 = res : 5.364E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -3.94734116544847E-03 -2.62411329739356E-01 y2 : -4.09195242574328E-01 -1.53367087861312E-01 y3 : -2.16985835405427E+00 9.01601900517834E-01 y4 : 3.94734116544831E-03 2.62411329739356E-01 y5 : -1.00000000000000E+00 -1.40650676537036E-16 y6 : 2.16985835405427E+00 -9.01601900517835E-01 y7 : 4.09195242574327E-01 1.53367087861313E-01 zz : -4.04750931942372E-16 3.13555142693198E-16 == err : 1.067E-14 = rco : 2.381E-03 = res : 2.004E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.04264299037993E+00 7.79521492595522E-01 y2 : -7.66395838700630E-01 6.79494984439854E-01 y3 : -1.00000000000000E+00 9.85226885753303E-17 y4 : -4.17992337783186E+00 -5.02611721439181E-01 y5 : 7.66395838700629E-01 -6.79494984439853E-01 y6 : -1.04264299037993E+00 -7.79521492595522E-01 y7 : 4.17992337783186E+00 5.02611721439179E-01 zz : 2.60572184189547E-15 -8.14974191946871E-16 == err : 2.822E-14 = rco : 3.151E-03 = res : 3.908E-14 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.13004037744433E-01 3.15802415738887E-01 y2 : 3.82836877738912E-01 2.89255254941478E-01 y3 : -1.00000000000000E+00 1.13924044722046E-16 y4 : -3.07364269806777E-01 7.80559005376913E-02 y5 : -3.82836877738912E-01 -2.89255254941478E-01 y6 : 1.13004037744433E-01 -3.15802415738887E-01 y7 : 3.07364269806777E-01 -7.80559005376914E-02 zz : -4.01186489390348E-18 4.25505744425564E-19 == err : 2.607E-15 = rco : 5.911E-03 = res : 7.754E-16 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.98822949545035E+00 -3.93275186307664E-01 y2 : -2.27400428383190E-01 -3.44644389289366E-01 y3 : -1.00000000000000E+00 4.64563707153335E-17 y4 : -5.82534823095888E+00 4.43788988745309E+00 y5 : 2.27400428383190E-01 3.44644389289366E-01 y6 : -1.98822949545035E+00 3.93275186307664E-01 y7 : 5.82534823095888E+00 -4.43788988745309E+00 zz : 3.75564005938354E-16 1.67129560100689E-15 == err : 2.803E-14 = rco : 8.350E-04 = res : 9.709E-14 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 3.02677374926898E-01 2.79288190402997E-01 y2 : -1.28998051713691E-01 3.90204795949059E-01 y3 : -8.62574354552782E-01 4.13825127188193E-01 y4 : -3.02677374926898E-01 -2.79288190402997E-01 y5 : -1.00000000000000E+00 1.29953046034625E-18 y6 : 8.62574354552782E-01 -4.13825127188193E-01 y7 : 1.28998051713691E-01 -3.90204795949059E-01 zz : -2.52990349251168E-17 -1.02742606145854E-17 == err : 4.724E-15 = rco : 9.257E-03 = res : 1.343E-15 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 6.44455749204416E-01 7.15661862958205E-01 y2 : -5.05713413541780E-01 1.12946908953498E+00 y3 : -2.12490908130303E-01 5.18226138952731E-01 y4 : -6.44455749204416E-01 -7.15661862958205E-01 y5 : -1.00000000000000E+00 6.76763751344890E-17 y6 : 2.12490908130303E-01 -5.18226138952731E-01 y7 : 5.05713413541780E-01 -1.12946908953498E+00 zz : -4.56829359072370E-17 -2.13188780571153E-18 == err : 9.449E-15 = rco : 3.462E-02 = res : 2.260E-15 == solution 11 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -2.24447714554037E-01 -6.46303087054843E-02 y2 : -1.14379921468457E+00 -4.44516401824471E-01 y3 : -1.00000000000000E+00 3.33478138568709E-16 y4 : 9.22157554221310E-01 9.97170215282143E-01 y5 : 1.14379921468457E+00 4.44516401824471E-01 y6 : 2.24447714554037E-01 6.46303087054843E-02 y7 : -9.22157554221310E-01 -9.97170215282144E-01 zz : 1.04518519516200E-16 6.13026897095782E-17 == err : 5.325E-15 = rco : 6.346E-03 = res : 2.614E-15 == solution 12 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.33259167429166E-01 2.58122264220049E-01 y2 : 1.11655240907339E+00 2.55908731503348E-01 y3 : 2.30600733988079E-01 -2.06832013163668E-01 y4 : -1.33259167429166E-01 -2.58122264220049E-01 y5 : -1.00000000000000E+00 7.74214599501140E-17 y6 : -2.30600733988079E-01 2.06832013163668E-01 y7 : -1.11655240907339E+00 -2.55908731503348E-01 zz : 6.67149776829040E-18 4.61245667114941E-18 == err : 6.649E-15 = rco : 1.172E-02 = res : 1.542E-15 == solution 13 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 3.47802595040417E+00 4.27963997771153E+00 y2 : 1.81031261902796E+00 1.25460177527775E+00 y3 : 6.17919196054940E+00 -7.41802968265913E+00 y4 : -3.47802595040417E+00 -4.27963997771153E+00 y5 : -1.00000000000000E+00 -4.63749080590656E-17 y6 : -6.17919196054940E+00 7.41802968265913E+00 y7 : -1.81031261902796E+00 -1.25460177527775E+00 zz : -5.31991479704432E-16 -3.76318596963763E-16 == err : 6.809E-14 = rco : 6.773E-06 = res : 3.580E-12 == solution 14 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.34804943375627E-01 2.87237553651136E-01 y2 : -4.41961147446885E-02 -1.26551187923827E-02 y3 : -1.00000000000000E+00 -2.61057131489991E-17 y4 : -5.21596604053880E-02 1.25452808905764E-01 y5 : 4.41961147446885E-02 1.26551187923827E-02 y6 : 1.34804943375627E-01 -2.87237553651136E-01 y7 : 5.21596604053880E-02 -1.25452808905764E-01 zz : -3.56493305220623E-20 6.60553155314633E-20 == err : 1.849E-15 = rco : 2.199E-04 = res : 4.209E-16 == solution 15 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 2.23170153588995E-01 -2.89577047967447E-01 y2 : 4.50022420473311E-16 1.00000000000000E+00 y3 : 2.89577047967447E-01 2.23170153588995E-01 y4 : -1.00000000000000E+00 4.37091042382109E-16 y5 : -2.23170153588995E-01 2.89577047967446E-01 y6 : -4.01635060022977E-16 -1.00000000000000E+00 y7 : -2.89577047967447E-01 -2.23170153588995E-01 zz : -3.96300676732767E-17 2.83312598475864E-18 == err : 1.016E-14 = rco : 2.819E-03 = res : 1.141E-15 == solution 16 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -9.35411310356865E+00 -4.42165683612901E+00 y2 : 9.41650214778735E+01 1.48303513451038E+02 y3 : -1.00000000000000E+00 7.36867204979863E-17 y4 : -1.83597540871860E+01 -9.05954264619504E+00 y5 : -9.41650214778736E+01 -1.48303513451038E+02 y6 : 9.35411310356865E+00 4.42165683612901E+00 y7 : 1.83597540871860E+01 9.05954264619504E+00 zz : 3.74398832060233E-14 -4.99604654844216E-14 == err : 2.903E-12 = rco : 3.596E-11 = res : 4.849E-07 == solution 17 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.92495757473776E+00 4.28388848727682E+00 y2 : -5.79831650075212E+00 9.66427235148478E-02 y3 : -5.20550169747046E-01 -1.12228631953053E+00 y4 : -1.92495757473776E+00 -4.28388848727682E+00 y5 : -1.00000000000000E+00 -3.01397763068420E-16 y6 : 5.20550169747046E-01 1.12228631953053E+00 y7 : 5.79831650075212E+00 -9.66427235148465E-02 zz : -2.08944097076696E-16 -2.94248775374756E-16 == err : 6.115E-14 = rco : 1.152E-04 = res : 4.599E-13 == solution 18 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 3.15473851150231E-01 1.39907835434866E+00 y2 : 3.68333753374680E-01 -2.56545394193717E-01 y3 : 9.90678246608816E-01 -1.12212163422221E+00 y4 : -3.15473851150231E-01 -1.39907835434866E+00 y5 : -1.00000000000000E+00 -1.09203731684384E-17 y6 : -9.90678246608816E-01 1.12212163422221E+00 y7 : -3.68333753374680E-01 2.56545394193717E-01 zz : 3.26163063601039E-16 1.13483475736131E-16 == err : 1.084E-14 = rco : 1.031E-02 = res : 6.716E-15 ==