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 ==