7 -1.10341193720649E+00*y1*x1 -5.86815682189835E-01*y1*x2 -7.92036085497022E-01*y1*x3 -5.77733959201612E-01*y2*x1 + 3.87368458550248E-01*y2*x2 + 1.28043505098815E+00*y2*x3 + 1.04041310144849E+00*y3*x1 + 1.07931536931741E-01*y3*x2 -3.40083678408469E-01*y3*x3 -5.68456000000000E-01*y1 + 1.05510000000000E-02*y2 + 8.21000000000000E-04*y3 -1.95379855738832E-01*x1 -1.94409521104426E-01*x2 -1.04439406278041E+00*x3 +(-2.94647216796875E-01 - 8.30932617187500E-01*i)*zz1 + 3.41541444787000E-01; -1.27667983027595E+00*y1*x1 -8.22293023657284E-01*y1*x2 + 9.85781640537901E-01*y1*x3 + 1.10445261409581E+00*y2*x1 -8.28754979219007E-02*y2*x2 + 1.48463358281623E+00*y2*x3 + 4.94115593345597E-01*y3*x1 + 2.03347173764983E-01*y3*x2 -4.33616705996826E-02*y3*x3 + 9.33643000000000E-01*y1 -1.33829000000000E-01*y2 + 1.04241900000000E+00*y3 + 2.63041345590506E-01*x1 -1.03548264961166E+00*x2 -7.93223555891750E-01*x3 +( 1.52557373046875E-01 + 5.05432128906250E-01*i)*zz1 + 4.19707164888500E-01; -8.83804023497621E-01*y1*x1 -1.78651736017982E-01*y1*x2 -7.38492559710131E-01*y1*x3 + 4.43434838274957E-01*y2*x1 + 8.09639929536600E-01*y2*x2 + 1.38546622633458E+00*y2*x3 + 1.56573040484672E+00*y3*x1 -8.99276927801036E-01*y3*x2 -4.05489960274242E-01*y3*x3 + 1.07621800000000E+00*y1 + 3.81121000000000E-01*y2 -6.69739000000000E-01*y3 + 7.52673504306374E-01*x1 -1.28749695700861E+00*x2 + 1.47238424191569E-01*x3 +(-5.32073974609375E-01 - 9.54101562500000E-01*i)*zz1 + 7.54400309061000E-01; -1.24212145914842E+00*y1*x1 -1.23465051231272E+00*y1*x2 -4.85226728194913E-01*y1*x3 -4.86814272583431E-01*y2*x1 -1.94381663901655E-01*y2*x2 + 1.63104483875388E+00*y2*x3 + 1.11153625371862E-01*y3*x1 + 6.84956479647339E-03*y3*x2 -6.08528904330562E-01*y3*x3 + 9.04135000000000E-01*y1 + 7.81815000000000E-01*y2 -3.95866000000000E-01*y3 + 5.18838101619745E-01*x1 + 5.93430553942240E-01*x2 -6.26769769282934E-01*x3 +( 3.85833740234375E-01 - 8.50158691406250E-01*i)*zz1 + 7.12048812833000E-01; -6.46023972517329E-01*y1*x1 -1.29375652786430E+00*y1*x2 -5.84812917010785E-01*y1*x3 + 1.62705334082809E-01*y2*x1 + 6.52017519795460E-01*y2*x2 + 2.86172998155648E-01*y2*x3 + 1.58054783715492E+00*y3*x1 -6.31169332666938E-01*y3*x2 -1.85713987157407E-01*y3*x3 -5.74712000000000E-01*y1 -7.49368000000000E-01*y2 + 6.30445000000000E-01*y3 -4.55403271303103E-01*x1 -5.80692051452173E-01*x2 -1.21733476968808E+00*x3 +(-1.09344482421875E-01 - 5.73364257812500E-01*i)*zz1 + 5.68373481377500E-01; zz1; +(-3.03985595703125E-01 - 1.58142089843750E-01*i)*y1 +(-3.71429443359375E-01 - 1.87988281250000E-01*i)*y2 +( 2.88665771484375E-01 - 5.29357910156250E-01*i)*y3 +( 6.60675048828125E-01 - 5.72875976562500E-01*i)*x1 +(-2.10266113281250E-02 + 5.40832519531250E-01*i)*x2 +(-2.72064208984375E-01 - 7.88574218750000E-02*i)*x3 +(-1.51458740234375E-01 + 1.86279296875000E-01*i)*zz1 +(-2.43377685546875E-01 - 7.99194335937500E-01*i); TITLE : spatial Burmester problem, sliced and embedded once. REFERENCES : Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler: "Numerical Irreducible Decomposition using PHCpack." In Algebra, Geometry and Software Systems, edited by M. Joswig and N. Takayama, pages 109-130, Springer-Verlag 2003. THE SOLUTIONS : 20 7 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -5.75362961203822E-01 3.45108378061290E-01 x1 : 9.07367131338646E-02 2.56130441694886E+00 x2 : 1.17544906147903E+00 2.14556505545216E+00 x3 : 3.34175865389979E+00 1.98945013374759E+00 y2 : -1.95258976282590E-02 -4.65713685948092E-01 y3 : 1.55014300412330E+00 1.07417491648536E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 2.432E-14 = rco : 7.093E-03 = res : 3.546E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 9.95356099958368E-02 -2.24537736903122E-01 x1 : 1.58040448241226E+00 4.21204587289315E+00 x2 : -7.51030829019180E-01 6.34803430898433E+00 x3 : -1.56218787406691E+00 -7.25239520599001E-01 y2 : 1.00928026063222E+00 5.20800931078480E-01 y3 : 9.11228535907468E-01 -1.59497843870782E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 2.577E-14 = rco : 2.649E-03 = res : 9.659E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -4.83937278877283E-01 -5.00593626860282E-01 x1 : -1.63455108239838E-01 5.98742224750061E-01 x2 : -7.04650838483631E-02 2.77283432872540E-01 x3 : -1.37534514018166E-01 6.45863298659398E-01 y2 : 2.91525659881554E-01 -3.62762745199961E-01 y3 : -1.65433094748974E-01 4.24632312535338E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 3.280E-15 = rco : 3.569E-02 = res : 1.513E-15 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -7.64178390458581E-01 8.82407484559513E-01 x1 : 4.81535796884424E-01 2.50488519515265E-01 x2 : -5.23794597497208E-02 -1.94093943950542E-01 x3 : -1.62501698729891E-01 -2.10096891018778E-01 y2 : -1.57037171712336E-01 -1.97971832182395E+00 y3 : -6.84289873090531E-01 -4.01344790302792E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 5.112E-15 = rco : 3.155E-02 = res : 1.471E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 4.36792683522841E-02 -3.43705017061662E-01 x1 : -8.07882506222979E-01 1.06118525090576E+00 x2 : -7.81451646703674E-01 -9.23478629204040E-02 x3 : 2.19280303539333E-01 -6.16926250947030E-01 y2 : 2.20779422454833E-01 3.33574447922284E-01 y3 : 2.75615685127246E-01 4.12757912533895E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 4.700E-15 = rco : 1.818E-02 = res : 2.234E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.05923670547834E+00 3.13606638878381E-02 x1 : -1.21822237812591E+00 -1.43118000998697E-01 x2 : 1.30619991794138E+00 -1.18435131783174E+00 x3 : -2.73738094537795E-01 7.51932151909790E-01 y2 : -5.30506012806050E-01 1.24733928050163E+00 y3 : -6.04247206299656E-02 5.40882158422279E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.338E-14 = rco : 3.303E-02 = res : 1.610E-15 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 5.88740896342661E-02 8.03501989282471E-01 x1 : 2.34337149028252E-02 2.45950196144845E-01 x2 : -5.13852902722540E-03 -5.67884805468359E-01 x3 : -1.45287294011458E+00 -1.04290202284987E+00 y2 : 4.12288756392184E-01 6.62432971110429E-02 y3 : -1.26963682903737E+00 -2.55522424245064E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.480E-14 = rco : 3.128E-02 = res : 2.484E-15 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.81775737472508E+00 6.64456006679454E+00 x1 : 5.84961764748592E-01 -1.38426656464723E-01 x2 : 3.36134469608928E-01 -8.90601193650915E-02 x3 : -3.32822519107526E-01 7.85259077123900E-03 y2 : 4.85893533265721E+00 -9.27821022462225E+00 y3 : 1.07233371555975E+00 2.72025009443606E+00 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 2.143E-14 = rco : 1.174E-03 = res : 1.121E-14 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 6.14626801568071E-01 -5.53628009648998E-01 x1 : 3.39253332027683E-01 1.14086968523055E+00 x2 : 1.07499796234689E+00 7.39132356258626E-01 x3 : -8.12489975917641E-01 1.24573006124177E-01 y2 : 3.61397279688335E-01 -4.89761823399873E-01 y3 : 8.34105027787190E-01 -3.45593860478607E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 5.667E-15 = rco : 2.436E-02 = res : 2.470E-15 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -7.47320617138995E-02 1.19178980792688E+00 x1 : -2.62449348536825E-01 -9.41287631380722E-02 x2 : 4.43543263496215E-01 -3.15556056135867E-01 x3 : -9.80217583823845E-01 -9.59518478400635E-01 y2 : 5.18895757181679E-01 5.05212685454755E-01 y3 : -1.10539566464564E+00 6.12064499996490E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 7.570E-15 = rco : 4.951E-02 = res : 1.638E-15 == solution 11 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 4.34213741144813E-01 -1.38488047702060E+00 x1 : 2.16767846491477E-01 -3.73195406923338E-01 x2 : 1.23763711519676E-01 3.80970218592606E-01 x3 : -1.30464465647587E-01 -2.68264777944912E-02 y2 : -3.58636333501841E+00 1.62221103286640E+00 y3 : -1.60746847303559E+00 -6.28668092383219E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 4.907E-15 = rco : 7.650E-03 = res : 2.449E-15 == solution 12 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 5.07020601818970E-01 -3.54414583917085E-01 x1 : 4.52964110565092E-01 6.15697061122384E-01 x2 : -1.15190702736784E+00 6.89474411743491E-01 x3 : -1.88636161394418E+00 -4.88748846082360E-01 y2 : 2.20717958976053E-01 -4.52074785522738E-01 y3 : -1.36808520090869E+00 4.48575753113287E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 9.712E-15 = rco : 2.753E-02 = res : 3.764E-15 == solution 13 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -9.63920202020482E-01 -7.66537135780349E-01 x1 : -3.20026339300358E+00 3.31712200151217E-02 x2 : -2.49766819571703E+00 -2.08602487127102E+00 x3 : -1.10782602638586E+00 -4.89670815818090E+00 y2 : -1.54597156693855E-01 9.56203903730063E-01 y3 : 2.45018275294659E+00 2.38942716307739E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.166E-14 = rco : 7.603E-03 = res : 1.962E-14 == solution 14 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.48954584965491E+00 -1.70664974916915E-01 x1 : 3.62762239258049E-01 1.83421541797011E-01 x2 : -2.18209982090775E+00 -1.58546705707904E-01 x3 : 7.53938569734182E-01 -7.50672655696986E-02 y2 : -2.64390210279355E+00 3.10795349792718E-01 y3 : -3.23467649581081E+00 6.63299954019576E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.320E-14 = rco : 1.737E-02 = res : 3.986E-15 == solution 15 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.41002903287562E+01 -8.08446927154036E+00 x1 : -2.85764877415983E+00 -1.81099388763202E+00 x2 : 4.80287169694539E-01 5.39984771731637E-01 x3 : 5.70455161728922E-01 -2.86416691270631E+00 y2 : -7.47593408482605E+00 1.00127187016175E+01 y3 : 1.33606639837731E+00 -7.93506898339922E+00 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.001E-13 = rco : 1.485E-03 = res : 4.263E-14 == solution 16 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.71452254069340E+00 4.64828051412434E+00 x1 : -6.33730371524877E+00 1.51916878073291E+00 x2 : 6.43181748632272E-01 -1.09440964072287E+00 x3 : -1.48719760246119E-01 5.18526325878268E+00 y2 : -3.42547183328350E+00 1.51192124992255E+00 y3 : 2.35958343838185E+00 1.52411882031309E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 2.678E-14 = rco : 1.018E-02 = res : 6.856E-14 == solution 17 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -2.71388326713256E-01 -7.97669217994968E-01 x1 : -1.09625621380726E-01 -9.73366547734584E-02 x2 : -3.02977868869616E-01 1.64342645658664E-01 x3 : -1.00014174239429E+00 1.21143608163210E+00 y2 : 4.56467389194471E-01 1.88791485002543E-01 y3 : -1.37633792076574E+00 1.24952813968987E+00 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 7.578E-15 = rco : 1.482E-02 = res : 2.241E-15 == solution 18 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 2.07115189728528E-01 -1.49588456987984E+00 x1 : -3.56015207325609E-01 -5.34780767975518E-01 x2 : -1.18478304409898E+00 -2.82687526005559E-02 x3 : -9.66342780293144E-01 1.20973464681699E+00 y2 : 1.80998166256862E+00 1.30972651089424E+00 y3 : -2.38798601855240E+00 3.40292648095661E+00 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.971E-14 = rco : 9.681E-03 = res : 7.480E-15 == solution 19 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 8.77160533986755E-01 -6.02973804456571E-01 x1 : -2.70911692250960E-01 -8.72432434755134E-01 x2 : -1.25191408760747E+00 -2.41323838783057E+00 x3 : 5.37262903983637E-01 5.59863728713715E+00 y2 : -1.51777023097419E+00 7.81806413070460E-01 y3 : -5.74743960765193E+00 1.14426599856658E+00 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 2.093E-14 = rco : 7.790E-03 = res : 1.357E-14 == solution 20 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 4.59205968933158E-01 2.84430676608638E-03 x1 : 7.29747846328558E-01 9.34274647393962E-01 x2 : 2.02448793751861E+00 7.61111697280167E-01 x3 : -5.71596170223300E-01 -2.49754484545627E-01 y2 : 1.08845851321563E+00 -7.32403435039304E-01 y3 : 1.03214581848701E+00 -1.36807189056245E-01 zz1 : 0.00000000000000E+00 0.00000000000000E+00 == err : 1.429E-14 = rco : 2.438E-02 = res : 3.178E-15 ==