13 + 1*t1*T1 +(-9.82663945711272E-01 + 1.85395711382851E-01*i)*zz1 -1; + 1*t2*T2 +(-6.06883537412198E-01 + 7.94790772479183E-01*i)*zz1 -1; + 1*t3*T3 +(-9.97690621485706E-01 - 6.79221893011784E-02*i)*zz1 -1; + 1*t4*T4 +( 3.42660717311994E-01 + 9.39459223602190E-01*i)*zz1 -1; + 1*t5*T5 +( 1.40373471592456E-01 + 9.90098625629327E-01*i)*zz1 -1; + 1*T6*t6 +(-3.58642418819352E-01 - 9.33475021317338E-01*i)*zz1 -1; + 7.10358341606050E-01*t1 + 4.60000000000000E-01*t2 -4.10000000000000E-01*t3 +( 7.59146786344824E-01 + 6.50919470274415E-01*i)*zz1 +( 2.40761300555120E-01 + 1.07248215701824E+00*i); +(-1.10000000000000E-01 + 4.90000000000000E-01*i)*t2 + 4.10000000000000E-01*t3 -5.02195181179590E-01*t4 + 4.10000000000000E-01*t5 +( 5.86108620815476E-01 + 8.10232487996982E-01*i)*zz1; + 5.02195181179590E-01*t4 +(-9.80434782608700E-02 + 4.36739130434780E-01*i)*t5 -7.75518556663660E-01*t6 +( 2.10018102272233E-01 - 9.77697497551246E-01*i)*zz1 -1.20000000000000E+00; + 7.10358341606050E-01*T1 + 4.60000000000000E-01*T2 -4.10000000000000E-01*T3 +( 9.99999540410766E-01 + 9.58737845553301E-04*i)*zz1 +( 2.40761300555120E-01 - 1.07248215701824E+00*i); +(-1.10000000000000E-01 - 4.90000000000000E-01*i)*T2 + 4.10000000000000E-01*T3 -5.02195181179590E-01*T4 + 4.10000000000000E-01*T5 +( 9.93875226626463E-01 - 1.10508071642741E-01*i)*zz1; -7.75518556663660E-01*T6 + 5.02195181179590E-01*T4 +(-9.80434782608700E-02 - 4.36739130434780E-01*i)*T5 +( 2.83672137272669E-01 - 9.58921330733213E-01*i)*zz1 -1.20000000000000E+00; +( 2.06548571937060E-01 + 9.78436348175374E-01*i)*t1 +(-9.36501214704945E-01 - 3.50664333595765E-01*i)*T1 +(-2.31035297832744E-02 - 9.99733077832055E-01*i)*T6 +( 9.09646477498280E-01 + 4.15383300067506E-01*i)*t2 +( 9.64817018644621E-01 + 2.62922270897132E-01*i)*T2 +(-1.83228392705332E-01 + 9.83070371899500E-01*i)*t3 +(-1.51754872396534E-01 + 9.88418159841224E-01*i)*T3 +( 8.27184027273669E-01 - 5.61931121244689E-01*i)*t4 +(-7.29317684887040E-01 - 6.84175207465901E-01*i)*T4 +( 7.07242354213735E-01 + 7.06971182161065E-01*i)*t5 +(-9.00641770228247E-01 - 4.34562310514994E-01*i)*T5 +( 3.87233307759338E-02 + 9.99249970554724E-01*i)*t6 +(-3.60431674345731E-01 - 9.32785617453621E-01*i)*zz1 +(-8.87860286386579E-01 - 4.60113151146043E-01*i); TITLE : seven bar mechanism which permits motion REFERENCES : Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler: "Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components." SIAM J. Numer. Anal. 38(6):2022-2046, 2001. THE SOLUTIONS with zz = 0 : 6 13 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -2.00856115602016E-01 -5.28919129835141E-01 T1 : -6.27481969195073E-01 1.65236301687478E+00 T6 : -1.74968006028292E+00 -2.50313499134116E-01 t2 : 1.01275336146284E+00 8.42491267965025E-01 T2 : 5.83564491103939E-01 -4.85456782231142E-01 t3 : 1.37548299914036E+00 2.64464883992378E+00 T3 : 1.54790037653236E-01 -2.97615669381030E-01 t4 : -1.04386423986078E+00 8.03622023398764E-01 T4 : -6.01491070872434E-01 -4.63059709273360E-01 t5 : -1.37548299914038E+00 -2.64464883992377E+00 T5 : -1.54790037653235E-01 2.97615669381030E-01 t6 : -5.60070181626972E-01 8.01250069118656E-02 zz1 : 5.11446368733129E-15 1.91878575942675E-15 == err : 6.690E-15 = rco : 1.000E+00 = res : 2.424E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 2.97762308629313E-01 -1.27917684893826E+00 T1 : 1.72620253840526E-01 7.41570796475579E-01 T6 : -6.85752223949406E-01 3.30860825075803E-01 t2 : -2.46594871192557E-02 -6.91363700751003E-01 T2 : -5.15250871018665E-02 1.44457890498649E+00 t3 : 1.07545335666090E+00 -3.76144122828918E-01 T3 : 8.28492677400076E-01 2.89768635227845E-01 t4 : 6.79976172111048E-01 1.27374496592994E-01 T4 : 1.42078508469285E+00 -2.66144303803678E-01 t5 : -1.07545335666089E+00 3.76144122828928E-01 T5 : -8.28492677400078E-01 -2.89768635227857E-01 t6 : -1.18289227832731E+00 -5.70720300299083E-01 zz1 : -1.55339562959215E-15 7.52606933338563E-17 == err : 7.279E-15 = rco : 1.000E+00 = res : 2.353E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 7.62555832973611E-01 -2.54909904780820E+00 T1 : 1.07714794755708E-01 3.60072887615209E-01 T6 : -3.27735298299225E-01 1.83968844246898E-01 t2 : -1.16697305787094E-01 -4.66492634293080E-01 T2 : -5.04672703668057E-01 2.01740817752416E+00 t3 : 1.77748399216149E+00 -2.32409323645651E+00 T3 : 2.07629170333930E-01 2.71478985235398E-01 t4 : 4.80725629172970E-01 -1.16836845181484E-02 T4 : 2.07896061833568E+00 5.05276159960098E-02 t5 : -1.77748399216148E+00 2.32409323645652E+00 T5 : -2.07629170333928E-01 -2.71478985235400E-01 t6 : -2.32016840357183E+00 -1.30238854916864E+00 zz1 : -3.01553362588048E-15 -1.06788950824667E-15 == err : 1.568E-14 = rco : 1.000E+00 = res : 2.468E-15 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -3.40847396227183E-01 -6.00949724221288E+00 T1 : -9.40781656947002E-03 1.65869677618999E-01 T6 : -1.63902412728482E-01 2.71524597010686E-02 t2 : 8.16083377691278E-02 7.28964514182194E+00 T2 : 1.53556190799670E-03 -1.37163698080266E-01 t3 : 8.82374263518028E-02 3.82493725346008E-01 T3 : 5.72645702576527E-01 -2.48231841224147E+00 t4 : -7.13050059189394E+00 -1.51708520640123E+00 T4 : -1.34169196349009E-01 2.85458363424324E-02 t5 : -8.82374263518005E-02 -3.82493725346006E-01 T5 : -5.72645702576527E-01 2.48231841224148E+00 t6 : -5.93822277478774E+00 -9.83739970048482E-01 zz1 : 2.75448582756694E-17 -3.39892830375874E-15 == err : 1.551E-14 = rco : 1.000E+00 = res : 5.463E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -5.83697419415100E-01 -2.74754565812118E-01 T1 : -1.40246897862797E+00 6.60161827808008E-01 T6 : -9.51325104619335E-01 -1.22381102308713E+00 t2 : 4.78345775572429E-01 -2.39702234146960E-01 T2 : 1.67094944485355E+00 8.37323826260852E-01 t3 : 1.12600064543888E-01 1.87084129656501E+00 T3 : 3.20548960381956E-02 -5.32589599377880E-01 t4 : 1.29105299789522E-01 5.19233727361093E-01 T4 : 4.50988469068829E-01 -1.81377855264843E+00 t5 : -1.12600064543881E-01 -1.87084129656500E+00 T5 : -3.20548960381935E-02 5.32589599377883E-01 t6 : -3.95934610357193E-01 5.09341273791705E-01 zz1 : -9.61595033944588E-16 1.48125072183152E-15 == err : 4.443E-15 = rco : 1.000E+00 = res : 1.718E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 6.55409910666377E-02 -3.53018891682697E-01 T1 : 5.08393022774153E-01 2.73832205644363E+00 T6 : -2.56046776898957E+00 1.09584485871705E+00 t2 : -4.88493977321997E-01 -2.05403451560476E+00 T2 : -1.09584699161710E-01 4.60785116930810E-01 t3 : 1.52711367581249E-01 -3.00350328320192E-01 T3 : 1.34510625239674E+00 2.64553393065488E+00 t4 : 2.11115377025613E+00 -2.67191973840489E-02 T4 : 4.73598778158793E-01 5.99396378073241E-03 t5 : -1.52711367581249E-01 3.00350328320194E-01 T5 : -1.34510625239673E+00 -2.64553393065489E+00 t6 : -3.30090279874494E-01 -1.41274082999171E-01 zz1 : -3.24487325082003E-15 9.98270297019926E-16 == err : 6.171E-15 = rco : 1.000E+00 = res : 3.186E-15 == 12 + 1*t1*T1 -1; + 1*t2*T2 -1; + 1*t3*T3 -1; + 1*t4*T4 -1; + 1*t5*T5 -1; + 1*T6*t6 -1; + 7.10358341606050E-01*t1 + 4.60000000000000E-01*t2 -4.10000000000000E-01*t3 +( 2.40761300555120E-01 + 1.07248215701824E+00*i); +(-1.10000000000000E-01 + 4.90000000000000E-01*i)*t2 + 4.10000000000000E-01*t3 -5.02195181179590E-01*t4 + 4.10000000000000E-01*t5; + 5.02195181179590E-01*t4 +(-9.80434782608700E-02 + 4.36739130434780E-01*i)*t5 -7.75518556663660E-01*t6 -1.20000000000000E+00; + 7.10358341606050E-01*T1 + 4.60000000000000E-01*T2 -4.10000000000000E-01*T3 +( 2.40761300555120E-01 - 1.07248215701824E+00*i); +(-1.10000000000000E-01 - 4.90000000000000E-01*i)*T2 + 4.10000000000000E-01*T3 -5.02195181179590E-01*T4 + 4.10000000000000E-01*T5; -7.75518556663660E-01*T6 + 5.02195181179590E-01*T4 +(-9.80434782608700E-02 - 4.36739130434780E-01*i)*T5 -1.20000000000000E+00; THE SOLUTIONS with zz = 0 : 6 12 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 3.53717078322842E-01 -5.30879118400571E-01 T1 : 8.69193907041778E-01 1.30453665759482E+00 T6 : -4.40509781239132E-01 4.61410384022371E-01 t2 : -5.99365365166591E-01 -1.57888836421937E+00 T2 : -2.10146778358550E-01 5.53582709999064E-01 t3 : 5.27607584716194E-01 -7.54168308853155E-02 T3 : 1.85739737768407E+00 2.65498503011434E-01 t4 : 5.86169848996847E-01 -8.37877878416882E-02 T4 : 1.67183103323241E+00 2.38973437749066E-01 t5 : -1.85739737768407E+00 2.65498503011427E-01 T5 : -5.27607584716193E-01 -7.54168308853131E-02 t6 : -1.08247082572555E+00 -1.13383016827929E+00 == err : 6.402E-15 = rco : 4.015E-03 = res : 1.639E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -1.24225818334613E+00 -8.07075027813308E-01 T1 : -5.66058532229593E-01 3.67759063106020E-01 T6 : -1.05957839449339E+00 -1.03531112257767E+00 t2 : 1.47332994921905E+00 -5.78910775622762E-01 T2 : 5.87958784214731E-01 2.31024744989665E-01 t3 : 8.79136932379953E-02 5.67977370543051E-01 T3 : 2.66141319725189E-01 -1.71943916132782E+00 t4 : 9.66290808831272E-02 6.24284218493858E-01 T4 : 2.42136902539458E-01 -1.56435563278512E+00 t5 : -2.66141319725164E-01 -1.71943916132782E+00 T5 : -8.79136932379879E-02 5.67977370543054E-01 t6 : -4.82817017275396E-01 4.71759173981639E-01 == err : 4.456E-15 = rco : 1.966E-03 = res : 1.287E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -5.66058532229594E-01 -3.67759063106020E-01 T1 : -1.24225818334613E+00 8.07075027813308E-01 T6 : -4.82817017275396E-01 -4.71759173981639E-01 t2 : 5.87958784214731E-01 -2.31024744989665E-01 T2 : 1.47332994921905E+00 5.78910775622763E-01 t3 : 2.66141319725189E-01 1.71943916132782E+00 T3 : 8.79136932379953E-02 -5.67977370543051E-01 t4 : 2.42136902539458E-01 1.56435563278512E+00 T4 : 9.66290808831273E-02 -6.24284218493859E-01 t5 : -8.79136932379880E-02 -5.67977370543054E-01 T5 : -2.66141319725164E-01 1.71943916132782E+00 t6 : -1.05957839449339E+00 1.03531112257767E+00 == err : 1.839E-15 = rco : 2.764E-03 = res : 9.051E-16 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : -5.45421549881404E-01 -8.38161877518279E-01 T1 : -5.45421549881404E-01 8.38161877518279E-01 T6 : -8.74935009483375E-01 4.84240363022668E-01 t2 : -5.49340801920860E-01 -8.35598398361884E-01 T2 : -5.49340801920860E-01 8.35598398361884E-01 t3 : -9.74098087752272E-01 2.26125884049939E-01 T3 : -9.74098087752272E-01 -2.26125884049939E-01 t4 : 1.78912046655934E-01 -9.83865071827121E-01 T4 : 1.78912046655934E-01 9.83865071827120E-01 t5 : 4.72153176961019E-02 -9.98884734979395E-01 T5 : 4.72153176961019E-02 9.98884734979395E-01 t6 : -8.74935009483376E-01 -4.84240363022668E-01 == err : 3.355E-15 = rco : 9.183E-03 = res : 1.179E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 8.69193907041778E-01 -1.30453665759482E+00 T1 : 3.53717078322842E-01 5.30879118400571E-01 T6 : -1.08247082572555E+00 1.13383016827929E+00 t2 : -2.10146778358550E-01 -5.53582709999064E-01 T2 : -5.99365365166591E-01 1.57888836421937E+00 t3 : 1.85739737768407E+00 -2.65498503011434E-01 T3 : 5.27607584716194E-01 7.54168308853154E-02 t4 : 1.67183103323241E+00 -2.38973437749066E-01 T4 : 5.86169848996847E-01 8.37877878416882E-02 t5 : -5.27607584716193E-01 7.54168308853132E-02 T5 : -1.85739737768407E+00 -2.65498503011427E-01 t6 : -4.40509781239132E-01 -4.61410384022371E-01 == err : 7.274E-15 = rco : 5.818E-03 = res : 9.273E-16 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : t1 : 2.80836878017553E-01 -9.59755514673062E-01 T1 : 2.80836878017553E-01 9.59755514673062E-01 T6 : -9.37276397924231E-01 -3.48587082225058E-01 t2 : -9.99161738567148E-01 4.09367827689773E-02 T2 : -9.99161738567148E-01 -4.09367827689773E-02 t3 : -4.72153176960935E-02 9.98884734979395E-01 T3 : -4.72153176960935E-02 -9.98884734979395E-01 t4 : 9.35633636119244E-01 -3.52972660360944E-01 T4 : 9.35633636119244E-01 3.52972660360944E-01 t5 : 9.74098087752276E-01 -2.26125884049923E-01 T5 : 9.74098087752276E-01 2.26125884049923E-01 t6 : -9.37276397924231E-01 3.48587082225058E-01 == err : 2.465E-15 = rco : 1.379E-02 = res : 9.934E-16 ==