11
z21**2 + z22**2 - 1.25830472585 + 1.05384271933*i;
z31**2 + z32**2 + z33**2 - 1;
z41**2 + z42**2 + z43**2 - 1;
z51**2 + z52**2 + z53**2 - 1;
z21*z31 + z22*z32 + (0.642935654806 + 0.819555356316*i)*z33
- 0.266880023988 - 0.452565255666*i;
z31*z41 + z32*z42 + z33*z43 - 0.26425551745 - 0.342483846503*i;
z41*z51 + z42*z52 + z43*z53 - 0.126010863922 - 0.864590917688*i;
(0.352598136811 + 0.116888144319*i)*z51 + (0.539042485525 +
0.687058436892*i)*z52 + (0.391154215376 + 0.128900893182*i)*z53
- 0.179560356712 - 0.8709166566*i;
(0.984138451804 + 0.414967172346*i)*z21 + (0.958341609741
+ 0.847442419999*i)*z22*z33 + (-0.496254299764 - 0.546020011741*i)*z22
+ (0.353268870498 + 0.389909226888*i)*z31 + (0.964759562277 +
0.71397074519*i)*z32*z43 + (0.0783739840935 - 1.33026494666*i)*z32
+ (-0.964759562277 - 0.71397074519*i)*z33*z42 + (0.204379350351 +
0.00374294529684*i)*z41 + (0.706319991205 + 0.120097702053*i)*z42*z53
+ (-0.706319991205 - 0.120097702053*i)*z43*z52 + (0.907681632783
+ 0.405209293447*i)*z51 + (0.148939301127 + 0.182393186752*i)*z52
+ (-0.0486385369088 - 0.496934768083*i)*z53 -0.437312713588 - 0.914780691357*i;
(-0.958341609741 - 0.847442419999*i)*z21*z33 + (0.496254299764 +
0.546020011741*i)*z21 + (0.984138451804 + 0.414967172346*i)*z22 +
(-0.964759562277 - 0.71397074519*i)*z31*z43 + (-0.0783739840935 +
1.33026494666*i)*z31 + (0.353268870498 + 0.389909226888*i)*z32 + (
0.964759562277 + 0.71397074519*i)*z33*z41 + (-0.706319991205 -
0.120097702053*i)*z41*z53 + (0.204379350351 + 0.00374294529684*i)*z42
+ (0.706319991205 + 0.120097702053*i)*z43*z51 + (-0.148939301127
- 0.182393186752*i)*z51 + (0.907681632783 + 0.405209293447*i)*z52
+ (0.134045297503 + 0.164748774862*i)*z53 - 0.719086796333 - 0.691791591267*i;
(0.958341609741 + 0.847442419999*i)*z21*z32 + (-0.958341609741 -
0.847442419999*i)*z22*z31 + (0.964759562277 + 0.71397074519*i)*z31*z42
+ (-0.964759562277 - 0.71397074519*i)*z32*z41 + (0.353268870498
+ 0.389909226888*i)*z33 + (0.706319991205 + 0.120097702053*i)*z41*z52
+ (-0.706319991205 - 0.120097702053*i)*z42*z51 + (0.204379350351
+ 0.00374294529684*i)*z43 + (0.0486385369088 + 0.496934768083*i)*z51
+ (-0.134045297503 - 0.164748774862*i)*z52 + (0.907681632783 +
0.405209293447*i)*z53 - 0.64863071126 + 0.983034576618*i;
TITLE : 6R inverse position problem
ROOT COUNTS :
total degree : 1024
2-homogeneous Bezout number : 320
with partition of the set of unknowns
{z21 z22 z41 z42 z43 }{z31 z32 z33 z51 z52 z53 }
mixed volume : 288
REFERENCES :
This system occurs as Example 3.3 in a paper by Charles Wampler:
`Bezout Number Calculations for Multi-Homogeneous Polynomial Systems',
Appl. Math. Comput. vol. 51 No. 2--3, pp. 143--157.
For the original formulation of the problem, see
Charles Wampler and Alexander Morgan:
`Solving the 6R inverse position problem using a generic-case solution
methodology', Mech. Mach. Theory, Vol. 26, No. 1, pp. 91-106, 1991.
THE SOLUTIONS :
16 11
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 6.81970587371378E-01 -3.01278759670484E-01
z22 : -9.94245757505745E-01 3.23318560369258E-01
z31 : 1.54317164315374E+00 1.22732850162926E+00
z32 : 2.81049048704997E+00 -2.10543814021222E+00
z33 : -1.63885386351178E+00 -2.45496893479488E+00
z41 : 7.45430227704065E-02 -7.84645108001499E-01
z42 : -2.18970540639891E+00 1.72598710872434E+00
z43 : 1.93298656378182E+00 1.98547325336408E+00
z51 : -4.85810385366990E-01 -1.91577771101302E-02
z52 : 8.02040331104181E-01 8.95211069183146E-01
z53 : 1.14998861063535E+00 -6.32443158732329E-01
===========================================================
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -2.29988814831986E+00 7.17373476683257E-01
z22 : -5.72716802703412E-01 -1.96075510964076E+00
z31 : -1.05919002787836E+01 -1.01539769854502E+01
z32 : 1.29304069556761E+01 -6.98352911298370E+00
z33 : -1.51983745802156E+00 1.13499230817198E+01
z41 : -2.26115998547828E+00 -2.30619259640485E+00
z42 : 2.29826614384850E+00 -9.38021915922095E-01
z43 : -1.36124344574155E+00 2.24709725201204E+00
z51 : 1.20186321306191E+00 9.51481508604946E+00
z52 : -4.68613276096745E+00 6.92544765419444E-02
z53 : 8.36052479275234E+00 -1.32898003834334E+00
===========================================================
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 2.31900494002716E+00 1.03059923298664E+00
z22 : 1.32834940110141E+00 -2.19587261433677E+00
z31 : -1.98899942836999E-01 -2.22362461956776E+00
z32 : -3.14587274622510E+00 6.60631118423487E-01
z33 : -7.98906814668026E-01 -2.04777652536797E+00
z41 : 1.15974652589259E+00 4.88001269453221E-01
z42 : 6.44033633724012E-01 -7.06892226861346E-01
z43 : -3.16643933663386E-01 3.49589540788267E-01
z51 : -1.98911687777511E-01 3.46032894830508E-01
z52 : 5.08266037265028E-01 6.81175484596863E-01
z53 : 1.15893315773104E+00 -2.39348037676245E-01
===========================================================
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 2.18365896571556E+00 1.80966630183061E+00
z22 : -2.08867754878658E+00 2.14423495250026E+00
z31 : 4.81843255481218E-01 -1.28960352454974E+00
z32 : 1.28096766972151E+00 5.54012907963960E-01
z33 : 1.05072189121983E+00 -8.40240066366523E-02
z41 : 1.38377970541543E+00 7.02652983565586E-01
z42 : -8.22435276063626E-02 5.55077060371756E-01
z43 : -9.32045843741309E-01 9.94227321855330E-01
z51 : 4.60315939424511E-02 7.58090249167758E-01
z52 : 1.00431532852023E+00 -1.23005221023206E-02
z53 : -7.51653759569038E-01 2.99905366510561E-02
===========================================================
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 7.71134077461239E-01 -1.60310626298905E+00
z22 : -1.83911572131467E+00 -3.85668232453787E-01
z31 : 7.15436855460271E-01 3.75135727257400E+00
z32 : 4.11440390040185E+00 -5.16225922774964E-01
z33 : 3.74022679580931E-01 -1.49696082941238E+00
z41 : 2.67123550670565E+00 3.63968154763343E+00
z42 : 3.90818573176344E+00 -1.95517606829489E+00
z43 : 9.14782577308518E-01 -2.27513665167066E+00
z51 : -1.54208851652428E-01 7.72887375790832E-01
z52 : 1.07832146306922E+00 2.63866014741125E-02
z53 : -6.56210053238007E-01 -1.38267976119325E-01
===========================================================
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -5.00298739274631E-01 7.28569554344603E-01
z22 : 1.24730734266016E+00 -1.30215645011854E-01
z31 : -2.59557520130261E-01 1.26107248022139E+00
z32 : 1.79339883932277E-01 -1.23797672992466E-01
z33 : 1.59810240637033E+00 2.18711081707326E-01
z41 : 1.03460193309950E+00 -3.36396532820201E+00
z42 : 2.20421439712519E+00 7.30737156380066E-01
z43 : -2.71919877539606E+00 -6.87578888217881E-01
z51 : 7.88171187095119E+00 1.92366451357321E+00
z52 : -1.25110941844950E+00 4.52025258099505E+00
z53 : 1.48883599407384E+00 -6.38514845983260E+00
===========================================================
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 4.37283248113123E-01 -8.89867543350970E-01
z22 : 1.36715441909459E+00 -1.00791240545673E-01
z31 : 1.35777808007717E+00 2.32721202802259E+00
z32 : -2.93583857521152E+00 1.00097708094547E+00
z33 : 1.26394993889499E-01 -1.74951827911779E+00
z41 : 1.17951403187495E+00 -3.82268107746705E-01
z42 : 5.72539886469541E-01 7.60633915352336E-01
z43 : 1.35911834386697E-01 1.13289188938522E-01
z51 : -1.74445648385240E-01 -7.79965796046422E-02
z52 : 1.02675480227886E+00 1.59890617318345E-01
z53 : -3.91452903018916E-01 4.54140515246899E-01
===========================================================
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -4.99555731911250E-01 -1.99352718827046E-01
z22 : 1.15808378738411E+00 -5.40987759134689E-01
z31 : 9.96145049016820E-01 8.92770129503533E-01
z32 : -6.72881997109053E-01 3.30844893859260E-01
z33 : 9.67579199603118E-01 -6.89048474559156E-01
z41 : -1.78127264665466E+00 -2.00700893282373E+00
z42 : -1.19361875314657E+00 -1.06585102756570E+00
z43 : -2.38607487445747E+00 2.03147434310734E+00
z51 : 5.31641031985409E-01 2.54846676122444E+00
z52 : -8.15719600381305E-01 5.03833222419370E-01
z53 : 2.63231201750030E+00 -3.58575601141483E-01
===========================================================
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -6.93496077720817E-01 4.47800546954007E-01
z22 : 1.01174599269264E+00 -2.13861422050516E-01
z31 : 1.31796815852552E+00 2.72604838998726E-01
z32 : 1.97007290719133E-01 2.97020663628960E-01
z33 : 4.60004324669482E-01 -9.08251752175657E-01
z41 : -1.52744073954701E+00 2.59712919706687E+00
z42 : -1.58175051283236E-01 -1.70226809471439E+00
z43 : 3.11368212509459E+00 1.18756650477780E+00
z51 : 9.07659227166610E-01 -1.11422882832944E+00
z52 : 1.18754351241644E+00 8.44385418578340E-01
z53 : -8.48816999698801E-01 -1.01266249374823E-02
===========================================================
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 2.66481908093091E-01 1.03468542077653E+00
z22 : 1.58559629965657E+00 -5.06211010358362E-01
z31 : 1.03192784739305E+00 6.05614083801033E-02
z32 : -1.40465652827588E-01 -6.99278370349753E-01
z33 : 6.80993270985605E-01 -2.36007613337429E-01
z41 : -2.48048950753664E-01 1.04682265786768E+00
z42 : 1.02980866774719E+00 -9.38275267389665E-02
z43 : 1.04794911629913E+00 3.39985650712270E-01
z51 : 1.86703262040419E-01 1.56751052502684E+00
z52 : -2.43231108514791E-01 4.74207995184804E-01
z53 : 1.89649275172717E+00 -9.34974266621054E-02
===========================================================
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -4.24372482841892E-01 -2.55077953700953E-01
z22 : -1.19422050504439E+00 5.31869467583539E-01
z31 : 1.33000807168359E+00 -5.59719764088956E-01
z32 : -2.33375825256275E+00 7.84567854695449E-02
z33 : 3.77457574160048E-01 2.45731186277628E+00
z41 : -3.99132109966974E+00 -6.86226521093363E+00
z42 : 1.44849134680965E+00 5.53289293503752E+00
z43 : 8.77276128081271E+00 -4.03565654346351E+00
z51 : 1.10215004388434E+01 -2.32718338903976E+00
z52 : -6.41460503032980E+00 -6.29127892527439E-01
z53 : 1.71539803044640E+00 1.25996680745978E+01
===========================================================
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 4.87850965635014E-01 -2.72293659516384E-01
z22 : -1.10525165799615E+00 3.56554665249834E-01
z31 : 1.59044041129975E+00 -4.14887275164169E-01
z32 : -4.83754873147209E-01 -3.00893289429040E+00
z33 : -2.74703433501972E+00 2.89669645510664E-01
z41 : 1.70497604559462E-01 -6.56512986106398E-01
z42 : -2.13168565776507E+00 2.95248167617524E-01
z43 : 4.12772990716655E-01 1.79592704115149E+00
z51 : -3.21819085095715E-02 4.19891179071096E-01
z52 : 3.87031339759075E-01 7.05910326233974E-01
z53 : 1.25173190410585E+00 -2.07469761656965E-01
===========================================================
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -5.90559815647211E-01 2.58616898000339E-01
z22 : 1.05039659740691E+00 -3.56239360430552E-01
z31 : 2.63598470254880E+00 -3.79914501992130E-01
z32 : -1.15083230253870E-01 1.25266368008375E+00
z33 : -5.37814968339840E-01 -2.13011809951994E+00
z41 : -1.59207930157738E+00 2.94522710245143E+00
z42 : 3.18521188165958E-02 -1.92266503551917E+00
z43 : 3.55287284964421E+00 1.33702394215690E+00
z51 : 6.77906630938475E-01 -9.95240102410020E-01
z52 : 1.17712104814013E+00 6.89051523949577E-01
z53 : -8.05485196406118E-01 1.69360266213584E-01
===========================================================
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 5.34143439798264E-01 -1.18595377304174E+00
z22 : -1.54409952017977E+00 -6.90033684466385E-02
z31 : 3.11720695681086E+00 1.28562073306320E+00
z32 : -2.94569379794773E-01 -2.25133343506636E+00
z33 : -1.93498179331454E+00 2.41383138732426E+00
z41 : -3.90567228413289E+00 3.45602251629957E+00
z42 : 4.96824948247023E+00 5.01301882348671E-01
z43 : -1.98695303582802E+00 -5.53988863311166E+00
z51 : -5.63213111173968E-01 4.10498656415486E+00
z52 : 2.16558434026454E+00 -1.67652165508189E+00
z53 : -4.20178006161903E+00 -1.41431279346757E+00
===========================================================
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : 4.72424479766080E-01 1.28627012257572E-01
z22 : -1.14648332074158E+00 5.12600487405710E-01
z31 : 7.64576575645645E-01 -2.87849426335379E-01
z32 : 2.63751846620218E-01 3.28380623272373E-01
z33 : 7.53602895326760E-01 1.77111757046538E-01
z41 : 3.23057782056952E+00 -1.99811513263696E+00
z42 : -5.24662170782476E+00 -1.45230873501893E-01
z43 : 9.77709738993738E-01 5.82288868548987E+00
z51 : -2.56590509833729E-02 -6.08883205401490E-01
z52 : 5.02536399363437E-01 1.25439650177534E+00
z53 : 1.68466338351569E+00 -3.83461332933145E-01
===========================================================
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
z21 : -4.86620350997175E-01 1.37939023721610E+00
z22 : -1.71211214327275E+00 -8.42923766987067E-02
z31 : -4.15641453124895E+00 -3.69261536234890E+00
z32 : 8.35006798523235E-01 -3.50958503030795E+00
z33 : -4.20643098093262E+00 2.95203055663223E+00
z41 : -3.35027746089680E+00 2.08467473024577E+00
z42 : -2.13241748444097E+00 -1.21058722743327E+00
z43 : 1.34211528021645E+00 3.28046439581095E+00
z51 : 3.97615337952964E-01 3.89751937495167E+00
z52 : -1.52655837892728E+00 2.59972513983676E-01
z53 : 3.72365650104253E+00 -3.09601668041693E-01
===========================================================