16 + 1*x11*x22 -1*x21*x12 +( 9.76966807157667E-01 - 2.13391325297339E-01*i)*zz1 +( 7.32132041795361E-01 - 6.81162736338795E-01*i)*zz2 +( 3.08305693103935E-01 + 9.51287338084399E-01*i)*zz3 +(-4.11367555380587E-01 + 9.11469546600543E-01*i)*zz4 +(-9.00308200231017E-01 - 4.35252966212509E-01*i)*zz5 +( 9.16218691472794E-01 - 4.00678561188243E-01*i)*zz6; -1*x22*x13 + 1*x12*x23 +( 3.23224346711021E-01 + 9.46322366687607E-01*i)*zz1 +(-5.29640989908266E-01 - 8.48221917783897E-01*i)*zz2 +(-4.26601498074277E-01 + 9.04439694971856E-01*i)*zz3 +(-9.46105232370403E-01 - 3.23859366517853E-01*i)*zz4 +(-3.47250148653844E-01 + 9.37772538657367E-01*i)*zz5 +( 2.36837318100152E-01 - 9.71549321833497E-01*i)*zz6; -1*x23*x14 + 1*x13*x24 +(-5.94389402377049E-01 - 8.04177367464327E-01*i)*zz1 +(-4.67672215285115E-01 - 8.83901973665809E-01*i)*zz2 +( 9.74662069879301E-01 - 2.23682474813285E-01*i)*zz3 +(-6.58239849717447E-01 - 7.52808275886997E-01*i)*zz4 +( 9.99471881907434E-01 - 3.24954962481180E-02*i)*zz5 +( 1.12508864787379E-01 + 9.93650721000219E-01*i)*zz6; -1*x24*x15 + 1*x14*x25 +(-7.78154572240959E-01 - 6.28072815603805E-01*i)*zz1 +( 6.30382781913786E-01 + 7.76284450615002E-01*i)*zz2 +( 2.85234662133370E-01 - 9.58457712952252E-01*i)*zz3 +( 4.89892194718595E-01 + 8.71783022060993E-01*i)*zz4 +(-4.49011770796382E-01 - 8.93525841644380E-01*i)*zz5 +( 4.42792131387070E-02 + 9.99019194652343E-01*i)*zz6; + 1*zz1; + 1*zz2; + 1*zz3; + 1*zz4; + 1*zz5; + 1*zz6; +( 2.20756701822633E-01 - 1.00449031912498E-01*i)*x11 +( 1.97162336087696E-01 + 1.41246389830704E-01*i)*x22 +(-2.35004950462634E-01 - 5.99683472326832E-02*i)*x21 +( 2.11483990086607E-01 - 1.18735215285158E-01*i)*x12 +( 2.39680556551800E-01 + 3.71047196834071E-02*i)*x23 +( 3.25484487675933E-02 - 2.40341689880445E-01*i)*x13 +( 7.70057040851794E-02 + 2.29986197303470E-01*i)*x24 +(-2.38231282570925E-01 + 4.54904980889089E-02*i)*x14 +( 1.71136475067048E-01 - 1.71859932251210E-01*i)*x25 +( 1.12439421556746E-01 - 2.14897431096207E-01*i)*x15 +( 1.60624582643256E-01 - 1.81723066401722E-01*i)*zz1 +(-1.37363470116830E-01 - 1.99886984291693E-01*i)*zz2 +( 2.41103622795265E-01 - 2.63167719670007E-02*i)*zz3 +( 2.25690341043803E-02 - 2.41483266731590E-01*i)*zz4 +( 2.35050876480714E-01 + 5.97880830719050E-02*i)*zz5 +( 2.38573179668268E-01 - 4.36619669132855E-02*i)*zz6 -2.42535625036333E-01; +(-2.62727616080783E-01 - 4.07668709759222E-02*i)*x11 +( 2.04312679908305E-01 - 1.00589554759636E-01*i)*x22 +( 2.58983530466945E-01 - 7.39610441955277E-02*i)*x21 +( 1.16963258796495E-01 + 2.15513307280300E-01*i)*x12 +(-7.91930394341164E-02 + 2.36705500901392E-01*i)*x23 +( 8.49929611271099E-02 + 2.56543604402548E-01*i)*x13 +( 1.39276572035164E-01 - 2.18389924865886E-01*i)*x24 +(-1.45165161901107E-01 + 1.65408236204502E-01*i)*x14 +( 2.23236080803864E-01 - 1.43899078629963E-02*i)*x25 +( 2.32385818517349E-01 + 4.48339911325322E-02*i)*x15 +( 2.19043718840636E-01 - 4.00150744113310E-02*i)*zz1 +(-1.94193803136847E-01 + 1.43085401859897E-01*i)*zz2 +( 1.55609082767851E-01 + 1.66535715285662E-01*i)*zz3 +( 1.99433598157042E-01 - 1.12089799321027E-01*i)*zz4 +(-1.68302960858899E-02 - 2.48688436448842E-01*i)*zz5 +( 1.88881107208662E-02 - 2.32480224445729E-01*i)*zz6 +( 2.73941850639616E-02 + 2.41922480439389E-01*i); +(-2.09693497423640E-01 - 6.06568664079198E-02*i)*x11 +(-2.02984943340787E-01 - 2.33330362274900E-02*i)*x22 +(-7.96396451226193E-02 + 1.78727905593491E-01*i)*x21 +( 1.29767485782508E-01 - 1.62416789564791E-01*i)*x12 +( 1.05865337479671E-01 + 3.38379688026668E-01*i)*x23 +( 7.22403589733253E-02 - 2.48075219261028E-01*i)*x13 +( 2.32680806639747E-01 - 3.22645371408787E-02*i)*x24 +(-1.54513327652626E-01 + 1.89469853493276E-01*i)*x14 +(-1.27086056346477E-01 + 1.50714600873571E-01*i)*x25 +( 2.04998253200700E-01 + 2.79842299664887E-01*i)*x15 +(-1.35351675620552E-01 + 1.03062460372505E-01*i)*zz1 +(-6.60543807505464E-02 + 1.69729916414890E-01*i)*zz2 +( 1.80272006814168E-01 - 1.12058530891744E-01*i)*zz3 +(-7.66429079614479E-02 + 1.47575237668489E-01*i)*zz4 +(-1.19342720611601E-01 + 2.50547168609670E-01*i)*zz5 +( 7.22418523912957E-03 + 2.90707284513123E-01*i)*zz6 +(-1.56740671199014E-01 + 2.03726165526657E-01*i); +(-1.78217812032658E-01 - 1.37740183029315E-01*i)*x11 +( 1.76366128817572E-01 - 1.37281992675087E-01*i)*x22 +(-2.13391091023043E-01 - 5.00042961440823E-02*i)*x21 +(-2.38726408752580E-01 + 1.14690918066742E-01*i)*x12 +( 5.11585866540688E-02 - 2.21034233568508E-01*i)*x23 +( 8.91381845605656E-02 - 2.02543611918654E-01*i)*x13 +( 2.18845057882866E-02 - 2.51535941481459E-01*i)*x24 +( 1.32508977283289E-02 + 2.15120175288947E-01*i)*x14 +( 7.89735746325954E-02 - 2.11079213625671E-01*i)*x25 +( 1.69163006386814E-01 + 2.01519061136395E-01*i)*x15 +( 1.77881081415859E-01 + 2.04984804960430E-01*i)*zz1 +( 4.11352234554249E-02 - 2.44456314978442E-01*i)*zz2 +( 1.67682172322111E-01 + 1.86209896457425E-01*i)*zz3 +(-1.90532181157046E-01 + 1.26555998365947E-01*i)*zz4 +( 2.13646521046309E-01 + 7.65807640423438E-02*i)*zz5 +(-2.48637685459653E-01 + 8.56461371047928E-02*i)*zz6 +( 1.54490973156368E-01 - 2.36046188756202E-01*i); +(-1.78512852802684E-01 + 1.48748306752198E-01*i)*x11 +(-1.07073274701626E-01 + 2.24903458963115E-01*i)*x22 +(-1.18716757689872E-01 - 2.35760801489987E-01*i)*x21 +(-1.69881146923019E-01 - 1.51749855325575E-01*i)*x12 +( 3.63466618040351E-02 - 1.89000343650865E-01*i)*x23 +(-3.27239206986125E-02 - 2.37494408838454E-01*i)*x13 +(-1.45237946245397E-01 + 1.45286825163767E-01*i)*x24 +(-2.11911767228211E-01 - 1.70889659228521E-01*i)*x14 +(-1.36888001175610E-01 - 7.77790039754083E-02*i)*x25 +( 1.39226832215687E-01 + 1.71755560389577E-01*i)*x15 +( 2.82842892134566E-01 - 1.55332754192193E-01*i)*zz1 +( 1.25207918876152E-01 + 2.24945252998996E-01*i)*zz2 +(-1.48825669196689E-01 + 1.74593468812471E-01*i)*zz3 +(-3.09195714043395E-02 + 1.35746416517854E-01*i)*zz4 +(-1.47599240842556E-02 - 2.68035686970032E-01*i)*zz5 +(-1.56684210426334E-01 - 1.07832157509084E-01*i)*zz6 +(-1.76686751056363E-01 + 3.09867446668728E-01*i); +( 9.55861411136862E-02 - 2.58823141424987E-01*i)*x11 +(-2.65718477608021E-01 - 9.41151676206837E-02*i)*x22 +(-1.33368461736316E-01 - 1.60300788018879E-03*i)*x21 +( 1.34194584126783E-01 - 9.15152021895769E-02*i)*x12 +(-1.70495498762514E-01 + 3.80806797340058E-02*i)*x23 +(-2.91891716982566E-01 - 3.46273195436124E-02*i)*x13 +( 1.83961937592046E-01 - 1.80191112244373E-01*i)*x24 +( 3.29438823683700E-02 - 3.87651557453669E-01*i)*x14 +(-8.00030115731351E-02 - 2.43854616368129E-01*i)*x25 +( 1.61302976257896E-01 - 2.04911835789341E-01*i)*x15 +(-6.69014278633332E-03 + 2.71927098211752E-01*i)*zz1 +( 2.14268339641692E-01 + 5.84268182931578E-02*i)*zz2 +( 1.84822693655970E-01 + 7.90017097508527E-02*i)*zz3 +( 2.57036167040563E-01 - 1.25432855696957E-01*i)*zz4 +( 6.72019562702417E-02 + 7.38057791568771E-02*i)*zz5 +(-2.05940149382709E-01 - 1.18970921651760E-01*i)*zz6 +( 5.09031712690785E-02 + 1.30919791929166E-01*i); TITLE : All adjacent 2-by-2 minors of a general 2-by-5 matrix REFERENCES : Persi Diaconis, David Eisenbud, and Bernd Sturmfels: "Lattice Walks and Primary Decomposition", pages 173-193, in Bruce E. Sagan, Richard P. Stanley (eds): "Mathematical Essays in Honor of Gian-Carlo Rota". Progress in Mathematics, Vol 161, Birkh"auser, 1998. Serkan Hosten and Jay Shapiro: "Primary Decomposition of Lattice Basis Ideals", Journal of Symbolic Computation Vol 29, No 4 and 5, pages 625-639, 2000. The original system before the embedding is 4 10 x11*x22 - x21*x12; x12*x23 - x22*x13; x13*x24 - x23*x14; x14*x25 - x24*x15; THE FACTORIZATION : 5 5 : 1 3 6 8 12 4 : 2 4 9 10 3 : 5 14 15 1 : 7 3 : 11 13 16 Drop in #factors : 9 -> 5 count : 0 calculated sum at samples : -3.45485308948970E-01 9.36104245889853E-01 value at the linear trace : -3.45485308948972E-01 9.36104245889848E-01 The witness points 1 3 6 8 12 define a factor. calculated sum at samples : -1.39150273877609E+00 5.91945108234292E-01 value at the linear trace : -1.39150273877609E+00 5.91945108234292E-01 The witness points 2 4 9 10 define a factor. calculated sum at samples : -6.78318216506547E-02 1.42932439328891E-01 value at the linear trace : -6.78318216506565E-02 1.42932439328890E-01 The witness points 5 14 15 define a factor. calculated sum at samples : -5.32505070414575E-01 -3.85179906719496E-01 value at the linear trace : -5.32505070414575E-01 -3.85179906719492E-01 The witness points 7 define a factor. calculated sum at samples : -8.68785225380793E-01 8.06719241710448E-01 value at the linear trace : -8.68785225380790E-01 8.06719241710452E-01 The witness points 11 13 16 define a factor. The factorization is certified. Number of monodromy loops : 2 THE SOLUTIONS : 16 16 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -4.02792442345340E-01 2.82890442697093E-01 x22 : 5.19199135667336E-01 2.56458306862698E-01 x21 : 6.79876046012451E-01 -7.13702260183599E-01 x12 : -2.29114177876060E-01 -1.76417895199900E-01 zz1 : 4.95853151380726E-32 4.62531593602291E-32 zz2 : -2.07355220499916E-32 3.26860389987339E-32 zz3 : -2.32066588951745E-32 7.09851938013008E-32 zz4 : 4.78116521075270E-32 1.11042877012610E-32 zz5 : 2.59356865726671E-32 1.83068718981485E-32 zz6 : 2.61125445185065E-32 -2.11422408949171E-32 x13 : -3.95343978979226E-01 3.53856003007300E-01 x23 : 6.37379840672619E-01 -8.50133741938881E-01 x14 : 1.27033604949863E-01 6.71853773797299E-01 x24 : -5.13308143474273E-01 -1.26944557655065E+00 x15 : 1.57136547272155E-01 -4.49502552492658E-01 x25 : -1.32044490550863E-01 9.44408490894696E-01 == err : 2.013E-15 = rco : 5.410E-03 = res : 2.397E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : 2.54120344556252E+00 -1.36440338969540E+00 x22 : 1.13092517329978E+00 5.87447217930033E+00 x21 : 1.88330661795086E+00 -3.80369542022606E+00 x12 : -1.68780714078324E+00 3.69843468129138E+00 zz1 : 1.30208340995976E-30 1.17868039937629E-30 zz2 : -2.57733477756749E-31 4.60752678498606E-31 zz3 : -1.61728129255025E-30 -4.32688236445986E-31 zz4 : -3.67084075684706E-31 2.41846988110817E-31 zz5 : -2.36232564889147E-31 -2.52526280455982E-31 zz6 : -5.22361708503139E-31 -9.00988706255638E-31 x13 : -2.11597186973453E-31 -6.81482472961144E-32 x23 : -3.41813647666559E-31 2.76223881271267E-31 x14 : -4.26112183549748E+00 2.26573769500856E+00 x24 : -3.58878747835045E+00 -3.59455925992387E-01 x15 : 2.18315144874178E+00 -1.34762745979995E+00 x25 : 1.91618450809536E+00 6.80500708863341E-02 == err : 1.687E-14 = rco : 4.108E-03 = res : 1.149E-14 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : 6.96715371570828E-01 -1.39085202068993E+00 x22 : 3.21771223641426E+00 1.16608289121480E+00 x21 : 4.99918306565874E-01 -1.41591908339907E+00 x12 : 3.15687171753085E+00 1.61414616531553E+00 zz1 : -6.97478607050926E-31 2.32161874129707E-31 zz2 : -1.99153784838375E-31 2.20327961060837E-31 zz3 : 4.73799191572054E-32 -4.33336343440044E-32 zz4 : -4.58076614213853E-31 5.01013255725108E-32 zz5 : 1.28870900861402E-31 -4.14943339063743E-31 zz6 : 1.21838160108472E-31 5.77645200685296E-31 x13 : -5.32937896113768E-01 1.44728427090334E+00 x23 : -3.36270505126628E-01 1.45025984624331E+00 x14 : -1.60448575184931E+00 2.27072460837738E+00 x24 : -1.26345921783857E+00 2.36784497243580E+00 x15 : -1.81954243418771E-01 -1.71162510664752E+00 x25 : -3.80223062490493E-01 -1.61740977734699E+00 == err : 9.754E-15 = rco : 5.762E-03 = res : 9.111E-15 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -6.03561187322007E-01 -5.28642968832677E-02 x22 : -4.55505424733111E-01 1.17747520957719E-01 x21 : 3.55374037757914E-01 -1.25812490381688E+00 x12 : 9.30452291262949E-02 1.97185649347973E-01 zz1 : -6.25303376343621E-32 -7.19970073072649E-32 zz2 : -9.70336893739213E-32 -8.33859922002304E-32 zz3 : 1.89207875735270E-32 -1.89205840180534E-32 zz4 : -3.24660457675347E-32 1.87923629856375E-32 zz5 : -3.91994065092135E-32 -2.52798824650777E-32 zz6 : 4.50252582164007E-32 -4.44188860452640E-32 x13 : -2.40394443745908E-31 -3.31342618360523E-31 x23 : 1.94599703105937E-30 -2.18197671530394E-31 x14 : -2.43252359633523E-01 2.63065522581427E-01 x24 : -3.68044090545412E-01 -1.31464726406526E+00 x15 : 9.85824483618760E-02 -3.67198117596963E-01 x25 : 9.94825817477303E-01 1.05306449121776E+00 == err : 3.084E-15 = rco : 1.602E-03 = res : 2.207E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : 1.25195158369531E-01 5.13211816172975E-01 x22 : 7.97155682713747E-32 1.29016673093533E-31 x21 : 2.05204085221300E+00 -8.72096258549346E-01 x12 : -1.14429283847436E-31 1.17255057418005E-31 zz1 : 1.60546546626302E-31 -9.64106826826650E-32 zz2 : -1.23325842207493E-31 -8.00406323717541E-32 zz3 : 1.40345248983598E-31 1.61234386263336E-31 zz4 : 8.50285640633324E-32 -1.08509621783969E-31 zz5 : -1.84949185566028E-32 3.53935228242398E-32 zz6 : -9.11713237463569E-32 7.45621093599962E-32 x13 : 1.30223933802824E+00 1.78312577641953E+00 x23 : -8.61263876596566E-01 5.81173573781052E-01 x14 : -8.54297997584674E-01 2.45532524296868E-01 x24 : -1.00517104362420E-01 -4.06015283701706E-01 x15 : 3.42702364361880E-01 8.50267545708326E-01 x25 : -4.05819443308829E-01 1.46280287848649E-01 == err : 3.025E-15 = rco : 1.334E-02 = res : 3.417E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -1.58585173294861E+00 -3.92940495216886E-01 x22 : 1.25604297710578E-01 8.46474487063739E-01 x21 : 6.93968463756436E-01 2.19550625174710E-01 x12 : -4.01975882251105E-01 -1.87830435959793E+00 zz1 : 5.75644083567789E-32 7.83756704350078E-31 zz2 : 7.12967659224891E-31 -4.66657101373678E-31 zz3 : 6.34202358473769E-31 -5.19559039612782E-32 zz4 : -1.01239570196281E-31 -1.04390591592878E-32 zz5 : 2.88959319506800E-31 -1.94941415465405E-32 zz6 : 1.64045061221999E-31 -1.51804094480917E-31 x13 : -1.23738755550439E+00 2.91612076555745E+00 x23 : 6.32616478873512E-01 -1.26153487575973E+00 x14 : -7.71479973746101E-01 1.21711174911154E+00 x24 : 3.77424192991156E-01 -5.19319361574002E-01 x15 : -2.26031479734620E+00 8.37758411173823E-01 x25 : 1.02864251060671E+00 -3.08553238682322E-01 == err : 9.088E-15 = rco : 8.632E-03 = res : 7.133E-15 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -3.83477115067011E+00 1.40771684393325E+00 x22 : -5.48670566697772E-31 1.36262973686310E-31 x21 : 3.47362417103546E-01 2.04099673275027E+00 x12 : 2.87389317196967E-31 3.05846375113693E-31 zz1 : -8.76018811816934E-31 -3.97340554642623E-31 zz2 : -8.65538814260155E-31 1.08283893984941E-30 zz3 : -4.06423325386366E-31 -9.58414783058875E-32 zz4 : 1.63365453489266E-30 5.70695191032608E-31 zz5 : 3.86015475973118E-32 -3.27849096680890E-32 zz6 : -2.79627697190279E-31 -1.70519098216601E-31 x13 : -2.95477949148234E-02 6.02834612030409E+00 x23 : -3.99345377739847E+00 -6.14515915417807E-01 x14 : -1.94002276251365E-31 2.31386440827521E-31 x24 : 1.02498783182501E-31 -2.54372582149637E-31 x15 : -3.22979026536074E+00 4.04733964764523E+00 x25 : 3.32986407251973E+00 -3.97473547944497E+00 == err : 1.567E-14 = rco : 3.875E-03 = res : 7.473E-15 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -5.40518698437404E-01 8.98935272557128E-01 x22 : 4.15637067470138E-04 -1.31219608106124E+00 x21 : 3.87962503957247E-01 5.13918200286603E-01 x12 : 1.98309019538790E+00 -7.97772961078341E-01 zz1 : -1.79126925134633E-31 -4.25349468524433E-32 zz2 : 4.47704216165853E-32 -4.30854903086982E-32 zz3 : -8.74679957594854E-32 -1.98091250271509E-32 zz4 : 5.41392549644287E-32 -1.82366752750538E-32 zz5 : 5.42472581587300E-32 -2.75156050461733E-32 zz6 : -5.38420648256219E-32 -1.72386382582626E-32 x13 : -8.37566525822542E-01 5.21452451732883E-01 x23 : 1.04893654866312E-01 5.96518288564238E-01 x14 : 4.35718230176988E-01 -5.74760113668320E-01 x24 : -2.27390648322055E-01 -3.79908467239117E-01 x15 : -4.31477359808418E-01 -7.05707668471017E-01 x25 : -5.00800505829877E-01 8.38915346780128E-02 == err : 1.817E-15 = rco : 1.126E-02 = res : 3.886E-15 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : 8.63389074085771E-01 6.63674091904428E-01 x22 : 1.34728746804558E+00 -1.33883410854320E+00 x21 : 1.34305211516686E+00 -5.90738104298573E-01 x12 : 1.35188827008441E+00 3.99714168490215E-01 zz1 : -2.66278905483773E-32 1.27325482648769E-31 zz2 : 3.38918351839698E-32 -6.30435087370376E-32 zz3 : 1.38444327123482E-32 -1.50551386262962E-31 zz4 : 1.58189957099195E-31 -3.62695654628270E-32 zz5 : 7.29073834735042E-33 5.94283636521983E-33 zz6 : -3.14254159807355E-33 -4.13196636445168E-32 x13 : -2.10890327521524E-32 -1.96495060217972E-31 x23 : -9.55648388446136E-32 -2.83176275923319E-31 x14 : 6.09576069800974E-01 -7.74193138411012E-02 x24 : -7.96433717722620E-01 -1.97931031132035E-01 x15 : 9.50505968956196E-01 -1.43327714095925E+00 x25 : -1.87564142390645E+00 1.32578161013022E+00 == err : 4.422E-15 = rco : 9.070E-03 = res : 3.851E-15 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -2.26320448760651E+00 1.36942876286019E+00 x22 : 6.58776436130619E-02 8.15337884133541E-02 x21 : -7.54048781855414E-01 1.53966575207705E-01 x12 : 3.07442355835692E-01 1.87850900161594E-01 zz1 : -1.87361837906248E-31 -2.58906036909461E-31 zz2 : -5.64384304110381E-33 6.13593355015373E-33 zz3 : -1.91664640140638E-31 -2.36561672044296E-31 zz4 : -4.91846992886261E-32 -7.52047939892023E-32 zz5 : 3.61100609937912E-32 -1.24882573938856E-31 zz6 : 8.37132301108733E-32 -6.05107913933189E-32 x13 : -1.41613736189591E-31 -4.72007935787077E-31 x23 : -6.04755438533669E-32 6.04784245928098E-31 x14 : 1.07850447943484E+00 4.44287570217665E-01 x24 : -2.75792325260109E-01 -2.04256447991321E+00 x15 : 2.35807277616793E-01 7.06507174562634E-01 x25 : 8.71458878738111E-01 -9.86253830106695E-01 == err : 6.306E-15 = rco : 3.707E-03 = res : 4.066E-15 == solution 11 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : 1.69821341678413E+00 -7.89040673624857E-02 x22 : 8.27823430184650E-01 -1.68937439958290E+00 x21 : 2.38127686856269E+00 -1.25846000981595E+00 x12 : 9.26752335398411E-01 -7.42440401316091E-01 zz1 : 4.76698497730361E-32 -2.46809049585496E-33 zz2 : 7.20942414565495E-32 -5.91430613651074E-32 zz3 : 4.16493714769804E-32 9.14648134340969E-32 zz4 : 2.14512952324489E-32 -9.46003562921824E-32 zz5 : 1.23199838303494E-32 2.98098133028423E-32 zz6 : 5.53711966838445E-32 -3.07298692794187E-33 x13 : 4.24852812198359E-01 1.89026616504074E-01 x23 : 7.36540019801048E-01 -1.55572681189518E-02 x14 : -2.01762496287152E-32 7.86720653672912E-32 x24 : -2.77986441316423E-32 -1.66587240328678E-31 x15 : 7.76551051334962E-01 -1.62500772242198E+00 x25 : -2.66985665031433E+00 2.81281406850061E+00 == err : 3.115E-15 = rco : 5.158E-03 = res : 5.163E-15 == solution 12 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -4.69268601324407E-01 2.38983070563039E-04 x22 : -4.85062559247390E-01 2.57305152611897E-01 x21 : 4.43272256449569E-01 -1.25321864720210E+00 x12 : 1.42801993675243E-01 1.31072878274053E-01 zz1 : -7.94052829057839E-32 -7.24275683639089E-33 zz2 : 6.50218186948754E-32 -7.81469590527154E-32 zz3 : -6.87392020458527E-32 5.17873312726918E-32 zz4 : -6.46373811446582E-32 1.09443295868090E-32 zz5 : 5.05039716864011E-33 5.76133469803534E-32 zz6 : -6.30177937130280E-33 -5.36516147249260E-32 x13 : 3.59065316892816E-02 -7.12484780034330E-02 x23 : 1.56274109064944E-01 1.63272282297889E-01 x14 : -3.85522575109033E-01 2.80639593328517E-01 x24 : -3.84645084504299E-01 -1.29485703449216E+00 x15 : 2.22718093799789E-01 -3.89889152895370E-01 x25 : 8.30358868345176E-01 9.63499269340215E-01 == err : 3.086E-15 = rco : 2.042E-03 = res : 2.270E-15 == solution 13 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -1.59880170261084E+00 -7.94206641981988E-01 x22 : 1.01108970082073E-01 -1.25718988196333E+00 x21 : 1.46680253970366E+00 -8.31265550914877E-01 x12 : -1.16297103919313E+00 6.56501553908253E-01 zz1 : -5.42260152309161E-31 -2.14325166295471E-31 zz2 : -2.13519110329718E-32 1.45817350693006E-31 zz3 : 7.24558955332876E-31 -7.04721362568615E-31 zz4 : -3.16141806186303E-31 -1.72049198055714E-31 zz5 : 1.65775604483548E-31 4.36179028955540E-32 zz6 : 2.32087711450514E-31 1.24697191477136E-31 x13 : 3.43589003985197E-01 4.50002577178820E+00 x23 : -3.70320734317127E+00 -2.11028275364739E+00 x14 : 1.49863811520532E-33 3.48188178459239E-32 x24 : -3.84437830804187E-32 1.04129058524601E-32 x15 : -2.56644770667886E+00 1.68455079402361E+00 x25 : 2.85784537596312E+00 1.13084535365197E+00 == err : 6.913E-15 = rco : 6.964E-03 = res : 7.556E-15 == solution 14 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -4.49381258568412E-01 -1.77663133362104E-01 x22 : 4.26849042206608E-30 -4.65270743919520E-32 x21 : 4.97379027034167E-01 -1.22437228957284E+00 x12 : -1.45557039726093E-31 -1.41558623903635E-30 zz1 : 7.98454356239326E-32 7.76006863821764E-33 zz2 : 7.00787332261422E-32 -1.53997629576535E-31 zz3 : 1.25087191449540E-31 -1.04574392039314E-32 zz4 : -1.20689384427245E-31 1.65979733312853E-32 zz5 : 3.16138576435756E-32 -3.26357706500299E-32 zz6 : -7.47016182780190E-32 3.88236866177928E-32 x13 : -1.80569691995130E-01 1.13335631476038E-01 x23 : 2.99117170701117E-01 -4.32824128514627E-01 x14 : -6.97718110988808E-02 4.96392666899318E-01 x24 : -3.25110803009834E-01 -1.19358420115199E+00 x15 : 1.93506505206605E-02 -5.83866127509192E-01 x25 : 5.24620193371832E-01 1.34284979277686E+00 == err : 3.071E-15 = rco : 2.737E-03 = res : 2.009E-15 == solution 15 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -2.51329713186576E+00 9.23866607869702E-01 x22 : -3.74649632153522E-31 1.02317120893095E-30 x21 : -8.32419547115605E-01 -1.80910081884219E-01 x12 : 3.14544783675379E-31 3.39829252436615E-30 zz1 : -1.03959453486593E-31 3.80770515253086E-31 zz2 : 5.63772719935235E-32 4.94710396559869E-32 zz3 : 8.54560887063446E-32 -3.60141799576621E-31 zz4 : 2.22666638598801E-31 -1.19073176486129E-31 zz5 : 2.37734116245113E-32 1.39846439543824E-31 zz6 : 6.56526569902356E-32 -4.58067064975505E-31 x13 : 1.22032018417581E-01 1.20376429316825E-01 x23 : 6.40011518258671E-02 -2.66131387033610E-01 x14 : 1.11164826662483E+00 7.26337816731773E-01 x24 : 7.67230752990431E-02 -2.11906425386394E+00 x15 : -6.46966583801054E-02 8.11173172593789E-01 x25 : 1.16263528282179E+00 -5.80339947292539E-01 == err : 9.104E-15 = rco : 2.769E-03 = res : 3.940E-15 == solution 16 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x11 : -1.13284606121760E+00 1.12725698417250E-01 x22 : 2.72823148570831E-02 -8.17089313076077E-01 x21 : -1.39586773380786E-01 3.68380948503060E-01 x12 : 2.14948876507054E+00 -9.80616677277688E-01 zz1 : 3.97778816079700E-32 2.78549841307738E-31 zz2 : -2.68837040909064E-32 -2.10983271978553E-31 zz3 : -1.31081535444202E-31 9.56178872453105E-32 zz4 : -2.66329559319259E-31 2.23520029589300E-31 zz5 : 5.31223125993142E-32 -1.27996080161038E-31 zz6 : 1.64224481727243E-32 -4.42299445457877E-32 x13 : -1.28717580216266E+00 1.06521947219650E+00 x23 : 1.31771571970734E-01 5.62932296161822E-01 x14 : 1.28175144648903E-32 1.19789679359056E-33 x24 : 8.67111038036259E-32 2.11397862276576E-31 x15 : -1.36945169799908E+00 -6.06663398080392E-01 x25 : 5.18398220930855E-01 -3.59132360569460E-01 == err : 4.286E-15 = rco : 1.029E-02 = res : 3.698E-15 ==