Given partitions l and m in the Grassmannian Gr(k,n), and a set of fixed flags G1,...,Gd, where d=k*(k-n) - |l| - |m|. The function solves the system taking the first d-1 flags, and replacing the last one for a simpler one Gm. Then it uses homotopy continuation to track the solutions of this simpler system to solutions of the original system. This function is used to solve Simple Schubert Problems, as described in the paper: Leykin and Sottile, "Galois groups of Schubert problems via homotopy continuation", Mathematics of Computation, 78 (2009) 1749--1765.
i1 : k = 3 o1 = 3 |
i2 : n = 7 o2 = 7 |
i3 : l = {2,1,0}
o3 = {2, 1, 0}
o3 : List
|
i4 : m = {1,1,0}
o4 = {1, 1, 0}
o4 : List
|
i5 : d = k*(n-k)-sum(l)-sum(m); |
i6 : G = apply(d, i->matrix apply(n-k,i->apply(n,j->random CC))); |
i7 : Sols =solveSimpleSchubert((k,n),l,m,G) --This problem has 77 solutions! --
o7 = {{2.83037-1.16682*ii, .339087-1.17121*ii, -.179497+2.13795*ii,
------------------------------------------------------------------------
-.155164-1.83616*ii, .594075-1.25791*ii, .375115+1.07551*ii,
------------------------------------------------------------------------
-.767582+.750854*ii}, {.616511-1.23608*ii, 1.14351-.428504*ii,
------------------------------------------------------------------------
.61279-.237252*ii, 2.40519-.943408*ii, 1.52285+4.31747*ii,
------------------------------------------------------------------------
.158879+.160696*ii, .252295+.536086*ii}, {1.59564-3.53412*ii,
------------------------------------------------------------------------
1.4881+.73784*ii, .103491+2.3495*ii, 1.95469-.49702*ii,
------------------------------------------------------------------------
.985635+1.07916*ii, .139753+2.59479*ii, -.572996+1.78227*ii},
------------------------------------------------------------------------
{1.00034+1.16377*ii, .282334-.0623693*ii, -.0261111+.469647*ii,
------------------------------------------------------------------------
.84702+.456431*ii, 1.37268-.081691*ii, -.727831+.904989*ii,
------------------------------------------------------------------------
-1.29211+.851385*ii}, {1.31908-.09193*ii, 1.68667+.214682*ii,
------------------------------------------------------------------------
-.157446-.621006*ii, .512377+2.35174*ii, .727981+4.07791*ii,
------------------------------------------------------------------------
.405833-.485107*ii, -.922487-.546294*ii}, {-.177866+.2745*ii,
------------------------------------------------------------------------
-1.0785+.377005*ii, .033043-1.20722*ii, -.182675+.322299*ii,
------------------------------------------------------------------------
.972502+.039856*ii, -.844351-.697949*ii, -.586467-.339161*ii},
------------------------------------------------------------------------
{.918986+.729155*ii, .0544907+.48707*ii, 1.76017+.099046*ii,
------------------------------------------------------------------------
-.989923+.209755*ii, 1.21071+.830863*ii, -7.50874-4.28251*ii,
------------------------------------------------------------------------
-10.5236+7.00191*ii}, {-4.8344-2.30609*ii, -1.04978-6.47208*ii,
------------------------------------------------------------------------
-4.0858+.430332*ii, -.247438-.570484*ii, .312555+.57111*ii,
------------------------------------------------------------------------
.339541+.238912*ii, .142301+1.32292*ii}, {.698366+.608809*ii,
------------------------------------------------------------------------
.95351-.341281*ii, .277886-.784558*ii, 1.09216+.199628*ii,
------------------------------------------------------------------------
-.560935-1.56259*ii, -.044748-1.86422*ii, -2.47285-1.90376*ii},
------------------------------------------------------------------------
{.738961+1.08457*ii, -.735094+.575263*ii, .930967+.024263*ii,
------------------------------------------------------------------------
-.669722+.129668*ii, .739605+.671634*ii, .0666671-.264572*ii,
------------------------------------------------------------------------
-.69609+.75765*ii}, {.965771-.629416*ii, -.316157-.403439*ii,
------------------------------------------------------------------------
-1.51768+5.13956*ii, 1.46815-2.03927*ii, 1.07465-.506629*ii,
------------------------------------------------------------------------
-.61724-1.18922*ii, -.969504-.803241*ii}, {.091364-1.0877*ii,
------------------------------------------------------------------------
-.205565-.533216*ii, -.152703-.917898*ii, .697898+3.35222*ii,
------------------------------------------------------------------------
4.37021-2.46295*ii, .189392-.770681*ii, .211364-.380062*ii},
------------------------------------------------------------------------
{.970958+1.03881*ii, -.033912+.601984*ii, .421707+.091466*ii,
------------------------------------------------------------------------
-.951042+.158509*ii, 1.44278+1.4802*ii, -.200247-.439407*ii,
------------------------------------------------------------------------
-.505303+.153709*ii}, {.667701-.7178*ii, .0224798-.107527*ii,
------------------------------------------------------------------------
-1.76825+.263386*ii, 1.20835-.249924*ii, 1.49888-.221283*ii,
------------------------------------------------------------------------
-.413561+.0570748*ii, -.545814+.074177*ii}, {.611252-.923722*ii,
------------------------------------------------------------------------
.017085-.593473*ii, -3.57302-1.4063*ii, 2.50843+2.46452*ii,
------------------------------------------------------------------------
1.81309-.66578*ii, .055338-1.25873*ii, -.035530-.931*ii},
------------------------------------------------------------------------
{4.72049+1.33919*ii, 1.75729+.246846*ii, -.903759+3.65303*ii,
------------------------------------------------------------------------
3.18925+.216125*ii, -1.1456+2.32551*ii, .131337+1.33329*ii,
------------------------------------------------------------------------
.72027+.505613*ii}, {.785901+.098456*ii, -.23242+.0295552*ii,
------------------------------------------------------------------------
.739642+.296011*ii, .136402-.0477763*ii, .59205+.235903*ii,
------------------------------------------------------------------------
8.42502+6.70125*ii, 3.23608+6.26523*ii}, {-.142789-2.54626*ii,
------------------------------------------------------------------------
1.31922-1.49604*ii, .280374-1.55877*ii, .266205-.217297*ii,
------------------------------------------------------------------------
.095254+1.73734*ii, -.372531-.340654*ii, .40685+.389897*ii},
------------------------------------------------------------------------
{-.965005-.524762*ii, -.850863-.680911*ii, .0666037-.0517023*ii,
------------------------------------------------------------------------
-.172818-.0192463*ii, .171706+.860751*ii, -.279174+.225652*ii,
------------------------------------------------------------------------
-.135133+.986769*ii}, {-.578466-2.46713*ii, 1.24047-1.46576*ii,
------------------------------------------------------------------------
.063654-.835605*ii, .166326-.413034*ii, .443282+.686889*ii,
------------------------------------------------------------------------
.070334+1.00916*ii, -.460264+1.57546*ii}, {.958026+.682366*ii,
------------------------------------------------------------------------
.406162+.547165*ii, 1.23458-.823822*ii, -1.77795+1.15503*ii,
------------------------------------------------------------------------
2.23779+2.10422*ii, -.817004-.111244*ii, -1.03764+.816608*ii},
------------------------------------------------------------------------
{6.71719-.064777*ii, 5.87225-1.43526*ii, 2.57362-3.43779*ii,
------------------------------------------------------------------------
-.424259-.658763*ii, -.027455+3.22171*ii, .0617571-.256373*ii,
------------------------------------------------------------------------
.201933-.081954*ii}, {.837651-.01776*ii, .080552+1.0221*ii,
------------------------------------------------------------------------
-.048032-1.42918*ii, -.458712+.739391*ii, -.957983+1.48391*ii,
------------------------------------------------------------------------
-.0057591+.228492*ii, .0801215+.334954*ii}, {-.335264+.468981*ii,
------------------------------------------------------------------------
-.85052-.249673*ii, .078588+.709592*ii, -.0051331-.0727716*ii,
------------------------------------------------------------------------
.038605+1.00938*ii, -1.45296+2.2789*ii, .184977+1.65745*ii},
------------------------------------------------------------------------
{1.25726+.441114*ii, -.209568+.615339*ii, .506669+1.36158*ii,
------------------------------------------------------------------------
.401848+.102313*ii, .814918+.447657*ii, -5.44325-5.09058*ii,
------------------------------------------------------------------------
.354587-2.67153*ii}, {.991809+.282546*ii, 1.31351+.625964*ii,
------------------------------------------------------------------------
-1.18737-1.67876*ii, -2.39781+2.38038*ii, -2.77821+1.32197*ii,
------------------------------------------------------------------------
-.0792051+.419036*ii, .316059+.434391*ii}, {.786403+.423102*ii,
------------------------------------------------------------------------
-.254866-.311113*ii, -.411882-.43632*ii, .569311+.437771*ii,
------------------------------------------------------------------------
1.10602+.197325*ii, -.734128+.775301*ii, -.512867+.597257*ii},
------------------------------------------------------------------------
{.530206+.182987*ii, .267353-.627555*ii, .136504-.0534943*ii,
------------------------------------------------------------------------
.055419-.527812*ii, -.189794-.615281*ii, .092370-.839385*ii,
------------------------------------------------------------------------
-.118704-1.5459*ii}, {.354697-2.21884*ii, .468827-.231337*ii,
------------------------------------------------------------------------
-.242795-.698118*ii, -.539902+.406311*ii, -.319066+1.10558*ii,
------------------------------------------------------------------------
.347758-.301442*ii, .234016+.762547*ii}, {.083327-1.68596*ii,
------------------------------------------------------------------------
1.13553+.87302*ii, 4.72372-1.51816*ii, .101769-1.11528*ii,
------------------------------------------------------------------------
.721827+.439285*ii, 1.05034-2.47462*ii, 1.24974+.957912*ii},
------------------------------------------------------------------------
{.349036+.480496*ii, -.442291+.7817*ii, .700609+.562738*ii,
------------------------------------------------------------------------
-.00782018-.0302859*ii, .561071+.642179*ii, -.012391-3.46218*ii,
------------------------------------------------------------------------
.060909-1.02606*ii}, {1.39166-.170938*ii, 1.41613-.126288*ii,
------------------------------------------------------------------------
-1.05682+.761826*ii, 7.14911+7.32129*ii, -2.13623+7.32394*ii,
------------------------------------------------------------------------
-.016024+.865674*ii, .610208+.799856*ii}, {-1.45486+3.55806*ii,
------------------------------------------------------------------------
-23.9773+10.1617*ii, 13.5641+20.0492*ii, -.318982-.96501*ii,
------------------------------------------------------------------------
-.0515422+.12378*ii, .02413-2.20945*ii, 3.00757+.650103*ii},
------------------------------------------------------------------------
{-.518932-4.29838*ii, 2.08586-.507361*ii, .507326+1.57303*ii,
------------------------------------------------------------------------
2.03021-.245073*ii, .622707+1.62675*ii, 2.06576+1.41166*ii,
------------------------------------------------------------------------
.425359+1.54847*ii}, {.617738-.407646*ii, -.426388-.138073*ii,
------------------------------------------------------------------------
7.1245+.928229*ii, -2.53532-1.15553*ii, 1.12701-.548861*ii,
------------------------------------------------------------------------
-.846797-.646969*ii, -1.30067-.772363*ii}, {.412591-.247387*ii,
------------------------------------------------------------------------
1.77301-1.87985*ii, -.593417+.034869*ii, -.35955-.11525*ii,
------------------------------------------------------------------------
-.607773-.047087*ii, .408996-.710548*ii, -.558421-.577332*ii},
------------------------------------------------------------------------
{.448486+.466528*ii, .145996+.84424*ii, .068363-2.02747*ii,
------------------------------------------------------------------------
-1.52147+1.11863*ii, 1.39177+1.04669*ii, -1.02401+1.29007*ii,
------------------------------------------------------------------------
-2.0382+.423085*ii}, {.88539+.386903*ii, .328355-.541645*ii,
------------------------------------------------------------------------
.785763+.047963*ii, .0425523+.0898986*ii, .44867+.269815*ii,
------------------------------------------------------------------------
1.32757+.591549*ii, 1.00823+.636428*ii}, {1.90755-.213533*ii,
------------------------------------------------------------------------
.770571+2.89298*ii, 1.05303-2.2697*ii, -.846758-.334234*ii,
------------------------------------------------------------------------
-.078368+.551162*ii, .321975-.428153*ii, -.205606+.64375*ii},
------------------------------------------------------------------------
{1.07608-.050741*ii, 1.39746-.282675*ii, -.0928957-.132527*ii,
------------------------------------------------------------------------
-3.90339-3.90227*ii, -7.82381-8.83392*ii, .078951-.15352*ii,
------------------------------------------------------------------------
-.573059-.163445*ii}, {.816078+.275593*ii, 1.12942-.411091*ii,
------------------------------------------------------------------------
-.194283-.869602*ii, .503989-1.17673*ii, -.96889-1.17963*ii,
------------------------------------------------------------------------
-.187246-.520936*ii, -1.11249-1.19833*ii}, {.598506+.607586*ii,
------------------------------------------------------------------------
-.357378+.515676*ii, -.400765-.0240624*ii, -.91291-.169604*ii,
------------------------------------------------------------------------
.075919+.846655*ii, .058203-1.32517*ii, .129987+.485521*ii},
------------------------------------------------------------------------
{.649368-.281033*ii, .178564+.477535*ii, 2.18503+.212868*ii,
------------------------------------------------------------------------
.0588415-.420831*ii, .937315+.335758*ii, 1.76197-3.05745*ii,
------------------------------------------------------------------------
1.6167+.652616*ii}, {.80873+.766799*ii, .585551+.490728*ii,
------------------------------------------------------------------------
.414654-.875804*ii, -1.74775+.587978*ii, 2.92108+4.14704*ii,
------------------------------------------------------------------------
-.248523-.228073*ii, -.386832+.194522*ii}, {.689862-.080104*ii,
------------------------------------------------------------------------
.771525+.991817*ii, -.383983-1.21437*ii, -.748579+.829531*ii,
------------------------------------------------------------------------
-1.25648+.877242*ii, -.049215+.294826*ii, .189683+.531035*ii},
------------------------------------------------------------------------
{.881167+.427014*ii, .268105-.0096692*ii, .765203+.076744*ii,
------------------------------------------------------------------------
.228207+.0175461*ii, 1.29618-.357272*ii, -.717145+.124914*ii,
------------------------------------------------------------------------
-3.51734-.227384*ii}, {1.7251+.928577*ii, 2.74863+1.97259*ii,
------------------------------------------------------------------------
3.52728-2.47956*ii, .19062-1.59231*ii, -.843351+.684587*ii,
------------------------------------------------------------------------
-.994148-.674488*ii, -.788133-.455214*ii}, {.837498+1.39153*ii,
------------------------------------------------------------------------
1.1407+2.58084*ii, 2.41347+.232758*ii, -.703573-.491564*ii,
------------------------------------------------------------------------
2.38398+2.20851*ii, .225157-.254973*ii, .0682961-.110237*ii},
------------------------------------------------------------------------
{1.44651-1.79*ii, 2.20384-1.74707*ii, -.187375-1.68581*ii,
------------------------------------------------------------------------
-.254739-.514403*ii, -.685064+1.31354*ii, -.408477-.334541*ii,
------------------------------------------------------------------------
.606803-.45191*ii}, {-2.22799+1.00517*ii, 2.20445-.436488*ii,
------------------------------------------------------------------------
4.71575-1.86952*ii, .994985+1.72538*ii, -.107391-.92427*ii,
------------------------------------------------------------------------
1.50233-1.6995*ii, -.309709-.0107719*ii}, {.373175-.949261*ii,
------------------------------------------------------------------------
1.89583-.546296*ii, -.259622-2.11873*ii, -.305812-.726001*ii,
------------------------------------------------------------------------
-.219359+.900303*ii, -1.50091-2.7817*ii, 2.34084+1.06788*ii},
------------------------------------------------------------------------
{1.33596-.229447*ii, -.117514-1.85582*ii, -1.21232+3.63221*ii,
------------------------------------------------------------------------
-.390801-1.18822*ii, .679468-.552979*ii, -.276353-.490547*ii,
------------------------------------------------------------------------
-.827168+.144626*ii}, {1.13662-.022903*ii, .40874+.247727*ii,
------------------------------------------------------------------------
.499645+1.90144*ii, .628111-1.33391*ii, .900587-.128164*ii,
------------------------------------------------------------------------
3.69554-1.66978*ii, .797363-4.78321*ii}, {.222182-.24866*ii,
------------------------------------------------------------------------
-.30128-.930265*ii, -.193887-.187332*ii, .221136+.0942152*ii,
------------------------------------------------------------------------
-7.25787+4.50238*ii, .0564447+.057707*ii, .0722465+.0022400*ii},
------------------------------------------------------------------------
{.716201+2.06053*ii, -1.54182+4.60067*ii, 4.35754+4.02669*ii,
------------------------------------------------------------------------
.48999-.975936*ii, .255998+.449672*ii, -.778497-1.40891*ii,
------------------------------------------------------------------------
-.042823-.573077*ii}, {1.64276+.001373*ii, .155719+1.27799*ii,
------------------------------------------------------------------------
.863647+.417604*ii, -.734295+.185368*ii, -.608821+1.99639*ii,
------------------------------------------------------------------------
-.519068-.36595*ii, -.110819+.0334624*ii}, {-3.10025+9.02146*ii,
------------------------------------------------------------------------
-9.14471+6.34299*ii, 2.88861-2.63229*ii, .640979-1.71262*ii,
------------------------------------------------------------------------
1.20153-.499412*ii, -1.1635-1.60127*ii, .0059969-.349524*ii},
------------------------------------------------------------------------
{2.89934-1.99216*ii, -.181976+2.17916*ii, .761259+5.06574*ii,
------------------------------------------------------------------------
1.19648-1.13168*ii, .753024+.260107*ii, -2.38512+1.58541*ii,
------------------------------------------------------------------------
-1.88844+.696083*ii}, {2.24734-1.53041*ii, 1.27731-.976219*ii,
------------------------------------------------------------------------
-.458681-.263437*ii, -.693793-2.51314*ii, -.776581-4.66298*ii,
------------------------------------------------------------------------
-.217371+.460229*ii, -.3899+.211753*ii}, {1.04966+.19065*ii,
------------------------------------------------------------------------
3.48792-.907152*ii, -1.95764-2.32365*ii, -.374345-1.19025*ii,
------------------------------------------------------------------------
-.665604-.076337*ii, -.176124+.0087169*ii, -.616265-.442341*ii},
------------------------------------------------------------------------
{.66296+.455059*ii, 1.78698-.460051*ii, -.797804+.681177*ii,
------------------------------------------------------------------------
-1.37486-.754645*ii, 1.02864-.746415*ii, .101123+.387554*ii,
------------------------------------------------------------------------
.683733+.14124*ii}, {1.40291+.759787*ii, -.13922-16.7338*ii,
------------------------------------------------------------------------
-12.1419+4.8153*ii, -.199024-.746779*ii, -.0110879-.104156*ii,
------------------------------------------------------------------------
-.594961+.114508*ii, -.523647-.759479*ii}, {.384968-.947665*ii,
------------------------------------------------------------------------
-.874706-.207024*ii, .252759+.642969*ii, -.150054+.202211*ii,
------------------------------------------------------------------------
1.49303+1.13119*ii, -.24877-.453296*ii, -.1631-.0184815*ii},
------------------------------------------------------------------------
{-.187379-.449934*ii, -.473294+.563438*ii, -.656045+.007513*ii,
------------------------------------------------------------------------
-.441614+.514702*ii, .674192+.794424*ii, .166846-.977591*ii,
------------------------------------------------------------------------
.0267801-.0950368*ii}, {20.8103+9.22064*ii, 11.1472+18.607*ii,
------------------------------------------------------------------------
-.445469-5.25292*ii, 4.66263+1.01282*ii, 3.73826+2.39834*ii,
------------------------------------------------------------------------
-1.15462-2.31624*ii, .0768598-.0242366*ii}, {-7.58981-6.69024*ii,
------------------------------------------------------------------------
-3.67984-12.2069*ii, -4.40577+8.48214*ii, -.197522+3.42999*ii,
------------------------------------------------------------------------
-.028529+3.06459*ii, -.112578-2.26272*ii, -.203835+.205897*ii},
------------------------------------------------------------------------
{1.13201-.09404*ii, 2.12189-.531349*ii, -1.46063+.323137*ii,
------------------------------------------------------------------------
-1.92117-.877422*ii, -1.08384-1.66549*ii, -.372825-.0162201*ii,
------------------------------------------------------------------------
-.493548+.620201*ii}, {-1.13176+1.05717*ii, -1.77255+1.67698*ii,
------------------------------------------------------------------------
6.66399-2.53852*ii, -.722445-1.80758*ii, .551661+.148602*ii,
------------------------------------------------------------------------
-.919012-2.44407*ii, .637682-.722628*ii}, {.689389-.111679*ii,
------------------------------------------------------------------------
.426006+.157143*ii, .707821-1.73559*ii, .802128+2.63315*ii,
------------------------------------------------------------------------
2.9584-2.4331*ii, -.730366-.863828*ii, -.444016-1.38785*ii},
------------------------------------------------------------------------
{1.13045+.171283*ii, .0063398+.177547*ii, .002924+1.55916*ii,
------------------------------------------------------------------------
.292584-.821949*ii, .696866-.340073*ii, 1.44421+.878123*ii,
------------------------------------------------------------------------
.380053-1.36285*ii}, {-.787263+.077468*ii, .452768+.238344*ii,
------------------------------------------------------------------------
2.08545-1.49246*ii, -2.08942+.87208*ii, 2.52232-.269961*ii,
------------------------------------------------------------------------
.759489-.770694*ii, .0325181+.321439*ii}, {-.145165+1.18519*ii,
------------------------------------------------------------------------
.55228+3.18289*ii, 2.50872+.474219*ii, -.817847-.631736*ii,
------------------------------------------------------------------------
3.0161+1.92997*ii, .244827-.145556*ii, .0493243-.0336758*ii},
------------------------------------------------------------------------
{-.436358-.63454*ii, -.501912+.008873*ii, .672959-1.37972*ii,
------------------------------------------------------------------------
-1.34522+2.20124*ii, 2.84431-.550887*ii, .485699-.786291*ii,
------------------------------------------------------------------------
.33601-.104919*ii}, {4.57017+.430589*ii, 1.24963+2.1152*ii,
------------------------------------------------------------------------
.225496+5.04844*ii, 1.12434-.636565*ii, 1.00494+.320403*ii,
------------------------------------------------------------------------
-1.73957-2.54459*ii, -.0571936-.351009*ii}, {.98573+.806019*ii,
------------------------------------------------------------------------
.084274+1.00173*ii, 1.30713+.059866*ii, -.285565+.197953*ii,
------------------------------------------------------------------------
1.07001+.952795*ii, 1.0868-1.25217*ii, -.734249-.184477*ii},
------------------------------------------------------------------------
{1.03559-.491715*ii, 5.39495+3.50224*ii, 1.80583-2.99227*ii,
------------------------------------------------------------------------
-.001327-.623464*ii, -.201381+.318454*ii, .107246+.318594*ii,
------------------------------------------------------------------------
-.51064+.018030*ii}, {.831677-1.62408*ii, 1.49992-.677834*ii,
------------------------------------------------------------------------
-.166718-1.15969*ii, -.441149-.425255*ii, -.792299+1.35599*ii,
------------------------------------------------------------------------
-1.39974-1.04683*ii, .585051-.831685*ii}}
o7 : List
|
i8 : E := skewSchubertVariety((k,n),l,m);
3 7
o8 : Matrix (CC [x1, x2, x3, x4, x5, x6, x7]) <--- (CC [x1, x2, x3, x4, x5, x6, x7])
53 53
|
i9 : apply(Sols ,s-> sub(E,matrix{s}) )
o9 = {| 1 2.83037-1.16682i .339087-1.17121i -.179497+2.13795i
| 0 0 1 -.155164-1.83616i
| 0 0 0 0
------------------------------------------------------------------------
0 0 0 |, | 1
.594075-1.25791i 0 0 | | 0
1 .375115+1.07551i -.767582+.750854i | | 0
------------------------------------------------------------------------
.616511-1.23608i 1.14351-.428504i .61279-.237252i 0
0 1 2.40519-.943408i 1.52285+4.31747i
0 0 0 1
------------------------------------------------------------------------
0 0 |, | 1 1.59564-3.53412i 1.4881+.73784i
0 0 | | 0 0 1
.158879+.160696i .252295+.536086i | | 0 0 0
------------------------------------------------------------------------
.103491+2.3495i 0 0 0 |, |
1.95469-.49702i .985635+1.07916i 0 0 | |
0 1 .139753+2.59479i -.572996+1.78227i | |
------------------------------------------------------------------------
1 1.00034+1.16377i .282334-.0623693i -.0261111+.469647i 0
0 0 1 .84702+.456431i 1.37268-.081691i
0 0 0 0 1
------------------------------------------------------------------------
0 0 |, | 1 1.31908-.09193i
0 0 | | 0 0
-.727831+.904989i -1.29211+.851385i | | 0 0
------------------------------------------------------------------------
1.68667+.214682i -.157446-.621006i 0 0
1 .512377+2.35174i .727981+4.07791i 0
0 0 1 .405833-.485107i
------------------------------------------------------------------------
0 |, | 1 -.177866+.2745i -1.0785+.377005i
0 | | 0 0 1
-.922487-.546294i | | 0 0 0
------------------------------------------------------------------------
.033043-1.20722i 0 0 0
-.182675+.322299i .972502+.039856i 0 0
0 1 -.844351-.697949i -.586467-.339161i
------------------------------------------------------------------------
|, | 1 .918986+.729155i .0544907+.48707i 1.76017+.099046i
| | 0 0 1 -.989923+.209755i
| | 0 0 0 0
------------------------------------------------------------------------
0 0 0 |, | 1
1.21071+.830863i 0 0 | | 0
1 -7.50874-4.28251i -10.5236+7.00191i | | 0
------------------------------------------------------------------------
-4.8344-2.30609i -1.04978-6.47208i -4.0858+.430332i 0
0 1 -.247438-.570484i .312555+.57111i
0 0 0 1
------------------------------------------------------------------------
0 0 |, | 1 .698366+.608809i
0 0 | | 0 0
.339541+.238912i .142301+1.32292i | | 0 0
------------------------------------------------------------------------
.95351-.341281i .277886-.784558i 0 0
1 1.09216+.199628i -.560935-1.56259i 0
0 0 1 -.044748-1.86422i
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0 |, | 1 .738961+1.08457i -.735094+.575263i
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o9 : List
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