02341_02413_02431_20341_20413_20431_23041
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3127, 17398, 98984, 572823, 3360355, 19935519, 119394778, 720894171, 4383495872, 26819792074, 164992863443, 1019976977915, 6333035600619, 39476901695957, 246958060310719, 1549934430709729, 9756458799133413, 61581969546515962, 389676011595264549, 2471493290055118424, 15708940959882182770, 100046052223484758616, 638350521182417754797, 4080103712648456239394, 26120864887309751706807, 167480559865141965508982, 1075379739329261662952164, 6914224565290645208777329, 44511885202312903000015275, 286898860916948531519820219, 1851287649091624836490888232, 11958737978907289158494454581, 77328443590817506547625458678, 500510912167362420269619763133, 3242557583847504776513701457713, 21025322820491595136400326930008, 136445985886392317076617189184428, 886187179363953838425823167297956, 5759985105168504322594140923253541, 37465717173345340224129953826548868, 243865320325666542616086124513645953, 1588388362002659768517976314057124437, 10352425962744672201297765940677019988, 67514210565582660740092613965728664406, 440560314060276277988363185192778760894, 2876489355997361302882406803382135738476, 18791352925970001840754990036301334959602, 122823759372605625562876985031471821685508, 803206921204293572864380640767161231541668, 5255152511788036995739989350379325618872961, 34399216846551515966736422285770534514279104, 225273467559360374863374218205053596049797635, 1475920824800563697802023720163844481227105233, 9673891479795617353288481730568300321236363403, 63433462379954635290712445857659575292406837472, 416110709429643978209892081324924697281980094737, 2730656870774467325518132132027205082888198041508, 17926185205561255162138282643305928814284843688230, 117724303435790578711656621461694443007620634648295, 773387416654022573546022872551992034136585044558189, 5082486448852736259057018282386950794678281800486943, 33411744216298473072229120331931850592244591468811569, 219715999407649980933346102830048100450640432465328785, 1445306107951234131453304580969962749075748331329050843, 9510202995977116189956744757950259417108882136190941501, 62596184626049111713074972729494807662618061505458238157, 412126507742207046601944760655338165005788379084430793739, 2714153914566480914683775132126630525578711097574805588955, 17879542152783505033791051652188417623128708249025864535579, 117812996676337105222259014158793726254431838912402463162095, 776500805829505459227529306042953121972617265704260961006837, 5119171075375775604791582054437114747413968333286357107982751, 33756983818110421242902558086853540090421638010341398522732603, 222654371569626442274600291974996134853257376314817755471199081, 1468925782545888640650550827861066920445932856978361138638826463, 9693197208387908942578817151385817070171020426050009819471202809, 63977966480824876159345511973919382738893638483102011052981710095, 422364793356165254194516841740985835875373256338290512704106761253, 2788923933529392657007892049704193539058354022342540764210513512301, 18419387061011963304844053552022679521830198734244143885178029593999, 121674946120177161013799997109091384354083395261560219807199437048697, 803919647824159106640374266884595434717365806681265005038178503383699, 5312607007755004862090990357893015186164012532981153830950027657446831, 35114334823630042175840259485236126972578796963520318157466514486357253, 232135258517585380135064287738784634419861982211831435097316118869802529, 1534885352053814718025696389134836548639272810148178314075833100689501945, 10150495850311974624719647713522841896775310723646293908164900969945748205, 67138777476616166800895454245162534109896958653919400039744163852487694109, 444153282262700309323030735500434458518889445190080965811583907669953521289, 2938759659136788906458331139803463645883414668774566296014907460906437926246, 19447578282034178403387748638536848743063222866021655463145878639791557360221, 128716972321246606023223092935703512781000148172305316855792912825318615857604, 852066594599862286862959245556950217480014542317766558058209930148152596689186, 5641275989432267926426271653456250894727872853655674988674532126601057701585634
Implicit equation for the generating function in Maple syntax:
x*(4*x^2+2*x-1)*(x-1)^2*F(x)^4-(x-1)*(12*x^3-17*x^2-2*x+2)*F(x)^3+(8*x^4-13*x^3-18*x^2+32*x-8)*F(x)^2-(-2+x)*(12*x^2-20*x+5)*F(x)+2*(-2+x)*(2*x^2-4*x+1) = 0
Implicit equation for the generating function in latex syntax:
x \left(4 x^{2}+2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)^{4}-\left(x -1\right) \left(12 x^{3}-17 x^{2}-2 x +2\right) F \! \left(x \right)^{3}+\left(8 x^{4}-13 x^{3}-18 x^{2}+32 x -8\right) F \! \left(x \right)^{2}-\left(-2+x \right) \left(12 x^{2}-20 x +5\right) F \! \left(x \right)+2 \left(-2+x \right) \left(2 x^{2}-4 x +1\right) = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3127
a(8) = 17398
a(9) = 98984
a(10) = 572823
a(11) = 3360355
a(12) = 19935519
a(13) = 119394778
a(14) = 720894171
a(15) = 4383495872
a(16) = 26819792074
a(17) = 164992863443
a(18) = 1019976977915
a(19) = 6333035600619
a(20) = 39476901695957
a(21) = 246958060310719
a(22) = 1549934430709729
a(23) = 9756458799133413
a(24) = 61581969546515962
a(25) = 389676011595264549
a(26) = 2471493290055118424
a(27) = 15708940959882182770
a(28) = 100046052223484758616
a(29) = 638350521182417754797
a(30) = 4080103712648456239394
a(31) = 26120864887309751706807
a(32) = 167480559865141965508982
a(33) = 1075379739329261662952164
a(34) = 6914224565290645208777329
a(35) = 44511885202312903000015275
a(36) = 286898860916948531519820219
a(37) = 1851287649091624836490888232
a(38) = 11958737978907289158494454581
a(39) = 77328443590817506547625458678
a(40) = 500510912167362420269619763133
a(41) = 3242557583847504776513701457713
a(n+42) = 3200*(1467324814*n^3+14579197638*n^2+47302397807*n+50058546060)/(n+43)/(n+42)/(n+41)*a(n+2)-480*(84615878662*n^3+1090611219197*n^2+4620467773613*n+6438628721568)/(n+43)/(n+42)/(n+41)*a(n+3)+10*(24701049706913*n^3+391076856829671*n^2+2040976302251410*n+3515305574460696)/(n+43)/(n+42)/(n+41)*a(n+4)-5*(223990653261883*n^3+4202897091370239*n^2+26024857172055212*n+53252972027173188)/(n+43)/(n+42)/(n+41)*a(n+5)+15/2*(521241435892999*n^3+11298423971028131*n^2+80826214193543352*n+191101779468922492)/(n+43)/(n+42)/(n+41)*a(n+6)-3/4*(14210002236495701*n^3+348887728966247147*n^2+2824555177776138942*n+7551223670005359220)/(n+43)/(n+42)/(n+41)*a(n+7)+3/8*(60270764331515475*n^3+1648316318708856137*n^2+14830571345409299158*n+43960000078852199940)/(n+43)/(n+42)/(n+41)*a(n+8)-1/16*(575006556226792459*n^3+17207554984351263231*n^2+168473146288267795832*n+540067620536987988600)/(n+43)/(n+42)/(n+41)*a(n+9)+3/16*(197448166361766480*n^3+6238341114049340043*n^2+63137480269135675743*n+203345782167723630320)/(n+43)/(n+42)/(n+41)*a(n+10)-3/64*(76416657766936911*n^3-1144813465611684025*n^2-79377689277446652552*n-648697125524895424436)/(n+43)/(n+42)/(n+41)*a(n+11)-1/32*(2624456810635294552*n^3+116480323364816064561*n^2+1744568450893818823784*n+8742687541572233502222)/(n+43)/(n+42)/(n+41)*a(n+12)+1/128*(27155365408029953486*n^3+1249863027889127868081*n^2+19289978429288169533923*n+99501229130592542661240)/(n+43)/(n+42)/(n+41)*a(n+13)-3/512*(58719030854975530289*n^3+2880426183096232477239*n^2+47189292290406384867786*n+257758075291581625555760)/(n+43)/(n+42)/(n+41)*a(n+14)-3/512*(2571540551000817993*n^3+187397326650668743526*n^2+4540594284663509350991*n+36571980266960204034768)/(n+43)/(n+42)/(n+41)*a(n+25)+9/512*(338248211082511082*n^3+25759502411652131899*n^2+652717452771693973167*n+5502393811222308097308)/(n+43)/(n+42)/(n+41)*a(n+26)-3/512*(345257477993130252*n^3+27387999701866046643*n^2+723180683795386490125*n+6355918225908805491864)/(n+43)/(n+42)/(n+41)*a(n+27)+1/512*(303883774231233805*n^3+25044560306065831248*n^2+687228113529633932615*n+6278525732422025734020)/(n+43)/(n+42)/(n+41)*a(n+28)-3/256*(12772893909386545*n^3+1091252707329362969*n^2+31046300494637265516*n+294128269108461180140)/(n+43)/(n+42)/(n+41)*a(n+29)+1/256*(8251633892449861*n^3+729346064531128179*n^2+21468895850853209006*n+210457739022792215628)/(n+43)/(n+42)/(n+41)*a(n+30)-1/256*(1500025176740003*n^3+136894291355725029*n^2+4160627605271346472*n+42112999900893644148)/(n+43)/(n+42)/(n+41)*a(n+31)+3/256*(75257506007428*n^3+7075426434032831*n^2+221518385534534353*n+2309488870523174768)/(n+43)/(n+42)/(n+41)*a(n+32)+2918400000*(2*n+3)*(2*n+1)*(n+2)/(n+43)/(n+42)/(n+41)*a(n)-1/128*(58576407631*n^3+5698258815102*n^2+183363010690355*n+1949055598429920)/(n+43)/(n+42)/(n+41)*a(n+35)-1/64*(1324254251*n^3+162896417556*n^2+6588268615753*n+87838497063072)/(n+43)/(n+42)/(n+41)*a(n+36)-1/256*(27148350124093*n^3+2621069885974878*n^2+84249170884165589*n+901551083521177008)/(n+43)/(n+42)/(n+41)*a(n+33)+1/128*(1203060539992*n^3+118478598069903*n^2+3881625707288177*n+42301705991279460)/(n+43)/(n+42)/(n+41)*a(n+34)-1/4*(10841*n^2+860975*n+17092860)/(n+42)/(n+43)*a(n+40)+9/2*(17*n+683)/(n+43)*a(n+41)-29184000*(2*n+3)*(5837*n^2+31948*n+43121)/(n+43)/(n+42)/(n+41)*a(n+1)+1/256*(8396123624358852397*n^3+582887480247032019642*n^2+13437798610554075641720*n+102829035658373592854640)/(n+43)/(n+42)/(n+41)*a(n+24)+1/512*(48064138372727441954*n^3+2951854940103539705685*n^2+59723481461861450047027*n+396909313377476966311572)/(n+43)/(n+42)/(n+41)*a(n+22)-1/512*(31101983011309607099*n^3+2043110475127566575067*n^2+44460975099707972891956*n+320184712381498817878272)/(n+43)/(n+42)/(n+41)*a(n+23)-1/512*(59303085233011707575*n^3+3312700744632902758881*n^2+59931156205922133595276*n+346618336612633164172656)/(n+43)/(n+42)/(n+41)*a(n+21)+3/256*(8567530415680937803*n^3+392872759644333982897*n^2+5211134218165823889722*n+15530797486984765514188)/(n+43)/(n+42)/(n+41)*a(n+20)-1/512*(12497602668145275908*n^3-398563930563484394319*n^2-30810686215543483635191*n-356676340287998257857444)/(n+43)/(n+42)/(n+41)*a(n+19)-3/512*(19053127315495184496*n^3+1529583058608077167399*n^2+37547066456406839593917*n+291821804118548181303644)/(n+43)/(n+42)/(n+41)*a(n+18)-1/256*(99773734421571385094*n^3+5714002645036334232660*n^2+108260591852219193162007*n+679041845732710309833486)/(n+43)/(n+42)/(n+41)*a(n+16)+1/512*(138500659097221159456*n^3+8849076246166889137917*n^2+184525598462021571911147*n+1261740151757873814961188)/(n+43)/(n+42)/(n+41)*a(n+17)+1/512*(213467022030358701911*n^3+11255769644823473950551*n^2+197462429109300780615196*n+1151772880342606799924460)/(n+43)/(n+42)/(n+41)*a(n+15)+1/32*(227253541*n^3+25923685422*n^2+985197121967*n+12473551625958)/(n+43)/(n+42)/(n+41)*a(n+37)-1/16*(13025483*n^3+1503745248*n^2+57857826679*n+741917431470)/(n+43)/(n+42)/(n+41)*a(n+38)+1/8*(464899*n^3+54758742*n^2+2149664651*n+28126135404)/(n+43)/(n+42)/(n+41)*a(n+39), n >= 42
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3127
a(8) = 17398
a(9) = 98984
a(10) = 572823
a(11) = 3360355
a(12) = 19935519
a(13) = 119394778
a(14) = 720894171
a(15) = 4383495872
a(16) = 26819792074
a(17) = 164992863443
a(18) = 1019976977915
a(19) = 6333035600619
a(20) = 39476901695957
a(21) = 246958060310719
a(22) = 1549934430709729
a(23) = 9756458799133413
a(24) = 61581969546515962
a(25) = 389676011595264549
a(26) = 2471493290055118424
a(27) = 15708940959882182770
a(28) = 100046052223484758616
a(29) = 638350521182417754797
a(30) = 4080103712648456239394
a(31) = 26120864887309751706807
a(32) = 167480559865141965508982
a(33) = 1075379739329261662952164
a(34) = 6914224565290645208777329
a(35) = 44511885202312903000015275
a(36) = 286898860916948531519820219
a(37) = 1851287649091624836490888232
a(38) = 11958737978907289158494454581
a(39) = 77328443590817506547625458678
a(40) = 500510912167362420269619763133
a(41) = 3242557583847504776513701457713
a{\left(n + 42 \right)} = \frac{2918400000 \left(n + 2\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{9 \left(17 n + 683\right) a{\left(n + 41 \right)}}{2 \left(n + 43\right)} - \frac{\left(10841 n^{2} + 860975 n + 17092860\right) a{\left(n + 40 \right)}}{4 \left(n + 42\right) \left(n + 43\right)} - \frac{29184000 \left(2 n + 3\right) \left(5837 n^{2} + 31948 n + 43121\right) a{\left(n + 1 \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(464899 n^{3} + 54758742 n^{2} + 2149664651 n + 28126135404\right) a{\left(n + 39 \right)}}{8 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(13025483 n^{3} + 1503745248 n^{2} + 57857826679 n + 741917431470\right) a{\left(n + 38 \right)}}{16 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(227253541 n^{3} + 25923685422 n^{2} + 985197121967 n + 12473551625958\right) a{\left(n + 37 \right)}}{32 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(1324254251 n^{3} + 162896417556 n^{2} + 6588268615753 n + 87838497063072\right) a{\left(n + 36 \right)}}{64 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{3200 \left(1467324814 n^{3} + 14579197638 n^{2} + 47302397807 n + 50058546060\right) a{\left(n + 2 \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(58576407631 n^{3} + 5698258815102 n^{2} + 183363010690355 n + 1949055598429920\right) a{\left(n + 35 \right)}}{128 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{480 \left(84615878662 n^{3} + 1090611219197 n^{2} + 4620467773613 n + 6438628721568\right) a{\left(n + 3 \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(1203060539992 n^{3} + 118478598069903 n^{2} + 3881625707288177 n + 42301705991279460\right) a{\left(n + 34 \right)}}{128 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{10 \left(24701049706913 n^{3} + 391076856829671 n^{2} + 2040976302251410 n + 3515305574460696\right) a{\left(n + 4 \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(27148350124093 n^{3} + 2621069885974878 n^{2} + 84249170884165589 n + 901551083521177008\right) a{\left(n + 33 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{3 \left(75257506007428 n^{3} + 7075426434032831 n^{2} + 221518385534534353 n + 2309488870523174768\right) a{\left(n + 32 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{5 \left(223990653261883 n^{3} + 4202897091370239 n^{2} + 26024857172055212 n + 53252972027173188\right) a{\left(n + 5 \right)}}{\left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{15 \left(521241435892999 n^{3} + 11298423971028131 n^{2} + 80826214193543352 n + 191101779468922492\right) a{\left(n + 6 \right)}}{2 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(1500025176740003 n^{3} + 136894291355725029 n^{2} + 4160627605271346472 n + 42112999900893644148\right) a{\left(n + 31 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(8251633892449861 n^{3} + 729346064531128179 n^{2} + 21468895850853209006 n + 210457739022792215628\right) a{\left(n + 30 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(12772893909386545 n^{3} + 1091252707329362969 n^{2} + 31046300494637265516 n + 294128269108461180140\right) a{\left(n + 29 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(14210002236495701 n^{3} + 348887728966247147 n^{2} + 2824555177776138942 n + 7551223670005359220\right) a{\left(n + 7 \right)}}{4 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{3 \left(60270764331515475 n^{3} + 1648316318708856137 n^{2} + 14830571345409299158 n + 43960000078852199940\right) a{\left(n + 8 \right)}}{8 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(76416657766936911 n^{3} - 1144813465611684025 n^{2} - 79377689277446652552 n - 648697125524895424436\right) a{\left(n + 11 \right)}}{64 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{3 \left(197448166361766480 n^{3} + 6238341114049340043 n^{2} + 63137480269135675743 n + 203345782167723630320\right) a{\left(n + 10 \right)}}{16 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(303883774231233805 n^{3} + 25044560306065831248 n^{2} + 687228113529633932615 n + 6278525732422025734020\right) a{\left(n + 28 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{9 \left(338248211082511082 n^{3} + 25759502411652131899 n^{2} + 652717452771693973167 n + 5502393811222308097308\right) a{\left(n + 26 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(345257477993130252 n^{3} + 27387999701866046643 n^{2} + 723180683795386490125 n + 6355918225908805491864\right) a{\left(n + 27 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(575006556226792459 n^{3} + 17207554984351263231 n^{2} + 168473146288267795832 n + 540067620536987988600\right) a{\left(n + 9 \right)}}{16 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(2571540551000817993 n^{3} + 187397326650668743526 n^{2} + 4540594284663509350991 n + 36571980266960204034768\right) a{\left(n + 25 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(2624456810635294552 n^{3} + 116480323364816064561 n^{2} + 1744568450893818823784 n + 8742687541572233502222\right) a{\left(n + 12 \right)}}{32 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(8396123624358852397 n^{3} + 582887480247032019642 n^{2} + 13437798610554075641720 n + 102829035658373592854640\right) a{\left(n + 24 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{3 \left(8567530415680937803 n^{3} + 392872759644333982897 n^{2} + 5211134218165823889722 n + 15530797486984765514188\right) a{\left(n + 20 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(12497602668145275908 n^{3} - 398563930563484394319 n^{2} - 30810686215543483635191 n - 356676340287998257857444\right) a{\left(n + 19 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(19053127315495184496 n^{3} + 1529583058608077167399 n^{2} + 37547066456406839593917 n + 291821804118548181303644\right) a{\left(n + 18 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(27155365408029953486 n^{3} + 1249863027889127868081 n^{2} + 19289978429288169533923 n + 99501229130592542661240\right) a{\left(n + 13 \right)}}{128 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(31101983011309607099 n^{3} + 2043110475127566575067 n^{2} + 44460975099707972891956 n + 320184712381498817878272\right) a{\left(n + 23 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(48064138372727441954 n^{3} + 2951854940103539705685 n^{2} + 59723481461861450047027 n + 396909313377476966311572\right) a{\left(n + 22 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{3 \left(58719030854975530289 n^{3} + 2880426183096232477239 n^{2} + 47189292290406384867786 n + 257758075291581625555760\right) a{\left(n + 14 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(59303085233011707575 n^{3} + 3312700744632902758881 n^{2} + 59931156205922133595276 n + 346618336612633164172656\right) a{\left(n + 21 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} - \frac{\left(99773734421571385094 n^{3} + 5714002645036334232660 n^{2} + 108260591852219193162007 n + 679041845732710309833486\right) a{\left(n + 16 \right)}}{256 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(138500659097221159456 n^{3} + 8849076246166889137917 n^{2} + 184525598462021571911147 n + 1261740151757873814961188\right) a{\left(n + 17 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)} + \frac{\left(213467022030358701911 n^{3} + 11255769644823473950551 n^{2} + 197462429109300780615196 n + 1151772880342606799924460\right) a{\left(n + 15 \right)}}{512 \left(n + 41\right) \left(n + 42\right) \left(n + 43\right)}, \quad n \geq 42
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24718/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[24,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]*F[2,x]
F[15,x] = 1/F[20,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[0,x]+F[18,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[58,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[34,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = -F[0,x]+F[27,x]
F[27,x] = 1/F[20,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[20,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[24,x]
F[33,x] = F[25,x]
F[34,x] = F[35,x]
F[35,x] = F[0,x]*F[20,x]*F[36,x]*F[68,x]
F[36,x] = -F[65,x]+F[37,x]
F[37,x] = 1/F[20,x]/F[41,x]/F[58,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]+F[54,x]
F[40,x] = F[2,x]*F[41,x]
F[41,x] = F[1,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[20,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[1,x]+F[20,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]+F[53,x]
F[48,x] = 0
F[49,x] = F[20,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[20,x]
F[52,x] = F[47,x]
F[53,x] = F[20,x]*F[42,x]
F[54,x] = F[55,x]
F[55,x] = F[20,x]*F[41,x]*F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[2,x]*F[58,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[20,x]*F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[20,x]*F[58,x]*F[63,x]
F[63,x] = F[23,x]+F[64,x]
F[64,x] = F[0,x]*F[37,x]
F[65,x] = F[58,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[20,x]*F[37,x]*F[58,x]
F[68,x] = 1/F[20,x]/F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[4,x]+F[71,x]
F[71,x] = -F[124,x]+F[72,x]
F[72,x] = F[121,x]+F[73,x]
F[73,x] = F[74,x]+F[83,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = -1+(x^2-2*x)*F[75,x]^2+(2+x)*F[75,x]
F[76,x] = F[77,x]
F[77,x] = F[20,x]*F[75,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[75,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[20,x]*F[75,x]*F[78,x]
F[82,x] = F[80,x]
F[83,x] = F[84,x]
F[84,x] = F[20,x]*F[85,x]
F[85,x] = 1/F[20,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[92,x]+F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[91,x]+F[26,x]
F[91,x] = (x*F[91,x]+x-2*F[91,x])*(x*F[91,x]+x-1)
F[92,x] = F[26,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[20,x]*F[95,x]
F[95,x] = F[100,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[20,x]*F[68,x]*F[98,x]
F[98,x] = 1/F[20,x]*F[99,x]
F[99,x] = F[26,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[20,x]
F[102,x] = 1/F[20,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[20,x]
F[105,x] = 1/F[20,x]/F[58,x]*F[106,x]
F[106,x] = F[107,x]
F[107,x] = -F[115,x]+F[108,x]
F[108,x] = 1/F[20,x]*F[109,x]
F[109,x] = F[110,x]
F[110,x] = -F[114,x]+F[111,x]
F[111,x] = F[112,x]+F[5,x]
F[112,x] = F[113,x]
F[113,x] = F[20,x]*F[5,x]*F[68,x]
F[114,x] = F[2,x]*F[75,x]
F[115,x] = F[116,x]*F[2,x]
F[116,x] = 1/F[20,x]*F[117,x]
F[117,x] = F[118,x]
F[118,x] = -F[110,x]+F[119,x]
F[119,x] = -F[120,x]+F[71,x]
F[120,x] = F[0,x]*F[75,x]
F[121,x] = -F[83,x]+F[122,x]
F[122,x] = 1/F[20,x]*F[123,x]
F[123,x] = F[90,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[126,x]+F[26,x]
F[126,x] = F[94,x]
F[127,x] = -F[111,x]+F[121,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{24}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{58}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)
F_{33}\! \left(x \right) = F_{25}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{36}\! \left(x \right) F_{68}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{65}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{58}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{54}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{48}\! \left(x \right) = 0
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{42}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{2}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{0}\! \left(x \right) F_{37}\! \left(x \right)
F_{65}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right) F_{58}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{20}\! \left(x \right) F_{4}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{121}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{83}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = x^{2} F_{75} \left(x \right)^{2}-2 x F_{75} \left(x \right)^{2}+F_{75}\! \left(x \right) x +2 F_{75}\! \left(x \right)-1
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{20}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{26}\! \left(x \right)
F_{91}\! \left(x \right) = x^{2} F_{91} \left(x \right)^{2}+2 x^{2} F_{91}\! \left(x \right)-2 x F_{91} \left(x \right)^{2}+x^{2}-3 x F_{91}\! \left(x \right)-x +2 F_{91}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{26}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{20}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{20}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{20}\! \left(x \right) F_{58}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{109}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{5}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{2}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{71}\! \left(x \right)
F_{120}\! \left(x \right) = F_{0}\! \left(x \right) F_{75}\! \left(x \right)
F_{121}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = \frac{F_{123}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{123}\! \left(x \right) = F_{90}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{26}\! \left(x \right)
F_{126}\! \left(x \right) = F_{94}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{121}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x)*F_2(x))
Eq(F_15(x), F_16(x)/F_20(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), -F_0(x) + F_18(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_58(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_34(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), -F_0(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_20(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_20(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_24(x))
Eq(F_33(x), F_25(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_0(x)*F_20(x)*F_36(x)*F_68(x))
Eq(F_36(x), F_37(x) - F_65(x))
Eq(F_37(x), F_38(x)/(F_20(x)*F_41(x)*F_58(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) + F_54(x))
Eq(F_40(x), F_2(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_20(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_1(x) + F_20(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x) + F_53(x))
Eq(F_48(x), 0)
Eq(F_49(x), F_20(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_20(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_20(x)*F_42(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_20(x)*F_41(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_2(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_20(x)*F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_20(x)*F_58(x)*F_63(x))
Eq(F_63(x), F_23(x) + F_64(x))
Eq(F_64(x), F_0(x)*F_37(x))
Eq(F_65(x), F_58(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_20(x)*F_37(x)*F_58(x))
Eq(F_68(x), F_69(x)/(F_20(x)*F_4(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_4(x) + F_71(x))
Eq(F_71(x), -F_124(x) + F_72(x))
Eq(F_72(x), F_121(x) + F_73(x))
Eq(F_73(x), F_74(x) + F_83(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), x*(x - 2)*F_75(x)**2 + (x + 2)*F_75(x) - 1)
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_20(x)*F_75(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_75(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_20(x)*F_75(x)*F_78(x))
Eq(F_82(x), F_80(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_20(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_20(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x) - F_92(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_26(x) - F_91(x))
Eq(F_91(x), x*(x - 2)*(F_91(x) + 1)**2 + (x + 1)*(F_91(x) + 1) + F_91(x) - 1)
Eq(F_92(x), F_26(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_20(x)*F_95(x))
Eq(F_95(x), F_100(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_20(x)*F_68(x)*F_98(x))
Eq(F_98(x), F_99(x)/F_20(x))
Eq(F_99(x), F_26(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_20(x))
Eq(F_102(x), F_103(x)/F_20(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_20(x))
Eq(F_105(x), F_106(x)/(F_20(x)*F_58(x)))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x) - F_115(x))
Eq(F_108(x), F_109(x)/F_20(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x) - F_114(x))
Eq(F_111(x), F_112(x) + F_5(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_20(x)*F_5(x)*F_68(x))
Eq(F_114(x), F_2(x)*F_75(x))
Eq(F_115(x), F_116(x)*F_2(x))
Eq(F_116(x), F_117(x)/F_20(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), -F_110(x) + F_119(x))
Eq(F_119(x), -F_120(x) + F_71(x))
Eq(F_120(x), F_0(x)*F_75(x))
Eq(F_121(x), F_122(x) - F_83(x))
Eq(F_122(x), F_123(x)/F_20(x))
Eq(F_123(x), F_90(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_126(x) + F_26(x))
Eq(F_126(x), F_94(x))
Eq(F_127(x), -F_111(x) + F_121(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, 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"obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25013/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[24,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]*F[2,x]
F[15,x] = 1/F[20,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[0,x]+F[18,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[62,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[38,x]
F[25,x] = F[26,x]+F[33,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = (x*F[27,x]+x-2*F[27,x])*(x*F[27,x]+x-1)
F[28,x] = -F[2,x]+F[29,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[20,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = -1+(x^2-2*x)*F[32,x]^2+(2+x)*F[32,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[24,x]
F[37,x] = F[25,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[20,x]*F[40,x]*F[72,x]
F[40,x] = -F[69,x]+F[41,x]
F[41,x] = 1/F[20,x]/F[45,x]/F[62,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[58,x]
F[44,x] = F[2,x]*F[45,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[1,x]+F[20,x]
F[50,x] = F[46,x]+F[51,x]
F[51,x] = F[52,x]+F[53,x]+F[57,x]
F[52,x] = 0
F[53,x] = F[20,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[20,x]
F[56,x] = F[51,x]
F[57,x] = F[20,x]*F[46,x]
F[58,x] = F[59,x]
F[59,x] = F[20,x]*F[45,x]*F[60,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[2,x]*F[62,x]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[20,x]*F[62,x]
F[65,x] = F[66,x]
F[66,x] = F[20,x]*F[62,x]*F[67,x]
F[67,x] = F[23,x]+F[68,x]
F[68,x] = F[0,x]*F[41,x]
F[69,x] = F[62,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[20,x]*F[41,x]*F[62,x]
F[72,x] = 1/F[20,x]/F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[4,x]+F[75,x]
F[75,x] = -F[125,x]+F[76,x]
F[76,x] = F[122,x]+F[77,x]
F[77,x] = F[78,x]+F[86,x]
F[78,x] = F[32,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[20,x]*F[32,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[32,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[20,x]*F[32,x]*F[81,x]
F[85,x] = F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[93,x]+F[91,x]
F[91,x] = 1/F[20,x]*F[92,x]
F[92,x] = F[28,x]
F[93,x] = F[26,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[20,x]*F[96,x]
F[96,x] = F[104,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[20,x]*F[99,x]
F[99,x] = 1/F[20,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[20,x]*F[72,x]
F[102,x] = 1/F[20,x]*F[103,x]
F[103,x] = F[26,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[20,x]
F[106,x] = 1/F[20,x]/F[62,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = -F[116,x]+F[109,x]
F[109,x] = 1/F[20,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[115,x]+F[112,x]
F[112,x] = F[113,x]+F[5,x]
F[113,x] = F[114,x]
F[114,x] = F[20,x]*F[5,x]*F[72,x]
F[115,x] = F[2,x]*F[32,x]
F[116,x] = F[117,x]*F[2,x]
F[117,x] = 1/F[20,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = -F[111,x]+F[120,x]
F[120,x] = -F[121,x]+F[75,x]
F[121,x] = F[0,x]*F[32,x]
F[122,x] = -F[86,x]+F[123,x]
F[123,x] = 1/F[20,x]*F[124,x]
F[124,x] = F[28,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[127,x]
F[127,x] = F[26,x]+F[94,x]
F[128,x] = -F[112,x]+F[122,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{24}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{2}+2 x^{2} F_{27}\! \left(x \right)-2 x F_{27} \left(x \right)^{2}+x^{2}-3 x F_{27}\! \left(x \right)-x +2 F_{27}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}-2 x F_{32} \left(x \right)^{2}+F_{32}\! \left(x \right) x +2 F_{32}\! \left(x \right)-1
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{40}\! \left(x \right) F_{72}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{20}\! \left(x \right) F_{45}\! \left(x \right) F_{62}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = 0
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right) F_{45}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{20}\! \left(x \right) F_{4}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{122}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{32}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{32}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right) F_{81}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{28}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{20}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{104}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{20}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{20}\! \left(x \right) F_{72}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{26}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{20}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{20}\! \left(x \right) F_{62}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{5}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{115}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{75}\! \left(x \right)
F_{121}\! \left(x \right) = F_{0}\! \left(x \right) F_{32}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{122}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x)*F_2(x))
Eq(F_15(x), F_16(x)/F_20(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), -F_0(x) + F_18(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_62(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_38(x))
Eq(F_25(x), F_26(x) + F_33(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), x*(x - 2)*(F_27(x) + 1)**2 + (x + 1)*(F_27(x) + 1) + F_27(x) - 1)
Eq(F_28(x), -F_2(x) + F_29(x))
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_20(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), x*(x - 2)*F_32(x)**2 + (x + 2)*F_32(x) - 1)
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_24(x))
Eq(F_37(x), F_25(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_20(x)*F_40(x)*F_72(x))
Eq(F_40(x), F_41(x) - F_69(x))
Eq(F_41(x), F_42(x)/(F_20(x)*F_45(x)*F_62(x)))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_58(x))
Eq(F_44(x), F_2(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_1(x) + F_20(x))
Eq(F_50(x), F_46(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_53(x) + F_57(x))
Eq(F_52(x), 0)
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_20(x))
Eq(F_56(x), F_51(x))
Eq(F_57(x), F_20(x)*F_46(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_20(x)*F_45(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_2(x)*F_62(x))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_20(x)*F_62(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_20(x)*F_62(x)*F_67(x))
Eq(F_67(x), F_23(x) + F_68(x))
Eq(F_68(x), F_0(x)*F_41(x))
Eq(F_69(x), F_62(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_20(x)*F_41(x)*F_62(x))
Eq(F_72(x), F_73(x)/(F_20(x)*F_4(x)))
Eq(F_73(x), F_74(x))
Eq(F_74(x), -F_4(x) + F_75(x))
Eq(F_75(x), -F_125(x) + F_76(x))
Eq(F_76(x), F_122(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_86(x))
Eq(F_78(x), F_32(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_20(x)*F_32(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_32(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_20(x)*F_32(x)*F_81(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x) - F_93(x))
Eq(F_91(x), F_92(x)/F_20(x))
Eq(F_92(x), F_28(x))
Eq(F_93(x), F_26(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_20(x)*F_96(x))
Eq(F_96(x), F_104(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_20(x)*F_99(x))
Eq(F_99(x), F_100(x)/F_20(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_20(x)*F_72(x))
Eq(F_102(x), F_103(x)/F_20(x))
Eq(F_103(x), F_26(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_20(x))
Eq(F_106(x), F_107(x)/(F_20(x)*F_62(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) - F_116(x))
Eq(F_109(x), F_110(x)/F_20(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x) - F_115(x))
Eq(F_112(x), F_113(x) + F_5(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_20(x)*F_5(x)*F_72(x))
Eq(F_115(x), F_2(x)*F_32(x))
Eq(F_116(x), F_117(x)*F_2(x))
Eq(F_117(x), F_118(x)/F_20(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), -F_111(x) + F_120(x))
Eq(F_120(x), -F_121(x) + F_75(x))
Eq(F_121(x), F_0(x)*F_32(x))
Eq(F_122(x), F_123(x) - F_86(x))
Eq(F_123(x), F_124(x)/F_20(x))
Eq(F_124(x), F_28(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_26(x) + F_94(x))
Eq(F_128(x), -F_112(x) + F_122(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": 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[[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25226/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[24,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]*F[2,x]
F[15,x] = 1/F[20,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[0,x]+F[18,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[58,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[34,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = -F[0,x]+F[27,x]
F[27,x] = 1/F[20,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[20,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[24,x]
F[33,x] = F[25,x]
F[34,x] = F[35,x]
F[35,x] = F[0,x]*F[20,x]*F[36,x]*F[68,x]
F[36,x] = -F[65,x]+F[37,x]
F[37,x] = 1/F[20,x]/F[41,x]/F[58,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]+F[54,x]
F[40,x] = F[2,x]*F[41,x]
F[41,x] = F[1,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[20,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[1,x]+F[20,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]+F[53,x]
F[48,x] = 0
F[49,x] = F[20,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[20,x]
F[52,x] = F[47,x]
F[53,x] = F[20,x]*F[42,x]
F[54,x] = F[55,x]
F[55,x] = F[20,x]*F[41,x]*F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[2,x]*F[58,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[20,x]*F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[20,x]*F[58,x]*F[63,x]
F[63,x] = F[23,x]+F[64,x]
F[64,x] = F[0,x]*F[37,x]
F[65,x] = F[58,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[20,x]*F[37,x]*F[58,x]
F[68,x] = 1/F[20,x]/F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[4,x]+F[71,x]
F[71,x] = -F[124,x]+F[72,x]
F[72,x] = F[121,x]+F[73,x]
F[73,x] = F[74,x]+F[83,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = -1+(x^2-2*x)*F[75,x]^2+(2+x)*F[75,x]
F[76,x] = F[77,x]
F[77,x] = F[20,x]*F[75,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[75,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[20,x]*F[75,x]*F[78,x]
F[82,x] = F[80,x]
F[83,x] = F[84,x]
F[84,x] = F[20,x]*F[85,x]
F[85,x] = 1/F[20,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[92,x]+F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[91,x]+F[26,x]
F[91,x] = (x*F[91,x]+x-1)*(x*F[91,x]+x-2*F[91,x])
F[92,x] = F[26,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[20,x]*F[95,x]
F[95,x] = F[100,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[20,x]*F[68,x]*F[98,x]
F[98,x] = 1/F[20,x]*F[99,x]
F[99,x] = F[26,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[20,x]
F[102,x] = 1/F[20,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[20,x]
F[105,x] = 1/F[20,x]/F[58,x]*F[106,x]
F[106,x] = F[107,x]
F[107,x] = -F[115,x]+F[108,x]
F[108,x] = 1/F[20,x]*F[109,x]
F[109,x] = F[110,x]
F[110,x] = -F[114,x]+F[111,x]
F[111,x] = F[112,x]+F[5,x]
F[112,x] = F[113,x]
F[113,x] = F[20,x]*F[5,x]*F[68,x]
F[114,x] = F[2,x]*F[75,x]
F[115,x] = F[116,x]*F[2,x]
F[116,x] = 1/F[20,x]*F[117,x]
F[117,x] = F[118,x]
F[118,x] = -F[110,x]+F[119,x]
F[119,x] = -F[120,x]+F[71,x]
F[120,x] = F[0,x]*F[75,x]
F[121,x] = -F[83,x]+F[122,x]
F[122,x] = 1/F[20,x]*F[123,x]
F[123,x] = F[90,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[126,x]+F[26,x]
F[126,x] = F[94,x]
F[127,x] = -F[111,x]+F[121,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{24}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{58}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)
F_{33}\! \left(x \right) = F_{25}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{36}\! \left(x \right) F_{68}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{65}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{58}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{54}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{48}\! \left(x \right) = 0
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{42}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{2}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{0}\! \left(x \right) F_{37}\! \left(x \right)
F_{65}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right) F_{58}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{20}\! \left(x \right) F_{4}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{121}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{83}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = x^{2} F_{75} \left(x \right)^{2}-2 x F_{75} \left(x \right)^{2}+F_{75}\! \left(x \right) x +2 F_{75}\! \left(x \right)-1
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{20}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{26}\! \left(x \right)
F_{91}\! \left(x \right) = x^{2} F_{91} \left(x \right)^{2}+2 x^{2} F_{91}\! \left(x \right)-2 x F_{91} \left(x \right)^{2}+x^{2}-3 x F_{91}\! \left(x \right)-x +2 F_{91}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{26}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{20}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{20}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{20}\! \left(x \right) F_{58}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{109}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{5}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{2}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{71}\! \left(x \right)
F_{120}\! \left(x \right) = F_{0}\! \left(x \right) F_{75}\! \left(x \right)
F_{121}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = \frac{F_{123}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{123}\! \left(x \right) = F_{90}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{26}\! \left(x \right)
F_{126}\! \left(x \right) = F_{94}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{121}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x)*F_2(x))
Eq(F_15(x), F_16(x)/F_20(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), -F_0(x) + F_18(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_58(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_34(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), -F_0(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_20(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_20(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_24(x))
Eq(F_33(x), F_25(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_0(x)*F_20(x)*F_36(x)*F_68(x))
Eq(F_36(x), F_37(x) - F_65(x))
Eq(F_37(x), F_38(x)/(F_20(x)*F_41(x)*F_58(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) + F_54(x))
Eq(F_40(x), F_2(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_20(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_1(x) + F_20(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x) + F_53(x))
Eq(F_48(x), 0)
Eq(F_49(x), F_20(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_20(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_20(x)*F_42(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_20(x)*F_41(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_2(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_20(x)*F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_20(x)*F_58(x)*F_63(x))
Eq(F_63(x), F_23(x) + F_64(x))
Eq(F_64(x), F_0(x)*F_37(x))
Eq(F_65(x), F_58(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_20(x)*F_37(x)*F_58(x))
Eq(F_68(x), F_69(x)/(F_20(x)*F_4(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_4(x) + F_71(x))
Eq(F_71(x), -F_124(x) + F_72(x))
Eq(F_72(x), F_121(x) + F_73(x))
Eq(F_73(x), F_74(x) + F_83(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), x*(x - 2)*F_75(x)**2 + (x + 2)*F_75(x) - 1)
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_20(x)*F_75(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_75(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_20(x)*F_75(x)*F_78(x))
Eq(F_82(x), F_80(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_20(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_20(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x) - F_92(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_26(x) - F_91(x))
Eq(F_91(x), x*(x - 2)*(F_91(x) + 1)**2 + (x + 1)*(F_91(x) + 1) + F_91(x) - 1)
Eq(F_92(x), F_26(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_20(x)*F_95(x))
Eq(F_95(x), F_100(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_20(x)*F_68(x)*F_98(x))
Eq(F_98(x), F_99(x)/F_20(x))
Eq(F_99(x), F_26(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_20(x))
Eq(F_102(x), F_103(x)/F_20(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_20(x))
Eq(F_105(x), F_106(x)/(F_20(x)*F_58(x)))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x) - F_115(x))
Eq(F_108(x), F_109(x)/F_20(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x) - F_114(x))
Eq(F_111(x), F_112(x) + F_5(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_20(x)*F_5(x)*F_68(x))
Eq(F_114(x), F_2(x)*F_75(x))
Eq(F_115(x), F_116(x)*F_2(x))
Eq(F_116(x), F_117(x)/F_20(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), -F_110(x) + F_119(x))
Eq(F_119(x), -F_120(x) + F_71(x))
Eq(F_120(x), F_0(x)*F_75(x))
Eq(F_121(x), F_122(x) - F_83(x))
Eq(F_122(x), F_123(x)/F_20(x))
Eq(F_123(x), F_90(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_126(x) + F_26(x))
Eq(F_126(x), F_94(x))
Eq(F_127(x), -F_111(x) + F_121(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": 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[0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25341/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[24,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]*F[2,x]
F[15,x] = 1/F[20,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[0,x]+F[18,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[62,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[38,x]
F[25,x] = F[26,x]+F[33,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = (x*F[27,x]+x-2*F[27,x])*(x*F[27,x]+x-1)
F[28,x] = -F[2,x]+F[29,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[20,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = -1+(x^2-2*x)*F[32,x]^2+(2+x)*F[32,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[24,x]
F[37,x] = F[25,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[20,x]*F[40,x]*F[72,x]
F[40,x] = -F[69,x]+F[41,x]
F[41,x] = 1/F[20,x]/F[45,x]/F[62,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[58,x]
F[44,x] = F[2,x]*F[45,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[1,x]+F[20,x]
F[50,x] = F[46,x]+F[51,x]
F[51,x] = F[52,x]+F[53,x]+F[57,x]
F[52,x] = 0
F[53,x] = F[20,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[20,x]
F[56,x] = F[51,x]
F[57,x] = F[20,x]*F[46,x]
F[58,x] = F[59,x]
F[59,x] = F[20,x]*F[45,x]*F[60,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[2,x]*F[62,x]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[20,x]*F[62,x]
F[65,x] = F[66,x]
F[66,x] = F[20,x]*F[62,x]*F[67,x]
F[67,x] = F[23,x]+F[68,x]
F[68,x] = F[0,x]*F[41,x]
F[69,x] = F[62,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[20,x]*F[41,x]*F[62,x]
F[72,x] = 1/F[20,x]/F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[4,x]+F[75,x]
F[75,x] = -F[125,x]+F[76,x]
F[76,x] = F[122,x]+F[77,x]
F[77,x] = F[78,x]+F[86,x]
F[78,x] = F[32,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[20,x]*F[32,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[32,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[20,x]*F[32,x]*F[81,x]
F[85,x] = F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[93,x]+F[91,x]
F[91,x] = 1/F[20,x]*F[92,x]
F[92,x] = F[28,x]
F[93,x] = F[26,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[20,x]*F[96,x]
F[96,x] = F[104,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[20,x]*F[99,x]
F[99,x] = 1/F[20,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[20,x]*F[72,x]
F[102,x] = 1/F[20,x]*F[103,x]
F[103,x] = F[26,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[20,x]
F[106,x] = 1/F[20,x]/F[62,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = -F[116,x]+F[109,x]
F[109,x] = 1/F[20,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[115,x]+F[112,x]
F[112,x] = F[113,x]+F[5,x]
F[113,x] = F[114,x]
F[114,x] = F[20,x]*F[5,x]*F[72,x]
F[115,x] = F[2,x]*F[32,x]
F[116,x] = F[117,x]*F[2,x]
F[117,x] = 1/F[20,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = -F[111,x]+F[120,x]
F[120,x] = -F[121,x]+F[75,x]
F[121,x] = F[0,x]*F[32,x]
F[122,x] = -F[86,x]+F[123,x]
F[123,x] = 1/F[20,x]*F[124,x]
F[124,x] = F[28,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[127,x]
F[127,x] = F[26,x]+F[94,x]
F[128,x] = -F[112,x]+F[122,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{24}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{2}+2 x^{2} F_{27}\! \left(x \right)-2 x F_{27} \left(x \right)^{2}+x^{2}-3 x F_{27}\! \left(x \right)-x +2 F_{27}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}-2 x F_{32} \left(x \right)^{2}+F_{32}\! \left(x \right) x +2 F_{32}\! \left(x \right)-1
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{40}\! \left(x \right) F_{72}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{20}\! \left(x \right) F_{45}\! \left(x \right) F_{62}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = 0
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right) F_{45}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{20}\! \left(x \right) F_{4}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{122}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{32}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{32}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right) F_{81}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{28}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{20}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{104}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{20}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{20}\! \left(x \right) F_{72}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{26}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{20}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{20}\! \left(x \right) F_{62}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{5}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{115}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{75}\! \left(x \right)
F_{121}\! \left(x \right) = F_{0}\! \left(x \right) F_{32}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{122}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x)*F_2(x))
Eq(F_15(x), F_16(x)/F_20(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), -F_0(x) + F_18(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_62(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_38(x))
Eq(F_25(x), F_26(x) + F_33(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), x*(x - 2)*(F_27(x) + 1)**2 + (x + 1)*(F_27(x) + 1) + F_27(x) - 1)
Eq(F_28(x), -F_2(x) + F_29(x))
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_20(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), x*(x - 2)*F_32(x)**2 + (x + 2)*F_32(x) - 1)
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_24(x))
Eq(F_37(x), F_25(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_20(x)*F_40(x)*F_72(x))
Eq(F_40(x), F_41(x) - F_69(x))
Eq(F_41(x), F_42(x)/(F_20(x)*F_45(x)*F_62(x)))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_58(x))
Eq(F_44(x), F_2(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_1(x) + F_20(x))
Eq(F_50(x), F_46(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_53(x) + F_57(x))
Eq(F_52(x), 0)
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_20(x))
Eq(F_56(x), F_51(x))
Eq(F_57(x), F_20(x)*F_46(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_20(x)*F_45(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_2(x)*F_62(x))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_20(x)*F_62(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_20(x)*F_62(x)*F_67(x))
Eq(F_67(x), F_23(x) + F_68(x))
Eq(F_68(x), F_0(x)*F_41(x))
Eq(F_69(x), F_62(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_20(x)*F_41(x)*F_62(x))
Eq(F_72(x), F_73(x)/(F_20(x)*F_4(x)))
Eq(F_73(x), F_74(x))
Eq(F_74(x), -F_4(x) + F_75(x))
Eq(F_75(x), -F_125(x) + F_76(x))
Eq(F_76(x), F_122(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_86(x))
Eq(F_78(x), F_32(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_20(x)*F_32(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_32(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_20(x)*F_32(x)*F_81(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x) - F_93(x))
Eq(F_91(x), F_92(x)/F_20(x))
Eq(F_92(x), F_28(x))
Eq(F_93(x), F_26(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_20(x)*F_96(x))
Eq(F_96(x), F_104(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_20(x)*F_99(x))
Eq(F_99(x), F_100(x)/F_20(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_20(x)*F_72(x))
Eq(F_102(x), F_103(x)/F_20(x))
Eq(F_103(x), F_26(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_20(x))
Eq(F_106(x), F_107(x)/(F_20(x)*F_62(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) - F_116(x))
Eq(F_109(x), F_110(x)/F_20(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x) - F_115(x))
Eq(F_112(x), F_113(x) + F_5(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_20(x)*F_5(x)*F_72(x))
Eq(F_115(x), F_2(x)*F_32(x))
Eq(F_116(x), F_117(x)*F_2(x))
Eq(F_117(x), F_118(x)/F_20(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), -F_111(x) + F_120(x))
Eq(F_120(x), -F_121(x) + F_75(x))
Eq(F_121(x), F_0(x)*F_32(x))
Eq(F_122(x), F_123(x) - F_86(x))
Eq(F_123(x), F_124(x)/F_20(x))
Eq(F_124(x), F_28(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_26(x) + F_94(x))
Eq(F_128(x), -F_112(x) + F_122(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 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0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/25511/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[9,x]
F[3,x] = F[1,x]+F[4,x]+F[45,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[32,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]*F[9,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = F[13,x,1,k[0]]
F[14,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[34,x,k[0],k[1]]+F[44,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[9,x]
F[16,x,k[0],k[1]] = F[1,x]+F[10,x,k[1]]+F[17,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[32,x,k[1]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[9,x]
F[18,x,k[0],k[1]] = F[19,x,1,k[0],k[1]]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[20,x,k[0],k[1],k[2]]*k[0]-F[20,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[1,x]+F[21,x,k[0],k[1],k[2]]+F[23,x,k[0],k[2]]+F[27,x,k[0],k[1],k[2]]+F[29,x,k[0],k[2]]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1],k[2]]*F[9,x]
F[22,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[20,x,k[0],k[1],k[2]]*k[0]-F[20,x,1,k[1],k[2]])
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[26,x,k[0]]
F[24,x,k[0],k[1]] = (F[25,x,k[0],1]*k[0]-F[25,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1]*k[2],k[2]]
F[28,x,k[0],k[1],k[2]] = F[13,x,k[0],k[2]]*F[26,x,k[1]]
F[29,x,k[0],k[1]] = F[26,x,k[1]]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = (-F[14,x,1,k[1]]*k[1]+F[14,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[31,x,k[0],k[1]] = F[12,x,k[1]]*F[26,x,k[1]]
F[32,x,k[0]] = F[26,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[30,x,1,k[0]]
F[34,x,k[0],k[1]] = F[26,x,k[1]]*F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1],1]
F[36,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1],k[0]*k[2]]
F[37,x,k[0],k[1],k[2]] = F[38,x,k[0]*k[1],k[2],k[1]]
F[38,x,k[0],k[1],k[2]] = F[1,x]+F[27,x,k[0],k[1],k[2]]+F[29,x,k[0],k[2]]+F[39,x,k[0],k[1],k[2]]+F[41,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = F[40,x,k[0],k[1],k[2]]*F[9,x]
F[40,x,k[0],k[1],k[2]] = (-F[16,x,k[1],k[2]]*k[1]*k[2]+F[16,x,k[0]/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[41,x,k[0],k[1],k[2]] = F[26,x,k[0]]*F[42,x,k[0],k[1],k[2]]
F[42,x,k[0],k[1],k[2]] = (-F[43,x,k[0],k[1]/k[0],k[2]]*k[1]*k[2]+F[43,x,k[0],1/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[43,x,k[0],k[1],k[2]] = F[38,x,k[0],k[0]*k[1],k[2]]
F[44,x,k[0],k[1]] = F[29,x,k[0]*k[1],k[1]]
F[45,x] = F[46,x]*F[9,x]
F[46,x] = F[12,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{45}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{8}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y_{0}\right) = -\frac{-F_{6}\! \left(x , y_{0}\right) y_{0}+F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = -\frac{-F_{12}\! \left(x , y_{0}\right) y_{0}+F_{12}\! \left(x , 1\right)}{-1+y_{0}}
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x \right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , 1, y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{26}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{25}\! \left(x , y_{0}, 1\right) y_{0}-F_{25}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{26}\! \left(x , y_{0}\right) = y_{0} x
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0}, y_{2}\right) F_{26}\! \left(x , y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{14}\! \left(x , 1, y_{1}\right) y_{1}-F_{14}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{1}\right)
F_{32}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{30}\! \left(x , 1, y_{0}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}, 1\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1}, y_{0} y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{38}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{16}\! \left(x , y_{1}, y_{2}\right) y_{1} y_{2}-F_{16}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right) y_{0}}{-y_{1} y_{2}+y_{0}}
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} y_{2} F_{43}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)+y_{0} F_{43}\! \left(x , y_{0}, \frac{1}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{38}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{9}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_9(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_45(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_32(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_9(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_14(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_34(x, k_0, k_1) + F_44(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_9(x))
Eq(F_16(x, k_0, k_1), F_1(x) + F_10(x, k_1) + F_17(x, k_0, k_1) + F_31(x, k_0, k_1) + F_32(x, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_9(x))
Eq(F_18(x, k_0, k_1), F_19(x, 1, k_0, k_1))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, k_1, k_2) + F_20(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_20(x, k_0, k_1, k_2), F_1(x) + F_21(x, k_0, k_1, k_2) + F_23(x, k_0, k_2) + F_27(x, k_0, k_1, k_2) + F_29(x, k_0, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_1, k_2)*F_9(x))
Eq(F_22(x, k_0, k_1, k_2), (k_0*F_20(x, k_0, k_1, k_2) - F_20(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_26(x, k_0))
Eq(F_24(x, k_0, k_1), (-k_0*F_25(x, k_0, 1) + k_1*F_25(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1*k_2, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_13(x, k_0, k_2)*F_26(x, k_1))
Eq(F_29(x, k_0, k_1), F_26(x, k_1)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (-k_0*F_14(x, k_0/k_1, k_1) + k_1*F_14(x, 1, k_1))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1), F_12(x, k_1)*F_26(x, k_1))
Eq(F_32(x, k_0), F_26(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_30(x, 1, k_0))
Eq(F_34(x, k_0, k_1), F_26(x, k_1)*F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1, 1))
Eq(F_36(x, k_0, k_1, k_2), F_37(x, k_0, k_1, k_0*k_2))
Eq(F_37(x, k_0, k_1, k_2), F_38(x, k_0*k_1, k_2, k_1))
Eq(F_38(x, k_0, k_1, k_2), F_1(x) + F_27(x, k_0, k_1, k_2) + F_29(x, k_0, k_2) + F_39(x, k_0, k_1, k_2) + F_41(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), F_40(x, k_0, k_1, k_2)*F_9(x))
Eq(F_40(x, k_0, k_1, k_2), (-k_0*F_16(x, k_0/k_2, k_2) + k_1*k_2*F_16(x, k_1, k_2))/(-k_0 + k_1*k_2))
Eq(F_41(x, k_0, k_1, k_2), F_26(x, k_0)*F_42(x, k_0, k_1, k_2))
Eq(F_42(x, k_0, k_1, k_2), (-k_0*F_43(x, k_0, 1/k_2, k_2) + k_1*k_2*F_43(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1*k_2))
Eq(F_43(x, k_0, k_1, k_2), F_38(x, k_0, k_0*k_1, k_2))
Eq(F_44(x, k_0, k_1), F_29(x, k_0*k_1, k_1))
Eq(F_45(x), F_46(x)*F_9(x))
Eq(F_46(x), F_12(x, 1))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "assumption": {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], 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