01342_01432_10342_10432_20341_20431_30241
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3126, 17374, 98635, 568830, 3320717, 19577014, 116356107, 696326804, 4191791684, 25364160068, 154174416991, 940936870642, 5763511006885, 35419534841928, 218323607428448, 1349433815019146, 8361822087024797, 51935694963204472, 323276184778460816, 2016320010896597384, 12599849191510286397, 78875006319416159244, 494577912053573018941, 3106051896873561222486, 19535413091103474018724, 123038470854251737975590, 775945355650387374831293, 4899629882138913838094638, 30974882684151743305434025, 196040009550069440565708438, 1242065917706771384470023524, 7877480909129650500506543272, 50009471307421788812196579877, 317775293688441306270831195144, 2021030991857014064823901935365, 12864530839527038759301855843994, 81953454384625948497666149993046, 522490097468490417520723373628166, 3333591569254815905256726347499039, 21284188202281942577166154774252994, 135987744485001626018306968632768077, 869418202580080230129683641559894618, 5562024656675600168693501127521755679, 35604251489800753943442229476590831396, 228047693374577870225610717865899721704, 1461487168587776642380004658734063775592, 9371323714443465605238578693567192168671, 60122225624120354934598632617101661897782, 385912924782611819671501842312571953551109, 2478312985279263455699086413023504604794664, 15923124646192743631440748875905485158224208, 102352595734716824795357678211367336714746982, 658205171158198934764607858603344110267490693, 4234570116213556741174121835657273203891513636, 27254424349475676022114068031059702612955991335, 175484457079191245790300257785931781541007474240, 1130339293318173674601894462678632500432757389560, 7283536992468951535643200912923789184632294130180, 46949850359331745159232234164233173509348011910195, 302746915832506617451299713360823138639050500452734, 1952874508303583153117762852120958180895302288935427, 12601251888284965615089150058911284281576557246679508, 81338026952661440110070086339110601912291738027278322, 525182404901601007860256699933865752981189453455944426, 3392028315219308369230482921097763484342326382660101813, 21914817891824357423053162194085402477154494623514299756, 141625623591180640562167513943610166196817488966408204901, 915520327891565671803924040351103530795950259787767728776, 5919882463473394489149639050943036502573533359817319432942, 38288996717703221058893898609198042140228316687002122722200, 247712369527797988427410920639162776170174301573456490370223, 1602991844304314806373236950520688779214536608227220344789530, 10375811191984067257838399273611714444603690824680074021289685, 67176481899090415604161159278369966440889338252755816263163520, 435025100773233410490461581126357423309379020228925923715274112, 2817803818372236982122492280874545122497231677498721328016673310, 18255938620818386930430296099411075662748920284886571692265815165, 118302042386081070154106535042516532923568787478903214124811343380, 766783477594236616864079755802425774748863855985718150769017854273, 4970997243826597607281115007091428805564134841375485107605572172632, 32233130651969485014387587176839792961829792759588425823492829841314, 209048778095899071134130022030455806903899710125883437830802579700020, 1356054090612108061177086672586093977147660529464244136301304557816847, 8798097052743650923081287288598864361339350969840480472562449487313990, 57092757837010154256963974591999582542048638120430324895757239842339077, 370554486020404940509594482183291390287317495292095225624220031070155456, 2405471452033255493638586674783593803490219219198345602087371912869817504, 15617940715925903476699236985748723558361254527586829908877760507581589906, 101419430759665285571781058152664297425145675920918919348059675060737269013, 658704844849770981032605228892834811773826942495901558184016314428779770520, 4278892145339301271643963224934762950599149050185583405415935369277262760952, 27799767443112439098807365609238652035070227951048140360379661695646376555584, 180642077657972637525676268104295173866476894093855329624760067561488118792365, 1173986883540652160888696158668416051053684563582389281357235739207629319838548
Implicit equation for the generating function in Maple syntax:
(x^7-8*x^6+15*x^5-16*x^4+13*x^3-10*x^2+6*x-2)*F(x)^6+(x^6-10*x^5+28*x^4-46*x^3+53*x^2-38*x+14)*F(x)^5+(x^6-7*x^5-4*x^4+50*x^3-99*x^2+92*x-40)*F(x)^4+(2*x^5-9*x^4-14*x^3+79*x^2-108*x+60)*F(x)^3+(x^4-3*x^3-23*x^2+62*x-50)*F(x)^2+(-14*x+22)*F(x)-4 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}-8 x^{6}+15 x^{5}-16 x^{4}+13 x^{3}-10 x^{2}+6 x -2\right) F \! \left(x \right)^{6}+\left(x^{6}-10 x^{5}+28 x^{4}-46 x^{3}+53 x^{2}-38 x +14\right) F \! \left(x \right)^{5}+\left(x^{6}-7 x^{5}-4 x^{4}+50 x^{3}-99 x^{2}+92 x -40\right) F \! \left(x \right)^{4}+\left(2 x^{5}-9 x^{4}-14 x^{3}+79 x^{2}-108 x +60\right) F \! \left(x \right)^{3}+\left(x^{4}-3 x^{3}-23 x^{2}+62 x -50\right) F \! \left(x \right)^{2}+\left(-14 x +22\right) F \! \left(x \right)-4 = 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) = 3126
a(8) = 17374
a(9) = 98635
a(10) = 568830
a(11) = 3320717
a(12) = 19577014
a(13) = 116356107
a(14) = 696326804
a(15) = 4191791684
a(16) = 25364160068
a(17) = 154174416991
a(18) = 940936870642
a(19) = 5763511006885
a(20) = 35419534841928
a(21) = 218323607428448
a(22) = 1349433815019146
a(23) = 8361822087024797
a(24) = 51935694963204472
a(25) = 323276184778460816
a(26) = 2016320010896597384
a(27) = 12599849191510286397
a(28) = 78875006319416159244
a(29) = 494577912053573018941
a(30) = 3106051896873561222486
a(31) = 19535413091103474018724
a(32) = 123038470854251737975590
a(33) = 775945355650387374831293
a(34) = 4899629882138913838094638
a(35) = 30974882684151743305434025
a(36) = 196040009550069440565708438
a(37) = 1242065917706771384470023524
a(38) = 7877480909129650500506543272
a(39) = 50009471307421788812196579877
a(40) = 317775293688441306270831195144
a(41) = 2021030991857014064823901935365
a(42) = 12864530839527038759301855843994
a(43) = 81953454384625948497666149993046
a(44) = 522490097468490417520723373628166
a(45) = 3333591569254815905256726347499039
a(46) = 21284188202281942577166154774252994
a(47) = 135987744485001626018306968632768077
a(48) = 869418202580080230129683641559894618
a(49) = 5562024656675600168693501127521755679
a(50) = 35604251489800753943442229476590831396
a(51) = 228047693374577870225610717865899721704
a(52) = 1461487168587776642380004658734063775592
a(53) = 9371323714443465605238578693567192168671
a(54) = 60122225624120354934598632617101661897782
a(55) = 385912924782611819671501842312571953551109
a(56) = 2478312985279263455699086413023504604794664
a(57) = 15923124646192743631440748875905485158224208
a(58) = 102352595734716824795357678211367336714746982
a(59) = 658205171158198934764607858603344110267490693
a(60) = 4234570116213556741174121835657273203891513636
a(61) = 27254424349475676022114068031059702612955991335
a(62) = 175484457079191245790300257785931781541007474240
a(63) = 1130339293318173674601894462678632500432757389560
a(64) = 7283536992468951535643200912923789184632294130180
a(65) = 46949850359331745159232234164233173509348011910195
a(66) = 302746915832506617451299713360823138639050500452734
a(67) = 1952874508303583153117762852120958180895302288935427
a(68) = 12601251888284965615089150058911284281576557246679508
a(69) = 81338026952661440110070086339110601912291738027278322
a(70) = 525182404901601007860256699933865752981189453455944426
a(71) = 3392028315219308369230482921097763484342326382660101813
a(72) = 21914817891824357423053162194085402477154494623514299756
a(73) = 141625623591180640562167513943610166196817488966408204901
a(74) = 915520327891565671803924040351103530795950259787767728776
a(75) = 5919882463473394489149639050943036502573533359817319432942
a(76) = 38288996717703221058893898609198042140228316687002122722200
a(77) = 247712369527797988427410920639162776170174301573456490370223
a(78) = 1602991844304314806373236950520688779214536608227220344789530
a(79) = 10375811191984067257838399273611714444603690824680074021289685
a(80) = 67176481899090415604161159278369966440889338252755816263163520
a(81) = 435025100773233410490461581126357423309379020228925923715274112
a(82) = 2817803818372236982122492280874545122497231677498721328016673310
a(83) = 18255938620818386930430296099411075662748920284886571692265815165
a(n+84) = 7/1228800*(n+3)*(2201246*n^4+33474387*n^3+187314439*n^2+456452418*n+407469240)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+2)-1/11520*(55239481*n^2+8687012969*n+341520195618)/(n+83)/(n+84)*a(n+82)+1/23040*(2435321*n+192443358)/(n+84)*a(n+83)+1/184320*(23704567223*n^3+5560539748728*n^2+434775183767719*n+11331186917154186)/(n+82)/(n+83)/(n+84)*a(n+81)-1/30720*(71301793825*n^4+22169017111148*n^3+2584665376381367*n^2+133924596245833112*n+2602125871985769924)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+80)+1/14745600*(68322043521359522106440826839*n^5+13838736640639641214752069922480*n^4+1118983673935624358867344163731915*n^3+45137203630502050418231546062251500*n^2+908012218102615165796910273171773286*n+7284898050762793170955588198198401060)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+42)-1/5898240*(21459420519768051849389809579*n^5+4342431149725831515600797197880*n^4+350104246333949706278595017049629*n^3+14048375140593359669949736276453780*n^2+280319569235306458199606908217162436*n+2222841562474277682474350939247296160)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+43)+1/29491200*(62663866870786498174174542263*n^5+12345250873904958089679284012485*n^4+961194872793076966259597053154095*n^3+36845515641248969086501891030020395*n^2+691912131032808245563183093375374402*n+5052738531460724079103683637172988120)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+44)+1/5898240*(17281011677562190617508659373*n^5+3387656706513636483569565524939*n^4+265519256569115040839215945438445*n^3+10401264513903397838809105613914237*n^2+203650252410747259521764362233156630*n+1594395323814554272278840387719706840)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+38)-1/14745600*(56465531621928307283605508333*n^5+11172813600714037895201121531985*n^4+883890091018363787912066844820735*n^3+34946737883623871817897595553045405*n^2+690545712155467181769920839271936142*n+5455683444992893241980179369132035280)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+39)+1/14745600*(67444231685717721884271145606*n^5+13463113827798639432692957801045*n^4+1074219509813773111401632148142580*n^3+42823423150609689926624502406563595*n^2+852888681878932467358515651756433974*n+6788837007787739161412008137528025560)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+40)-1/29491200*(145118434030180389368265146353*n^5+29212103511690862119857974605410*n^4+2349354565910547608345922293462075*n^3+94348917536222235891326484833316610*n^2+1891770445484823262439046628064126952*n+15148371054165013470583000644634972080)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+41)+1/29491200*(10543227429830118936460679143*n^5+1915032501581931665116758029345*n^4+139162879873142677134166928848115*n^3+5056593618749425947179561638890535*n^2+91859494510364708436275447735660022*n+667367597119879762369121591166205080)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+34)-1/29491200*(21388408371981072329553463199*n^5+4002774803235638458732774973380*n^4+299426042864122468148800529892145*n^3+11190980156174211179620961106050360*n^2+208975080349373068192421265857531196*n+1559764168948571402767683815356799520)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+35)+1/9830400*(12701318954312184147187778479*n^5+2426236085948736680566245200195*n^4+185232355949007677931003003889935*n^3+7065257647228520600456333683173245*n^2+134642821411032254233627429118365546*n+1025623763515673513027128545268421400)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+36)-1/14745600*(30192700817004614597397844991*n^5+5853146974236371181401044699015*n^4+453592022469045112047391783566895*n^3+17565524630578132610929047537097265*n^2+339934758634263728954366090274761394*n+2630121330965195189887467689967753600)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+37)-1/9830400*(287465515996601071303710551*n^5+41828443915569378096730421380*n^4+2424160935143525592658082940405*n^3+69897891558371254971668509015900*n^2+1001859712379419035969080778668324*n+5704403334604480368112688098383360)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+31)+1/29491200*(1812324412924564851395363041*n^5+290216544209065923436496554805*n^4+18657330952780052386614738429125*n^3+601936249363631814718369058962795*n^2+9746160033393731137829178822489114*n+63355243568871312410710478072304240)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+32)-1/29491200*(4547957349467104895720358989*n^5+788069706333091490171373353440*n^4+54752136748748374872725395080055*n^3+1905902453919155881979864636130920*n^2+33230504344713587844881641083552996*n+232104113315434278904029124183024320)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+33)+1/14745600*(200912782953503283441561506*n^5+28557186075413443219901150665*n^4+1624603934351786736738580038790*n^3+46238466240322530264874231357775*n^2+658375499101564578444914143078464*n+3751798615750636595338931583689880)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+28)-1/29491200*(546882873910585576659132779*n^5+78273921359675090633531648080*n^4+4478224240293092983657515053125*n^3+128007112858287088558488669202340*n^2+1827943537119062989876737619009356*n+10431328326685441210208466430681680)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+29)+1/7372800*(159317531402468808673401728*n^5+22604785600019632613329617115*n^4+1276392210103597864870196033170*n^3+35820178887365329371618893919815*n^2+499031404520728970459897543377512*n+2756909986959160693069837861788540)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+30)+1/29491200*(16405798641228900181152089*n^5+1967114517747542054247854275*n^4+94353100679651262919949925745*n^3+2262760956963627229075235673725*n^2+27128613247939071658585429541286*n+130065435470984230669599932430960)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+24)-1/2949120*(4286011058673723831691603*n^5+546634800166214640406360649*n^4+27920737806853093105270986785*n^3+713869843460378506116561376537*n^2+9135709242743505736658587437582*n+46811959082191810142601933304440)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+25)+1/9830400*(36219573939086503419629457*n^5+4855624320457593899398088385*n^4+260675725493642652516663736805*n^3+7004616443023505095671674115535*n^2+94202676383546101607571877989018*n+507219985331758815571956255375840)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+26)-1/245760*(1948357473852206932112297*n^5+270699938965702991438668526*n^4+15057676690472688259804765837*n^3+419144534106540301028490553416*n^2+5838256211318665044428669733844*n+32552553428076742729997560171596)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+27)+7/15360*(2*n+3)*(2*n+1)*(n+3)*(n+2)*(n+1)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n)-7/368640*(2*n+3)*(n+3)*(n+2)*(5822*n^2+38499*n+60508)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+1)-1/29491200*(157967724460667035473677*n^5+14750785260839982875306140*n^4+548142386137351220744336875*n^3+10123742020929269455875425600*n^2+92829840078511641130749701028*n+337610630617117362922185735840)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+19)+1/5898240*(100642073386357938009221*n^5+9989683819070410774233799*n^4+395511352109122796105157085*n^3+7804373113569344688933922505*n^2+76715611608423686200516279878*n+300358645269524763922696533624)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+20)-1/5898240*(272680504738361010864535*n^5+28420447311899962160051060*n^4+1182290691351819458732508377*n^3+24530415356304464554455975688*n^2+253753199087380512053918943396*n+1046514657067792520102630436096)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+21)+1/29491200*(3192937706975322782012803*n^5+346624618976339483407867265*n^4+15018060126612755536267277075*n^3+324492594702186373058579009455*n^2+3495002093498304033912448683042*n+15004247349664535517956723805000)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+22)-1/29491200*(6986918408276877612384421*n^5+791576484354214981810092290*n^4+35808401710890189028960697735*n^3+808225050966088246473395199370*n^2+9098618613974029188334157586744*n+40852612445231890752893360114400)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+23)+1/9830400*(17156929755212350883*n^5+3646036236918694679800*n^4+193123956945073579937245*n^3+4368975969475348089636260*n^2+45606521154040967348515332*n+181323139320651808511171760)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+15)+1/3686400*(157608898634114049082*n^5+9741809418060821536955*n^4+202303891061786035740455*n^3+1172752374710793917088085*n^2-9901277899515976752337797*n-103187448078814076954407110)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+16)-1/29491200*(9020827451762367829433*n^5+702370112637302030565760*n^4+21245420209537941538911655*n^3+308022281304936973599935420*n^2+2088178890890309176798962012*n+5004865129860436520769163920)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+17)+1/5898240*(8398118579677393037149*n^5+726263629990595886141137*n^4+24844268422053350831586713*n^3+419083000595185298014869727*n^2+3472285312780630085306326938*n+11238521502478291002154808784)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+18)-1/14745600*(51291452468751496*n^5+3023704072667046455*n^4+71923991009589579590*n^3+860386645161907408285*n^2+5163859397602663874574*n+12416779940189905772280)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+10)+1/9830400*(411928587088403341*n^5+26396776067887817290*n^4+679053864312276998935*n^3+8753715269012467969530*n^2+56486148761711897285184*n+145839820252824557078400)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+11)-1/14745600*(4106670727051210132*n^5+287067247064714392055*n^4+8039012551092989729210*n^3+112619348907589031383225*n^2+788649786230080721471178*n+2207318556965346106301880)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+12)+1/3686400*(4560259281970758059*n^5+351268050188473923850*n^4+10805143287108142280920*n^3+165797519859651208032275*n^2+1268545856689347594177096*n+3870909336881011951346760)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+13)-1/29491200*(101176985250621002251*n^5+8994005653977675548825*n^4+314739364163779359553235*n^3+5433619473854249816875015*n^2+46370686732450848688769754*n+156749319151071256014172920)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+14)-1/1228800*(533007024*n^5+12388173195*n^4+114178642270*n^3+521738509905*n^2+1182036658466*n+1062187142520)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+3)+1/2457600*(24967485494*n^5+704749911215*n^4+7909967163900*n^3+44137196525685*n^2+122455839665906*n+135149459137320)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+4)-1/2457600*(416497648029*n^5+13818671293650*n^4+182544253841105*n^3+12005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200*(59773481587242604858338*n^5+21018328565112257441317895*n^4+2925568081308092353161227220*n^3+201865935684285911585231327825*n^2+6914605810215590261416225285922*n+94164266574467777618458866609600)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+64)-1/9830400*(393033166405383948828151747*n^5+108063223513612516809827175600*n^4+11877620731936555733913099373985*n^3+652339951936698990862678826092960*n^2+17901524170150575240786272952014108*n+196356021397318761438930203161598400)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+57)+1/5898240*(42493383019885249797340057*n^5+11703713476977797616814075589*n^4+1286362496623333117423910159873*n^3+70510253875438949423384495791675*n^2+1926976671772524354958106991773358*n+20998706460888843611509933942756632)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+58)+1/2949120*(7146905879566839115655098*n^5+2074136900814403237602218477*n^4+241281296817485264612899663364*n^3+14062288762680835058622599863675*n^2+410580698874740175616255660869258*n+4803975192124261966955418836811360)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+59)-1/9830400*(26231933621505707220389627*n^5+7619526427839495508256212345*n^4+885989192662363812998817131815*n^3+51551633058888027020839683140295*n^2+1500961189591840710780918876646598*n+17494343707114902827150509696011000)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+60)-1/29491200*(9289010324890075319370096157*n^5+2536993027326404625203274245660*n^4+276734177907647700132762800324435*n^3+15071842616249488980302367730142920*n^2+409901783297839139922105479299676748*n+4453869924063951447578037217290601200)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+53)+1/2457600*(741422518615430154765632681*n^5+200223672498638035608119124245*n^4+21626731951716814839746493731795*n^3+1167885894910398121848502760388085*n^2+31531321088520239266804493734630994*n+340489974917454285707404929551045520)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+54)-1/29491200*(6146278898948456222533393589*n^5+1663558455011778227511688499260*n^4+180111599116201659929267547049495*n^3+9750501973593673288471228576101020*n^2+263929321930339169211764709511477356*n+2857637994813525449044863507769300800)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+55)+1/5898240*(640376099908495338257313203*n^5+174557531018805707115459427909*n^4+19029720879696244330204337050267*n^3+1037091338757675356677543513896035*n^2+28254148096020335259529075123437066*n+307827429834392136210172456250404416)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+56)-1/29491200*(23987917253209488594419026783*n^5+5615107612001684518244754774515*n^4+523830128674394877836403604838435*n^3+24330154514540000453079226919769565*n^2+562222938600896310722728805538282942*n+5166327207766346570552634745782482160)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+50)+1/2457600*(558543861216036536572922704*n^5+115964899590965868148610420925*n^4+9174448147390738173155292767340*n^3+334685457572822008308285942636885*n^2+5187984329568141231373854793072946*n+19255859480119592078715263098735920)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+51)+1/14745600*(2343641934276616417521119842*n^5+706197957873560625810779361185*n^4+83324387498862640190070762082190*n^3+4837174424219681968012179358282135*n^2+138647409826007050746756226597524888*n+1573635195461296285953522847187749560)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+52)-1/9830400*(4729640317218353870568756413*n^5+651969717780367189372793926750*n^4+22484235985265776656073260898255*n^3-578756794023498191757188300111690*n^2-48006381883542216177741741924909248*n-740161554837875193296178712355694480)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+45)-1/5898240*(5182146280192458766664560819*n^5+1355484420567389588859911581193*n^4+139195697396599031524956606135083*n^3+7044860665898613981045310693426375*n^2+176246821031421723033545464166288634*n+1747389928046451786847810979540898696)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+46)+1/29491200*(49188635181702715568401869853*n^5+11891398146362257221932921535770*n^4+1147039052490976154113780982517695*n^3+55194808897342453983822096343012210*n^2+1325157351744111449974483762533140952*n+12701037547921429770296210898146860320)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+47)-1/5898240*(10663326350273471642579813885*n^5+2544277947328406955233970462355*n^4+242655475706516631516135985315813*n^3+11562899903953417383942721326111821*n^2+275283729761919754835770334609873118*n+2619424069103542266876195757675687968)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+48)+1/14745600*(21121358515757715824754235051*n^5+5016687711814993559345970536645*n^4+476189320076447551422080530507805*n^3+22577300720273000773602124629658705*n^2+534615371101343067884734284540031134*n+5057305652563181260965908091677443320)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+49), n >= 84
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) = 3126
a(8) = 17374
a(9) = 98635
a(10) = 568830
a(11) = 3320717
a(12) = 19577014
a(13) = 116356107
a(14) = 696326804
a(15) = 4191791684
a(16) = 25364160068
a(17) = 154174416991
a(18) = 940936870642
a(19) = 5763511006885
a(20) = 35419534841928
a(21) = 218323607428448
a(22) = 1349433815019146
a(23) = 8361822087024797
a(24) = 51935694963204472
a(25) = 323276184778460816
a(26) = 2016320010896597384
a(27) = 12599849191510286397
a(28) = 78875006319416159244
a(29) = 494577912053573018941
a(30) = 3106051896873561222486
a(31) = 19535413091103474018724
a(32) = 123038470854251737975590
a(33) = 775945355650387374831293
a(34) = 4899629882138913838094638
a(35) = 30974882684151743305434025
a(36) = 196040009550069440565708438
a(37) = 1242065917706771384470023524
a(38) = 7877480909129650500506543272
a(39) = 50009471307421788812196579877
a(40) = 317775293688441306270831195144
a(41) = 2021030991857014064823901935365
a(42) = 12864530839527038759301855843994
a(43) = 81953454384625948497666149993046
a(44) = 522490097468490417520723373628166
a(45) = 3333591569254815905256726347499039
a(46) = 21284188202281942577166154774252994
a(47) = 135987744485001626018306968632768077
a(48) = 869418202580080230129683641559894618
a(49) = 5562024656675600168693501127521755679
a(50) = 35604251489800753943442229476590831396
a(51) = 228047693374577870225610717865899721704
a(52) = 1461487168587776642380004658734063775592
a(53) = 9371323714443465605238578693567192168671
a(54) = 60122225624120354934598632617101661897782
a(55) = 385912924782611819671501842312571953551109
a(56) = 2478312985279263455699086413023504604794664
a(57) = 15923124646192743631440748875905485158224208
a(58) = 102352595734716824795357678211367336714746982
a(59) = 658205171158198934764607858603344110267490693
a(60) = 4234570116213556741174121835657273203891513636
a(61) = 27254424349475676022114068031059702612955991335
a(62) = 175484457079191245790300257785931781541007474240
a(63) = 1130339293318173674601894462678632500432757389560
a(64) = 7283536992468951535643200912923789184632294130180
a(65) = 46949850359331745159232234164233173509348011910195
a(66) = 302746915832506617451299713360823138639050500452734
a(67) = 1952874508303583153117762852120958180895302288935427
a(68) = 12601251888284965615089150058911284281576557246679508
a(69) = 81338026952661440110070086339110601912291738027278322
a(70) = 525182404901601007860256699933865752981189453455944426
a(71) = 3392028315219308369230482921097763484342326382660101813
a(72) = 21914817891824357423053162194085402477154494623514299756
a(73) = 141625623591180640562167513943610166196817488966408204901
a(74) = 915520327891565671803924040351103530795950259787767728776
a(75) = 5919882463473394489149639050943036502573533359817319432942
a(76) = 38288996717703221058893898609198042140228316687002122722200
a(77) = 247712369527797988427410920639162776170174301573456490370223
a(78) = 1602991844304314806373236950520688779214536608227220344789530
a(79) = 10375811191984067257838399273611714444603690824680074021289685
a(80) = 67176481899090415604161159278369966440889338252755816263163520
a(81) = 435025100773233410490461581126357423309379020228925923715274112
a(82) = 2817803818372236982122492280874545122497231677498721328016673310
a(83) = 18255938620818386930430296099411075662748920284886571692265815165
a{\left(n + 84 \right)} = \frac{7 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{15360 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{7 \left(n + 2\right) \left(n + 3\right) \left(2 n + 3\right) \left(5822 n^{2} + 38499 n + 60508\right) a{\left(n + 1 \right)}}{368640 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{7 \left(n + 3\right) \left(2201246 n^{4} + 33474387 n^{3} + 187314439 n^{2} + 456452418 n + 407469240\right) a{\left(n + 2 \right)}}{1228800 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2435321 n + 192443358\right) a{\left(n + 83 \right)}}{23040 \left(n + 84\right)} - \frac{\left(55239481 n^{2} + 8687012969 n + 341520195618\right) a{\left(n + 82 \right)}}{11520 \left(n + 83\right) \left(n + 84\right)} + \frac{\left(23704567223 n^{3} + 5560539748728 n^{2} + 434775183767719 n + 11331186917154186\right) a{\left(n + 81 \right)}}{184320 \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(71301793825 n^{4} + 22169017111148 n^{3} + 2584665376381367 n^{2} + 133924596245833112 n + 2602125871985769924\right) a{\left(n + 80 \right)}}{30720 \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(533007024 n^{5} + 12388173195 n^{4} + 114178642270 n^{3} + 521738509905 n^{2} + 1182036658466 n + 1062187142520\right) a{\left(n + 3 \right)}}{1228800 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(24967485494 n^{5} + 704749911215 n^{4} + 7909967163900 n^{3} + 44137196525685 n^{2} + 122455839665906 n + 135149459137320\right) a{\left(n + 4 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(416497648029 n^{5} + 13818671293650 n^{4} + 182544253841105 n^{3} + 1200513046372380 n^{2} + 3931475445046516 n + 5129619101524320\right) a{\left(n + 5 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(5039503065427 n^{5} + 192055333608735 n^{4} + 2915404837946195 n^{3} + 22045033269448905 n^{2} + 83062712364063858 n + 124790222130654480\right) a{\left(n + 6 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(27734630608297 n^{5} + 10712897294419865 n^{4} + 1655110734112119965 n^{3} + 127847653940062553215 n^{2} + 4937465625241132495338 n + 76269522614820661936440\right) a{\left(n + 79 \right)}}{921600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(260411512308073 n^{5} + 11203951257338120 n^{4} + 191916282263903435 n^{3} + 1637147750164393480 n^{2} + 6958670181083985972 n + 11794842405945181440\right) a{\left(n + 7 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(533834630214937 n^{5} + 203716595641822235 n^{4} + 31094367520759484405 n^{3} + 2372917618860258058525 n^{2} + 90537637809721642168938 n + 1381691717016628284240480\right) a{\left(n + 78 \right)}}{1843200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1426950368679958 n^{5} + 68312710590033185 n^{4} + 1298703538042981580 n^{3} + 12271085895619905475 n^{2} + 57680980061085683682 n + 107986803887059295760\right) a{\left(n + 8 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1919867850404458 n^{5} + 723723864621486155 n^{4} + 109120590253383173060 n^{3} + 8225883537922375998265 n^{2} + 310027489142328653074422 n + 4673576793011219176950360\right) a{\left(n + 77 \right)}}{921600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(1929880929789727 n^{5} + 98917213617363890 n^{4} + 1940932277250306665 n^{3} + 18228644314839762310 n^{2} + 81439430552111191728 n + 136293156342196416000\right) a{\left(n + 9 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(10013823188770811 n^{5} + 3728958447603304000 n^{4} + 555386137659017108845 n^{3} + 41355350439601392324740 n^{2} + 1539560736357347622261324 n + 22923431768302975799488080\right) a{\left(n + 76 \right)}}{921600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(21402538098657377 n^{5} + 8157326097529131385 n^{4} + 1236141880602390976645 n^{3} + 93146460609693703233575 n^{2} + 3491563956142268028060618 n + 52102166070902495892796080\right) a{\left(n + 74 \right)}}{1843200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(51291452468751496 n^{5} + 3023704072667046455 n^{4} + 71923991009589579590 n^{3} + 860386645161907408285 n^{2} + 5163859397602663874574 n + 12416779940189905772280\right) a{\left(n + 10 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(131505639460373701 n^{5} + 48410312027349142535 n^{4} + 7126939595920299105245 n^{3} + 524502848777988876010705 n^{2} + 19296119563821016118443014 n + 283894602636674717290951920\right) a{\left(n + 75 \right)}}{3686400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(411928587088403341 n^{5} + 26396776067887817290 n^{4} + 679053864312276998935 n^{3} + 8753715269012467969530 n^{2} + 56486148761711897285184 n + 145839820252824557078400\right) a{\left(n + 11 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(661822470025170617 n^{5} + 235443316873591179235 n^{4} + 33515073767571236393755 n^{3} + 2386289074371064016959745 n^{2} + 84985584346312829259223368 n + 1211175943693528678802317800\right) a{\left(n + 73 \right)}}{921600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(4106670727051210132 n^{5} + 287067247064714392055 n^{4} + 8039012551092989729210 n^{3} + 112619348907589031383225 n^{2} + 788649786230080721471178 n + 2207318556965346106301880\right) a{\left(n + 12 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(4560259281970758059 n^{5} + 351268050188473923850 n^{4} + 10805143287108142280920 n^{3} + 165797519859651208032275 n^{2} + 1268545856689347594177096 n + 3870909336881011951346760\right) a{\left(n + 13 \right)}}{3686400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(13069590591923402291 n^{5} + 4592041629564069683585 n^{4} + 645509283842313968199995 n^{3} + 45380463737927935897373055 n^{2} + 1595556570911777126012499234 n + 22445514151227341651377922640\right) a{\left(n + 72 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(17156929755212350883 n^{5} + 3646036236918694679800 n^{4} + 193123956945073579937245 n^{3} + 4368975969475348089636260 n^{2} + 45606521154040967348515332 n + 181323139320651808511171760\right) a{\left(n + 15 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(56565608872427351899 n^{5} + 19583272347317740103855 n^{4} + 2712356926970531306473215 n^{3} + 187868654416644199736551705 n^{2} + 6507513732176876209850061926 n + 90183430920317664260430725880\right) a{\left(n + 71 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(101176985250621002251 n^{5} + 8994005653977675548825 n^{4} + 314739364163779359553235 n^{3} + 5433619473854249816875015 n^{2} + 46370686732450848688769754 n + 156749319151071256014172920\right) a{\left(n + 14 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(157608898634114049082 n^{5} + 9741809418060821536955 n^{4} + 202303891061786035740455 n^{3} + 1172752374710793917088085 n^{2} - 9901277899515976752337797 n - 103187448078814076954407110\right) a{\left(n + 16 \right)}}{3686400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(201931836175157858363 n^{5} + 73510784391365972823430 n^{4} + 10638003789191077894385749 n^{3} + 765599897175704819101960934 n^{2} + 27419904864297142696822736844 n + 391182134655584126848400562816\right) a{\left(n + 68 \right)}}{1474560 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(239902970697023298173 n^{5} + 81584628510293883317200 n^{4} + 11098493305982664444622075 n^{3} + 754955910338113268929156280 n^{2} + 25679730476652931796604256752 n + 349438375841654778466869396360\right) a{\left(n + 70 \right)}}{3686400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(1385245407016433682449 n^{5} + 454926188042693540230375 n^{4} + 59701889488049252977712965 n^{3} + 3913517516106077809760554865 n^{2} + 128134969299089766871328394426 n + 1676364409185703912510278695640\right) a{\left(n + 69 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(3081089970830489841804 n^{5} + 1056263823643356258560865 n^{4} + 144664894604297783119226910 n^{3} + 9895077339561117297962486035 n^{2} + 338041460305799594258757294026 n + 4614580098160624397447678219280\right) a{\left(n + 67 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(8398118579677393037149 n^{5} + 726263629990595886141137 n^{4} + 24844268422053350831586713 n^{3} + 419083000595185298014869727 n^{2} + 3472285312780630085306326938 n + 11238521502478291002154808784\right) a{\left(n + 18 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(9020827451762367829433 n^{5} + 702370112637302030565760 n^{4} + 21245420209537941538911655 n^{3} + 308022281304936973599935420 n^{2} + 2088178890890309176798962012 n + 5004865129860436520769163920\right) a{\left(n + 17 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(59773481587242604858338 n^{5} + 21018328565112257441317895 n^{4} + 2925568081308092353161227220 n^{3} + 201865935684285911585231327825 n^{2} + 6914605810215590261416225285922 n + 94164266574467777618458866609600\right) a{\left(n + 64 \right)}}{4915200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(99810003576103420384103 n^{5} + 34865492817151803538668355 n^{4} + 4837682683781497717203223075 n^{3} + 333632188382694409588734019085 n^{2} + 11445925495282116063652629503142 n + 156375548063052229854290506874400\right) a{\left(n + 65 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(100642073386357938009221 n^{5} + 9989683819070410774233799 n^{4} + 395511352109122796105157085 n^{3} + 7804373113569344688933922505 n^{2} + 76715611608423686200516279878 n + 300358645269524763922696533624\right) a{\left(n + 20 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(111832808406699409666559 n^{5} + 38185285186929929734357825 n^{4} + 5203777702312012320418247635 n^{3} + 353862266437676346061125546695 n^{2} + 12009319542297358490591828164926 n + 162752497284793178568993598395720\right) a{\left(n + 66 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(157967724460667035473677 n^{5} + 14750785260839982875306140 n^{4} + 548142386137351220744336875 n^{3} + 10123742020929269455875425600 n^{2} + 92829840078511641130749701028 n + 337610630617117362922185735840\right) a{\left(n + 19 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(272680504738361010864535 n^{5} + 28420447311899962160051060 n^{4} + 1182290691351819458732508377 n^{3} + 24530415356304464554455975688 n^{2} + 253753199087380512053918943396 n + 1046514657067792520102630436096\right) a{\left(n + 21 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(612453387759645579977643 n^{5} + 194260873690682746605376010 n^{4} + 24657603560790833406488893725 n^{3} + 1565495165538945237946463825430 n^{2} + 49712083286475070128157409737672 n + 631607802388587506146716097637520\right) a{\left(n + 63 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(1948357473852206932112297 n^{5} + 270699938965702991438668526 n^{4} + 15057676690472688259804765837 n^{3} + 419144534106540301028490553416 n^{2} + 5838256211318665044428669733844 n + 32552553428076742729997560171596\right) a{\left(n + 27 \right)}}{245760 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(3192937706975322782012803 n^{5} + 346624618976339483407867265 n^{4} + 15018060126612755536267277075 n^{3} + 324492594702186373058579009455 n^{2} + 3495002093498304033912448683042 n + 15004247349664535517956723805000\right) a{\left(n + 22 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(4286011058673723831691603 n^{5} + 546634800166214640406360649 n^{4} + 27920737806853093105270986785 n^{3} + 713869843460378506116561376537 n^{2} + 9135709242743505736658587437582 n + 46811959082191810142601933304440\right) a{\left(n + 25 \right)}}{2949120 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(4994964459724893406359653 n^{5} + 1506354913567479137819202835 n^{4} + 181860906445521955182320351365 n^{3} + 10986929350150929160850062276625 n^{2} + 332150554153826094311614712715642 n + 4019767939830957537242426116040280\right) a{\left(n + 62 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(6986918408276877612384421 n^{5} + 791576484354214981810092290 n^{4} + 35808401710890189028960697735 n^{3} + 808225050966088246473395199370 n^{2} + 9098618613974029188334157586744 n + 40852612445231890752893360114400\right) a{\left(n + 23 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(7146905879566839115655098 n^{5} + 2074136900814403237602218477 n^{4} + 241281296817485264612899663364 n^{3} + 14062288762680835058622599863675 n^{2} + 410580698874740175616255660869258 n + 4803975192124261966955418836811360\right) a{\left(n + 59 \right)}}{2949120 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(16405798641228900181152089 n^{5} + 1967114517747542054247854275 n^{4} + 94353100679651262919949925745 n^{3} + 2262760956963627229075235673725 n^{2} + 27128613247939071658585429541286 n + 130065435470984230669599932430960\right) a{\left(n + 24 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(17780793371926937368869079 n^{5} + 5241503474107107822031580135 n^{4} + 618422139334461943367933969375 n^{3} + 36504766082848264960685164009705 n^{2} + 1078076530802199170279298458100906 n + 12743075709121854338167401715209120\right) a{\left(n + 61 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(26231933621505707220389627 n^{5} + 7619526427839495508256212345 n^{4} + 885989192662363812998817131815 n^{3} + 51551633058888027020839683140295 n^{2} + 1500961189591840710780918876646598 n + 17494343707114902827150509696011000\right) a{\left(n + 60 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(36219573939086503419629457 n^{5} + 4855624320457593899398088385 n^{4} + 260675725493642652516663736805 n^{3} + 7004616443023505095671674115535 n^{2} + 94202676383546101607571877989018 n + 507219985331758815571956255375840\right) a{\left(n + 26 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(42493383019885249797340057 n^{5} + 11703713476977797616814075589 n^{4} + 1286362496623333117423910159873 n^{3} + 70510253875438949423384495791675 n^{2} + 1926976671772524354958106991773358 n + 20998706460888843611509933942756632\right) a{\left(n + 58 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(159317531402468808673401728 n^{5} + 22604785600019632613329617115 n^{4} + 1276392210103597864870196033170 n^{3} + 35820178887365329371618893919815 n^{2} + 499031404520728970459897543377512 n + 2756909986959160693069837861788540\right) a{\left(n + 30 \right)}}{7372800 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(200912782953503283441561506 n^{5} + 28557186075413443219901150665 n^{4} + 1624603934351786736738580038790 n^{3} + 46238466240322530264874231357775 n^{2} + 658375499101564578444914143078464 n + 3751798615750636595338931583689880\right) a{\left(n + 28 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(287465515996601071303710551 n^{5} + 41828443915569378096730421380 n^{4} + 2424160935143525592658082940405 n^{3} + 69897891558371254971668509015900 n^{2} + 1001859712379419035969080778668324 n + 5704403334604480368112688098383360\right) a{\left(n + 31 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(393033166405383948828151747 n^{5} + 108063223513612516809827175600 n^{4} + 11877620731936555733913099373985 n^{3} + 652339951936698990862678826092960 n^{2} + 17901524170150575240786272952014108 n + 196356021397318761438930203161598400\right) a{\left(n + 57 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(546882873910585576659132779 n^{5} + 78273921359675090633531648080 n^{4} + 4478224240293092983657515053125 n^{3} + 128007112858287088558488669202340 n^{2} + 1827943537119062989876737619009356 n + 10431328326685441210208466430681680\right) a{\left(n + 29 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(558543861216036536572922704 n^{5} + 115964899590965868148610420925 n^{4} + 9174448147390738173155292767340 n^{3} + 334685457572822008308285942636885 n^{2} + 5187984329568141231373854793072946 n + 19255859480119592078715263098735920\right) a{\left(n + 51 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(640376099908495338257313203 n^{5} + 174557531018805707115459427909 n^{4} + 19029720879696244330204337050267 n^{3} + 1037091338757675356677543513896035 n^{2} + 28254148096020335259529075123437066 n + 307827429834392136210172456250404416\right) a{\left(n + 56 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(741422518615430154765632681 n^{5} + 200223672498638035608119124245 n^{4} + 21626731951716814839746493731795 n^{3} + 1167885894910398121848502760388085 n^{2} + 31531321088520239266804493734630994 n + 340489974917454285707404929551045520\right) a{\left(n + 54 \right)}}{2457600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1812324412924564851395363041 n^{5} + 290216544209065923436496554805 n^{4} + 18657330952780052386614738429125 n^{3} + 601936249363631814718369058962795 n^{2} + 9746160033393731137829178822489114 n + 63355243568871312410710478072304240\right) a{\left(n + 32 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2343641934276616417521119842 n^{5} + 706197957873560625810779361185 n^{4} + 83324387498862640190070762082190 n^{3} + 4837174424219681968012179358282135 n^{2} + 138647409826007050746756226597524888 n + 1573635195461296285953522847187749560\right) a{\left(n + 52 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(4547957349467104895720358989 n^{5} + 788069706333091490171373353440 n^{4} + 54752136748748374872725395080055 n^{3} + 1905902453919155881979864636130920 n^{2} + 33230504344713587844881641083552996 n + 232104113315434278904029124183024320\right) a{\left(n + 33 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(4729640317218353870568756413 n^{5} + 651969717780367189372793926750 n^{4} + 22484235985265776656073260898255 n^{3} - 578756794023498191757188300111690 n^{2} - 48006381883542216177741741924909248 n - 740161554837875193296178712355694480\right) a{\left(n + 45 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(5182146280192458766664560819 n^{5} + 1355484420567389588859911581193 n^{4} + 139195697396599031524956606135083 n^{3} + 7044860665898613981045310693426375 n^{2} + 176246821031421723033545464166288634 n + 1747389928046451786847810979540898696\right) a{\left(n + 46 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(6146278898948456222533393589 n^{5} + 1663558455011778227511688499260 n^{4} + 180111599116201659929267547049495 n^{3} + 9750501973593673288471228576101020 n^{2} + 263929321930339169211764709511477356 n + 2857637994813525449044863507769300800\right) a{\left(n + 55 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(9289010324890075319370096157 n^{5} + 2536993027326404625203274245660 n^{4} + 276734177907647700132762800324435 n^{3} + 15071842616249488980302367730142920 n^{2} + 409901783297839139922105479299676748 n + 4453869924063951447578037217290601200\right) a{\left(n + 53 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(10543227429830118936460679143 n^{5} + 1915032501581931665116758029345 n^{4} + 139162879873142677134166928848115 n^{3} + 5056593618749425947179561638890535 n^{2} + 91859494510364708436275447735660022 n + 667367597119879762369121591166205080\right) a{\left(n + 34 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(10663326350273471642579813885 n^{5} + 2544277947328406955233970462355 n^{4} + 242655475706516631516135985315813 n^{3} + 11562899903953417383942721326111821 n^{2} + 275283729761919754835770334609873118 n + 2619424069103542266876195757675687968\right) a{\left(n + 48 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(12701318954312184147187778479 n^{5} + 2426236085948736680566245200195 n^{4} + 185232355949007677931003003889935 n^{3} + 7065257647228520600456333683173245 n^{2} + 134642821411032254233627429118365546 n + 1025623763515673513027128545268421400\right) a{\left(n + 36 \right)}}{9830400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(17281011677562190617508659373 n^{5} + 3387656706513636483569565524939 n^{4} + 265519256569115040839215945438445 n^{3} + 10401264513903397838809105613914237 n^{2} + 203650252410747259521764362233156630 n + 1594395323814554272278840387719706840\right) a{\left(n + 38 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(21121358515757715824754235051 n^{5} + 5016687711814993559345970536645 n^{4} + 476189320076447551422080530507805 n^{3} + 22577300720273000773602124629658705 n^{2} + 534615371101343067884734284540031134 n + 5057305652563181260965908091677443320\right) a{\left(n + 49 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(21388408371981072329553463199 n^{5} + 4002774803235638458732774973380 n^{4} + 299426042864122468148800529892145 n^{3} + 11190980156174211179620961106050360 n^{2} + 208975080349373068192421265857531196 n + 1559764168948571402767683815356799520\right) a{\left(n + 35 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(21459420519768051849389809579 n^{5} + 4342431149725831515600797197880 n^{4} + 350104246333949706278595017049629 n^{3} + 14048375140593359669949736276453780 n^{2} + 280319569235306458199606908217162436 n + 2222841562474277682474350939247296160\right) a{\left(n + 43 \right)}}{5898240 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(23987917253209488594419026783 n^{5} + 5615107612001684518244754774515 n^{4} + 523830128674394877836403604838435 n^{3} + 24330154514540000453079226919769565 n^{2} + 562222938600896310722728805538282942 n + 5166327207766346570552634745782482160\right) a{\left(n + 50 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(30192700817004614597397844991 n^{5} + 5853146974236371181401044699015 n^{4} + 453592022469045112047391783566895 n^{3} + 17565524630578132610929047537097265 n^{2} + 339934758634263728954366090274761394 n + 2630121330965195189887467689967753600\right) a{\left(n + 37 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(49188635181702715568401869853 n^{5} + 11891398146362257221932921535770 n^{4} + 1147039052490976154113780982517695 n^{3} + 55194808897342453983822096343012210 n^{2} + 1325157351744111449974483762533140952 n + 12701037547921429770296210898146860320\right) a{\left(n + 47 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(56465531621928307283605508333 n^{5} + 11172813600714037895201121531985 n^{4} + 883890091018363787912066844820735 n^{3} + 34946737883623871817897595553045405 n^{2} + 690545712155467181769920839271936142 n + 5455683444992893241980179369132035280\right) a{\left(n + 39 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(62663866870786498174174542263 n^{5} + 12345250873904958089679284012485 n^{4} + 961194872793076966259597053154095 n^{3} + 36845515641248969086501891030020395 n^{2} + 691912131032808245563183093375374402 n + 5052738531460724079103683637172988120\right) a{\left(n + 44 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(67444231685717721884271145606 n^{5} + 13463113827798639432692957801045 n^{4} + 1074219509813773111401632148142580 n^{3} + 42823423150609689926624502406563595 n^{2} + 852888681878932467358515651756433974 n + 6788837007787739161412008137528025560\right) a{\left(n + 40 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(68322043521359522106440826839 n^{5} + 13838736640639641214752069922480 n^{4} + 1118983673935624358867344163731915 n^{3} + 45137203630502050418231546062251500 n^{2} + 908012218102615165796910273171773286 n + 7284898050762793170955588198198401060\right) a{\left(n + 42 \right)}}{14745600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(145118434030180389368265146353 n^{5} + 29212103511690862119857974605410 n^{4} + 2349354565910547608345922293462075 n^{3} + 94348917536222235891326484833316610 n^{2} + 1891770445484823262439046628064126952 n + 15148371054165013470583000644634972080\right) a{\left(n + 41 \right)}}{29491200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)}, \quad n \geq 84
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24577/
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[22,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[22,x]*F[8,x]
F[8,x] = F[31,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[17,x]*F[22,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[23,x]+F[13,x]
F[13,x] = 1/F[22,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[22,x]
F[17,x] = 1/F[22,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[0,x]+F[20,x]
F[20,x] = 1/F[22,x]*F[21,x]
F[21,x] = F[2,x]
F[22,x] = x
F[23,x] = -F[30,x]+F[24,x]
F[24,x] = 1/F[22,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[27,x]
F[27,x] = -F[29,x]+F[28,x]
F[28,x] = F[0,x]+F[15,x]
F[29,x] = 2+F[29,x]^2+(-2+x)*F[29,x]
F[30,x] = F[11,x]*F[2,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[2,x]*F[28,x]
F[33,x] = F[34,x]
F[34,x] = F[22,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = 1/F[22,x]*F[38,x]
F[38,x] = F[9,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[5,x]
F[41,x] = 1/F[2,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[76,x]+F[44,x]
F[44,x] = 1/F[22,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[48,x]+F[68,x]
F[48,x] = F[49,x]
F[49,x] = F[28,x]*F[50,x]
F[50,x] = F[51,x]+F[66,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = F[0,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[0,x]*F[22,x]*F[55,x]
F[55,x] = 1/F[22,x]/F[28,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[61,x]+F[58,x]
F[58,x] = 1/F[22,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[2,x]+F[19,x]
F[61,x] = -F[62,x]+F[17,x]
F[62,x] = -F[63,x]+F[13,x]
F[63,x] = F[64,x]+F[9,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[55,x]*F[9,x]
F[66,x] = F[67,x]
F[67,x] = F[22,x]*F[9,x]
F[68,x] = 1/F[22,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[75,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[22,x]*F[73,x]
F[73,x] = 1/F[22,x]*F[74,x]
F[74,x] = F[9,x]
F[75,x] = F[19,x]+F[66,x]
F[76,x] = -F[77,x]+F[37,x]
F[77,x] = F[17,x]+F[9,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_{22}\! \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_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{31}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{22}\! \left(x \right) F_{28}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{17}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{13}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right)+F_{66}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{37}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \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_22(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_22(x)*F_8(x))
Eq(F_8(x), F_31(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_17(x)*F_22(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_23(x))
Eq(F_13(x), F_14(x)/F_22(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_22(x))
Eq(F_17(x), F_18(x)/F_22(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_0(x) + F_20(x))
Eq(F_20(x), F_21(x)/F_22(x))
Eq(F_21(x), F_2(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x) - F_30(x))
Eq(F_24(x), F_25(x)/F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_27(x))
Eq(F_27(x), F_28(x) - F_29(x))
Eq(F_28(x), F_0(x) + F_15(x))
Eq(F_29(x), (x - 2)*F_29(x) + F_29(x)**2 + 2)
Eq(F_30(x), F_11(x)*F_2(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_2(x)*F_28(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_22(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_38(x)/F_22(x))
Eq(F_38(x), F_9(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_5(x))
Eq(F_41(x), F_42(x)/F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) - F_76(x))
Eq(F_44(x), F_45(x)/F_22(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_68(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_28(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_66(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_0(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_0(x)*F_22(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_22(x)*F_28(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_61(x))
Eq(F_58(x), F_59(x)/F_22(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x) - F_2(x))
Eq(F_61(x), F_17(x) - F_62(x))
Eq(F_62(x), F_13(x) - F_63(x))
Eq(F_63(x), F_64(x) + F_9(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_55(x)*F_9(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_22(x)*F_9(x))
Eq(F_68(x), F_69(x)/F_22(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_75(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_22(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_22(x))
Eq(F_74(x), F_9(x))
Eq(F_75(x), F_19(x) + F_66(x))
Eq(F_76(x), F_37(x) - F_77(x))
Eq(F_77(x), F_17(x) + F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": 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}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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]]}, 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{"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], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}], [{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25546/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[17,x]*F[7,x]
F[7,x] = F[18,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[17,x]
F[12,x] = 1/F[17,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = -F[0,x]+F[15,x]
F[15,x] = 1/F[17,x]*F[16,x]
F[16,x] = F[2,x]
F[17,x] = x
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[20,x]
F[20,x] = F[21,x]+F[29,x]
F[21,x] = F[0,x]*F[22,x]
F[22,x] = 1/F[17,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[17,x]*F[26,x]
F[26,x] = 1/F[17,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = (1+F[28,x])*x+F[28,x]^2
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[5,x]
F[31,x] = 1/F[17,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[65,x]
F[34,x] = -F[0,x]+F[35,x]
F[35,x] = -F[64,x]+F[36,x]
F[36,x] = F[15,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[17,x]*F[39,x]
F[39,x] = 1/F[17,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = -F[58,x]+F[42,x]
F[42,x] = 1/F[17,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[2,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[17,x]*F[47,x]
F[47,x] = F[48,x]+F[56,x]
F[48,x] = F[49,x]
F[49,x] = F[17,x]*F[50,x]*F[9,x]
F[50,x] = 1/F[17,x]/F[55,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[55,x]+F[53,x]
F[53,x] = 1/F[17,x]*F[54,x]
F[54,x] = F[10,x]
F[55,x] = F[24,x]+F[9,x]
F[56,x] = -F[57,x]+F[12,x]
F[57,x] = F[48,x]+F[9,x]
F[58,x] = F[15,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[17,x]*F[61,x]
F[61,x] = 1/F[17,x]/F[63,x]*F[62,x]
F[62,x] = F[56,x]
F[63,x] = 2+F[63,x]^2+(-2+x)*F[63,x]
F[64,x] = F[59,x]
F[65,x] = F[66,x]
F[66,x] = F[17,x]*F[24,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_{17}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{17}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{18}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{29}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{28}\! \left(x \right) x +F_{28} \left(x \right)^{2}+x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{5}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{65}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{64}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{56}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{17}\! \left(x \right) F_{50}\! \left(x \right) F_{9}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{17}\! \left(x \right) F_{55}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{10}\! \left(x \right)
F_{55}\! \left(x \right) = F_{24}\! \left(x \right)+F_{9}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{12}\! \left(x \right)
F_{57}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{17}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{17}\! \left(x \right) F_{63}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{56}\! \left(x \right)
F_{63}\! \left(x \right) = F_{63}\! \left(x \right) x +F_{63} \left(x \right)^{2}-2 F_{63}\! \left(x \right)+2
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{17}\! \left(x \right) F_{24}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_17(x)*F_7(x))
Eq(F_7(x), F_18(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_17(x))
Eq(F_12(x), F_13(x)/F_17(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), -F_0(x) + F_15(x))
Eq(F_15(x), F_16(x)/F_17(x))
Eq(F_16(x), F_2(x))
Eq(F_17(x), x)
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_29(x))
Eq(F_21(x), F_0(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_17(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_17(x)*F_26(x))
Eq(F_26(x), F_27(x)/F_17(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), (x - 3)*(F_28(x) + 1) + (F_28(x) + 1)**2 + F_28(x) + 2)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_5(x))
Eq(F_31(x), F_32(x)/F_17(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_65(x))
Eq(F_34(x), -F_0(x) + F_35(x))
Eq(F_35(x), F_36(x) - F_64(x))
Eq(F_36(x), F_15(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_17(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_17(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x) - F_58(x))
Eq(F_42(x), F_43(x)/F_17(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_2(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_17(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_56(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_17(x)*F_50(x)*F_9(x))
Eq(F_50(x), F_51(x)/(F_17(x)*F_55(x)))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) - F_55(x))
Eq(F_53(x), F_54(x)/F_17(x))
Eq(F_54(x), F_10(x))
Eq(F_55(x), F_24(x) + F_9(x))
Eq(F_56(x), F_12(x) - F_57(x))
Eq(F_57(x), F_48(x) + F_9(x))
Eq(F_58(x), F_15(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_17(x)*F_61(x))
Eq(F_61(x), F_62(x)/(F_17(x)*F_63(x)))
Eq(F_62(x), F_56(x))
Eq(F_63(x), (x - 2)*F_63(x) + F_63(x)**2 + 2)
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_17(x)*F_24(x))
Pack JSON:
{"name": "point_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_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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 1], [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, 1], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [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, 1], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 0], [1, 0], [1, 1], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [2, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [2, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 3], [2, 2], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 3], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 2], [2, 3], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 3], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 3], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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, 0, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 3], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "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": false}}, "idx": 0}}]}, {"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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25576/
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[24,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[24,x]*F[8,x]
F[8,x] = F[31,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[17,x]*F[24,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[25,x]+F[13,x]
F[13,x] = 1/F[24,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[24,x]
F[17,x] = 1/F[24,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = -F[2,x]+F[21,x]
F[21,x] = -F[0,x]+F[22,x]
F[22,x] = 1/F[24,x]*F[23,x]
F[23,x] = F[2,x]
F[24,x] = x
F[25,x] = -F[30,x]+F[26,x]
F[26,x] = 1/F[24,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[29,x]+F[15,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = F[11,x]*F[2,x]
F[31,x] = F[32,x]+F[34,x]
F[32,x] = F[2,x]*F[33,x]
F[33,x] = F[0,x]+F[15,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[2,x]*F[38,x]
F[38,x] = 1/F[24,x]*F[39,x]
F[39,x] = F[9,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]*F[5,x]
F[42,x] = 1/F[2,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[76,x]+F[45,x]
F[45,x] = 1/F[24,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[24,x]*F[48,x]
F[48,x] = F[49,x]+F[68,x]
F[49,x] = F[50,x]
F[50,x] = F[33,x]*F[51,x]
F[51,x] = F[52,x]+F[66,x]
F[52,x] = -F[0,x]+F[53,x]
F[53,x] = F[0,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[24,x]*F[56,x]
F[56,x] = 1/F[24,x]/F[33,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[24,x]*F[60,x]
F[60,x] = F[20,x]
F[61,x] = -F[62,x]+F[17,x]
F[62,x] = -F[63,x]+F[13,x]
F[63,x] = F[64,x]+F[9,x]
F[64,x] = F[65,x]
F[65,x] = F[24,x]*F[56,x]*F[9,x]
F[66,x] = F[67,x]
F[67,x] = F[24,x]*F[9,x]
F[68,x] = 1/F[24,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[75,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[24,x]*F[73,x]
F[73,x] = 1/F[24,x]*F[74,x]
F[74,x] = F[9,x]
F[75,x] = F[19,x]+F[66,x]
F[76,x] = -F[77,x]+F[38,x]
F[77,x] = F[17,x]+F[9,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_{24}\! \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_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{31}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{24}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = x
F_{25}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{24}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{68}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{33}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{24}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{24}\! \left(x \right) F_{33}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{20}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{17}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{13}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{24}\! \left(x \right) F_{56}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{24}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{24}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right)+F_{66}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{38}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \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_24(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_24(x)*F_8(x))
Eq(F_8(x), F_31(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_17(x)*F_24(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_25(x))
Eq(F_13(x), F_14(x)/F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_24(x))
Eq(F_17(x), F_18(x)/F_24(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), -F_2(x) + F_21(x))
Eq(F_21(x), -F_0(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_24(x))
Eq(F_23(x), F_2(x))
Eq(F_24(x), x)
Eq(F_25(x), F_26(x) - F_30(x))
Eq(F_26(x), F_27(x)/F_24(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_15(x) - F_29(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), F_11(x)*F_2(x))
Eq(F_31(x), F_32(x) + F_34(x))
Eq(F_32(x), F_2(x)*F_33(x))
Eq(F_33(x), F_0(x) + F_15(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_2(x)*F_38(x))
Eq(F_38(x), F_39(x)/F_24(x))
Eq(F_39(x), F_9(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x)*F_5(x))
Eq(F_42(x), F_43(x)/F_2(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x) - F_76(x))
Eq(F_45(x), F_46(x)/F_24(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_24(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_68(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_33(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_66(x))
Eq(F_52(x), -F_0(x) + F_53(x))
Eq(F_53(x), F_0(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_24(x)*F_56(x))
Eq(F_56(x), F_57(x)/(F_24(x)*F_33(x)))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x) - F_61(x))
Eq(F_59(x), F_60(x)/F_24(x))
Eq(F_60(x), F_20(x))
Eq(F_61(x), F_17(x) - F_62(x))
Eq(F_62(x), F_13(x) - F_63(x))
Eq(F_63(x), F_64(x) + F_9(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_24(x)*F_56(x)*F_9(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_24(x)*F_9(x))
Eq(F_68(x), F_69(x)/F_24(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_75(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_24(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_24(x))
Eq(F_74(x), F_9(x))
Eq(F_75(x), F_19(x) + F_66(x))
Eq(F_76(x), F_38(x) - F_77(x))
Eq(F_77(x), F_17(x) + F_9(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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 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0, 2, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}], [{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25627/
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[22,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[22,x]*F[8,x]
F[8,x] = F[31,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[17,x]*F[22,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[23,x]+F[13,x]
F[13,x] = 1/F[22,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[22,x]
F[17,x] = 1/F[22,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[0,x]+F[20,x]
F[20,x] = 1/F[22,x]*F[21,x]
F[21,x] = F[2,x]
F[22,x] = x
F[23,x] = -F[30,x]+F[24,x]
F[24,x] = 1/F[22,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[27,x]
F[27,x] = -F[29,x]+F[28,x]
F[28,x] = F[0,x]+F[15,x]
F[29,x] = 2+F[29,x]^2+(-2+x)*F[29,x]
F[30,x] = F[11,x]*F[2,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[2,x]*F[28,x]
F[33,x] = F[34,x]
F[34,x] = F[22,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = 1/F[22,x]*F[38,x]
F[38,x] = F[9,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[5,x]
F[41,x] = 1/F[2,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[76,x]+F[44,x]
F[44,x] = 1/F[22,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[48,x]+F[68,x]
F[48,x] = F[49,x]
F[49,x] = F[28,x]*F[50,x]
F[50,x] = F[51,x]+F[66,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = F[0,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[0,x]*F[22,x]*F[55,x]
F[55,x] = 1/F[22,x]/F[28,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[61,x]+F[58,x]
F[58,x] = 1/F[22,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[2,x]+F[19,x]
F[61,x] = -F[62,x]+F[17,x]
F[62,x] = -F[63,x]+F[13,x]
F[63,x] = F[64,x]+F[9,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[55,x]*F[9,x]
F[66,x] = F[67,x]
F[67,x] = F[22,x]*F[9,x]
F[68,x] = 1/F[22,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[75,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[22,x]*F[73,x]
F[73,x] = 1/F[22,x]*F[74,x]
F[74,x] = F[9,x]
F[75,x] = F[19,x]+F[66,x]
F[76,x] = -F[77,x]+F[37,x]
F[77,x] = F[17,x]+F[9,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_{22}\! \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_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{31}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{22}\! \left(x \right) F_{28}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{17}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{13}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right)+F_{66}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{37}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \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_22(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_22(x)*F_8(x))
Eq(F_8(x), F_31(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_17(x)*F_22(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_23(x))
Eq(F_13(x), F_14(x)/F_22(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_22(x))
Eq(F_17(x), F_18(x)/F_22(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_0(x) + F_20(x))
Eq(F_20(x), F_21(x)/F_22(x))
Eq(F_21(x), F_2(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x) - F_30(x))
Eq(F_24(x), F_25(x)/F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_27(x))
Eq(F_27(x), F_28(x) - F_29(x))
Eq(F_28(x), F_0(x) + F_15(x))
Eq(F_29(x), (x - 2)*F_29(x) + F_29(x)**2 + 2)
Eq(F_30(x), F_11(x)*F_2(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_2(x)*F_28(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_22(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_38(x)/F_22(x))
Eq(F_38(x), F_9(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_5(x))
Eq(F_41(x), F_42(x)/F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) - F_76(x))
Eq(F_44(x), F_45(x)/F_22(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_68(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_28(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_66(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_0(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_0(x)*F_22(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_22(x)*F_28(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_61(x))
Eq(F_58(x), F_59(x)/F_22(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x) - F_2(x))
Eq(F_61(x), F_17(x) - F_62(x))
Eq(F_62(x), F_13(x) - F_63(x))
Eq(F_63(x), F_64(x) + F_9(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_55(x)*F_9(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_22(x)*F_9(x))
Eq(F_68(x), F_69(x)/F_22(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_75(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_22(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_22(x))
Eq(F_74(x), F_9(x))
Eq(F_75(x), F_19(x) + F_66(x))
Eq(F_76(x), F_37(x) - F_77(x))
Eq(F_77(x), F_17(x) + F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": 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}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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]]}, 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{"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], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}], [{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25799/
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[22,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[22,x]*F[8,x]
F[8,x] = F[31,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[17,x]*F[22,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[23,x]+F[13,x]
F[13,x] = 1/F[22,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[22,x]
F[17,x] = 1/F[22,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[0,x]+F[20,x]
F[20,x] = 1/F[22,x]*F[21,x]
F[21,x] = F[2,x]
F[22,x] = x
F[23,x] = -F[30,x]+F[24,x]
F[24,x] = 1/F[22,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[27,x]
F[27,x] = -F[29,x]+F[28,x]
F[28,x] = F[0,x]+F[15,x]
F[29,x] = 2+F[29,x]^2+(-2+x)*F[29,x]
F[30,x] = F[11,x]*F[2,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[2,x]*F[28,x]
F[33,x] = F[34,x]
F[34,x] = F[22,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = 1/F[22,x]*F[38,x]
F[38,x] = F[9,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[5,x]
F[41,x] = 1/F[2,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[76,x]+F[44,x]
F[44,x] = 1/F[22,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[48,x]+F[68,x]
F[48,x] = F[49,x]
F[49,x] = F[28,x]*F[50,x]
F[50,x] = F[51,x]+F[66,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = F[0,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[0,x]*F[22,x]*F[55,x]
F[55,x] = 1/F[22,x]/F[28,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[61,x]+F[58,x]
F[58,x] = 1/F[22,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[2,x]+F[19,x]
F[61,x] = -F[62,x]+F[17,x]
F[62,x] = -F[63,x]+F[13,x]
F[63,x] = F[64,x]+F[9,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[55,x]*F[9,x]
F[66,x] = F[67,x]
F[67,x] = F[22,x]*F[9,x]
F[68,x] = 1/F[22,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[75,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[22,x]*F[73,x]
F[73,x] = 1/F[22,x]*F[74,x]
F[74,x] = F[9,x]
F[75,x] = F[19,x]+F[66,x]
F[76,x] = -F[77,x]+F[37,x]
F[77,x] = F[17,x]+F[9,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_{22}\! \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_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{31}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{22}\! \left(x \right) F_{28}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{17}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{13}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right)+F_{66}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{37}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \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_22(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_22(x)*F_8(x))
Eq(F_8(x), F_31(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_17(x)*F_22(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_23(x))
Eq(F_13(x), F_14(x)/F_22(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_22(x))
Eq(F_17(x), F_18(x)/F_22(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_0(x) + F_20(x))
Eq(F_20(x), F_21(x)/F_22(x))
Eq(F_21(x), F_2(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x) - F_30(x))
Eq(F_24(x), F_25(x)/F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_27(x))
Eq(F_27(x), F_28(x) - F_29(x))
Eq(F_28(x), F_0(x) + F_15(x))
Eq(F_29(x), (x - 2)*F_29(x) + F_29(x)**2 + 2)
Eq(F_30(x), F_11(x)*F_2(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_2(x)*F_28(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_22(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_38(x)/F_22(x))
Eq(F_38(x), F_9(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_5(x))
Eq(F_41(x), F_42(x)/F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) - F_76(x))
Eq(F_44(x), F_45(x)/F_22(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_68(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_28(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_66(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_0(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_0(x)*F_22(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_22(x)*F_28(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_61(x))
Eq(F_58(x), F_59(x)/F_22(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x) - F_2(x))
Eq(F_61(x), F_17(x) - F_62(x))
Eq(F_62(x), F_13(x) - F_63(x))
Eq(F_63(x), F_64(x) + F_9(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_55(x)*F_9(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_22(x)*F_9(x))
Eq(F_68(x), F_69(x)/F_22(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_75(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_22(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_22(x))
Eq(F_74(x), F_9(x))
Eq(F_75(x), F_19(x) + F_66(x))
Eq(F_76(x), F_37(x) - F_77(x))
Eq(F_77(x), F_17(x) + F_9(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, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], 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