01243_02143_02413_10243_12043_20143_20413_21043
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3028, 16692, 94296, 542900, 3173868, 18791204, 112448824, 679075704, 4133407792, 25333151648, 156207460864, 968381106644, 6032128924364, 37736408939396, 236991619184744, 1493585406457976, 9443108065939544, 59878143978488360, 380702284574747248, 2426465440977233992, 15500739770480348856, 99231060790774595112, 636494522603083487552, 4090111487652434340224, 26327915048953925562088, 169742697623706424836744, 1096013579230025743122192, 7086825885626899662692052, 45884163070714741841375372, 297451642655025093757440452, 1930556111819659612877230760, 12543923684457078348066993816, 81591304889987150530011285784, 531239534408042119084590801128, 3462192514348142315483085091152, 22584278603173936241058957445720, 147447263147427778119465144292648, 963441371347043693059804951979448, 6300220235027813406491448103408592, 41229958118990064038878995266880848, 270011723861287058457778617477849920, 1769504446698260790036692552162562912, 11603996073868856035957616889304452416, 76144527119122601715510379478133937544, 499958603680275128470524025114240805048, 3284606139355099347407471886893926047080, 21591196957500587152176278053176313303696, 142005483890029711610434723869732874054960, 934458057586587928401651229871790754947376, 6152230587240847185266336369515168315823504, 40524318744603843138908725754569637400581888, 267055672713366385122557811470559273029638480, 1760693978993627311027468068761206402305883824, 11613291067967984137913639377331381672518417488, 76631937787755523645622036355852524597944382864, 505872862158324497709742152318351680357112499344, 3340752762724747744182364978458701050308491870168, 22070554419479784460959589274192508558360425641432, 145862256756382538578787426372127097965668025994288, 964336173507564019704307145257429490966180539040980, 6377715169889235358139847762981151511295431476076044, 42193777900507668858039881584118081090889562957573188, 279237688101997647201976229128952249890662155646830632, 1848578369407550370658157675495375820625943182647089112, 12241537635937913015608425408667647289210721194537516184, 81089491139992341310243079054732804423110450101270269416, 537303981445914144791604917833630156300679287239824708816, 3561221233456902097535655448138765769360146150428564745016, 23610105783079240847695819337569832511631363381998479875912, 156571891913781639251892505081646422268801225275431878911512, 1038588438449678740185718857152398670486679109610202384720464, 6891028334948177015886691790613124345365779588999068423538768, 45733308208738376761406190441833537708882695342453904677393888, 303589328303906970750402881083187833841687421014693989127259776, 2015779656316582557892895028285509129481112231259583012721798016, 13387508438642262122100107867692671720496067270195614300486709464, 88931202030926005649418510324919810009280469549795806233094703080, 590886302421118711960242545602993679438231012608786504172123606392, 3926872238389312840900067515855733305279415074504143819140213614128, 26102404975772217712064965165952544032588211080958701073787698616080, 173541388395925570221190104483266610228482051763572878255131300842832, 1154017425773986426634655068860075723904328484553428609293828387650224, 7675496049568662759275720935046167062994451894266437836330095293596576, 51060307142168677782578118891614860191133490471747548204961146624065520, 339735898307006833608701136154045267580528814661988747186979009324856848, 2260886304891671087186180300383883804318582320884151008155871407372366640, 15048511848248410757164764314916654603520666027985908921517851530383460032, 100180747626510638640086862070624102660947899666864027183197234302363648576, 667035968389577687371710834892999775307312247084219765675251300174401808464, 4442085842222428657402757417675470246146118635345426101899504357917966281232, 29586652997561909244554050663076983062012194685112681668773969671138237913632, 197094479919792233611388910591347272550812514481260615303547171841556107039112, 1313171336829443115206424105088179826597114478460084295801231293249433309377592, 8750548194735404447606642818967072515887396171059757765183986567188742195308520
Implicit equation for the generating function in Maple syntax:
4*x^2*F(x)^6+(32*x^3-68*x^2+16*x-2)*F(x)^5+(16*x^5-20*x^4-132*x^3+276*x^2-84*x+11)*F(x)^4+(-16*x^5+28*x^4+216*x^3-496*x^2+174*x-24)*F(x)^3+(4*x^5-8*x^4-168*x^3+452*x^2-178*x+26)*F(x)^2+(-2*x^4+58*x^3-204*x^2+90*x-14)*F(x)+x^4-6*x^3+36*x^2-18*x+3 = 0
Implicit equation for the generating function in latex syntax:
4 x^{2} F \! \left(x \right)^{6}+\left(32 x^{3}-68 x^{2}+16 x -2\right) F \! \left(x \right)^{5}+\left(16 x^{5}-20 x^{4}-132 x^{3}+276 x^{2}-84 x +11\right) F \! \left(x \right)^{4}+\left(-16 x^{5}+28 x^{4}+216 x^{3}-496 x^{2}+174 x -24\right) F \! \left(x \right)^{3}+\left(4 x^{5}-8 x^{4}-168 x^{3}+452 x^{2}-178 x +26\right) F \! \left(x \right)^{2}+\left(-2 x^{4}+58 x^{3}-204 x^{2}+90 x -14\right) F \! \left(x \right)+x^{4}-6 x^{3}+36 x^{2}-18 x +3 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3028
a(8) = 16692
a(9) = 94296
a(10) = 542900
a(11) = 3173868
a(12) = 18791204
a(13) = 112448824
a(14) = 679075704
a(15) = 4133407792
a(16) = 25333151648
a(17) = 156207460864
a(18) = 968381106644
a(19) = 6032128924364
a(20) = 37736408939396
a(21) = 236991619184744
a(22) = 1493585406457976
a(23) = 9443108065939544
a(24) = 59878143978488360
a(25) = 380702284574747248
a(26) = 2426465440977233992
a(27) = 15500739770480348856
a(28) = 99231060790774595112
a(29) = 636494522603083487552
a(30) = 4090111487652434340224
a(31) = 26327915048953925562088
a(32) = 169742697623706424836744
a(33) = 1096013579230025743122192
a(34) = 7086825885626899662692052
a(35) = 45884163070714741841375372
a(36) = 297451642655025093757440452
a(37) = 1930556111819659612877230760
a(38) = 12543923684457078348066993816
a(39) = 81591304889987150530011285784
a(40) = 531239534408042119084590801128
a(41) = 3462192514348142315483085091152
a(42) = 22584278603173936241058957445720
a(43) = 147447263147427778119465144292648
a(44) = 963441371347043693059804951979448
a(45) = 6300220235027813406491448103408592
a(46) = 41229958118990064038878995266880848
a(47) = 270011723861287058457778617477849920
a(48) = 1769504446698260790036692552162562912
a(49) = 11603996073868856035957616889304452416
a(50) = 76144527119122601715510379478133937544
a(51) = 499958603680275128470524025114240805048
a(52) = 3284606139355099347407471886893926047080
a(53) = 21591196957500587152176278053176313303696
a(54) = 142005483890029711610434723869732874054960
a(55) = 934458057586587928401651229871790754947376
a(n+56) = 1/2880*(220956972707033389*n^5+42272181623363922040*n^4+3201278496394875164615*n^3+119678133175696870035920*n^2+2201471398250071002718236*n+15864831462558179994201360)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+43)-1/960*(27744066123945909*n^5+5798668621234730245*n^4+484188223284826964005*n^3+20189515660615296896215*n^2+420387382996974191592466*n+3496712844109981440228360)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+44)+1/360*(1716234289607411*n^5+370461787322282630*n^4+31962952148067783790*n^3+1377840266177970423970*n^2+29675707254259528863999*n+255472961415664233198780)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+45)-1/480*(229898341683497*n^5+50703115699812980*n^4+4469233742633225275*n^3+196806738094353207100*n^2+4329660069835079787348*n+38068221698951901107520)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+46)+1/720*(16666019372443*n^5+3680915428743895*n^4+324422224746611945*n^3+14260440906686381075*n^2+312563387504034129942*n+2732229553019701929840)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+47)+1/720*(872450834629*n^5+217830107198215*n^4+21684402459226085*n^3+1076116710279935945*n^2+26629171838820885126*n+262919867636059479360)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+48)-1/1440*(444103286557*n^5+108109626396670*n^4+10522636080790415*n^3+511887849825790190*n^2+12445595720283321408*n+120986776796198662080)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+49)+1/360*(6443676229*n^5+1584111169180*n^4+155694198750125*n^3+7647188601991250*n^2+187703129096079996*n+1841913783624180240)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+50)+1/360*(506869702*n^5+128546325175*n^4+13040393239640*n^3+661454406722645*n^2+16775973213147678*n+170194045247832600)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+51)-1/360*(134028682*n^5+34396883335*n^4+3530419345160*n^3+181147000849085*n^2+4646601602355498*n+47668439137264920)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+52)-1/18*(37447*n^4+7948088*n^3+632315491*n^2+22347017250*n+296030746800)/(n+55)/(n+58)/(n+52)/(n+56)*a(n+54)+1/18*(n+54)*(1225*n^2+133073*n+3605328)/(n+53)/(n+58)/(n+56)*a(n+55)+1/72*(2629717*n^4+549295836*n^3+43009601099*n^2+1496152725120*n+19509908418900)/(n+55)/(n+53)/(n+58)/(n+56)*a(n+53)+1/11520*(684119246962763644619*n^5+138265662310827513711410*n^4+11167662375070544754750805*n^3+450608598316998301720399750*n^2+9083210699340324483766456536*n+73178770510147475531198167200)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+40)-1/11520*(92557465324283718253*n^5+19353644133904230541330*n^4+1616081231371536035865935*n^3+67369223227943644843003610*n^2+1402147391229329124400166592*n+11656894918489971712617297600)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+41)+1/5760*(2876564353847223497*n^5+652358054648258492780*n^4+58659089330489514678115*n^3+2617686496816364014229740*n^2+58034982964073288466685548*n+511806506477014369310593680)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+42)+1/1920*(4313399157556194897476*n^5+856454101214968300606890*n^4+67380060320678911567584405*n^3+2629573904573331809257724035*n^2+50966432864408559807662758214*n+392848633332918419467773013440)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+36)-1/23040*(62059711014977137544669*n^5+11742785546180915594427770*n^4+887895859070762231214883375*n^3+33535989249383379770976320050*n^2+632755598670290906636407362936*n+4771371867632995136405136791040)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+37)+1/1920*(2114633170884457333584*n^5+406689699740256959852780*n^4+31265233230861976528247545*n^3+1201017982372006010240253755*n^2+23053424967437408808896647866*n+176896031605850843253042641520)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+38)-1/2304*(693362120327765903863*n^5+136444620475462942854952*n^4+10732750223914667212929521*n^3+421835384726944276960776596*n^2+8284404921981907547201580804*n+65037640339873762769796729984)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+39)+1/2880*(1025859221166732942130183*n^5+168382238429254427420197510*n^4+11052836917372764334404056285*n^3+362688221561869798914661858100*n^2+5949472432545124135710854412612*n+39030287826738030303224331833760)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+33)-1/5760*(585568881876520259640997*n^5+98155211197154104044078235*n^4+6578554121250693289891703870*n^3+220363832171150054615598998120*n^2+3689298958154950847306214619788*n+24696292951364197176758805135840)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+34)+1/5760*(93054059748275184757733*n^5+15603588629730031872937865*n^4+1044459373131591979395007060*n^3+34880296428373788558749833900*n^2+581050762836797590181075100672*n+3861847476035461869552991062720)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+35)+2013265920*n*(n-1)*(2*n+3)*(2*n+1)*(2*n-3)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n)-1/2880*(11410141747397456926932439*n^5+1698169450629980046516175750*n^4+101132763855553011023194315955*n^3+3012596588015342511059616338600*n^2+44888434386811841333499269286576*n+267649991688270417800930195052240)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+30)+1/720*(1440636473196466680101426*n^5+222964669347550327889425835*n^4+13804784804808715144721778640*n^3+427413668681344441347267996925*n^2+6617514818647967203936301436369*n+40988417891244282474921579785760)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+31)-1/1920*(1781339502713891698880321*n^5+284691149919752350813373440*n^4+18198031397068496171506499545*n^3+581582384796114780089704253650*n^2+9292603382285472437424822720464*n+59387568799038752672095931905200)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+32)+1/720*(20888648906742153293876261*n^5+2752614384077663580444980375*n^4+145089670940710094238298964425*n^3+3823874396752578258531031612855*n^2+50391382540631383466508914051724*n+265640117285438648956510837653600)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+27)-1/720*(11409385657778167984079114*n^5+1559363769991214201924847125*n^4+85262042685989833353356523325*n^3+2331377684326115371127248334230*n^2+31881083266477501552619727748626*n+174430092274010765898041794739040)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+28)+1/288*(2275725347053487206470578*n^5+324200318517546633861429935*n^4+18481273301497905812137676458*n^3+526988000598141867790050802465*n^2+7516822353607995733983335694600*n+42907748519651062100173771105224)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+29)-1/90*(3703522219585910581029506*n^5+442834473059898301967097230*n^4+21185688001360495828688652880*n^3+506897567140961685124050884965*n^2+6065491632069042034968090115359*n+29037668627160399559640983937460)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+24)+1/180*(9097205967744551217048067*n^5+1122422345341092993228731215*n^4+55397740369173818236158497330*n^3+1367181061362839061858148050215*n^2+16871698529142712894138920556833*n+83287683486898965261026741382300)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+25)-1/360*(15770855530596627764168098*n^5+2009746047769719080453446675*n^4+102442474423747861933718212340*n^3+2610880765640828669948872048655*n^2+33271085653242490035754994814552*n+169595554404051688596900395395320)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+26)+2/15*(27978039856862695081734*n^5+2429863358757344560529270*n^4+83858149290807866857693735*n^3+1441228765648819564284068385*n^2+12392960231408872483541140246*n+42986272735292463261569820480)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+21)-1/6*(29193813717116295330465*n^5+3195593337199636201839332*n^4+141643900957545775999758863*n^3+3174859117091192016241305524*n^2+35939235933213303919405624424*n+164125029102820069468386822504)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+22)+1/30*(617583815509511667449699*n^5+71680945458885932515162420*n^4+3331940880935136103121680215*n^3+77522738161837736904284820040*n^2+902697570060791339259164660286*n+4207961655009263586868549374480)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+23)+8/45*(53048284831600981113304*n^5+4121109435346208406419650*n^4+127916221239864533648639345*n^3+1983081438638077597082865590*n^2+15356297213723925330239419251*n+47521050701271890166770661900)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+17)-16/15*(13329527253422208783039*n^5+1101755336224706941503985*n^4+36411078302183222651974360*n^3+601502384671845025747635535*n^2+4967879197317800891547712786*n+16413752167975604467326992340)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+18)+2/9*(71053900839736908943601*n^5+6172045704497552468879789*n^4+214393182444893494679584189*n^3+3723502527737613260924230171*n^2+32342531603906191414235221074*n+112436752745095427599269666696)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+19)-2/15*(83126025286330979595819*n^5+7419786639311891029531660*n^4+264537662058945333968349650*n^3+4711216339780844043779503605*n^2+41935846232719720832358832346*n+149371352181753212095533549480)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+20)-32/45*(1102252245843331527889*n^5+66670705367577925722490*n^4+1598591380165481985943820*n^3+18958913595005842318340045*n^2+110941362183910740409625316*n+255365104127707911433190220)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+14)+16/15*(2038827704410320458349*n^5+135608512380989247443075*n^4+3590720068583269130640045*n^3+47283823230723066929013585*n^2+309424123922332533009778286*n+804243395972787958770855900)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+15)-8/9*(5597898192700406302139*n^5+404499976441174797165362*n^4+11662768466329491285045919*n^3+167696461818676241368359784*n^2+1202303506630782548172249552*n+3437801614344403925849852568)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+16)-64/45*(27439494102212118253*n^5+1202761949080050018520*n^4+19271292886792837806185*n^3+128021390037831296925230*n^2+215977302423609593206332*n-655205597467259592651840)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+12)+32/45*(306941197595026187201*n^5+16498959723742913035115*n^4+347676299913910644239425*n^3+3565718897626250950813225*n^2+17598827109665165379995034*n+32761675610323852945824360)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+13)-512/15*(26026991134785952*n^5+1306081911518973320*n^4+25782711940706413780*n^3+251167634878020213715*n^2+1209901303917990607033*n+2308066689190599412890)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+9)+256/9*(91733060821287100*n^5+5246856316104110182*n^4+117371459344748906435*n^3+1289514362805502785107*n^2+6979168748595371581746*n+14916795789662262401472)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+10)+128/45*(53652275152200332*n^5-39174311374998170425*n^4-1704726147259299882485*n^3-27117172956015481509005*n^2-190264893417518875623297*n-498535090618002226356060)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+11)-8192/15*(19315178316272*n^5+1381851368454300*n^4+27358571523526660*n^3+237906809756147965*n^2+968051993419097383*n+1511823098961165660)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+7)+2048/3*(217720806252872*n^5+11049485796124224*n^4+209500289800481808*n^3+1907223551103605683*n^2+8446808908459182059*n+14658182586315081252)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+8)+1048576/9*(1243243676*n^5+21782894054*n^4+138205736821*n^3+397201203667*n^2+505399489707*n+210413193318)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+4)-262144/45*(2787787504*n^5+140369414830*n^4-563873203570*n^3-17946168870490*n^2-83418008648019*n-115794415809135)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+5)-32768/9*(186961125568*n^5-6750356337332*n^4-183121889596582*n^3-1535066011807159*n^2-5567311957908927*n-7540383975500430)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+6)+8388608/9*(8635016*n^5+90618704*n^4+342453820*n^3+574016677*n^2+412856055*n+99279810)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+2)-2097152/45*(1097233952*n^5+16419255320*n^4+93284272000*n^3+252726412075*n^2+326625850533*n+160879233060)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+3)-33554432/9*n*(2*n+3)*(74728*n^3+270562*n^2+79145*n-119389)/(n+55)/(n+53)/(n+52)/(n+58)/(n+56)*a(n+1), n >= 56
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3028
a(8) = 16692
a(9) = 94296
a(10) = 542900
a(11) = 3173868
a(12) = 18791204
a(13) = 112448824
a(14) = 679075704
a(15) = 4133407792
a(16) = 25333151648
a(17) = 156207460864
a(18) = 968381106644
a(19) = 6032128924364
a(20) = 37736408939396
a(21) = 236991619184744
a(22) = 1493585406457976
a(23) = 9443108065939544
a(24) = 59878143978488360
a(25) = 380702284574747248
a(26) = 2426465440977233992
a(27) = 15500739770480348856
a(28) = 99231060790774595112
a(29) = 636494522603083487552
a(30) = 4090111487652434340224
a(31) = 26327915048953925562088
a(32) = 169742697623706424836744
a(33) = 1096013579230025743122192
a(34) = 7086825885626899662692052
a(35) = 45884163070714741841375372
a(36) = 297451642655025093757440452
a(37) = 1930556111819659612877230760
a(38) = 12543923684457078348066993816
a(39) = 81591304889987150530011285784
a(40) = 531239534408042119084590801128
a(41) = 3462192514348142315483085091152
a(42) = 22584278603173936241058957445720
a(43) = 147447263147427778119465144292648
a(44) = 963441371347043693059804951979448
a(45) = 6300220235027813406491448103408592
a(46) = 41229958118990064038878995266880848
a(47) = 270011723861287058457778617477849920
a(48) = 1769504446698260790036692552162562912
a(49) = 11603996073868856035957616889304452416
a(50) = 76144527119122601715510379478133937544
a(51) = 499958603680275128470524025114240805048
a(52) = 3284606139355099347407471886893926047080
a(53) = 21591196957500587152176278053176313303696
a(54) = 142005483890029711610434723869732874054960
a(55) = 934458057586587928401651229871790754947376
a{\left(n + 56 \right)} = \frac{2013265920 n \left(n - 1\right) \left(2 n - 3\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{\left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{33554432 n \left(2 n + 3\right) \left(74728 n^{3} + 270562 n^{2} + 79145 n - 119389\right) a{\left(n + 1 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(n + 54\right) \left(1225 n^{2} + 133073 n + 3605328\right) a{\left(n + 55 \right)}}{18 \left(n + 53\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2629717 n^{4} + 549295836 n^{3} + 43009601099 n^{2} + 1496152725120 n + 19509908418900\right) a{\left(n + 53 \right)}}{72 \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(37447 n^{4} + 7948088 n^{3} + 632315491 n^{2} + 22347017250 n + 296030746800\right) a{\left(n + 54 \right)}}{18 \left(n + 52\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{8388608 \left(8635016 n^{5} + 90618704 n^{4} + 342453820 n^{3} + 574016677 n^{2} + 412856055 n + 99279810\right) a{\left(n + 2 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(134028682 n^{5} + 34396883335 n^{4} + 3530419345160 n^{3} + 181147000849085 n^{2} + 4646601602355498 n + 47668439137264920\right) a{\left(n + 52 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(506869702 n^{5} + 128546325175 n^{4} + 13040393239640 n^{3} + 661454406722645 n^{2} + 16775973213147678 n + 170194045247832600\right) a{\left(n + 51 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{2097152 \left(1097233952 n^{5} + 16419255320 n^{4} + 93284272000 n^{3} + 252726412075 n^{2} + 326625850533 n + 160879233060\right) a{\left(n + 3 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{1048576 \left(1243243676 n^{5} + 21782894054 n^{4} + 138205736821 n^{3} + 397201203667 n^{2} + 505399489707 n + 210413193318\right) a{\left(n + 4 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{262144 \left(2787787504 n^{5} + 140369414830 n^{4} - 563873203570 n^{3} - 17946168870490 n^{2} - 83418008648019 n - 115794415809135\right) a{\left(n + 5 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(6443676229 n^{5} + 1584111169180 n^{4} + 155694198750125 n^{3} + 7647188601991250 n^{2} + 187703129096079996 n + 1841913783624180240\right) a{\left(n + 50 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{32768 \left(186961125568 n^{5} - 6750356337332 n^{4} - 183121889596582 n^{3} - 1535066011807159 n^{2} - 5567311957908927 n - 7540383975500430\right) a{\left(n + 6 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(444103286557 n^{5} + 108109626396670 n^{4} + 10522636080790415 n^{3} + 511887849825790190 n^{2} + 12445595720283321408 n + 120986776796198662080\right) a{\left(n + 49 \right)}}{1440 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(872450834629 n^{5} + 217830107198215 n^{4} + 21684402459226085 n^{3} + 1076116710279935945 n^{2} + 26629171838820885126 n + 262919867636059479360\right) a{\left(n + 48 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(16666019372443 n^{5} + 3680915428743895 n^{4} + 324422224746611945 n^{3} + 14260440906686381075 n^{2} + 312563387504034129942 n + 2732229553019701929840\right) a{\left(n + 47 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{8192 \left(19315178316272 n^{5} + 1381851368454300 n^{4} + 27358571523526660 n^{3} + 237906809756147965 n^{2} + 968051993419097383 n + 1511823098961165660\right) a{\left(n + 7 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2048 \left(217720806252872 n^{5} + 11049485796124224 n^{4} + 209500289800481808 n^{3} + 1907223551103605683 n^{2} + 8446808908459182059 n + 14658182586315081252\right) a{\left(n + 8 \right)}}{3 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(229898341683497 n^{5} + 50703115699812980 n^{4} + 4469233742633225275 n^{3} + 196806738094353207100 n^{2} + 4329660069835079787348 n + 38068221698951901107520\right) a{\left(n + 46 \right)}}{480 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1716234289607411 n^{5} + 370461787322282630 n^{4} + 31962952148067783790 n^{3} + 1377840266177970423970 n^{2} + 29675707254259528863999 n + 255472961415664233198780\right) a{\left(n + 45 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{512 \left(26026991134785952 n^{5} + 1306081911518973320 n^{4} + 25782711940706413780 n^{3} + 251167634878020213715 n^{2} + 1209901303917990607033 n + 2308066689190599412890\right) a{\left(n + 9 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(27744066123945909 n^{5} + 5798668621234730245 n^{4} + 484188223284826964005 n^{3} + 20189515660615296896215 n^{2} + 420387382996974191592466 n + 3496712844109981440228360\right) a{\left(n + 44 \right)}}{960 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{128 \left(53652275152200332 n^{5} - 39174311374998170425 n^{4} - 1704726147259299882485 n^{3} - 27117172956015481509005 n^{2} - 190264893417518875623297 n - 498535090618002226356060\right) a{\left(n + 11 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{256 \left(91733060821287100 n^{5} + 5246856316104110182 n^{4} + 117371459344748906435 n^{3} + 1289514362805502785107 n^{2} + 6979168748595371581746 n + 14916795789662262401472\right) a{\left(n + 10 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(220956972707033389 n^{5} + 42272181623363922040 n^{4} + 3201278496394875164615 n^{3} + 119678133175696870035920 n^{2} + 2201471398250071002718236 n + 15864831462558179994201360\right) a{\left(n + 43 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2876564353847223497 n^{5} + 652358054648258492780 n^{4} + 58659089330489514678115 n^{3} + 2617686496816364014229740 n^{2} + 58034982964073288466685548 n + 511806506477014369310593680\right) a{\left(n + 42 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{64 \left(27439494102212118253 n^{5} + 1202761949080050018520 n^{4} + 19271292886792837806185 n^{3} + 128021390037831296925230 n^{2} + 215977302423609593206332 n - 655205597467259592651840\right) a{\left(n + 12 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(92557465324283718253 n^{5} + 19353644133904230541330 n^{4} + 1616081231371536035865935 n^{3} + 67369223227943644843003610 n^{2} + 1402147391229329124400166592 n + 11656894918489971712617297600\right) a{\left(n + 41 \right)}}{11520 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{32 \left(306941197595026187201 n^{5} + 16498959723742913035115 n^{4} + 347676299913910644239425 n^{3} + 3565718897626250950813225 n^{2} + 17598827109665165379995034 n + 32761675610323852945824360\right) a{\left(n + 13 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(684119246962763644619 n^{5} + 138265662310827513711410 n^{4} + 11167662375070544754750805 n^{3} + 450608598316998301720399750 n^{2} + 9083210699340324483766456536 n + 73178770510147475531198167200\right) a{\left(n + 40 \right)}}{11520 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(693362120327765903863 n^{5} + 136444620475462942854952 n^{4} + 10732750223914667212929521 n^{3} + 421835384726944276960776596 n^{2} + 8284404921981907547201580804 n + 65037640339873762769796729984\right) a{\left(n + 39 \right)}}{2304 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{32 \left(1102252245843331527889 n^{5} + 66670705367577925722490 n^{4} + 1598591380165481985943820 n^{3} + 18958913595005842318340045 n^{2} + 110941362183910740409625316 n + 255365104127707911433190220\right) a{\left(n + 14 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{16 \left(2038827704410320458349 n^{5} + 135608512380989247443075 n^{4} + 3590720068583269130640045 n^{3} + 47283823230723066929013585 n^{2} + 309424123922332533009778286 n + 804243395972787958770855900\right) a{\left(n + 15 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2114633170884457333584 n^{5} + 406689699740256959852780 n^{4} + 31265233230861976528247545 n^{3} + 1201017982372006010240253755 n^{2} + 23053424967437408808896647866 n + 176896031605850843253042641520\right) a{\left(n + 38 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(4313399157556194897476 n^{5} + 856454101214968300606890 n^{4} + 67380060320678911567584405 n^{3} + 2629573904573331809257724035 n^{2} + 50966432864408559807662758214 n + 392848633332918419467773013440\right) a{\left(n + 36 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{8 \left(5597898192700406302139 n^{5} + 404499976441174797165362 n^{4} + 11662768466329491285045919 n^{3} + 167696461818676241368359784 n^{2} + 1202303506630782548172249552 n + 3437801614344403925849852568\right) a{\left(n + 16 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{16 \left(13329527253422208783039 n^{5} + 1101755336224706941503985 n^{4} + 36411078302183222651974360 n^{3} + 601502384671845025747635535 n^{2} + 4967879197317800891547712786 n + 16413752167975604467326992340\right) a{\left(n + 18 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2 \left(27978039856862695081734 n^{5} + 2429863358757344560529270 n^{4} + 83858149290807866857693735 n^{3} + 1441228765648819564284068385 n^{2} + 12392960231408872483541140246 n + 42986272735292463261569820480\right) a{\left(n + 21 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(29193813717116295330465 n^{5} + 3195593337199636201839332 n^{4} + 141643900957545775999758863 n^{3} + 3174859117091192016241305524 n^{2} + 35939235933213303919405624424 n + 164125029102820069468386822504\right) a{\left(n + 22 \right)}}{6 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{8 \left(53048284831600981113304 n^{5} + 4121109435346208406419650 n^{4} + 127916221239864533648639345 n^{3} + 1983081438638077597082865590 n^{2} + 15356297213723925330239419251 n + 47521050701271890166770661900\right) a{\left(n + 17 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(62059711014977137544669 n^{5} + 11742785546180915594427770 n^{4} + 887895859070762231214883375 n^{3} + 33535989249383379770976320050 n^{2} + 632755598670290906636407362936 n + 4771371867632995136405136791040\right) a{\left(n + 37 \right)}}{23040 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2 \left(71053900839736908943601 n^{5} + 6172045704497552468879789 n^{4} + 214393182444893494679584189 n^{3} + 3723502527737613260924230171 n^{2} + 32342531603906191414235221074 n + 112436752745095427599269666696\right) a{\left(n + 19 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{2 \left(83126025286330979595819 n^{5} + 7419786639311891029531660 n^{4} + 264537662058945333968349650 n^{3} + 4711216339780844043779503605 n^{2} + 41935846232719720832358832346 n + 149371352181753212095533549480\right) a{\left(n + 20 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(93054059748275184757733 n^{5} + 15603588629730031872937865 n^{4} + 1044459373131591979395007060 n^{3} + 34880296428373788558749833900 n^{2} + 581050762836797590181075100672 n + 3861847476035461869552991062720\right) a{\left(n + 35 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(585568881876520259640997 n^{5} + 98155211197154104044078235 n^{4} + 6578554121250693289891703870 n^{3} + 220363832171150054615598998120 n^{2} + 3689298958154950847306214619788 n + 24696292951364197176758805135840\right) a{\left(n + 34 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(617583815509511667449699 n^{5} + 71680945458885932515162420 n^{4} + 3331940880935136103121680215 n^{3} + 77522738161837736904284820040 n^{2} + 902697570060791339259164660286 n + 4207961655009263586868549374480\right) a{\left(n + 23 \right)}}{30 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1025859221166732942130183 n^{5} + 168382238429254427420197510 n^{4} + 11052836917372764334404056285 n^{3} + 362688221561869798914661858100 n^{2} + 5949472432545124135710854412612 n + 39030287826738030303224331833760\right) a{\left(n + 33 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1440636473196466680101426 n^{5} + 222964669347550327889425835 n^{4} + 13804784804808715144721778640 n^{3} + 427413668681344441347267996925 n^{2} + 6617514818647967203936301436369 n + 40988417891244282474921579785760\right) a{\left(n + 31 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(1781339502713891698880321 n^{5} + 284691149919752350813373440 n^{4} + 18198031397068496171506499545 n^{3} + 581582384796114780089704253650 n^{2} + 9292603382285472437424822720464 n + 59387568799038752672095931905200\right) a{\left(n + 32 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2275725347053487206470578 n^{5} + 324200318517546633861429935 n^{4} + 18481273301497905812137676458 n^{3} + 526988000598141867790050802465 n^{2} + 7516822353607995733983335694600 n + 42907748519651062100173771105224\right) a{\left(n + 29 \right)}}{288 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(3703522219585910581029506 n^{5} + 442834473059898301967097230 n^{4} + 21185688001360495828688652880 n^{3} + 506897567140961685124050884965 n^{2} + 6065491632069042034968090115359 n + 29037668627160399559640983937460\right) a{\left(n + 24 \right)}}{90 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(9097205967744551217048067 n^{5} + 1122422345341092993228731215 n^{4} + 55397740369173818236158497330 n^{3} + 1367181061362839061858148050215 n^{2} + 16871698529142712894138920556833 n + 83287683486898965261026741382300\right) a{\left(n + 25 \right)}}{180 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(11409385657778167984079114 n^{5} + 1559363769991214201924847125 n^{4} + 85262042685989833353356523325 n^{3} + 2331377684326115371127248334230 n^{2} + 31881083266477501552619727748626 n + 174430092274010765898041794739040\right) a{\left(n + 28 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(11410141747397456926932439 n^{5} + 1698169450629980046516175750 n^{4} + 101132763855553011023194315955 n^{3} + 3012596588015342511059616338600 n^{2} + 44888434386811841333499269286576 n + 267649991688270417800930195052240\right) a{\left(n + 30 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(15770855530596627764168098 n^{5} + 2009746047769719080453446675 n^{4} + 102442474423747861933718212340 n^{3} + 2610880765640828669948872048655 n^{2} + 33271085653242490035754994814552 n + 169595554404051688596900395395320\right) a{\left(n + 26 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(20888648906742153293876261 n^{5} + 2752614384077663580444980375 n^{4} + 145089670940710094238298964425 n^{3} + 3823874396752578258531031612855 n^{2} + 50391382540631383466508914051724 n + 265640117285438648956510837653600\right) a{\left(n + 27 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)}, \quad n \geq 56
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24396/
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[26,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[26,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[26,x]
F[12,x] = 1/F[26,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[27,x]
F[15,x] = F[16,x]*F[5,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[26,x]
F[19,x] = 1/F[26,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = -F[2,x]+F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[26,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = x
F[27,x] = F[28,x]*F[32,x]
F[28,x] = -F[30,x]+F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[0,x]+F[33,x]
F[33,x] = F[34,x]+F[43,x]
F[34,x] = F[35,x]
F[35,x] = F[26,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[26,x]*F[37,x]
F[40,x] = F[41,x]
F[41,x] = F[26,x]*F[36,x]*F[37,x]*F[42,x]
F[42,x] = F[1,x]+F[34,x]
F[43,x] = -F[67,x]+F[44,x]
F[44,x] = 1/F[26,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[66,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[26,x]*F[49,x]
F[49,x] = 1/F[26,x]/F[63,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[26,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[62,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[26,x]*F[56,x]
F[56,x] = 1/F[26,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[26,x]*F[60,x]
F[60,x] = F[22,x]
F[61,x] = F[2,x]*F[24,x]
F[62,x] = F[19,x]*F[2,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = -F[0,x]+F[65,x]
F[65,x] = 1/F[26,x]*F[31,x]
F[66,x] = F[26,x]*F[34,x]
F[67,x] = F[68,x]
F[68,x] = F[26,x]*F[42,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[17,x]*F[42,x]
F[71,x] = F[72,x]
F[72,x] = F[26,x]*F[36,x]*F[49,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_{26}\! \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_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{0}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{43}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \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_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{26}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{37}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{26}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{26}\! \left(x \right) F_{63}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{26}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{26}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{26}\! \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_{26}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{62}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{26}\! \left(x \right) F_{34}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{26}\! \left(x \right) F_{42}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right) F_{42}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{49}\! \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_26(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_26(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_26(x))
Eq(F_12(x), F_13(x)/F_26(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_27(x))
Eq(F_15(x), F_16(x)*F_5(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_26(x))
Eq(F_19(x), F_20(x)/F_26(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), -F_2(x) + F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_26(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), x)
Eq(F_27(x), F_28(x)*F_32(x))
Eq(F_28(x), F_29(x) - F_30(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_0(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_43(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_26(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_26(x)*F_37(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_26(x)*F_36(x)*F_37(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_34(x))
Eq(F_43(x), F_44(x) - F_67(x))
Eq(F_44(x), F_45(x)/F_26(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_66(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_26(x)*F_49(x))
Eq(F_49(x), F_50(x)/(F_26(x)*F_63(x)))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_26(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) - F_62(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_26(x)*F_56(x))
Eq(F_56(x), F_57(x)/F_26(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_26(x))
Eq(F_60(x), F_22(x))
Eq(F_61(x), F_2(x)*F_24(x))
Eq(F_62(x), F_19(x)*F_2(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), -F_0(x) + F_65(x))
Eq(F_65(x), F_31(x)/F_26(x))
Eq(F_66(x), F_26(x)*F_34(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_26(x)*F_42(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_17(x)*F_42(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_26(x)*F_36(x)*F_49(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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", 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[0, 5], [2, 5]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 1], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 4], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 1], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 4], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 4], [0, 5], [2, 5], [2, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 4], [0, 4], [0, 5], [0, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 5], [0, 1], [0, 5], [0, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 5], [0, 4], [0, 5], [0, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 5], [0, 4], [0, 5], [2, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 3]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24913/
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[26,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[26,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[26,x]
F[12,x] = 1/F[26,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[27,x]
F[15,x] = F[16,x]*F[5,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[26,x]
F[19,x] = 1/F[26,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = -F[2,x]+F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[26,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = x
F[27,x] = F[28,x]*F[32,x]
F[28,x] = -F[30,x]+F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[0,x]+F[33,x]
F[33,x] = F[34,x]+F[43,x]
F[34,x] = F[35,x]
F[35,x] = F[26,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[26,x]*F[37,x]
F[40,x] = F[41,x]
F[41,x] = F[26,x]*F[36,x]*F[37,x]*F[42,x]
F[42,x] = F[1,x]+F[34,x]
F[43,x] = -F[67,x]+F[44,x]
F[44,x] = 1/F[26,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[66,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[26,x]*F[49,x]
F[49,x] = 1/F[26,x]/F[63,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[26,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[62,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[26,x]*F[56,x]
F[56,x] = 1/F[26,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[26,x]*F[60,x]
F[60,x] = F[22,x]
F[61,x] = F[2,x]*F[24,x]
F[62,x] = F[19,x]*F[2,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = -F[0,x]+F[65,x]
F[65,x] = 1/F[26,x]*F[31,x]
F[66,x] = F[26,x]*F[34,x]
F[67,x] = F[68,x]
F[68,x] = F[26,x]*F[42,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[17,x]*F[42,x]
F[71,x] = F[72,x]
F[72,x] = F[26,x]*F[36,x]*F[49,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_{26}\! \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_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{0}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{43}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \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_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{26}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{37}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{26}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{26}\! \left(x \right) F_{63}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{26}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{26}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{26}\! \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_{26}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{62}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{26}\! \left(x \right) F_{34}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{26}\! \left(x \right) F_{42}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right) F_{42}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{49}\! \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_26(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_26(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_26(x))
Eq(F_12(x), F_13(x)/F_26(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_27(x))
Eq(F_15(x), F_16(x)*F_5(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_26(x))
Eq(F_19(x), F_20(x)/F_26(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), -F_2(x) + F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_26(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), x)
Eq(F_27(x), F_28(x)*F_32(x))
Eq(F_28(x), F_29(x) - F_30(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_0(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_43(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_26(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_26(x)*F_37(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_26(x)*F_36(x)*F_37(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_34(x))
Eq(F_43(x), F_44(x) - F_67(x))
Eq(F_44(x), F_45(x)/F_26(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_66(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_26(x)*F_49(x))
Eq(F_49(x), F_50(x)/(F_26(x)*F_63(x)))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_26(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) - F_62(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_26(x)*F_56(x))
Eq(F_56(x), F_57(x)/F_26(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_26(x))
Eq(F_60(x), F_22(x))
Eq(F_61(x), F_2(x)*F_24(x))
Eq(F_62(x), F_19(x)*F_2(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), -F_0(x) + F_65(x))
Eq(F_65(x), F_31(x)/F_26(x))
Eq(F_66(x), F_26(x)*F_34(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_26(x)*F_42(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_17(x)*F_42(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_26(x)*F_36(x)*F_49(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 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[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24964/
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[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[24,x]
F[12,x] = 1/F[24,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[25,x]
F[15,x] = F[16,x]*F[5,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[24,x]
F[19,x] = 1/F[24,x]*F[20,x]
F[20,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[26,x]*F[30,x]
F[26,x] = -F[28,x]+F[27,x]
F[27,x] = F[5,x]
F[28,x] = F[29,x]
F[29,x] = F[2,x]
F[30,x] = F[31,x]+F[40,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[24,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[24,x]*F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[24,x]*F[31,x]*F[34,x]*F[35,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = -F[68,x]+F[42,x]
F[42,x] = 1/F[24,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[67,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[24,x]*F[47,x]
F[47,x] = 1/F[24,x]/F[62,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[24,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[61,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[24,x]*F[54,x]
F[54,x] = 1/F[24,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = -F[60,x]+F[57,x]
F[57,x] = 1/F[24,x]*F[58,x]
F[58,x] = F[59,x]
F[59,x] = -F[2,x]+F[21,x]
F[60,x] = F[2,x]*F[22,x]
F[61,x] = F[19,x]*F[2,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = (x*F[63,x]^3+(2*x-1)*F[63,x]^2+(x^2-x+1)*F[63,x]+x^2)*(1+F[63,x])
F[64,x] = -F[66,x]+F[65,x]
F[65,x] = 1/F[24,x]*F[29,x]
F[66,x] = 1+x*F[66,x]^4+F[66,x]^2*(x^2-2*x+3)+F[66,x]^3*(-1-x)+(-2+2*x)*F[66,x]
F[67,x] = F[24,x]*F[32,x]
F[68,x] = F[69,x]
F[69,x] = F[24,x]*F[31,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[17,x]*F[31,x]
F[72,x] = F[73,x]
F[73,x] = F[24,x]*F[34,x]*F[47,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_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{20}\! \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_{26}\! \left(x \right) F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{5}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{40}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{24}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{24}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{24}\! \left(x \right) F_{62}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{24}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right) F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = x F_{63} \left(x \right)^{4}+x^{2} F_{63} \left(x \right)^{2}+3 x F_{63} \left(x \right)^{3}+2 x^{2} F_{63}\! \left(x \right)+x F_{63} \left(x \right)^{2}-F_{63} \left(x \right)^{3}+x^{2}-F_{63}\! \left(x \right) x +F_{63}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{66}\! \left(x \right) = x F_{66} \left(x \right)^{4}+x^{2} F_{66} \left(x \right)^{2}-F_{66} \left(x \right)^{3} x -2 x F_{66} \left(x \right)^{2}-F_{66} \left(x \right)^{3}+2 F_{66}\! \left(x \right) x +3 F_{66} \left(x \right)^{2}-2 F_{66}\! \left(x \right)+1
F_{67}\! \left(x \right) = F_{24}\! \left(x \right) F_{32}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{17}\! \left(x \right) F_{31}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{24}\! \left(x \right) F_{34}\! \left(x \right) F_{47}\! \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_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_24(x))
Eq(F_12(x), F_13(x)/F_24(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_25(x))
Eq(F_15(x), F_16(x)*F_5(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_24(x))
Eq(F_19(x), F_20(x)/F_24(x))
Eq(F_20(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_28(x))
Eq(F_27(x), F_5(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_2(x))
Eq(F_30(x), F_31(x) + F_40(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_24(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_24(x)*F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_24(x)*F_31(x)*F_34(x)*F_35(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_68(x))
Eq(F_42(x), F_43(x)/F_24(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x) - F_67(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_24(x)*F_47(x))
Eq(F_47(x), F_48(x)/(F_24(x)*F_62(x)))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_24(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) - F_61(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_24(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_24(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x) - F_60(x))
Eq(F_57(x), F_58(x)/F_24(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), -F_2(x) + F_21(x))
Eq(F_60(x), F_2(x)*F_22(x))
Eq(F_61(x), F_19(x)*F_2(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), x*(F_63(x) + 1)**4 + (-x - 1)*(F_63(x) + 1)**3 + (2*x - 3)*(F_63(x) + 1) + (F_63(x) + 1)**2*(x**2 - 2*x + 3) + F_63(x) + 1)
Eq(F_64(x), F_65(x) - F_66(x))
Eq(F_65(x), F_29(x)/F_24(x))
Eq(F_66(x), x*F_66(x)**4 + (-x - 1)*F_66(x)**3 + (2*x - 2)*F_66(x) + (x**2 - 2*x + 3)*F_66(x)**2 + 1)
Eq(F_67(x), F_24(x)*F_32(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_24(x)*F_31(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_17(x)*F_31(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_24(x)*F_34(x)*F_47(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "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:
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{"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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}}]}
Specification 4
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25634/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[61,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[59,x]+F[60,x]+F[7,x]
F[7,x] = F[3,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[13,x,k[0]]+F[58,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[18,x,k[0]]+F[19,x,k[0]]
F[17,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[18,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[19,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[26,x,k[0]]*F[3,x]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[20,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[41,x,k[0]]
F[28,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[36,x]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[33,x,k[0]]+F[35,x,k[0]]
F[31,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[33,x,k[0]] = F[3,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[30,x,k[0]]*k[0]-F[30,x,1])
F[35,x,k[0]] = F[20,x,k[0]]*F[30,x,k[0]]
F[36,x] = F[1,x]+F[37,x]+F[39,x]
F[37,x] = F[3,x]*F[38,x]
F[38,x] = F[16,x,1]
F[39,x] = F[3,x]*F[40,x]
F[40,x] = F[30,x,1]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[3,x]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[51,x,k[0]]
F[44,x,k[0]] = F[45,x]*F[48,x,k[0]]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[45,x]^2*F[3,x]
F[49,x,k[0]] = F[3,x]*F[48,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[15,x,k[0]] = F[30,x,k[0]]+F[50,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[53,x]+F[54,x,k[0]]+F[56,x,k[0]]
F[53,x] = 0
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[23,x,k[0]]*F[26,x,k[0]]*F[3,x]*F[45,x]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[3,x]*F[45,x]*F[52,x,k[0]]
F[58,x,k[0]] = F[15,x,k[0]]*F[20,x,k[0]]
F[59,x] = F[3,x]*F[8,x]
F[60,x] = F[58,x,1]
F[61,x] = F[3,x]*F[6,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{61}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{36}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-F_{16}\! \left(x , y\right) y +F_{16}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{30}\! \left(x , y\right)+F_{30}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{3}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{39}\! \left(x \right) = F_{3}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{3}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x \right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{53}\! \left(x \right) = 0
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{3}\! \left(x \right) F_{45}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{45}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_61(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_59(x) + F_60(x) + F_7(x))
Eq(F_7(x), F_3(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_13(x, k_0) + F_58(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_18(x, k_0) + F_19(x, k_0))
Eq(F_17(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_18(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_19(x, k_0), F_16(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_26(x, k_0)*F_3(x))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_20(x, k_0)*F_23(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_41(x, k_0))
Eq(F_28(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_36(x))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0) + F_33(x, k_0) + F_35(x, k_0))
Eq(F_31(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_3(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_20(x, k_0)*F_30(x, k_0))
Eq(F_36(x), F_1(x) + F_37(x) + F_39(x))
Eq(F_37(x), F_3(x)*F_38(x))
Eq(F_38(x), F_16(x, 1))
Eq(F_39(x), F_3(x)*F_40(x))
Eq(F_40(x), F_30(x, 1))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_3(x)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_51(x, k_0))
Eq(F_44(x, k_0), F_45(x)*F_48(x, k_0))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_3(x)*F_45(x)**2)
Eq(F_49(x, k_0), F_3(x)*F_48(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_15(x, k_0), F_30(x, k_0) + F_50(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x) + F_54(x, k_0) + F_56(x, k_0))
Eq(F_53(x), 0)
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_23(x, k_0)*F_26(x, k_0)*F_3(x)*F_45(x))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_3(x)*F_45(x)*F_52(x, k_0))
Eq(F_58(x, k_0), F_15(x, k_0)*F_20(x, k_0))
Eq(F_59(x), F_3(x)*F_8(x))
Eq(F_60(x), F_58(x, 1))
Eq(F_61(x), F_3(x)*F_6(x))
Pack JSON:
{"name": "row_and_col_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_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}], [{"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:
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0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 5], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 5], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], 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0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 5], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [2, 0], [2, 5], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 5], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 5], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 5]]}]}]}], "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": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 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": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 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": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25858/
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[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[24,x]
F[12,x] = 1/F[24,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[25,x]
F[15,x] = F[16,x]*F[5,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[24,x]
F[19,x] = 1/F[24,x]*F[20,x]
F[20,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[26,x]*F[30,x]
F[26,x] = -F[28,x]+F[27,x]
F[27,x] = F[5,x]
F[28,x] = F[29,x]
F[29,x] = F[2,x]
F[30,x] = F[31,x]+F[40,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[24,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[24,x]*F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[24,x]*F[31,x]*F[34,x]*F[35,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = -F[68,x]+F[42,x]
F[42,x] = 1/F[24,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[67,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[24,x]*F[47,x]
F[47,x] = 1/F[24,x]/F[62,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[24,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[61,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[24,x]*F[54,x]
F[54,x] = 1/F[24,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = -F[60,x]+F[57,x]
F[57,x] = 1/F[24,x]*F[58,x]
F[58,x] = F[59,x]
F[59,x] = -F[2,x]+F[21,x]
F[60,x] = F[2,x]*F[22,x]
F[61,x] = F[19,x]*F[2,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = (1+F[63,x])*(x*F[63,x]^3+(2*x-1)*F[63,x]^2+(x^2-x+1)*F[63,x]+x^2)
F[64,x] = -F[66,x]+F[65,x]
F[65,x] = 1/F[24,x]*F[29,x]
F[66,x] = 1+x*F[66,x]^4+F[66,x]^2*(x^2-2*x+3)+F[66,x]^3*(-1-x)+(-2+2*x)*F[66,x]
F[67,x] = F[24,x]*F[32,x]
F[68,x] = F[69,x]
F[69,x] = F[24,x]*F[31,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[17,x]*F[31,x]
F[72,x] = F[73,x]
F[73,x] = F[24,x]*F[34,x]*F[47,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_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{20}\! \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_{26}\! \left(x \right) F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{5}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{40}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{24}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{24}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{24}\! \left(x \right) F_{62}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{24}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right) F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = x F_{63} \left(x \right)^{4}+x^{2} F_{63} \left(x \right)^{2}+3 x F_{63} \left(x \right)^{3}+2 x^{2} F_{63}\! \left(x \right)+x F_{63} \left(x \right)^{2}-F_{63} \left(x \right)^{3}+x^{2}-F_{63}\! \left(x \right) x +F_{63}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{24}\! \left(x \right)}
F_{66}\! \left(x \right) = x F_{66} \left(x \right)^{4}+x^{2} F_{66} \left(x \right)^{2}-F_{66} \left(x \right)^{3} x -2 x F_{66} \left(x \right)^{2}-F_{66} \left(x \right)^{3}+2 F_{66}\! \left(x \right) x +3 F_{66} \left(x \right)^{2}-2 F_{66}\! \left(x \right)+1
F_{67}\! \left(x \right) = F_{24}\! \left(x \right) F_{32}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{17}\! \left(x \right) F_{31}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{24}\! \left(x \right) F_{34}\! \left(x \right) F_{47}\! \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_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_24(x))
Eq(F_12(x), F_13(x)/F_24(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_25(x))
Eq(F_15(x), F_16(x)*F_5(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_24(x))
Eq(F_19(x), F_20(x)/F_24(x))
Eq(F_20(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_28(x))
Eq(F_27(x), F_5(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_2(x))
Eq(F_30(x), F_31(x) + F_40(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_24(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_24(x)*F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_24(x)*F_31(x)*F_34(x)*F_35(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_68(x))
Eq(F_42(x), F_43(x)/F_24(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x) - F_67(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_24(x)*F_47(x))
Eq(F_47(x), F_48(x)/(F_24(x)*F_62(x)))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_24(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) - F_61(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_24(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_24(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x) - F_60(x))
Eq(F_57(x), F_58(x)/F_24(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), -F_2(x) + F_21(x))
Eq(F_60(x), F_2(x)*F_22(x))
Eq(F_61(x), F_19(x)*F_2(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), x*(F_63(x) + 1)**4 + (-x - 1)*(F_63(x) + 1)**3 + (2*x - 3)*(F_63(x) + 1) + (F_63(x) + 1)**2*(x**2 - 2*x + 3) + F_63(x) + 1)
Eq(F_64(x), F_65(x) - F_66(x))
Eq(F_65(x), F_29(x)/F_24(x))
Eq(F_66(x), x*F_66(x)**4 + (-x - 1)*F_66(x)**3 + (2*x - 2)*F_66(x) + (x**2 - 2*x + 3)*F_66(x)**2 + 1)
Eq(F_67(x), F_24(x)*F_32(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_24(x)*F_31(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_17(x)*F_31(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_24(x)*F_34(x)*F_47(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3]], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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", 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