02431_03412_03421_04312_04321_13402_14302
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3139, 17500, 99772, 578776, 3405089, 20269718, 121869038, 739015133, 4514754917, 27760850118, 171678490387, 1067100692285, 6662955903479, 41773543226571, 262868106119301, 1659699442472225, 10511097379593102, 66754711794724532, 425042894136874547, 2712774605779759537, 17351924803873950301, 111215625138092765752, 714178134717729765251, 4594248529257237170046, 29603265548417261359584, 191045446833411670337024, 1234708906787529804034607, 7990718489586348724436119, 51780497680111387335752242, 335949812589365341220112511, 2182134901189588893803852599, 14189310870605689682019965570, 92361098172145492590672590974, 601786382315511826292004432973, 3924643205381700198106970393195, 25617877283422343005358956650902, 167360583381100994034720642578192, 1094242264018218441687029729916607, 7159923231160759605436958332402913, 46883839122967264822577159404458662, 307216243188291654497696144589684371, 2014459476187210445480157726964631976, 13217648289968400907432279662670064548, 86780033108798404823097713720436484910, 570091722400177847394156953686489081695, 3747303955134870262265960820998411884616, 24645231451214091769640614836648655689534, 162172695155985792144636225215890951585521, 1067689500499923554258840462338518456098067, 7032773331770830543050385125426637725507858, 46346304274964681356799464201277440410796121, 305564755534146780273879791244355865236341215, 2015506792349892200704981025215696833213525456, 13300000538177858476571591284907794892249071836, 87800965264632579654896266930171294813458603779, 579857546632521997240026571214953347193835800149, 3831000072038010202260530650464724910244452400915, 25320164569351197809118948213708240738876370473048, 167409209612012049860492688995492332490162593625078, 1107250276910500044952246508825569308245797161922254, 7325904752286539272331439074776763696256503033034929, 48486557470265773976421679583231115271967749268157128, 321012416819435819538512553273581507836950152930910184, 2125977569504206146336473800989163671841368354610962909, 14084065289113849308139582631707255737431652167231965262, 93331057447208285841946308940708463993695146982612272191, 618656530646421749435190611143926600653942404720769853536, 4101992608004989335233658536504847809972913756417911730595, 27205626777495382133917958886735139708129744972880859039255, 180483728051579089723239383691730982361427362236615571250773, 1197649705402304959828082033071649612592297855617166974964838, 7949340789222171092670837982116285868484571075462099990199018, 52776328922151745602872692263146962752785491890569148238251572, 350470378045523863832489802869409194017059232965467129628908951, 2327903385194452197647095248744943041261278462873975100812874142, 15465985387232392117707534626336083124064093054719032914722734225, 102774849983394678983186981822772792694214762802733088258436728405, 683109632638760808656705203482191008047459903052780213893599949111, 4541361152582170533440993168989317011631383714113914572690033570904, 30197542041274486266439722518050155645912237642122699091439599883652, 200837587178049872033991662600122885718768034776914485470534540133092, 1335993168921402603400216272338840454862831827791623027501921004708107, 8888886983578056413609960768870220909325346960782297790396992663445074, 59152426372310150177562378509062195403673685980758917722961185175638415, 393711377075049641152997794418565405241864171633058530517366858509588483, 2620968713422873384628305668726658377955573874177250560275621844000136593, 17451087068497389316240941097025816230549638464422025790814071927375175412, 116213952054775605143846996005078338276363744472634499357657084526874391920, 774047484820642426295896187258483840477664966561903679151206494452766293807, 5156427873487160042578386669847826632384266809549471086138712300731355934590, 34355858911043288441307540669659163187032542019937904017874192022938818912503, 228940037019216864416771068020920176603285346386248992470430721241841694211159, 1525844796720016609609944100927531989937254028415727031869184601839717210994279, 10171038283148823527197305964575677476369772872884314591473834776751230825797837
Implicit equation for the generating function in Maple syntax:
x^3*(x-1)*F(x)^5-x^2*(x-1)*(2*x-3)*F(x)^4+(-3*x^3+5*x^2+x+1)*F(x)^3+(-x^2-2*x-5)*F(x)^2+8*F(x)-4 = 0
Implicit equation for the generating function in latex syntax:
x^{3} \left(x -1\right) F \! \left(x \right)^{5}-x^{2} \left(x -1\right) \left(2 x -3\right) F \! \left(x \right)^{4}+\left(-3 x^{3}+5 x^{2}+x +1\right) F \! \left(x \right)^{3}+\left(-x^{2}-2 x -5\right) F \! \left(x \right)^{2}+8 F \! \left(x \right)-4 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 581
a(7) = 3139
a(8) = 17500
a(9) = 99772
a(10) = 578776
a(11) = 3405089
a(12) = 20269718
a(13) = 121869038
a(14) = 739015133
a(15) = 4514754917
a(16) = 27760850118
a(17) = 171678490387
a(18) = 1067100692285
a(19) = 6662955903479
a(20) = 41773543226571
a(21) = 262868106119301
a(22) = 1659699442472225
a(23) = 10511097379593102
a(24) = 66754711794724532
a(25) = 425042894136874547
a(26) = 2712774605779759537
a(27) = 17351924803873950301
a(28) = 111215625138092765752
a(29) = 714178134717729765251
a(30) = 4594248529257237170046
a(31) = 29603265548417261359584
a(32) = 191045446833411670337024
a(33) = 1234708906787529804034607
a(34) = 7990718489586348724436119
a(35) = 51780497680111387335752242
a(36) = 335949812589365341220112511
a(37) = 2182134901189588893803852599
a(38) = 14189310870605689682019965570
a(39) = 92361098172145492590672590974
a(40) = 601786382315511826292004432973
a(41) = 3924643205381700198106970393195
a(42) = 25617877283422343005358956650902
a(43) = 167360583381100994034720642578192
a(44) = 1094242264018218441687029729916607
a(45) = 7159923231160759605436958332402913
a(46) = 46883839122967264822577159404458662
a(47) = 307216243188291654497696144589684371
a(48) = 2014459476187210445480157726964631976
a(n+49) = -3767606827189/5*n*(n+3)*(n+2)*(n+1)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n)+2021/5*(28238316830*n+107365190291)*(n+3)*(n+2)*(n+1)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+1)+1/10*(n+3)*(2937850015385398*n^3+41740968971361747*n^2+196587669037905707*n+306509744999905245)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+3)-1/40*(57338*n^3+8060845*n^2+377574589*n+5892594692)/(n+50)/(n+49)/(2*n+101)*a(n+47)-1/320*(11161090486313*n^4+1815303106738325*n^3+110542506258176710*n^2+2987274516076916536*n+30229987343378104218)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+38)-1/160*(1397473958326*n^4+216563773470975*n^3+12571932477254642*n^2+324010212807851922*n+3127864620193062894)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+39)+1/320*(1004333031115*n^4+163898321148717*n^3+10029159749444384*n^2+272732585882700660*n+2781049349231249928)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+40)-1/640*(237170405486*n^4+40442025214215*n^3+2584924850489563*n^2+73400604469397862*n+781284456669850368)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+41)-1/320*(3394459894*n^4+493921276668*n^3+26114058309077*n^2+585579572412111*n+4560244271972298)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+42)+1/640*(6136991490*n^4+1057759121669*n^3+68349310008075*n^2+1962375602418502*n+21122381501350296)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+43)-1/320*(410241945*n^4+73443528770*n^3+4930700188062*n^2+147126946186693*n+1646337844515876)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+44)+1/80*(3239891*n^4+619149338*n^3+44302284700*n^2+1406874587317*n+16731646684614)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+45)+1/80*(765811*n^4+139517384*n^3+9523243640*n^2+288640063147*n+3277437749970)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+46)+1/640*(23592405948071158*n^4+1838554672523878175*n^3+29879701426565782313*n^2-644276118975941360600*n-15706408913344418725272)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+31)+1/640*(109905585467737568*n^4+14852840585693894845*n^3+752619095443594533943*n^2+16947387913246928559242*n+143088766327097185851096)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+32)-1/320*(27383951364279680*n^4+3756858132200832032*n^3+193261896081863137864*n^2+4418187540507889524733*n+37873004630472380615442)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+33)+1/640*(11285111271059802*n^4+1587693168947198365*n^3+83734400068220877903*n^2+1961997309167643272510*n+17232883764997469888052)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+34)+3/320*(90749746266249*n^4+13075661796062555*n^3+708359480637454974*n^2+17101331772601241991*n+155247470590497361588)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+35)-1/320*(496464566823943*n^4+73838093138246014*n^3+4119346286012481623*n^2+102168753070017360608*n+950525042230363967586)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+36)+1/640*(265469800314274*n^4+40789516164065719*n^3+2350314767739207341*n^2+60190921234148936774*n+578062063886063472768)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+37)+1/320*(29466424275665033319*n^4+2951784723011174636842*n^3+110714475255371122912767*n^2+1842745061723509897002782*n+11483405386731997642324344)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+24)-1/640*(48700903523066779442*n^4+4981077020721326249687*n^3+190809709526821970525053*n^2+3244315214119336658097664*n+20657104025398178364162108)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+25)+1/320*(12766544158333342024*n^4+1337346070708452471074*n^3+52454696318682520561571*n^2+912913282502345706496477*n+5947502795228955649329582)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+26)-1/640*(6850572697097133572*n^4+724124605053318632687*n^3+28603108980924412402003*n^2+500183768713666587529378*n+3265546328358626478845016)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+27)-1/640*(1095182150231720140*n^4+138658618965785370519*n^3+6520871903734645989581*n^2+135201396315248102130714*n+1043929238413855618597404)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+28)+1/160*(474408101665695936*n^4+56721906799189000642*n^3+2540210323419533589477*n^2+50497385327601946223315*n+375952878720834816437982)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+29)-1/640*(742438770388733784*n^4+89698100526323982521*n^3+4055653962786953045439*n^2+81319510782751927686076*n+609959168103285776928468)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+30)-3/20*(n+3)*(n+2)*(514277482176014*n^2+4405429126785254*n+9396926337982697)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+2)-1/40*(24027875084673232*n^4+486731333139426320*n^3+3677414278520319857*n^2+12271910992242903751*n+15248540530093316922)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+4)+3/40*(714533808369091*n^4-29170025834485518*n^3-672308323503434621*n^2-4262107798247729400*n-8596016517272382176)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+5)+1/40*(161426699054292668*n^4+5252482297962464353*n^3+62617357824753755230*n^2+325330818680209958633*n+623086556997783459072)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+6)-1/160*(2434236057501410494*n^4+86821636393050800484*n^3+1146455464407518473355*n^2+6649674628467200823963*n+14306486978573823934464)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+7)+1/80*(2661641226876060215*n^4+105516395853346770897*n^3+1553909654577380284381*n^2+10079684462182074943584*n+24309239015213590584330)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+8)-1/320*(15282750157919709658*n^4+676333184657934871960*n^3+11126371380199943137493*n^2+80667192327398566316519*n+217542936758213717129538)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+9)+1/320*(11849150073753485332*n^4+615321778587984032929*n^3+11738850311502705569777*n^2+97836660472256368847198*n+301313855560040744395428)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+10)+1/320*(6614535911630723275*n^4+171385913342386364616*n^3+406312218740865612701*n^2-18404424759873275742414*n-120363671111476080756624)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+11)-1/640*(82354825250731340918*n^4+3724559200543369105071*n^3+61864092715493979062977*n^2+444099017570051223996048*n+1148981115502212550117308)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+12)+1/320*(83806689305070961418*n^4+4146849813159875182881*n^3+76018177169995886009785*n^2+610065169431970924628556*n+1800766835236262656263396)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+13)-1/640*(240535095690493951244*n^4+12617951173375116933505*n^3+245122423418992007761243*n^2+2083779039284955893950628*n+6512469690773607512113932)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+14)+1/640*(273720309364049278174*n^4+15148953482930377420051*n^3+310089612866803977082805*n^2+2773299349124586372682304*n+9101093245329040426087032)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+15)-1/640*(253858678708561257756*n^4+14907049415478806209699*n^3+324196655836613006826573*n^2+3087766005343445816352110*n+10834551047862484950834216)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+16)+3/320*(31832105202637336254*n^4+2007106207682007427653*n^3+47141568470015328133035*n^2+488955292286476589806141*n+1891097593940168132554214)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+17)-1/640*(117369035455142427782*n^4+8090580405278867449051*n^3+209636772756552719247901*n^2+2425488190666036597495574*n+10602819313907175957584772)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+18)+3/320*(11031482531251448377*n^4+842369726409146808156*n^3+24300757366847579320775*n^2+314359672417914189719357*n+1540803401192894500994300)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+19)-1/320*(21541903879397745871*n^4+1745185370080318340869*n^3+53239846233118006589828*n^2+725475520210016059567118*n+3728900035826397129701310)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+20)+3/640*(8377681239583737686*n^4+651207869789535996117*n^3+18768470992765264520783*n^2+237161978830493576296698*n+1105167422620684615662384)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+21)+1/320*(3267432211933192831*n^4+454271154724284504226*n^3+20769133745246058246587*n^2+393417653024990181936932*n+2674503247666513338315138)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+22)-1/320*(21171084178172935298*n^4+2124283604158655523459*n^3+79561476649751392136917*n^2+1318824022674310040831946*n+8166423963766963017349524)/(n+50)/(n+49)/(n+48)/(2*n+101)*a(n+23)+1/10*(851*n^2+81903*n+1969057)/(2*n+101)/(n+50)*a(n+48), n >= 49
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 581
a(7) = 3139
a(8) = 17500
a(9) = 99772
a(10) = 578776
a(11) = 3405089
a(12) = 20269718
a(13) = 121869038
a(14) = 739015133
a(15) = 4514754917
a(16) = 27760850118
a(17) = 171678490387
a(18) = 1067100692285
a(19) = 6662955903479
a(20) = 41773543226571
a(21) = 262868106119301
a(22) = 1659699442472225
a(23) = 10511097379593102
a(24) = 66754711794724532
a(25) = 425042894136874547
a(26) = 2712774605779759537
a(27) = 17351924803873950301
a(28) = 111215625138092765752
a(29) = 714178134717729765251
a(30) = 4594248529257237170046
a(31) = 29603265548417261359584
a(32) = 191045446833411670337024
a(33) = 1234708906787529804034607
a(34) = 7990718489586348724436119
a(35) = 51780497680111387335752242
a(36) = 335949812589365341220112511
a(37) = 2182134901189588893803852599
a(38) = 14189310870605689682019965570
a(39) = 92361098172145492590672590974
a(40) = 601786382315511826292004432973
a(41) = 3924643205381700198106970393195
a(42) = 25617877283422343005358956650902
a(43) = 167360583381100994034720642578192
a(44) = 1094242264018218441687029729916607
a(45) = 7159923231160759605436958332402913
a(46) = 46883839122967264822577159404458662
a(47) = 307216243188291654497696144589684371
a(48) = 2014459476187210445480157726964631976
a{\left(n + 49 \right)} = - \frac{3767606827189 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) a{\left(n \right)}}{5 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{2021 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(28238316830 n + 107365190291\right) a{\left(n + 1 \right)}}{5 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{3 \left(n + 2\right) \left(n + 3\right) \left(514277482176014 n^{2} + 4405429126785254 n + 9396926337982697\right) a{\left(n + 2 \right)}}{20 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(n + 3\right) \left(2937850015385398 n^{3} + 41740968971361747 n^{2} + 196587669037905707 n + 306509744999905245\right) a{\left(n + 3 \right)}}{10 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(851 n^{2} + 81903 n + 1969057\right) a{\left(n + 48 \right)}}{10 \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(57338 n^{3} + 8060845 n^{2} + 377574589 n + 5892594692\right) a{\left(n + 47 \right)}}{40 \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(765811 n^{4} + 139517384 n^{3} + 9523243640 n^{2} + 288640063147 n + 3277437749970\right) a{\left(n + 46 \right)}}{80 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(3239891 n^{4} + 619149338 n^{3} + 44302284700 n^{2} + 1406874587317 n + 16731646684614\right) a{\left(n + 45 \right)}}{80 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(410241945 n^{4} + 73443528770 n^{3} + 4930700188062 n^{2} + 147126946186693 n + 1646337844515876\right) a{\left(n + 44 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(3394459894 n^{4} + 493921276668 n^{3} + 26114058309077 n^{2} + 585579572412111 n + 4560244271972298\right) a{\left(n + 42 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(6136991490 n^{4} + 1057759121669 n^{3} + 68349310008075 n^{2} + 1962375602418502 n + 21122381501350296\right) a{\left(n + 43 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(237170405486 n^{4} + 40442025214215 n^{3} + 2584924850489563 n^{2} + 73400604469397862 n + 781284456669850368\right) a{\left(n + 41 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(1004333031115 n^{4} + 163898321148717 n^{3} + 10029159749444384 n^{2} + 272732585882700660 n + 2781049349231249928\right) a{\left(n + 40 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(1397473958326 n^{4} + 216563773470975 n^{3} + 12571932477254642 n^{2} + 324010212807851922 n + 3127864620193062894\right) a{\left(n + 39 \right)}}{160 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(11161090486313 n^{4} + 1815303106738325 n^{3} + 110542506258176710 n^{2} + 2987274516076916536 n + 30229987343378104218\right) a{\left(n + 38 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{3 \left(90749746266249 n^{4} + 13075661796062555 n^{3} + 708359480637454974 n^{2} + 17101331772601241991 n + 155247470590497361588\right) a{\left(n + 35 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(265469800314274 n^{4} + 40789516164065719 n^{3} + 2350314767739207341 n^{2} + 60190921234148936774 n + 578062063886063472768\right) a{\left(n + 37 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(496464566823943 n^{4} + 73838093138246014 n^{3} + 4119346286012481623 n^{2} + 102168753070017360608 n + 950525042230363967586\right) a{\left(n + 36 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{3 \left(714533808369091 n^{4} - 29170025834485518 n^{3} - 672308323503434621 n^{2} - 4262107798247729400 n - 8596016517272382176\right) a{\left(n + 5 \right)}}{40 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(11285111271059802 n^{4} + 1587693168947198365 n^{3} + 83734400068220877903 n^{2} + 1961997309167643272510 n + 17232883764997469888052\right) a{\left(n + 34 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(23592405948071158 n^{4} + 1838554672523878175 n^{3} + 29879701426565782313 n^{2} - 644276118975941360600 n - 15706408913344418725272\right) a{\left(n + 31 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(24027875084673232 n^{4} + 486731333139426320 n^{3} + 3677414278520319857 n^{2} + 12271910992242903751 n + 15248540530093316922\right) a{\left(n + 4 \right)}}{40 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(27383951364279680 n^{4} + 3756858132200832032 n^{3} + 193261896081863137864 n^{2} + 4418187540507889524733 n + 37873004630472380615442\right) a{\left(n + 33 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(109905585467737568 n^{4} + 14852840585693894845 n^{3} + 752619095443594533943 n^{2} + 16947387913246928559242 n + 143088766327097185851096\right) a{\left(n + 32 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(161426699054292668 n^{4} + 5252482297962464353 n^{3} + 62617357824753755230 n^{2} + 325330818680209958633 n + 623086556997783459072\right) a{\left(n + 6 \right)}}{40 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(474408101665695936 n^{4} + 56721906799189000642 n^{3} + 2540210323419533589477 n^{2} + 50497385327601946223315 n + 375952878720834816437982\right) a{\left(n + 29 \right)}}{160 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(742438770388733784 n^{4} + 89698100526323982521 n^{3} + 4055653962786953045439 n^{2} + 81319510782751927686076 n + 609959168103285776928468\right) a{\left(n + 30 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(1095182150231720140 n^{4} + 138658618965785370519 n^{3} + 6520871903734645989581 n^{2} + 135201396315248102130714 n + 1043929238413855618597404\right) a{\left(n + 28 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(2434236057501410494 n^{4} + 86821636393050800484 n^{3} + 1146455464407518473355 n^{2} + 6649674628467200823963 n + 14306486978573823934464\right) a{\left(n + 7 \right)}}{160 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(2661641226876060215 n^{4} + 105516395853346770897 n^{3} + 1553909654577380284381 n^{2} + 10079684462182074943584 n + 24309239015213590584330\right) a{\left(n + 8 \right)}}{80 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(3267432211933192831 n^{4} + 454271154724284504226 n^{3} + 20769133745246058246587 n^{2} + 393417653024990181936932 n + 2674503247666513338315138\right) a{\left(n + 22 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(6614535911630723275 n^{4} + 171385913342386364616 n^{3} + 406312218740865612701 n^{2} - 18404424759873275742414 n - 120363671111476080756624\right) a{\left(n + 11 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(6850572697097133572 n^{4} + 724124605053318632687 n^{3} + 28603108980924412402003 n^{2} + 500183768713666587529378 n + 3265546328358626478845016\right) a{\left(n + 27 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{3 \left(8377681239583737686 n^{4} + 651207869789535996117 n^{3} + 18768470992765264520783 n^{2} + 237161978830493576296698 n + 1105167422620684615662384\right) a{\left(n + 21 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{3 \left(11031482531251448377 n^{4} + 842369726409146808156 n^{3} + 24300757366847579320775 n^{2} + 314359672417914189719357 n + 1540803401192894500994300\right) a{\left(n + 19 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(11849150073753485332 n^{4} + 615321778587984032929 n^{3} + 11738850311502705569777 n^{2} + 97836660472256368847198 n + 301313855560040744395428\right) a{\left(n + 10 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(12766544158333342024 n^{4} + 1337346070708452471074 n^{3} + 52454696318682520561571 n^{2} + 912913282502345706496477 n + 5947502795228955649329582\right) a{\left(n + 26 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(15282750157919709658 n^{4} + 676333184657934871960 n^{3} + 11126371380199943137493 n^{2} + 80667192327398566316519 n + 217542936758213717129538\right) a{\left(n + 9 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(21171084178172935298 n^{4} + 2124283604158655523459 n^{3} + 79561476649751392136917 n^{2} + 1318824022674310040831946 n + 8166423963766963017349524\right) a{\left(n + 23 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(21541903879397745871 n^{4} + 1745185370080318340869 n^{3} + 53239846233118006589828 n^{2} + 725475520210016059567118 n + 3728900035826397129701310\right) a{\left(n + 20 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(29466424275665033319 n^{4} + 2951784723011174636842 n^{3} + 110714475255371122912767 n^{2} + 1842745061723509897002782 n + 11483405386731997642324344\right) a{\left(n + 24 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{3 \left(31832105202637336254 n^{4} + 2007106207682007427653 n^{3} + 47141568470015328133035 n^{2} + 488955292286476589806141 n + 1891097593940168132554214\right) a{\left(n + 17 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(48700903523066779442 n^{4} + 4981077020721326249687 n^{3} + 190809709526821970525053 n^{2} + 3244315214119336658097664 n + 20657104025398178364162108\right) a{\left(n + 25 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(82354825250731340918 n^{4} + 3724559200543369105071 n^{3} + 61864092715493979062977 n^{2} + 444099017570051223996048 n + 1148981115502212550117308\right) a{\left(n + 12 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(83806689305070961418 n^{4} + 4146849813159875182881 n^{3} + 76018177169995886009785 n^{2} + 610065169431970924628556 n + 1800766835236262656263396\right) a{\left(n + 13 \right)}}{320 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(117369035455142427782 n^{4} + 8090580405278867449051 n^{3} + 209636772756552719247901 n^{2} + 2425488190666036597495574 n + 10602819313907175957584772\right) a{\left(n + 18 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(240535095690493951244 n^{4} + 12617951173375116933505 n^{3} + 245122423418992007761243 n^{2} + 2083779039284955893950628 n + 6512469690773607512113932\right) a{\left(n + 14 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} - \frac{\left(253858678708561257756 n^{4} + 14907049415478806209699 n^{3} + 324196655836613006826573 n^{2} + 3087766005343445816352110 n + 10834551047862484950834216\right) a{\left(n + 16 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)} + \frac{\left(273720309364049278174 n^{4} + 15148953482930377420051 n^{3} + 310089612866803977082805 n^{2} + 2773299349124586372682304 n + 9101093245329040426087032\right) a{\left(n + 15 \right)}}{640 \left(n + 48\right) \left(n + 49\right) \left(n + 50\right) \left(2 n + 101\right)}, \quad n \geq 49
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24656/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[0,x]^2*F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = -F[47,x]+F[19,x]
F[19,x] = F[20,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = 1/F[16,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[9,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]^2
F[28,x] = F[29,x]+F[32,x]
F[29,x] = -F[0,x]+F[30,x]
F[30,x] = 1/F[16,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]*F[4,x]
F[36,x] = F[0,x]*F[2,x]*F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[2,x]*F[30,x]
F[43,x] = F[37,x]*F[44,x]
F[44,x] = -F[0,x]+F[4,x]
F[45,x] = F[46,x]
F[46,x] = F[16,x]*F[17,x]*F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[16,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[0,x]*F[4,x]
F[52,x] = F[0,x]*F[29,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_0(x)**2*F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_47(x))
Eq(F_19(x), F_20(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x) - F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)**2)
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), -F_0(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_16(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x)*F_4(x))
Eq(F_36(x), F_0(x)*F_2(x)*F_37(x))
Eq(F_37(x), F_0(x) + F_38(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_2(x)*F_30(x))
Eq(F_43(x), F_37(x)*F_44(x))
Eq(F_44(x), -F_0(x) + F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_16(x)*F_17(x)*F_30(x))
Eq(F_47(x), F_0(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_16(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_0(x)*F_4(x))
Eq(F_52(x), F_0(x)*F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], 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[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 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{"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 4], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 4], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 4], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24871/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[0,x]^2*F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = -F[47,x]+F[19,x]
F[19,x] = F[20,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = 1/F[16,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[9,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]^2
F[28,x] = F[29,x]+F[32,x]
F[29,x] = -F[0,x]+F[30,x]
F[30,x] = 1/F[16,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]*F[4,x]
F[36,x] = F[0,x]*F[2,x]*F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[2,x]*F[30,x]
F[43,x] = F[37,x]*F[44,x]
F[44,x] = -F[0,x]+F[4,x]
F[45,x] = F[46,x]
F[46,x] = F[16,x]*F[17,x]*F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[16,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[0,x]*F[4,x]
F[52,x] = F[0,x]*F[29,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_0(x)**2*F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_47(x))
Eq(F_19(x), F_20(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x) - F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)**2)
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), -F_0(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_16(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x)*F_4(x))
Eq(F_36(x), F_0(x)*F_2(x)*F_37(x))
Eq(F_37(x), F_0(x) + F_38(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_2(x)*F_30(x))
Eq(F_43(x), F_37(x)*F_44(x))
Eq(F_44(x), -F_0(x) + F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_16(x)*F_17(x)*F_30(x))
Eq(F_47(x), F_0(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_16(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_0(x)*F_4(x))
Eq(F_52(x), F_0(x)*F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": 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0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24888/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[0,x]^2*F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = -F[47,x]+F[19,x]
F[19,x] = F[20,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = 1/F[16,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[9,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]^2
F[28,x] = F[29,x]+F[32,x]
F[29,x] = -F[0,x]+F[30,x]
F[30,x] = 1/F[16,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]*F[4,x]
F[36,x] = F[0,x]*F[2,x]*F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[2,x]*F[30,x]
F[43,x] = F[37,x]*F[44,x]
F[44,x] = -F[0,x]+F[4,x]
F[45,x] = F[46,x]
F[46,x] = F[16,x]*F[17,x]*F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[16,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[0,x]*F[4,x]
F[52,x] = F[0,x]*F[29,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_0(x)**2*F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_47(x))
Eq(F_19(x), F_20(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x) - F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)**2)
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), -F_0(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_16(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x)*F_4(x))
Eq(F_36(x), F_0(x)*F_2(x)*F_37(x))
Eq(F_37(x), F_0(x) + F_38(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_2(x)*F_30(x))
Eq(F_43(x), F_37(x)*F_44(x))
Eq(F_44(x), -F_0(x) + F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_16(x)*F_17(x)*F_30(x))
Eq(F_47(x), F_0(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_16(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_0(x)*F_4(x))
Eq(F_52(x), F_0(x)*F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 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3, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, 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0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25318/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[0,x]^2*F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = -F[47,x]+F[19,x]
F[19,x] = F[20,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = 1/F[16,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[9,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]^2
F[28,x] = F[29,x]+F[32,x]
F[29,x] = -F[0,x]+F[30,x]
F[30,x] = 1/F[16,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]*F[4,x]
F[36,x] = F[0,x]*F[2,x]*F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[2,x]*F[30,x]
F[43,x] = F[37,x]*F[44,x]
F[44,x] = -F[0,x]+F[4,x]
F[45,x] = F[46,x]
F[46,x] = F[16,x]*F[17,x]*F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[16,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[0,x]*F[4,x]
F[52,x] = F[0,x]*F[29,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_0(x)**2*F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_47(x))
Eq(F_19(x), F_20(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x) - F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)**2)
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), -F_0(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_16(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x)*F_4(x))
Eq(F_36(x), F_0(x)*F_2(x)*F_37(x))
Eq(F_37(x), F_0(x) + F_38(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_2(x)*F_30(x))
Eq(F_43(x), F_37(x)*F_44(x))
Eq(F_44(x), -F_0(x) + F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_16(x)*F_17(x)*F_30(x))
Eq(F_47(x), F_0(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_16(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_0(x)*F_4(x))
Eq(F_52(x), F_0(x)*F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [1, 3, 4, 0, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 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3, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 4], [0, 4], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, 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0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25701/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[0,x]^2*F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = -F[48,x]+F[19,x]
F[19,x] = F[20,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = 1/F[16,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[46,x]
F[25,x] = -F[9,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]^2
F[28,x] = F[29,x]
F[29,x] = F[0,x]*F[16,x]*F[30,x]
F[30,x] = F[31,x]+F[36,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[0,x]+F[34,x]
F[34,x] = 1/F[16,x]*F[35,x]
F[35,x] = F[2,x]
F[36,x] = F[37,x]
F[37,x] = F[16,x]*F[34,x]*F[38,x]
F[38,x] = F[0,x]+F[39,x]
F[39,x] = F[2,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[16,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[2,x]*F[34,x]
F[44,x] = F[38,x]*F[45,x]
F[45,x] = -F[0,x]+F[4,x]
F[46,x] = F[47,x]
F[47,x] = F[16,x]*F[17,x]*F[34,x]
F[48,x] = F[0,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[16,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[0,x]*F[4,x]
F[53,x] = F[0,x]*F[33,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{46}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{38}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right) F_{33}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_0(x)**2*F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_48(x))
Eq(F_19(x), F_20(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_23(x)/F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_46(x))
Eq(F_25(x), F_26(x) - F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_0(x)*F_16(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_36(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_0(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_16(x))
Eq(F_35(x), F_2(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_16(x)*F_34(x)*F_38(x))
Eq(F_38(x), F_0(x) + F_39(x))
Eq(F_39(x), F_2(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_16(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_2(x)*F_34(x))
Eq(F_44(x), F_38(x)*F_45(x))
Eq(F_45(x), -F_0(x) + F_4(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_16(x)*F_17(x)*F_34(x))
Eq(F_48(x), F_0(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_16(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_0(x)*F_4(x))
Eq(F_53(x), F_0(x)*F_33(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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