01342_03142_10342_13042_13402_30142_31042_31402
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3030, 16724, 94608, 545272, 3189000, 18872340, 112779866, 679514008, 4122937606, 25167922580, 154451420008, 952297701396, 5896151321776, 36643283656576, 228503737216904, 1429326441677912, 8965885886777164, 56386895687059192, 355466251344673822, 2245826442501313628, 14218140955315353518, 90185530031538881032, 573064229028994820510, 3647477066430960618660, 23251975008904605853710, 148444611542465006149492, 949006660390786335574592, 6074918000763760916118260, 38935596953997423138785708, 249838829358447256889842160, 1604919941016812290104099300, 10320549125280147070675347688, 66433278929879354530943470000, 428036790472685270939759215384, 2760384508652111998450674316552, 17816935646171125082472749372832, 115094474740830546914993598206008, 744077487077645731877047066900080, 4814035417458883230541541050733572, 31168360030688263198846657327244296, 201938513036393048377335457423691796, 1309220047953368892528431383188277776, 8493426071344294854835183067056274662, 55133947940722315532583872596076591372, 358105467169884759464384102574180579790, 2327280988896044554087038282221254332104, 15132948869162683768659249984438291301786, 98452451153391445152525711717596404471452, 640839891248155414073662996932814996651690, 4173350074840689939605884156579656111641284, 27190988899019776032124360070525934725071402, 177240555484119341541067438097039332342426888, 1155826024581813177456398213972686838821667230, 7540615199788804780438629719652997851300862360, 49215286235427613774480963638047353025200099746, 321341224588693563026005865309310235765184188524, 2098942790196173048630055890232497273751791915966, 13715046138891172111208638655579103031967098769524, 89650245322421037660377020243527471747071596179680, 586217090292074652499374729851103498536771698354908, 3834543848319574738544108801906212531738039726408772, 25090703274546397301618791387860930513136941397845048, 164229697965566975466500985696024904033139032342043064, 1075291725956388957683034322808639506783341206547836472, 7042597159139230681121067790053982982166082000895254948, 46138945464222646432741419441076348329981048756961989584, 302362024668630366003619369147768402107869680405756912348, 1982020854544761610715750240253831606947563653631289784400, 12995929709449070966014153809987626339087588649700160240364, 85235701179192482896097534636253596374394859717736199140320, 559175049555270059256400486320238658336129377055174328478600, 3669299993260000083399923770691069181876219388029423782997488, 24083803683790096018068935281123913710102155626623046983115200, 158114135530961136165210318308516004624984805333536802309819480, 1038287235084026843973425975871118573597225647586822373603256744, 6819665266820786375764093804312777453626869929170716173382506792, 44802778464403526739422604165040358985672391853432810402836561040, 294402088225645924433674416587656196678702014829587972352987956152, 1934945147170387246480196841615417558474388412870647059964963601232, 12719971097719699542438519428012282105809651853341568732412892138920, 83635608500067976216344666422690216072418745499006159828876153232192, 550024396000053663311485579250606815950049014962191016012380544034504, 3617898614953699006470709046241579789943107163186911093854748884940300, 23801957559923315554755935216479771726122641979787903836499217283253568, 156620643219135907078376685965390676351791251236628339210743148711472060, 1030774412809698219472972241119725431944463698951842172642402662444576968, 6785078366920866769855353340992299286612589079585250432307561204456438564, 44670528032373224295663618172961805196815772181856307901563224210629604080, 294144479513588841829665084829049963176202945695377220686555680177068360468, 1937189844115173842151600406531197121631485649110139093295414354467802227392, 12760099065029331500917727699221511272619869032348380464191436134536405016582, 84062993336970120552389561329926197235894730764638216742617018447120862216396, 553889587355801105275653068966455403759028685202794028829211561677091197406518, 3650125054193133492883229180673276058518266525257048269952024179186243721688584
Implicit equation for the generating function in Maple syntax:
-F(x)^6+(2*x^2-3*x+7)*F(x)^5+(-4*x^3-7*x^2+15*x-20)*F(x)^4+(2*x^4+7*x^3+12*x^2-31*x+30)*F(x)^3+(-4*x^4-x^3-13*x^2+33*x-25)*F(x)^2+(x-1)*(x^3-x^2+7*x-11)*F(x)-2*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
-F \! \left(x \right)^{6}+\left(2 x^{2}-3 x +7\right) F \! \left(x \right)^{5}+\left(-4 x^{3}-7 x^{2}+15 x -20\right) F \! \left(x \right)^{4}+\left(2 x^{4}+7 x^{3}+12 x^{2}-31 x +30\right) F \! \left(x \right)^{3}+\left(-4 x^{4}-x^{3}-13 x^{2}+33 x -25\right) F \! \left(x \right)^{2}+\left(x -1\right) \left(x^{3}-x^{2}+7 x -11\right) F \! \left(x \right)-2 \left(x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3030
a(8) = 16724
a(9) = 94608
a(10) = 545272
a(11) = 3189000
a(12) = 18872340
a(13) = 112779866
a(14) = 679514008
a(15) = 4122937606
a(16) = 25167922580
a(17) = 154451420008
a(18) = 952297701396
a(19) = 5896151321776
a(20) = 36643283656576
a(21) = 228503737216904
a(22) = 1429326441677912
a(23) = 8965885886777164
a(24) = 56386895687059192
a(25) = 355466251344673822
a(26) = 2245826442501313628
a(27) = 14218140955315353518
a(28) = 90185530031538881032
a(29) = 573064229028994820510
a(30) = 3647477066430960618660
a(31) = 23251975008904605853710
a(32) = 148444611542465006149492
a(33) = 949006660390786335574592
a(34) = 6074918000763760916118260
a(35) = 38935596953997423138785708
a(36) = 249838829358447256889842160
a(37) = 1604919941016812290104099300
a(38) = 10320549125280147070675347688
a(39) = 66433278929879354530943470000
a(40) = 428036790472685270939759215384
a(41) = 2760384508652111998450674316552
a(42) = 17816935646171125082472749372832
a(43) = 115094474740830546914993598206008
a(44) = 744077487077645731877047066900080
a(45) = 4814035417458883230541541050733572
a(46) = 31168360030688263198846657327244296
a(n+47) = 48/5*(617616454064874*n^5-79384729348888610*n^4-4990982186689823175*n^3-100676686325950138530*n^2-872989249574926102489*n-2803048421737554949170)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+14)+8/5*(131421848193909448*n^5+10067626327861173650*n^4+303678827200360538465*n^3+4522739140154747797720*n^2+33332350588112295161067*n+97414392190319576449650)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+15)-16*(45181220545851251*n^5+3434008447132168384*n^4+103916924619670165495*n^3+1565544500788769106290*n^2+11745052574053106133990*n+35110657113642681271506)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+16)+8/5*(953311396848095269*n^5+75460711633158531680*n^4+2382190639064845099685*n^3+37491273599126987829760*n^2+294165718392391512919896*n+920563505531629535625210)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+17)-4/5*(2986075196508907282*n^5+248590311063100669565*n^4+8259330564302876097485*n^3+136895054390346868625665*n^2+1131887851149054440325573*n+3734798545683822623978790)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+18)+49152*(n+1)*(909270*n^4+13595079*n^3+66932558*n^2+136096063*n+98640894)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+3)+2/5*(448*n^2+39875*n+886833)/(n+47)/(2*n+93)*a(n+46)-4*(1886*n^3+246138*n^2+10706323*n+155213118)/(2*n+93)/(n+47)/(n+46)*a(n+45)-3145728/5*n*(n-1)*(n+1)*(406*n^2+665*n+291)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+1)+262144*n*(n+1)*(4118*n^3-3751*n^2-43216*n-40401)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+2)+6*(32769*n^4+5605114*n^3+359516663*n^2+10248336358*n+109547262168)/(n+45)/(2*n+93)/(n+47)/(n+46)*a(n+44)+25165824/5*n*(n-1)*(n-2)*(2*n-1)*(n+1)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n)-1/5*(n+43)*(17563298*n^4+2945172341*n^3+185198191157*n^2+5175715813614*n+54240738737400)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+43)+24/5*(624247070216599027*n^5+54818303141565806795*n^4+1922310312277667223705*n^3+33647856321160606568815*n^2+293983180116366951167528*n+1025655822318377506760670)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+19)-8/5*(1970930740755408008*n^5+182551050986910083995*n^4+6755126773924562705590*n^3+124833743674791046290590*n^2+1152079720117342524268092*n+4247929379878857571230405)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+20)+4/5*(3538179155811609146*n^5+344869744246956736060*n^4+13434092814903458091055*n^3+261430500046886394616940*n^2+2541591913576640608714149*n+9875390765570027431020270)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+21)-8/5*(1350966080939435101*n^5+138194871689534139350*n^4+5650989693476935926140*n^3+115468083725263415218735*n^2+1179002633617430319309429*n+4812649498721108891674305)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+22)+4/5*(1767879836108839171*n^5+189542851173632926685*n^4+8126000038137534908285*n^3+174134978630711500013245*n^2+1865310752710538825036484*n+7990605458014804708417830)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+23)-2*(411932820125763254*n^5+46346999497893677215*n^4+2086005228940855790566*n^3+46950265158095553163517*n^2+528458512359986869484868*n+2379831047184684882830796)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+24)+4/5*(572886235259146069*n^5+67833392455949589080*n^4+3214400210469102470375*n^3+76201646417186378812240*n^2+903760481636841792497766*n+4290157565989638928885350)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+25)-6/5*(217590402462500689*n^5+27144744909935490545*n^4+1355419769263526853235*n^3+33862347804992852888535*n^2+423270484350090551551856*n+2117718917069046214982700)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+26)+(155910453691014310*n^5+20431309674371487905*n^4+1071455379316840630148*n^3+28106822460268497230551*n^2+368809369219073615837190*n+1936543968969020238778560)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+27)-6*(15618135818809313*n^5+2137735266040948552*n^4+117057607360034590763*n^3+3205295260255050866240*n^2+43888549430042697317432*n+240398496503120752744644)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+28)+4/5*(66043576423588492*n^5+9389373102903869420*n^4+533898693394796531195*n^3+15177567301730307914065*n^2+215705788189258712430948*n+1226093221305392097915270)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+29)-2*(13183020942014822*n^5+1938845147883676993*n^4+114033627807689924716*n^3+3352680290560702539311*n^2+49274111830859147121642*n+289601852395628111883084)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+30)+1/5*(56359727465027998*n^5+8552847683407311755*n^4+519033700832189909900*n^3+15744639025737181033825*n^2+238738112633071203604602*n+1447612987609944433159920)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+31)-4*(1017473949503387*n^5+159069529231348300*n^4+9944705710706242027*n^3+310776394407849197156*n^2+4854620483103866081532*n+30325213285892546895702)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+32)+24/5*(256945930245669*n^5+41335109834601630*n^4+2659122595485235205*n^3+85508495256377680885*n^2+1374458387938102397346*n+8834769273879031152195)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+33)-4/5*(389678724426908*n^5+64431035625163630*n^4+4260084767373069835*n^3+140794285526019721100*n^2+2325918139238942162607*n+15365099986017957973080)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+34)+2/5*(162210625293118*n^5+27525684785774015*n^4+1867699139809815080*n^3+63342172883737618525*n^2+1073725959592995918042*n+7277722878315739988700)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+35)-4/5*(13508677780592*n^5+2347209728753275*n^4+163056949253401090*n^3+5660809223367192215*n^2+98211551525594932188*n+681199197914341577520)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+36)+12/5*(560387574512*n^5+99229911611280*n^4+7022138550774605*n^3+248232406857229560*n^2+4383163390905550043*n+30925925916246532740)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+37)-4/5*(123318885487*n^5+21819270529115*n^4+1539101280253385*n^3+54081134371933015*n^2+946164485217658338*n+6589703951040057300)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+38)-2/5*(8193839008*n^5+1856934501905*n^4+164371806966410*n^3+7146049196850955*n^2+153189390547889682*n+1298990779307215200)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+39)+6/5*(1939002588*n^5+389504500145*n^4+31282750160380*n^3+1255659217192195*n^2+25189453566480212*n+202041750251615880)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+40)-4*(101011969*n^5+20491564676*n^4+1662663540635*n^3+67448191122478*n^2+1367957532200034*n+11096882123154516)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+41)+6/5*(37305381*n^5+7704812035*n^4+636499396035*n^3+26289915863765*n^2+542919579443544*n+4484631419578800)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+42)+256*(320873322310*n^5+7758304578491*n^4+68748580331036*n^3+256932531742861*n^2+283646491053522*n-257698257758028)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+7)-128/5*(4517476131284*n^5+19608472844110*n^4-1649168539495805*n^3-24816441889892800*n^2-132301053074854059*n-246920088668642730)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+8)-128/5*(6725073736426*n^5+761659747262855*n^4+19612521826542080*n^3+212624862807791035*n^2+1058548673477277654*n+2002601600535656430)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+9)+64/5*(193195583364608*n^5+10388640754686475*n^4+213544833714540460*n^3+2127280219448160365*n^2+10355433018033202452*n+19811217941829631080)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+10)-32*(364306364455796*n^5+17764746073851376*n^4+343248631847261941*n^3+3284912768179820858*n^2+15567570481470252999*n+29215834139383337286)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+11)+96/5*(1657375652636702*n^5+80844447955339070*n^4+1551602678241364765*n^3+14577253574181253660*n^2+66556404691724993253*n+116733736758007769670)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+12)-96/5*(2556877209096213*n^5+121525771566718395*n^4+2177653145971761720*n^3+17575008418637832445*n^2+55946198097562152167*n+19814085580846510020)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+13)-4096/5*(1030242116*n^5+19761394180*n^4+144126993595*n^3+504852806510*n^2+853083766269*n+556554827610)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+4)+2048/5*(16817905192*n^5+386160057830*n^4+3455353182425*n^3+15129611276740*n^2+32507197625853*n+27457659484200)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+5)-512/5*(303682184156*n^5+7789692344080*n^4+78594808790845*n^3+390418988274080*n^2+955958280413259*n+924022444956300)/(n+44)/(2*n+93)/(n+47)/(n+46)/(n+45)*a(n+6), n >= 47
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3030
a(8) = 16724
a(9) = 94608
a(10) = 545272
a(11) = 3189000
a(12) = 18872340
a(13) = 112779866
a(14) = 679514008
a(15) = 4122937606
a(16) = 25167922580
a(17) = 154451420008
a(18) = 952297701396
a(19) = 5896151321776
a(20) = 36643283656576
a(21) = 228503737216904
a(22) = 1429326441677912
a(23) = 8965885886777164
a(24) = 56386895687059192
a(25) = 355466251344673822
a(26) = 2245826442501313628
a(27) = 14218140955315353518
a(28) = 90185530031538881032
a(29) = 573064229028994820510
a(30) = 3647477066430960618660
a(31) = 23251975008904605853710
a(32) = 148444611542465006149492
a(33) = 949006660390786335574592
a(34) = 6074918000763760916118260
a(35) = 38935596953997423138785708
a(36) = 249838829358447256889842160
a(37) = 1604919941016812290104099300
a(38) = 10320549125280147070675347688
a(39) = 66433278929879354530943470000
a(40) = 428036790472685270939759215384
a(41) = 2760384508652111998450674316552
a(42) = 17816935646171125082472749372832
a(43) = 115094474740830546914993598206008
a(44) = 744077487077645731877047066900080
a(45) = 4814035417458883230541541050733572
a(46) = 31168360030688263198846657327244296
a{\left(n + 47 \right)} = \frac{25165824 n \left(n - 2\right) \left(n - 1\right) \left(n + 1\right) \left(2 n - 1\right) a{\left(n \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{3145728 n \left(n - 1\right) \left(n + 1\right) \left(406 n^{2} + 665 n + 291\right) a{\left(n + 1 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{262144 n \left(n + 1\right) \left(4118 n^{3} - 3751 n^{2} - 43216 n - 40401\right) a{\left(n + 2 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{49152 \left(n + 1\right) \left(909270 n^{4} + 13595079 n^{3} + 66932558 n^{2} + 136096063 n + 98640894\right) a{\left(n + 3 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{\left(n + 43\right) \left(17563298 n^{4} + 2945172341 n^{3} + 185198191157 n^{2} + 5175715813614 n + 54240738737400\right) a{\left(n + 43 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(448 n^{2} + 39875 n + 886833\right) a{\left(n + 46 \right)}}{5 \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1886 n^{3} + 246138 n^{2} + 10706323 n + 155213118\right) a{\left(n + 45 \right)}}{\left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(32769 n^{4} + 5605114 n^{3} + 359516663 n^{2} + 10248336358 n + 109547262168\right) a{\left(n + 44 \right)}}{\left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(37305381 n^{5} + 7704812035 n^{4} + 636499396035 n^{3} + 26289915863765 n^{2} + 542919579443544 n + 4484631419578800\right) a{\left(n + 42 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(101011969 n^{5} + 20491564676 n^{4} + 1662663540635 n^{3} + 67448191122478 n^{2} + 1367957532200034 n + 11096882123154516\right) a{\left(n + 41 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4096 \left(1030242116 n^{5} + 19761394180 n^{4} + 144126993595 n^{3} + 504852806510 n^{2} + 853083766269 n + 556554827610\right) a{\left(n + 4 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(1939002588 n^{5} + 389504500145 n^{4} + 31282750160380 n^{3} + 1255659217192195 n^{2} + 25189453566480212 n + 202041750251615880\right) a{\left(n + 40 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(8193839008 n^{5} + 1856934501905 n^{4} + 164371806966410 n^{3} + 7146049196850955 n^{2} + 153189390547889682 n + 1298990779307215200\right) a{\left(n + 39 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2048 \left(16817905192 n^{5} + 386160057830 n^{4} + 3455353182425 n^{3} + 15129611276740 n^{2} + 32507197625853 n + 27457659484200\right) a{\left(n + 5 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(123318885487 n^{5} + 21819270529115 n^{4} + 1539101280253385 n^{3} + 54081134371933015 n^{2} + 946164485217658338 n + 6589703951040057300\right) a{\left(n + 38 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{512 \left(303682184156 n^{5} + 7789692344080 n^{4} + 78594808790845 n^{3} + 390418988274080 n^{2} + 955958280413259 n + 924022444956300\right) a{\left(n + 6 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{256 \left(320873322310 n^{5} + 7758304578491 n^{4} + 68748580331036 n^{3} + 256932531742861 n^{2} + 283646491053522 n - 257698257758028\right) a{\left(n + 7 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{12 \left(560387574512 n^{5} + 99229911611280 n^{4} + 7022138550774605 n^{3} + 248232406857229560 n^{2} + 4383163390905550043 n + 30925925916246532740\right) a{\left(n + 37 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(4517476131284 n^{5} + 19608472844110 n^{4} - 1649168539495805 n^{3} - 24816441889892800 n^{2} - 132301053074854059 n - 246920088668642730\right) a{\left(n + 8 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(6725073736426 n^{5} + 761659747262855 n^{4} + 19612521826542080 n^{3} + 212624862807791035 n^{2} + 1058548673477277654 n + 2002601600535656430\right) a{\left(n + 9 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(13508677780592 n^{5} + 2347209728753275 n^{4} + 163056949253401090 n^{3} + 5660809223367192215 n^{2} + 98211551525594932188 n + 681199197914341577520\right) a{\left(n + 36 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(162210625293118 n^{5} + 27525684785774015 n^{4} + 1867699139809815080 n^{3} + 63342172883737618525 n^{2} + 1073725959592995918042 n + 7277722878315739988700\right) a{\left(n + 35 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{64 \left(193195583364608 n^{5} + 10388640754686475 n^{4} + 213544833714540460 n^{3} + 2127280219448160365 n^{2} + 10355433018033202452 n + 19811217941829631080\right) a{\left(n + 10 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(256945930245669 n^{5} + 41335109834601630 n^{4} + 2659122595485235205 n^{3} + 85508495256377680885 n^{2} + 1374458387938102397346 n + 8834769273879031152195\right) a{\left(n + 33 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{32 \left(364306364455796 n^{5} + 17764746073851376 n^{4} + 343248631847261941 n^{3} + 3284912768179820858 n^{2} + 15567570481470252999 n + 29215834139383337286\right) a{\left(n + 11 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(389678724426908 n^{5} + 64431035625163630 n^{4} + 4260084767373069835 n^{3} + 140794285526019721100 n^{2} + 2325918139238942162607 n + 15365099986017957973080\right) a{\left(n + 34 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{48 \left(617616454064874 n^{5} - 79384729348888610 n^{4} - 4990982186689823175 n^{3} - 100676686325950138530 n^{2} - 872989249574926102489 n - 2803048421737554949170\right) a{\left(n + 14 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1017473949503387 n^{5} + 159069529231348300 n^{4} + 9944705710706242027 n^{3} + 310776394407849197156 n^{2} + 4854620483103866081532 n + 30325213285892546895702\right) a{\left(n + 32 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{96 \left(1657375652636702 n^{5} + 80844447955339070 n^{4} + 1551602678241364765 n^{3} + 14577253574181253660 n^{2} + 66556404691724993253 n + 116733736758007769670\right) a{\left(n + 12 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{96 \left(2556877209096213 n^{5} + 121525771566718395 n^{4} + 2177653145971761720 n^{3} + 17575008418637832445 n^{2} + 55946198097562152167 n + 19814085580846510020\right) a{\left(n + 13 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(13183020942014822 n^{5} + 1938845147883676993 n^{4} + 114033627807689924716 n^{3} + 3352680290560702539311 n^{2} + 49274111830859147121642 n + 289601852395628111883084\right) a{\left(n + 30 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(15618135818809313 n^{5} + 2137735266040948552 n^{4} + 117057607360034590763 n^{3} + 3205295260255050866240 n^{2} + 43888549430042697317432 n + 240398496503120752744644\right) a{\left(n + 28 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{16 \left(45181220545851251 n^{5} + 3434008447132168384 n^{4} + 103916924619670165495 n^{3} + 1565544500788769106290 n^{2} + 11745052574053106133990 n + 35110657113642681271506\right) a{\left(n + 16 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(56359727465027998 n^{5} + 8552847683407311755 n^{4} + 519033700832189909900 n^{3} + 15744639025737181033825 n^{2} + 238738112633071203604602 n + 1447612987609944433159920\right) a{\left(n + 31 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(66043576423588492 n^{5} + 9389373102903869420 n^{4} + 533898693394796531195 n^{3} + 15177567301730307914065 n^{2} + 215705788189258712430948 n + 1226093221305392097915270\right) a{\left(n + 29 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(131421848193909448 n^{5} + 10067626327861173650 n^{4} + 303678827200360538465 n^{3} + 4522739140154747797720 n^{2} + 33332350588112295161067 n + 97414392190319576449650\right) a{\left(n + 15 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(155910453691014310 n^{5} + 20431309674371487905 n^{4} + 1071455379316840630148 n^{3} + 28106822460268497230551 n^{2} + 368809369219073615837190 n + 1936543968969020238778560\right) a{\left(n + 27 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(217590402462500689 n^{5} + 27144744909935490545 n^{4} + 1355419769263526853235 n^{3} + 33862347804992852888535 n^{2} + 423270484350090551551856 n + 2117718917069046214982700\right) a{\left(n + 26 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(411932820125763254 n^{5} + 46346999497893677215 n^{4} + 2086005228940855790566 n^{3} + 46950265158095553163517 n^{2} + 528458512359986869484868 n + 2379831047184684882830796\right) a{\left(n + 24 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(572886235259146069 n^{5} + 67833392455949589080 n^{4} + 3214400210469102470375 n^{3} + 76201646417186378812240 n^{2} + 903760481636841792497766 n + 4290157565989638928885350\right) a{\left(n + 25 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(624247070216599027 n^{5} + 54818303141565806795 n^{4} + 1922310312277667223705 n^{3} + 33647856321160606568815 n^{2} + 293983180116366951167528 n + 1025655822318377506760670\right) a{\left(n + 19 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(953311396848095269 n^{5} + 75460711633158531680 n^{4} + 2382190639064845099685 n^{3} + 37491273599126987829760 n^{2} + 294165718392391512919896 n + 920563505531629535625210\right) a{\left(n + 17 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1350966080939435101 n^{5} + 138194871689534139350 n^{4} + 5650989693476935926140 n^{3} + 115468083725263415218735 n^{2} + 1179002633617430319309429 n + 4812649498721108891674305\right) a{\left(n + 22 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(1767879836108839171 n^{5} + 189542851173632926685 n^{4} + 8126000038137534908285 n^{3} + 174134978630711500013245 n^{2} + 1865310752710538825036484 n + 7990605458014804708417830\right) a{\left(n + 23 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1970930740755408008 n^{5} + 182551050986910083995 n^{4} + 6755126773924562705590 n^{3} + 124833743674791046290590 n^{2} + 1152079720117342524268092 n + 4247929379878857571230405\right) a{\left(n + 20 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(2986075196508907282 n^{5} + 248590311063100669565 n^{4} + 8259330564302876097485 n^{3} + 136895054390346868625665 n^{2} + 1131887851149054440325573 n + 3734798545683822623978790\right) a{\left(n + 18 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(3538179155811609146 n^{5} + 344869744246956736060 n^{4} + 13434092814903458091055 n^{3} + 261430500046886394616940 n^{2} + 2541591913576640608714149 n + 9875390765570027431020270\right) a{\left(n + 21 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)}, \quad n \geq 47
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24445/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[53,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[16,x]
F[14,x] = 1/F[11,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 2+F[19,x]^2+(-2+x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = 1/F[11,x]/F[47,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[32,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[19,x]+F[9,x]
F[32,x] = F[33,x]+F[9,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[16,x]*F[37,x]
F[37,x] = F[19,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[37,x]^2*F[11,x]
F[40,x] = F[41,x]
F[41,x] = F[11,x]*F[16,x]*F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[25,x]+F[45,x]
F[45,x] = 1/F[11,x]*F[46,x]
F[46,x] = F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]
F[50,x] = 1/F[11,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[0,x]+F[14,x]
F[53,x] = F[54,x]
F[54,x] = F[11,x]*F[16,x]*F[50,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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{53}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{47}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{37} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{46}\! \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_{11}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{50}\! \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_11(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_11(x)*F_7(x))
Eq(F_7(x), F_53(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_16(x))
Eq(F_14(x), F_15(x)/F_11(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), (x - 2)*F_19(x) + F_19(x)**2 + 2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_47(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_32(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), -F_19(x) + F_9(x))
Eq(F_32(x), F_33(x) + F_9(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_16(x)*F_37(x))
Eq(F_37(x), F_19(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x)**2)
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_11(x)*F_16(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_25(x) + F_45(x))
Eq(F_45(x), F_46(x)/F_11(x))
Eq(F_46(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_11(x)*F_50(x))
Eq(F_50(x), F_51(x)/F_11(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_0(x) + F_14(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_11(x)*F_16(x)*F_50(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 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"OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24783/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[27,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[11,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[11,x,k[0]] = k[0]*F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[15,x,k[0]]+F[16,x,k[0]]
F[15,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[17,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[15,x,k[0]]+F[18,x,k[0]]+F[26,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[19,x,k[0]] = F[20,x,1,k[0]]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[21,x,k[0],k[1]] = F[1,x]+F[11,x,k[1]]+F[15,x,k[1]]+F[22,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[3,x]
F[23,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[24,x,k[0],k[1]] = k[0]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[3,x]
F[26,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[27,x] = F[3,x]*F[6,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = y F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , 1, y\right)
F_{20}\! \left(x , y , z\right) = -\frac{-y F_{21}\! \left(x , y , z\right)+F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{21}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , z\right)+F_{15}\! \left(x , z\right)+F_{22}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y , z\right) = -\frac{-y F_{21}\! \left(x , y , z\right)+F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{24}\! \left(x , y , z\right) = y F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{27}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_27(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_11(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_11(x, k_0), k_0*F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_11(x, k_0) + F_15(x, k_0) + F_16(x, k_0))
Eq(F_15(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_17(x, k_0), F_1(x) + F_11(x, k_0) + F_15(x, k_0) + F_18(x, k_0) + F_26(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_19(x, k_0), F_20(x, 1, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, k_1) + F_21(x, 1, k_1))/(1 - k_0))
Eq(F_21(x, k_0, k_1), F_1(x) + F_11(x, k_1) + F_15(x, k_1) + F_22(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_3(x))
Eq(F_23(x, k_0, k_1), (k_0*F_21(x, k_0, k_1) - F_21(x, 1, k_1))/(k_0 - 1))
Eq(F_24(x, k_0, k_1), k_0*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_23(x, k_0, k_1)*F_3(x))
Eq(F_26(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_27(x), F_3(x)*F_6(x))
Pack JSON:
{"name": "col_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 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": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], 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3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 5], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 4]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 4], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 3]], [[1, 0], [1, 1], [1, 2], [1, 4], [1, 5]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 4], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25124/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[52,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[16,x]
F[14,x] = 1/F[11,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 2+F[19,x]^2+(-2+x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[29,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[0,x]+F[9,x]
F[29,x] = F[30,x]+F[9,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[33,x]+F[37,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[19,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]^2*F[11,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]*F[16,x]*F[39,x]
F[39,x] = 1/F[11,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = -F[25,x]+F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[28,x]
F[45,x] = (1+F[45,x])*x+F[45,x]^2
F[46,x] = F[0,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = 1/F[11,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[0,x]+F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[16,x]*F[49,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{52}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{28}\! \left(x \right)
F_{45}\! \left(x \right) = F_{45}\! \left(x \right) x +F_{45} \left(x \right)^{2}+x
F_{46}\! \left(x \right) = F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{49}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(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_11(x)*F_7(x))
Eq(F_7(x), F_52(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_16(x))
Eq(F_14(x), F_15(x)/F_11(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), (x - 2)*F_19(x) + F_19(x)**2 + 2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_29(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_0(x) + F_9(x))
Eq(F_29(x), F_30(x) + F_9(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_37(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_19(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_34(x)**2)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x)*F_16(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_11(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), -F_25(x) + F_42(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_28(x) - F_45(x))
Eq(F_45(x), (x - 3)*(F_45(x) + 1) + (F_45(x) + 1)**2 + F_45(x) + 2)
Eq(F_46(x), F_0(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_11(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), -F_0(x) + F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_16(x)*F_49(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 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"rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [3, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [3, 2]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 4], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 5], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[3, 5], [3, 5], [3, 5]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 5], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 5], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 5], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 2]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 5], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 5], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 5], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 6], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[3, 6], [3, 6], [3, 6]]}, {"patt": [2, 0, 1], "pos": [[0, 5], [0, 3], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 6], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 6], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 5], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 6], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25459/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[53,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[16,x]
F[14,x] = 1/F[11,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 2+F[19,x]^2+(-2+x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = 1/F[11,x]/F[47,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[32,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[19,x]+F[9,x]
F[32,x] = F[33,x]+F[9,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[16,x]*F[37,x]
F[37,x] = F[19,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[37,x]^2*F[11,x]
F[40,x] = F[41,x]
F[41,x] = F[11,x]*F[16,x]*F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[25,x]+F[45,x]
F[45,x] = 1/F[11,x]*F[46,x]
F[46,x] = F[30,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]
F[50,x] = 1/F[11,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[0,x]+F[14,x]
F[53,x] = F[54,x]
F[54,x] = F[11,x]*F[16,x]*F[50,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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{53}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{47}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{37} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{46}\! \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_{11}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{50}\! \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_11(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_11(x)*F_7(x))
Eq(F_7(x), F_53(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_16(x))
Eq(F_14(x), F_15(x)/F_11(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), (x - 2)*F_19(x) + F_19(x)**2 + 2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_47(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_32(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), -F_19(x) + F_9(x))
Eq(F_32(x), F_33(x) + F_9(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_16(x)*F_37(x))
Eq(F_37(x), F_19(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x)**2)
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_11(x)*F_16(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_25(x) + F_45(x))
Eq(F_45(x), F_46(x)/F_11(x))
Eq(F_46(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_11(x)*F_50(x))
Eq(F_50(x), F_51(x)/F_11(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_0(x) + F_14(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_11(x)*F_16(x)*F_50(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 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0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 2]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 5], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 5], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 5], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 5], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 6], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[3, 6], [3, 6], [3, 6]]}, {"patt": [2, 0, 1], "pos": [[0, 5], [0, 3], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 6], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 6], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 5], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 6], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25615/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[52,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[16,x]
F[14,x] = 1/F[11,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 2+F[19,x]^2+(-2+x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[29,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[0,x]+F[9,x]
F[29,x] = F[30,x]+F[9,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[33,x]+F[37,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[19,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]^2*F[11,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]*F[16,x]*F[39,x]
F[39,x] = 1/F[11,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = -F[25,x]+F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[28,x]
F[45,x] = (1+F[45,x])*x+F[45,x]^2
F[46,x] = F[0,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = 1/F[11,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[0,x]+F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[16,x]*F[49,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{52}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{28}\! \left(x \right)
F_{45}\! \left(x \right) = F_{45}\! \left(x \right) x +F_{45} \left(x \right)^{2}+x
F_{46}\! \left(x \right) = F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{49}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(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_11(x)*F_7(x))
Eq(F_7(x), F_52(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_16(x))
Eq(F_14(x), F_15(x)/F_11(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), (x - 2)*F_19(x) + F_19(x)**2 + 2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_29(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_0(x) + F_9(x))
Eq(F_29(x), F_30(x) + F_9(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_37(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_19(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_34(x)**2)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x)*F_16(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_11(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), -F_25(x) + F_42(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_28(x) - F_45(x))
Eq(F_45(x), (x - 3)*(F_45(x) + 1) + (F_45(x) + 1)**2 + F_45(x) + 2)
Eq(F_46(x), F_0(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_11(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), -F_0(x) + F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_16(x)*F_49(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 0, 1, 4, 2], [3, 1, 0, 4, 2], [3, 1, 4, 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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 4, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "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": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 4, 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": 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