01342_01423_01432_10342_10423_10432_14023_14032
Counting sequence:
1, 1, 2, 6, 24, 112, 564, 2962, 15979, 87859, 490111, 2765506, 15751689, 90427297, 522637799, 3038435130, 17755947580, 104240384583, 614500651695, 3636061794753, 21588200582950, 128573596366639, 767940324813101, 4598826613773475, 27607376734175875, 166106182569093219, 1001523055562012760, 6050473492996107670, 36619775678126661806, 222018764347215037957, 1348235147786662996297, 8199772713234994099679, 49941312419702632545380, 304582499804427990862636, 1859963807673270299185705, 11371789089113481145999831, 69606584236156526836900267, 426524107060818220121482431, 2616284313312028204784916056, 16063953098757297709538258472, 98724654351695353636122196650, 607275112194017657138116871272, 3738645146437149545446515117913, 23035376349819287398528338223830, 142040813301600316116450971336349, 876502604999921150955678619075474, 5412549081889987322702280249410397, 33446158547007658043138999244196048, 206811341700337971720651504519842039, 1279601768198336009243451124430711782, 7922039393691333891589357492558700934, 49073922518480966652199105844493182451, 304163181604339116198448716712813884097, 1886234195447996922554118107846948107799, 11703322725347986747324261220247343975960, 72650614092099378126547673444631146185270, 451209574014560013504544270584920938208420, 2803618973145672345918311397405956216425007, 17428277581758303455663914163712542704044083, 108387252895527183617197792600766844912498264, 674347888665114965303089483327334730877780110, 4197260623568291237131437562643002798231533035, 26134752098394464132353639939969141197161395779, 162793095368037380608675728007610777621481209488, 1014410201522325733866252330604008737120677862436, 6323337790158689511352829072683484557771775300517, 39430259810689092073156397173801320200116592483790, 245956848068265460354754615159892277404774915101117, 1534722849106113485547789948560336096589688795504917, 9579408163687924012883422948101975032014908121966782, 59811014556271417880519485015365256092281206420836948, 373554255337533737370990175591850321528720805160568433, 2333740940633456510602692483370325657733853708491985150, 14583930873832299638108555030703445162853565144030469252, 91162502696736197118256353095387707232997534663957205350, 569999399529974721257726052567975463723102210712720144444, 3564889100029360779305856894321470199261826570872604108880, 22301197573646130390062197371399272218789297305188890505398, 139546215391351193882835248444381304007042075109490576186666, 873399507223357589480107580492812211159517412743358954349164, 5467769688418423728322457233957188627495892626382842970807753, 34237918834686162535236466668113775978876886494639914401959437, 214438101144705360193199611524425774436043845085684653854895618, 1343357672409316791863758566109739189037806211952975015749023230, 8417327503392288933400298419209654847427126508398621550958827059, 52753037677842693312560968904807554892537818969111903044323146033, 330681046023742440256879339402736282400314975269260805402945395806, 2073278707100759165879858681965671619887507369341390101783189851407, 13001416395563020057026569695640101147066231668341859313080260394351, 81546692303929364577182701872163437654681512846250157139838947181467, 511567450164870788636151382715390471264415005658209629306354038511891, 3209804326028241129134769005218506584222888160044928217391404094066908, 20143345425263273755658769063296388335799886502602295473211249922450176, 126432979336729869142268129464625763763169469301137529165685959332729153, 793712587680038730129593376350949732751203624269718178840389063148528536, 4983549003375021268695514871400618175228618896585300091670931776695495193, 31295742570648078687640855984615528675707825041822892830894569697344453891, 196562827559351031284172275708463926821985209550567211907016679317109260038, 1234768971834348849664371715394143208839223105457093533954364448775287963377, 7757768904421073018953084023035929054443023427969741971060320306081192658426, 48747623784273511095154155319513768668270471000036623668978708426847964812568
Implicit equation for the generating function in Maple syntax:
-x*(2*x^3-7*x^2+8*x-2)*F(x)^9+(x^4-x^3-18*x^2+37*x-11)*x*F(x)^8+(5*x^4+20*x^3-86*x^2+32*x-1)*F(x)^7+(-4*x^4-12*x^3+133*x^2-62*x+5)*F(x)^6+(2*x^4-145*x^2+80*x-10)*F(x)^5+(5*x^3+114*x^2-67*x+10)*F(x)^4+(-3*x^3-66*x^2+36*x-5)*F(x)^3+(x^3+27*x^2-12*x+1)*F(x)^2-x*(7*x-2)*F(x)+x^2 = 0
Implicit equation for the generating function in latex syntax:
-x \left(2 x^{3}-7 x^{2}+8 x -2\right) F \! \left(x \right)^{9}+\left(x^{4}-x^{3}-18 x^{2}+37 x -11\right) x F \! \left(x \right)^{8}+\left(5 x^{4}+20 x^{3}-86 x^{2}+32 x -1\right) F \! \left(x \right)^{7}+\left(-4 x^{4}-12 x^{3}+133 x^{2}-62 x +5\right) F \! \left(x \right)^{6}+\left(2 x^{4}-145 x^{2}+80 x -10\right) F \! \left(x \right)^{5}+\left(5 x^{3}+114 x^{2}-67 x +10\right) F \! \left(x \right)^{4}+\left(-3 x^{3}-66 x^{2}+36 x -5\right) F \! \left(x \right)^{3}+\left(x^{3}+27 x^{2}-12 x +1\right) F \! \left(x \right)^{2}-x \left(7 x -2\right) F \! \left(x \right)+x^{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) = 564
a(7) = 2962
a(8) = 15979
a(9) = 87859
a(10) = 490111
a(11) = 2765506
a(12) = 15751689
a(13) = 90427297
a(14) = 522637799
a(15) = 3038435130
a(16) = 17755947580
a(17) = 104240384583
a(18) = 614500651695
a(19) = 3636061794753
a(20) = 21588200582950
a(21) = 128573596366639
a(22) = 767940324813101
a(23) = 4598826613773475
a(24) = 27607376734175875
a(25) = 166106182569093219
a(26) = 1001523055562012760
a(27) = 6050473492996107670
a(28) = 36619775678126661806
a(29) = 222018764347215037957
a(30) = 1348235147786662996297
a(31) = 8199772713234994099679
a(32) = 49941312419702632545380
a(33) = 304582499804427990862636
a(34) = 1859963807673270299185705
a(35) = 11371789089113481145999831
a(36) = 69606584236156526836900267
a(37) = 426524107060818220121482431
a(38) = 2616284313312028204784916056
a(39) = 16063953098757297709538258472
a(40) = 98724654351695353636122196650
a(41) = 607275112194017657138116871272
a(42) = 3738645146437149545446515117913
a(43) = 23035376349819287398528338223830
a(44) = 142040813301600316116450971336349
a(45) = 876502604999921150955678619075474
a(46) = 5412549081889987322702280249410397
a(47) = 33446158547007658043138999244196048
a(48) = 206811341700337971720651504519842039
a(49) = 1279601768198336009243451124430711782
a(50) = 7922039393691333891589357492558700934
a(51) = 49073922518480966652199105844493182451
a(52) = 304163181604339116198448716712813884097
a(53) = 1886234195447996922554118107846948107799
a(54) = 11703322725347986747324261220247343975960
a(55) = 72650614092099378126547673444631146185270
a(56) = 451209574014560013504544270584920938208420
a(57) = 2803618973145672345918311397405956216425007
a(58) = 17428277581758303455663914163712542704044083
a(59) = 108387252895527183617197792600766844912498264
a(60) = 674347888665114965303089483327334730877780110
a(61) = 4197260623568291237131437562643002798231533035
a(62) = 26134752098394464132353639939969141197161395779
a(63) = 162793095368037380608675728007610777621481209488
a(64) = 1014410201522325733866252330604008737120677862436
a(65) = 6323337790158689511352829072683484557771775300517
a(66) = 39430259810689092073156397173801320200116592483790
a(67) = 245956848068265460354754615159892277404774915101117
a(68) = 1534722849106113485547789948560336096589688795504917
a(69) = 9579408163687924012883422948101975032014908121966782
a(70) = 59811014556271417880519485015365256092281206420836948
a(71) = 373554255337533737370990175591850321528720805160568433
a(72) = 2333740940633456510602692483370325657733853708491985150
a(73) = 14583930873832299638108555030703445162853565144030469252
a(74) = 91162502696736197118256353095387707232997534663957205350
a(75) = 569999399529974721257726052567975463723102210712720144444
a(76) = 3564889100029360779305856894321470199261826570872604108880
a(77) = 22301197573646130390062197371399272218789297305188890505398
a(78) = 139546215391351193882835248444381304007042075109490576186666
a(79) = 873399507223357589480107580492812211159517412743358954349164
a(80) = 5467769688418423728322457233957188627495892626382842970807753
a(81) = 34237918834686162535236466668113775978876886494639914401959437
a(82) = 214438101144705360193199611524425774436043845085684653854895618
a(83) = 1343357672409316791863758566109739189037806211952975015749023230
a(84) = 8417327503392288933400298419209654847427126508398621550958827059
a(85) = 52753037677842693312560968904807554892537818969111903044323146033
a(86) = 330681046023742440256879339402736282400314975269260805402945395806
a(87) = 2073278707100759165879858681965671619887507369341390101783189851407
a(88) = 13001416395563020057026569695640101147066231668341859313080260394351
a(89) = 81546692303929364577182701872163437654681512846250157139838947181467
a(90) = 511567450164870788636151382715390471264415005658209629306354038511891
a(91) = 3209804326028241129134769005218506584222888160044928217391404094066908
a(92) = 20143345425263273755658769063296388335799886502602295473211249922450176
a(93) = 126432979336729869142268129464625763763169469301137529165685959332729153
a(94) = 793712587680038730129593376350949732751203624269718178840389063148528536
a(95) = 4983549003375021268695514871400618175228618896585300091670931776695495193
a(96) = 31295742570648078687640855984615528675707825041822892830894569697344453891
a(97) = 196562827559351031284172275708463926821985209550567211907016679317109260038
a(98) = 1234768971834348849664371715394143208839223105457093533954364448775287963377
a(99) = 7757768904421073018953084023035929054443023427969741971060320306081192658426
a(100) = 48747623784273511095154155319513768668270471000036623668978708426847964812568
a(101) = 306361546065425205609702896864203988873877325899372769907537962116232371184495
a(102) = 1925652815693671781119901772820493964412812575737482470354051499379441000855374
a(103) = 12105519786606224283662117488670648257776830298796570664638282343226213271728870
a(104) = 76111350497242640240890711136610851588264401852641401372989824503281661914238061
a(105) = 478602318060020631917602825581439073869826129211678051331068417568095102963615140
a(106) = 3009944127331366934593576675025214709809791970854782005342182394491416210301459388
a(107) = 18932120099507702991071473428181908035184066276969358363005962522646462083944471103
a(108) = 119095730445042273993675621838094563536002966407315144239910864783695794738625303084
a(109) = 749287058781220213383178069960136002629515111593127878409328835287788918611281936271
a(110) = 4714703328199136209054537699488681042858096828127340381116944424477536427986869434788
a(111) = 29669732791582007210271901279987779573750426838609301728739978068187485607002234530592
a(112) = 186734722531648277199390113562341464624750663231714501142777715800829477170287474017980
a(113) = 1175405682224537189977646826485647169673341696490015612894661214682679566240300362043695
a(114) = 7399474088613559208154300041238604474308584093218768595810639986302390473335379475093378
a(115) = 46586856892042132429080037602712784749305566454736506602564881876192170902636041820177353
a(116) = 293342240973301198795704656525484397128523426885868950813104371611002329659253544769840858
a(117) = 1847283745896143987436869499187385304493779455989414464775610683548899912012233288977339158
a(118) = 11634282708809089999569239106139290487482752763322066515273717050497635362758301860921495348
a(119) = 73281074565560055386551191570056025636139304803743778320040406394258325176675388140485013612
a(120) = 461625179292876475283512540422557761997177683900751859659678042179395626099468752635540069953
a(121) = 2908250720505486800037687173154584695520856012450593869705502609953656635553676611703827161550
a(122) = 18323910553571902470342211742015785265158315768340356310060476675060688228054911334620123230482
a(123) = 115464301462253075282442178997975944601898843559950748154021116266886559965433227425807367686638
a(124) = 727645514402665546410011904599536752380001681689674019165719065778689649359696297898773880677904
a(125) = 4585997944292127937038959544844595235079701130317881407694424788975200385439764065563636602163705
a(126) = 28906071133374028262478375026901276727450268860966028483283923118018555420627737075765998919383390
a(127) = 182215301081489049348278869984893480177541520974573436571908571582952284976331034784845318822795635
a(n+128) = 1/161280*(1106478364288*n^7+964354115870528*n^6+360204322745911000*n^5+74745382195891407140*n^4+9306077131347493832062*n^3+695177611917711697293827*n^2+28850145930879372116429745*n+513120177435817483746212700)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(4*n+507)/(2*n+257)*a(n+126)-1/21646635171840*(16931541387485452070655222097818962070633129455059*n^8+3809877512901722870824854406073076222373838500185043*n^7+373624020590504961372878489817434347040564188391562953*n^6+20866537415660626758257244852161007910036817405365230013*n^5+726161309878988614307850941848843097241269321439938290736*n^4+16129054913796025901411930047284407599106323739904727472032*n^3+223347002197058137864653007166423947331083025555465485710412*n^2+1763244837189375057733059793354718872898878895471182075191432*n+6077042199699973410124728213361999919617273796122271226493920)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+25)-1/64939905515520*(153209838218284427662176799254031880005668575864074*n^8+36058585395921576334106136743077274112484605633188687*n^7+3696521869172784070587737453799904172959852621149181087*n^6+215693828964614764569565958066229820048437322236283090205*n^5+7838494211158067705383813519477983960998338613631443985751*n^4+181727056922651440736381851019126017645224965350759252765268*n^3+2625526162860766656777693298140420552639531768958516360097688*n^2+21617424683265212907092202438799219222541607315661230398326200*n+77675290876091672534951703072592111125566902901145310810486560)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+26)-1/21646635171840*(136494624740571370846669737744581145632277238245731*n^8+33556058792617247194868963076091226231548980929654976*n^7+3591735517998989428459997121941494486526819739200660189*n^6+218733735726978408721528156634750625205337031951553069377*n^5+8292811590263974889896017407956066531085970453618216822254*n^4+200498899949710587374813688903098132861879976443663427485799*n^3+3019766668395329088655816374350027585615742830272809376315866*n^2+25910567956405520376923835979246648880385736124107640156986368*n+96991411310553352273319705447369224413867082407823291721001120)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+27)-1/9277129359360*(143948565742438946626398901757595844101537968622602*n^8+36859548933740631029075560756769276502943035836853382*n^7+4109236072697913871074274595214235758718996535811664655*n^6+260618471044323109454409310584695392658655294520514923549*n^5+10288594636820768792152948258996385536218119036618410761413*n^4+258969830945614223538700786386777432418371825568986944869813*n^3+4059790854617068672359222540343058856434044379059742508890730*n^2+36249905339159438956574657808388362791227736174545265148044496*n+141178600168701801716312689964606006301938436086315907545156640)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+28)-1/64939905515520*(3031206137485231801039959085056440981091728702395*n^8+618487176691877294774134596457381987493282604047378*n^7+55114661915908539643578067036450128839546086046603416*n^6+2802653400534647373376446902117549821070864374994621126*n^5+88974334722643843263801096827804543321181468357655323625*n^4+1806026199186134469263467235960571581650711031151212434472*n^3+22892319718519703757494541243273815223471160736967484982724*n^2+165678335687558245947654975663125496639998240094219657637824*n+524173312160190272742247035758386527086247310491445145410560)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+23)-1/21646635171840*(4768739014710745915308520127600321868926703535501*n^8+1023728383527657676874822025394773322828548449295541*n^7+95856061193587781657158630653585824266246622567549551*n^6+5115272549772051638084102798657308257322455352375653343*n^5+170209944795531658692164583042201995024705041033737828604*n^4+3617186508851599838616924970943791918894395110843118791524*n^3+47951908620833832307922732037189217291240821468581084151024*n^2+362604438118142143764162544680259410403121879619880300367472*n+1197612743145069742261276212552485439304186782213525648237120)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+24)+94143178827/41943040*(3*n+5)*(3*n+4)*(n+2)*(752782842*n^5+7935097149*n^4+30323713487*n^3+49582061351*n^2+29113571631*n-177660)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+1)+1/1202590842880*(2147016700781041528844755514313417069039754979*n^8+388290065220884421590933865320429300062608883453*n^7+30560843239122046630352545960489074978258292831084*n^6+1367797756785428392892912661816041085103443863169982*n^5+38089679510678427505205965170757242912003643441982411*n^4+676038943027312333864113808172296438946870084115185957*n^3+7470540359665010478802607740414138953115600194549122446*n^2+47006113712119310803812493473961961005267128177993420488*n+128975463245202854489505189807306813526385048397800484480)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2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507)/(2*n+257)*a(n+60)-1/259759622062080*(17859981317119677922814022176723948236007967149449544893*n^8+12804904523722978962704900590603110237661432448347049850488*n^7+3579521200929957028658739703888093047566579120365699871752462*n^6+531101331566342892253484582133599274391080120776255694024487604*n^5+46767554821255154794873243299717140049415799652815393781415706137*n^4+2536219701302443219861565419191972642549788268122353537236327066692*n^3+83434210867331745865977046965618983905891960451414022085349084335068*n^2+1531323801373332987975896565774132069538061022895849902633657667160016*n+12056230587568900476766568369286091280995830158475319067640574890519360)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+53)+1/21646635171840*(76159312174158107478348465220782781509906063373718686314*n^8+33201297186678717169350890150174290772207691839244616719035*n^7+6306151937857147658987588094188191751049225851377209088049533*n^6+681601029222606515849400653272325445736342206445141012686197303*n^5+45851163743409553952590354970798690397075106009304058801916048651*n^4+1965569967023079733647305412803100062186256551524274457434342863010*n^3+52431360110255997834110116294679176885484625597178658625616190014582*n^2+795549693727933753845645515584952120432879032718533082972072185065972*n+5255794877731535675441084039821560501576543349103858233210871763182640)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+54)-1/2520*(60366368*n^5+37825838256*n^4+9480491261232*n^3+1188042404560234*n^2+74437520607251595*n+1865523557825012475)/(2*n+253)/(4*n+505)/(n+128)/(4*n+507)/(2*n+257)*a(n+127)+1/259759622062080*(508649668646666387779186955273345321279456373595013909189*n^8+259044467105493042586547948694567248624499372694754603493748*n^7+57162848337650352088229793085383675469231661955555391676980358*n^6+7148612126222873754947074029997608859239134375442686394495475780*n^5+554732044970624767359774553977329208453416948351368228137009364841*n^4+27375945654286036788521301210586651493087961824985894470885320183432*n^3+839611640565281956652600921892306422893410307052619530789107277793132*n^2+14639887568704459034681268718862684981483627790106317452268826831701600*n+111164351165149432371056145034333013894092451995084936511163123549384000)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+57)+531441/75161927680*(51713953566927839173543570510*n^8+4028201381507465413800865242473*n^7+136480186961149028843437630202255*n^6+2627846836416112478187928069913009*n^5+31457092080877062352119716892746035*n^4+239770605646476317783373797391361582*n^3+1136531304435107167085867131474960760*n^2+3063292289686704015535592940293899456*n+3594592427222118402529774303146114240)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+8)+177147/75161927680*(3925305696698281346649324192374*n^8+336351126374946880742835984787183*n^7+12554871950288804312074102584032065*n^6+266666715224173512644635705242170723*n^5+3525526029995663902382283777168938661*n^4+29710635411847539334858737509858293902*n^3+155868699854519410101637609172478480300*n^2+465441416570304900078637268439847280232*n+605699567293753841977784362117398718560)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+9)+1/31708938240*(3659567973420730574081538693392852*n^8+3311381003091063734956524439365973276*n^7+1310831018606909346944291932032723971075*n^6+296501053866158421772646362964065454813977*n^5+41914633271909645524276124003356211880904583*n^4+3791969266483711012751758612567277973841779169*n^3+214399392719547927489114570252530783554590484770*n^2+6926656970625060800459923761031818951204354940218*n+97899652638590876156011571557994451642947352955440)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+115)-1/15854469120*(140169274233459923611741929553760*n^8+127957608248558591543946244001409124*n^7+51102155729178538881626779967889331850*n^6+11661540425126401178932692124674324407062*n^5+1663160501139134172581995916766846617845775*n^4+151800700456428878256091555502302235780541016*n^3+8659138388467473432624336175908183469467084075*n^2+282240078442232878160780462534417656627765723338*n+4024591108257353325780227607952254126080976920760)/(2*n+253)/(2*n+251)/(4*n+505)/(n+128)/(n+127)/(n+126)/(4*n+507)/(2*n+257)*a(n+116), n >= 128
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 564
a(7) = 2962
a(8) = 15979
a(9) = 87859
a(10) = 490111
a(11) = 2765506
a(12) = 15751689
a(13) = 90427297
a(14) = 522637799
a(15) = 3038435130
a(16) = 17755947580
a(17) = 104240384583
a(18) = 614500651695
a(19) = 3636061794753
a(20) = 21588200582950
a(21) = 128573596366639
a(22) = 767940324813101
a(23) = 4598826613773475
a(24) = 27607376734175875
a(25) = 166106182569093219
a(26) = 1001523055562012760
a(27) = 6050473492996107670
a(28) = 36619775678126661806
a(29) = 222018764347215037957
a(30) = 1348235147786662996297
a(31) = 8199772713234994099679
a(32) = 49941312419702632545380
a(33) = 304582499804427990862636
a(34) = 1859963807673270299185705
a(35) = 11371789089113481145999831
a(36) = 69606584236156526836900267
a(37) = 426524107060818220121482431
a(38) = 2616284313312028204784916056
a(39) = 16063953098757297709538258472
a(40) = 98724654351695353636122196650
a(41) = 607275112194017657138116871272
a(42) = 3738645146437149545446515117913
a(43) = 23035376349819287398528338223830
a(44) = 142040813301600316116450971336349
a(45) = 876502604999921150955678619075474
a(46) = 5412549081889987322702280249410397
a(47) = 33446158547007658043138999244196048
a(48) = 206811341700337971720651504519842039
a(49) = 1279601768198336009243451124430711782
a(50) = 7922039393691333891589357492558700934
a(51) = 49073922518480966652199105844493182451
a(52) = 304163181604339116198448716712813884097
a(53) = 1886234195447996922554118107846948107799
a(54) = 11703322725347986747324261220247343975960
a(55) = 72650614092099378126547673444631146185270
a(56) = 451209574014560013504544270584920938208420
a(57) = 2803618973145672345918311397405956216425007
a(58) = 17428277581758303455663914163712542704044083
a(59) = 108387252895527183617197792600766844912498264
a(60) = 674347888665114965303089483327334730877780110
a(61) = 4197260623568291237131437562643002798231533035
a(62) = 26134752098394464132353639939969141197161395779
a(63) = 162793095368037380608675728007610777621481209488
a(64) = 1014410201522325733866252330604008737120677862436
a(65) = 6323337790158689511352829072683484557771775300517
a(66) = 39430259810689092073156397173801320200116592483790
a(67) = 245956848068265460354754615159892277404774915101117
a(68) = 1534722849106113485547789948560336096589688795504917
a(69) = 9579408163687924012883422948101975032014908121966782
a(70) = 59811014556271417880519485015365256092281206420836948
a(71) = 373554255337533737370990175591850321528720805160568433
a(72) = 2333740940633456510602692483370325657733853708491985150
a(73) = 14583930873832299638108555030703445162853565144030469252
a(74) = 91162502696736197118256353095387707232997534663957205350
a(75) = 569999399529974721257726052567975463723102210712720144444
a(76) = 3564889100029360779305856894321470199261826570872604108880
a(77) = 22301197573646130390062197371399272218789297305188890505398
a(78) = 139546215391351193882835248444381304007042075109490576186666
a(79) = 873399507223357589480107580492812211159517412743358954349164
a(80) = 5467769688418423728322457233957188627495892626382842970807753
a(81) = 34237918834686162535236466668113775978876886494639914401959437
a(82) = 214438101144705360193199611524425774436043845085684653854895618
a(83) = 1343357672409316791863758566109739189037806211952975015749023230
a(84) = 8417327503392288933400298419209654847427126508398621550958827059
a(85) = 52753037677842693312560968904807554892537818969111903044323146033
a(86) = 330681046023742440256879339402736282400314975269260805402945395806
a(87) = 2073278707100759165879858681965671619887507369341390101783189851407
a(88) = 13001416395563020057026569695640101147066231668341859313080260394351
a(89) = 81546692303929364577182701872163437654681512846250157139838947181467
a(90) = 511567450164870788636151382715390471264415005658209629306354038511891
a(91) = 3209804326028241129134769005218506584222888160044928217391404094066908
a(92) = 20143345425263273755658769063296388335799886502602295473211249922450176
a(93) = 126432979336729869142268129464625763763169469301137529165685959332729153
a(94) = 793712587680038730129593376350949732751203624269718178840389063148528536
a(95) = 4983549003375021268695514871400618175228618896585300091670931776695495193
a(96) = 31295742570648078687640855984615528675707825041822892830894569697344453891
a(97) = 196562827559351031284172275708463926821985209550567211907016679317109260038
a(98) = 1234768971834348849664371715394143208839223105457093533954364448775287963377
a(99) = 7757768904421073018953084023035929054443023427969741971060320306081192658426
a(100) = 48747623784273511095154155319513768668270471000036623668978708426847964812568
a(101) = 306361546065425205609702896864203988873877325899372769907537962116232371184495
a(102) = 1925652815693671781119901772820493964412812575737482470354051499379441000855374
a(103) = 12105519786606224283662117488670648257776830298796570664638282343226213271728870
a(104) = 76111350497242640240890711136610851588264401852641401372989824503281661914238061
a(105) = 478602318060020631917602825581439073869826129211678051331068417568095102963615140
a(106) = 3009944127331366934593576675025214709809791970854782005342182394491416210301459388
a(107) = 18932120099507702991071473428181908035184066276969358363005962522646462083944471103
a(108) = 119095730445042273993675621838094563536002966407315144239910864783695794738625303084
a(109) = 749287058781220213383178069960136002629515111593127878409328835287788918611281936271
a(110) = 4714703328199136209054537699488681042858096828127340381116944424477536427986869434788
a(111) = 29669732791582007210271901279987779573750426838609301728739978068187485607002234530592
a(112) = 186734722531648277199390113562341464624750663231714501142777715800829477170287474017980
a(113) = 1175405682224537189977646826485647169673341696490015612894661214682679566240300362043695
a(114) = 7399474088613559208154300041238604474308584093218768595810639986302390473335379475093378
a(115) = 46586856892042132429080037602712784749305566454736506602564881876192170902636041820177353
a(116) = 293342240973301198795704656525484397128523426885868950813104371611002329659253544769840858
a(117) = 1847283745896143987436869499187385304493779455989414464775610683548899912012233288977339158
a(118) = 11634282708809089999569239106139290487482752763322066515273717050497635362758301860921495348
a(119) = 73281074565560055386551191570056025636139304803743778320040406394258325176675388140485013612
a(120) = 461625179292876475283512540422557761997177683900751859659678042179395626099468752635540069953
a(121) = 2908250720505486800037687173154584695520856012450593869705502609953656635553676611703827161550
a(122) = 18323910553571902470342211742015785265158315768340356310060476675060688228054911334620123230482
a(123) = 115464301462253075282442178997975944601898843559950748154021116266886559965433227425807367686638
a(124) = 727645514402665546410011904599536752380001681689674019165719065778689649359696297898773880677904
a(125) = 4585997944292127937038959544844595235079701130317881407694424788975200385439764065563636602163705
a(126) = 28906071133374028262478375026901276727450268860966028483283923118018555420627737075765998919383390
a(127) = 182215301081489049348278869984893480177541520974573436571908571582952284976331034784845318822795635
a{\left(n + 128 \right)} = - \frac{836273857520241 \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) \left(3 n + 1\right) \left(3 n + 2\right) \left(3 n + 4\right) \left(3 n + 5\right) a{\left(n \right)}}{10485760 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{94143178827 \left(n + 2\right) \left(3 n + 4\right) \left(3 n + 5\right) \left(752782842 n^{5} + 7935097149 n^{4} + 30323713487 n^{3} + 49582061351 n^{2} + 29113571631 n - 177660\right) a{\left(n + 1 \right)}}{41943040 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(60366368 n^{5} + 37825838256 n^{4} + 9480491261232 n^{3} + 1188042404560234 n^{2} + 74437520607251595 n + 1865523557825012475\right) a{\left(n + 127 \right)}}{2520 \left(n + 128\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(1106478364288 n^{7} + 964354115870528 n^{6} + 360204322745911000 n^{5} + 74745382195891407140 n^{4} + 9306077131347493832062 n^{3} + 695177611917711697293827 n^{2} + 28850145930879372116429745 n + 513120177435817483746212700\right) a{\left(n + 126 \right)}}{161280 \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{10460353203 \left(82534581586890 n^{8} + 1980704840814819 n^{7} + 20360825269609755 n^{6} + 117032481722471301 n^{5} + 410865986583475675 n^{4} + 899988896046821056 n^{3} + 1196383408054212680 n^{2} + 876530541248258624 n + 267841553414366400\right) a{\left(n + 2 \right)}}{587202560 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(157066855693088 n^{8} + 154836282268366048 n^{7} + 66776214343944619148 n^{6} + 16455666749702799016000 n^{5} + 2534379971412125527238447 n^{4} + 249798795677553615492669712 n^{3} + 15387611705133629905059077322 n^{2} + 541621815844973266498070274165 n + 8340288737988213632482922695500\right) a{\left(n + 125 \right)}}{276480 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{1162261467 \left(4070108756127942 n^{8} + 68466717823956417 n^{7} + 144871044952059426 n^{6} - 4592479976257264770 n^{5} - 46742736468847382922 n^{4} - 207596533294672865567 n^{3} - 493743817109483769286 n^{2} - 612600351922555293640 n - 311619216337480352000\right) a{\left(n + 3 \right)}}{1174405120 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(4068547656077929792 n^{8} + 3983886234660069884000 n^{7} + 1706641810378735719190744 n^{6} + 417762664887521236832085908 n^{5} + 63912630059189073011265554698 n^{4} + 6257682082200285496859770262165 n^{3} + 382921762051420358427718635454431 n^{2} + 13389311525619319885405579626049842 n + 204820846309842063210609981269715720\right) a{\left(n + 124 \right)}}{30965760 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{43046721 \left(220128775706581011792 n^{8} + 9362749002073617598830 n^{7} + 172549703780432619270273 n^{6} + 1799792039294831968206723 n^{5} + 11619632628482502748519913 n^{4} + 47533299437239004081725095 n^{3} + 120265416810724808731564102 n^{2} + 171959091030394134296858472 n + 106290164620953026256977280\right) a{\left(n + 4 \right)}}{2348810240 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(1050316041970093871392 n^{8} + 1020615772103714787263456 n^{7} + 433884338760854564446881556 n^{6} + 105399601186500218956118535572 n^{5} + 16002038055050159258020921353853 n^{4} + 1554829966904033235377725022632499 n^{3} + 94419522242895935506344523829642154 n^{2} + 3276377224778398615408677726282873078 n + 49738797815795221137699791388207909420\right) a{\left(n + 123 \right)}}{123863040 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{14348907 \left(24840425148275486165616 n^{8} + 1214802189913276730475630 n^{7} + 25862064300793021653360659 n^{6} + 312997119656722015719461985 n^{5} + 2354906120444009744465957439 n^{4} + 11276423518577891947961893345 n^{3} + 33552739711233118544489885686 n^{2} + 56702291534651877501577625480 n + 41653898115175418771765861760\right) a{\left(n + 5 \right)}}{4697620480 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(48128342637299086560016 n^{8} + 46413073051881159969776776 n^{7} + 19581681913116531987858038064 n^{6} + 4720780212458966112062103401694 n^{5} + 711294971689569533602746363947119 n^{4} + 68589525580238874476784215235222404 n^{3} + 4133690760573991870448268589609650631 n^{2} + 142354829747849804371218780696701316756 n + 2144749371148021358858029533679394619900\right) a{\left(n + 122 \right)}}{165150720 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{4782969 \left(2746842991671980993011942 n^{8} + 155801184853029300542338391 n^{7} + 3837467565744641478015347576 n^{6} + 53660242744851913715414433760 n^{5} + 466250584375214408090067871908 n^{4} + 2579100427678009422997229885409 n^{3} + 8872687619408003113161417204414 n^{2} + 17360501274209394871049425231080 n + 14793065619068264339482676174400\right) a{\left(n + 6 \right)}}{18790481920 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(12907677501698315803857808 n^{8} + 12351260204251081947203087192 n^{7} + 5170647583578776252191007019208 n^{6} + 1236895402436619909151051895636114 n^{5} + 184924060041371398877551589173945477 n^{4} + 17694007264426609245627614315135550488 n^{3} + 1058111256040898306219809187928154196187 n^{2} + 36156861405730757436960907363441599617166 n + 540530803762701735133969363215525670338600\right) a{\left(n + 121 \right)}}{1981808640 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{1594323 \left(147674622356770210709186556 n^{8} + 9680430358312127804397341388 n^{7} + 275646478797125749390904882853 n^{6} + 4456396171787127129654962702763 n^{5} + 44768598995419208114394191861509 n^{4} + 286312689402757896212864907915657 n^{3} + 1138838189046321195858010255860722 n^{2} + 2576672232865762577012029057899672 n + 2539534053482742812938278094198080\right) a{\left(n + 7 \right)}}{37580963840 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(438560131389559622553012584 n^{8} + 416129795598919799417860423852 n^{7} + 172742278170351421250130552138530 n^{6} + 40975332957416984418795244088062849 n^{5} + 6074609754641827181938920699681590501 n^{4} + 576349915212407407185196445734497985453 n^{3} + 34176378695014241042558746379147790473385 n^{2} + 1158029713353659350819979087042405181925086 n + 17166559945035278995076945626524628210616400\right) a{\left(n + 120 \right)}}{3963617280 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(4633776808489178150614339952 n^{8} + 4354331707477311465009267720608 n^{7} + 1790096953164980527528071583970256 n^{6} + 420517503582953895198708528793587352 n^{5} + 61739355126459092325818343231052017673 n^{4} + 5801101753079625982228743873820697519742 n^{3} + 340666353130101617836249845309308370527319 n^{2} + 11431421376214969191348597188954031961045458 n + 167818370933775677484730559715030254358056040\right) a{\left(n + 119 \right)}}{2642411520 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{531441 \left(51713953566927839173543570510 n^{8} + 4028201381507465413800865242473 n^{7} + 136480186961149028843437630202255 n^{6} + 2627846836416112478187928069913009 n^{5} + 31457092080877062352119716892746035 n^{4} + 239770605646476317783373797391361582 n^{3} + 1136531304435107167085867131474960760 n^{2} + 3063292289686704015535592940293899456 n + 3594592427222118402529774303146114240\right) a{\left(n + 8 \right)}}{75161927680 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(161884714699543846371163490712 n^{8} + 150558841755545502997859881904484 n^{7} + 61259213929665885946216302895676638 n^{6} + 14242463544103444311951224578669155871 n^{5} + 2069499538983199366526467623615342085293 n^{4} + 192447351829829709923274421531929266508131 n^{3} + 11184714026448572188535927606298178667440937 n^{2} + 371437723980769495067193116915347480903795014 n + 5396489355872897682547124615420103950730651480\right) a{\left(n + 118 \right)}}{5284823040 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{177147 \left(3925305696698281346649324192374 n^{8} + 336351126374946880742835984787183 n^{7} + 12554871950288804312074102584032065 n^{6} + 266666715224173512644635705242170723 n^{5} + 3525526029995663902382283777168938661 n^{4} + 29710635411847539334858737509858293902 n^{3} + 155868699854519410101637609172478480300 n^{2} + 465441416570304900078637268439847280232 n + 605699567293753841977784362117398718560\right) a{\left(n + 9 \right)}}{75161927680 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(8769726930847338742900753728856 n^{8} + 8077980651564042814106572966882436 n^{7} + 3255224668419832511319779724128581006 n^{6} + 749556430697990950802350727965331267519 n^{5} + 107867562172842552885148635332842758670069 n^{4} + 9934371571786286277594664959205229248327619 n^{3} + 571811481048477692311048908282427006135936569 n^{2} + 18806591636583817344704031216835773811011608406 n + 270600164644262754780217835735839497568424243160\right) a{\left(n + 117 \right)}}{15854469120 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(140169274233459923611741929553760 n^{8} + 127957608248558591543946244001409124 n^{7} + 51102155729178538881626779967889331850 n^{6} + 11661540425126401178932692124674324407062 n^{5} + 1663160501139134172581995916766846617845775 n^{4} + 151800700456428878256091555502302235780541016 n^{3} + 8659138388467473432624336175908183469467084075 n^{2} + 282240078442232878160780462534417656627765723338 n + 4024591108257353325780227607952254126080976920760\right) a{\left(n + 116 \right)}}{15854469120 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{59049 \left(355012996135418379926773248687774 n^{8} + 33334192168563068420882184076616715 n^{7} + 1363854024001268750433116964063233892 n^{6} + 31763555538066121616512296642388658064 n^{5} + 460626778338491782478989755740424175376 n^{4} + 4259677270962890297853364793281242331365 n^{3} + 24533081372965704667796437163777008691518 n^{2} + 80461858069190395292657232501396804330096 n + 115062077144560104907926997046344580404800\right) a{\left(n + 10 \right)}}{150323855360 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) 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507\right)} + \frac{\left(682565175758492607504294905959732309004689535729390877815 n^{8} + 309495445463732030465323715672297980064704731090065917976044 n^{7} + 61178540665733204967018575467874634909438396378487836416068742 n^{6} + 6886062878479178566369270990852920624209936359884562546441744072 n^{5} + 482715075458188788263439693081073844442680771771020966822740726215 n^{4} + 21580200928403892836542015492223160512289666217812595655799795806476 n^{3} + 600834490934693667408181935892170165929860372198442619426291621045468 n^{2} + 9524744042177176812627918175452940162772169832814662069488100930826208 n + 65817434234508774214978439358109802383464073518407796322563595578227520\right) a{\left(n + 55 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(1054584492190382163501468665655617125689613971221317878325 n^{8} + 507804150343122628013526597261515229566314812547376957523836 n^{7} + 106965128432037681573352204069406827444578678419888624603712178 n^{6} + 12874196242880821442351956324816584033750054518549112276727070864 n^{5} + 968408810426281304772200541898007512759519023540255032749321678045 n^{4} + 46619009891022278561837126676188671672937815884420468287872748980964 n^{3} + 1402597547886231853532296152319721561282813638747672939335666714249852 n^{2} + 24112717907297646014948700301303743303292652917261760179909916445020496 n + 181346749388114111973847672412152710549733007752198825611850103979680640\right) a{\left(n + 59 \right)}}{519519244124160 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(1190284070699604910751412647693050443877990138994633546375 n^{8} + 664555549855638228803767345361164561430854533989880534999928 n^{7} + 162146068425626192808458326146335421410451627396225656723190746 n^{6} + 22580495741997461495572613282403496054231485863721585782577036100 n^{5} + 1962913648348613356302181246845243364353879569056063853587730774555 n^{4} + 109062883245021994179486794050342904125545822165493818848644086999412 n^{3} + 3782026374089707823813633765679428909595956367759937852103406892401444 n^{2} + 74831641554357651444614527953902184786885851374068391182401235023715120 n + 646739953171412548152137949495985920633073019783488970980529109821750400\right) a{\left(n + 72 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(1420681709669113628656108091819099912607458815160933366755 n^{8} + 791748810638442082461003646796583406758186786196030576010300 n^{7} + 192769079685078567847888313726918895372609496383871784528788762 n^{6} + 26783836994794131707384098148067461200122423887999838981754034804 n^{5} + 2323002995570238415517438109621142586028742749431528061775732517335 n^{4} + 128796067203652288844986649494729022760150045884234751574534272002240 n^{3} + 4458229708627593608816046998175128065978512266612242665967215934699788 n^{2} + 88092610679263057387093660821743616540262033493384792397941366880028656 n + 760808857447120151502908659973991082314755951997304585268577719819986560\right) a{\left(n + 67 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(1636033044810151734077670586701361546391421926999497446331 n^{8} + 969354608080046579920871310297467912525992187822551241332196 n^{7} + 251246354277157506639908098079122681020977138311626186845080294 n^{6} + 37207184729583069456928964270919125100338552156569148094014903480 n^{5} + 3443352517885264278017137576845728243106145277927275942823029071739 n^{4} + 203921683155671304555810353044397437687919949792236675594687055503444 n^{3} + 7546964509139084112223420402806940403274087641835896676154225723652196 n^{2} + 159584185490268031590632116098230426229425035497501013850258190407907600 n + 1476154824955365581683862756083503207595078718898533961123583436698008960\right) a{\left(n + 75 \right)}}{519519244124160 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(1766215726376310264121953921117843084026036000878932696089 n^{8} + 972431502775907478092818847124137306757485578142986025346892 n^{7} + 234210909085730510604033992220378912326090207769542426490073562 n^{6} + 32230168797253956093161081663227113595482698385444253055779905496 n^{5} + 2771622580134512068905406298823971746554633647908600626316351663721 n^{4} + 152514873951222836512434677120914669211836441683057716709686736903388 n^{3} + 5244299535101696069162591092886735075848441765813738872689253595609188 n^{2} + 103022563789641980819031742445013583196393817772780438702378948124335104 n + 885224166383042219732115963242251182945812877799410180023952157317124800\right) a{\left(n + 69 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(1983113290731072904626197643238703199627777987859614264061 n^{8} + 1084066148746922656953133169548614572025440352238333810987760 n^{7} + 259339245262456295908987647936330437381321527546014816641777566 n^{6} + 35461623504744754722195770744655590503020955861875020178694229564 n^{5} + 3031342804232615060523554385865908854916150484487258091369919077169 n^{4} + 165877648053242918817486057471511238242745582002770607048766137375220 n^{3} + 5674240458166455835128132158122426226234724828210232524499259403135924 n^{2} + 110934717459654878426006670407912631071712826858468088260038884317918176 n + 949017823674632529288076576894275259374498049550371912687415548347304320\right) a{\left(n + 68 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} + \frac{\left(2038387021667563826221270382194346418689394675781810124093 n^{8} + 1129703158984133340724267624573368546738068580662807565901864 n^{7} + 273676276042382152724523610045639561766106074988376379858861762 n^{6} + 37850446692066885317011661718642494449017716726960876289031898104 n^{5} + 3268619116646417923322752392424148334065167725976414770159859049837 n^{4} + 180466024579162547478167539259864554672636503911577171286107739695376 n^{3} + 6220721104771178639455848557262741756441873512670179754081574269577908 n^{2} + 122392819262216166341371772807193783119707086344187827428528321895756016 n + 1052272662702023449416424541231017477628716935171006698841274376852038080\right) a{\left(n + 71 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)} - \frac{\left(2047546881604087822602960616516300106717601432249068945453 n^{8} + 1020553699526148627079877778378796497311895098742857612666056 n^{7} + 222138311836290682739867055431325127273603638101554499006707346 n^{6} + 27574173087709356012804303413111190000404906146070401765713021136 n^{5} + 2134524376862069941896634203911761446601133063118005579170309060637 n^{4} + 105490922389906526566673515721707480313437227953409723825190934012824 n^{3} + 3249546910211600741079240864211100460370605959496888272460617782544484 n^{2} + 57024708266081907943882880953659105836772128160447558501448873200340944 n + 436296796772157997147581055612781532268245729342035379501233105939669760\right) a{\left(n + 65 \right)}}{259759622062080 \left(n + 126\right) \left(n + 127\right) \left(n + 128\right) \left(2 n + 251\right) \left(2 n + 253\right) \left(2 n + 257\right) \left(4 n + 505\right) \left(4 n + 507\right)}, \quad n \geq 128
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24723/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]+F[22,x]
F[17,x] = F[18,x]+F[20,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 1+(F[19,x]^3-F[19,x]^2+F[19,x])*x
F[20,x] = F[21,x]
F[21,x] = F[19,x]^2*F[15,x]*F[16,x]
F[22,x] = F[19,x]*F[5,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[2,x]*F[27,x]
F[27,x] = 1/F[15,x]*F[28,x]
F[28,x] = F[11,x]
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]*F[32,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = 1/F[15,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[43,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = x*(1+F[36,x])*(F[36,x]^2+F[36,x]+1)
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[39,x]*F[42,x]
F[39,x] = F[19,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[19,x]^2*F[15,x]*F[39,x]
F[42,x] = F[2,x]+F[5,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[15,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{3}-x F_{19} \left(x \right)^{2}+x F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = x F_{36} \left(x \right)^{3}+2 x F_{36} \left(x \right)^{2}+2 F_{36}\! \left(x \right) x +x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_22(x))
Eq(F_17(x), F_18(x) + F_20(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), x*F_19(x)**3 - x*F_19(x)**2 + x*F_19(x) + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)*F_19(x)**2)
Eq(F_22(x), F_19(x)*F_5(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_2(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_15(x))
Eq(F_28(x), F_11(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x)*F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), F_33(x)/F_15(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_43(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), x*(F_36(x) + 1)**3 - x*(F_36(x) + 1)**2 + (x - 1)*(F_36(x) + 1) + F_36(x) + 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_39(x)*F_42(x))
Eq(F_39(x), F_19(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_19(x)**2*F_39(x))
Eq(F_42(x), F_2(x) + F_5(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_15(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 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:
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{"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24788/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]+F[22,x]
F[17,x] = F[18,x]+F[20,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 1+(F[19,x]^3-F[19,x]^2+F[19,x])*x
F[20,x] = F[21,x]
F[21,x] = F[19,x]^2*F[15,x]*F[16,x]
F[22,x] = F[19,x]*F[5,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[2,x]*F[27,x]
F[27,x] = 1/F[15,x]*F[28,x]
F[28,x] = F[11,x]
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]*F[32,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = 1/F[15,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[43,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = x*(1+F[36,x])*(F[36,x]^2+F[36,x]+1)
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[39,x]*F[42,x]
F[39,x] = F[19,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[19,x]^2*F[15,x]*F[39,x]
F[42,x] = F[2,x]+F[5,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[15,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{3}-x F_{19} \left(x \right)^{2}+x F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = x F_{36} \left(x \right)^{3}+2 x F_{36} \left(x \right)^{2}+2 F_{36}\! \left(x \right) x +x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_22(x))
Eq(F_17(x), F_18(x) + F_20(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), x*F_19(x)**3 - x*F_19(x)**2 + x*F_19(x) + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)*F_19(x)**2)
Eq(F_22(x), F_19(x)*F_5(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_2(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_15(x))
Eq(F_28(x), F_11(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x)*F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), F_33(x)/F_15(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_43(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), x*(F_36(x) + 1)**3 - x*(F_36(x) + 1)**2 + (x - 1)*(F_36(x) + 1) + F_36(x) + 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_39(x)*F_42(x))
Eq(F_39(x), F_19(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_19(x)**2*F_39(x))
Eq(F_42(x), F_2(x) + F_5(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_15(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 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{"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": true}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25153/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]+F[22,x]
F[17,x] = F[18,x]+F[20,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 1+(F[19,x]^3-F[19,x]^2+F[19,x])*x
F[20,x] = F[21,x]
F[21,x] = F[19,x]^2*F[15,x]*F[16,x]
F[22,x] = F[19,x]*F[5,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[2,x]*F[27,x]
F[27,x] = 1/F[15,x]*F[28,x]
F[28,x] = F[11,x]
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]*F[32,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = 1/F[15,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[43,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = x*(1+F[36,x])*(F[36,x]^2+F[36,x]+1)
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[39,x]*F[42,x]
F[39,x] = F[19,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[19,x]^2*F[15,x]*F[39,x]
F[42,x] = F[2,x]+F[5,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[15,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{3}-x F_{19} \left(x \right)^{2}+x F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = x F_{36} \left(x \right)^{3}+2 x F_{36} \left(x \right)^{2}+2 F_{36}\! \left(x \right) x +x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_22(x))
Eq(F_17(x), F_18(x) + F_20(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), x*F_19(x)**3 - x*F_19(x)**2 + x*F_19(x) + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)*F_19(x)**2)
Eq(F_22(x), F_19(x)*F_5(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_2(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_15(x))
Eq(F_28(x), F_11(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x)*F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), F_33(x)/F_15(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_43(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), x*(F_36(x) + 1)**3 - x*(F_36(x) + 1)**2 + (x - 1)*(F_36(x) + 1) + F_36(x) + 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_39(x)*F_42(x))
Eq(F_39(x), F_19(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_19(x)**2*F_39(x))
Eq(F_42(x), F_2(x) + F_5(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_15(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 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, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, 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4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 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{"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25494/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]+F[22,x]
F[17,x] = F[18,x]+F[20,x]
F[18,x] = F[0,x]*F[19,x]
F[19,x] = 1+(F[19,x]^3-F[19,x]^2+F[19,x])*x
F[20,x] = F[21,x]
F[21,x] = F[19,x]^2*F[15,x]*F[16,x]
F[22,x] = F[19,x]*F[5,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[2,x]*F[27,x]
F[27,x] = 1/F[15,x]*F[28,x]
F[28,x] = F[11,x]
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]*F[32,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = 1/F[15,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[43,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = x*(1+F[36,x])*(F[36,x]^2+F[36,x]+1)
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[39,x]*F[42,x]
F[39,x] = F[19,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[19,x]^2*F[15,x]*F[39,x]
F[42,x] = F[2,x]+F[5,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[15,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{3}-x F_{19} \left(x \right)^{2}+x F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = x F_{36} \left(x \right)^{3}+2 x F_{36} \left(x \right)^{2}+2 F_{36}\! \left(x \right) x +x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_22(x))
Eq(F_17(x), F_18(x) + F_20(x))
Eq(F_18(x), F_0(x)*F_19(x))
Eq(F_19(x), x*F_19(x)**3 - x*F_19(x)**2 + x*F_19(x) + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)*F_19(x)**2)
Eq(F_22(x), F_19(x)*F_5(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_2(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_15(x))
Eq(F_28(x), F_11(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x)*F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), F_33(x)/F_15(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_43(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), x*(F_36(x) + 1)**3 - x*(F_36(x) + 1)**2 + (x - 1)*(F_36(x) + 1) + F_36(x) + 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_39(x)*F_42(x))
Eq(F_39(x), F_19(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_19(x)**2*F_39(x))
Eq(F_42(x), F_2(x) + F_5(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_15(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 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{"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2]], "symmetry": true}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25940/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[20,x]
F[12,x] = F[13,x]+F[28,x]
F[13,x] = F[0,x]*F[14,x]
F[14,x] = 1/F[20,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[20,x]*F[21,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[22,x]+F[27,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = F[0,x]*F[24,x]
F[24,x] = 1+(F[24,x]^3-F[24,x]^2+F[24,x])*x
F[25,x] = F[26,x]
F[26,x] = F[24,x]^2*F[20,x]*F[21,x]
F[27,x] = F[24,x]*F[5,x]
F[28,x] = F[29,x]
F[29,x] = F[24,x]*F[30,x]*F[31,x]
F[30,x] = -F[0,x]+F[18,x]
F[31,x] = 1/F[20,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[39,x]
F[34,x] = F[35,x]
F[35,x] = F[20,x]*F[36,x]*F[4,x]
F[36,x] = F[24,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[24,x]^2*F[20,x]*F[36,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[20,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right) F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{0}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = x F_{24} \left(x \right)^{3}-x F_{24} \left(x \right)^{2}+x F_{24}\! \left(x \right)+1
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{20}\! \left(x \right) F_{21}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right) F_{5}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{24}\! \left(x \right) F_{30}\! \left(x \right) F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{20}\! \left(x \right) F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_20(x))
Eq(F_12(x), F_13(x) + F_28(x))
Eq(F_13(x), F_0(x)*F_14(x))
Eq(F_14(x), F_15(x)/F_20(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_20(x)*F_21(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x) + F_27(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_0(x)*F_24(x))
Eq(F_24(x), x*F_24(x)**3 - x*F_24(x)**2 + x*F_24(x) + 1)
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_20(x)*F_21(x)*F_24(x)**2)
Eq(F_27(x), F_24(x)*F_5(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_24(x)*F_30(x)*F_31(x))
Eq(F_30(x), -F_0(x) + F_18(x))
Eq(F_31(x), F_32(x)/F_20(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_39(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_20(x)*F_36(x)*F_4(x))
Eq(F_36(x), F_24(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_24(x)**2*F_36(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_20(x))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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