01243_01342_01432_10243_10342_10432_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2925, 15560, 84057, 459562, 2537429, 14127425, 79222292, 447042018, 2536551186, 14463343813, 82832989904, 476279412635, 2748436555670, 15912503444657, 92406258823648, 538108842191647, 3141612746114930, 18385145904195307, 107830153583816408, 633733000526866141, 3731694238570409215, 22013326930739516649, 130075766538144015070, 769827958968206215136, 4562857060370257583645, 27082494876269420148349, 160958849050328637079478, 957820020811397180721392, 5706459711491088457163599, 34035844022008516453773393, 203220887518262081479671413, 1214616406611479540258508763, 7266537068608404263389725569, 43512441947897353111815094750, 260782507413822165944651751406, 1564246380779534527739541394567, 9390254575369350211311304973203, 56413094773531806365932274586012, 339155324011006919126247193923075, 2040422906658068268900063480090480, 12283781252637969788479902922973569, 73998434377117801231329917654180597, 446046868032002673171960421500481997, 2690267924665752198103273542273417461, 16235206290127166017716260613405735031, 98029782040661407992245678856556554690, 592225945082255830049070680329882716949, 3579626222750628156761878641561137612934, 21647159760572698817834385654143534322798, 130969357105924543014594089844509691945682, 792751230416805969007648319659338865831316, 4800604084783181175996613276989033946555998, 29083067192249473605065902279835954147543403, 176264072512007571583145211088225819610400485, 1068712500231074110014119641996782520061683682, 6482252834387820795872778985463047835917316298, 39332701929987489807030254010333949376284874450, 238747770138344506940186226556694396228138528827, 1449698913083579101423469977600480187397776897083, 8805716109565543638616916549128985540016128248534, 53505146364430309719443643742809444912652778060771, 325211776945124964390283600290923255590544185847310, 1977301083734011785475225143969306773715198010596102, 12025727142025498994067062991553053740405800151631427, 73160761449000507865100646537354384170588092976377122, 445215112209177797447830660653752395239520590776257804, 2710085603883433155845435466864710873926461080847494422, 16501153688932652123938890812340528586582656717805103768, 100498755198367138155862476731277436286700858179569862472, 612236383969340824284775386107338787036222862862750526104, 3730669605977283090899164433547133322207131951355987761639, 22738450900227892197879481334682320784101050476675664663507, 138624095587396036209513175187208870917286325049228799275530, 845313445292451250351997123765399052148721953873773516365443, 5155793974516053648131018398801712949503451798104549334417446, 31453550493111084560517777086745828525487402372372222943568581, 191927781166862928387198130331025310993646730319576298897324037, 1171380088503943754214307077879111010262817297570292813744698649, 7150682926286958803037488666472819917373950076987787934645423809, 43660110207937705139010268959384121421056371324868161830017991487, 266629232035094170956754015574506035434865808219842691335763056530, 1628599869262904965756417912904972441621668427852862681138476032427, 9949536862328323333886857258816343832746298822987114589629435904479, 60795490822554456008689171568628442959526940720537516601148192959796, 371550767848027386815235448996567820494095936926095674738977741556600, 2271127734210012307996067809601649107562598820255479694546875942893917, 13884809600446810636245192802993670928420283211228471048730269992785012, 84900781043076149610683048885183727020588821620958288252189341926829827, 519224646331387183773250395922784347683586364436635778601893399626139982, 3175918031843981577898503981809483144163053910847115222112027701648703436, 19429078551737367641396887597743118865054076982375021897179967643539679796, 118878320542105808679254370959272358600027071446333400471972423332469513626, 727477058389826798295925265788384553079418562486070934474433883142804254874, 4452468074464020537888370276999812270684868953029286974680636532804439167977
Implicit equation for the generating function in Maple syntax:
x^3*(4*x^3-10*x^2+7*x-2)*F(x)^6-x^2*(10*x^3-27*x^2+23*x-8)*F(x)^5+x*(8*x^4-21*x^3+9*x^2+10*x-9)*F(x)^4-(-2+x)*(8*x^3-17*x^2+10*x+1)*F(x)^3+(4*x^4-21*x^3+30*x^2-8*x-6)*F(x)^2+(x-1)*(-2+x)*(2*x+3)*F(x)-(x-1)*(-2+x) = 0
Implicit equation for the generating function in latex syntax:
x^{3} \left(4 x^{3}-10 x^{2}+7 x -2\right) F \! \left(x \right)^{6}-x^{2} \left(10 x^{3}-27 x^{2}+23 x -8\right) F \! \left(x \right)^{5}+x \left(8 x^{4}-21 x^{3}+9 x^{2}+10 x -9\right) F \! \left(x \right)^{4}-\left(-2+x \right) \left(8 x^{3}-17 x^{2}+10 x +1\right) F \! \left(x \right)^{3}+\left(4 x^{4}-21 x^{3}+30 x^{2}-8 x -6\right) F \! \left(x \right)^{2}+\left(x -1\right) \left(-2+x \right) \left(2 x +3\right) F \! \left(x \right)-\left(x -1\right) \left(-2+x \right) = 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) = 562
a(7) = 2925
a(8) = 15560
a(9) = 84057
a(10) = 459562
a(11) = 2537429
a(12) = 14127425
a(13) = 79222292
a(14) = 447042018
a(15) = 2536551186
a(16) = 14463343813
a(17) = 82832989904
a(18) = 476279412635
a(19) = 2748436555670
a(20) = 15912503444657
a(21) = 92406258823648
a(22) = 538108842191647
a(23) = 3141612746114930
a(24) = 18385145904195307
a(25) = 107830153583816408
a(26) = 633733000526866141
a(27) = 3731694238570409215
a(28) = 22013326930739516649
a(29) = 130075766538144015070
a(30) = 769827958968206215136
a(31) = 4562857060370257583645
a(32) = 27082494876269420148349
a(33) = 160958849050328637079478
a(34) = 957820020811397180721392
a(35) = 5706459711491088457163599
a(36) = 34035844022008516453773393
a(37) = 203220887518262081479671413
a(38) = 1214616406611479540258508763
a(39) = 7266537068608404263389725569
a(40) = 43512441947897353111815094750
a(41) = 260782507413822165944651751406
a(42) = 1564246380779534527739541394567
a(43) = 9390254575369350211311304973203
a(44) = 56413094773531806365932274586012
a(45) = 339155324011006919126247193923075
a(46) = 2040422906658068268900063480090480
a(47) = 12283781252637969788479902922973569
a(48) = 73998434377117801231329917654180597
a(49) = 446046868032002673171960421500481997
a(50) = 2690267924665752198103273542273417461
a(51) = 16235206290127166017716260613405735031
a(52) = 98029782040661407992245678856556554690
a(53) = 592225945082255830049070680329882716949
a(54) = 3579626222750628156761878641561137612934
a(55) = 21647159760572698817834385654143534322798
a(56) = 130969357105924543014594089844509691945682
a(57) = 792751230416805969007648319659338865831316
a(58) = 4800604084783181175996613276989033946555998
a(59) = 29083067192249473605065902279835954147543403
a(60) = 176264072512007571583145211088225819610400485
a(61) = 1068712500231074110014119641996782520061683682
a(62) = 6482252834387820795872778985463047835917316298
a(63) = 39332701929987489807030254010333949376284874450
a(64) = 238747770138344506940186226556694396228138528827
a(65) = 1449698913083579101423469977600480187397776897083
a(66) = 8805716109565543638616916549128985540016128248534
a(67) = 53505146364430309719443643742809444912652778060771
a(68) = 325211776945124964390283600290923255590544185847310
a(69) = 1977301083734011785475225143969306773715198010596102
a(70) = 12025727142025498994067062991553053740405800151631427
a(71) = 73160761449000507865100646537354384170588092976377122
a(72) = 445215112209177797447830660653752395239520590776257804
a(73) = 2710085603883433155845435466864710873926461080847494422
a(74) = 16501153688932652123938890812340528586582656717805103768
a(75) = 100498755198367138155862476731277436286700858179569862472
a(76) = 612236383969340824284775386107338787036222862862750526104
a(77) = 3730669605977283090899164433547133322207131951355987761639
a(78) = 22738450900227892197879481334682320784101050476675664663507
a(79) = 138624095587396036209513175187208870917286325049228799275530
a(80) = 845313445292451250351997123765399052148721953873773516365443
a(81) = 5155793974516053648131018398801712949503451798104549334417446
a(82) = 31453550493111084560517777086745828525487402372372222943568581
a(n+83) = 29779558400000/11741919*(2*n+3)*(2*n+1)*(n+3)*(n+2)*(n+1)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n)-20971520000/3913973*(2*n+3)*(n+3)*(n+2)*(78075*n^2+518645*n+814306)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+1)-1/9393535200*(125603618246190455*n^4+39035031651274469022*n^3+4549048951911104366173*n^2+235606196850856402625670*n+4575796908055581679020720)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+79)+1/782794600*(329194542744687*n^3+77212292690311839*n^2+6036520895170225682*n+157308980077743488216)/(n+82)/(n+83)/(n+84)*a(n+80)-1/4809490022400*(110372962151000810581226231848766942676781*n^5+22666926608685394897701302278935331004599349*n^4+1861890906319537566926106723403533623731259993*n^3+76463190851484727019542763735330280623130048523*n^2+1569935495282326808906361461417716135103153116746*n+12892189174241443415174114528301503711427188481552)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+41)+1/24047450112000*(462854431367983026679140289917476741317322*n^5+97922931988223658419783270989627900698445345*n^4+8286703189274273949347481861949325707772636200*n^3+350624933128715955818098526675552788968626421515*n^2+7417602004033860779209311745846771367890787528778*n+62766786842084313266650757782594746813530826928200)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+42)-1/8015816704000*(130891669873460244738587862843026347908196*n^5+28510296208794187616669744307751447363718145*n^4+2483967149465325016136768674234772237628959720*n^3+108206117107969588676773627022764156633589530435*n^2+2356769046325811476564519115431256078225468119364*n+20531885754030024191235515062342898531996245340460)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+43)-1/4007908352000*(160769037524725292175541165416044436804582*n^5+29561074043400562118117452057943887942753335*n^4+2173538659120853737178779134965760852286712940*n^3+79881328795138904111770205916058271008038984035*n^2+1467386783327789569766193312741265239838218124348*n+10778174341713926307244040220578860807451602909680)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+37)+1/2404745011200*(89017068086695007533258722663247745546935*n^5+16807757369590107252059459217262172565954119*n^4+1269058275159202185043892176977387413827397039*n^3+47894967045708362541073284657360128067593513479*n^2+903493779396945583266064636517592505845459060960*n+6815019017525832638218712357415673665895600569360)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+38)-1/6011862528000*(195047009872890911843049832677399369920167*n^5+37834681813933461653833337494258219123746965*n^4+2934914563502775073712664977847645553253718785*n^3+113803917115145155430488788638981208062340017920*n^2+2205801470710459580679432481838262491914360916223*n+17096351931547523856905293929379655680550407022490)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+39)+1/2404745011200*(66072261491368122479930363284601872074718*n^5+13179760153063342587015312759291610677382073*n^4+1051443579539198895510024703937208188747998322*n^3+41933180849984621093926929078855819263175186463*n^2+836018167687153571314752362256957349890118405764*n+6665639807606108832559182971880297016570761746364)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+40)-1/12023725056000*(463447629540611963850561669320871678500681*n^5+80758585089633037404788837077979896844404615*n^4+5627320835060492275404871731486998674157935075*n^3+195993409634292423671582245812741455161061020205*n^2+3411923610523408168966518334566162044404319946444*n+23749566345021771340946032296612210920866444816980)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+35)+1/4007908352000*(163414045526822894470762047339554166030986*n^5+29258521054068844763715913780444958800174135*n^4+2094806686102230341666744428327980298915045220*n^3+74966272850713052860188981844096310103587529615*n^2+1340940123322961065001144335347281804688030256504*n+9590797607638231628778902840200744686353141185620)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+36)-1/3005931264000*(81339177977659679040502335331755492071282*n^5+13388923687155284272272622516881203735234980*n^4+881194826301054228952757493067095743643968905*n^3+28985292978812293315872277043615163780850944275*n^2+476487125486416655063275158097996386817120680348*n+3131624361792500242750246001871856338452510069040)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+33)+1/400790835200*(13498670471429693495838880326576039859062*n^5+2287414736159883537920351043891146585717179*n^4+154992317563864018329105924012458084772175408*n^3+5249137338102452617057712082232092026306309471*n^2+88852300713949408625289774565110683776769339228*n+601356648309450864830298455134683648569018332908)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+34)-1/3005931264000*(12566725044465035960811831246036879549388*n^5+1808329934445932216143367813502725375719430*n^4+103872652610723119282676005744378491735247535*n^3+2976561515797013769333847028008153231187150980*n^2+42541951154312279437590341737745434479509429157*n+242538962837061466683103652887529754237067237350)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+29)+1/1001977088000*(7947293089743456512378139324680268309364*n^5+1187474248172185871102760187627296823420630*n^4+7088564989541515301894886061946325377191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12023725056000*(26227231008695071087977041904744690076*n^5+7772356324731869237988131082932560409555*n^4+921376511982948091245258866490650685760115*n^3+54615549115639180433837416880699957370711280*n^2+1618790902667395874624491124356684784465482614*n+19193360794914262270014444166361222639865579810)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+59)+1/24047450112000*(5137904500466987453917574569483239401497*n^5+1402501404423600483529497738381534804421715*n^4+153141933894557975315371931087934008859434825*n^3+8361211285048903747087590765729549732009106375*n^2+228259683961387646902897999041000451388599901448*n+2492670373291183493045255134341942257836460963760)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+54)-1/4809490022400*(471592169000995327059768469797940416152*n^5+130931341517770441210093559646867104909989*n^4+14541148183094306858749527728989200199771438*n^3+807499889753035281881316767289476813119640297*n^2+22422062686664437918741244233711748665644829632*n+249051173821699743616628585565641667139621225632)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+55)+1/24047450112000*(1010325409252882835627534324062966201984*n^5+285221637336746932137828289863184700581595*n^4+32209563348999504127811614016537109139157870*n^3+1818775022773502343633483200523122602834453135*n^2+51352961186621354423515824814716669241018771836*n+580009288651990901204765944650623929710340154640)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+56)-1/24047450112000*(35234025489769206104319400190335551728558*n^5+9124934102149668967375438067874358900401745*n^4+945251054233849903912261668892160690007417940*n^3+48958229470448253791559429268258932072212770985*n^2+1267845853813005874181933000967506785835595233712*n+13132896513597500408420992190631747402225037984440)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+51)+1/24047450112000*(19860135449940915816776695868345926688596*n^5+5236077624490152747883696639016673353847665*n^4+552191316144628451547077266036293145619629970*n^3+29116799730693594518825424330810993831734547805*n^2+767660521737136404584955048862701709332944577024*n+8095751904708472671167612281256812434205260827160)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+52)-1/4809490022400*(2090704323165689940384751690321633164263*n^5+560955585654047685727048918966165458399592*n^4+60204894220773216602744997087810095275018273*n^3+3230824605657813715160820710229008126520577286*n^2+86691001471328913244803671781319172467031541486*n+930474535097060414703708381209928231241340892120)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+53)-1/24047450112000*(90415102755893451050594131944321812839717*n^5+22566221074107187406619996756771989477778560*n^4+2252697397367166795079850873407871234553507395*n^3+112430641472589432731367556944612430413967926790*n^2+2805472027219299279510683441451513990794866075998*n+28000010234027483616445038679192377979726947399840)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+49)+1/8015816704000*(19461162281869823567560770192505785762537*n^5+4948950774542839537151746748833679887305345*n^4+503380169333407105883365469875045873873373465*n^3+25599357297072891746948404983381704627287260605*n^2+650898642383619557018568496812931039338936690668*n+6619730943359824336981744919917255943319621163320)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+50)+1/24047450112000*(131063152205423043601926335468837517110602*n^5+32085454758805554098880821846557099973246315*n^4+3141592227204746816184187675190440746754886840*n^3+153786187117712945858264632263337343774435868415*n^2+3763678936692390056196804640915263118244055344328*n+36840651420368039637819921461833377912029433448200)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+48)-1/24047450112000*(178399264546760953857668260109921809420273*n^5+42802517591283742417010447828815169786363015*n^4+4107243447598838899311846373986365639667860135*n^3+197037261895047286256765829020198965054505214745*n^2+4725686630094540144709696035867963020603572590492*n+45330645440328002986067962568369684569476051111360)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+47)-1/24047450112000*(281455227551583812196132192022967519994662*n^5+64603458087743745793854149291131312877491465*n^4+5930814442895318065751275565597527647141057850*n^3+272204666313165575420028012213903041242378728065*n^2+6245970936552570653927067181084264394439137062458*n+57321558991366539782033173222911653436182460666300)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+45)+1/1603163340800*(15292522732093502722692687568465181463961*n^5+3591656958825752794184697283194146481803908*n^4+337375379300413510779555009386560280111214979*n^3+15843322869633872721638663396575029064964309276*n^2+371958929474515229918751349343751932974877784580*n+3492616981860431939141465068981294075672424015748)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+46)+1/24047450112000*(334578523478508106303758925718077150049404*n^5+74896589051342138058448314042436245445474775*n^4+6705927420143581264709754341735723862239359910*n^3+300190875825546993126046396568534678296706861995*n^2+6718571557597782335872429351522212788492163341016*n+60143154819664269070898877351621896878475588633820)/(n+80)/(n+84)/(n+83)/(n+82)/(n+81)*a(n+44), n >= 83
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2925
a(8) = 15560
a(9) = 84057
a(10) = 459562
a(11) = 2537429
a(12) = 14127425
a(13) = 79222292
a(14) = 447042018
a(15) = 2536551186
a(16) = 14463343813
a(17) = 82832989904
a(18) = 476279412635
a(19) = 2748436555670
a(20) = 15912503444657
a(21) = 92406258823648
a(22) = 538108842191647
a(23) = 3141612746114930
a(24) = 18385145904195307
a(25) = 107830153583816408
a(26) = 633733000526866141
a(27) = 3731694238570409215
a(28) = 22013326930739516649
a(29) = 130075766538144015070
a(30) = 769827958968206215136
a(31) = 4562857060370257583645
a(32) = 27082494876269420148349
a(33) = 160958849050328637079478
a(34) = 957820020811397180721392
a(35) = 5706459711491088457163599
a(36) = 34035844022008516453773393
a(37) = 203220887518262081479671413
a(38) = 1214616406611479540258508763
a(39) = 7266537068608404263389725569
a(40) = 43512441947897353111815094750
a(41) = 260782507413822165944651751406
a(42) = 1564246380779534527739541394567
a(43) = 9390254575369350211311304973203
a(44) = 56413094773531806365932274586012
a(45) = 339155324011006919126247193923075
a(46) = 2040422906658068268900063480090480
a(47) = 12283781252637969788479902922973569
a(48) = 73998434377117801231329917654180597
a(49) = 446046868032002673171960421500481997
a(50) = 2690267924665752198103273542273417461
a(51) = 16235206290127166017716260613405735031
a(52) = 98029782040661407992245678856556554690
a(53) = 592225945082255830049070680329882716949
a(54) = 3579626222750628156761878641561137612934
a(55) = 21647159760572698817834385654143534322798
a(56) = 130969357105924543014594089844509691945682
a(57) = 792751230416805969007648319659338865831316
a(58) = 4800604084783181175996613276989033946555998
a(59) = 29083067192249473605065902279835954147543403
a(60) = 176264072512007571583145211088225819610400485
a(61) = 1068712500231074110014119641996782520061683682
a(62) = 6482252834387820795872778985463047835917316298
a(63) = 39332701929987489807030254010333949376284874450
a(64) = 238747770138344506940186226556694396228138528827
a(65) = 1449698913083579101423469977600480187397776897083
a(66) = 8805716109565543638616916549128985540016128248534
a(67) = 53505146364430309719443643742809444912652778060771
a(68) = 325211776945124964390283600290923255590544185847310
a(69) = 1977301083734011785475225143969306773715198010596102
a(70) = 12025727142025498994067062991553053740405800151631427
a(71) = 73160761449000507865100646537354384170588092976377122
a(72) = 445215112209177797447830660653752395239520590776257804
a(73) = 2710085603883433155845435466864710873926461080847494422
a(74) = 16501153688932652123938890812340528586582656717805103768
a(75) = 100498755198367138155862476731277436286700858179569862472
a(76) = 612236383969340824284775386107338787036222862862750526104
a(77) = 3730669605977283090899164433547133322207131951355987761639
a(78) = 22738450900227892197879481334682320784101050476675664663507
a(79) = 138624095587396036209513175187208870917286325049228799275530
a(80) = 845313445292451250351997123765399052148721953873773516365443
a(81) = 5155793974516053648131018398801712949503451798104549334417446
a(82) = 31453550493111084560517777086745828525487402372372222943568581
a{\left(n + 83 \right)} = \frac{29779558400000 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{20971520000 \left(n + 2\right) \left(n + 3\right) \left(2 n + 3\right) \left(78075 n^{2} + 518645 n + 814306\right) a{\left(n + 1 \right)}}{3913973 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{26214400 \left(n + 3\right) \left(5600737646 n^{4} + 86598676132 n^{3} + 490343280249 n^{2} + 1204486728683 n + 1080895412620\right) a{\left(n + 2 \right)}}{3913973 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1128830174 n + 89343616797\right) a{\left(n + 82 \right)}}{7987700 \left(n + 84\right)} - \frac{\left(1074339828625 n^{2} + 169031572814318 n + 6648544008992593\right) a{\left(n + 81 \right)}}{111827800 \left(n + 83\right) \left(n + 84\right)} + \frac{\left(329194542744687 n^{3} + 77212292690311839 n^{2} + 6036520895170225682 n + 157308980077743488216\right) a{\left(n + 80 \right)}}{782794600 \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(125603618246190455 n^{4} + 39035031651274469022 n^{3} + 4549048951911104366173 n^{2} + 235606196850856402625670 n + 4575796908055581679020720\right) a{\left(n + 79 \right)}}{9393535200 \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{6553600 \left(2060487883694 n^{5} + 49033177862827 n^{4} + 460753627134418 n^{3} + 2139002207120033 n^{2} + 4909112187115668 n + 4458091922072640\right) a{\left(n + 3 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{81920 \left(3701627733443639 n^{5} + 107550232226158621 n^{4} + 1237471921092206047 n^{3} + 7053760874022674243 n^{2} + 19931063075663953482 n + 22343977089399972960\right) a{\left(n + 4 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{4096 \left(1267193514756759721 n^{5} + 43375708364916678431 n^{4} + 589111212543545305397 n^{3} + 3970990914140658149065 n^{2} + 13291747143084166374138 n + 17681611945578930950400\right) a{\left(n + 5 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(15500860504936109543 n^{5} + 5983657356310899010270 n^{4} + 923877577584346060365775 n^{3} + 71319630364778949175739420 n^{2} + 2752648891432471937342696412 n + 42494209593352958662866077760\right) a{\left(n + 78 \right)}}{46967676000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(206534072625714121221 n^{5} + 78745276642031460873075 n^{4} + 12008717139882886896777625 n^{3} + 915626161161444932366910865 n^{2} + 34905142183275830553772275814 n + 532231317918316543046282073240\right) a{\left(n + 77 \right)}}{31311784000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{1024 \left(341417638840988202733 n^{5} + 13433320744094569648085 n^{4} + 209999001955485467453885 n^{3} + 1631357188689146634887275 n^{2} + 6300588397068036062058582 n + 9682077940270792095790080\right) a{\left(n + 6 \right)}}{58709595 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2064829310154056418068 n^{5} + 777459739178879881675513 n^{4} + 117088320995398903149782644 n^{3} + 8816604865513181399096227637 n^{2} + 331926177879655339272178682814 n + 4998321074528111406840668492436\right) a{\left(n + 76 \right)}}{18787070400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(97676450864678997026104 n^{5} + 36314550403361116410375300 n^{4} + 5400277977858757843704452675 n^{3} + 401519320063373802814390896555 n^{2} + 14926290872100852044584525385916 n + 221943637089358318610297317969500\right) a{\left(n + 75 \right)}}{62623568000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{256 \left(123904681978712055703731 n^{5} + 5504988114488975258748505 n^{4} + 97268217660727828750190515 n^{3} + 854797498095109708526093375 n^{2} + 3737788451477444763148678034 n + 6508272770798353722763460880\right) a{\left(n + 7 \right)}}{489246625 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{128 \left(6682860925694523462587947 n^{5} + 330819420639137133535755770 n^{4} + 6516862825034841387091499195 n^{3} + 63887940440623123380230724730 n^{2} + 311817659656725676650360138318 n + 606338816307815609500873378320\right) a{\left(n + 8 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(28799199887764456123921234 n^{5} + 10570654986110155876756608035 n^{4} + 1551925365260659125096275782700 n^{3} + 113919350618767311975112946005645 n^{2} + 4181019315073675943662313481666306 n + 61378335745572390554501284557424320\right) a{\left(n + 74 \right)}}{1502965632000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{64 \left(100881703787730384383434138 n^{5} + 5506657674247564601653819145 n^{4} + 119659306872942536786544123920 n^{3} + 1294475039363614250322084827005 n^{2} + 6974184234169615712501884018152 n + 14975239260238351200815659194780\right) a{\left(n + 9 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(394693600902462485831968489 n^{5} + 141135148034288425432209055024 n^{4} + 20186618585316776123745104197895 n^{3} + 1443629051746757559296639935843456 n^{2} + 51619242325664384533032420066425296 n + 738281419740672437279257884950019168\right) a{\left(n + 72 \right)}}{200395417600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(620432800522334051782826593 n^{5} + 224790698222575594692877661405 n^{4} + 32577088632713988329243226014525 n^{3} + 2360515526901551749457070219417235 n^{2} + 85518960670411109495284249896202722 n + 1239279366162144080722266178261916400\right) a{\left(n + 73 \right)}}{3005931264000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{32 \left(1295113194030930074567825792 n^{5} + 77312930075158319654134247470 n^{4} + 1837587670935605864904854829655 n^{3} + 21747229623634231622810740882280 n^{2} + 128199412282062068296383282576333 n + 301248611405396512409490668253630\right) a{\left(n + 10 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{16 \left(4756588240907822745601037601 n^{5} + 308494776469232440507576097895 n^{4} + 7965776805415995459372868297370 n^{3} + 102413755062028034575930750202105 n^{2} + 655866710807459326452977226511289 n + 1674325820879276788103517413970240\right) a{\left(n + 11 \right)}}{489246625 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{4 \left(54275821371003917746818929959 n^{5} + 3804570363748598584493901355703 n^{4} + 106146484765034363507347278009827 n^{3} + 1474198612481472083843887147827943 n^{2} + 10196618168369554621568531482248984 n + 28110196347403803607360313954052588\right) a{\left(n + 12 \right)}}{293547975 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(201883940500105921508617658359 n^{5} + 71235391812394893116750436950870 n^{4} + 10054168344827884287497822274317705 n^{3} + 709517572324863419752683648495994930 n^{2} + 25034976819667220565822665939202020616 n + 353336596875721256818592048639238279360\right) a{\left(n + 71 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{2 \left(446041865114757586537939770311 n^{5} + 33661411903522449966142239959434 n^{4} + 1010472772028669848681367347272958 n^{3} + 15092198378924157306633656718118562 n^{2} + 112215911924046414920130713759258169 n + 332444393880155884051958180272473378\right) a{\left(n + 13 \right)}}{293547975 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1548361543630586469812420474111 n^{5} + 539027408223423746363565265201525 n^{4} + 75060012487105016735807450256898495 n^{3} + 5226080977549395582806088123978170615 n^{2} + 181933951680146007498431025598433029014 n + 2533447285683737216451515792700977113920\right) a{\left(n + 70 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(5373511403261042550609412810079 n^{5} + 1845289771886185993850222960297650 n^{4} + 253473937124236256006257083111676225 n^{3} + 17409039816175329055047559316040679100 n^{2} + 597846268901146606659613476558621831846 n + 8212357349906145116909615413135350795540\right) a{\left(n + 69 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(11307808669055388679267711938278 n^{5} + 3829783685948577786400559710125095 n^{4} + 518842302591382577196040549489620450 n^{3} + 35145709291509220765393936822223492295 n^{2} + 1190379663125595698265737533544418673202 n + 16127437834447152260593750604512875888900\right) a{\left(n + 68 \right)}}{2003954176000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(15771858280360244991620144320837 n^{5} + 1278424763644235549725139231722250 n^{4} + 41173699558318486307775692709580430 n^{3} + 659187880070440865656476867350913400 n^{2} + 5249901114150414174287022229101627453 n + 16648981029525607943204924728707594330\right) a{\left(n + 14 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(94614748358499338434979343718177 n^{5} + 8237733968800186637181647027510870 n^{4} + 284387067273205507611331924628607665 n^{3} + 4872398424562604136966091281702765070 n^{2} + 41471473666951044966222688229794876728 n + 140401631308544693987370694586795540250\right) a{\left(n + 15 \right)}}{2935479750 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(195629600418074086782942598082167 n^{5} + 65333981218346314791346764184155635 n^{4} + 8727944388761879426992694129499150080 n^{3} + 582993339928007094149658362875419730390 n^{2} + 19471278381137556702433047852979578239868 n + 260132761072916987298575556943318787810640\right) a{\left(n + 67 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(463925269995932806632110012239579 n^{5} + 43623262949921496114069613436404880 n^{4} + 1619297547591683983025754003624806600 n^{3} + 29730984154566468509639880401105014240 n^{2} + 270472241277633300429645544217910330381 n + 976631534810239128483876464918899656900\right) a{\left(n + 16 \right)}}{5870959500 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(554294653894545610707244584314049 n^{5} + 57724528289290596418314178428945190 n^{4} + 2342055491733101991564406615896070435 n^{3} + 46574614862907282438098279109632092850 n^{2} + 455875402781813489870600366387288027666 n + 1762137030462212400993740115709994328390\right) a{\left(n + 17 \right)}}{3913973000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1034358711256448092316132607587626 n^{5} + 340566320082917006487853698000090065 n^{4} + 44854226590228568589103994070696731150 n^{3} + 2953838240294477956642039289877724659160 n^{2} + 97264016065062273297622264408530464083449 n + 1281121508826580882418718934486675832872830\right) a{\left(n + 66 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2163961750090844234331588622164902 n^{5} + 323305268140871784987830043987378925 n^{4} + 16352109240980218802675847411101948815 n^{3} + 380115491277848176309212238125139943945 n^{2} + 4195366176538028846342961610478244742983 n + 17874100054178627854713373725819000868530\right) a{\left(n + 18 \right)}}{23483838000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - 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\frac{\left(51020651128941614040875576242306723 n^{5} + 5029740793821740570967950895647258940 n^{4} + 200130385222148355640318930918785723325 n^{3} + 4024809073846518616013932528229059390905 n^{2} + 40977588940497192607303661623217393300827 n + 169180537921458117066415485326069890585380\right) a{\left(n + 20 \right)}}{15655892000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(338366250302183863636685894296950196 n^{5} + 36246542903629403137920343225558912835 n^{4} + 1565946932275277676970872664386999066200 n^{3} + 34122326614533905264347587666246463064535 n^{2} + 375114261526062722661851525422934483405854 n + 1664355600429818508550621240219723372360320\right) a{\left(n + 21 \right)}}{31311784000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(374322016431348049027266780681022973 n^{5} + 117959902479101418459352292228477073340 n^{4} + 14869699875926003277759535048180769286805 n^{3} + 937258332248026719317750797176132158439770 n^{2} + 29539712108897335377696280658622950366611632 n + 372420491807304071918801359512237267040332000\right) a{\left(n + 63 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(479425678431816633378238151915479672 n^{5} + 148827178909338225458620570343106892215 n^{4} + 18480937114482807934159902857026357032030 n^{3} + 1147511538147339648785943567651138522823415 n^{2} + 35627225618399896166972331908746681666112328 n + 442475619538977194313886704968420162299072020\right) a{\left(n + 62 \right)}}{8015816704000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(566746756852599560109700449417393894 n^{5} + 170611412593419940717034097881236751241 n^{4} + 20545215318271499564907944427463061826516 n^{3} + 1237107546195512369337589981347513517339721 n^{2} + 37247652064141965767882061467914665164439784 n + 448616837546702222244069698364598416835446810\right) a{\left(n + 60 \right)}}{801581670400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - 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\frac{\left(35234025489769206104319400190335551728558 n^{5} + 9124934102149668967375438067874358900401745 n^{4} + 945251054233849903912261668892160690007417940 n^{3} + 48958229470448253791559429268258932072212770985 n^{2} + 1267845853813005874181933000967506785835595233712 n + 13132896513597500408420992190631747402225037984440\right) a{\left(n + 51 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(66072261491368122479930363284601872074718 n^{5} + 13179760153063342587015312759291610677382073 n^{4} + 1051443579539198895510024703937208188747998322 n^{3} + 41933180849984621093926929078855819263175186463 n^{2} + 836018167687153571314752362256957349890118405764 n + 6665639807606108832559182971880297016570761746364\right) a{\left(n + 40 \right)}}{2404745011200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(81339177977659679040502335331755492071282 n^{5} + 13388923687155284272272622516881203735234980 n^{4} + 881194826301054228952757493067095743643968905 n^{3} + 28985292978812293315872277043615163780850944275 n^{2} + 476487125486416655063275158097996386817120680348 n + 3131624361792500242750246001871856338452510069040\right) a{\left(n + 33 \right)}}{3005931264000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(89017068086695007533258722663247745546935 n^{5} + 16807757369590107252059459217262172565954119 n^{4} + 1269058275159202185043892176977387413827397039 n^{3} + 47894967045708362541073284657360128067593513479 n^{2} + 903493779396945583266064636517592505845459060960 n + 6815019017525832638218712357415673665895600569360\right) a{\left(n + 38 \right)}}{2404745011200 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(90415102755893451050594131944321812839717 n^{5} + 22566221074107187406619996756771989477778560 n^{4} + 2252697397367166795079850873407871234553507395 n^{3} + 112430641472589432731367556944612430413967926790 n^{2} + 2805472027219299279510683441451513990794866075998 n + 28000010234027483616445038679192377979726947399840\right) a{\left(n + 49 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(110372962151000810581226231848766942676781 n^{5} + 22666926608685394897701302278935331004599349 n^{4} + 1861890906319537566926106723403533623731259993 n^{3} + 76463190851484727019542763735330280623130048523 n^{2} + 1569935495282326808906361461417716135103153116746 n + 12892189174241443415174114528301503711427188481552\right) a{\left(n + 41 \right)}}{4809490022400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(130891669873460244738587862843026347908196 n^{5} + 28510296208794187616669744307751447363718145 n^{4} + 2483967149465325016136768674234772237628959720 n^{3} + 108206117107969588676773627022764156633589530435 n^{2} + 2356769046325811476564519115431256078225468119364 n + 20531885754030024191235515062342898531996245340460\right) a{\left(n + 43 \right)}}{8015816704000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(131063152205423043601926335468837517110602 n^{5} + 32085454758805554098880821846557099973246315 n^{4} + 3141592227204746816184187675190440746754886840 n^{3} + 153786187117712945858264632263337343774435868415 n^{2} + 3763678936692390056196804640915263118244055344328 n + 36840651420368039637819921461833377912029433448200\right) a{\left(n + 48 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(160769037524725292175541165416044436804582 n^{5} + 29561074043400562118117452057943887942753335 n^{4} + 2173538659120853737178779134965760852286712940 n^{3} + 79881328795138904111770205916058271008038984035 n^{2} + 1467386783327789569766193312741265239838218124348 n + 10778174341713926307244040220578860807451602909680\right) a{\left(n + 37 \right)}}{4007908352000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(163414045526822894470762047339554166030986 n^{5} + 29258521054068844763715913780444958800174135 n^{4} + 2094806686102230341666744428327980298915045220 n^{3} + 74966272850713052860188981844096310103587529615 n^{2} + 1340940123322961065001144335347281804688030256504 n + 9590797607638231628778902840200744686353141185620\right) a{\left(n + 36 \right)}}{4007908352000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(178399264546760953857668260109921809420273 n^{5} + 42802517591283742417010447828815169786363015 n^{4} + 4107243447598838899311846373986365639667860135 n^{3} + 197037261895047286256765829020198965054505214745 n^{2} + 4725686630094540144709696035867963020603572590492 n + 45330645440328002986067962568369684569476051111360\right) a{\left(n + 47 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(195047009872890911843049832677399369920167 n^{5} + 37834681813933461653833337494258219123746965 n^{4} + 2934914563502775073712664977847645553253718785 n^{3} + 113803917115145155430488788638981208062340017920 n^{2} + 2205801470710459580679432481838262491914360916223 n + 17096351931547523856905293929379655680550407022490\right) a{\left(n + 39 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(281455227551583812196132192022967519994662 n^{5} + 64603458087743745793854149291131312877491465 n^{4} + 5930814442895318065751275565597527647141057850 n^{3} + 272204666313165575420028012213903041242378728065 n^{2} + 6245970936552570653927067181084264394439137062458 n + 57321558991366539782033173222911653436182460666300\right) a{\left(n + 45 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(334578523478508106303758925718077150049404 n^{5} + 74896589051342138058448314042436245445474775 n^{4} + 6705927420143581264709754341735723862239359910 n^{3} + 300190875825546993126046396568534678296706861995 n^{2} + 6718571557597782335872429351522212788492163341016 n + 60143154819664269070898877351621896878475588633820\right) a{\left(n + 44 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(462854431367983026679140289917476741317322 n^{5} + 97922931988223658419783270989627900698445345 n^{4} + 8286703189274273949347481861949325707772636200 n^{3} + 350624933128715955818098526675552788968626421515 n^{2} + 7417602004033860779209311745846771367890787528778 n + 62766786842084313266650757782594746813530826928200\right) a{\left(n + 42 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(463447629540611963850561669320871678500681 n^{5} + 80758585089633037404788837077979896844404615 n^{4} + 5627320835060492275404871731486998674157935075 n^{3} + 195993409634292423671582245812741455161061020205 n^{2} + 3411923610523408168966518334566162044404319946444 n + 23749566345021771340946032296612210920866444816980\right) a{\left(n + 35 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)}, \quad n \geq 83
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24662/
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[4,x]*F[42,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[42,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[42,x]*F[62,x]
F[12,x] = 1/F[42,x]/F[52,x]/F[55,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[42,x]
F[15,x] = 1/F[42,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]+F[49,x]
F[18,x] = F[19,x]+F[48,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = (x*F[20,x]+x-1)*(x*F[20,x]+x-2*F[20,x])
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[42,x]
F[23,x] = F[24,x]+F[47,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+(x^2-2*x)*F[26,x]^2+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[30,x]*F[42,x]
F[29,x] = F[2,x]+F[5,x]
F[30,x] = 1/F[42,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = -F[26,x]+F[33,x]
F[33,x] = 1/F[0,x]*F[34,x]
F[34,x] = -F[43,x]+F[35,x]
F[35,x] = 1/F[42,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]+F[38,x]
F[38,x] = -F[2,x]+F[39,x]
F[39,x] = -F[26,x]+F[40,x]
F[40,x] = 1/F[42,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = x
F[43,x] = -F[46,x]+F[44,x]
F[44,x] = 1/F[42,x]*F[45,x]
F[45,x] = F[38,x]
F[46,x] = F[2,x]*F[33,x]
F[47,x] = F[26,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[42,x]*F[51,x]
F[51,x] = F[14,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[42,x]*F[52,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[42,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[42,x]*F[59,x]
F[62,x] = 1/F[42,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[104,x]+F[65,x]
F[65,x] = -F[4,x]+F[66,x]
F[66,x] = F[102,x]+F[67,x]
F[67,x] = 1/F[42,x]/F[75,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[42,x]*F[72,x]
F[72,x] = F[73,x]+F[92,x]
F[73,x] = F[74,x]
F[74,x] = F[42,x]*F[75,x]*F[77,x]
F[75,x] = -F[24,x]+F[76,x]
F[76,x] = -F[47,x]+F[12,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = 1/F[42,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = -F[85,x]+F[81,x]
F[81,x] = 1/F[42,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[2,x]+F[84,x]
F[84,x] = -F[0,x]+F[78,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[2,x]*F[78,x]
F[87,x] = F[88,x]
F[88,x] = F[42,x]*F[89,x]*F[90,x]
F[89,x] = F[20,x]+F[25,x]
F[90,x] = 1/F[42,x]*F[91,x]
F[91,x] = F[80,x]
F[92,x] = F[93,x]
F[93,x] = F[42,x]*F[75,x]*F[94,x]
F[94,x] = 1/F[42,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[42,x]*F[67,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[42,x]
F[101,x] = F[64,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[2,x]+F[6,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[42,x]
F[106,x] = F[107,x]
F[107,x] = F[42,x]*F[62,x]*F[75,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_{4}\! \left(x \right) F_{42}\! \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_{42}\! \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_{42}\! \left(x \right) F_{62}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{42}\! \left(x \right) F_{52}\! \left(x \right) F_{55}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}+2 x^{2} F_{20}\! \left(x \right)-2 x F_{20} \left(x \right)^{2}+x^{2}-3 x F_{20}\! \left(x \right)-x +2 F_{20}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{30}\! \left(x \right) F_{42}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{34}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = x
F_{43}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{33}\! \left(x \right)
F_{47}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{42}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{42}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{102}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{42}\! \left(x \right) F_{75}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{42}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right) F_{75}\! \left(x \right) F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{12}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{78}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{42}\! \left(x \right) F_{89}\! \left(x \right) F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{80}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{42}\! \left(x \right) F_{75}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{42}\! \left(x \right) F_{67}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{42}\! \left(x \right)
F_{101}\! \left(x \right) = F_{64}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{42}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{42}\! \left(x \right) F_{62}\! \left(x \right) F_{75}\! \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_4(x)*F_42(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_42(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_42(x)*F_62(x))
Eq(F_12(x), F_13(x)/(F_42(x)*F_52(x)*F_55(x)))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_42(x))
Eq(F_15(x), F_16(x)/F_42(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) + F_49(x))
Eq(F_18(x), F_19(x) + F_48(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*(F_20(x) + 1)**2 + (x + 1)*(F_20(x) + 1) + F_20(x) - 1)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_42(x))
Eq(F_23(x), F_24(x) + F_47(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_30(x)*F_42(x))
Eq(F_29(x), F_2(x) + F_5(x))
Eq(F_30(x), F_31(x)/F_42(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), -F_26(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_0(x))
Eq(F_34(x), F_35(x) - F_43(x))
Eq(F_35(x), F_36(x)/F_42(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x) + F_38(x))
Eq(F_38(x), -F_2(x) + F_39(x))
Eq(F_39(x), -F_26(x) + F_40(x))
Eq(F_40(x), F_41(x)/F_42(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), x)
Eq(F_43(x), F_44(x) - F_46(x))
Eq(F_44(x), F_45(x)/F_42(x))
Eq(F_45(x), F_38(x))
Eq(F_46(x), F_2(x)*F_33(x))
Eq(F_47(x), F_26(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_42(x)*F_51(x))
Eq(F_51(x), F_14(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_42(x)*F_52(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_42(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_42(x)*F_59(x))
Eq(F_62(x), F_63(x)/F_42(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), -F_104(x) + F_65(x))
Eq(F_65(x), -F_4(x) + F_66(x))
Eq(F_66(x), F_102(x) + F_67(x))
Eq(F_67(x), F_68(x)/(F_42(x)*F_75(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_42(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_92(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_42(x)*F_75(x)*F_77(x))
Eq(F_75(x), -F_24(x) + F_76(x))
Eq(F_76(x), F_12(x) - F_47(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x)/F_42(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x) - F_85(x))
Eq(F_81(x), F_82(x)/F_42(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), -F_2(x) + F_84(x))
Eq(F_84(x), -F_0(x) + F_78(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_2(x)*F_78(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_42(x)*F_89(x)*F_90(x))
Eq(F_89(x), F_20(x) + F_25(x))
Eq(F_90(x), F_91(x)/F_42(x))
Eq(F_91(x), F_80(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_42(x)*F_75(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_42(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_42(x)*F_67(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_42(x))
Eq(F_101(x), F_64(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_2(x) + F_6(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_42(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_42(x)*F_62(x)*F_75(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 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[4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", 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0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24976/
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[4,x]*F[41,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[41,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[41,x]*F[62,x]
F[12,x] = 1/F[41,x]/F[52,x]/F[55,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[41,x]
F[15,x] = 1/F[41,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]+F[49,x]
F[18,x] = F[19,x]+F[48,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = (x*F[20,x]+x-2*F[20,x])*(x*F[20,x]+x-1)
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[41,x]
F[23,x] = F[24,x]+F[47,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+(x^2-2*x)*F[26,x]^2+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[31,x]*F[41,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[2,x]+F[6,x]
F[31,x] = 1/F[41,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[26,x]+F[34,x]
F[34,x] = 1/F[0,x]*F[35,x]
F[35,x] = -F[42,x]+F[36,x]
F[36,x] = 1/F[41,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[0,x]+F[39,x]
F[39,x] = 1/F[41,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = x
F[42,x] = -F[46,x]+F[43,x]
F[43,x] = 1/F[41,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[20,x]+F[38,x]
F[46,x] = F[2,x]*F[34,x]
F[47,x] = F[26,x]*F[30,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[41,x]*F[51,x]
F[51,x] = F[14,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[52,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[41,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[41,x]*F[59,x]
F[62,x] = 1/F[41,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[103,x]+F[65,x]
F[65,x] = -F[4,x]+F[66,x]
F[66,x] = F[102,x]+F[67,x]
F[67,x] = 1/F[41,x]/F[75,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[41,x]*F[72,x]
F[72,x] = F[73,x]+F[92,x]
F[73,x] = F[74,x]
F[74,x] = F[41,x]*F[75,x]*F[77,x]
F[75,x] = -F[24,x]+F[76,x]
F[76,x] = -F[47,x]+F[12,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = 1/F[41,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = -F[85,x]+F[81,x]
F[81,x] = 1/F[41,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[2,x]+F[84,x]
F[84,x] = -F[0,x]+F[78,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[2,x]*F[78,x]
F[87,x] = F[88,x]
F[88,x] = F[41,x]*F[89,x]*F[90,x]
F[89,x] = F[20,x]+F[25,x]
F[90,x] = 1/F[41,x]*F[91,x]
F[91,x] = F[80,x]
F[92,x] = F[93,x]
F[93,x] = F[41,x]*F[75,x]*F[94,x]
F[94,x] = 1/F[41,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[41,x]*F[67,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[41,x]
F[101,x] = F[64,x]
F[102,x] = F[103,x]+F[5,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[41,x]
F[105,x] = F[106,x]
F[106,x] = F[41,x]*F[62,x]*F[75,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_{4}\! \left(x \right) F_{41}\! \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_{41}\! \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_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{41}\! \left(x \right) F_{52}\! \left(x \right) F_{55}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}+2 x^{2} F_{20}\! \left(x \right)-2 x F_{20} \left(x \right)^{2}+x^{2}-3 x F_{20}\! \left(x \right)-x +2 F_{20}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{41}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{31}\! \left(x \right) F_{41}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{35}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{102}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{41}\! \left(x \right) F_{75}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{41}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{41}\! \left(x \right) F_{75}\! \left(x \right) F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{12}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{78}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{41}\! \left(x \right) F_{89}\! \left(x \right) F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{80}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{41}\! \left(x \right) F_{75}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{41}\! \left(x \right) F_{67}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{41}\! \left(x \right)
F_{101}\! \left(x \right) = F_{64}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{5}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{41}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{41}\! \left(x \right) F_{62}\! \left(x \right) F_{75}\! \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_4(x)*F_41(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_41(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_41(x)*F_62(x))
Eq(F_12(x), F_13(x)/(F_41(x)*F_52(x)*F_55(x)))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_41(x))
Eq(F_15(x), F_16(x)/F_41(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) + F_49(x))
Eq(F_18(x), F_19(x) + F_48(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*(F_20(x) + 1)**2 + (x + 1)*(F_20(x) + 1) + F_20(x) - 1)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_41(x))
Eq(F_23(x), F_24(x) + F_47(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_31(x)*F_41(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_2(x) + F_6(x))
Eq(F_31(x), F_32(x)/F_41(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_26(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_0(x))
Eq(F_35(x), F_36(x) - F_42(x))
Eq(F_36(x), F_37(x)/F_41(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), -F_0(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_41(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), x)
Eq(F_42(x), F_43(x) - F_46(x))
Eq(F_43(x), F_44(x)/F_41(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), -F_20(x) + F_38(x))
Eq(F_46(x), F_2(x)*F_34(x))
Eq(F_47(x), F_26(x)*F_30(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_41(x)*F_51(x))
Eq(F_51(x), F_14(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_52(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_41(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_41(x)*F_59(x))
Eq(F_62(x), F_63(x)/F_41(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), -F_103(x) + F_65(x))
Eq(F_65(x), -F_4(x) + F_66(x))
Eq(F_66(x), F_102(x) + F_67(x))
Eq(F_67(x), F_68(x)/(F_41(x)*F_75(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_41(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_92(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_41(x)*F_75(x)*F_77(x))
Eq(F_75(x), -F_24(x) + F_76(x))
Eq(F_76(x), F_12(x) - F_47(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x)/F_41(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x) - F_85(x))
Eq(F_81(x), F_82(x)/F_41(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), -F_2(x) + F_84(x))
Eq(F_84(x), -F_0(x) + F_78(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_2(x)*F_78(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_41(x)*F_89(x)*F_90(x))
Eq(F_89(x), F_20(x) + F_25(x))
Eq(F_90(x), F_91(x)/F_41(x))
Eq(F_91(x), F_80(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_41(x)*F_75(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_41(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_41(x)*F_67(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_41(x))
Eq(F_101(x), F_64(x))
Eq(F_102(x), F_103(x) + F_5(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_41(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_41(x)*F_62(x)*F_75(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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"pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "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], [0, 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, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25550/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[26,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = 1/F[22,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[25,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[22,x]*F[4,x]
F[19,x] = 1/F[22,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = (x*F[21,x]+x-1)*(x*F[21,x]+x-2*F[21,x])
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[22,x]
F[25,x] = F[23,x]
F[26,x] = F[27,x]
F[27,x] = F[22,x]*F[28,x]*F[56,x]
F[28,x] = 1/F[22,x]/F[36,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[33,x]+F[31,x]
F[31,x] = 1/F[22,x]*F[32,x]
F[32,x] = F[5,x]
F[33,x] = F[0,x]*F[34,x]
F[34,x] = 1/F[22,x]*F[35,x]
F[35,x] = F[2,x]
F[36,x] = F[37,x]+F[44,x]
F[37,x] = F[38,x]*F[41,x]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[22,x]*F[38,x]
F[41,x] = F[0,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[36,x]
F[44,x] = F[45,x]
F[45,x] = F[22,x]*F[38,x]*F[46,x]
F[46,x] = 1/F[0,x]/F[22,x]/F[55,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[54,x]+F[49,x]
F[49,x] = 1/F[22,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = 1/F[22,x]*F[53,x]
F[53,x] = F[2,x]
F[54,x] = F[0,x]*F[52,x]
F[55,x] = -1+(x^2-2*x)*F[55,x]^2+(2+x)*F[55,x]
F[56,x] = F[44,x]+F[57,x]
F[57,x] = F[38,x]*F[58,x]
F[58,x] = -F[59,x]+F[41,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[22,x]*F[62,x]
F[62,x] = F[38,x]+F[63,x]
F[63,x] = F[60,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[63,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{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_{26}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{25}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{2}+2 x^{2} F_{21}\! \left(x \right)-2 x F_{21} \left(x \right)^{2}+x^{2}-3 x F_{21}\! \left(x \right)-x +2 F_{21}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right) F_{28}\! \left(x \right) F_{56}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{22}\! \left(x \right) F_{36}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right) F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{0}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right) F_{38}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{55}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = x^{2} F_{55} \left(x \right)^{2}-2 x F_{55} \left(x \right)^{2}+F_{55}\! \left(x \right) x +2 F_{55}\! \left(x \right)-1
F_{56}\! \left(x \right) = F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{38}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{41}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{22}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{38}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_26(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x)/F_22(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_25(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_22(x)*F_4(x))
Eq(F_19(x), F_20(x)/F_22(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), x*(x - 2)*(F_21(x) + 1)**2 + (x + 1)*(F_21(x) + 1) + F_21(x) - 1)
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_22(x))
Eq(F_25(x), F_23(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_22(x)*F_28(x)*F_56(x))
Eq(F_28(x), F_29(x)/(F_22(x)*F_36(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_33(x))
Eq(F_31(x), F_32(x)/F_22(x))
Eq(F_32(x), F_5(x))
Eq(F_33(x), F_0(x)*F_34(x))
Eq(F_34(x), F_35(x)/F_22(x))
Eq(F_35(x), F_2(x))
Eq(F_36(x), F_37(x) + F_44(x))
Eq(F_37(x), F_38(x)*F_41(x))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_22(x)*F_38(x))
Eq(F_41(x), F_0(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_36(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_22(x)*F_38(x)*F_46(x))
Eq(F_46(x), F_47(x)/(F_0(x)*F_22(x)*F_55(x)))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) - F_54(x))
Eq(F_49(x), F_50(x)/F_22(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_53(x)/F_22(x))
Eq(F_53(x), F_2(x))
Eq(F_54(x), F_0(x)*F_52(x))
Eq(F_55(x), x*(x - 2)*F_55(x)**2 + (x + 2)*F_55(x) - 1)
Eq(F_56(x), F_44(x) + F_57(x))
Eq(F_57(x), F_38(x)*F_58(x))
Eq(F_58(x), F_41(x) - F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_22(x)*F_62(x))
Eq(F_62(x), F_38(x) + F_63(x))
Eq(F_63(x), F_60(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_63(x))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 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[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25898/
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[4,x]*F[42,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[42,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[42,x]*F[62,x]
F[12,x] = 1/F[42,x]/F[52,x]/F[55,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[42,x]
F[15,x] = 1/F[42,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]+F[49,x]
F[18,x] = F[19,x]+F[48,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = (x*F[20,x]+x-1)*(x*F[20,x]+x-2*F[20,x])
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[42,x]
F[23,x] = F[24,x]+F[47,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+(x^2-2*x)*F[26,x]^2+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[30,x]*F[42,x]
F[29,x] = F[2,x]+F[5,x]
F[30,x] = 1/F[42,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = -F[26,x]+F[33,x]
F[33,x] = 1/F[0,x]*F[34,x]
F[34,x] = -F[43,x]+F[35,x]
F[35,x] = 1/F[42,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]+F[38,x]
F[38,x] = -F[2,x]+F[39,x]
F[39,x] = -F[26,x]+F[40,x]
F[40,x] = 1/F[42,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = x
F[43,x] = -F[46,x]+F[44,x]
F[44,x] = 1/F[42,x]*F[45,x]
F[45,x] = F[38,x]
F[46,x] = F[2,x]*F[33,x]
F[47,x] = F[26,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[42,x]*F[51,x]
F[51,x] = F[14,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[42,x]*F[52,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[42,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[42,x]*F[59,x]
F[62,x] = 1/F[42,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[104,x]+F[65,x]
F[65,x] = -F[4,x]+F[66,x]
F[66,x] = F[102,x]+F[67,x]
F[67,x] = 1/F[42,x]/F[75,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[42,x]*F[72,x]
F[72,x] = F[73,x]+F[92,x]
F[73,x] = F[74,x]
F[74,x] = F[42,x]*F[75,x]*F[77,x]
F[75,x] = -F[24,x]+F[76,x]
F[76,x] = -F[47,x]+F[12,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = 1/F[42,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = -F[85,x]+F[81,x]
F[81,x] = 1/F[42,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[2,x]+F[84,x]
F[84,x] = -F[0,x]+F[78,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[2,x]*F[78,x]
F[87,x] = F[88,x]
F[88,x] = F[42,x]*F[89,x]*F[90,x]
F[89,x] = F[20,x]+F[25,x]
F[90,x] = 1/F[42,x]*F[91,x]
F[91,x] = F[80,x]
F[92,x] = F[93,x]
F[93,x] = F[42,x]*F[75,x]*F[94,x]
F[94,x] = 1/F[42,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[42,x]*F[67,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[42,x]
F[101,x] = F[64,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[2,x]+F[6,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[42,x]
F[106,x] = F[107,x]
F[107,x] = F[42,x]*F[62,x]*F[75,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_{4}\! \left(x \right) F_{42}\! \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_{42}\! \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_{42}\! \left(x \right) F_{62}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{42}\! \left(x \right) F_{52}\! \left(x \right) F_{55}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}+2 x^{2} F_{20}\! \left(x \right)-2 x F_{20} \left(x \right)^{2}+x^{2}-3 x F_{20}\! \left(x \right)-x +2 F_{20}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{30}\! \left(x \right) F_{42}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{34}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = x
F_{43}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{33}\! \left(x \right)
F_{47}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{42}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{42}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{102}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{42}\! \left(x \right) F_{75}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{42}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right) F_{75}\! \left(x \right) F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{12}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{78}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{42}\! \left(x \right) F_{89}\! \left(x \right) F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{80}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{42}\! \left(x \right) F_{75}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{42}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{42}\! \left(x \right) F_{67}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{42}\! \left(x \right)
F_{101}\! \left(x \right) = F_{64}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{42}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{42}\! \left(x \right) F_{62}\! \left(x \right) F_{75}\! \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_4(x)*F_42(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_42(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_42(x)*F_62(x))
Eq(F_12(x), F_13(x)/(F_42(x)*F_52(x)*F_55(x)))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_42(x))
Eq(F_15(x), F_16(x)/F_42(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) + F_49(x))
Eq(F_18(x), F_19(x) + F_48(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*(F_20(x) + 1)**2 + (x + 1)*(F_20(x) + 1) + F_20(x) - 1)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_42(x))
Eq(F_23(x), F_24(x) + F_47(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_30(x)*F_42(x))
Eq(F_29(x), F_2(x) + F_5(x))
Eq(F_30(x), F_31(x)/F_42(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), -F_26(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_0(x))
Eq(F_34(x), F_35(x) - F_43(x))
Eq(F_35(x), F_36(x)/F_42(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x) + F_38(x))
Eq(F_38(x), -F_2(x) + F_39(x))
Eq(F_39(x), -F_26(x) + F_40(x))
Eq(F_40(x), F_41(x)/F_42(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), x)
Eq(F_43(x), F_44(x) - F_46(x))
Eq(F_44(x), F_45(x)/F_42(x))
Eq(F_45(x), F_38(x))
Eq(F_46(x), F_2(x)*F_33(x))
Eq(F_47(x), F_26(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_42(x)*F_51(x))
Eq(F_51(x), F_14(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_42(x)*F_52(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_42(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_42(x)*F_59(x))
Eq(F_62(x), F_63(x)/F_42(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), -F_104(x) + F_65(x))
Eq(F_65(x), -F_4(x) + F_66(x))
Eq(F_66(x), F_102(x) + F_67(x))
Eq(F_67(x), F_68(x)/(F_42(x)*F_75(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_42(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_92(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_42(x)*F_75(x)*F_77(x))
Eq(F_75(x), -F_24(x) + F_76(x))
Eq(F_76(x), F_12(x) - F_47(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x)/F_42(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x) - F_85(x))
Eq(F_81(x), F_82(x)/F_42(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), -F_2(x) + F_84(x))
Eq(F_84(x), -F_0(x) + F_78(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_2(x)*F_78(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_42(x)*F_89(x)*F_90(x))
Eq(F_89(x), F_20(x) + F_25(x))
Eq(F_90(x), F_91(x)/F_42(x))
Eq(F_91(x), F_80(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_42(x)*F_75(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_42(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_42(x)*F_67(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_42(x))
Eq(F_101(x), F_64(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_2(x) + F_6(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_42(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_42(x)*F_62(x)*F_75(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25921/
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[4,x]*F[41,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[41,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[41,x]*F[62,x]
F[12,x] = 1/F[41,x]/F[52,x]/F[55,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[41,x]
F[15,x] = 1/F[41,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]+F[49,x]
F[18,x] = F[19,x]+F[48,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = (x*F[20,x]+x-1)*(x*F[20,x]+x-2*F[20,x])
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[41,x]
F[23,x] = F[24,x]+F[47,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+(x^2-2*x)*F[26,x]^2+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[31,x]*F[41,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[2,x]+F[6,x]
F[31,x] = 1/F[41,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[26,x]+F[34,x]
F[34,x] = 1/F[0,x]*F[35,x]
F[35,x] = -F[42,x]+F[36,x]
F[36,x] = 1/F[41,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[0,x]+F[39,x]
F[39,x] = 1/F[41,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = x
F[42,x] = -F[46,x]+F[43,x]
F[43,x] = 1/F[41,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[20,x]+F[38,x]
F[46,x] = F[2,x]*F[34,x]
F[47,x] = F[26,x]*F[30,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[41,x]*F[51,x]
F[51,x] = F[14,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[52,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[41,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[41,x]*F[59,x]
F[62,x] = 1/F[41,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[103,x]+F[65,x]
F[65,x] = -F[4,x]+F[66,x]
F[66,x] = F[102,x]+F[67,x]
F[67,x] = 1/F[41,x]/F[75,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[41,x]*F[72,x]
F[72,x] = F[73,x]+F[92,x]
F[73,x] = F[74,x]
F[74,x] = F[41,x]*F[75,x]*F[77,x]
F[75,x] = -F[24,x]+F[76,x]
F[76,x] = -F[47,x]+F[12,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = 1/F[41,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = -F[85,x]+F[81,x]
F[81,x] = 1/F[41,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[2,x]+F[84,x]
F[84,x] = -F[0,x]+F[78,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[2,x]*F[78,x]
F[87,x] = F[88,x]
F[88,x] = F[41,x]*F[89,x]*F[90,x]
F[89,x] = F[20,x]+F[25,x]
F[90,x] = 1/F[41,x]*F[91,x]
F[91,x] = F[80,x]
F[92,x] = F[93,x]
F[93,x] = F[41,x]*F[75,x]*F[94,x]
F[94,x] = 1/F[41,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[41,x]*F[67,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[41,x]
F[101,x] = F[64,x]
F[102,x] = F[103,x]+F[5,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[41,x]
F[105,x] = F[106,x]
F[106,x] = F[41,x]*F[62,x]*F[75,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_{4}\! \left(x \right) F_{41}\! \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_{41}\! \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_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{41}\! \left(x \right) F_{52}\! \left(x \right) F_{55}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}+2 x^{2} F_{20}\! \left(x \right)-2 x F_{20} \left(x \right)^{2}+x^{2}-3 x F_{20}\! \left(x \right)-x +2 F_{20}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{41}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{31}\! \left(x \right) F_{41}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{35}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{102}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{41}\! \left(x \right) F_{75}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{41}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{41}\! \left(x \right) F_{75}\! \left(x \right) F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{12}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{78}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{41}\! \left(x \right) F_{89}\! \left(x \right) F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{80}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{41}\! \left(x \right) F_{75}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{41}\! \left(x \right) F_{67}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{41}\! \left(x \right)
F_{101}\! \left(x \right) = F_{64}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{5}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{41}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{41}\! \left(x \right) F_{62}\! \left(x \right) F_{75}\! \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_4(x)*F_41(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_41(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_41(x)*F_62(x))
Eq(F_12(x), F_13(x)/(F_41(x)*F_52(x)*F_55(x)))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_41(x))
Eq(F_15(x), F_16(x)/F_41(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) + F_49(x))
Eq(F_18(x), F_19(x) + F_48(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*(F_20(x) + 1)**2 + (x + 1)*(F_20(x) + 1) + F_20(x) - 1)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_41(x))
Eq(F_23(x), F_24(x) + F_47(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_31(x)*F_41(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_2(x) + F_6(x))
Eq(F_31(x), F_32(x)/F_41(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_26(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_0(x))
Eq(F_35(x), F_36(x) - F_42(x))
Eq(F_36(x), F_37(x)/F_41(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), -F_0(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_41(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), x)
Eq(F_42(x), F_43(x) - F_46(x))
Eq(F_43(x), F_44(x)/F_41(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), -F_20(x) + F_38(x))
Eq(F_46(x), F_2(x)*F_34(x))
Eq(F_47(x), F_26(x)*F_30(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_41(x)*F_51(x))
Eq(F_51(x), F_14(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_52(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_41(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_41(x)*F_59(x))
Eq(F_62(x), F_63(x)/F_41(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), -F_103(x) + F_65(x))
Eq(F_65(x), -F_4(x) + F_66(x))
Eq(F_66(x), F_102(x) + F_67(x))
Eq(F_67(x), F_68(x)/(F_41(x)*F_75(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_41(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_92(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_41(x)*F_75(x)*F_77(x))
Eq(F_75(x), -F_24(x) + F_76(x))
Eq(F_76(x), F_12(x) - F_47(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x)/F_41(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x) - F_85(x))
Eq(F_81(x), F_82(x)/F_41(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), -F_2(x) + F_84(x))
Eq(F_84(x), -F_0(x) + F_78(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_2(x)*F_78(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_41(x)*F_89(x)*F_90(x))
Eq(F_89(x), F_20(x) + F_25(x))
Eq(F_90(x), F_91(x)/F_41(x))
Eq(F_91(x), F_80(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_41(x)*F_75(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_41(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_41(x)*F_67(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_41(x))
Eq(F_101(x), F_64(x))
Eq(F_102(x), F_103(x) + F_5(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_41(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_41(x)*F_62(x)*F_75(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"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, 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": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 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, 3, 2], "pos": [[0, 1], [0, 1], [0, 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