01342_01423_01432_02341_02431_10342_10423_10432
Counting sequence:
1, 1, 2, 6, 24, 112, 564, 2966, 16064, 88953, 501271, 2865259, 16572146, 96808194, 570342525, 3384930335, 20218528788, 121451581249, 733220612479, 4446437515379, 27073168981837, 165442503689901, 1014357616003908, 6237996123527893, 38467946829232199, 237824193986746435, 1473773207993449231, 9152651609627961796, 56955688768220870132, 355091680605951351767, 2217698589977330333523, 13873112728557615082343, 86918068781091878825440, 545343883585318825329115, 3426242638459271496086192, 21553575456715898810007219, 135751035472153119971575395, 855975224152437185974331759, 5403153522643834799668111257, 34141088643945332110979691680, 215937992972501066314536210616, 1367041588602489198185622133813, 8661960149701601392406136410204, 54930630621412208866499647924170, 348626439626592217599949141343052, 2214307262807366435237662696087189, 14074493919980352301430852655929157, 89522349261981471446511696723126105, 569798397874338437479695194243322811, 3629026336070400705835279441114567769, 23127407344571725883511939171032608348, 147475937593103881938872988055926682415, 940941952086625881575928887154119777422, 6006791758715250771737639234498627054272, 38366444059165575626852231383372755312848, 245177936546515376876137159390319378790020, 1567559991969006310797588352176289594700912, 10027032139115053634398351887441372836533421, 64168071373932842848239191496119442345648454, 410825283368447835626802808729951468155169565, 2631361590564207320797558149808582186956213735, 16860987182493995925188243512297172743070487997, 108083343176089458547945188162888066008970975900, 693110258255224311459662172188865951479978033684, 4446398779402181668423773005911734781873878115771, 28534614184697593592208632230738984094445082656923, 183184331331242219047746480324402636888048608228368, 1176393982503786368379938717459981301551583955173604, 7557202290099598189075145417155024970196616816111011, 48563379772403050618700990375738297100873284011505117, 312170862194694262639664893270087894837658583789456535, 2007278335954389652659502860618544469292669221873152637, 12910734026005793034431634772376621357493443369832276417, 83065150404804185371457952597576249154355208190823771867, 534574189207704865586205063528813365945509355346713427590, 3441240966202115377230683495252977008481474191699607556580, 22158330650413331379694439709977584302553519923583710463495, 142715406356379559332173775087361121710934565651403110129958, 919419410379639213931532256100799605080348350873428086545475, 5924650034843305095354572848831649597164017908891430884542267, 38186978608338771440533286363689663820484524463671897943186486, 246189140974189588197262651485593880737329733106698709865057187, 1587526625721949575524960667831007831071392268005269947650746909, 10239277028826365688065216490324918477478156551612995999583949756, 66055871129567057033473060955377605664079232720135491944266615055, 426231161863095396096106104770681396639542292122290061876771780740, 2750859935181292562499974949783090039826374037521257983444552851429, 17757392848512534099691919213971046811349419888124727973319435050453, 114650348763164799643534667430624127569276657993802958006459830663738, 740380694642671477765320266769470733608909408397507029227867259722846, 4782075848943554463454621265897403237574371561583861104829295452348031, 30892830677214707344236157611714841183555407311596538618102392007612266, 199607602209512514099037366770768002971436796252051542622873293141264141, 1289950061342399009520901889825095637434047161667348748382944626392937578, 8337647569966748760264128653837688879325039355383371866637817508240197096, 53899831558554003813740595003233086652900546771086095257045750186140044367, 348500167873006678941444637616685955331705645162684694107290439557718350974, 2253662110410882282304376414826989432405232460455009225782747257109680135640, 14576169392758162200650319737477099736434762752861330112513374207198402169555, 94289950926221229866318268215849057177294805172844913206371491930190696337687, 610033186429790552002443410743235842099025103878177456852524569110560606911770
Implicit equation for the generating function in Maple syntax:
2*x^2*(x^3-15*x^2+23*x-10)*(x-1)^2*F(x)^6+x*(x-1)*(x^5+43*x^4-147*x^3+155*x^2-47*x-6)*F(x)^5-x*(x-1)*(x^5+21*x^4-84*x^3+104*x^2-23*x-20)*F(x)^4+(x-1)*(7*x^5+x^4-26*x^3+39*x^2-30*x+1)*F(x)^3+(-2*x^6-12*x^5+72*x^4-121*x^3+89*x^2-30*x+3)*F(x)^2+(x-1)*(5*x^4-20*x^3+33*x^2-14*x+3)*F(x)-x^5+3*x^4-7*x^3+9*x^2-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
2 x^{2} \left(x^{3}-15 x^{2}+23 x -10\right) \left(x -1\right)^{2} F \! \left(x \right)^{6}+x \left(x -1\right) \left(x^{5}+43 x^{4}-147 x^{3}+155 x^{2}-47 x -6\right) F \! \left(x \right)^{5}-x \left(x -1\right) \left(x^{5}+21 x^{4}-84 x^{3}+104 x^{2}-23 x -20\right) F \! \left(x \right)^{4}+\left(x -1\right) \left(7 x^{5}+x^{4}-26 x^{3}+39 x^{2}-30 x +1\right) F \! \left(x \right)^{3}+\left(-2 x^{6}-12 x^{5}+72 x^{4}-121 x^{3}+89 x^{2}-30 x +3\right) F \! \left(x \right)^{2}+\left(x -1\right) \left(5 x^{4}-20 x^{3}+33 x^{2}-14 x +3\right) F \! \left(x \right)-x^{5}+3 x^{4}-7 x^{3}+9 x^{2}-4 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 564
a(7) = 2966
a(8) = 16064
a(9) = 88953
a(10) = 501271
a(11) = 2865259
a(12) = 16572146
a(13) = 96808194
a(14) = 570342525
a(15) = 3384930335
a(16) = 20218528788
a(17) = 121451581249
a(18) = 733220612479
a(19) = 4446437515379
a(20) = 27073168981837
a(21) = 165442503689901
a(22) = 1014357616003908
a(23) = 6237996123527893
a(24) = 38467946829232199
a(25) = 237824193986746435
a(26) = 1473773207993449231
a(27) = 9152651609627961796
a(28) = 56955688768220870132
a(29) = 355091680605951351767
a(30) = 2217698589977330333523
a(31) = 13873112728557615082343
a(32) = 86918068781091878825440
a(33) = 545343883585318825329115
a(34) = 3426242638459271496086192
a(35) = 21553575456715898810007219
a(36) = 135751035472153119971575395
a(37) = 855975224152437185974331759
a(38) = 5403153522643834799668111257
a(39) = 34141088643945332110979691680
a(40) = 215937992972501066314536210616
a(41) = 1367041588602489198185622133813
a(42) = 8661960149701601392406136410204
a(43) = 54930630621412208866499647924170
a(44) = 348626439626592217599949141343052
a(45) = 2214307262807366435237662696087189
a(46) = 14074493919980352301430852655929157
a(47) = 89522349261981471446511696723126105
a(48) = 569798397874338437479695194243322811
a(49) = 3629026336070400705835279441114567769
a(50) = 23127407344571725883511939171032608348
a(51) = 147475937593103881938872988055926682415
a(52) = 940941952086625881575928887154119777422
a(53) = 6006791758715250771737639234498627054272
a(54) = 38366444059165575626852231383372755312848
a(55) = 245177936546515376876137159390319378790020
a(56) = 1567559991969006310797588352176289594700912
a(57) = 10027032139115053634398351887441372836533421
a(58) = 64168071373932842848239191496119442345648454
a(59) = 410825283368447835626802808729951468155169565
a(60) = 2631361590564207320797558149808582186956213735
a(61) = 16860987182493995925188243512297172743070487997
a(62) = 108083343176089458547945188162888066008970975900
a(63) = 693110258255224311459662172188865951479978033684
a(64) = 4446398779402181668423773005911734781873878115771
a(65) = 28534614184697593592208632230738984094445082656923
a(66) = 183184331331242219047746480324402636888048608228368
a(67) = 1176393982503786368379938717459981301551583955173604
a(68) = 7557202290099598189075145417155024970196616816111011
a(69) = 48563379772403050618700990375738297100873284011505117
a(70) = 312170862194694262639664893270087894837658583789456535
a(71) = 2007278335954389652659502860618544469292669221873152637
a(72) = 12910734026005793034431634772376621357493443369832276417
a(73) = 83065150404804185371457952597576249154355208190823771867
a(74) = 534574189207704865586205063528813365945509355346713427590
a(75) = 3441240966202115377230683495252977008481474191699607556580
a(76) = 22158330650413331379694439709977584302553519923583710463495
a(77) = 142715406356379559332173775087361121710934565651403110129958
a(78) = 919419410379639213931532256100799605080348350873428086545475
a(79) = 5924650034843305095354572848831649597164017908891430884542267
a(80) = 38186978608338771440533286363689663820484524463671897943186486
a(81) = 246189140974189588197262651485593880737329733106698709865057187
a(82) = 1587526625721949575524960667831007831071392268005269947650746909
a(83) = 10239277028826365688065216490324918477478156551612995999583949756
a(84) = 66055871129567057033473060955377605664079232720135491944266615055
a(85) = 426231161863095396096106104770681396639542292122290061876771780740
a(86) = 2750859935181292562499974949783090039826374037521257983444552851429
a(87) = 17757392848512534099691919213971046811349419888124727973319435050453
a(88) = 114650348763164799643534667430624127569276657993802958006459830663738
a(89) = 740380694642671477765320266769470733608909408397507029227867259722846
a(90) = 4782075848943554463454621265897403237574371561583861104829295452348031
a(91) = 30892830677214707344236157611714841183555407311596538618102392007612266
a(92) = 199607602209512514099037366770768002971436796252051542622873293141264141
a(93) = 1289950061342399009520901889825095637434047161667348748382944626392937578
a(94) = 8337647569966748760264128653837688879325039355383371866637817508240197096
a(95) = 53899831558554003813740595003233086652900546771086095257045750186140044367
a(96) = 348500167873006678941444637616685955331705645162684694107290439557718350974
a(97) = 2253662110410882282304376414826989432405232460455009225782747257109680135640
a(98) = 14576169392758162200650319737477099736434762752861330112513374207198402169555
a(99) = 94289950926221229866318268215849057177294805172844913206371491930190696337687
a(100) = 610033186429790552002443410743235842099025103878177456852524569110560606911770
a(101) = 3947355604769906810728853230652016340087952393392023056308794603096738110265740
a(102) = 25545976594485901209966940666948702009742578796025285877315231869438823767697352
a(103) = 165348781860394778570168129540919462026284844940864922087417716307854242024194001
a(104) = 1070386253348218604583957366725260447548549108687410172392258917328658957141369119
a(105) = 6930106596264332289282204593089319624578120113686955770813432716917806534126394691
a(106) = 44874336862247388161162438096852500499110456919009779487238652411051826063731234332
a(107) = 290612178470779191729320829449522647747207018662977277930073129790785844872742706397
a(108) = 1882288306630420460665711755188715929009733437718244361356603366992726667210638144148
a(109) = 12193096384416650397521717758059540467472412275146545286625792550053814621524670204491
a(110) = 78994414843789465190316826649644143096491454913003679068443575930185120202794741876581
a(111) = 511837732675532387305722209252988245114902236459156649833617031702282518203622391138259
a(112) = 3316811472378312223735550525529012338130782989080032591198925486860917264638266361151032
a(113) = 21496161598770234941689445660474502053446706026925753482433091305452951577723569805391011
a(114) = 139332293350846843020411772112538441513435985285288871401623422873228167141364067329988970
a(115) = 903217835203817120359016809597763043539751514492035804360635798955874256141888145230677939
a(116) = 5855745792980182568145176696609420106026577011653662033386939833689780389057468030649759699
a(117) = 37968206047987876838781402776679219264993976030598562540355271292903932495011165076377281934
a(118) = 246209765940019509227711135087975762072726716610072836491332173233944284321385482431352873492
a(119) = 1596750316446236320901755138385536465780489721444333762446933158781520941394237855999029704967
a(120) = 10356535727923214943141344846129270310899223465260993156177607552460873884951330577578225127804
a(121) = 67179537290277255122296474885874578556026059968195747713673037889750054037816896506921564043533
a(122) = 435816605276927735806105372546798329901557577044227207486286716877673347673701211618879092775801
a(123) = 2827574671115508581076762405054664554906392347506050995070697033014702543849175270076260799173960
a(124) = 18347091732574631318203522685175246470287449854315328530692196194076618268013042660514936746387932
a(125) = 119059083778058928436146124221830269802090519064711797979201786208260190542242009112765156956529900
a(126) = 772679381978730981325004786709285933473717057149094996302426458249383300044300810692575800921205671
a(127) = 5015069328685694310693423149326015064731887802402809359506046275906926364940624352014301551525706782
a(128) = 32553279664885108795981093702587213385101350005650186290489091389268470947911763240238034291802808798
a(129) = 211325606522648894839026230372722996180704829051640808776086693591045937856528305304208756125125822727
a(130) = 1371982134428155865633823774745708890865604224861893288891456781300360266988572032277570691804870034098
a(131) = 8908060331597338769215795722858896726125066650109982511298860388517686960218760714685571013398151046214
a(132) = 57843641094954509086951754369024311419093015168433371654007404182634417706398078240955627998766590692453
a(133) = 375634355859536260046341507141595455036935884486912042068906939098238602733284727726390057813474379962273
a(134) = 2439560789321419161056724698338026008002010282524030398584675496443214071960539628562039156134583129533193
a(135) = 15845067478334780728309837867084360190925397738634046264379663869833406211440542740533187917707426346870146
a(136) = 102922925106233069821577414942277832875448495228025444026988898326386714724977382454691368057704829263645433
a(137) = 668598205685456537647021436980012934567916193708329135203849733670690997175551003764423213266482354504414939
a(138) = 4343630189308691543953684317556129030080203950822266436419593284013766039523762875778715834297967917884902793
a(139) = 28221138573664637450309625751808746137612342966949885786870654529108270403775304547848213049063962313358498002
a(140) = 183370633193016206553869229963785584681731086359994221793398738944165338404233058007910835529360676004531891630
a(141) = 1191566065100694576997877626063554798680688354229624234902635589466609188849620978279813665660437436513764281103
a(142) = 7743531862775451760886060746495546805513221354258935084552678138477683541665249128445707710516069861165108575378
a(143) = 50325977360288355368642868300827425582004183279758075083976561616583587412834445624369848210853106035484504096145
a(144) = 327097378561487985150716608977657710944882898298489983093803376947547496969343369507466545539439111530189278996957
a(145) = 2126146514239526577172822205296322724625843501771689236071740109146300922669478287714461363896564035971176311703146
a(146) = 13821022192942178460356342055681398046882782270367393753739663784026094917377354926005346933657321200935627462216238
a(147) = 89849894203885749822242574861766356054559322853094168411655499646254874799251826974538610678098912046353654690005701
a(148) = 584150824787501249939776765744069785105886895041685492884612479916852573621313738772535866209250289778784881365990631
a(149) = 3798061855100307476511042687893776170828468983601133373217817946762650487115205234579224809558330644560072583161580424
a(150) = 24696095285035598906196859560644217905218638707622176062049001116307022166512102428935345228486330279785063858149714588
a(151) = 160591806307793205366534651372063341731405983283792520641810018075745029026362777740094204327230932404986451890178739545
a(152) = 1044352056240046533219545529961156823299284371965422402048952090392705830158302267553878019668299957983557088388240068658
a(153) = 6792013637434333427970493817347539384857359172469108870818946310047344851974876639486410395779323022357394492855955156474
a(154) = 44175135174438777573235843050561706511189637040258208007689786675430304754237193261956494297067869916685804206057562241015
a(155) = 287332387642375937325109964431141929042850637884822251512587414611402997638108612160646026793032718794171414323763274727098
a(n+156) = 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57510380850200062198004934021941181782196361735686010*n^3+553560339064632829395010948524434396881161833660017296625864848125*n^2+28633808808116440605140979748971208333392336608159043789511167082302*n+592265439556112585696496901828097676637445007942861837194343469856820)/(n+154)/(2*n+313)/(2*n+309)/(n+157)/(n+156)*a(n+105), n >= 156
Recurrence in latex format:
a{\left(0 \right)} = 1
a{\left(1 \right)} = 1
a{\left(2 \right)} = 2
a{\left(3 \right)} = 6
a{\left(4 \right)} = 24
a{\left(5 \right)} = 112
a{\left(6 \right)} = 564
a{\left(7 \right)} = 2966
a{\left(8 \right)} = 16064
a{\left(9 \right)} = 88953
a{\left(10 \right)} = 501271
a{\left(11 \right)} = 2865259
a{\left(12 \right)} = 16572146
a{\left(13 \right)} = 96808194
a{\left(14 \right)} = 570342525
a{\left(15 \right)} = 3384930335
a{\left(16 \right)} = 20218528788
a{\left(17 \right)} = 121451581249
a{\left(18 \right)} = 733220612479
a{\left(19 \right)} = 4446437515379
a{\left(20 \right)} = 27073168981837
a{\left(21 \right)} = 165442503689901
a{\left(22 \right)} = 1014357616003908
a{\left(23 \right)} = 6237996123527893
a{\left(24 \right)} = 38467946829232199
a{\left(25 \right)} = 237824193986746435
a{\left(26 \right)} = 1473773207993449231
a{\left(27 \right)} = 9152651609627961796
a{\left(28 \right)} = 56955688768220870132
a{\left(29 \right)} = 355091680605951351767
a{\left(30 \right)} = 2217698589977330333523
a{\left(31 \right)} = 13873112728557615082343
a{\left(32 \right)} = 86918068781091878825440
a{\left(33 \right)} = 545343883585318825329115
a{\left(34 \right)} = 3426242638459271496086192
a{\left(35 \right)} = 21553575456715898810007219
a{\left(36 \right)} = 135751035472153119971575395
a{\left(37 \right)} = 855975224152437185974331759
a{\left(38 \right)} = 5403153522643834799668111257
a{\left(39 \right)} = 34141088643945332110979691680
a{\left(40 \right)} = 215937992972501066314536210616
a{\left(41 \right)} = 1367041588602489198185622133813
a{\left(42 \right)} = 8661960149701601392406136410204
a{\left(43 \right)} = 54930630621412208866499647924170
a{\left(44 \right)} = 348626439626592217599949141343052
a{\left(45 \right)} = 2214307262807366435237662696087189
a{\left(46 \right)} = 14074493919980352301430852655929157
a{\left(47 \right)} = 89522349261981471446511696723126105
a{\left(48 \right)} = 569798397874338437479695194243322811
a{\left(49 \right)} = 3629026336070400705835279441114567769
a{\left(50 \right)} = 23127407344571725883511939171032608348
a{\left(51 \right)} = 147475937593103881938872988055926682415
a{\left(52 \right)} = 940941952086625881575928887154119777422
a{\left(53 \right)} = 6006791758715250771737639234498627054272
a{\left(54 \right)} = 38366444059165575626852231383372755312848
a{\left(55 \right)} = 245177936546515376876137159390319378790020
a{\left(56 \right)} = 1567559991969006310797588352176289594700912
a{\left(57 \right)} = 10027032139115053634398351887441372836533421
a{\left(58 \right)} = 64168071373932842848239191496119442345648454
a{\left(59 \right)} = 410825283368447835626802808729951468155169565
a{\left(60 \right)} = 2631361590564207320797558149808582186956213735
a{\left(61 \right)} = 16860987182493995925188243512297172743070487997
a{\left(62 \right)} = 108083343176089458547945188162888066008970975900
a{\left(63 \right)} = 693110258255224311459662172188865951479978033684
a{\left(64 \right)} = 4446398779402181668423773005911734781873878115771
a{\left(65 \right)} = 28534614184697593592208632230738984094445082656923
a{\left(66 \right)} = 183184331331242219047746480324402636888048608228368
a{\left(67 \right)} = 1176393982503786368379938717459981301551583955173604
a{\left(68 \right)} = 7557202290099598189075145417155024970196616816111011
a{\left(69 \right)} = 48563379772403050618700990375738297100873284011505117
a{\left(70 \right)} = 312170862194694262639664893270087894837658583789456535
a{\left(71 \right)} = 2007278335954389652659502860618544469292669221873152637
a{\left(72 \right)} = 12910734026005793034431634772376621357493443369832276417
a{\left(73 \right)} = 83065150404804185371457952597576249154355208190823771867
a{\left(74 \right)} = 534574189207704865586205063528813365945509355346713427590
a{\left(75 \right)} = 3441240966202115377230683495252977008481474191699607556580
a{\left(76 \right)} = 22158330650413331379694439709977584302553519923583710463495
a{\left(77 \right)} = 142715406356379559332173775087361121710934565651403110129958
a{\left(78 \right)} = 919419410379639213931532256100799605080348350873428086545475
a{\left(79 \right)} = 5924650034843305095354572848831649597164017908891430884542267
a{\left(80 \right)} = 38186978608338771440533286363689663820484524463671897943186486
a{\left(81 \right)} = 246189140974189588197262651485593880737329733106698709865057187
a{\left(82 \right)} = 1587526625721949575524960667831007831071392268005269947650746909
a{\left(83 \right)} = 10239277028826365688065216490324918477478156551612995999583949756
a{\left(84 \right)} = 66055871129567057033473060955377605664079232720135491944266615055
a{\left(85 \right)} = 426231161863095396096106104770681396639542292122290061876771780740
a{\left(86 \right)} = 2750859935181292562499974949783090039826374037521257983444552851429
a{\left(87 \right)} = 17757392848512534099691919213971046811349419888124727973319435050453
a{\left(88 \right)} = 114650348763164799643534667430624127569276657993802958006459830663738
a{\left(89 \right)} = 740380694642671477765320266769470733608909408397507029227867259722846
a{\left(90 \right)} = 4782075848943554463454621265897403237574371561583861104829295452348031
a{\left(91 \right)} = 30892830677214707344236157611714841183555407311596538618102392007612266
a{\left(92 \right)} = 199607602209512514099037366770768002971436796252051542622873293141264141
a{\left(93 \right)} = 1289950061342399009520901889825095637434047161667348748382944626392937578
a{\left(94 \right)} = 8337647569966748760264128653837688879325039355383371866637817508240197096
a{\left(95 \right)} = 53899831558554003813740595003233086652900546771086095257045750186140044367
a{\left(96 \right)} = 348500167873006678941444637616685955331705645162684694107290439557718350974
a{\left(97 \right)} = 2253662110410882282304376414826989432405232460455009225782747257109680135640
a{\left(98 \right)} = 14576169392758162200650319737477099736434762752861330112513374207198402169555
a{\left(99 \right)} = 94289950926221229866318268215849057177294805172844913206371491930190696337687
a{\left(100 \right)} = 610033186429790552002443410743235842099025103878177456852524569110560606911770
a{\left(101 \right)} = 3947355604769906810728853230652016340087952393392023056308794603096738110265740
a{\left(102 \right)} = 25545976594485901209966940666948702009742578796025285877315231869438823767697352
a{\left(103 \right)} = 165348781860394778570168129540919462026284844940864922087417716307854242024194001
a{\left(104 \right)} = 1070386253348218604583957366725260447548549108687410172392258917328658957141369119
a{\left(105 \right)} = 6930106596264332289282204593089319624578120113686955770813432716917806534126394691
a{\left(106 \right)} = 44874336862247388161162438096852500499110456919009779487238652411051826063731234332
a{\left(107 \right)} = 290612178470779191729320829449522647747207018662977277930073129790785844872742706397
a{\left(108 \right)} = 1882288306630420460665711755188715929009733437718244361356603366992726667210638144148
a{\left(109 \right)} = 12193096384416650397521717758059540467472412275146545286625792550053814621524670204491
a{\left(110 \right)} = 78994414843789465190316826649644143096491454913003679068443575930185120202794741876581
a{\left(111 \right)} = 511837732675532387305722209252988245114902236459156649833617031702282518203622391138259
a{\left(112 \right)} = 3316811472378312223735550525529012338130782989080032591198925486860917264638266361151032
a{\left(113 \right)} = 21496161598770234941689445660474502053446706026925753482433091305452951577723569805391011
a{\left(114 \right)} = 139332293350846843020411772112538441513435985285288871401623422873228167141364067329988970
a{\left(115 \right)} = 903217835203817120359016809597763043539751514492035804360635798955874256141888145230677939
a{\left(116 \right)} = 5855745792980182568145176696609420106026577011653662033386939833689780389057468030649759699
a{\left(117 \right)} = 37968206047987876838781402776679219264993976030598562540355271292903932495011165076377281934
a{\left(118 \right)} = 246209765940019509227711135087975762072726716610072836491332173233944284321385482431352873492
a{\left(119 \right)} = 1596750316446236320901755138385536465780489721444333762446933158781520941394237855999029704967
a{\left(120 \right)} = 10356535727923214943141344846129270310899223465260993156177607552460873884951330577578225127804
a{\left(121 \right)} = 67179537290277255122296474885874578556026059968195747713673037889750054037816896506921564043533
a{\left(122 \right)} = 435816605276927735806105372546798329901557577044227207486286716877673347673701211618879092775801
a{\left(123 \right)} = 2827574671115508581076762405054664554906392347506050995070697033014702543849175270076260799173960
a{\left(124 \right)} = 18347091732574631318203522685175246470287449854315328530692196194076618268013042660514936746387932
a{\left(125 \right)} = 119059083778058928436146124221830269802090519064711797979201786208260190542242009112765156956529900
a{\left(126 \right)} = 772679381978730981325004786709285933473717057149094996302426458249383300044300810692575800921205671
a{\left(127 \right)} = 5015069328685694310693423149326015064731887802402809359506046275906926364940624352014301551525706782
a{\left(128 \right)} = 32553279664885108795981093702587213385101350005650186290489091389268470947911763240238034291802808798
a{\left(129 \right)} = 211325606522648894839026230372722996180704829051640808776086693591045937856528305304208756125125822727
a{\left(130 \right)} = 1371982134428155865633823774745708890865604224861893288891456781300360266988572032277570691804870034098
a{\left(131 \right)} = 8908060331597338769215795722858896726125066650109982511298860388517686960218760714685571013398151046214
a{\left(132 \right)} = 57843641094954509086951754369024311419093015168433371654007404182634417706398078240955627998766590692453
a{\left(133 \right)} = 375634355859536260046341507141595455036935884486912042068906939098238602733284727726390057813474379962273
a{\left(134 \right)} = 2439560789321419161056724698338026008002010282524030398584675496443214071960539628562039156134583129533193
a{\left(135 \right)} = 15845067478334780728309837867084360190925397738634046264379663869833406211440542740533187917707426346870146
a{\left(136 \right)} = 102922925106233069821577414942277832875448495228025444026988898326386714724977382454691368057704829263645433
a{\left(137 \right)} = 668598205685456537647021436980012934567916193708329135203849733670690997175551003764423213266482354504414939
a{\left(138 \right)} = 4343630189308691543953684317556129030080203950822266436419593284013766039523762875778715834297967917884902793
a{\left(139 \right)} = 28221138573664637450309625751808746137612342966949885786870654529108270403775304547848213049063962313358498002
a{\left(140 \right)} = 183370633193016206553869229963785584681731086359994221793398738944165338404233058007910835529360676004531891630
a{\left(141 \right)} = 1191566065100694576997877626063554798680688354229624234902635589466609188849620978279813665660437436513764281103
a{\left(142 \right)} = 7743531862775451760886060746495546805513221354258935084552678138477683541665249128445707710516069861165108575378
a{\left(143 \right)} = 50325977360288355368642868300827425582004183279758075083976561616583587412834445624369848210853106035484504096145
a{\left(144 \right)} = 327097378561487985150716608977657710944882898298489983093803376947547496969343369507466545539439111530189278996957
a{\left(145 \right)} = 2126146514239526577172822205296322724625843501771689236071740109146300922669478287714461363896564035971176311703146
a{\left(146 \right)} = 13821022192942178460356342055681398046882782270367393753739663784026094917377354926005346933657321200935627462216238
a{\left(147 \right)} = 89849894203885749822242574861766356054559322853094168411655499646254874799251826974538610678098912046353654690005701
a{\left(148 \right)} = 584150824787501249939776765744069785105886895041685492884612479916852573621313738772535866209250289778784881365990631
a{\left(149 \right)} = 3798061855100307476511042687893776170828468983601133373217817946762650487115205234579224809558330644560072583161580424
a{\left(150 \right)} = 24696095285035598906196859560644217905218638707622176062049001116307022166512102428935345228486330279785063858149714588
a{\left(151 \right)} = 160591806307793205366534651372063341731405983283792520641810018075745029026362777740094204327230932404986451890178739545
a{\left(152 \right)} = 1044352056240046533219545529961156823299284371965422402048952090392705830158302267553878019668299957983557088388240068658
a{\left(153 \right)} = 6792013637434333427970493817347539384857359172469108870818946310047344851974876639486410395779323022357394492855955156474
a{\left(154 \right)} = 44175135174438777573235843050561706511189637040258208007689786675430304754237193261956494297067869916685804206057562241015
a{\left(155 \right)} = 287332387642375937325109964431141929042850637884822251512587414611402997638108612160646026793032718794171414323763274727098
a{\left(n + 156 \right)} = \frac{6493 n \left(n + 1\right) \left(2 n + 1\right) \left(4 n + 3\right) \left(4 n + 5\right) a{\left(n \right)}}{34012224000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(n + 1\right) \left(5195200687 n^{4} + 44571579516 n^{3} + 139301085128 n^{2} + 188883174216 n + 94022114256\right) a{\left(n + 1 \right)}}{272097792000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1075876 n^{4} + 664549048 n^{3} + 153928436063 n^{2} + 15846154638428 n + 611724579069537\right) a{\left(n + 155 \right)}}{2160 \left(n + 154\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(26201333138 n^{5} + 20169024402173 n^{4} + 6210172003588332 n^{3} + 956069829660371248 n^{2} + 73594073746516776049 n + 2265965561186092055160\right) a{\left(n + 154 \right)}}{972000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(11234234062571 n^{5} + 160860645706543 n^{4} + 920183714068867 n^{3} + 2618156691061643 n^{2} + 3693295239808056 n + 2061154709806860\right) a{\left(n + 2 \right)}}{2720977920000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(60232312235370 n^{5} + 46242831067429566 n^{4} + 14200796700633130895 n^{3} + 2180441501021388267415 n^{2} + 167393891905118841165710 n + 5140296884636861662130604\right) a{\left(n + 153 \right)}}{87480000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(1342433093390840 n^{5} + 27289375530917277 n^{4} + 220035462946387972 n^{3} + 880571628343037175 n^{2} + 1749167465375220276 n + 1379086953201455580\right) a{\left(n + 3 \right)}}{2720977920000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(5169338343199736 n^{5} + 3729501133897205081 n^{4} + 1073134977462979374279 n^{3} + 153888675700836811300966 n^{2} + 10993363612314505490779978 n + 312826566562168717270605480\right) a{\left(n + 152 \right)}}{1312200000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(283564441379314774 n^{5} + 7064920326193946845 n^{4} + 69552081446573044400 n^{3} + 339491080280906727185 n^{2} + 823559773848263214096 n + 795460240346254795080\right) a{\left(n + 4 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(498131282384199007 n^{5} + 48483363146137165160 n^{4} + 908989286599274042045 n^{3} + 7043652801491804747800 n^{2} + 24964292113620968918568 n + 33608074125845325425940\right) a{\left(n + 5 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(90455989442771881926 n^{5} + 67754562664111460803875 n^{4} + 20298546548638747805457398 n^{3} + 3040366929005116790094819267 n^{2} + 227678058316142683708627043362 n + 6819301796337197800934662251072\right) a{\left(n + 151 \right)}}{78732000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(268041429557713430921 n^{5} + 13806285337634490855755 n^{4} + 247507335188677685008705 n^{3} + 2066952826019369386972525 n^{2} + 8269360559811822825179814 n + 12858808309714931748590520\right) a{\left(n + 6 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(2822299641903454875082 n^{5} + 68446280631400948973675 n^{4} + 466293950940313154374040 n^{3} - 965709745303412262543695 n^{2} - 22163782046915045589465942 n - 64791007575196792245512040\right) a{\left(n + 7 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(67813667565275261727553 n^{5} + 50596318549585712418970039 n^{4} + 15099507918759471704003917585 n^{3} + 2252987142431606407948851948905 n^{2} + 168076312803876262603685111094562 n + 5015289556709492255543939918023656\right) a{\left(n + 150 \right)}}{1180980000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(181287066877277272980884 n^{5} + 8134479317224585209232871 n^{4} + 145676945682552324556012558 n^{3} + 1301492665255014952618668229 n^{2} + 5800552366459348072435589634 n + 10317029882382253590224474160\right) a{\left(n + 8 \right)}}{10883911680000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(10812902434082333145458683 n^{5} + 554028314713678597907950700 n^{4} + 11260034905683710418494304725 n^{3} + 113703881866729899329882934280 n^{2} + 571333500156287158801365808092 n + 1144056897188472923496376408440\right) a{\left(n + 9 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(13415864281762881215203634 n^{5} + 9954092853088502937092401673 n^{4} + 2954145838358185999207349139360 n^{3} + 438348290293766600417458837698415 n^{2} + 32520990111688891317942291542388286 n + 965061876622513515229921287420860952\right) a{\left(n + 149 \right)}}{7085880000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(171781004338000638989354999 n^{5} + 126685318638150950172194334396 n^{4} + 37370346898097829255899594199736 n^{3} + 5511726019564431803386180051376412 n^{2} + 406450545325601317084783946729025135 n + 11988844588438048491912410377400552742\right) a{\left(n + 148 \right)}}{3542940000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(261272643609976787824804129 n^{5} + 13127014044920918821118391135 n^{4} + 265033326931514117615405834705 n^{3} + 2687697931431762537719212848705 n^{2} + 13688378268056104508869152066846 n + 28004481976858277322321396538920\right) a{\left(n + 10 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1281678086030666855159502296 n^{5} + 71749159951679791161835674765 n^{4} + 1609960242633305742971636168350 n^{3} + 18103985274752823797971493161407 n^{2} + 102040664469447171356447626261134 n + 230657890662005945789430892114848\right) a{\left(n + 11 \right)}}{10883911680000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(5334067893279972468657495646 n^{5} + 240017712021432164105800098465 n^{4} + 3390492732309173461189832309420 n^{3} + 7088303340404634014653314053955 n^{2} - 188615348454066442666929567812646 n - 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\frac{\left(15858494711352204551898034935041346650778043911 n^{5} + 2293339687849515419369161351188750611550562544102 n^{4} + 132472423662222365827376853445167369559872407390613 n^{3} + 3820185623543734365495122955359312324199132430883026 n^{2} + 54989311718502624315467080949313074234162648417979588 n + 316023990198043608055498568276003254815487304318308632\right) a{\left(n + 30 \right)}}{10883911680000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(27157004152076065064132502132636898211083009061 n^{5} + 17801921539180800167252954950385566382433663203760 n^{4} + 4667778792974671027187963113550344054336241763105115 n^{3} + 611958580234465791489910082382420600810273870218004450 n^{2} + 40114572915858277917426105482596368212111663488274966754 n + 1051818224749344561951767842312357192554678465918059757480\right) a{\left(n + 131 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(137535336808108136056276056489687408035018972427 n^{5} + 89488531009788173986342596702680881832000534384590 n^{4} + 23290513172945738655594570064761967203082006528044615 n^{3} + 3030814449757360866671908899237555333789137329123565210 n^{2} + 197200611842213648720071311451490985477687572372437271118 n + 5132344218779061532507185017159751795347051127036083613360\right) a{\left(n + 130 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(518655663182714755226124051178697377635285608461 n^{5} + 78064887734155057544473698106638221458139603843905 n^{4} + 4695722208049361139426945543993469311666233739609245 n^{3} + 141090300550099130922610754766384540601564734536543555 n^{2} + 2117407108782137919495610479518501767284485732775557994 n + 12696209617597046400739012868977374029162093280341368920\right) a{\left(n + 31 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(1027896003114548482647284794006581564714752317723 n^{5} + 160489895753114104399909833455212088271928248224850 n^{4} + 10016994729791858642802487094838152700410574621954025 n^{3} + 312398619473598168383158765978664147641214772003896250 n^{2} + 4867897339361763179306030128361625849816208788856886232 n + 30318024925682067275510013287315951250620997243363655080\right) a{\left(n + 32 \right)}}{18139852800000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(1321115300654396858542627625290362961099873046012 n^{5} + 853180727672308369553543468537023044886033295815485 n^{4} + 220394203082652971634504064687288893654601438781325730 n^{3} + 28466110569672677256844473331063221426951460051666585875 n^{2} + 1838336182711663228253247334386768982340963971733818323978 n + 47487637999848460913568590638911003429773968175732627380560\right) a{\left(n + 129 \right)}}{27209779200000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(6024730411445401173966052523162102709982880682461 n^{5} + 3861579610712378872437030843459275375352353543571840 n^{4} + 990036913447567131322719325810673338894454920579767715 n^{3} + 126913207500584254673341087472707229005621960327358259780 n^{2} + 8134508087347319354180155720231855406868852410908981601484 n + 208552213593186387225252926497635389684697742020920587314720\right) a{\left(n + 128 \right)}}{27209779200000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(13057909041545525254963561433996512787009446669011 n^{5} + 8306321091726978275643910005509243045937164654672945 n^{4} + 2113503605682462717878049376416360667301248583064255435 n^{3} + 268884946912510278608807140975260570894801237574603445575 n^{2} + 17104059910707141320992899194089134582818561580354851290794 n + 435202260382776458304316067732697069769902616571323221420840\right) a{\left(n + 127 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(16760575450635641236186592044371386889541866229163 n^{5} + 2707571777205088078048746248088984638585619745779655 n^{4} + 174876641235127251657026232990270338311312466091786295 n^{3} + 5644709067038070245110262814053712103490216539857872945 n^{2} + 91053211421521685692956256394697010006275178556248089582 n + 587175130507762663564263657751289552483164825492508111040\right) a{\left(n + 33 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(83638295327297906396141855596757300384270553846743 n^{5} + 13949935688045255223547801148411814703792034408222660 n^{4} + 930338075919356939600969197898930115889515035207870365 n^{3} + 31010707059803287780479697249641661179032445250222863880 n^{2} + 516624250378826521453740422177685081599022479728134704472 n + 3441195020637994771831534344131943099394781732365914367440\right) a{\left(n + 34 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(96112183373034866420370633410055344466044068684978 n^{5} + 16521397124605552552373155201646134596013950986202245 n^{4} + 1135638629621091775348503689500253426897172082416944285 n^{3} + 39017670433433462480474211005884530611816128153934524690 n^{2} + 670042708560068566828729275286622103591222192234457458012 n + 4600925271573242989999807381992825337264932218505651866220\right) a{\left(n + 35 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(107706526159917476581434242391270311510915549557229 n^{5} + 67993352709302990481962108551104256377715552154519305 n^{4} + 17169207350106556067925592559766237788011347368636611255 n^{3} + 2167721091149425057747614288153023478930297141345636881285 n^{2} + 136844054437606594477330628364317703932294264893542777950886 n + 3455475561751926012419060819299640541366275222835937823652720\right) a{\left(n + 126 \right)}}{27209779200000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(211476036696525786769760239605692548362643313358328 n^{5} + 132482317036315652249125301688023326116234849194134240 n^{4} + 33198168580805653106977688028529169803781719209960048425 n^{3} + 4159487391413627040431012189068212598640091059146269960140 n^{2} + 260576338483229616794753493139653046651103338087385211131097 n + 6529645617625232939510700132415562445847693021550727453088470\right) a{\left(n + 125 \right)}}{13604889600000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(639872934515894612076400029297712025477380477501141 n^{5} + 116293993589105307952929339932241402017616840287793276 n^{4} + 8452001407738594321307781814871080672327090068643962869 n^{3} + 307046901283684804896190159897494517081718771244030997698 n^{2} + 5575534376254562369903755806881829675563397790647504481296 n + 40484445347389003506717221364934091031476551391142572984088\right) a{\left(n + 37 \right)}}{5441955840000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - 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\frac{\left(367240845814437979468559388887240603570669567084890420137876620 n^{5} + 136889693477898430491984451685672188275095538556875583034019365415 n^{4} + 20410528482315511017871252849099887403466456505131456708636431917370 n^{3} + 1521634060660818063628560726080294680989702844853474450234764996744977 n^{2} + 56720148647608554422764466684462826347332758543660090888998108954355786 n + 845715545724812258919577602070913098632639596023617901248975846850362768\right) a{\left(n + 75 \right)}}{10883911680000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(443436863312281893631797416479762263458712106745912993833263771 n^{5} + 183572752913317473403840091619129550947367202359832784349362697520 n^{4} + 30372657268317254976893701155528520355881624688407468275994421915205 n^{3} + 2510387546815949394578552666759340753254739875075678589496024302940060 n^{2} + 103646596488818599172888561582344702306869051756399663427751952458178324 n + 1709959309987233032816707660403734886856423675602875907958204743477593920\right) a{\left(n + 85 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(555802152627344878052903561663787252656689805055527835706088326 n^{5} + 196655081497929157216364382356355256904826246247951995075113069725 n^{4} + 27834193353919567649247504310477612429207723992211017203622901907300 n^{3} + 1969924999685842224963555032199710950141992394864676333663074940941685 n^{2} + 69713575544272668334238228450313153349065373187219051734164455150712804 n + 986894277949732930675414673669132846275056708401286857794485440971346100\right) a{\left(n + 71 \right)}}{27209779200000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(625169767758973760280520063732553181665427223990089853332767351 n^{5} + 241691176442820951195689094211902903118269475353143452270915058120 n^{4} + 37372883364160028583641133438752096857811943839534752723143850891685 n^{3} + 2889304978293980727978795084907113817451847638504175731161707211349820 n^{2} + 111678363190466824641067369524966496292454886558934382294273780589126824 n + 1726519087853208017051499672440269976953446704009776861864675154164405200\right) a{\left(n + 78 \right)}}{18139852800000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(712451030417536505432445022480793684248822185778779707254969511 n^{5} + 245254435866755400229403767160936710058918800318170281971263633525 n^{4} + 33773426723254065057734389811837784305100039305868418360563068594635 n^{3} + 2325620781205111445296894237288476099256811652534832996165727010944715 n^{2} + 80076902335090345034302476881734418950624527372690800133230339881396734 n + 1102984135109148075864090249914881791640851131028670953809497594563286560\right) a{\left(n + 69 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(880269794212247939610104545393785531344725113483085655514312699 n^{5} + 358994238135225954112645293392088401522276250021238131446686991080 n^{4} + 58540818087331668323346383254413813097219060193331662137608576136365 n^{3} + 4771239192447707833887973802590469095057676983845283597824577915658840 n^{2} + 194354938556859486217615296749123986523083521928062694401260274428148336 n + 3165426566534748710389107528062292850550645515515837340114006571100701760\right) a{\left(n + 83 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(904242167048759224011192177948854013416024106363855200313244023 n^{5} + 315615318696080830050038589253374278387800739368873927557110294570 n^{4} + 44068085972978890021354063927862145718723841856615214084408772614485 n^{3} + 3076749878097437720515362246623140919397116693195545106121011580343630 n^{2} + 107414062991368809475200822348325643650436496412432698395792978655116652 n + 1500099505454472867534137798366221775209362710386033167953517904674380640\right) a{\left(n + 70 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1323382785305633031337015820323908034407606974588117657461303651 n^{5} + 474549925683457472506221228828895282900979428093179143955406886465 n^{4} + 68070960775759014869069978974201895057816445998727250639560466535315 n^{3} + 4882411919469346943316071553909509304478348593812310351837591248750275 n^{2} + 175104983016850453765092758273608563191984874829313463764840028296773614 n + 2512135674866951481734327998155727934526770444206206460551144704786111880\right) a{\left(n + 72 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1580513428550492101787178013314604616602483624410112055423916281 n^{5} + 625126614426234007615825085777379061297750281044205255428191894040 n^{4} + 98886784090187571534801823974189771940380859586714823269300785230775 n^{3} + 7820163004991594984543630259568246122878202662163685631218076347172860 n^{2} + 309169979684251920976527853076874201505239552633912456667835043753287124 n + 4888428879859621958452345357746565417146648602607554926003023962173978440\right) a{\left(n + 80 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1701626472194199344024226023177578046958157293007406815922622212 n^{5} + 626296204957080027300641675028718145991860687741149560284132051185 n^{4} + 92207570143327053208932357680856758414172798168170000564678185760170 n^{3} + 6787869709076452613393850149678236636358949930736047073977250247516015 n^{2} + 249850007595589074523589523175236159479786340517754274949874834214936618 n + 3678688108385634976051693864418891548886026402913989554690939876597819960\right) a{\left(n + 74 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} + \frac{\left(1915380494370592181326101229143759714780894632375312729909165824 n^{5} + 722888654374234946081147816922397969266948773310587000030627459985 n^{4} + 109129661939329978271458054604339464857235421067011537942359037598590 n^{3} + 8237166300891317950658625339298295140197957508135583467052599108367835 n^{2} + 310867266319113433853588894858865502594466630108450936078454260768603766 n + 4692699504321859080405093268232494087318860687924106537520699151197408520\right) a{\left(n + 76 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)} - \frac{\left(1929681911191904793107785252085541147263552117987763195987368492 n^{5} + 737200744362148958016436196976331001657563250371280346902384627705 n^{4} + 112649884605292037089804353556924905444330927647362840985662380883690 n^{3} + 8606548311624256162379461640723889344737483109451007133536104083219035 n^{2} + 328759872145452435532867734803478495886430951878562373600020542762823718 n + 5023059424131237959663476013600144141676227827591308150212592520965217920\right) a{\left(n + 77 \right)}}{54419558400000000 \left(n + 154\right) \left(n + 156\right) \left(n + 157\right) \left(2 n + 309\right) \left(2 n + 313\right)}, \quad n \geq 156
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24744/
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[23,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[23,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[23,x]
F[12,x] = F[13,x]+F[86,x]
F[13,x] = F[14,x]*F[38,x]
F[14,x] = F[15,x]+F[84,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = F[15,x]+F[19,x]
F[19,x] = F[20,x]+F[24,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[23,x]*F[28,x]*F[35,x]
F[28,x] = 1/F[23,x]/F[56,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[34,x]+F[31,x]
F[31,x] = 1/F[23,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[2,x]+F[20,x]
F[34,x] = F[2,x]*F[35,x]
F[35,x] = F[0,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[23,x]*F[38,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[35,x]+F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[23,x]*F[42,x]
F[42,x] = F[6,x]
F[43,x] = F[44,x]
F[44,x] = F[23,x]*F[45,x]*F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[23,x]*F[45,x]
F[48,x] = 1/F[23,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = -F[51,x]+F[8,x]
F[51,x] = F[52,x]+F[9,x]
F[52,x] = F[53,x]
F[53,x] = F[23,x]*F[48,x]*F[54,x]
F[54,x] = F[46,x]+F[55,x]
F[55,x] = -F[45,x]+F[15,x]
F[56,x] = 1/F[23,x]/F[45,x]/F[71,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[23,x]*F[45,x]*F[60,x]
F[60,x] = 1/F[23,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[69,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[67,x]+F[9,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[23,x]*F[38,x]
F[69,x] = F[70,x]
F[70,x] = F[23,x]*F[58,x]
F[71,x] = F[1,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[23,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[1,x]+F[23,x]
F[76,x] = F[72,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]+F[83,x]
F[78,x] = 0
F[79,x] = F[23,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[23,x]
F[82,x] = F[77,x]
F[83,x] = F[23,x]*F[72,x]
F[84,x] = F[85,x]
F[85,x] = F[15,x]*F[23,x]*F[35,x]
F[86,x] = F[136,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = -F[135,x]+F[89,x]
F[89,x] = F[133,x]+F[90,x]
F[90,x] = F[128,x]+F[91,x]
F[91,x] = F[15,x]*F[92,x]
F[92,x] = F[1,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[23,x]*F[95,x]
F[95,x] = F[103,x]+F[96,x]
F[96,x] = F[1,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[96,x]
F[100,x] = F[101,x]+F[23,x]
F[101,x] = F[102,x]
F[102,x] = F[23,x]*F[97,x]
F[103,x] = F[104,x]+F[72,x]
F[104,x] = F[105,x]+F[126,x]+F[78,x]
F[105,x] = F[106,x]*F[23,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[97,x]
F[108,x] = F[102,x]+F[109,x]+F[78,x]
F[109,x] = F[110,x]*F[23,x]
F[110,x] = F[100,x]
F[111,x] = F[104,x]+F[112,x]
F[112,x] = F[113,x]+F[117,x]+F[118,x]+F[78,x]
F[113,x] = F[114,x]*F[23,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[108,x]
F[116,x] = F[112,x]
F[117,x] = F[104,x]*F[23,x]
F[118,x] = F[119,x]*F[23,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[77,x]
F[121,x] = 2*F[78,x]+F[117,x]+F[122,x]
F[122,x] = F[123,x]*F[23,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[101,x]
F[125,x] = F[121,x]
F[126,x] = F[127,x]*F[23,x]
F[127,x] = F[103,x]+F[120,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[15,x]*F[23,x]
F[130,x] = 1/F[23,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = -F[92,x]+F[35,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[23,x]*F[45,x]
F[135,x] = F[133,x]+F[14,x]
F[136,x] = F[137,x]*F[276,x]
F[137,x] = 1/F[93,x]*F[138,x]
F[138,x] = -F[88,x]+F[139,x]
F[139,x] = F[140,x]+F[275,x]
F[140,x] = -F[274,x]+F[141,x]
F[141,x] = 1/F[23,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[271,x]+F[144,x]
F[144,x] = F[145,x]+F[244,x]
F[145,x] = F[146,x]+F[93,x]
F[146,x] = F[147,x]+F[195,x]+F[78,x]
F[147,x] = F[148,x]*F[23,x]
F[148,x] = F[149,x]+F[158,x]
F[149,x] = F[150,x]+F[23,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[23,x]
F[152,x] = F[149,x]+F[153,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[155,x]
F[155,x] = x^2
F[156,x] = F[157,x]
F[157,x] = F[150,x]*F[23,x]
F[158,x] = F[159,x]+F[171,x]
F[159,x] = F[160,x]+F[170,x]+F[78,x]
F[160,x] = F[161,x]*F[23,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[154,x]+F[23,x]
F[163,x] = F[159,x]+F[164,x]
F[164,x] = 2*F[78,x]+F[165,x]+F[169,x]
F[165,x] = F[166,x]*F[23,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[154,x]
F[168,x] = F[164,x]
F[169,x] = F[159,x]*F[23,x]
F[170,x] = F[23,x]*F[46,x]
F[171,x] = 2*F[78,x]+F[172,x]+F[193,x]
F[172,x] = F[173,x]*F[23,x]
F[173,x] = F[174,x]+F[178,x]
F[174,x] = F[150,x]+F[175,x]
F[175,x] = 2*F[78,x]+F[157,x]+F[176,x]
F[176,x] = F[177,x]*F[23,x]
F[177,x] = F[153,x]
F[178,x] = F[171,x]+F[179,x]
F[179,x] = 2*F[78,x]+F[180,x]+F[184,x]+F[185,x]
F[180,x] = F[181,x]*F[23,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[175,x]
F[183,x] = F[179,x]
F[184,x] = F[171,x]*F[23,x]
F[185,x] = F[186,x]*F[23,x]
F[186,x] = F[187,x]
F[187,x] = F[164,x]+F[188,x]
F[188,x] = 3*F[78,x]+F[184,x]+F[189,x]
F[189,x] = F[190,x]*F[23,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[156,x]
F[192,x] = F[188,x]
F[193,x] = F[194,x]*F[23,x]
F[194,x] = F[158,x]+F[187,x]
F[195,x] = F[196,x]*F[23,x]
F[196,x] = F[197,x]+F[208,x]
F[197,x] = F[198,x]+F[46,x]
F[198,x] = F[199,x]+F[202,x]+F[78,x]
F[199,x] = F[200,x]*F[23,x]
F[200,x] = F[201,x]+F[23,x]
F[201,x] = F[170,x]+F[199,x]+F[78,x]
F[202,x] = F[203,x]*F[23,x]
F[203,x] = F[197,x]+F[204,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[170,x]
F[206,x] = F[207,x]
F[207,x] = F[198,x]*F[23,x]
F[208,x] = F[209,x]+F[220,x]
F[209,x] = F[210,x]
F[210,x] = F[211,x]*F[23,x]
F[211,x] = F[212,x]+F[213,x]
F[212,x] = F[205,x]+F[46,x]
F[213,x] = F[209,x]+F[214,x]
F[214,x] = 2*F[78,x]+F[215,x]+F[219,x]
F[215,x] = F[216,x]*F[23,x]
F[216,x] = F[217,x]+F[218,x]
F[217,x] = F[205,x]
F[218,x] = F[214,x]
F[219,x] = F[209,x]*F[23,x]
F[220,x] = 2*F[78,x]+F[221,x]+F[242,x]
F[221,x] = F[222,x]*F[23,x]
F[222,x] = F[223,x]+F[227,x]
F[223,x] = F[198,x]+F[224,x]
F[224,x] = 2*F[78,x]+F[207,x]+F[225,x]
F[225,x] = F[226,x]*F[23,x]
F[226,x] = F[204,x]
F[227,x] = F[220,x]+F[228,x]
F[228,x] = 2*F[78,x]+F[229,x]+F[233,x]+F[234,x]
F[229,x] = F[23,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[224,x]
F[232,x] = F[228,x]
F[233,x] = F[220,x]*F[23,x]
F[234,x] = F[23,x]*F[235,x]
F[235,x] = F[236,x]
F[236,x] = F[214,x]+F[237,x]
F[237,x] = 3*F[78,x]+F[233,x]+F[238,x]
F[238,x] = F[23,x]*F[239,x]
F[239,x] = F[240,x]+F[241,x]
F[240,x] = F[206,x]
F[241,x] = F[237,x]
F[242,x] = F[23,x]*F[243,x]
F[243,x] = F[208,x]+F[236,x]
F[244,x] = F[245,x]
F[245,x] = F[23,x]*F[246,x]
F[246,x] = F[247,x]+F[261,x]
F[247,x] = F[248,x]*F[55,x]
F[248,x] = F[249,x]+F[251,x]
F[249,x] = F[250,x]+F[92,x]
F[250,x] = F[146,x]+F[93,x]
F[251,x] = F[252,x]+F[253,x]
F[252,x] = F[46,x]*F[92,x]
F[253,x] = F[254,x]
F[254,x] = F[23,x]*F[255,x]
F[255,x] = F[256,x]+F[97,x]
F[256,x] = F[104,x]+F[257,x]
F[257,x] = F[258,x]
F[258,x] = F[23,x]*F[259,x]
F[259,x] = F[23,x]+F[260,x]
F[260,x] = F[257,x]+F[77,x]
F[261,x] = F[262,x]+F[270,x]
F[262,x] = F[263,x]
F[263,x] = F[15,x]*F[23,x]*F[264,x]
F[264,x] = 1/F[23,x]*F[265,x]
F[265,x] = F[266,x]
F[266,x] = F[267,x]+F[269,x]
F[267,x] = F[268,x]
F[268,x] = F[130,x]*F[23,x]
F[269,x] = F[55,x]*F[93,x]
F[270,x] = F[145,x]*F[84,x]
F[271,x] = F[272,x]
F[272,x] = F[23,x]*F[249,x]*F[273,x]
F[273,x] = F[0,x]+F[84,x]
F[274,x] = F[16,x]*F[248,x]
F[275,x] = F[16,x]*F[251,x]
F[276,x] = F[277,x]+F[36,x]
F[277,x] = -F[5,x]+F[40,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_{23}\! \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_{23}\! \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_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{86}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{84}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right) F_{56}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right) F_{48}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{15}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{71}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{58}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = 0
F_{79}\! \left(x \right) = F_{23}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{23}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = F_{23}\! \left(x \right) F_{72}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{35}\! \left(x \right)
F_{86}\! \left(x \right) = F_{136}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{133}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{128}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{15}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{23}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{103}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{1}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{23}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{23}\! \left(x \right) F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{72}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{126}\! \left(x \right)+F_{78}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{97}\! \left(x \right)
F_{108}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)+F_{78}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{100}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{78}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{23}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{108}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = F_{104}\! \left(x \right) F_{23}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{77}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{23}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{101}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{23}\! \left(x \right)
F_{127}\! \left(x \right) = F_{103}\! \left(x \right)+F_{120}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{15}\! \left(x \right) F_{23}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{35}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right)+F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{276}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{93}\! \left(x \right)}
F_{138}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{275}\! \left(x \right)
F_{140}\! \left(x \right) = -F_{274}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{271}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{244}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{195}\! \left(x \right)+F_{78}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{23}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{158}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{23}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{23}\! \left(x \right)
F_{152}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = x^{2}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{150}\! \left(x \right) F_{23}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{171}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{170}\! \left(x \right)+F_{78}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{23}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{154}\! \left(x \right)+F_{23}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{23}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{154}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{159}\! \left(x \right) F_{23}\! \left(x \right)
F_{170}\! \left(x \right) = F_{23}\! \left(x \right) F_{46}\! \left(x \right)
F_{171}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{172}\! \left(x \right)+F_{193}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{23}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{178}\! \left(x \right)
F_{174}\! \left(x \right) = F_{150}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{157}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{23}\! \left(x \right)
F_{177}\! \left(x \right) = F_{153}\! \left(x \right)
F_{178}\! \left(x \right) = F_{171}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{180}\! \left(x \right)+F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{23}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{175}\! \left(x \right)
F_{183}\! \left(x \right) = F_{179}\! \left(x \right)
F_{184}\! \left(x \right) = F_{171}\! \left(x \right) F_{23}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{23}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{164}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{184}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{23}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{156}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right) F_{23}\! \left(x \right)
F_{194}\! \left(x \right) = F_{158}\! \left(x \right)+F_{187}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{23}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{208}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{46}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{202}\! \left(x \right)+F_{78}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{23}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{23}\! \left(x \right)
F_{201}\! \left(x \right) = F_{170}\! \left(x \right)+F_{199}\! \left(x \right)+F_{78}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{23}\! \left(x \right)
F_{203}\! \left(x \right) = F_{197}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{170}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{198}\! \left(x \right) F_{23}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{220}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{23}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{213}\! \left(x \right)
F_{212}\! \left(x \right) = F_{205}\! \left(x \right)+F_{46}\! \left(x \right)
F_{213}\! \left(x \right) = F_{209}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{215}\! \left(x \right)+F_{219}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right) F_{23}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{218}\! \left(x \right)
F_{217}\! \left(x \right) = F_{205}\! \left(x \right)
F_{218}\! \left(x \right) = F_{214}\! \left(x \right)
F_{219}\! \left(x \right) = F_{209}\! \left(x \right) F_{23}\! \left(x \right)
F_{220}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{221}\! \left(x \right)+F_{242}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{23}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{227}\! \left(x \right)
F_{223}\! \left(x \right) = F_{198}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{207}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{23}\! \left(x \right)
F_{226}\! \left(x \right) = F_{204}\! \left(x \right)
F_{227}\! \left(x \right) = F_{220}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{229}\! \left(x \right)+F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{229}\! \left(x \right) = F_{23}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{224}\! \left(x \right)
F_{232}\! \left(x \right) = F_{228}\! \left(x \right)
F_{233}\! \left(x \right) = F_{220}\! \left(x \right) F_{23}\! \left(x \right)
F_{234}\! \left(x \right) = F_{23}\! \left(x \right) F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{214}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{233}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{23}\! \left(x \right) F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{241}\! \left(x \right)
F_{240}\! \left(x \right) = F_{206}\! \left(x \right)
F_{241}\! \left(x \right) = F_{237}\! \left(x \right)
F_{242}\! \left(x \right) = F_{23}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{208}\! \left(x \right)+F_{236}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{23}\! \left(x \right) F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{261}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right) F_{55}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{251}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{92}\! \left(x \right)
F_{250}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{253}\! \left(x \right)
F_{252}\! \left(x \right) = F_{46}\! \left(x \right) F_{92}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{23}\! \left(x \right) F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)+F_{97}\! \left(x \right)
F_{256}\! \left(x \right) = F_{104}\! \left(x \right)+F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{23}\! \left(x \right) F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{23}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{257}\! \left(x \right)+F_{77}\! \left(x \right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)+F_{270}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = \frac{F_{265}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{269}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{130}\! \left(x \right) F_{23}\! \left(x \right)
F_{269}\! \left(x \right) = F_{55}\! \left(x \right) F_{93}\! \left(x \right)
F_{270}\! \left(x \right) = F_{145}\! \left(x \right) F_{84}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{23}\! \left(x \right) F_{249}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{274}\! \left(x \right) = F_{16}\! \left(x \right) F_{248}\! \left(x \right)
F_{275}\! \left(x \right) = F_{16}\! \left(x \right) F_{251}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{36}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{40}\! \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_23(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_23(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_23(x))
Eq(F_12(x), F_13(x) + F_86(x))
Eq(F_13(x), F_14(x)*F_38(x))
Eq(F_14(x), F_15(x) + F_84(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_15(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_24(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_23(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x)/(F_23(x)*F_56(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_34(x))
Eq(F_31(x), F_32(x)/F_23(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_2(x) + F_20(x))
Eq(F_34(x), F_2(x)*F_35(x))
Eq(F_35(x), F_0(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_23(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_35(x) + F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_23(x))
Eq(F_42(x), F_6(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_23(x)*F_45(x)*F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_23(x)*F_45(x))
Eq(F_48(x), F_49(x)/F_23(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), -F_51(x) + F_8(x))
Eq(F_51(x), F_52(x) + F_9(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_23(x)*F_48(x)*F_54(x))
Eq(F_54(x), F_46(x) + F_55(x))
Eq(F_55(x), F_15(x) - F_45(x))
Eq(F_56(x), F_57(x)/(F_23(x)*F_45(x)*F_71(x)))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_23(x)*F_45(x)*F_60(x))
Eq(F_60(x), F_61(x)/F_23(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_69(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_9(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_23(x)*F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_23(x)*F_58(x))
Eq(F_71(x), F_1(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_23(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_1(x) + F_23(x))
Eq(F_76(x), F_72(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x) + F_83(x))
Eq(F_78(x), 0)
Eq(F_79(x), F_23(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_23(x))
Eq(F_82(x), F_77(x))
Eq(F_83(x), F_23(x)*F_72(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_15(x)*F_23(x)*F_35(x))
Eq(F_86(x), F_136(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), -F_135(x) + F_89(x))
Eq(F_89(x), F_133(x) + F_90(x))
Eq(F_90(x), F_128(x) + F_91(x))
Eq(F_91(x), F_15(x)*F_92(x))
Eq(F_92(x), F_1(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_23(x)*F_95(x))
Eq(F_95(x), F_103(x) + F_96(x))
Eq(F_96(x), F_1(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_96(x))
Eq(F_100(x), F_101(x) + F_23(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_23(x)*F_97(x))
Eq(F_103(x), F_104(x) + F_72(x))
Eq(F_104(x), F_105(x) + F_126(x) + F_78(x))
Eq(F_105(x), F_106(x)*F_23(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_97(x))
Eq(F_108(x), F_102(x) + F_109(x) + F_78(x))
Eq(F_109(x), F_110(x)*F_23(x))
Eq(F_110(x), F_100(x))
Eq(F_111(x), F_104(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_117(x) + F_118(x) + F_78(x))
Eq(F_113(x), F_114(x)*F_23(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_108(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), F_104(x)*F_23(x))
Eq(F_118(x), F_119(x)*F_23(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_77(x))
Eq(F_121(x), F_117(x) + F_122(x) + 2*F_78(x))
Eq(F_122(x), F_123(x)*F_23(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_101(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), F_127(x)*F_23(x))
Eq(F_127(x), F_103(x) + F_120(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_15(x)*F_23(x))
Eq(F_130(x), F_131(x)/F_23(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_35(x) - F_92(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_23(x)*F_45(x))
Eq(F_135(x), F_133(x) + F_14(x))
Eq(F_136(x), F_137(x)*F_276(x))
Eq(F_137(x), F_138(x)/F_93(x))
Eq(F_138(x), F_139(x) - F_88(x))
Eq(F_139(x), F_140(x) + F_275(x))
Eq(F_140(x), F_141(x) - F_274(x))
Eq(F_141(x), F_142(x)/F_23(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x) - F_271(x))
Eq(F_144(x), F_145(x) + F_244(x))
Eq(F_145(x), F_146(x) + F_93(x))
Eq(F_146(x), F_147(x) + F_195(x) + F_78(x))
Eq(F_147(x), F_148(x)*F_23(x))
Eq(F_148(x), F_149(x) + F_158(x))
Eq(F_149(x), F_150(x) + F_23(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_23(x))
Eq(F_152(x), F_149(x) + F_153(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), x**2)
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_150(x)*F_23(x))
Eq(F_158(x), F_159(x) + F_171(x))
Eq(F_159(x), F_160(x) + F_170(x) + F_78(x))
Eq(F_160(x), F_161(x)*F_23(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_154(x) + F_23(x))
Eq(F_163(x), F_159(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_169(x) + 2*F_78(x))
Eq(F_165(x), F_166(x)*F_23(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_154(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_159(x)*F_23(x))
Eq(F_170(x), F_23(x)*F_46(x))
Eq(F_171(x), F_172(x) + F_193(x) + 2*F_78(x))
Eq(F_172(x), F_173(x)*F_23(x))
Eq(F_173(x), F_174(x) + F_178(x))
Eq(F_174(x), F_150(x) + F_175(x))
Eq(F_175(x), F_157(x) + F_176(x) + 2*F_78(x))
Eq(F_176(x), F_177(x)*F_23(x))
Eq(F_177(x), F_153(x))
Eq(F_178(x), F_171(x) + F_179(x))
Eq(F_179(x), F_180(x) + F_184(x) + F_185(x) + 2*F_78(x))
Eq(F_180(x), F_181(x)*F_23(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_175(x))
Eq(F_183(x), F_179(x))
Eq(F_184(x), F_171(x)*F_23(x))
Eq(F_185(x), F_186(x)*F_23(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_164(x) + F_188(x))
Eq(F_188(x), F_184(x) + F_189(x) + 3*F_78(x))
Eq(F_189(x), F_190(x)*F_23(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_156(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_194(x)*F_23(x))
Eq(F_194(x), F_158(x) + F_187(x))
Eq(F_195(x), F_196(x)*F_23(x))
Eq(F_196(x), F_197(x) + F_208(x))
Eq(F_197(x), F_198(x) + F_46(x))
Eq(F_198(x), F_199(x) + F_202(x) + F_78(x))
Eq(F_199(x), F_200(x)*F_23(x))
Eq(F_200(x), F_201(x) + F_23(x))
Eq(F_201(x), F_170(x) + F_199(x) + F_78(x))
Eq(F_202(x), F_203(x)*F_23(x))
Eq(F_203(x), F_197(x) + F_204(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_170(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_198(x)*F_23(x))
Eq(F_208(x), F_209(x) + F_220(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_211(x)*F_23(x))
Eq(F_211(x), F_212(x) + F_213(x))
Eq(F_212(x), F_205(x) + F_46(x))
Eq(F_213(x), F_209(x) + F_214(x))
Eq(F_214(x), F_215(x) + F_219(x) + 2*F_78(x))
Eq(F_215(x), F_216(x)*F_23(x))
Eq(F_216(x), F_217(x) + F_218(x))
Eq(F_217(x), F_205(x))
Eq(F_218(x), F_214(x))
Eq(F_219(x), F_209(x)*F_23(x))
Eq(F_220(x), F_221(x) + F_242(x) + 2*F_78(x))
Eq(F_221(x), F_222(x)*F_23(x))
Eq(F_222(x), F_223(x) + F_227(x))
Eq(F_223(x), F_198(x) + F_224(x))
Eq(F_224(x), F_207(x) + F_225(x) + 2*F_78(x))
Eq(F_225(x), F_226(x)*F_23(x))
Eq(F_226(x), F_204(x))
Eq(F_227(x), F_220(x) + F_228(x))
Eq(F_228(x), F_229(x) + F_233(x) + F_234(x) + 2*F_78(x))
Eq(F_229(x), F_23(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_224(x))
Eq(F_232(x), F_228(x))
Eq(F_233(x), F_220(x)*F_23(x))
Eq(F_234(x), F_23(x)*F_235(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_214(x) + F_237(x))
Eq(F_237(x), F_233(x) + F_238(x) + 3*F_78(x))
Eq(F_238(x), F_23(x)*F_239(x))
Eq(F_239(x), F_240(x) + F_241(x))
Eq(F_240(x), F_206(x))
Eq(F_241(x), F_237(x))
Eq(F_242(x), F_23(x)*F_243(x))
Eq(F_243(x), F_208(x) + F_236(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_23(x)*F_246(x))
Eq(F_246(x), F_247(x) + F_261(x))
Eq(F_247(x), F_248(x)*F_55(x))
Eq(F_248(x), F_249(x) + F_251(x))
Eq(F_249(x), F_250(x) + F_92(x))
Eq(F_250(x), F_146(x) + F_93(x))
Eq(F_251(x), F_252(x) + F_253(x))
Eq(F_252(x), F_46(x)*F_92(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_23(x)*F_255(x))
Eq(F_255(x), F_256(x) + F_97(x))
Eq(F_256(x), F_104(x) + F_257(x))
Eq(F_257(x), F_258(x))
Eq(F_258(x), F_23(x)*F_259(x))
Eq(F_259(x), F_23(x) + F_260(x))
Eq(F_260(x), F_257(x) + F_77(x))
Eq(F_261(x), F_262(x) + F_270(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_15(x)*F_23(x)*F_264(x))
Eq(F_264(x), F_265(x)/F_23(x))
Eq(F_265(x), F_266(x))
Eq(F_266(x), F_267(x) + F_269(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_130(x)*F_23(x))
Eq(F_269(x), F_55(x)*F_93(x))
Eq(F_270(x), F_145(x)*F_84(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_23(x)*F_249(x)*F_273(x))
Eq(F_273(x), F_0(x) + F_84(x))
Eq(F_274(x), F_16(x)*F_248(x))
Eq(F_275(x), F_16(x)*F_251(x))
Eq(F_276(x), F_277(x) + F_36(x))
Eq(F_277(x), F_40(x) - F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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"Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24756/
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[28,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[28,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[28,x]
F[12,x] = F[13,x]+F[85,x]
F[13,x] = F[14,x]*F[51,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[28,x]*F[84,x]
F[18,x] = F[0,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[28,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[28,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = x
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[28,x]*F[33,x]*F[84,x]
F[33,x] = 1/F[28,x]/F[39,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = -F[38,x]+F[36,x]
F[36,x] = 1/F[28,x]*F[37,x]
F[37,x] = F[24,x]
F[38,x] = F[2,x]*F[26,x]
F[39,x] = 1/F[83,x]*F[40,x]
F[40,x] = -F[81,x]+F[41,x]
F[41,x] = 1/F[28,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[78,x]
F[44,x] = F[45,x]+F[73,x]
F[45,x] = F[2,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[28,x]*F[48,x]
F[48,x] = F[49,x]+F[9,x]
F[49,x] = F[50,x]
F[50,x] = F[18,x]*F[28,x]*F[51,x]
F[51,x] = F[52,x]+F[60,x]
F[52,x] = F[4,x]+F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[55,x]
F[55,x] = F[28,x]*F[51,x]
F[56,x] = -F[5,x]+F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[28,x]*F[59,x]
F[59,x] = F[6,x]
F[60,x] = F[61,x]
F[61,x] = F[28,x]*F[62,x]*F[65,x]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[28,x]*F[62,x]
F[65,x] = 1/F[28,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[68,x]+F[8,x]
F[68,x] = F[69,x]+F[9,x]
F[69,x] = F[70,x]
F[70,x] = F[28,x]*F[65,x]*F[71,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = -F[62,x]+F[18,x]
F[73,x] = F[74,x]
F[74,x] = F[28,x]*F[39,x]*F[75,x]
F[75,x] = F[2,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[28,x]*F[33,x]
F[78,x] = F[79,x]
F[79,x] = F[28,x]*F[80,x]
F[80,x] = F[34,x]
F[81,x] = F[82,x]
F[82,x] = F[28,x]*F[33,x]*F[39,x]
F[83,x] = F[0,x]+F[76,x]
F[84,x] = F[0,x]+F[54,x]
F[85,x] = F[147,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = -F[146,x]+F[88,x]
F[88,x] = F[144,x]+F[89,x]
F[89,x] = F[139,x]+F[90,x]
F[90,x] = F[18,x]*F[91,x]
F[91,x] = F[1,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[28,x]*F[94,x]
F[94,x] = F[102,x]+F[95,x]
F[95,x] = F[1,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[28,x]*F[98,x]
F[98,x] = F[95,x]+F[99,x]
F[99,x] = F[100,x]+F[28,x]
F[100,x] = F[101,x]
F[101,x] = F[28,x]*F[96,x]
F[102,x] = F[103,x]+F[115,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[28,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[1,x]+F[28,x]
F[107,x] = F[103,x]+F[108,x]
F[108,x] = F[109,x]+F[110,x]+F[114,x]
F[109,x] = 0
F[110,x] = F[111,x]*F[28,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[28,x]
F[113,x] = F[108,x]
F[114,x] = F[103,x]*F[28,x]
F[115,x] = F[109,x]+F[116,x]+F[137,x]
F[116,x] = F[117,x]*F[28,x]
F[117,x] = F[118,x]+F[122,x]
F[118,x] = F[119,x]+F[96,x]
F[119,x] = F[101,x]+F[109,x]+F[120,x]
F[120,x] = F[121,x]*F[28,x]
F[121,x] = F[99,x]
F[122,x] = F[115,x]+F[123,x]
F[123,x] = F[109,x]+F[124,x]+F[128,x]+F[129,x]
F[124,x] = F[125,x]*F[28,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[119,x]
F[127,x] = F[123,x]
F[128,x] = F[115,x]*F[28,x]
F[129,x] = F[130,x]*F[28,x]
F[130,x] = F[131,x]
F[131,x] = F[108,x]+F[132,x]
F[132,x] = 2*F[109,x]+F[128,x]+F[133,x]
F[133,x] = F[134,x]*F[28,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[100,x]
F[136,x] = F[132,x]
F[137,x] = F[138,x]*F[28,x]
F[138,x] = F[102,x]+F[131,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[18,x]*F[28,x]
F[141,x] = 1/F[28,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[91,x]+F[84,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[28,x]*F[62,x]
F[146,x] = F[14,x]+F[144,x]
F[147,x] = F[148,x]*F[53,x]
F[148,x] = 1/F[92,x]*F[149,x]
F[149,x] = -F[87,x]+F[150,x]
F[150,x] = F[151,x]+F[285,x]
F[151,x] = -F[284,x]+F[152,x]
F[152,x] = 1/F[28,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = -F[282,x]+F[155,x]
F[155,x] = F[156,x]+F[255,x]
F[156,x] = F[157,x]+F[92,x]
F[157,x] = F[109,x]+F[158,x]+F[206,x]
F[158,x] = F[159,x]*F[28,x]
F[159,x] = F[160,x]+F[169,x]
F[160,x] = F[161,x]+F[28,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[28,x]
F[163,x] = F[160,x]+F[164,x]
F[164,x] = F[165,x]+F[167,x]
F[165,x] = F[166,x]
F[166,x] = x^2
F[167,x] = F[168,x]
F[168,x] = F[161,x]*F[28,x]
F[169,x] = F[170,x]+F[182,x]
F[170,x] = F[109,x]+F[171,x]+F[181,x]
F[171,x] = F[172,x]*F[28,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[165,x]+F[28,x]
F[174,x] = F[170,x]+F[175,x]
F[175,x] = 2*F[109,x]+F[176,x]+F[180,x]
F[176,x] = F[177,x]*F[28,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[165,x]
F[179,x] = F[175,x]
F[180,x] = F[170,x]*F[28,x]
F[181,x] = F[28,x]*F[63,x]
F[182,x] = 2*F[109,x]+F[183,x]+F[204,x]
F[183,x] = F[184,x]*F[28,x]
F[184,x] = F[185,x]+F[189,x]
F[185,x] = F[161,x]+F[186,x]
F[186,x] = 2*F[109,x]+F[168,x]+F[187,x]
F[187,x] = F[188,x]*F[28,x]
F[188,x] = F[164,x]
F[189,x] = F[182,x]+F[190,x]
F[190,x] = 2*F[109,x]+F[191,x]+F[195,x]+F[196,x]
F[191,x] = F[192,x]*F[28,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[186,x]
F[194,x] = F[190,x]
F[195,x] = F[182,x]*F[28,x]
F[196,x] = F[197,x]*F[28,x]
F[197,x] = F[198,x]
F[198,x] = F[175,x]+F[199,x]
F[199,x] = 3*F[109,x]+F[195,x]+F[200,x]
F[200,x] = F[201,x]*F[28,x]
F[201,x] = F[202,x]+F[203,x]
F[202,x] = F[167,x]
F[203,x] = F[199,x]
F[204,x] = F[205,x]*F[28,x]
F[205,x] = F[169,x]+F[198,x]
F[206,x] = F[207,x]*F[28,x]
F[207,x] = F[208,x]+F[219,x]
F[208,x] = F[209,x]+F[63,x]
F[209,x] = F[109,x]+F[210,x]+F[213,x]
F[210,x] = F[211,x]*F[28,x]
F[211,x] = F[212,x]+F[28,x]
F[212,x] = F[109,x]+F[181,x]+F[210,x]
F[213,x] = F[214,x]*F[28,x]
F[214,x] = F[208,x]+F[215,x]
F[215,x] = F[216,x]+F[217,x]
F[216,x] = F[181,x]
F[217,x] = F[218,x]
F[218,x] = F[209,x]*F[28,x]
F[219,x] = F[220,x]+F[231,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[28,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[216,x]+F[63,x]
F[224,x] = F[220,x]+F[225,x]
F[225,x] = 2*F[109,x]+F[226,x]+F[230,x]
F[226,x] = F[227,x]*F[28,x]
F[227,x] = F[228,x]+F[229,x]
F[228,x] = F[216,x]
F[229,x] = F[225,x]
F[230,x] = F[220,x]*F[28,x]
F[231,x] = 2*F[109,x]+F[232,x]+F[253,x]
F[232,x] = F[233,x]*F[28,x]
F[233,x] = F[234,x]+F[238,x]
F[234,x] = F[209,x]+F[235,x]
F[235,x] = 2*F[109,x]+F[218,x]+F[236,x]
F[236,x] = F[237,x]*F[28,x]
F[237,x] = F[215,x]
F[238,x] = F[231,x]+F[239,x]
F[239,x] = 2*F[109,x]+F[240,x]+F[244,x]+F[245,x]
F[240,x] = F[241,x]*F[28,x]
F[241,x] = F[242,x]+F[243,x]
F[242,x] = F[235,x]
F[243,x] = F[239,x]
F[244,x] = F[231,x]*F[28,x]
F[245,x] = F[246,x]*F[28,x]
F[246,x] = F[247,x]
F[247,x] = F[225,x]+F[248,x]
F[248,x] = 3*F[109,x]+F[244,x]+F[249,x]
F[249,x] = F[250,x]*F[28,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[217,x]
F[252,x] = F[248,x]
F[253,x] = F[254,x]*F[28,x]
F[254,x] = F[219,x]+F[247,x]
F[255,x] = F[256,x]
F[256,x] = F[257,x]*F[28,x]
F[257,x] = F[258,x]+F[272,x]
F[258,x] = F[259,x]*F[72,x]
F[259,x] = F[260,x]+F[262,x]
F[260,x] = F[261,x]+F[91,x]
F[261,x] = F[157,x]+F[92,x]
F[262,x] = F[263,x]+F[264,x]
F[263,x] = F[63,x]*F[91,x]
F[264,x] = F[265,x]
F[265,x] = F[266,x]*F[28,x]
F[266,x] = F[267,x]+F[96,x]
F[267,x] = F[115,x]+F[268,x]
F[268,x] = F[269,x]
F[269,x] = F[270,x]*F[28,x]
F[270,x] = F[271,x]+F[28,x]
F[271,x] = F[108,x]+F[268,x]
F[272,x] = F[273,x]+F[281,x]
F[273,x] = F[274,x]
F[274,x] = F[18,x]*F[275,x]*F[28,x]
F[275,x] = 1/F[28,x]*F[276,x]
F[276,x] = F[277,x]
F[277,x] = F[278,x]+F[280,x]
F[278,x] = F[279,x]
F[279,x] = F[141,x]*F[28,x]
F[280,x] = F[72,x]*F[92,x]
F[281,x] = F[156,x]*F[16,x]
F[282,x] = F[283,x]
F[283,x] = F[15,x]*F[260,x]*F[28,x]
F[284,x] = F[19,x]*F[259,x]
F[285,x] = F[19,x]*F[262,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_{28}\! \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_{28}\! \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_{28}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{85}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right) F_{84}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{28}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right) F_{84}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{28}\! \left(x \right) F_{39}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{83}\! \left(x \right)}
F_{40}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{78}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{28}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{9}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{60}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{28}\! \left(x \right) F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{28}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{28}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{8}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{9}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{18}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{28}\! \left(x \right) F_{39}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{28}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{34}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right) F_{39}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right)+F_{76}\! \left(x \right)
F_{84}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{85}\! \left(x \right) = F_{147}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{146}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{144}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{139}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{28}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{102}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{28}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{28}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{28}\! \left(x \right) F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{115}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{28}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{109}\! \left(x \right) = 0
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{28}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{28}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)
F_{114}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right)+F_{116}\! \left(x \right)+F_{137}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{28}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{96}\! \left(x \right)
F_{119}\! \left(x \right) = F_{101}\! \left(x \right)+F_{109}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{28}\! \left(x \right)
F_{121}\! \left(x \right) = F_{99}\! \left(x \right)
F_{122}\! \left(x \right) = F_{115}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{109}\! \left(x \right)+F_{124}\! \left(x \right)+F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{119}\! \left(x \right)
F_{127}\! \left(x \right) = F_{123}\! \left(x \right)
F_{128}\! \left(x \right) = F_{115}\! \left(x \right) F_{28}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{28}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{108}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{128}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{28}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{100}\! \left(x \right)
F_{136}\! \left(x \right) = F_{132}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{28}\! \left(x \right)
F_{138}\! \left(x \right) = F_{102}\! \left(x \right)+F_{131}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{84}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{28}\! \left(x \right) F_{62}\! \left(x \right)
F_{146}\! \left(x \right) = F_{14}\! \left(x \right)+F_{144}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{53}\! \left(x \right)
F_{148}\! \left(x \right) = \frac{F_{149}\! \left(x \right)}{F_{92}\! \left(x \right)}
F_{149}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{285}\! \left(x \right)
F_{151}\! \left(x \right) = -F_{284}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{282}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{255}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{92}\! \left(x \right)
F_{157}\! \left(x \right) = F_{109}\! \left(x \right)+F_{158}\! \left(x \right)+F_{206}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{28}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{169}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{28}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{28}\! \left(x \right)
F_{163}\! \left(x \right) = F_{160}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{167}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = x^{2}
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{161}\! \left(x \right) F_{28}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{182}\! \left(x \right)
F_{170}\! \left(x \right) = F_{109}\! \left(x \right)+F_{171}\! \left(x \right)+F_{181}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{28}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{165}\! \left(x \right)+F_{28}\! \left(x \right)
F_{174}\! \left(x \right) = F_{170}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{176}\! \left(x \right)+F_{180}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{28}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{165}\! \left(x \right)
F_{179}\! \left(x \right) = F_{175}\! \left(x \right)
F_{180}\! \left(x \right) = F_{170}\! \left(x \right) F_{28}\! \left(x \right)
F_{181}\! \left(x \right) = F_{28}\! \left(x \right) F_{63}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{183}\! \left(x \right)+F_{204}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{28}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{189}\! \left(x \right)
F_{185}\! \left(x \right) = F_{161}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{168}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{28}\! \left(x \right)
F_{188}\! \left(x \right) = F_{164}\! \left(x \right)
F_{189}\! \left(x \right) = F_{182}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{191}\! \left(x \right)+F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{28}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{186}\! \left(x \right)
F_{194}\! \left(x \right) = F_{190}\! \left(x \right)
F_{195}\! \left(x \right) = F_{182}\! \left(x \right) F_{28}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right) F_{28}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{175}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = 3 F_{109}\! \left(x \right)+F_{195}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{28}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{203}\! \left(x \right)
F_{202}\! \left(x \right) = F_{167}\! \left(x \right)
F_{203}\! \left(x \right) = F_{199}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{28}\! \left(x \right)
F_{205}\! \left(x \right) = F_{169}\! \left(x \right)+F_{198}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right) F_{28}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{219}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{63}\! \left(x \right)
F_{209}\! \left(x \right) = F_{109}\! \left(x \right)+F_{210}\! \left(x \right)+F_{213}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{28}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{28}\! \left(x \right)
F_{212}\! \left(x \right) = F_{109}\! \left(x \right)+F_{181}\! \left(x \right)+F_{210}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right) F_{28}\! \left(x \right)
F_{214}\! \left(x \right) = F_{208}\! \left(x \right)+F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{217}\! \left(x \right)
F_{216}\! \left(x \right) = F_{181}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{209}\! \left(x \right) F_{28}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{231}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{28}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{216}\! \left(x \right)+F_{63}\! \left(x \right)
F_{224}\! \left(x \right) = F_{220}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{226}\! \left(x \right)+F_{230}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right) F_{28}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{229}\! \left(x \right)
F_{228}\! \left(x \right) = F_{216}\! \left(x \right)
F_{229}\! \left(x \right) = F_{225}\! \left(x \right)
F_{230}\! \left(x \right) = F_{220}\! \left(x \right) F_{28}\! \left(x \right)
F_{231}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{232}\! \left(x \right)+F_{253}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{28}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{238}\! \left(x \right)
F_{234}\! \left(x \right) = F_{209}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{218}\! \left(x \right)+F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{28}\! \left(x \right)
F_{237}\! \left(x \right) = F_{215}\! \left(x \right)
F_{238}\! \left(x \right) = F_{231}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{240}\! \left(x \right)+F_{244}\! \left(x \right)+F_{245}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right) F_{28}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{243}\! \left(x \right)
F_{242}\! \left(x \right) = F_{235}\! \left(x \right)
F_{243}\! \left(x \right) = F_{239}\! \left(x \right)
F_{244}\! \left(x \right) = F_{231}\! \left(x \right) F_{28}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{28}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{225}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = 3 F_{109}\! \left(x \right)+F_{244}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right) F_{28}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{217}\! \left(x \right)
F_{252}\! \left(x \right) = F_{248}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right) F_{28}\! \left(x \right)
F_{254}\! \left(x \right) = F_{219}\! \left(x \right)+F_{247}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right) F_{28}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)+F_{272}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right) F_{72}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{262}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{91}\! \left(x \right)
F_{261}\! \left(x \right) = F_{157}\! \left(x \right)+F_{92}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{264}\! \left(x \right)
F_{263}\! \left(x \right) = F_{63}\! \left(x \right) F_{91}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right) F_{28}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{96}\! \left(x \right)
F_{267}\! \left(x \right) = F_{115}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right) F_{28}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{28}\! \left(x \right)
F_{271}\! \left(x \right) = F_{108}\! \left(x \right)+F_{268}\! \left(x \right)
F_{272}\! \left(x \right) = F_{273}\! \left(x \right)+F_{281}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{18}\! \left(x \right) F_{275}\! \left(x \right) F_{28}\! \left(x \right)
F_{275}\! \left(x \right) = \frac{F_{276}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{280}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{141}\! \left(x \right) F_{28}\! \left(x \right)
F_{280}\! \left(x \right) = F_{72}\! \left(x \right) F_{92}\! \left(x \right)
F_{281}\! \left(x \right) = F_{156}\! \left(x \right) F_{16}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{15}\! \left(x \right) F_{260}\! \left(x \right) F_{28}\! \left(x \right)
F_{284}\! \left(x \right) = F_{19}\! \left(x \right) F_{259}\! \left(x \right)
F_{285}\! \left(x \right) = F_{19}\! \left(x \right) F_{262}\! \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_28(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_28(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_28(x))
Eq(F_12(x), F_13(x) + F_85(x))
Eq(F_13(x), F_14(x)*F_51(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_28(x)*F_84(x))
Eq(F_18(x), F_0(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_28(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_28(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), x)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_28(x)*F_33(x)*F_84(x))
Eq(F_33(x), F_34(x)/(F_28(x)*F_39(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) - F_38(x))
Eq(F_36(x), F_37(x)/F_28(x))
Eq(F_37(x), F_24(x))
Eq(F_38(x), F_2(x)*F_26(x))
Eq(F_39(x), F_40(x)/F_83(x))
Eq(F_40(x), F_41(x) - F_81(x))
Eq(F_41(x), F_42(x)/F_28(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_78(x))
Eq(F_44(x), F_45(x) + F_73(x))
Eq(F_45(x), F_2(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_28(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_9(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_18(x)*F_28(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_60(x))
Eq(F_52(x), F_4(x) + F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_28(x)*F_51(x))
Eq(F_56(x), -F_5(x) + F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_28(x))
Eq(F_59(x), F_6(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_28(x)*F_62(x)*F_65(x))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_28(x)*F_62(x))
Eq(F_65(x), F_66(x)/F_28(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), -F_68(x) + F_8(x))
Eq(F_68(x), F_69(x) + F_9(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_28(x)*F_65(x)*F_71(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), F_18(x) - F_62(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_28(x)*F_39(x)*F_75(x))
Eq(F_75(x), F_2(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_28(x)*F_33(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_28(x)*F_80(x))
Eq(F_80(x), F_34(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_28(x)*F_33(x)*F_39(x))
Eq(F_83(x), F_0(x) + F_76(x))
Eq(F_84(x), F_0(x) + F_54(x))
Eq(F_85(x), F_147(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), -F_146(x) + F_88(x))
Eq(F_88(x), F_144(x) + F_89(x))
Eq(F_89(x), F_139(x) + F_90(x))
Eq(F_90(x), F_18(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_28(x)*F_94(x))
Eq(F_94(x), F_102(x) + F_95(x))
Eq(F_95(x), F_1(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_28(x)*F_98(x))
Eq(F_98(x), F_95(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_28(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_28(x)*F_96(x))
Eq(F_102(x), F_103(x) + F_115(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_28(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_1(x) + F_28(x))
Eq(F_107(x), F_103(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_110(x) + F_114(x))
Eq(F_109(x), 0)
Eq(F_110(x), F_111(x)*F_28(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_28(x))
Eq(F_113(x), F_108(x))
Eq(F_114(x), F_103(x)*F_28(x))
Eq(F_115(x), F_109(x) + F_116(x) + F_137(x))
Eq(F_116(x), F_117(x)*F_28(x))
Eq(F_117(x), F_118(x) + F_122(x))
Eq(F_118(x), F_119(x) + F_96(x))
Eq(F_119(x), F_101(x) + F_109(x) + F_120(x))
Eq(F_120(x), F_121(x)*F_28(x))
Eq(F_121(x), F_99(x))
Eq(F_122(x), F_115(x) + F_123(x))
Eq(F_123(x), F_109(x) + F_124(x) + F_128(x) + F_129(x))
Eq(F_124(x), F_125(x)*F_28(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_119(x))
Eq(F_127(x), F_123(x))
Eq(F_128(x), F_115(x)*F_28(x))
Eq(F_129(x), F_130(x)*F_28(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_108(x) + F_132(x))
Eq(F_132(x), 2*F_109(x) + F_128(x) + F_133(x))
Eq(F_133(x), F_134(x)*F_28(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_100(x))
Eq(F_136(x), F_132(x))
Eq(F_137(x), F_138(x)*F_28(x))
Eq(F_138(x), F_102(x) + F_131(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_18(x)*F_28(x))
Eq(F_141(x), F_142(x)/F_28(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_84(x) - F_91(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_28(x)*F_62(x))
Eq(F_146(x), F_14(x) + F_144(x))
Eq(F_147(x), F_148(x)*F_53(x))
Eq(F_148(x), F_149(x)/F_92(x))
Eq(F_149(x), F_150(x) - F_87(x))
Eq(F_150(x), F_151(x) + F_285(x))
Eq(F_151(x), F_152(x) - F_284(x))
Eq(F_152(x), F_153(x)/F_28(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x) - F_282(x))
Eq(F_155(x), F_156(x) + F_255(x))
Eq(F_156(x), F_157(x) + F_92(x))
Eq(F_157(x), F_109(x) + F_158(x) + F_206(x))
Eq(F_158(x), F_159(x)*F_28(x))
Eq(F_159(x), F_160(x) + F_169(x))
Eq(F_160(x), F_161(x) + F_28(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_28(x))
Eq(F_163(x), F_160(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_167(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), x**2)
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_161(x)*F_28(x))
Eq(F_169(x), F_170(x) + F_182(x))
Eq(F_170(x), F_109(x) + F_171(x) + F_181(x))
Eq(F_171(x), F_172(x)*F_28(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_165(x) + F_28(x))
Eq(F_174(x), F_170(x) + F_175(x))
Eq(F_175(x), 2*F_109(x) + F_176(x) + F_180(x))
Eq(F_176(x), F_177(x)*F_28(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_165(x))
Eq(F_179(x), F_175(x))
Eq(F_180(x), F_170(x)*F_28(x))
Eq(F_181(x), F_28(x)*F_63(x))
Eq(F_182(x), 2*F_109(x) + F_183(x) + F_204(x))
Eq(F_183(x), F_184(x)*F_28(x))
Eq(F_184(x), F_185(x) + F_189(x))
Eq(F_185(x), F_161(x) + F_186(x))
Eq(F_186(x), 2*F_109(x) + F_168(x) + F_187(x))
Eq(F_187(x), F_188(x)*F_28(x))
Eq(F_188(x), F_164(x))
Eq(F_189(x), F_182(x) + F_190(x))
Eq(F_190(x), 2*F_109(x) + F_191(x) + F_195(x) + F_196(x))
Eq(F_191(x), F_192(x)*F_28(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_186(x))
Eq(F_194(x), F_190(x))
Eq(F_195(x), F_182(x)*F_28(x))
Eq(F_196(x), F_197(x)*F_28(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_175(x) + F_199(x))
Eq(F_199(x), 3*F_109(x) + F_195(x) + F_200(x))
Eq(F_200(x), F_201(x)*F_28(x))
Eq(F_201(x), F_202(x) + F_203(x))
Eq(F_202(x), F_167(x))
Eq(F_203(x), F_199(x))
Eq(F_204(x), F_205(x)*F_28(x))
Eq(F_205(x), F_169(x) + F_198(x))
Eq(F_206(x), F_207(x)*F_28(x))
Eq(F_207(x), F_208(x) + F_219(x))
Eq(F_208(x), F_209(x) + F_63(x))
Eq(F_209(x), F_109(x) + F_210(x) + F_213(x))
Eq(F_210(x), F_211(x)*F_28(x))
Eq(F_211(x), F_212(x) + F_28(x))
Eq(F_212(x), F_109(x) + F_181(x) + F_210(x))
Eq(F_213(x), F_214(x)*F_28(x))
Eq(F_214(x), F_208(x) + F_215(x))
Eq(F_215(x), F_216(x) + F_217(x))
Eq(F_216(x), F_181(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_209(x)*F_28(x))
Eq(F_219(x), F_220(x) + F_231(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_28(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_216(x) + F_63(x))
Eq(F_224(x), F_220(x) + F_225(x))
Eq(F_225(x), 2*F_109(x) + F_226(x) + F_230(x))
Eq(F_226(x), F_227(x)*F_28(x))
Eq(F_227(x), F_228(x) + F_229(x))
Eq(F_228(x), F_216(x))
Eq(F_229(x), F_225(x))
Eq(F_230(x), F_220(x)*F_28(x))
Eq(F_231(x), 2*F_109(x) + F_232(x) + F_253(x))
Eq(F_232(x), F_233(x)*F_28(x))
Eq(F_233(x), F_234(x) + F_238(x))
Eq(F_234(x), F_209(x) + F_235(x))
Eq(F_235(x), 2*F_109(x) + F_218(x) + F_236(x))
Eq(F_236(x), F_237(x)*F_28(x))
Eq(F_237(x), F_215(x))
Eq(F_238(x), F_231(x) + F_239(x))
Eq(F_239(x), 2*F_109(x) + F_240(x) + F_244(x) + F_245(x))
Eq(F_240(x), F_241(x)*F_28(x))
Eq(F_241(x), F_242(x) + F_243(x))
Eq(F_242(x), F_235(x))
Eq(F_243(x), F_239(x))
Eq(F_244(x), F_231(x)*F_28(x))
Eq(F_245(x), F_246(x)*F_28(x))
Eq(F_246(x), F_247(x))
Eq(F_247(x), F_225(x) + F_248(x))
Eq(F_248(x), 3*F_109(x) + F_244(x) + F_249(x))
Eq(F_249(x), F_250(x)*F_28(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_217(x))
Eq(F_252(x), F_248(x))
Eq(F_253(x), F_254(x)*F_28(x))
Eq(F_254(x), F_219(x) + F_247(x))
Eq(F_255(x), F_256(x))
Eq(F_256(x), F_257(x)*F_28(x))
Eq(F_257(x), F_258(x) + F_272(x))
Eq(F_258(x), F_259(x)*F_72(x))
Eq(F_259(x), F_260(x) + F_262(x))
Eq(F_260(x), F_261(x) + F_91(x))
Eq(F_261(x), F_157(x) + F_92(x))
Eq(F_262(x), F_263(x) + F_264(x))
Eq(F_263(x), F_63(x)*F_91(x))
Eq(F_264(x), F_265(x))
Eq(F_265(x), F_266(x)*F_28(x))
Eq(F_266(x), F_267(x) + F_96(x))
Eq(F_267(x), F_115(x) + F_268(x))
Eq(F_268(x), F_269(x))
Eq(F_269(x), F_270(x)*F_28(x))
Eq(F_270(x), F_271(x) + F_28(x))
Eq(F_271(x), F_108(x) + F_268(x))
Eq(F_272(x), F_273(x) + F_281(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_18(x)*F_275(x)*F_28(x))
Eq(F_275(x), F_276(x)/F_28(x))
Eq(F_276(x), F_277(x))
Eq(F_277(x), F_278(x) + F_280(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_141(x)*F_28(x))
Eq(F_280(x), F_72(x)*F_92(x))
Eq(F_281(x), F_156(x)*F_16(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_15(x)*F_260(x)*F_28(x))
Eq(F_284(x), F_19(x)*F_259(x))
Eq(F_285(x), F_19(x)*F_262(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 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[0, 2]]}, {"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, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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"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, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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[[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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24943/
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[23,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[23,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[23,x]
F[12,x] = F[13,x]+F[86,x]
F[13,x] = F[14,x]*F[38,x]
F[14,x] = F[15,x]+F[84,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = F[15,x]+F[19,x]
F[19,x] = F[20,x]+F[24,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[23,x]*F[28,x]*F[35,x]
F[28,x] = 1/F[23,x]/F[56,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[34,x]+F[31,x]
F[31,x] = 1/F[23,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[2,x]+F[20,x]
F[34,x] = F[2,x]*F[35,x]
F[35,x] = F[0,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[23,x]*F[38,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[35,x]+F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[23,x]*F[42,x]
F[42,x] = F[6,x]
F[43,x] = F[44,x]
F[44,x] = F[23,x]*F[45,x]*F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[23,x]*F[45,x]
F[48,x] = 1/F[23,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = -F[51,x]+F[8,x]
F[51,x] = F[52,x]+F[9,x]
F[52,x] = F[53,x]
F[53,x] = F[23,x]*F[48,x]*F[54,x]
F[54,x] = F[46,x]+F[55,x]
F[55,x] = -F[45,x]+F[15,x]
F[56,x] = 1/F[23,x]/F[45,x]/F[71,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[23,x]*F[45,x]*F[60,x]
F[60,x] = 1/F[23,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[69,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[67,x]+F[9,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[23,x]*F[38,x]
F[69,x] = F[70,x]
F[70,x] = F[23,x]*F[58,x]
F[71,x] = F[1,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[23,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[1,x]+F[23,x]
F[76,x] = F[72,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]+F[83,x]
F[78,x] = 0
F[79,x] = F[23,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[23,x]
F[82,x] = F[77,x]
F[83,x] = F[23,x]*F[72,x]
F[84,x] = F[85,x]
F[85,x] = F[15,x]*F[23,x]*F[35,x]
F[86,x] = F[136,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = -F[135,x]+F[89,x]
F[89,x] = F[133,x]+F[90,x]
F[90,x] = F[128,x]+F[91,x]
F[91,x] = F[15,x]*F[92,x]
F[92,x] = F[1,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[23,x]*F[95,x]
F[95,x] = F[103,x]+F[96,x]
F[96,x] = F[1,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[96,x]
F[100,x] = F[101,x]+F[23,x]
F[101,x] = F[102,x]
F[102,x] = F[23,x]*F[97,x]
F[103,x] = F[104,x]+F[72,x]
F[104,x] = F[105,x]+F[126,x]+F[78,x]
F[105,x] = F[106,x]*F[23,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[97,x]
F[108,x] = F[102,x]+F[109,x]+F[78,x]
F[109,x] = F[110,x]*F[23,x]
F[110,x] = F[100,x]
F[111,x] = F[104,x]+F[112,x]
F[112,x] = F[113,x]+F[117,x]+F[118,x]+F[78,x]
F[113,x] = F[114,x]*F[23,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[108,x]
F[116,x] = F[112,x]
F[117,x] = F[104,x]*F[23,x]
F[118,x] = F[119,x]*F[23,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[77,x]
F[121,x] = 2*F[78,x]+F[117,x]+F[122,x]
F[122,x] = F[123,x]*F[23,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[101,x]
F[125,x] = F[121,x]
F[126,x] = F[127,x]*F[23,x]
F[127,x] = F[103,x]+F[120,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[15,x]*F[23,x]
F[130,x] = 1/F[23,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = -F[92,x]+F[35,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[23,x]*F[45,x]
F[135,x] = F[133,x]+F[14,x]
F[136,x] = F[137,x]*F[276,x]
F[137,x] = 1/F[93,x]*F[138,x]
F[138,x] = -F[88,x]+F[139,x]
F[139,x] = F[140,x]+F[275,x]
F[140,x] = -F[274,x]+F[141,x]
F[141,x] = 1/F[23,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[271,x]+F[144,x]
F[144,x] = F[145,x]+F[244,x]
F[145,x] = F[146,x]+F[93,x]
F[146,x] = F[147,x]+F[195,x]+F[78,x]
F[147,x] = F[148,x]*F[23,x]
F[148,x] = F[149,x]+F[158,x]
F[149,x] = F[150,x]+F[23,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[23,x]
F[152,x] = F[149,x]+F[153,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[155,x]
F[155,x] = x^2
F[156,x] = F[157,x]
F[157,x] = F[150,x]*F[23,x]
F[158,x] = F[159,x]+F[171,x]
F[159,x] = F[160,x]+F[170,x]+F[78,x]
F[160,x] = F[161,x]*F[23,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[154,x]+F[23,x]
F[163,x] = F[159,x]+F[164,x]
F[164,x] = 2*F[78,x]+F[165,x]+F[169,x]
F[165,x] = F[166,x]*F[23,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[154,x]
F[168,x] = F[164,x]
F[169,x] = F[159,x]*F[23,x]
F[170,x] = F[23,x]*F[46,x]
F[171,x] = 2*F[78,x]+F[172,x]+F[193,x]
F[172,x] = F[173,x]*F[23,x]
F[173,x] = F[174,x]+F[178,x]
F[174,x] = F[150,x]+F[175,x]
F[175,x] = 2*F[78,x]+F[157,x]+F[176,x]
F[176,x] = F[177,x]*F[23,x]
F[177,x] = F[153,x]
F[178,x] = F[171,x]+F[179,x]
F[179,x] = 2*F[78,x]+F[180,x]+F[184,x]+F[185,x]
F[180,x] = F[181,x]*F[23,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[175,x]
F[183,x] = F[179,x]
F[184,x] = F[171,x]*F[23,x]
F[185,x] = F[186,x]*F[23,x]
F[186,x] = F[187,x]
F[187,x] = F[164,x]+F[188,x]
F[188,x] = 3*F[78,x]+F[184,x]+F[189,x]
F[189,x] = F[190,x]*F[23,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[156,x]
F[192,x] = F[188,x]
F[193,x] = F[194,x]*F[23,x]
F[194,x] = F[158,x]+F[187,x]
F[195,x] = F[196,x]*F[23,x]
F[196,x] = F[197,x]+F[208,x]
F[197,x] = F[198,x]+F[46,x]
F[198,x] = F[199,x]+F[202,x]+F[78,x]
F[199,x] = F[200,x]*F[23,x]
F[200,x] = F[201,x]+F[23,x]
F[201,x] = F[170,x]+F[199,x]+F[78,x]
F[202,x] = F[203,x]*F[23,x]
F[203,x] = F[197,x]+F[204,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[170,x]
F[206,x] = F[207,x]
F[207,x] = F[198,x]*F[23,x]
F[208,x] = F[209,x]+F[220,x]
F[209,x] = F[210,x]
F[210,x] = F[211,x]*F[23,x]
F[211,x] = F[212,x]+F[213,x]
F[212,x] = F[205,x]+F[46,x]
F[213,x] = F[209,x]+F[214,x]
F[214,x] = 2*F[78,x]+F[215,x]+F[219,x]
F[215,x] = F[216,x]*F[23,x]
F[216,x] = F[217,x]+F[218,x]
F[217,x] = F[205,x]
F[218,x] = F[214,x]
F[219,x] = F[209,x]*F[23,x]
F[220,x] = 2*F[78,x]+F[221,x]+F[242,x]
F[221,x] = F[222,x]*F[23,x]
F[222,x] = F[223,x]+F[227,x]
F[223,x] = F[198,x]+F[224,x]
F[224,x] = 2*F[78,x]+F[207,x]+F[225,x]
F[225,x] = F[226,x]*F[23,x]
F[226,x] = F[204,x]
F[227,x] = F[220,x]+F[228,x]
F[228,x] = 2*F[78,x]+F[229,x]+F[233,x]+F[234,x]
F[229,x] = F[23,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[224,x]
F[232,x] = F[228,x]
F[233,x] = F[220,x]*F[23,x]
F[234,x] = F[23,x]*F[235,x]
F[235,x] = F[236,x]
F[236,x] = F[214,x]+F[237,x]
F[237,x] = 3*F[78,x]+F[233,x]+F[238,x]
F[238,x] = F[23,x]*F[239,x]
F[239,x] = F[240,x]+F[241,x]
F[240,x] = F[206,x]
F[241,x] = F[237,x]
F[242,x] = F[23,x]*F[243,x]
F[243,x] = F[208,x]+F[236,x]
F[244,x] = F[245,x]
F[245,x] = F[23,x]*F[246,x]
F[246,x] = F[247,x]+F[261,x]
F[247,x] = F[248,x]*F[55,x]
F[248,x] = F[249,x]+F[251,x]
F[249,x] = F[250,x]+F[92,x]
F[250,x] = F[146,x]+F[93,x]
F[251,x] = F[252,x]+F[253,x]
F[252,x] = F[46,x]*F[92,x]
F[253,x] = F[254,x]
F[254,x] = F[23,x]*F[255,x]
F[255,x] = F[256,x]+F[97,x]
F[256,x] = F[104,x]+F[257,x]
F[257,x] = F[258,x]
F[258,x] = F[23,x]*F[259,x]
F[259,x] = F[23,x]+F[260,x]
F[260,x] = F[257,x]+F[77,x]
F[261,x] = F[262,x]+F[270,x]
F[262,x] = F[263,x]
F[263,x] = F[15,x]*F[23,x]*F[264,x]
F[264,x] = 1/F[23,x]*F[265,x]
F[265,x] = F[266,x]
F[266,x] = F[267,x]+F[269,x]
F[267,x] = F[268,x]
F[268,x] = F[130,x]*F[23,x]
F[269,x] = F[55,x]*F[93,x]
F[270,x] = F[145,x]*F[84,x]
F[271,x] = F[272,x]
F[272,x] = F[23,x]*F[249,x]*F[273,x]
F[273,x] = F[0,x]+F[84,x]
F[274,x] = F[16,x]*F[248,x]
F[275,x] = F[16,x]*F[251,x]
F[276,x] = F[277,x]+F[36,x]
F[277,x] = -F[5,x]+F[40,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_{23}\! \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_{23}\! \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_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{86}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{84}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right) F_{56}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right) F_{48}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{15}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{71}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{58}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = 0
F_{79}\! \left(x \right) = F_{23}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{23}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = F_{23}\! \left(x \right) F_{72}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{35}\! \left(x \right)
F_{86}\! \left(x \right) = F_{136}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{133}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{128}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{15}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{23}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{103}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{1}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{23}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{23}\! \left(x \right) F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{72}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{126}\! \left(x \right)+F_{78}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{97}\! \left(x \right)
F_{108}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)+F_{78}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{100}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{78}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{23}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{108}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = F_{104}\! \left(x \right) F_{23}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{77}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{23}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{101}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{23}\! \left(x \right)
F_{127}\! \left(x \right) = F_{103}\! \left(x \right)+F_{120}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{15}\! \left(x \right) F_{23}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{35}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right)+F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{276}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{93}\! \left(x \right)}
F_{138}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{275}\! \left(x \right)
F_{140}\! \left(x \right) = -F_{274}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{271}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{244}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{195}\! \left(x \right)+F_{78}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{23}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{158}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{23}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{23}\! \left(x \right)
F_{152}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = x^{2}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{150}\! \left(x \right) F_{23}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{171}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{170}\! \left(x \right)+F_{78}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{23}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{154}\! \left(x \right)+F_{23}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{23}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{154}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{159}\! \left(x \right) F_{23}\! \left(x \right)
F_{170}\! \left(x \right) = F_{23}\! \left(x \right) F_{46}\! \left(x \right)
F_{171}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{172}\! \left(x \right)+F_{193}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{23}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{178}\! \left(x \right)
F_{174}\! \left(x \right) = F_{150}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{157}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{23}\! \left(x \right)
F_{177}\! \left(x \right) = F_{153}\! \left(x \right)
F_{178}\! \left(x \right) = F_{171}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{180}\! \left(x \right)+F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{23}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{175}\! \left(x \right)
F_{183}\! \left(x \right) = F_{179}\! \left(x \right)
F_{184}\! \left(x \right) = F_{171}\! \left(x \right) F_{23}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{23}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{164}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{184}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{23}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{156}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right) F_{23}\! \left(x \right)
F_{194}\! \left(x \right) = F_{158}\! \left(x \right)+F_{187}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{23}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{208}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{46}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{202}\! \left(x \right)+F_{78}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{23}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{23}\! \left(x \right)
F_{201}\! \left(x \right) = F_{170}\! \left(x \right)+F_{199}\! \left(x \right)+F_{78}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{23}\! \left(x \right)
F_{203}\! \left(x \right) = F_{197}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{170}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{198}\! \left(x \right) F_{23}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{220}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{23}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{213}\! \left(x \right)
F_{212}\! \left(x \right) = F_{205}\! \left(x \right)+F_{46}\! \left(x \right)
F_{213}\! \left(x \right) = F_{209}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{215}\! \left(x \right)+F_{219}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right) F_{23}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{218}\! \left(x \right)
F_{217}\! \left(x \right) = F_{205}\! \left(x \right)
F_{218}\! \left(x \right) = F_{214}\! \left(x \right)
F_{219}\! \left(x \right) = F_{209}\! \left(x \right) F_{23}\! \left(x \right)
F_{220}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{221}\! \left(x \right)+F_{242}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{23}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{227}\! \left(x \right)
F_{223}\! \left(x \right) = F_{198}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{207}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{23}\! \left(x \right)
F_{226}\! \left(x \right) = F_{204}\! \left(x \right)
F_{227}\! \left(x \right) = F_{220}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{229}\! \left(x \right)+F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{229}\! \left(x \right) = F_{23}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{224}\! \left(x \right)
F_{232}\! \left(x \right) = F_{228}\! \left(x \right)
F_{233}\! \left(x \right) = F_{220}\! \left(x \right) F_{23}\! \left(x \right)
F_{234}\! \left(x \right) = F_{23}\! \left(x \right) F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{214}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{233}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{23}\! \left(x \right) F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{241}\! \left(x \right)
F_{240}\! \left(x \right) = F_{206}\! \left(x \right)
F_{241}\! \left(x \right) = F_{237}\! \left(x \right)
F_{242}\! \left(x \right) = F_{23}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{208}\! \left(x \right)+F_{236}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{23}\! \left(x \right) F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{261}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right) F_{55}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{251}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{92}\! \left(x \right)
F_{250}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{253}\! \left(x \right)
F_{252}\! \left(x \right) = F_{46}\! \left(x \right) F_{92}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{23}\! \left(x \right) F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)+F_{97}\! \left(x \right)
F_{256}\! \left(x \right) = F_{104}\! \left(x \right)+F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{23}\! \left(x \right) F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{23}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{257}\! \left(x \right)+F_{77}\! \left(x \right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)+F_{270}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = \frac{F_{265}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{269}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{130}\! \left(x \right) F_{23}\! \left(x \right)
F_{269}\! \left(x \right) = F_{55}\! \left(x \right) F_{93}\! \left(x \right)
F_{270}\! \left(x \right) = F_{145}\! \left(x \right) F_{84}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{23}\! \left(x \right) F_{249}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{274}\! \left(x \right) = F_{16}\! \left(x \right) F_{248}\! \left(x \right)
F_{275}\! \left(x \right) = F_{16}\! \left(x \right) F_{251}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{36}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{40}\! \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_23(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_23(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_23(x))
Eq(F_12(x), F_13(x) + F_86(x))
Eq(F_13(x), F_14(x)*F_38(x))
Eq(F_14(x), F_15(x) + F_84(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_15(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_24(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_23(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x)/(F_23(x)*F_56(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_34(x))
Eq(F_31(x), F_32(x)/F_23(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_2(x) + F_20(x))
Eq(F_34(x), F_2(x)*F_35(x))
Eq(F_35(x), F_0(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_23(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_35(x) + F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_23(x))
Eq(F_42(x), F_6(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_23(x)*F_45(x)*F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_23(x)*F_45(x))
Eq(F_48(x), F_49(x)/F_23(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), -F_51(x) + F_8(x))
Eq(F_51(x), F_52(x) + F_9(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_23(x)*F_48(x)*F_54(x))
Eq(F_54(x), F_46(x) + F_55(x))
Eq(F_55(x), F_15(x) - F_45(x))
Eq(F_56(x), F_57(x)/(F_23(x)*F_45(x)*F_71(x)))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_23(x)*F_45(x)*F_60(x))
Eq(F_60(x), F_61(x)/F_23(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_69(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_9(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_23(x)*F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_23(x)*F_58(x))
Eq(F_71(x), F_1(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_23(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_1(x) + F_23(x))
Eq(F_76(x), F_72(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x) + F_83(x))
Eq(F_78(x), 0)
Eq(F_79(x), F_23(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_23(x))
Eq(F_82(x), F_77(x))
Eq(F_83(x), F_23(x)*F_72(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_15(x)*F_23(x)*F_35(x))
Eq(F_86(x), F_136(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), -F_135(x) + F_89(x))
Eq(F_89(x), F_133(x) + F_90(x))
Eq(F_90(x), F_128(x) + F_91(x))
Eq(F_91(x), F_15(x)*F_92(x))
Eq(F_92(x), F_1(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_23(x)*F_95(x))
Eq(F_95(x), F_103(x) + F_96(x))
Eq(F_96(x), F_1(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_96(x))
Eq(F_100(x), F_101(x) + F_23(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_23(x)*F_97(x))
Eq(F_103(x), F_104(x) + F_72(x))
Eq(F_104(x), F_105(x) + F_126(x) + F_78(x))
Eq(F_105(x), F_106(x)*F_23(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_97(x))
Eq(F_108(x), F_102(x) + F_109(x) + F_78(x))
Eq(F_109(x), F_110(x)*F_23(x))
Eq(F_110(x), F_100(x))
Eq(F_111(x), F_104(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_117(x) + F_118(x) + F_78(x))
Eq(F_113(x), F_114(x)*F_23(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_108(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), F_104(x)*F_23(x))
Eq(F_118(x), F_119(x)*F_23(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_77(x))
Eq(F_121(x), F_117(x) + F_122(x) + 2*F_78(x))
Eq(F_122(x), F_123(x)*F_23(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_101(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), F_127(x)*F_23(x))
Eq(F_127(x), F_103(x) + F_120(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_15(x)*F_23(x))
Eq(F_130(x), F_131(x)/F_23(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_35(x) - F_92(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_23(x)*F_45(x))
Eq(F_135(x), F_133(x) + F_14(x))
Eq(F_136(x), F_137(x)*F_276(x))
Eq(F_137(x), F_138(x)/F_93(x))
Eq(F_138(x), F_139(x) - F_88(x))
Eq(F_139(x), F_140(x) + F_275(x))
Eq(F_140(x), F_141(x) - F_274(x))
Eq(F_141(x), F_142(x)/F_23(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x) - F_271(x))
Eq(F_144(x), F_145(x) + F_244(x))
Eq(F_145(x), F_146(x) + F_93(x))
Eq(F_146(x), F_147(x) + F_195(x) + F_78(x))
Eq(F_147(x), F_148(x)*F_23(x))
Eq(F_148(x), F_149(x) + F_158(x))
Eq(F_149(x), F_150(x) + F_23(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_23(x))
Eq(F_152(x), F_149(x) + F_153(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), x**2)
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_150(x)*F_23(x))
Eq(F_158(x), F_159(x) + F_171(x))
Eq(F_159(x), F_160(x) + F_170(x) + F_78(x))
Eq(F_160(x), F_161(x)*F_23(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_154(x) + F_23(x))
Eq(F_163(x), F_159(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_169(x) + 2*F_78(x))
Eq(F_165(x), F_166(x)*F_23(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_154(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_159(x)*F_23(x))
Eq(F_170(x), F_23(x)*F_46(x))
Eq(F_171(x), F_172(x) + F_193(x) + 2*F_78(x))
Eq(F_172(x), F_173(x)*F_23(x))
Eq(F_173(x), F_174(x) + F_178(x))
Eq(F_174(x), F_150(x) + F_175(x))
Eq(F_175(x), F_157(x) + F_176(x) + 2*F_78(x))
Eq(F_176(x), F_177(x)*F_23(x))
Eq(F_177(x), F_153(x))
Eq(F_178(x), F_171(x) + F_179(x))
Eq(F_179(x), F_180(x) + F_184(x) + F_185(x) + 2*F_78(x))
Eq(F_180(x), F_181(x)*F_23(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_175(x))
Eq(F_183(x), F_179(x))
Eq(F_184(x), F_171(x)*F_23(x))
Eq(F_185(x), F_186(x)*F_23(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_164(x) + F_188(x))
Eq(F_188(x), F_184(x) + F_189(x) + 3*F_78(x))
Eq(F_189(x), F_190(x)*F_23(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_156(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_194(x)*F_23(x))
Eq(F_194(x), F_158(x) + F_187(x))
Eq(F_195(x), F_196(x)*F_23(x))
Eq(F_196(x), F_197(x) + F_208(x))
Eq(F_197(x), F_198(x) + F_46(x))
Eq(F_198(x), F_199(x) + F_202(x) + F_78(x))
Eq(F_199(x), F_200(x)*F_23(x))
Eq(F_200(x), F_201(x) + F_23(x))
Eq(F_201(x), F_170(x) + F_199(x) + F_78(x))
Eq(F_202(x), F_203(x)*F_23(x))
Eq(F_203(x), F_197(x) + F_204(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_170(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_198(x)*F_23(x))
Eq(F_208(x), F_209(x) + F_220(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_211(x)*F_23(x))
Eq(F_211(x), F_212(x) + F_213(x))
Eq(F_212(x), F_205(x) + F_46(x))
Eq(F_213(x), F_209(x) + F_214(x))
Eq(F_214(x), F_215(x) + F_219(x) + 2*F_78(x))
Eq(F_215(x), F_216(x)*F_23(x))
Eq(F_216(x), F_217(x) + F_218(x))
Eq(F_217(x), F_205(x))
Eq(F_218(x), F_214(x))
Eq(F_219(x), F_209(x)*F_23(x))
Eq(F_220(x), F_221(x) + F_242(x) + 2*F_78(x))
Eq(F_221(x), F_222(x)*F_23(x))
Eq(F_222(x), F_223(x) + F_227(x))
Eq(F_223(x), F_198(x) + F_224(x))
Eq(F_224(x), F_207(x) + F_225(x) + 2*F_78(x))
Eq(F_225(x), F_226(x)*F_23(x))
Eq(F_226(x), F_204(x))
Eq(F_227(x), F_220(x) + F_228(x))
Eq(F_228(x), F_229(x) + F_233(x) + F_234(x) + 2*F_78(x))
Eq(F_229(x), F_23(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_224(x))
Eq(F_232(x), F_228(x))
Eq(F_233(x), F_220(x)*F_23(x))
Eq(F_234(x), F_23(x)*F_235(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_214(x) + F_237(x))
Eq(F_237(x), F_233(x) + F_238(x) + 3*F_78(x))
Eq(F_238(x), F_23(x)*F_239(x))
Eq(F_239(x), F_240(x) + F_241(x))
Eq(F_240(x), F_206(x))
Eq(F_241(x), F_237(x))
Eq(F_242(x), F_23(x)*F_243(x))
Eq(F_243(x), F_208(x) + F_236(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_23(x)*F_246(x))
Eq(F_246(x), F_247(x) + F_261(x))
Eq(F_247(x), F_248(x)*F_55(x))
Eq(F_248(x), F_249(x) + F_251(x))
Eq(F_249(x), F_250(x) + F_92(x))
Eq(F_250(x), F_146(x) + F_93(x))
Eq(F_251(x), F_252(x) + F_253(x))
Eq(F_252(x), F_46(x)*F_92(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_23(x)*F_255(x))
Eq(F_255(x), F_256(x) + F_97(x))
Eq(F_256(x), F_104(x) + F_257(x))
Eq(F_257(x), F_258(x))
Eq(F_258(x), F_23(x)*F_259(x))
Eq(F_259(x), F_23(x) + F_260(x))
Eq(F_260(x), F_257(x) + F_77(x))
Eq(F_261(x), F_262(x) + F_270(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_15(x)*F_23(x)*F_264(x))
Eq(F_264(x), F_265(x)/F_23(x))
Eq(F_265(x), F_266(x))
Eq(F_266(x), F_267(x) + F_269(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_130(x)*F_23(x))
Eq(F_269(x), F_55(x)*F_93(x))
Eq(F_270(x), F_145(x)*F_84(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_23(x)*F_249(x)*F_273(x))
Eq(F_273(x), F_0(x) + F_84(x))
Eq(F_274(x), F_16(x)*F_248(x))
Eq(F_275(x), F_16(x)*F_251(x))
Eq(F_276(x), F_277(x) + F_36(x))
Eq(F_277(x), F_40(x) - F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 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[0, 2]]}, {"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, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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"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, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], 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"Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25269/
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[23,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[23,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[23,x]
F[12,x] = F[13,x]+F[86,x]
F[13,x] = F[14,x]*F[38,x]
F[14,x] = F[15,x]+F[84,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = F[15,x]+F[19,x]
F[19,x] = F[20,x]+F[24,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[23,x]*F[28,x]*F[35,x]
F[28,x] = 1/F[23,x]/F[56,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[34,x]+F[31,x]
F[31,x] = 1/F[23,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[2,x]+F[20,x]
F[34,x] = F[2,x]*F[35,x]
F[35,x] = F[0,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[23,x]*F[38,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[35,x]+F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[23,x]*F[42,x]
F[42,x] = F[6,x]
F[43,x] = F[44,x]
F[44,x] = F[23,x]*F[45,x]*F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[23,x]*F[45,x]
F[48,x] = 1/F[23,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = -F[51,x]+F[8,x]
F[51,x] = F[52,x]+F[9,x]
F[52,x] = F[53,x]
F[53,x] = F[23,x]*F[48,x]*F[54,x]
F[54,x] = F[46,x]+F[55,x]
F[55,x] = -F[45,x]+F[15,x]
F[56,x] = 1/F[23,x]/F[45,x]/F[71,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[23,x]*F[45,x]*F[60,x]
F[60,x] = 1/F[23,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[69,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[67,x]+F[9,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[23,x]*F[38,x]
F[69,x] = F[70,x]
F[70,x] = F[23,x]*F[58,x]
F[71,x] = F[1,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[23,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[1,x]+F[23,x]
F[76,x] = F[72,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]+F[83,x]
F[78,x] = 0
F[79,x] = F[23,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[23,x]
F[82,x] = F[77,x]
F[83,x] = F[23,x]*F[72,x]
F[84,x] = F[85,x]
F[85,x] = F[15,x]*F[23,x]*F[35,x]
F[86,x] = F[136,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = -F[135,x]+F[89,x]
F[89,x] = F[133,x]+F[90,x]
F[90,x] = F[128,x]+F[91,x]
F[91,x] = F[15,x]*F[92,x]
F[92,x] = F[1,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[23,x]*F[95,x]
F[95,x] = F[103,x]+F[96,x]
F[96,x] = F[1,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[96,x]
F[100,x] = F[101,x]+F[23,x]
F[101,x] = F[102,x]
F[102,x] = F[23,x]*F[97,x]
F[103,x] = F[104,x]+F[72,x]
F[104,x] = F[105,x]+F[126,x]+F[78,x]
F[105,x] = F[106,x]*F[23,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[97,x]
F[108,x] = F[102,x]+F[109,x]+F[78,x]
F[109,x] = F[110,x]*F[23,x]
F[110,x] = F[100,x]
F[111,x] = F[104,x]+F[112,x]
F[112,x] = F[113,x]+F[117,x]+F[118,x]+F[78,x]
F[113,x] = F[114,x]*F[23,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[108,x]
F[116,x] = F[112,x]
F[117,x] = F[104,x]*F[23,x]
F[118,x] = F[119,x]*F[23,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[77,x]
F[121,x] = 2*F[78,x]+F[117,x]+F[122,x]
F[122,x] = F[123,x]*F[23,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[101,x]
F[125,x] = F[121,x]
F[126,x] = F[127,x]*F[23,x]
F[127,x] = F[103,x]+F[120,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[15,x]*F[23,x]
F[130,x] = 1/F[23,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = -F[92,x]+F[35,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[23,x]*F[45,x]
F[135,x] = F[133,x]+F[14,x]
F[136,x] = F[137,x]*F[276,x]
F[137,x] = 1/F[93,x]*F[138,x]
F[138,x] = -F[88,x]+F[139,x]
F[139,x] = F[140,x]+F[275,x]
F[140,x] = -F[274,x]+F[141,x]
F[141,x] = 1/F[23,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[271,x]+F[144,x]
F[144,x] = F[145,x]+F[244,x]
F[145,x] = F[146,x]+F[93,x]
F[146,x] = F[147,x]+F[195,x]+F[78,x]
F[147,x] = F[148,x]*F[23,x]
F[148,x] = F[149,x]+F[158,x]
F[149,x] = F[150,x]+F[23,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[23,x]
F[152,x] = F[149,x]+F[153,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[155,x]
F[155,x] = x^2
F[156,x] = F[157,x]
F[157,x] = F[150,x]*F[23,x]
F[158,x] = F[159,x]+F[171,x]
F[159,x] = F[160,x]+F[170,x]+F[78,x]
F[160,x] = F[161,x]*F[23,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[154,x]+F[23,x]
F[163,x] = F[159,x]+F[164,x]
F[164,x] = 2*F[78,x]+F[165,x]+F[169,x]
F[165,x] = F[166,x]*F[23,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[154,x]
F[168,x] = F[164,x]
F[169,x] = F[159,x]*F[23,x]
F[170,x] = F[23,x]*F[46,x]
F[171,x] = 2*F[78,x]+F[172,x]+F[193,x]
F[172,x] = F[173,x]*F[23,x]
F[173,x] = F[174,x]+F[178,x]
F[174,x] = F[150,x]+F[175,x]
F[175,x] = 2*F[78,x]+F[157,x]+F[176,x]
F[176,x] = F[177,x]*F[23,x]
F[177,x] = F[153,x]
F[178,x] = F[171,x]+F[179,x]
F[179,x] = 2*F[78,x]+F[180,x]+F[184,x]+F[185,x]
F[180,x] = F[181,x]*F[23,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[175,x]
F[183,x] = F[179,x]
F[184,x] = F[171,x]*F[23,x]
F[185,x] = F[186,x]*F[23,x]
F[186,x] = F[187,x]
F[187,x] = F[164,x]+F[188,x]
F[188,x] = 3*F[78,x]+F[184,x]+F[189,x]
F[189,x] = F[190,x]*F[23,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[156,x]
F[192,x] = F[188,x]
F[193,x] = F[194,x]*F[23,x]
F[194,x] = F[158,x]+F[187,x]
F[195,x] = F[196,x]*F[23,x]
F[196,x] = F[197,x]+F[208,x]
F[197,x] = F[198,x]+F[46,x]
F[198,x] = F[199,x]+F[202,x]+F[78,x]
F[199,x] = F[200,x]*F[23,x]
F[200,x] = F[201,x]+F[23,x]
F[201,x] = F[170,x]+F[199,x]+F[78,x]
F[202,x] = F[203,x]*F[23,x]
F[203,x] = F[197,x]+F[204,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[170,x]
F[206,x] = F[207,x]
F[207,x] = F[198,x]*F[23,x]
F[208,x] = F[209,x]+F[220,x]
F[209,x] = F[210,x]
F[210,x] = F[211,x]*F[23,x]
F[211,x] = F[212,x]+F[213,x]
F[212,x] = F[205,x]+F[46,x]
F[213,x] = F[209,x]+F[214,x]
F[214,x] = 2*F[78,x]+F[215,x]+F[219,x]
F[215,x] = F[216,x]*F[23,x]
F[216,x] = F[217,x]+F[218,x]
F[217,x] = F[205,x]
F[218,x] = F[214,x]
F[219,x] = F[209,x]*F[23,x]
F[220,x] = 2*F[78,x]+F[221,x]+F[242,x]
F[221,x] = F[222,x]*F[23,x]
F[222,x] = F[223,x]+F[227,x]
F[223,x] = F[198,x]+F[224,x]
F[224,x] = 2*F[78,x]+F[207,x]+F[225,x]
F[225,x] = F[226,x]*F[23,x]
F[226,x] = F[204,x]
F[227,x] = F[220,x]+F[228,x]
F[228,x] = 2*F[78,x]+F[229,x]+F[233,x]+F[234,x]
F[229,x] = F[23,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[224,x]
F[232,x] = F[228,x]
F[233,x] = F[220,x]*F[23,x]
F[234,x] = F[23,x]*F[235,x]
F[235,x] = F[236,x]
F[236,x] = F[214,x]+F[237,x]
F[237,x] = 3*F[78,x]+F[233,x]+F[238,x]
F[238,x] = F[23,x]*F[239,x]
F[239,x] = F[240,x]+F[241,x]
F[240,x] = F[206,x]
F[241,x] = F[237,x]
F[242,x] = F[23,x]*F[243,x]
F[243,x] = F[208,x]+F[236,x]
F[244,x] = F[245,x]
F[245,x] = F[23,x]*F[246,x]
F[246,x] = F[247,x]+F[261,x]
F[247,x] = F[248,x]*F[55,x]
F[248,x] = F[249,x]+F[251,x]
F[249,x] = F[250,x]+F[92,x]
F[250,x] = F[146,x]+F[93,x]
F[251,x] = F[252,x]+F[253,x]
F[252,x] = F[46,x]*F[92,x]
F[253,x] = F[254,x]
F[254,x] = F[23,x]*F[255,x]
F[255,x] = F[256,x]+F[97,x]
F[256,x] = F[104,x]+F[257,x]
F[257,x] = F[258,x]
F[258,x] = F[23,x]*F[259,x]
F[259,x] = F[23,x]+F[260,x]
F[260,x] = F[257,x]+F[77,x]
F[261,x] = F[262,x]+F[270,x]
F[262,x] = F[263,x]
F[263,x] = F[15,x]*F[23,x]*F[264,x]
F[264,x] = 1/F[23,x]*F[265,x]
F[265,x] = F[266,x]
F[266,x] = F[267,x]+F[269,x]
F[267,x] = F[268,x]
F[268,x] = F[130,x]*F[23,x]
F[269,x] = F[55,x]*F[93,x]
F[270,x] = F[145,x]*F[84,x]
F[271,x] = F[272,x]
F[272,x] = F[23,x]*F[249,x]*F[273,x]
F[273,x] = F[0,x]+F[84,x]
F[274,x] = F[16,x]*F[248,x]
F[275,x] = F[16,x]*F[251,x]
F[276,x] = F[277,x]+F[36,x]
F[277,x] = -F[5,x]+F[40,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_{23}\! \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_{23}\! \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_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{86}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{84}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right) F_{56}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right) F_{48}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{15}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{71}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{58}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = 0
F_{79}\! \left(x \right) = F_{23}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{23}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = F_{23}\! \left(x \right) F_{72}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{35}\! \left(x \right)
F_{86}\! \left(x \right) = F_{136}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{133}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{128}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{15}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{23}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{103}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{1}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{23}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{23}\! \left(x \right) F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{72}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{126}\! \left(x \right)+F_{78}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{97}\! \left(x \right)
F_{108}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)+F_{78}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{100}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{78}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{23}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{108}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = F_{104}\! \left(x \right) F_{23}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{77}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{23}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{101}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{23}\! \left(x \right)
F_{127}\! \left(x \right) = F_{103}\! \left(x \right)+F_{120}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{15}\! \left(x \right) F_{23}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{35}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right)+F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{276}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{93}\! \left(x \right)}
F_{138}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{275}\! \left(x \right)
F_{140}\! \left(x \right) = -F_{274}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{271}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{244}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{195}\! \left(x \right)+F_{78}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{23}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{158}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{23}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{23}\! \left(x \right)
F_{152}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = x^{2}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{150}\! \left(x \right) F_{23}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{171}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{170}\! \left(x \right)+F_{78}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{23}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{154}\! \left(x \right)+F_{23}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{23}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{154}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{159}\! \left(x \right) F_{23}\! \left(x \right)
F_{170}\! \left(x \right) = F_{23}\! \left(x \right) F_{46}\! \left(x \right)
F_{171}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{172}\! \left(x \right)+F_{193}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{23}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{178}\! \left(x \right)
F_{174}\! \left(x \right) = F_{150}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{157}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{23}\! \left(x \right)
F_{177}\! \left(x \right) = F_{153}\! \left(x \right)
F_{178}\! \left(x \right) = F_{171}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{180}\! \left(x \right)+F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{23}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{175}\! \left(x \right)
F_{183}\! \left(x \right) = F_{179}\! \left(x \right)
F_{184}\! \left(x \right) = F_{171}\! \left(x \right) F_{23}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{23}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{164}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{184}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{23}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{156}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right) F_{23}\! \left(x \right)
F_{194}\! \left(x \right) = F_{158}\! \left(x \right)+F_{187}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{23}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{208}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{46}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{202}\! \left(x \right)+F_{78}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{23}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{23}\! \left(x \right)
F_{201}\! \left(x \right) = F_{170}\! \left(x \right)+F_{199}\! \left(x \right)+F_{78}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{23}\! \left(x \right)
F_{203}\! \left(x \right) = F_{197}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{170}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{198}\! \left(x \right) F_{23}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{220}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{23}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{213}\! \left(x \right)
F_{212}\! \left(x \right) = F_{205}\! \left(x \right)+F_{46}\! \left(x \right)
F_{213}\! \left(x \right) = F_{209}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{215}\! \left(x \right)+F_{219}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right) F_{23}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{218}\! \left(x \right)
F_{217}\! \left(x \right) = F_{205}\! \left(x \right)
F_{218}\! \left(x \right) = F_{214}\! \left(x \right)
F_{219}\! \left(x \right) = F_{209}\! \left(x \right) F_{23}\! \left(x \right)
F_{220}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{221}\! \left(x \right)+F_{242}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{23}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{227}\! \left(x \right)
F_{223}\! \left(x \right) = F_{198}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{207}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{23}\! \left(x \right)
F_{226}\! \left(x \right) = F_{204}\! \left(x \right)
F_{227}\! \left(x \right) = F_{220}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = 2 F_{78}\! \left(x \right)+F_{229}\! \left(x \right)+F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{229}\! \left(x \right) = F_{23}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{224}\! \left(x \right)
F_{232}\! \left(x \right) = F_{228}\! \left(x \right)
F_{233}\! \left(x \right) = F_{220}\! \left(x \right) F_{23}\! \left(x \right)
F_{234}\! \left(x \right) = F_{23}\! \left(x \right) F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{214}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = 3 F_{78}\! \left(x \right)+F_{233}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{23}\! \left(x \right) F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{241}\! \left(x \right)
F_{240}\! \left(x \right) = F_{206}\! \left(x \right)
F_{241}\! \left(x \right) = F_{237}\! \left(x \right)
F_{242}\! \left(x \right) = F_{23}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{208}\! \left(x \right)+F_{236}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{23}\! \left(x \right) F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{261}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right) F_{55}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{251}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{92}\! \left(x \right)
F_{250}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{253}\! \left(x \right)
F_{252}\! \left(x \right) = F_{46}\! \left(x \right) F_{92}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{23}\! \left(x \right) F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)+F_{97}\! \left(x \right)
F_{256}\! \left(x \right) = F_{104}\! \left(x \right)+F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{23}\! \left(x \right) F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{23}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{257}\! \left(x \right)+F_{77}\! \left(x \right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)+F_{270}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = \frac{F_{265}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{269}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{130}\! \left(x \right) F_{23}\! \left(x \right)
F_{269}\! \left(x \right) = F_{55}\! \left(x \right) F_{93}\! \left(x \right)
F_{270}\! \left(x \right) = F_{145}\! \left(x \right) F_{84}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{23}\! \left(x \right) F_{249}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{274}\! \left(x \right) = F_{16}\! \left(x \right) F_{248}\! \left(x \right)
F_{275}\! \left(x \right) = F_{16}\! \left(x \right) F_{251}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{36}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{40}\! \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_23(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_23(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_23(x))
Eq(F_12(x), F_13(x) + F_86(x))
Eq(F_13(x), F_14(x)*F_38(x))
Eq(F_14(x), F_15(x) + F_84(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_15(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_24(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_23(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x)/(F_23(x)*F_56(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_34(x))
Eq(F_31(x), F_32(x)/F_23(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_2(x) + F_20(x))
Eq(F_34(x), F_2(x)*F_35(x))
Eq(F_35(x), F_0(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_23(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_35(x) + F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_23(x))
Eq(F_42(x), F_6(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_23(x)*F_45(x)*F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_23(x)*F_45(x))
Eq(F_48(x), F_49(x)/F_23(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), -F_51(x) + F_8(x))
Eq(F_51(x), F_52(x) + F_9(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_23(x)*F_48(x)*F_54(x))
Eq(F_54(x), F_46(x) + F_55(x))
Eq(F_55(x), F_15(x) - F_45(x))
Eq(F_56(x), F_57(x)/(F_23(x)*F_45(x)*F_71(x)))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_23(x)*F_45(x)*F_60(x))
Eq(F_60(x), F_61(x)/F_23(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_69(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_9(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_23(x)*F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_23(x)*F_58(x))
Eq(F_71(x), F_1(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_23(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_1(x) + F_23(x))
Eq(F_76(x), F_72(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x) + F_83(x))
Eq(F_78(x), 0)
Eq(F_79(x), F_23(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_23(x))
Eq(F_82(x), F_77(x))
Eq(F_83(x), F_23(x)*F_72(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_15(x)*F_23(x)*F_35(x))
Eq(F_86(x), F_136(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), -F_135(x) + F_89(x))
Eq(F_89(x), F_133(x) + F_90(x))
Eq(F_90(x), F_128(x) + F_91(x))
Eq(F_91(x), F_15(x)*F_92(x))
Eq(F_92(x), F_1(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_23(x)*F_95(x))
Eq(F_95(x), F_103(x) + F_96(x))
Eq(F_96(x), F_1(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_96(x))
Eq(F_100(x), F_101(x) + F_23(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_23(x)*F_97(x))
Eq(F_103(x), F_104(x) + F_72(x))
Eq(F_104(x), F_105(x) + F_126(x) + F_78(x))
Eq(F_105(x), F_106(x)*F_23(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_97(x))
Eq(F_108(x), F_102(x) + F_109(x) + F_78(x))
Eq(F_109(x), F_110(x)*F_23(x))
Eq(F_110(x), F_100(x))
Eq(F_111(x), F_104(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_117(x) + F_118(x) + F_78(x))
Eq(F_113(x), F_114(x)*F_23(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_108(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), F_104(x)*F_23(x))
Eq(F_118(x), F_119(x)*F_23(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_77(x))
Eq(F_121(x), F_117(x) + F_122(x) + 2*F_78(x))
Eq(F_122(x), F_123(x)*F_23(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_101(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), F_127(x)*F_23(x))
Eq(F_127(x), F_103(x) + F_120(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_15(x)*F_23(x))
Eq(F_130(x), F_131(x)/F_23(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_35(x) - F_92(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_23(x)*F_45(x))
Eq(F_135(x), F_133(x) + F_14(x))
Eq(F_136(x), F_137(x)*F_276(x))
Eq(F_137(x), F_138(x)/F_93(x))
Eq(F_138(x), F_139(x) - F_88(x))
Eq(F_139(x), F_140(x) + F_275(x))
Eq(F_140(x), F_141(x) - F_274(x))
Eq(F_141(x), F_142(x)/F_23(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x) - F_271(x))
Eq(F_144(x), F_145(x) + F_244(x))
Eq(F_145(x), F_146(x) + F_93(x))
Eq(F_146(x), F_147(x) + F_195(x) + F_78(x))
Eq(F_147(x), F_148(x)*F_23(x))
Eq(F_148(x), F_149(x) + F_158(x))
Eq(F_149(x), F_150(x) + F_23(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_23(x))
Eq(F_152(x), F_149(x) + F_153(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), x**2)
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_150(x)*F_23(x))
Eq(F_158(x), F_159(x) + F_171(x))
Eq(F_159(x), F_160(x) + F_170(x) + F_78(x))
Eq(F_160(x), F_161(x)*F_23(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_154(x) + F_23(x))
Eq(F_163(x), F_159(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_169(x) + 2*F_78(x))
Eq(F_165(x), F_166(x)*F_23(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_154(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_159(x)*F_23(x))
Eq(F_170(x), F_23(x)*F_46(x))
Eq(F_171(x), F_172(x) + F_193(x) + 2*F_78(x))
Eq(F_172(x), F_173(x)*F_23(x))
Eq(F_173(x), F_174(x) + F_178(x))
Eq(F_174(x), F_150(x) + F_175(x))
Eq(F_175(x), F_157(x) + F_176(x) + 2*F_78(x))
Eq(F_176(x), F_177(x)*F_23(x))
Eq(F_177(x), F_153(x))
Eq(F_178(x), F_171(x) + F_179(x))
Eq(F_179(x), F_180(x) + F_184(x) + F_185(x) + 2*F_78(x))
Eq(F_180(x), F_181(x)*F_23(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_175(x))
Eq(F_183(x), F_179(x))
Eq(F_184(x), F_171(x)*F_23(x))
Eq(F_185(x), F_186(x)*F_23(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_164(x) + F_188(x))
Eq(F_188(x), F_184(x) + F_189(x) + 3*F_78(x))
Eq(F_189(x), F_190(x)*F_23(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_156(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_194(x)*F_23(x))
Eq(F_194(x), F_158(x) + F_187(x))
Eq(F_195(x), F_196(x)*F_23(x))
Eq(F_196(x), F_197(x) + F_208(x))
Eq(F_197(x), F_198(x) + F_46(x))
Eq(F_198(x), F_199(x) + F_202(x) + F_78(x))
Eq(F_199(x), F_200(x)*F_23(x))
Eq(F_200(x), F_201(x) + F_23(x))
Eq(F_201(x), F_170(x) + F_199(x) + F_78(x))
Eq(F_202(x), F_203(x)*F_23(x))
Eq(F_203(x), F_197(x) + F_204(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_170(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_198(x)*F_23(x))
Eq(F_208(x), F_209(x) + F_220(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_211(x)*F_23(x))
Eq(F_211(x), F_212(x) + F_213(x))
Eq(F_212(x), F_205(x) + F_46(x))
Eq(F_213(x), F_209(x) + F_214(x))
Eq(F_214(x), F_215(x) + F_219(x) + 2*F_78(x))
Eq(F_215(x), F_216(x)*F_23(x))
Eq(F_216(x), F_217(x) + F_218(x))
Eq(F_217(x), F_205(x))
Eq(F_218(x), F_214(x))
Eq(F_219(x), F_209(x)*F_23(x))
Eq(F_220(x), F_221(x) + F_242(x) + 2*F_78(x))
Eq(F_221(x), F_222(x)*F_23(x))
Eq(F_222(x), F_223(x) + F_227(x))
Eq(F_223(x), F_198(x) + F_224(x))
Eq(F_224(x), F_207(x) + F_225(x) + 2*F_78(x))
Eq(F_225(x), F_226(x)*F_23(x))
Eq(F_226(x), F_204(x))
Eq(F_227(x), F_220(x) + F_228(x))
Eq(F_228(x), F_229(x) + F_233(x) + F_234(x) + 2*F_78(x))
Eq(F_229(x), F_23(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_224(x))
Eq(F_232(x), F_228(x))
Eq(F_233(x), F_220(x)*F_23(x))
Eq(F_234(x), F_23(x)*F_235(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_214(x) + F_237(x))
Eq(F_237(x), F_233(x) + F_238(x) + 3*F_78(x))
Eq(F_238(x), F_23(x)*F_239(x))
Eq(F_239(x), F_240(x) + F_241(x))
Eq(F_240(x), F_206(x))
Eq(F_241(x), F_237(x))
Eq(F_242(x), F_23(x)*F_243(x))
Eq(F_243(x), F_208(x) + F_236(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_23(x)*F_246(x))
Eq(F_246(x), F_247(x) + F_261(x))
Eq(F_247(x), F_248(x)*F_55(x))
Eq(F_248(x), F_249(x) + F_251(x))
Eq(F_249(x), F_250(x) + F_92(x))
Eq(F_250(x), F_146(x) + F_93(x))
Eq(F_251(x), F_252(x) + F_253(x))
Eq(F_252(x), F_46(x)*F_92(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_23(x)*F_255(x))
Eq(F_255(x), F_256(x) + F_97(x))
Eq(F_256(x), F_104(x) + F_257(x))
Eq(F_257(x), F_258(x))
Eq(F_258(x), F_23(x)*F_259(x))
Eq(F_259(x), F_23(x) + F_260(x))
Eq(F_260(x), F_257(x) + F_77(x))
Eq(F_261(x), F_262(x) + F_270(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_15(x)*F_23(x)*F_264(x))
Eq(F_264(x), F_265(x)/F_23(x))
Eq(F_265(x), F_266(x))
Eq(F_266(x), F_267(x) + F_269(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_130(x)*F_23(x))
Eq(F_269(x), F_55(x)*F_93(x))
Eq(F_270(x), F_145(x)*F_84(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_23(x)*F_249(x)*F_273(x))
Eq(F_273(x), F_0(x) + F_84(x))
Eq(F_274(x), F_16(x)*F_248(x))
Eq(F_275(x), F_16(x)*F_251(x))
Eq(F_276(x), F_277(x) + F_36(x))
Eq(F_277(x), F_40(x) - F_5(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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[0, 2]]}, {"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, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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"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, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], 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{"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, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], 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"Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [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": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25373/
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[28,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[28,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[28,x]
F[12,x] = F[13,x]+F[85,x]
F[13,x] = F[14,x]*F[51,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[28,x]*F[84,x]
F[18,x] = F[0,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[28,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[28,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = x
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[28,x]*F[33,x]*F[84,x]
F[33,x] = 1/F[28,x]/F[39,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = -F[38,x]+F[36,x]
F[36,x] = 1/F[28,x]*F[37,x]
F[37,x] = F[24,x]
F[38,x] = F[2,x]*F[26,x]
F[39,x] = 1/F[83,x]*F[40,x]
F[40,x] = -F[81,x]+F[41,x]
F[41,x] = 1/F[28,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[78,x]
F[44,x] = F[45,x]+F[73,x]
F[45,x] = F[2,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[28,x]*F[48,x]
F[48,x] = F[49,x]+F[9,x]
F[49,x] = F[50,x]
F[50,x] = F[18,x]*F[28,x]*F[51,x]
F[51,x] = F[52,x]+F[60,x]
F[52,x] = F[4,x]+F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[55,x]
F[55,x] = F[28,x]*F[51,x]
F[56,x] = -F[5,x]+F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[28,x]*F[59,x]
F[59,x] = F[6,x]
F[60,x] = F[61,x]
F[61,x] = F[28,x]*F[62,x]*F[65,x]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[28,x]*F[62,x]
F[65,x] = 1/F[28,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[68,x]+F[8,x]
F[68,x] = F[69,x]+F[9,x]
F[69,x] = F[70,x]
F[70,x] = F[28,x]*F[65,x]*F[71,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = -F[62,x]+F[18,x]
F[73,x] = F[74,x]
F[74,x] = F[28,x]*F[39,x]*F[75,x]
F[75,x] = F[2,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[28,x]*F[33,x]
F[78,x] = F[79,x]
F[79,x] = F[28,x]*F[80,x]
F[80,x] = F[34,x]
F[81,x] = F[82,x]
F[82,x] = F[28,x]*F[33,x]*F[39,x]
F[83,x] = F[0,x]+F[76,x]
F[84,x] = F[0,x]+F[54,x]
F[85,x] = F[147,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = -F[146,x]+F[88,x]
F[88,x] = F[144,x]+F[89,x]
F[89,x] = F[139,x]+F[90,x]
F[90,x] = F[18,x]*F[91,x]
F[91,x] = F[1,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[28,x]*F[94,x]
F[94,x] = F[102,x]+F[95,x]
F[95,x] = F[1,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[28,x]*F[98,x]
F[98,x] = F[95,x]+F[99,x]
F[99,x] = F[100,x]+F[28,x]
F[100,x] = F[101,x]
F[101,x] = F[28,x]*F[96,x]
F[102,x] = F[103,x]+F[115,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[28,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[1,x]+F[28,x]
F[107,x] = F[103,x]+F[108,x]
F[108,x] = F[109,x]+F[110,x]+F[114,x]
F[109,x] = 0
F[110,x] = F[111,x]*F[28,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[28,x]
F[113,x] = F[108,x]
F[114,x] = F[103,x]*F[28,x]
F[115,x] = F[109,x]+F[116,x]+F[137,x]
F[116,x] = F[117,x]*F[28,x]
F[117,x] = F[118,x]+F[122,x]
F[118,x] = F[119,x]+F[96,x]
F[119,x] = F[101,x]+F[109,x]+F[120,x]
F[120,x] = F[121,x]*F[28,x]
F[121,x] = F[99,x]
F[122,x] = F[115,x]+F[123,x]
F[123,x] = F[109,x]+F[124,x]+F[128,x]+F[129,x]
F[124,x] = F[125,x]*F[28,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[119,x]
F[127,x] = F[123,x]
F[128,x] = F[115,x]*F[28,x]
F[129,x] = F[130,x]*F[28,x]
F[130,x] = F[131,x]
F[131,x] = F[108,x]+F[132,x]
F[132,x] = 2*F[109,x]+F[128,x]+F[133,x]
F[133,x] = F[134,x]*F[28,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[100,x]
F[136,x] = F[132,x]
F[137,x] = F[138,x]*F[28,x]
F[138,x] = F[102,x]+F[131,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[18,x]*F[28,x]
F[141,x] = 1/F[28,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[91,x]+F[84,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[28,x]*F[62,x]
F[146,x] = F[14,x]+F[144,x]
F[147,x] = F[148,x]*F[53,x]
F[148,x] = 1/F[92,x]*F[149,x]
F[149,x] = -F[87,x]+F[150,x]
F[150,x] = F[151,x]+F[285,x]
F[151,x] = -F[284,x]+F[152,x]
F[152,x] = 1/F[28,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = -F[282,x]+F[155,x]
F[155,x] = F[156,x]+F[255,x]
F[156,x] = F[157,x]+F[92,x]
F[157,x] = F[109,x]+F[158,x]+F[206,x]
F[158,x] = F[159,x]*F[28,x]
F[159,x] = F[160,x]+F[169,x]
F[160,x] = F[161,x]+F[28,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[28,x]
F[163,x] = F[160,x]+F[164,x]
F[164,x] = F[165,x]+F[167,x]
F[165,x] = F[166,x]
F[166,x] = x^2
F[167,x] = F[168,x]
F[168,x] = F[161,x]*F[28,x]
F[169,x] = F[170,x]+F[182,x]
F[170,x] = F[109,x]+F[171,x]+F[181,x]
F[171,x] = F[172,x]*F[28,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[165,x]+F[28,x]
F[174,x] = F[170,x]+F[175,x]
F[175,x] = 2*F[109,x]+F[176,x]+F[180,x]
F[176,x] = F[177,x]*F[28,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[165,x]
F[179,x] = F[175,x]
F[180,x] = F[170,x]*F[28,x]
F[181,x] = F[28,x]*F[63,x]
F[182,x] = 2*F[109,x]+F[183,x]+F[204,x]
F[183,x] = F[184,x]*F[28,x]
F[184,x] = F[185,x]+F[189,x]
F[185,x] = F[161,x]+F[186,x]
F[186,x] = 2*F[109,x]+F[168,x]+F[187,x]
F[187,x] = F[188,x]*F[28,x]
F[188,x] = F[164,x]
F[189,x] = F[182,x]+F[190,x]
F[190,x] = 2*F[109,x]+F[191,x]+F[195,x]+F[196,x]
F[191,x] = F[192,x]*F[28,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[186,x]
F[194,x] = F[190,x]
F[195,x] = F[182,x]*F[28,x]
F[196,x] = F[197,x]*F[28,x]
F[197,x] = F[198,x]
F[198,x] = F[175,x]+F[199,x]
F[199,x] = 3*F[109,x]+F[195,x]+F[200,x]
F[200,x] = F[201,x]*F[28,x]
F[201,x] = F[202,x]+F[203,x]
F[202,x] = F[167,x]
F[203,x] = F[199,x]
F[204,x] = F[205,x]*F[28,x]
F[205,x] = F[169,x]+F[198,x]
F[206,x] = F[207,x]*F[28,x]
F[207,x] = F[208,x]+F[219,x]
F[208,x] = F[209,x]+F[63,x]
F[209,x] = F[109,x]+F[210,x]+F[213,x]
F[210,x] = F[211,x]*F[28,x]
F[211,x] = F[212,x]+F[28,x]
F[212,x] = F[109,x]+F[181,x]+F[210,x]
F[213,x] = F[214,x]*F[28,x]
F[214,x] = F[208,x]+F[215,x]
F[215,x] = F[216,x]+F[217,x]
F[216,x] = F[181,x]
F[217,x] = F[218,x]
F[218,x] = F[209,x]*F[28,x]
F[219,x] = F[220,x]+F[231,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[28,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[216,x]+F[63,x]
F[224,x] = F[220,x]+F[225,x]
F[225,x] = 2*F[109,x]+F[226,x]+F[230,x]
F[226,x] = F[227,x]*F[28,x]
F[227,x] = F[228,x]+F[229,x]
F[228,x] = F[216,x]
F[229,x] = F[225,x]
F[230,x] = F[220,x]*F[28,x]
F[231,x] = 2*F[109,x]+F[232,x]+F[253,x]
F[232,x] = F[233,x]*F[28,x]
F[233,x] = F[234,x]+F[238,x]
F[234,x] = F[209,x]+F[235,x]
F[235,x] = 2*F[109,x]+F[218,x]+F[236,x]
F[236,x] = F[237,x]*F[28,x]
F[237,x] = F[215,x]
F[238,x] = F[231,x]+F[239,x]
F[239,x] = 2*F[109,x]+F[240,x]+F[244,x]+F[245,x]
F[240,x] = F[241,x]*F[28,x]
F[241,x] = F[242,x]+F[243,x]
F[242,x] = F[235,x]
F[243,x] = F[239,x]
F[244,x] = F[231,x]*F[28,x]
F[245,x] = F[246,x]*F[28,x]
F[246,x] = F[247,x]
F[247,x] = F[225,x]+F[248,x]
F[248,x] = 3*F[109,x]+F[244,x]+F[249,x]
F[249,x] = F[250,x]*F[28,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[217,x]
F[252,x] = F[248,x]
F[253,x] = F[254,x]*F[28,x]
F[254,x] = F[219,x]+F[247,x]
F[255,x] = F[256,x]
F[256,x] = F[257,x]*F[28,x]
F[257,x] = F[258,x]+F[272,x]
F[258,x] = F[259,x]*F[72,x]
F[259,x] = F[260,x]+F[262,x]
F[260,x] = F[261,x]+F[91,x]
F[261,x] = F[157,x]+F[92,x]
F[262,x] = F[263,x]+F[264,x]
F[263,x] = F[63,x]*F[91,x]
F[264,x] = F[265,x]
F[265,x] = F[266,x]*F[28,x]
F[266,x] = F[267,x]+F[96,x]
F[267,x] = F[115,x]+F[268,x]
F[268,x] = F[269,x]
F[269,x] = F[270,x]*F[28,x]
F[270,x] = F[271,x]+F[28,x]
F[271,x] = F[108,x]+F[268,x]
F[272,x] = F[273,x]+F[281,x]
F[273,x] = F[274,x]
F[274,x] = F[18,x]*F[275,x]*F[28,x]
F[275,x] = 1/F[28,x]*F[276,x]
F[276,x] = F[277,x]
F[277,x] = F[278,x]+F[280,x]
F[278,x] = F[279,x]
F[279,x] = F[141,x]*F[28,x]
F[280,x] = F[72,x]*F[92,x]
F[281,x] = F[156,x]*F[16,x]
F[282,x] = F[283,x]
F[283,x] = F[15,x]*F[260,x]*F[28,x]
F[284,x] = F[19,x]*F[259,x]
F[285,x] = F[19,x]*F[262,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_{28}\! \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_{28}\! \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_{28}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{85}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right) F_{84}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{28}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right) F_{84}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{28}\! \left(x \right) F_{39}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{83}\! \left(x \right)}
F_{40}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{78}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{28}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{9}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{60}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{28}\! \left(x \right) F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{28}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{28}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{8}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{9}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{18}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{28}\! \left(x \right) F_{39}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{28}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{34}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right) F_{39}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right)+F_{76}\! \left(x \right)
F_{84}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{85}\! \left(x \right) = F_{147}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{146}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{144}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{139}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{28}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{102}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{28}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{28}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{28}\! \left(x \right) F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{115}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{28}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{109}\! \left(x \right) = 0
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{28}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{28}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)
F_{114}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right)+F_{116}\! \left(x \right)+F_{137}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{28}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{96}\! \left(x \right)
F_{119}\! \left(x \right) = F_{101}\! \left(x \right)+F_{109}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{28}\! \left(x \right)
F_{121}\! \left(x \right) = F_{99}\! \left(x \right)
F_{122}\! \left(x \right) = F_{115}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{109}\! \left(x \right)+F_{124}\! \left(x \right)+F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{119}\! \left(x \right)
F_{127}\! \left(x \right) = F_{123}\! \left(x \right)
F_{128}\! \left(x \right) = F_{115}\! \left(x \right) F_{28}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{28}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{108}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{128}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{28}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{100}\! \left(x \right)
F_{136}\! \left(x \right) = F_{132}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{28}\! \left(x \right)
F_{138}\! \left(x \right) = F_{102}\! \left(x \right)+F_{131}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{84}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{28}\! \left(x \right) F_{62}\! \left(x \right)
F_{146}\! \left(x \right) = F_{14}\! \left(x \right)+F_{144}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{53}\! \left(x \right)
F_{148}\! \left(x \right) = \frac{F_{149}\! \left(x \right)}{F_{92}\! \left(x \right)}
F_{149}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{285}\! \left(x \right)
F_{151}\! \left(x \right) = -F_{284}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{282}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{255}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{92}\! \left(x \right)
F_{157}\! \left(x \right) = F_{109}\! \left(x \right)+F_{158}\! \left(x \right)+F_{206}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{28}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{169}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{28}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{28}\! \left(x \right)
F_{163}\! \left(x \right) = F_{160}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{167}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = x^{2}
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{161}\! \left(x \right) F_{28}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{182}\! \left(x \right)
F_{170}\! \left(x \right) = F_{109}\! \left(x \right)+F_{171}\! \left(x \right)+F_{181}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{28}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{165}\! \left(x \right)+F_{28}\! \left(x \right)
F_{174}\! \left(x \right) = F_{170}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{176}\! \left(x \right)+F_{180}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{28}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{165}\! \left(x \right)
F_{179}\! \left(x \right) = F_{175}\! \left(x \right)
F_{180}\! \left(x \right) = F_{170}\! \left(x \right) F_{28}\! \left(x \right)
F_{181}\! \left(x \right) = F_{28}\! \left(x \right) F_{63}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{183}\! \left(x \right)+F_{204}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{28}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{189}\! \left(x \right)
F_{185}\! \left(x \right) = F_{161}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{168}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{28}\! \left(x \right)
F_{188}\! \left(x \right) = F_{164}\! \left(x \right)
F_{189}\! \left(x \right) = F_{182}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{191}\! \left(x \right)+F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{28}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{186}\! \left(x \right)
F_{194}\! \left(x \right) = F_{190}\! \left(x \right)
F_{195}\! \left(x \right) = F_{182}\! \left(x \right) F_{28}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right) F_{28}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{175}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = 3 F_{109}\! \left(x \right)+F_{195}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{28}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{203}\! \left(x \right)
F_{202}\! \left(x \right) = F_{167}\! \left(x \right)
F_{203}\! \left(x \right) = F_{199}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{28}\! \left(x \right)
F_{205}\! \left(x \right) = F_{169}\! \left(x \right)+F_{198}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right) F_{28}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{219}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{63}\! \left(x \right)
F_{209}\! \left(x \right) = F_{109}\! \left(x \right)+F_{210}\! \left(x \right)+F_{213}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{28}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{28}\! \left(x \right)
F_{212}\! \left(x \right) = F_{109}\! \left(x \right)+F_{181}\! \left(x \right)+F_{210}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right) F_{28}\! \left(x \right)
F_{214}\! \left(x \right) = F_{208}\! \left(x \right)+F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{217}\! \left(x \right)
F_{216}\! \left(x \right) = F_{181}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{209}\! \left(x \right) F_{28}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{231}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{28}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{216}\! \left(x \right)+F_{63}\! \left(x \right)
F_{224}\! \left(x \right) = F_{220}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{226}\! \left(x \right)+F_{230}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right) F_{28}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{229}\! \left(x \right)
F_{228}\! \left(x \right) = F_{216}\! \left(x \right)
F_{229}\! \left(x \right) = F_{225}\! \left(x \right)
F_{230}\! \left(x \right) = F_{220}\! \left(x \right) F_{28}\! \left(x \right)
F_{231}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{232}\! \left(x \right)+F_{253}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{28}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{238}\! \left(x \right)
F_{234}\! \left(x \right) = F_{209}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{218}\! \left(x \right)+F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{28}\! \left(x \right)
F_{237}\! \left(x \right) = F_{215}\! \left(x \right)
F_{238}\! \left(x \right) = F_{231}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = 2 F_{109}\! \left(x \right)+F_{240}\! \left(x \right)+F_{244}\! \left(x \right)+F_{245}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right) F_{28}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{243}\! \left(x \right)
F_{242}\! \left(x \right) = F_{235}\! \left(x \right)
F_{243}\! \left(x \right) = F_{239}\! \left(x \right)
F_{244}\! \left(x \right) = F_{231}\! \left(x \right) F_{28}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{28}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{225}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = 3 F_{109}\! \left(x \right)+F_{244}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right) F_{28}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{217}\! \left(x \right)
F_{252}\! \left(x \right) = F_{248}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right) F_{28}\! \left(x \right)
F_{254}\! \left(x \right) = F_{219}\! \left(x \right)+F_{247}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right) F_{28}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)+F_{272}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right) F_{72}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{262}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{91}\! \left(x \right)
F_{261}\! \left(x \right) = F_{157}\! \left(x \right)+F_{92}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{264}\! \left(x \right)
F_{263}\! \left(x \right) = F_{63}\! \left(x \right) F_{91}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right) F_{28}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{96}\! \left(x \right)
F_{267}\! \left(x \right) = F_{115}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right) F_{28}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{28}\! \left(x \right)
F_{271}\! \left(x \right) = F_{108}\! \left(x \right)+F_{268}\! \left(x \right)
F_{272}\! \left(x \right) = F_{273}\! \left(x \right)+F_{281}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{18}\! \left(x \right) F_{275}\! \left(x \right) F_{28}\! \left(x \right)
F_{275}\! \left(x \right) = \frac{F_{276}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{280}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{141}\! \left(x \right) F_{28}\! \left(x \right)
F_{280}\! \left(x \right) = F_{72}\! \left(x \right) F_{92}\! \left(x \right)
F_{281}\! \left(x \right) = F_{156}\! \left(x \right) F_{16}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{15}\! \left(x \right) F_{260}\! \left(x \right) F_{28}\! \left(x \right)
F_{284}\! \left(x \right) = F_{19}\! \left(x \right) F_{259}\! \left(x \right)
F_{285}\! \left(x \right) = F_{19}\! \left(x \right) F_{262}\! \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_28(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_28(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_28(x))
Eq(F_12(x), F_13(x) + F_85(x))
Eq(F_13(x), F_14(x)*F_51(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_28(x)*F_84(x))
Eq(F_18(x), F_0(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_28(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_28(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), x)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_28(x)*F_33(x)*F_84(x))
Eq(F_33(x), F_34(x)/(F_28(x)*F_39(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) - F_38(x))
Eq(F_36(x), F_37(x)/F_28(x))
Eq(F_37(x), F_24(x))
Eq(F_38(x), F_2(x)*F_26(x))
Eq(F_39(x), F_40(x)/F_83(x))
Eq(F_40(x), F_41(x) - F_81(x))
Eq(F_41(x), F_42(x)/F_28(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_78(x))
Eq(F_44(x), F_45(x) + F_73(x))
Eq(F_45(x), F_2(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_28(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_9(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_18(x)*F_28(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_60(x))
Eq(F_52(x), F_4(x) + F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_28(x)*F_51(x))
Eq(F_56(x), -F_5(x) + F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_28(x))
Eq(F_59(x), F_6(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_28(x)*F_62(x)*F_65(x))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_28(x)*F_62(x))
Eq(F_65(x), F_66(x)/F_28(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), -F_68(x) + F_8(x))
Eq(F_68(x), F_69(x) + F_9(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_28(x)*F_65(x)*F_71(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), F_18(x) - F_62(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_28(x)*F_39(x)*F_75(x))
Eq(F_75(x), F_2(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_28(x)*F_33(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_28(x)*F_80(x))
Eq(F_80(x), F_34(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_28(x)*F_33(x)*F_39(x))
Eq(F_83(x), F_0(x) + F_76(x))
Eq(F_84(x), F_0(x) + F_54(x))
Eq(F_85(x), F_147(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), -F_146(x) + F_88(x))
Eq(F_88(x), F_144(x) + F_89(x))
Eq(F_89(x), F_139(x) + F_90(x))
Eq(F_90(x), F_18(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_28(x)*F_94(x))
Eq(F_94(x), F_102(x) + F_95(x))
Eq(F_95(x), F_1(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_28(x)*F_98(x))
Eq(F_98(x), F_95(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_28(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_28(x)*F_96(x))
Eq(F_102(x), F_103(x) + F_115(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_28(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_1(x) + F_28(x))
Eq(F_107(x), F_103(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_110(x) + F_114(x))
Eq(F_109(x), 0)
Eq(F_110(x), F_111(x)*F_28(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_28(x))
Eq(F_113(x), F_108(x))
Eq(F_114(x), F_103(x)*F_28(x))
Eq(F_115(x), F_109(x) + F_116(x) + F_137(x))
Eq(F_116(x), F_117(x)*F_28(x))
Eq(F_117(x), F_118(x) + F_122(x))
Eq(F_118(x), F_119(x) + F_96(x))
Eq(F_119(x), F_101(x) + F_109(x) + F_120(x))
Eq(F_120(x), F_121(x)*F_28(x))
Eq(F_121(x), F_99(x))
Eq(F_122(x), F_115(x) + F_123(x))
Eq(F_123(x), F_109(x) + F_124(x) + F_128(x) + F_129(x))
Eq(F_124(x), F_125(x)*F_28(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_119(x))
Eq(F_127(x), F_123(x))
Eq(F_128(x), F_115(x)*F_28(x))
Eq(F_129(x), F_130(x)*F_28(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_108(x) + F_132(x))
Eq(F_132(x), 2*F_109(x) + F_128(x) + F_133(x))
Eq(F_133(x), F_134(x)*F_28(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_100(x))
Eq(F_136(x), F_132(x))
Eq(F_137(x), F_138(x)*F_28(x))
Eq(F_138(x), F_102(x) + F_131(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_18(x)*F_28(x))
Eq(F_141(x), F_142(x)/F_28(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_84(x) - F_91(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_28(x)*F_62(x))
Eq(F_146(x), F_14(x) + F_144(x))
Eq(F_147(x), F_148(x)*F_53(x))
Eq(F_148(x), F_149(x)/F_92(x))
Eq(F_149(x), F_150(x) - F_87(x))
Eq(F_150(x), F_151(x) + F_285(x))
Eq(F_151(x), F_152(x) - F_284(x))
Eq(F_152(x), F_153(x)/F_28(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x) - F_282(x))
Eq(F_155(x), F_156(x) + F_255(x))
Eq(F_156(x), F_157(x) + F_92(x))
Eq(F_157(x), F_109(x) + F_158(x) + F_206(x))
Eq(F_158(x), F_159(x)*F_28(x))
Eq(F_159(x), F_160(x) + F_169(x))
Eq(F_160(x), F_161(x) + F_28(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_28(x))
Eq(F_163(x), F_160(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_167(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), x**2)
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_161(x)*F_28(x))
Eq(F_169(x), F_170(x) + F_182(x))
Eq(F_170(x), F_109(x) + F_171(x) + F_181(x))
Eq(F_171(x), F_172(x)*F_28(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_165(x) + F_28(x))
Eq(F_174(x), F_170(x) + F_175(x))
Eq(F_175(x), 2*F_109(x) + F_176(x) + F_180(x))
Eq(F_176(x), F_177(x)*F_28(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_165(x))
Eq(F_179(x), F_175(x))
Eq(F_180(x), F_170(x)*F_28(x))
Eq(F_181(x), F_28(x)*F_63(x))
Eq(F_182(x), 2*F_109(x) + F_183(x) + F_204(x))
Eq(F_183(x), F_184(x)*F_28(x))
Eq(F_184(x), F_185(x) + F_189(x))
Eq(F_185(x), F_161(x) + F_186(x))
Eq(F_186(x), 2*F_109(x) + F_168(x) + F_187(x))
Eq(F_187(x), F_188(x)*F_28(x))
Eq(F_188(x), F_164(x))
Eq(F_189(x), F_182(x) + F_190(x))
Eq(F_190(x), 2*F_109(x) + F_191(x) + F_195(x) + F_196(x))
Eq(F_191(x), F_192(x)*F_28(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_186(x))
Eq(F_194(x), F_190(x))
Eq(F_195(x), F_182(x)*F_28(x))
Eq(F_196(x), F_197(x)*F_28(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_175(x) + F_199(x))
Eq(F_199(x), 3*F_109(x) + F_195(x) + F_200(x))
Eq(F_200(x), F_201(x)*F_28(x))
Eq(F_201(x), F_202(x) + F_203(x))
Eq(F_202(x), F_167(x))
Eq(F_203(x), F_199(x))
Eq(F_204(x), F_205(x)*F_28(x))
Eq(F_205(x), F_169(x) + F_198(x))
Eq(F_206(x), F_207(x)*F_28(x))
Eq(F_207(x), F_208(x) + F_219(x))
Eq(F_208(x), F_209(x) + F_63(x))
Eq(F_209(x), F_109(x) + F_210(x) + F_213(x))
Eq(F_210(x), F_211(x)*F_28(x))
Eq(F_211(x), F_212(x) + F_28(x))
Eq(F_212(x), F_109(x) + F_181(x) + F_210(x))
Eq(F_213(x), F_214(x)*F_28(x))
Eq(F_214(x), F_208(x) + F_215(x))
Eq(F_215(x), F_216(x) + F_217(x))
Eq(F_216(x), F_181(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_209(x)*F_28(x))
Eq(F_219(x), F_220(x) + F_231(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_28(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_216(x) + F_63(x))
Eq(F_224(x), F_220(x) + F_225(x))
Eq(F_225(x), 2*F_109(x) + F_226(x) + F_230(x))
Eq(F_226(x), F_227(x)*F_28(x))
Eq(F_227(x), F_228(x) + F_229(x))
Eq(F_228(x), F_216(x))
Eq(F_229(x), F_225(x))
Eq(F_230(x), F_220(x)*F_28(x))
Eq(F_231(x), 2*F_109(x) + F_232(x) + F_253(x))
Eq(F_232(x), F_233(x)*F_28(x))
Eq(F_233(x), F_234(x) + F_238(x))
Eq(F_234(x), F_209(x) + F_235(x))
Eq(F_235(x), 2*F_109(x) + F_218(x) + F_236(x))
Eq(F_236(x), F_237(x)*F_28(x))
Eq(F_237(x), F_215(x))
Eq(F_238(x), F_231(x) + F_239(x))
Eq(F_239(x), 2*F_109(x) + F_240(x) + F_244(x) + F_245(x))
Eq(F_240(x), F_241(x)*F_28(x))
Eq(F_241(x), F_242(x) + F_243(x))
Eq(F_242(x), F_235(x))
Eq(F_243(x), F_239(x))
Eq(F_244(x), F_231(x)*F_28(x))
Eq(F_245(x), F_246(x)*F_28(x))
Eq(F_246(x), F_247(x))
Eq(F_247(x), F_225(x) + F_248(x))
Eq(F_248(x), 3*F_109(x) + F_244(x) + F_249(x))
Eq(F_249(x), F_250(x)*F_28(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_217(x))
Eq(F_252(x), F_248(x))
Eq(F_253(x), F_254(x)*F_28(x))
Eq(F_254(x), F_219(x) + F_247(x))
Eq(F_255(x), F_256(x))
Eq(F_256(x), F_257(x)*F_28(x))
Eq(F_257(x), F_258(x) + F_272(x))
Eq(F_258(x), F_259(x)*F_72(x))
Eq(F_259(x), F_260(x) + F_262(x))
Eq(F_260(x), F_261(x) + F_91(x))
Eq(F_261(x), F_157(x) + F_92(x))
Eq(F_262(x), F_263(x) + F_264(x))
Eq(F_263(x), F_63(x)*F_91(x))
Eq(F_264(x), F_265(x))
Eq(F_265(x), F_266(x)*F_28(x))
Eq(F_266(x), F_267(x) + F_96(x))
Eq(F_267(x), F_115(x) + F_268(x))
Eq(F_268(x), F_269(x))
Eq(F_269(x), F_270(x)*F_28(x))
Eq(F_270(x), F_271(x) + F_28(x))
Eq(F_271(x), F_108(x) + F_268(x))
Eq(F_272(x), F_273(x) + F_281(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_18(x)*F_275(x)*F_28(x))
Eq(F_275(x), F_276(x)/F_28(x))
Eq(F_276(x), F_277(x))
Eq(F_277(x), F_278(x) + F_280(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_141(x)*F_28(x))
Eq(F_280(x), F_72(x)*F_92(x))
Eq(F_281(x), F_156(x)*F_16(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_15(x)*F_260(x)*F_28(x))
Eq(F_284(x), F_19(x)*F_259(x))
Eq(F_285(x), F_19(x)*F_262(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 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[0, 2]]}, {"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, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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"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, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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