02341_02431_03241_03412_03421_04231_04312_04321_30241_30412_30421
Counting sequence:
1, 1, 2, 6, 24, 109, 526, 2623, 13384, 69549, 366922, 1960606, 10590042, 57731764, 317242585, 1755416756, 9772683866, 54700040613, 307642488298, 1737696278237, 9853398707117, 56069212265565, 320075109332352, 1832520622808504, 10519874964447126, 60540313921441465, 349196055292315927, 2018420954278116984, 11689793428650878076, 67825998041429014895, 394209604609649223579, 2294839421799674898420, 13379145041978304028653, 78111709814796039347755, 456646204329713078870458, 2672924786752240688785533, 15664147701916504855087561, 91899327716682456658867478, 539731779115927343352557144, 3173074293866772844924729178, 18672279753256748956474377044, 109978842922137030692246034530, 648331195045647687660684301305, 3825103925770484565641224942167, 22585612237981622823357710913786, 133458931116900789738552060241816, 789180573513090482357590447459865, 4669870358257255358274138174224615, 27651615413224335272530575658563495, 163836910077085221617502317192521698, 971331686718326836556677542646804865, 5762057474521740338495273254612634344, 34200470948534403572497789797764934524, 203105581275524422019740512466447173247, 1206808080605249584750389234432195102021, 7174190811465752866964601628921564906382, 42669565511164110078017189574367569157066, 253902355832662338952257922166566311770826, 1511511523757929778216388668421779019359326, 9002140378040492493581648993941221999783076, 53636864344553438318007386769293557334656393, 319711505903972042512070682780211493173638188, 1906446976896336452248914095132277565436181346, 11372536517908633194213391560378412661660460739, 67865790547894883908057027495764421246500594881, 405135691936858356308963764012803906080668957906, 2419365044070466797578216498302272113581955286263, 14452703478882376585373217134514103025786112608293, 86365296758851354053008476553238772966311514490523, 516259208035907233284990727082119655316276194313142, 3086958353098380752776313196697677160958463538251235, 18463939514263341484612323389135105230081246016091926, 110470160225771473831999943544227780996946733035570252, 661133467159188276916558360965783574445234126516998683, 3957796956642053354891754645579491132100100273659253887, 23699265605559643696192915360502137923217605168200095807, 141948302162151924980263298317720898092286440717839855135, 850425938481850618132376159238641581986372683722416254811, 5096252461336892815568724952261348040063613475376509093451, 30547155650769926477920451735592164716788883033004882120490, 183144296284747799079308858907881389456950557929167736902256, 1098288055958253750604277442482557843243334526797636857016760, 6587747198284212070418558802991831781815440573891183217315242, 39523285349465704516385599234722563098243692153892473232593958, 237171407111524785005117151999353007787477911587175373064675339, 1423516851860635242158779818976639331939006806946547403894998192, 8545781266191974932265014231798291751065620623011834579205685183, 51313042922459956369410571218693001899579162521632073306254151087, 308168775631054242914712865384056970228457957357996983996765771537, 1851110985472458667364077302932915921672571477112560781420645492355, 11121347328690562104647796816564602198925268502532795998069817971955, 66828496572421041741538439973580830603379139939872262175210665775533, 401646138287569928305458495426215161712776471384962020079326813872333, 2414356798874670005032995070752202661226545515016105353366573914558088, 14515554960846079887537475561309565013646302057918785532722651153466170, 87284798123629907574954830272479142695547042329152478239758526460361915, 524946251880500121491804729823639155999901727810028819219983690432673359, 3157627235434528494057274835771767766946714562863260652490843196399522358, 18996572506327611558165712386640873524506949569129134212666755487109190736, 114302737197230234034689566195136218077041712989884082585876425912212666820, 687865715533277916256584073586049566655794045713277383967836366149229921610
Implicit equation for the generating function in Maple syntax:
2*x^4*(x-2)*F(x)^7-x^4*(5*x-13)*F(x)^6+x^2*(3*x^3-15*x^2+4*x-1)*F(x)^5+x^2*(6*x-1)*(x-1)*F(x)^4+x*(x^2+x+2)*F(x)^3-2*x*(x+1)*F(x)^2+(x-1)*F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
2 x^{4} \left(x -2\right) F \! \left(x \right)^{7}-x^{4} \left(5 x -13\right) F \! \left(x \right)^{6}+x^{2} \left(3 x^{3}-15 x^{2}+4 x -1\right) F \! \left(x \right)^{5}+x^{2} \left(6 x -1\right) \left(x -1\right) F \! \left(x \right)^{4}+x \left(x^{2}+x +2\right) F \! \left(x \right)^{3}-2 x \left(x +1\right) F \! \left(x \right)^{2}+\left(x -1\right) F \! \left(x \right)+1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 526
a(7) = 2623
a(8) = 13384
a(9) = 69549
a(10) = 366922
a(11) = 1960606
a(12) = 10590042
a(13) = 57731764
a(14) = 317242585
a(15) = 1755416756
a(16) = 9772683866
a(17) = 54700040613
a(18) = 307642488298
a(19) = 1737696278237
a(20) = 9853398707117
a(21) = 56069212265565
a(22) = 320075109332352
a(23) = 1832520622808504
a(24) = 10519874964447126
a(25) = 60540313921441465
a(26) = 349196055292315927
a(27) = 2018420954278116984
a(28) = 11689793428650878076
a(29) = 67825998041429014895
a(30) = 394209604609649223579
a(31) = 2294839421799674898420
a(32) = 13379145041978304028653
a(33) = 78111709814796039347755
a(34) = 456646204329713078870458
a(35) = 2672924786752240688785533
a(36) = 15664147701916504855087561
a(37) = 91899327716682456658867478
a(38) = 539731779115927343352557144
a(39) = 3173074293866772844924729178
a(40) = 18672279753256748956474377044
a(41) = 109978842922137030692246034530
a(42) = 648331195045647687660684301305
a(43) = 3825103925770484565641224942167
a(44) = 22585612237981622823357710913786
a(45) = 133458931116900789738552060241816
a(46) = 789180573513090482357590447459865
a(47) = 4669870358257255358274138174224615
a(48) = 27651615413224335272530575658563495
a(49) = 163836910077085221617502317192521698
a(50) = 971331686718326836556677542646804865
a(51) = 5762057474521740338495273254612634344
a(52) = 34200470948534403572497789797764934524
a(53) = 203105581275524422019740512466447173247
a(54) = 1206808080605249584750389234432195102021
a(55) = 7174190811465752866964601628921564906382
a(56) = 42669565511164110078017189574367569157066
a(57) = 253902355832662338952257922166566311770826
a(58) = 1511511523757929778216388668421779019359326
a(59) = 9002140378040492493581648993941221999783076
a(60) = 53636864344553438318007386769293557334656393
a(61) = 319711505903972042512070682780211493173638188
a(62) = 1906446976896336452248914095132277565436181346
a(63) = 11372536517908633194213391560378412661660460739
a(64) = 67865790547894883908057027495764421246500594881
a(65) = 405135691936858356308963764012803906080668957906
a(66) = 2419365044070466797578216498302272113581955286263
a(67) = 14452703478882376585373217134514103025786112608293
a(68) = 86365296758851354053008476553238772966311514490523
a(69) = 516259208035907233284990727082119655316276194313142
a(70) = 3086958353098380752776313196697677160958463538251235
a(71) = 18463939514263341484612323389135105230081246016091926
a(72) = 110470160225771473831999943544227780996946733035570252
a(73) = 661133467159188276916558360965783574445234126516998683
a(74) = 3957796956642053354891754645579491132100100273659253887
a(75) = 23699265605559643696192915360502137923217605168200095807
a(76) = 141948302162151924980263298317720898092286440717839855135
a(77) = 850425938481850618132376159238641581986372683722416254811
a(78) = 5096252461336892815568724952261348040063613475376509093451
a(79) = 30547155650769926477920451735592164716788883033004882120490
a(80) = 183144296284747799079308858907881389456950557929167736902256
a(81) = 1098288055958253750604277442482557843243334526797636857016760
a(82) = 6587747198284212070418558802991831781815440573891183217315242
a(83) = 39523285349465704516385599234722563098243692153892473232593958
a(84) = 237171407111524785005117151999353007787477911587175373064675339
a(85) = 1423516851860635242158779818976639331939006806946547403894998192
a(86) = 8545781266191974932265014231798291751065620623011834579205685183
a(87) = 51313042922459956369410571218693001899579162521632073306254151087
a(88) = 308168775631054242914712865384056970228457957357996983996765771537
a(89) = 1851110985472458667364077302932915921672571477112560781420645492355
a(90) = 11121347328690562104647796816564602198925268502532795998069817971955
a(91) = 66828496572421041741538439973580830603379139939872262175210665775533
a(92) = 401646138287569928305458495426215161712776471384962020079326813872333
a(93) = 2414356798874670005032995070752202661226545515016105353366573914558088
a(94) = 14515554960846079887537475561309565013646302057918785532722651153466170
a(95) = 87284798123629907574954830272479142695547042329152478239758526460361915
a(96) = 524946251880500121491804729823639155999901727810028819219983690432673359
a(97) = 3157627235434528494057274835771767766946714562863260652490843196399522358
a(98) = 18996572506327611558165712386640873524506949569129134212666755487109190736
a(99) = 114302737197230234034689566195136218077041712989884082585876425912212666820
a(100) = 687865715533277916256584073586049566655794045713277383967836366149229921610
a(101) = 4140140231481855067806068804291196510953159944238906304178614858523180566581
a(102) = 24922381093238401584719021370395453418129745317891031306320584777481057567155
a(103) = 150046504961315889053848872709890030886922906954931803353098323690475349387384
a(104) = 903489098427651246114201287282247375229375574458107747177109850251398214448308
a(105) = 5441009406076774884705768898781801350990764803228054727030382151340930848593572
a(106) = 32771358274112065878586033108550747391518797027733592796994113756278341026331602
a(107) = 197408897047280706955130761130498206090732294901447049264899945873372686219193177
a(108) = 1189310509997318810258204300134873852056053523617117116118671616341284425472362059
a(109) = 7166036486897710594289347676243253898226041049489728218809168518484634361981580843
a(110) = 43183416008650380022034415114496378008036138394901558092760835262069942729940415794
a(n+111) = -1/239099904*(99251294954708*n^5+52467061109564336*n^4+11091284401874427611*n^3+1172001360678335892276*n^2+61904469606616869613728*n+1307524306052044331789760)/(n+110)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+108)-1/807607678919041024524288*(452129369756468551833860398000075842579963169125290522*n^6+102342974516063067696528924715072851191814907017106002357*n^5+9664645679384238052611189969132738498806382630836906794730*n^4+487394172110839824666700979833713558474270826044595078987755*n^3+13844841994780564007556521783716622557626067738949002734327968*n^2+210042392812410450126546998513133088321210469756753735194331988*n+1329681479364202193302952654050095550504934424499997122067855160)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+38)+1/269202559639680341508096*(844279633461300669831607872507026750496399556456439100*n^6+194664711221522016861124245666115594509961447332078728872*n^5+18690362569401514832301609096609964260444491175612287182835*n^4+956472580659553231917384769587064552494549184569459375604050*n^3+27514310972191019595355910296200639806771378446001668310992045*n^2+421826423908826328889605724598113777164540875706416835700763618*n+2692573434069054713389196584329976298687607436023202416312853320)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+39)-1/538405119279360683016192*(1620096788357676059973377355514024047088691738083446187*n^6+383256453590962737013028177988942574745740966241181671129*n^5+37723502653344909095852766442294929765260170634186059984465*n^4+1977342837278946624010907550242414958146413286021134158654635*n^3+58207852292053194024888620413378288061341017705320776711594348*n^2+912304035555298331766816832468642788024481141886873757644905556*n+5946916947370103210532375933377513579018191750538630147493288240)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+40)-1/538405119279360683016192*(3011817779408656861728827624423250405697660422785668973*n^6+732231243294361616910791698925189292137854189087627338287*n^5+74204178769752951007926614498001225466785658542931963919395*n^4+4012254792318436044201363087134386286080254905057300691779645*n^3+122084932995314554877096025824660989718309776108593949940383272*n^2+1982142578434090036311341949721383820615281266534738092834702508*n+13415493185376245930239499566734972636652167877931888662378366080)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+41)+1/1615215357838082049048576*(28431439269076266648717955602053881257680375390757220687*n^6+7092914744322520119770049530360063485406741190404377652679*n^5+737075489215423940393572704001542224011152989062524981042205*n^4+40838297696109527783573170967822781641172784294117611398299725*n^3+1272367238551146402152677616607417566854166615728281579502007308*n^2+21135838704342483545105276104103343420050984364632516747015215476*n+146243058748559569871199752333169789684796035666520619038969371360)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+42)-1/807607678919041024524288*(3105822232418465765315828379600124564359274026255409*n^6+850013430110262273949059117429488912415236047032401988*n^5+94288495385146665822390550055695230997476716247596560975*n^4+5456398342991105419885711656496336499013504799949603956140*n^3+174444576983294576556573997083718484811172608604505743892656*n^2+2930325232156540662082326127947154970337181849555038452868912*n+20253155603330902925559025152306253341202333877486214447358440)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+35)+1/403803839459520512262144*(135206640019748679998564457316155444564339069852191915*n^6+28500874835733912541180435813509039205129718817516400146*n^5+2499827936953068033945527845154401839226874341587444494945*n^4+116762859764672069260492310044151079232698948029612865105330*n^3+3062656257981815167828566720129951477049896935472056798684840*n^2+42765079046045604671043233492869961751413866594608661397509704*n+248300808916203163279720422821625026942628071680959980380720980)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+36)-1/269202559639680341508096*(148676022409417209177269740483398291687138164924512945*n^6+32106459815721661953532743241179438989900633240562411284*n^5+2881690416211678682659196736977502478208089462794741582485*n^4+137560988439451371721330369776966159238152860306584061383580*n^3+3682288522926118229998148285625664162243747918867427454114930*n^2+52386744710159835655998746838048292825780143638505085490890376*n+309308492789017641834283025828660115598569345951133093349297520)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+37)-5/269202559639680341508096*(168760371583803324833230321752609331336452019369657*n^6+28500610051386653534924821811871086352320719445487416*n^5+1971452128981315426062111182836081372443108298332691078*n^4+71080439011484929686832428506062329851116803083354687398*n^3+1395833318708042535402753866628378263154693254143653680005*n^2+13927084416494601035378900812287479106493803014555031104574*n+53396532918504230840398510746563514136423277481462826886808)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+11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/1615215357838082049048576*(53852849796679607577232228225490733984993075159331051555*n^6+20672324754212077045386649926975945993151496034774492963993*n^5+3304326290232526461975873173546925564523077816641592126546085*n^4+281505112382889581567283654882809249328944824433247473125314195*n^3+13480592528531009387472719697367022165660584496553643416638823760*n^2+344042314743011532995862757322408937527547129738267887970082861932*n+3655681449450171633503433222439393704653696629970459185526037995760)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+65)-1/269202559639680341508096*(7017850207872159475943243705397133735929097467239007252*n^6+2792591470093950769255670669732843924272548411431771565318*n^5+463004929723278523934862630576529128336221788742044006389285*n^4+40940045269050423158098445234887783308128699722185497419595800*n^3+2036193085092031915455708912810344887738988799949418929709575683*n^2+54009901858928891800463981295773358919999261017390206329037320382*n+596899619650274405688035903449790134830701436944406034963644516840)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+66)+5/807607678919041024524288*(2107292794406354559712600382490836675197291807412324893*n^6+871376374870903093291443136390226224171301543557634946363*n^5+150077995778039290757534654039540609652428735069546240834140*n^4+13780713365050825792176326660868203993589031655960923945335207*n^3+711535635798172853115253425791226743100842776786999660110982723*n^2+19587140904459298428017039253997776805393840143966999470671283514*n+224588637375969950359478826323929853198366811616310090436396010632)/(n+110)/(n+109)/(2*n+223)/(2*n+221)/(n+112)/(n+111)*a(n+67), n >= 111
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 526
a(7) = 2623
a(8) = 13384
a(9) = 69549
a(10) = 366922
a(11) = 1960606
a(12) = 10590042
a(13) = 57731764
a(14) = 317242585
a(15) = 1755416756
a(16) = 9772683866
a(17) = 54700040613
a(18) = 307642488298
a(19) = 1737696278237
a(20) = 9853398707117
a(21) = 56069212265565
a(22) = 320075109332352
a(23) = 1832520622808504
a(24) = 10519874964447126
a(25) = 60540313921441465
a(26) = 349196055292315927
a(27) = 2018420954278116984
a(28) = 11689793428650878076
a(29) = 67825998041429014895
a(30) = 394209604609649223579
a(31) = 2294839421799674898420
a(32) = 13379145041978304028653
a(33) = 78111709814796039347755
a(34) = 456646204329713078870458
a(35) = 2672924786752240688785533
a(36) = 15664147701916504855087561
a(37) = 91899327716682456658867478
a(38) = 539731779115927343352557144
a(39) = 3173074293866772844924729178
a(40) = 18672279753256748956474377044
a(41) = 109978842922137030692246034530
a(42) = 648331195045647687660684301305
a(43) = 3825103925770484565641224942167
a(44) = 22585612237981622823357710913786
a(45) = 133458931116900789738552060241816
a(46) = 789180573513090482357590447459865
a(47) = 4669870358257255358274138174224615
a(48) = 27651615413224335272530575658563495
a(49) = 163836910077085221617502317192521698
a(50) = 971331686718326836556677542646804865
a(51) = 5762057474521740338495273254612634344
a(52) = 34200470948534403572497789797764934524
a(53) = 203105581275524422019740512466447173247
a(54) = 1206808080605249584750389234432195102021
a(55) = 7174190811465752866964601628921564906382
a(56) = 42669565511164110078017189574367569157066
a(57) = 253902355832662338952257922166566311770826
a(58) = 1511511523757929778216388668421779019359326
a(59) = 9002140378040492493581648993941221999783076
a(60) = 53636864344553438318007386769293557334656393
a(61) = 319711505903972042512070682780211493173638188
a(62) = 1906446976896336452248914095132277565436181346
a(63) = 11372536517908633194213391560378412661660460739
a(64) = 67865790547894883908057027495764421246500594881
a(65) = 405135691936858356308963764012803906080668957906
a(66) = 2419365044070466797578216498302272113581955286263
a(67) = 14452703478882376585373217134514103025786112608293
a(68) = 86365296758851354053008476553238772966311514490523
a(69) = 516259208035907233284990727082119655316276194313142
a(70) = 3086958353098380752776313196697677160958463538251235
a(71) = 18463939514263341484612323389135105230081246016091926
a(72) = 110470160225771473831999943544227780996946733035570252
a(73) = 661133467159188276916558360965783574445234126516998683
a(74) = 3957796956642053354891754645579491132100100273659253887
a(75) = 23699265605559643696192915360502137923217605168200095807
a(76) = 141948302162151924980263298317720898092286440717839855135
a(77) = 850425938481850618132376159238641581986372683722416254811
a(78) = 5096252461336892815568724952261348040063613475376509093451
a(79) = 30547155650769926477920451735592164716788883033004882120490
a(80) = 183144296284747799079308858907881389456950557929167736902256
a(81) = 1098288055958253750604277442482557843243334526797636857016760
a(82) = 6587747198284212070418558802991831781815440573891183217315242
a(83) = 39523285349465704516385599234722563098243692153892473232593958
a(84) = 237171407111524785005117151999353007787477911587175373064675339
a(85) = 1423516851860635242158779818976639331939006806946547403894998192
a(86) = 8545781266191974932265014231798291751065620623011834579205685183
a(87) = 51313042922459956369410571218693001899579162521632073306254151087
a(88) = 308168775631054242914712865384056970228457957357996983996765771537
a(89) = 1851110985472458667364077302932915921672571477112560781420645492355
a(90) = 11121347328690562104647796816564602198925268502532795998069817971955
a(91) = 66828496572421041741538439973580830603379139939872262175210665775533
a(92) = 401646138287569928305458495426215161712776471384962020079326813872333
a(93) = 2414356798874670005032995070752202661226545515016105353366573914558088
a(94) = 14515554960846079887537475561309565013646302057918785532722651153466170
a(95) = 87284798123629907574954830272479142695547042329152478239758526460361915
a(96) = 524946251880500121491804729823639155999901727810028819219983690432673359
a(97) = 3157627235434528494057274835771767766946714562863260652490843196399522358
a(98) = 18996572506327611558165712386640873524506949569129134212666755487109190736
a(99) = 114302737197230234034689566195136218077041712989884082585876425912212666820
a(100) = 687865715533277916256584073586049566655794045713277383967836366149229921610
a(101) = 4140140231481855067806068804291196510953159944238906304178614858523180566581
a(102) = 24922381093238401584719021370395453418129745317891031306320584777481057567155
a(103) = 150046504961315889053848872709890030886922906954931803353098323690475349387384
a(104) = 903489098427651246114201287282247375229375574458107747177109850251398214448308
a(105) = 5441009406076774884705768898781801350990764803228054727030382151340930848593572
a(106) = 32771358274112065878586033108550747391518797027733592796994113756278341026331602
a(107) = 197408897047280706955130761130498206090732294901447049264899945873372686219193177
a(108) = 1189310509997318810258204300134873852056053523617117116118671616341284425472362059
a(109) = 7166036486897710594289347676243253898226041049489728218809168518484634361981580843
a(110) = 43183416008650380022034415114496378008036138394901558092760835262069942729940415794
a{\left(n + 111 \right)} = - \frac{1012372830448699625732551491 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) a{\left(n \right)}}{866996971464348925952 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{6603 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(85564287821272831706603951 n + 202877442506904387007329116\right) a{\left(n + 1 \right)}}{19940930343680025296896 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(1488134793214107657973977476453 n^{2} + 42092139139772669356706613137103 n + 185474911586898449115978420482590\right) a{\left(n + 2 \right)}}{19940930343680025296896 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(155338360304487707111895879334668 n^{3} + 2833642394045051735719257551609718 n^{2} + 16964923358430691513279586433880973 n + 33003596836554754348796991548327358\right) a{\left(n + 3 \right)}}{29911395515520037945344 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(n + 4\right) \left(n + 5\right) \left(327039799581252198891368793844253 n^{4} - 6547564394877901501308146997723145 n^{3} - 222430562653974945424363176325647420 n^{2} - 1713204910549210650438128409158778360 n - 4107275336979520642210275243915434028\right) a{\left(n + 4 \right)}}{89734186546560113836032 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(n + 5\right) \left(251091136719865128017869093212169817 n^{5} + 9500083951027115435139925787261145258 n^{4} + 142393327189644906386947398765990094195 n^{3} + 1057371595252934296725607304472080607690 n^{2} + 3891611499119823253918962298955374879968 n + 5681616937827230589352651006375433980032\right) a{\left(n + 5 \right)}}{538405119279360683016192 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(8361511 n^{2} + 1827677177 n + 99875758350\right) a{\left(n + 110 \right)}}{58374 \left(n + 112\right) \left(2 n + 223\right)} + \frac{\left(147862404100 n^{4} + 63252267330204 n^{3} + 10144505395505399 n^{2} + 722946167731721529 n + 19315798674260242104\right) a{\left(n + 109 \right)}}{14943744 \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(99251294954708 n^{5} + 52467061109564336 n^{4} + 11091284401874427611 n^{3} + 1172001360678335892276 n^{2} + 61904469606616869613728 n + 1307524306052044331789760\right) a{\left(n + 108 \right)}}{239099904 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(29577463817534616 n^{6} + 19167464009360257528 n^{5} + 5174298301541182686320 n^{4} + 744789398900736423593075 n^{3} + 60288794057512682822631124 n^{2} + 2602189812912177369390963237 n + 46787790106589023248922126620\right) a{\left(n + 107 \right)}}{3825598464 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(4935623667832629560 n^{6} + 3102575996462353041416 n^{5} + 812389964529206712958560 n^{4} + 113415989037038252614603435 n^{3} + 8903712511094762078824705165 n^{2} + 372671991829591350476832062304 n + 6497202728293611011399927743740\right) a{\left(n + 106 \right)}}{30604787712 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(246189849658697825476 n^{6} + 159842689341780643673188 n^{5} + 43209654924665601118657155 n^{4} + 6225313453881781877383571105 n^{3} + 504166050458589877815089426414 n^{2} + 21762495243123125766919623077592 n + 391174047923903144730926018971740\right) a{\left(n + 105 \right)}}{122419150848 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(101886534181549110101492 n^{6} + 63969124930642014909570204 n^{5} + 16734300094737543145347442715 n^{4} + 2334739470168060042445777794765 n^{3} + 183225983753779699494276007990733 n^{2} + 7668843924227165039070887760902301 n + 133738731746116635056753517570514800\right) a{\left(n + 104 \right)}}{1469029810176 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(3379657997594883462368720 n^{6} + 2067558170952919032484776696 n^{5} + 527015559742589038192277194370 n^{4} + 71644207287933900532952007219405 n^{3} + 5478425905246533879624284239905905 n^{2} + 223421602947984025579919397437098224 n + 3796476275711870492451817195300175640\right) a{\left(n + 103 \right)}}{11752238481408 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(327339072950536159078506268 n^{6} + 201574407546988432513428390672 n^{5} + 51716113771426736929096757837395 n^{4} + 7075862388675448901953132572515925 n^{3} + 544527422284596485138470206476074522 n^{2} + 22347208427640423511092892734979110138 n + 382102633865005324401820853686962931380\right) a{\left(n + 102 \right)}}{47008953925632 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(5393480224255843804652287484 n^{6} + 3266785183843612377049808275302 n^{5} + 824433111124194747789455826527570 n^{4} + 110964306733879711480085547109353645 n^{3} + 8400936378428433038654155388963880431 n^{2} + 339206738711342398748644478795422684548 n + 5706677321854598758891808769438745121040\right) a{\left(n + 101 \right)}}{94017907851264 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(45363912656661295257031967724 n^{6} + 27439549178516212557926208668838 n^{5} + 6914721297070442331253463239408190 n^{4} + 929211175746370103914526798606153940 n^{3} + 70229699162033487522451569088340902801 n^{2} + 2830549920449006418355662195217239633177 n + 47528625593022887536695032616024264450060\right) a{\left(n + 100 \right)}}{125357210468352 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(2669009352096263107144184880736 n^{6} + 1589546973716027113715241118452766 n^{5} + 394417592100419282508849675746950735 n^{4} + 52192550975377691357942977037953959360 n^{3} + 3884665469649003272298691897011207976534 n^{2} + 154194007337021452612989337698957764222909 n + 2549998187613702470428842418358124776358000\right) a{\left(n + 99 \right)}}{501428841873408 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(11784413011810325399451541888096 n^{6} + 6857086310557936568713661846265742 n^{5} + 1661970050259090604829227398162868255 n^{4} + 214764196780647816627929683095673087115 n^{3} + 15605305456898392978502392653328407795964 n^{2} + 604537010140101095597983841405896478500608 n + 9754288294482929106532944176184233628711300\right) a{\left(n + 98 \right)}}{2005715367493632 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(3671709112512556379471073725563252 n^{6} + 2145905255385318382936224771348398622 n^{5} + 522513364180092407919943935630551758300 n^{4} + 67848327283760164399882194271149949733505 n^{3} + 4955185337502425898564964995884216134091488 n^{2} + 192990626058858767381961380259700447046847543 n + 3131543536827449628425176532812726126023591330\right) a{\left(n + 97 \right)}}{24068584409923584 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(20579068768872722184323652940717096 n^{6} + 11824560211558911179774550179920956554 n^{5} + 2830113194364364821680584047565554597655 n^{4} + 361151250068595882318846210343104316669195 n^{3} + 25915619460887278186340004204863981721230044 n^{2} + 991503162986623090835903620064585430909518016 n + 15800585664545872426211426105900809250224192020\right) a{\left(n + 96 \right)}}{32091445879898112 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(373741261209864906675748748048833388 n^{6} + 7687467669619870851106725822531429519 n^{5} - 45561861844941619270538427326636454715 n^{4} - 2533818193787689161537711606203716154565 n^{3} - 26863823072108723139931267786529616378253 n^{2} - 120673472823352625738582764857389875205694 n - 202859310696231694384667862056966736514680\right) a{\left(n + 6 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(406672348234020596446011583248235904 n^{6} + 246811903034066410981796071666513004244 n^{5} + 62274395182864109369528844843947941037240 n^{4} + 8363196572177753459712381074007615876055215 n^{3} + 630600733099303577624790512421777225760288331 n^{2} + 25316230486092360442029035732206772497082667786 n + 422819443768272333730356435612905498909864906880\right) a{\left(n + 95 \right)}}{770194701117554688 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(4705422427048562880788889057963612404 n^{6} + 2705505690899058077719659697083484819076 n^{5} + 647931263954643175147443739339745701100055 n^{4} + 82729698746691119295268510455532810166364315 n^{3} + 5939921439402251771633055929504683526120253436 n^{2} + 227391072583554336074598561351092013885479443114 n + 3626099392800930571856296727629686510887298606660\right) a{\left(n + 94 \right)}}{1026926268156739584 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(15802631850012437546289432565536971777 n^{6} + 481518523380401194905540514336478977431 n^{5} + 517350792317396461234967196139002521105 n^{4} - 144218485134740721399521778421427212885455 n^{3} - 2188057262107682900928797695776664707436762 n^{2} - 13025523914347273074656540863836930698051856 n - 28491627622738470491751144377683527362450880\right) a{\left(n + 8 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(22372796789226936248020947167456599850 n^{6} + 1235314333356107877289960256136877915923 n^{5} + 28166046832492983355756806455178705553880 n^{4} + 339727719997924095063426450839895194697225 n^{3} + 2287592715483160562326357447919621284162310 n^{2} + 8157260772683678157620123293947518323927812 n + 12038503245466341648899385330343946621529120\right) a{\left(n + 7 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - 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\frac{5 \left(19726925900264695137257274348472544208084839255741665703 n^{6} + 6770740459886194829453422133047817116803487115591745208127 n^{5} + 968248250286197710847478182420473776418001889328131750128953 n^{4} + 73844976347142422451172015757110295329832673122715179631586325 n^{3} + 3167835268032688406154140767696921206313522133370677312114112048 n^{2} + 72474921477846123388164872894486435445794972287284246218760955340 n + 690854226015734931751564746896854635263251532418430362980913833136\right) a{\left(n + 57 \right)}}{538405119279360683016192 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(21220963399266451072520709789788458638197498131314180169 n^{6} + 5477206391472985185735078823423719800978246287958430292617 n^{5} + 568381504670338592898743101938272067066353465882943537305500 n^{4} + 29789142009511466234005615240921666459617450023620606134984225 n^{3} + 799685203577193893615724996549707500009748211295519148510955931 n^{2} + 9367313980040729586227903576303133178552273739591610483742578558 n + 20460482414966524144859823515408396904143782250842271776289095320\right) a{\left(n + 51 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(26663640870164197359543619952898141233198661218052554923 n^{6} + 10237710750801859444226694639860595447980292114399926301331 n^{5} + 1637669881490324289854224119717623039019000762883352603729815 n^{4} + 139701457242006485770131559898204398293229188707249870273493365 n^{3} + 6702724150406634554484814791535664855613925289136531647064282622 n^{2} + 171496293369601806325967724766308081379083136023421942572718723944 n + 1828108891071329464082991428251561738000167694586603815872804354000\right) a{\left(n + 63 \right)}}{538405119279360683016192 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(28431439269076266648717955602053881257680375390757220687 n^{6} + 7092914744322520119770049530360063485406741190404377652679 n^{5} + 737075489215423940393572704001542224011152989062524981042205 n^{4} + 40838297696109527783573170967822781641172784294117611398299725 n^{3} + 1272367238551146402152677616607417566854166615728281579502007308 n^{2} + 21135838704342483545105276104103343420050984364632516747015215476 n + 146243058748559569871199752333169789684796035666520619038969371360\right) a{\left(n + 42 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(31637207568146091902244179033776636655228541088627847969 n^{6} + 9911793024135664407551692580224259154366562769859274348413 n^{5} + 1290628280662388182930369959636995888098729813869539742812285 n^{4} + 89381417905175242365377321693944850463967656149622818108207475 n^{3} + 3471275481365421736917581590223666052184163378546166040994757506 n^{2} + 71656626318905642883321181986220011179507924731979628241632910632 n + 613996494484541788550821502266705330330543084224100699718071681440\right) a{\left(n + 55 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(35539517671787121309570812003527793935257233739224584037 n^{6} + 11540533826591878011531173336810063325279877604492662571192 n^{5} + 1560593227185507006465171504564100372240240017295804648416025 n^{4} + 112492709628556377140901422676500061898436079947069270730113660 n^{3} + 4558945720779273871548409392564362340271252401573875123229873438 n^{2} + 98490916444176815100031899221901231178377773061249558907140317168 n + 886174494437604815610922479832893610447809843739113437191912722960\right) a{\left(n + 53 \right)}}{269202559639680341508096 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(51359504836233975567849479029457231949919976324898437147 n^{6} + 14210133787575180685660031587855096255437613161266998451271 n^{5} + 1636811074759704543654613492288188986753261145304117834159355 n^{4} + 100470036866201297390942060155659515893992612006751845438298545 n^{3} + 3466092505393887325127901984131909838283540694501591280428544218 n^{2} + 63721984830194584645351065266492562352872198614982308731880723064 n + 487727749130888328169848851747982879047099787728325970798076891760\right) a{\left(n + 46 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(53852849796679607577232228225490733984993075159331051555 n^{6} + 20672324754212077045386649926975945993151496034774492963993 n^{5} + 3304326290232526461975873173546925564523077816641592126546085 n^{4} + 281505112382889581567283654882809249328944824433247473125314195 n^{3} + 13480592528531009387472719697367022165660584496553643416638823760 n^{2} + 344042314743011532995862757322408937527547129738267887970082861932 n + 3655681449450171633503433222439393704653696629970459185526037995760\right) a{\left(n + 65 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(72698829547961012510925759069641476798295033107590635995 n^{6} + 19835864002762743911842733897415902821000305750058090002837 n^{5} + 2253925403770689118698147823118678642385855379902734421696955 n^{4} + 136520843632611273612869605092938892881775437107186587864757155 n^{3} + 4648890420523570349136780766097763089598462090273974149055465530 n^{2} + 84384492627305408403051632837489089590290812670157123287399501688 n + 637858825154072898421702488702234745655786426314595684341857861840\right) a{\left(n + 47 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(78674661868721859255616696795328754898460299339882984661 n^{6} + 27403956661595323946826141734726077991546631883697430656793 n^{5} + 3979982373788766944497279888806767399579124720269420423911655 n^{4} + 308496547613701863946078211766585275521991888798015396008494315 n^{3} + 13460019788473881958465891636273729438344299798698760701347024164 n^{2} + 313432471079044124208048032626923338563268578057637348560073077692 n + 3043231450196718487375586914944113346298949347539215925263860966320\right) a{\left(n + 58 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(89666036023118595323205667783259466966124316973376488029 n^{6} + 32842704153042946800224251192882464364665593650269003431079 n^{5} + 5008557126161692366067613770944425463447833715324553853232805 n^{4} + 407059448187078587691425851927581741541959534758839229019818985 n^{3} + 18595008385627022776353488743174545020736060777093057512386000166 n^{2} + 452690938108241905491422528769287917293823562924273297867263426296 n + 4588394720341477095052903339194724703921339924259462993141902786160\right) a{\left(n + 61 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(91146571270821085464590290052705742837913920635622295727 n^{6} + 24340634711830706763320804521821905844231875211464060674749 n^{5} + 2707811074661073127462035101432351305471613885913923383801685 n^{4} + 160623627707645306282530777398274714271815753902202552449070455 n^{3} + 5358320916035750632303577728126313764116091179464559544255963148 n^{2} + 95313040638166416338133103701652259887041892389133786986303413916 n + 706269180065949000818022002621035684680745101132187482916440076080\right) a{\left(n + 45 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(92006528725450167368456173745795511510844944837647330449 n^{6} + 27058226346665197062076582414102624156123309111101390306045 n^{5} + 3313627107556355542444038289786455362963776384700824656069685 n^{4} + 216294592858869363174569856809306425571519505070058158660876155 n^{3} + 7936942781466231311723149823099437565067547996368335141410674586 n^{2} + 155241057545032249382993886697084545321221167507014928154279650920 n + 1264444330545607100267126070232019735592854035444324631904649262160\right) a{\left(n + 49 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(95700247069057611535057356354714183452816964245112958775 n^{6} + 29229912275158821393107978368299764668333684830846409388007 n^{5} + 3716239648522196590292674260099679086527513245424613549666125 n^{4} + 251729443659172020899381359335916455985301566181963255162066205 n^{3} + 9581271412820118042848245106484708677185437370890709832499195740 n^{2} + 194279328337215126481182797388708504385280331173862005778659164428 n + 1639501786654313740494926412962821962366042280503073971571948765680\right) a{\left(n + 52 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(105482628368260665775862595063805178618289254176744151327 n^{6} + 35228212010638689120249644471305790229170748305282305648107 n^{5} + 4897633957729479666875123850970112659552527127911321659915015 n^{4} + 362827320659103896819136085584483486327919845123485296564340325 n^{3} + 15106903048674873769542200548298406982348870621747738912881953738 n^{2} + 335202565339353045081780921807231599449923874823265018705980524848 n + 3096725047667603999675704043511695953874039737073591838657242190360\right) a{\left(n + 54 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(147799661542169816665546768474575738616072576863231421111 n^{6} + 41679285803794546375180118942671305165301599105175760731347 n^{5} + 4894744937526538398821218065453844116075256314977215656822595 n^{4} + 306412038262972557276970332078426081386843470236274027870872045 n^{3} + 10783605115995184700146595008436032539249252414603263369130568294 n^{2} + 202289314418350321440391340487341092670819177642447336581302858528 n + 1580208973666623091202614416487221326977086667515840792463675717200\right) a{\left(n + 48 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} - \frac{\left(171619176029576526297473579315012723504326404149351865775 n^{6} + 61859591501348999267286333147986448674044562412065309351151 n^{5} + 9295149611269692258761675352730185871175088299579107481374645 n^{4} + 745286881593816462464838720235398455126851874729453484671240925 n^{3} + 33630353622574572676229520730345014818799064518504121033191751060 n^{2} + 809758276576433932409506507692267397464285161401367460830943931644 n + 8128005091241634511969021442802584829021331904219226843793878176640\right) a{\left(n + 60 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(173587478078209782420166858073273886266425186115600388509 n^{6} + 64759131761490239934754419524500591821810285764281499647119 n^{5} + 10064567013848482068058737324956861424397315035450099677065385 n^{4} + 834086039801242170708143136028951426683212333744718898900478865 n^{3} + 38875171211580975675401620305897133573212645512844626691815885666 n^{2} + 966175205474102224153309771564083427072105340648108891718788991096 n + 10003495533073963284687718868781018882234470413705182002075778888000\right) a{\left(n + 62 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(180732268081730976442967839333825638439951059734162881795 n^{6} + 60803885249242832964399102280064799485725559116946074815249 n^{5} + 8524020644044302479866066241382851483776659822278697455215780 n^{4} + 637361627394582646114627275666478047427690053377008092941671065 n^{3} + 26808972443792502706403353658145523066437946246318774662972492325 n^{2} + 601456548957463756962271788989166438990944591642382707892258175026 n + 5622753331129659616341133095293895977607135942194852001964958144640\right) a{\left(n + 56 \right)}}{807607678919041024524288 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)} + \frac{\left(309497507109320036028262679702974152788997475671334757183 n^{6} + 109748878695409501653852683229827946140498551849211256950481 n^{5} + 16219928226483339790022340206547437969331691897570036551339995 n^{4} + 1278832443661222157801720181469284878207733546628077857762352855 n^{3} + 56730673444622884789936418198506911178619777768207111407066763582 n^{2} + 1342572631720711733133354874679135665285680281042723598171200044704 n + 13242283900598662999050240939381812103055993653024496411051908491280\right) a{\left(n + 59 \right)}}{1615215357838082049048576 \left(n + 109\right) \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(2 n + 221\right) \left(2 n + 223\right)}, \quad n \geq 111
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24548/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[41,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[332,x]
F[11,x] = F[12,x]+F[351,x]
F[12,x] = F[13,x]+F[2,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[41,x]
F[15,x] = F[16,x]+F[37,x]
F[16,x] = F[12,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[41,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[41,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[0,x]+F[12,x]
F[25,x] = F[26,x]*F[310,x]
F[26,x] = -F[350,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[2,x]^2
F[29,x] = -F[349,x]+F[30,x]
F[30,x] = -F[319,x]+F[31,x]
F[31,x] = 1/F[0,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[138,x]+F[34,x]
F[34,x] = 1/F[41,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[43,x]+F[37,x]
F[37,x] = -F[42,x]+F[38,x]
F[38,x] = 1/F[41,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[2,x]+F[6,x]
F[41,x] = x
F[42,x] = F[16,x]+F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[0,x]*F[41,x]*F[45,x]
F[45,x] = F[12,x]+F[46,x]
F[46,x] = F[126,x]+F[47,x]
F[47,x] = F[48,x]+F[74,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[41,x]*F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[53,x]+F[60,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[1,x]+F[53,x]
F[57,x] = F[41,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[41,x]*F[53,x]
F[60,x] = F[61,x]+F[62,x]+F[70,x]
F[61,x] = 0
F[62,x] = F[41,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[49,x]+F[60,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[67,x]
F[67,x] = F[41,x]*F[49,x]
F[68,x] = F[69,x]
F[69,x] = F[41,x]*F[60,x]
F[70,x] = F[41,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[41,x]+F[66,x]
F[73,x] = F[58,x]+F[68,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[41,x]*F[77,x]
F[77,x] = F[78,x]+F[85,x]
F[78,x] = F[74,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[41,x]*F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[78,x]*F[83,x]
F[83,x] = F[1,x]+F[41,x]
F[84,x] = F[76,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[41,x]*F[87,x]
F[87,x] = F[13,x]
F[88,x] = F[79,x]+F[89,x]
F[89,x] = F[53,x]+F[90,x]
F[90,x] = F[61,x]+F[91,x]+F[99,x]
F[91,x] = F[41,x]*F[92,x]
F[92,x] = F[89,x]+F[93,x]
F[93,x] = F[104,x]+F[94,x]
F[94,x] = F[61,x]+F[95,x]+F[99,x]
F[95,x] = F[41,x]*F[96,x]
F[96,x] = F[103,x]+F[97,x]
F[97,x] = F[53,x]+F[98,x]
F[98,x] = F[59,x]+F[61,x]+F[99,x]
F[99,x] = F[100,x]*F[41,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]+F[41,x]
F[102,x] = F[59,x]
F[103,x] = F[98,x]
F[104,x] = F[105,x]+F[110,x]+F[118,x]+F[61,x]
F[105,x] = F[106,x]*F[41,x]
F[106,x] = F[107,x]+F[123,x]
F[107,x] = F[108,x]+F[90,x]
F[108,x] = F[109,x]+F[110,x]+F[118,x]+F[61,x]
F[109,x] = F[41,x]*F[90,x]
F[110,x] = F[111,x]*F[41,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[108,x]+F[98,x]
F[113,x] = F[114,x]+F[119,x]
F[114,x] = F[115,x]+F[116,x]+F[118,x]+F[61,x]
F[115,x] = F[41,x]*F[98,x]
F[116,x] = F[117,x]*F[41,x]
F[117,x] = F[103,x]
F[118,x] = 0
F[119,x] = F[120,x]+F[121,x]+F[124,x]+F[125,x]+F[61,x]
F[120,x] = F[108,x]*F[41,x]
F[121,x] = F[122,x]*F[41,x]
F[122,x] = F[123,x]
F[123,x] = F[108,x]
F[124,x] = 0
F[125,x] = 0
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[41,x]*F[47,x]
F[128,x] = F[129,x]+F[24,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]
F[131,x] = F[0,x]^2*F[41,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]*F[41,x]
F[134,x] = F[135,x]
F[135,x] = F[0,x]*F[136,x]*F[41,x]
F[136,x] = F[137,x]+F[85,x]
F[137,x] = F[47,x]+F[88,x]
F[138,x] = -F[143,x]+F[139,x]
F[139,x] = 1/F[41,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]+F[36,x]
F[142,x] = F[17,x]+F[40,x]
F[143,x] = -F[147,x]+F[144,x]
F[144,x] = 1/F[41,x]*F[145,x]
F[145,x] = F[146,x]
F[146,x] = F[139,x]*F[41,x]
F[147,x] = F[148,x]+F[315,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[41,x]
F[150,x] = 1/F[41,x]*F[151,x]
F[151,x] = F[152,x]
F[152,x] = -F[167,x]+F[153,x]
F[153,x] = 1/F[41,x]*F[154,x]
F[154,x] = F[155,x]
F[155,x] = -F[158,x]+F[156,x]
F[156,x] = 1/F[41,x]*F[157,x]
F[157,x] = F[75,x]
F[158,x] = -F[161,x]+F[159,x]
F[159,x] = 1/F[41,x]*F[160,x]
F[160,x] = F[74,x]
F[161,x] = F[162,x]+F[47,x]
F[162,x] = -F[165,x]+F[163,x]
F[163,x] = 1/F[41,x]*F[164,x]
F[164,x] = F[6,x]
F[165,x] = F[16,x]+F[166,x]
F[166,x] = F[132,x]
F[167,x] = F[0,x]*F[168,x]
F[168,x] = F[169,x]+F[236,x]
F[169,x] = F[170,x]+F[47,x]
F[170,x] = -F[173,x]+F[171,x]
F[171,x] = 1/F[41,x]*F[172,x]
F[172,x] = F[6,x]
F[173,x] = F[174,x]+F[175,x]
F[174,x] = F[2,x]*F[47,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]*F[41,x]
F[177,x] = F[178,x]+F[233,x]
F[178,x] = F[179,x]+F[183,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[136,x]*F[2,x]
F[181,x] = F[182,x]
F[182,x] = F[0,x]*F[47,x]*F[5,x]
F[183,x] = F[184,x]+F[224,x]
F[184,x] = F[185,x]*F[2,x]
F[185,x] = F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[41,x]*F[188,x]
F[188,x] = F[170,x]
F[189,x] = F[136,x]+F[190,x]
F[190,x] = F[191,x]+F[222,x]
F[191,x] = F[0,x]*F[192,x]
F[192,x] = F[193,x]+F[41,x]
F[193,x] = F[194,x]+F[221,x]+F[61,x]
F[194,x] = F[195,x]*F[41,x]
F[195,x] = F[192,x]+F[196,x]
F[196,x] = F[197,x]+F[207,x]
F[197,x] = F[198,x]+F[206,x]+F[61,x]
F[198,x] = F[199,x]*F[41,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[197,x]+F[41,x]
F[201,x] = F[202,x]+F[204,x]
F[202,x] = F[203,x]
F[203,x] = x^2
F[204,x] = F[205,x]
F[205,x] = F[197,x]*F[41,x]
F[206,x] = x^2
F[207,x] = F[208,x]+F[216,x]+F[220,x]+F[61,x]
F[208,x] = F[209,x]*F[41,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[193,x]+F[207,x]
F[211,x] = F[212,x]+F[214,x]
F[212,x] = F[213,x]
F[213,x] = F[193,x]*F[41,x]
F[214,x] = F[215,x]
F[215,x] = F[207,x]*F[41,x]
F[216,x] = F[217,x]*F[41,x]
F[217,x] = F[218,x]+F[219,x]
F[218,x] = F[202,x]+F[212,x]
F[219,x] = F[204,x]+F[214,x]
F[220,x] = F[41,x]*F[58,x]
F[221,x] = F[41,x]*F[53,x]
F[222,x] = F[223,x]
F[223,x] = F[0,x]*F[41,x]*F[77,x]
F[224,x] = F[225,x]
F[225,x] = F[0,x]*F[226,x]*F[231,x]
F[226,x] = F[227,x]
F[227,x] = F[0,x]*F[228,x]*F[41,x]
F[228,x] = F[229,x]+F[47,x]
F[229,x] = F[230,x]
F[230,x] = F[49,x]+F[75,x]
F[231,x] = F[232,x]
F[232,x] = F[0,x]*F[41,x]*F[47,x]
F[233,x] = F[234,x]
F[234,x] = F[224,x]+F[235,x]
F[235,x] = F[190,x]*F[2,x]
F[236,x] = 1/F[310,x]*F[237,x]
F[237,x] = -F[309,x]+F[238,x]
F[238,x] = 1/F[41,x]*F[239,x]
F[239,x] = F[240,x]
F[240,x] = -F[243,x]+F[241,x]
F[241,x] = -F[255,x]+F[242,x]
F[242,x] = F[243,x]+F[253,x]
F[243,x] = F[244,x]+F[74,x]
F[244,x] = F[245,x]
F[245,x] = F[246,x]*F[41,x]
F[246,x] = F[247,x]+F[250,x]
F[247,x] = F[248,x]+F[77,x]
F[248,x] = F[249,x]+F[84,x]
F[249,x] = -F[229,x]+F[185,x]
F[250,x] = F[251,x]
F[251,x] = F[222,x]+F[252,x]
F[252,x] = F[192,x]*F[2,x]
F[253,x] = F[254,x]
F[254,x] = F[153,x]*F[41,x]
F[255,x] = F[2,x]*F[256,x]
F[256,x] = F[257,x]+F[262,x]
F[257,x] = F[1,x]+F[258,x]
F[258,x] = F[259,x]
F[259,x] = F[260,x]*F[41,x]
F[260,x] = F[261,x]+F[83,x]
F[261,x] = F[41,x]
F[262,x] = F[263,x]+F[49,x]
F[263,x] = F[264,x]+F[305,x]+F[61,x]
F[264,x] = F[265,x]*F[41,x]
F[265,x] = F[266,x]+F[267,x]
F[266,x] = F[258,x]+F[263,x]
F[267,x] = F[268,x]+F[281,x]
F[268,x] = F[269,x]+F[277,x]+F[61,x]
F[269,x] = F[270,x]*F[41,x]
F[270,x] = F[271,x]+F[272,x]
F[271,x] = F[258,x]+F[268,x]
F[272,x] = F[273,x]+F[275,x]
F[273,x] = F[274,x]
F[274,x] = F[258,x]*F[41,x]
F[275,x] = F[276,x]
F[276,x] = F[268,x]*F[41,x]
F[277,x] = F[278,x]*F[41,x]
F[278,x] = F[279,x]+F[280,x]
F[279,x] = F[202,x]+F[41,x]
F[280,x] = F[202,x]
F[281,x] = F[282,x]+F[290,x]+F[294,x]+F[61,x]
F[282,x] = F[283,x]*F[41,x]
F[283,x] = F[284,x]+F[285,x]
F[284,x] = F[263,x]+F[281,x]
F[285,x] = F[286,x]+F[288,x]
F[286,x] = F[287,x]
F[287,x] = F[263,x]*F[41,x]
F[288,x] = F[289,x]
F[289,x] = F[281,x]*F[41,x]
F[290,x] = F[291,x]*F[41,x]
F[291,x] = F[292,x]+F[293,x]
F[292,x] = F[273,x]+F[286,x]
F[293,x] = F[275,x]+F[288,x]
F[294,x] = F[295,x]*F[41,x]
F[295,x] = F[296,x]+F[304,x]
F[296,x] = F[297,x]+F[58,x]
F[297,x] = F[298,x]
F[298,x] = F[299,x]*F[41,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[41,x]
F[301,x] = F[302,x]+F[303,x]
F[302,x] = F[299,x]+F[41,x]
F[303,x] = F[202,x]+F[297,x]
F[304,x] = F[297,x]
F[305,x] = F[306,x]*F[41,x]
F[306,x] = F[307,x]+F[308,x]
F[307,x] = F[299,x]+F[53,x]
F[308,x] = F[299,x]
F[309,x] = F[24,x]*F[243,x]
F[310,x] = F[0,x]+F[311,x]
F[311,x] = F[312,x]
F[312,x] = F[0,x]*F[313,x]*F[41,x]
F[313,x] = F[24,x]+F[314,x]
F[314,x] = F[2,x]*F[310,x]
F[315,x] = F[316,x]
F[316,x] = F[0,x]*F[317,x]
F[317,x] = F[318,x]
F[318,x] = F[0,x]*F[134,x]*F[41,x]
F[319,x] = F[320,x]
F[320,x] = F[321,x]*F[41,x]
F[321,x] = -F[342,x]+F[322,x]
F[322,x] = 1/F[41,x]*F[323,x]
F[323,x] = F[324,x]
F[324,x] = -F[340,x]+F[325,x]
F[325,x] = F[326,x]+F[327,x]
F[326,x] = F[2,x]*F[45,x]
F[327,x] = -F[339,x]+F[328,x]
F[328,x] = 1/F[0,x]/F[41,x]*F[329,x]
F[329,x] = F[330,x]
F[330,x] = F[331,x]+F[332,x]
F[331,x] = F[0,x]*F[5,x]
F[332,x] = F[333,x]
F[333,x] = F[334,x]*F[41,x]
F[334,x] = F[335,x]+F[338,x]
F[335,x] = F[181,x]+F[336,x]
F[336,x] = F[224,x]+F[337,x]
F[337,x] = F[0,x]*F[190,x]
F[338,x] = F[224,x]
F[339,x] = F[0,x]*F[45,x]
F[340,x] = -F[341,x]+F[328,x]
F[341,x] = F[12,x]+F[168,x]
F[342,x] = -F[345,x]+F[343,x]
F[343,x] = 1/F[41,x]*F[344,x]
F[344,x] = F[324,x]
F[345,x] = F[346,x]
F[346,x] = F[0,x]*F[347,x]
F[347,x] = F[249,x]+F[348,x]
F[348,x] = F[0,x]*F[229,x]
F[349,x] = F[12,x]+F[28,x]
F[350,x] = F[2,x]^2*F[0,x]
F[351,x] = F[352,x]
F[352,x] = F[353,x]*F[41,x]
F[353,x] = F[354,x]+F[355,x]
F[354,x] = F[12,x]*F[4,x]
F[355,x] = F[0,x]*F[19,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{41}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{332}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{351}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{12}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{310}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{350}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{29}\! \left(x \right) = -F_{349}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{319}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{138}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = F_{16}\! \left(x \right)+F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{126}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{74}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{61}\! \left(x \right) = 0
F_{62}\! \left(x \right) = F_{41}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{49}\! \left(x \right)+F_{60}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{41}\! \left(x \right) F_{49}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{41}\! \left(x \right) F_{60}\! \left(x \right)
F_{70}\! \left(x \right) = F_{41}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{41}\! \left(x \right)+F_{66}\! \left(x \right)
F_{73}\! \left(x \right) = F_{58}\! \left(x \right)+F_{68}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{41}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{84}\! \left(x \right) = F_{76}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{13}\! \left(x \right)
F_{88}\! \left(x \right) = F_{79}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{53}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{61}\! \left(x \right)+F_{91}\! \left(x \right)+F_{99}\! \left(x \right)
F_{91}\! \left(x \right) = F_{41}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{104}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{61}\! \left(x \right)+F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{95}\! \left(x \right) = F_{41}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{53}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{41}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{41}\! \left(x \right)
F_{102}\! \left(x \right) = F_{59}\! \left(x \right)
F_{103}\! \left(x \right) = F_{98}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{110}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{41}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{123}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{90}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{109}\! \left(x \right) = F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{41}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)+F_{98}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{119}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{115}\! \left(x \right) = F_{41}\! \left(x \right) F_{98}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{41}\! \left(x \right)
F_{117}\! \left(x \right) = F_{103}\! \left(x \right)
F_{118}\! \left(x \right) = 0
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)+F_{124}\! \left(x \right)+F_{125}\! \left(x \right)+F_{61}\! \left(x \right)
F_{120}\! \left(x \right) = F_{108}\! \left(x \right) F_{41}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{41}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{108}\! \left(x \right)
F_{124}\! \left(x \right) = 0
F_{125}\! \left(x \right) = 0
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{41}\! \left(x \right) F_{47}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{24}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{41}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{41}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{0}\! \left(x \right) F_{136}\! \left(x \right) F_{41}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{85}\! \left(x \right)
F_{137}\! \left(x \right) = F_{47}\! \left(x \right)+F_{88}\! \left(x \right)
F_{138}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{36}\! \left(x \right)
F_{142}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{147}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = \frac{F_{145}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{139}\! \left(x \right) F_{41}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{315}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{41}\! \left(x \right)
F_{150}\! \left(x \right) = \frac{F_{151}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = -F_{167}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = \frac{F_{154}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = \frac{F_{157}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{157}\! \left(x \right) = F_{75}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{161}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = \frac{F_{160}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{160}\! \left(x \right) = F_{74}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{47}\! \left(x \right)
F_{162}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = \frac{F_{164}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{164}\! \left(x \right) = F_{6}\! \left(x \right)
F_{165}\! \left(x \right) = F_{16}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{132}\! \left(x \right)
F_{167}\! \left(x \right) = F_{0}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{236}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{47}\! \left(x \right)
F_{170}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = \frac{F_{172}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{172}\! \left(x \right) = F_{6}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{175}\! \left(x \right)
F_{174}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{41}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{233}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{183}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{136}\! \left(x \right) F_{2}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{0}\! \left(x \right) F_{47}\! \left(x \right) F_{5}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{224}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{2}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{170}\! \left(x \right)
F_{189}\! \left(x \right) = F_{136}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{222}\! \left(x \right)
F_{191}\! \left(x \right) = F_{0}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{41}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{221}\! \left(x \right)+F_{61}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{41}\! \left(x \right)
F_{195}\! \left(x \right) = F_{192}\! \left(x \right)+F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{207}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{206}\! \left(x \right)+F_{61}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{41}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{197}\! \left(x \right)+F_{41}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{204}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = x^{2}
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{197}\! \left(x \right) F_{41}\! \left(x \right)
F_{206}\! \left(x \right) = x^{2}
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{216}\! \left(x \right)+F_{220}\! \left(x \right)+F_{61}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{41}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{193}\! \left(x \right)+F_{207}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{214}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{193}\! \left(x \right) F_{41}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{207}\! \left(x \right) F_{41}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right) F_{41}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{219}\! \left(x \right)
F_{218}\! \left(x \right) = F_{202}\! \left(x \right)+F_{212}\! \left(x \right)
F_{219}\! \left(x \right) = F_{204}\! \left(x \right)+F_{214}\! \left(x \right)
F_{220}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{221}\! \left(x \right) = F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{77}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{0}\! \left(x \right) F_{226}\! \left(x \right) F_{231}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{0}\! \left(x \right) F_{228}\! \left(x \right) F_{41}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{47}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{49}\! \left(x \right)+F_{75}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{47}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{224}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{190}\! \left(x \right) F_{2}\! \left(x \right)
F_{236}\! \left(x \right) = \frac{F_{237}\! \left(x \right)}{F_{310}\! \left(x \right)}
F_{237}\! \left(x \right) = -F_{309}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = \frac{F_{239}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = -F_{243}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = -F_{255}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{253}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{74}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{41}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{250}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{77}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{84}\! \left(x \right)
F_{249}\! \left(x \right) = -F_{229}\! \left(x \right)+F_{185}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{222}\! \left(x \right)+F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{192}\! \left(x \right) F_{2}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{153}\! \left(x \right) F_{41}\! \left(x \right)
F_{255}\! \left(x \right) = F_{2}\! \left(x \right) F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{262}\! \left(x \right)
F_{257}\! \left(x \right) = F_{1}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right) F_{41}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{83}\! \left(x \right)
F_{261}\! \left(x \right) = F_{41}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{49}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{305}\! \left(x \right)+F_{61}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right) F_{41}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)+F_{267}\! \left(x \right)
F_{266}\! \left(x \right) = F_{258}\! \left(x \right)+F_{263}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{281}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{277}\! \left(x \right)+F_{61}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right) F_{41}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{272}\! \left(x \right)
F_{271}\! \left(x \right) = F_{258}\! \left(x \right)+F_{268}\! \left(x \right)
F_{272}\! \left(x \right) = F_{273}\! \left(x \right)+F_{275}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{258}\! \left(x \right) F_{41}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{268}\! \left(x \right) F_{41}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right) F_{41}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{280}\! \left(x \right)
F_{279}\! \left(x \right) = F_{202}\! \left(x \right)+F_{41}\! \left(x \right)
F_{280}\! \left(x \right) = F_{202}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{290}\! \left(x \right)+F_{294}\! \left(x \right)+F_{61}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right) F_{41}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)+F_{285}\! \left(x \right)
F_{284}\! \left(x \right) = F_{263}\! \left(x \right)+F_{281}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{288}\! \left(x \right)
F_{286}\! \left(x \right) = F_{287}\! \left(x \right)
F_{287}\! \left(x \right) = F_{263}\! \left(x \right) F_{41}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = F_{281}\! \left(x \right) F_{41}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{41}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{293}\! \left(x \right)
F_{292}\! \left(x \right) = F_{273}\! \left(x \right)+F_{286}\! \left(x \right)
F_{293}\! \left(x \right) = F_{275}\! \left(x \right)+F_{288}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{41}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)+F_{304}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{58}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{41}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{41}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)+F_{303}\! \left(x \right)
F_{302}\! \left(x \right) = F_{299}\! \left(x \right)+F_{41}\! \left(x \right)
F_{303}\! \left(x \right) = F_{202}\! \left(x \right)+F_{297}\! \left(x \right)
F_{304}\! \left(x \right) = F_{297}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right) F_{41}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)+F_{308}\! \left(x \right)
F_{307}\! \left(x \right) = F_{299}\! \left(x \right)+F_{53}\! \left(x \right)
F_{308}\! \left(x \right) = F_{299}\! \left(x \right)
F_{309}\! \left(x \right) = F_{24}\! \left(x \right) F_{243}\! \left(x \right)
F_{310}\! \left(x \right) = F_{0}\! \left(x \right)+F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{0}\! \left(x \right) F_{313}\! \left(x \right) F_{41}\! \left(x \right)
F_{313}\! \left(x \right) = F_{24}\! \left(x \right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{2}\! \left(x \right) F_{310}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{0}\! \left(x \right) F_{317}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)
F_{318}\! \left(x \right) = F_{0}\! \left(x \right) F_{134}\! \left(x \right) F_{41}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right) F_{41}\! \left(x \right)
F_{321}\! \left(x \right) = -F_{342}\! \left(x \right)+F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = \frac{F_{323}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = -F_{340}\! \left(x \right)+F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{327}\! \left(x \right)
F_{326}\! \left(x \right) = F_{2}\! \left(x \right) F_{45}\! \left(x \right)
F_{327}\! \left(x \right) = -F_{339}\! \left(x \right)+F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = \frac{F_{329}\! \left(x \right)}{F_{0}\! \left(x \right) F_{41}\! \left(x \right)}
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right)+F_{332}\! \left(x \right)
F_{331}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right) F_{41}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right)+F_{338}\! \left(x \right)
F_{335}\! \left(x \right) = F_{181}\! \left(x \right)+F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{224}\! \left(x \right)+F_{337}\! \left(x \right)
F_{337}\! \left(x \right) = F_{0}\! \left(x \right) F_{190}\! \left(x \right)
F_{338}\! \left(x \right) = F_{224}\! \left(x \right)
F_{339}\! \left(x \right) = F_{0}\! \left(x \right) F_{45}\! \left(x \right)
F_{340}\! \left(x \right) = -F_{341}\! \left(x \right)+F_{328}\! \left(x \right)
F_{341}\! \left(x \right) = F_{12}\! \left(x \right)+F_{168}\! \left(x \right)
F_{342}\! \left(x \right) = -F_{345}\! \left(x \right)+F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = \frac{F_{344}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{344}\! \left(x \right) = F_{324}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{0}\! \left(x \right) F_{347}\! \left(x \right)
F_{347}\! \left(x \right) = F_{249}\! \left(x \right)+F_{348}\! \left(x \right)
F_{348}\! \left(x \right) = F_{0}\! \left(x \right) F_{229}\! \left(x \right)
F_{349}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{350}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = F_{353}\! \left(x \right) F_{41}\! \left(x \right)
F_{353}\! \left(x \right) = F_{354}\! \left(x \right)+F_{355}\! \left(x \right)
F_{354}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{355}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_41(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_332(x))
Eq(F_11(x), F_12(x) + F_351(x))
Eq(F_12(x), F_13(x) + F_2(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_41(x))
Eq(F_15(x), F_16(x) + F_37(x))
Eq(F_16(x), F_12(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_41(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_41(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_0(x) + F_12(x))
Eq(F_25(x), F_26(x)*F_310(x))
Eq(F_26(x), F_27(x) - F_350(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_2(x)**2)
Eq(F_29(x), F_30(x) - F_349(x))
Eq(F_30(x), F_31(x) - F_319(x))
Eq(F_31(x), F_32(x)/F_0(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_138(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_41(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) - F_43(x))
Eq(F_37(x), F_38(x) - F_42(x))
Eq(F_38(x), F_39(x)/F_41(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_2(x) + F_6(x))
Eq(F_41(x), x)
Eq(F_42(x), F_16(x) + F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_0(x)*F_41(x)*F_45(x))
Eq(F_45(x), F_12(x) + F_46(x))
Eq(F_46(x), F_126(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_74(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_41(x)*F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_53(x) + F_60(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_1(x) + F_53(x))
Eq(F_57(x), F_41(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_41(x)*F_53(x))
Eq(F_60(x), F_61(x) + F_62(x) + F_70(x))
Eq(F_61(x), 0)
Eq(F_62(x), F_41(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_49(x) + F_60(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_41(x)*F_49(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_41(x)*F_60(x))
Eq(F_70(x), F_41(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_41(x) + F_66(x))
Eq(F_73(x), F_58(x) + F_68(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_41(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_85(x))
Eq(F_78(x), F_74(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_41(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_78(x)*F_83(x))
Eq(F_83(x), F_1(x) + F_41(x))
Eq(F_84(x), F_76(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_41(x))
Eq(F_87(x), F_13(x))
Eq(F_88(x), F_79(x) + F_89(x))
Eq(F_89(x), F_53(x) + F_90(x))
Eq(F_90(x), F_61(x) + F_91(x) + F_99(x))
Eq(F_91(x), F_41(x)*F_92(x))
Eq(F_92(x), F_89(x) + F_93(x))
Eq(F_93(x), F_104(x) + F_94(x))
Eq(F_94(x), F_61(x) + F_95(x) + F_99(x))
Eq(F_95(x), F_41(x)*F_96(x))
Eq(F_96(x), F_103(x) + F_97(x))
Eq(F_97(x), F_53(x) + F_98(x))
Eq(F_98(x), F_59(x) + F_61(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_41(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) + F_41(x))
Eq(F_102(x), F_59(x))
Eq(F_103(x), F_98(x))
Eq(F_104(x), F_105(x) + F_110(x) + F_118(x) + F_61(x))
Eq(F_105(x), F_106(x)*F_41(x))
Eq(F_106(x), F_107(x) + F_123(x))
Eq(F_107(x), F_108(x) + F_90(x))
Eq(F_108(x), F_109(x) + F_110(x) + F_118(x) + F_61(x))
Eq(F_109(x), F_41(x)*F_90(x))
Eq(F_110(x), F_111(x)*F_41(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_108(x) + F_98(x))
Eq(F_113(x), F_114(x) + F_119(x))
Eq(F_114(x), F_115(x) + F_116(x) + F_118(x) + F_61(x))
Eq(F_115(x), F_41(x)*F_98(x))
Eq(F_116(x), F_117(x)*F_41(x))
Eq(F_117(x), F_103(x))
Eq(F_118(x), 0)
Eq(F_119(x), F_120(x) + F_121(x) + F_124(x) + F_125(x) + F_61(x))
Eq(F_120(x), F_108(x)*F_41(x))
Eq(F_121(x), F_122(x)*F_41(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_108(x))
Eq(F_124(x), 0)
Eq(F_125(x), 0)
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_41(x)*F_47(x))
Eq(F_128(x), F_129(x) + F_24(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_0(x)**2*F_41(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x)*F_41(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_0(x)*F_136(x)*F_41(x))
Eq(F_136(x), F_137(x) + F_85(x))
Eq(F_137(x), F_47(x) + F_88(x))
Eq(F_138(x), F_139(x) - F_143(x))
Eq(F_139(x), F_140(x)/F_41(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x) + F_36(x))
Eq(F_142(x), F_17(x) + F_40(x))
Eq(F_143(x), F_144(x) - F_147(x))
Eq(F_144(x), F_145(x)/F_41(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_139(x)*F_41(x))
Eq(F_147(x), F_148(x) + F_315(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_41(x))
Eq(F_150(x), F_151(x)/F_41(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x) - F_167(x))
Eq(F_153(x), F_154(x)/F_41(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x) - F_158(x))
Eq(F_156(x), F_157(x)/F_41(x))
Eq(F_157(x), F_75(x))
Eq(F_158(x), F_159(x) - F_161(x))
Eq(F_159(x), F_160(x)/F_41(x))
Eq(F_160(x), F_74(x))
Eq(F_161(x), F_162(x) + F_47(x))
Eq(F_162(x), F_163(x) - F_165(x))
Eq(F_163(x), F_164(x)/F_41(x))
Eq(F_164(x), F_6(x))
Eq(F_165(x), F_16(x) + F_166(x))
Eq(F_166(x), F_132(x))
Eq(F_167(x), F_0(x)*F_168(x))
Eq(F_168(x), F_169(x) + F_236(x))
Eq(F_169(x), F_170(x) + F_47(x))
Eq(F_170(x), F_171(x) - F_173(x))
Eq(F_171(x), F_172(x)/F_41(x))
Eq(F_172(x), F_6(x))
Eq(F_173(x), F_174(x) + F_175(x))
Eq(F_174(x), F_2(x)*F_47(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x)*F_41(x))
Eq(F_177(x), F_178(x) + F_233(x))
Eq(F_178(x), F_179(x) + F_183(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_136(x)*F_2(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_0(x)*F_47(x)*F_5(x))
Eq(F_183(x), F_184(x) + F_224(x))
Eq(F_184(x), F_185(x)*F_2(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_41(x))
Eq(F_188(x), F_170(x))
Eq(F_189(x), F_136(x) + F_190(x))
Eq(F_190(x), F_191(x) + F_222(x))
Eq(F_191(x), F_0(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_41(x))
Eq(F_193(x), F_194(x) + F_221(x) + F_61(x))
Eq(F_194(x), F_195(x)*F_41(x))
Eq(F_195(x), F_192(x) + F_196(x))
Eq(F_196(x), F_197(x) + F_207(x))
Eq(F_197(x), F_198(x) + F_206(x) + F_61(x))
Eq(F_198(x), F_199(x)*F_41(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_197(x) + F_41(x))
Eq(F_201(x), F_202(x) + F_204(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), x**2)
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_197(x)*F_41(x))
Eq(F_206(x), x**2)
Eq(F_207(x), F_208(x) + F_216(x) + F_220(x) + F_61(x))
Eq(F_208(x), F_209(x)*F_41(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_193(x) + F_207(x))
Eq(F_211(x), F_212(x) + F_214(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_193(x)*F_41(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_207(x)*F_41(x))
Eq(F_216(x), F_217(x)*F_41(x))
Eq(F_217(x), F_218(x) + F_219(x))
Eq(F_218(x), F_202(x) + F_212(x))
Eq(F_219(x), F_204(x) + F_214(x))
Eq(F_220(x), F_41(x)*F_58(x))
Eq(F_221(x), F_41(x)*F_53(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_0(x)*F_41(x)*F_77(x))
Eq(F_224(x), F_225(x))
Eq(F_225(x), F_0(x)*F_226(x)*F_231(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_0(x)*F_228(x)*F_41(x))
Eq(F_228(x), F_229(x) + F_47(x))
Eq(F_229(x), F_230(x))
Eq(F_230(x), F_49(x) + F_75(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_0(x)*F_41(x)*F_47(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_224(x) + F_235(x))
Eq(F_235(x), F_190(x)*F_2(x))
Eq(F_236(x), F_237(x)/F_310(x))
Eq(F_237(x), F_238(x) - F_309(x))
Eq(F_238(x), F_239(x)/F_41(x))
Eq(F_239(x), F_240(x))
Eq(F_240(x), F_241(x) - F_243(x))
Eq(F_241(x), F_242(x) - F_255(x))
Eq(F_242(x), F_243(x) + F_253(x))
Eq(F_243(x), F_244(x) + F_74(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_246(x)*F_41(x))
Eq(F_246(x), F_247(x) + F_250(x))
Eq(F_247(x), F_248(x) + F_77(x))
Eq(F_248(x), F_249(x) + F_84(x))
Eq(F_249(x), F_185(x) - F_229(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_222(x) + F_252(x))
Eq(F_252(x), F_192(x)*F_2(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_153(x)*F_41(x))
Eq(F_255(x), F_2(x)*F_256(x))
Eq(F_256(x), F_257(x) + F_262(x))
Eq(F_257(x), F_1(x) + F_258(x))
Eq(F_258(x), F_259(x))
Eq(F_259(x), F_260(x)*F_41(x))
Eq(F_260(x), F_261(x) + F_83(x))
Eq(F_261(x), F_41(x))
Eq(F_262(x), F_263(x) + F_49(x))
Eq(F_263(x), F_264(x) + F_305(x) + F_61(x))
Eq(F_264(x), F_265(x)*F_41(x))
Eq(F_265(x), F_266(x) + F_267(x))
Eq(F_266(x), F_258(x) + F_263(x))
Eq(F_267(x), F_268(x) + F_281(x))
Eq(F_268(x), F_269(x) + F_277(x) + F_61(x))
Eq(F_269(x), F_270(x)*F_41(x))
Eq(F_270(x), F_271(x) + F_272(x))
Eq(F_271(x), F_258(x) + F_268(x))
Eq(F_272(x), F_273(x) + F_275(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_258(x)*F_41(x))
Eq(F_275(x), F_276(x))
Eq(F_276(x), F_268(x)*F_41(x))
Eq(F_277(x), F_278(x)*F_41(x))
Eq(F_278(x), F_279(x) + F_280(x))
Eq(F_279(x), F_202(x) + F_41(x))
Eq(F_280(x), F_202(x))
Eq(F_281(x), F_282(x) + F_290(x) + F_294(x) + F_61(x))
Eq(F_282(x), F_283(x)*F_41(x))
Eq(F_283(x), F_284(x) + F_285(x))
Eq(F_284(x), F_263(x) + F_281(x))
Eq(F_285(x), F_286(x) + F_288(x))
Eq(F_286(x), F_287(x))
Eq(F_287(x), F_263(x)*F_41(x))
Eq(F_288(x), F_289(x))
Eq(F_289(x), F_281(x)*F_41(x))
Eq(F_290(x), F_291(x)*F_41(x))
Eq(F_291(x), F_292(x) + F_293(x))
Eq(F_292(x), F_273(x) + F_286(x))
Eq(F_293(x), F_275(x) + F_288(x))
Eq(F_294(x), F_295(x)*F_41(x))
Eq(F_295(x), F_296(x) + F_304(x))
Eq(F_296(x), F_297(x) + F_58(x))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_299(x)*F_41(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_41(x))
Eq(F_301(x), F_302(x) + F_303(x))
Eq(F_302(x), F_299(x) + F_41(x))
Eq(F_303(x), F_202(x) + F_297(x))
Eq(F_304(x), F_297(x))
Eq(F_305(x), F_306(x)*F_41(x))
Eq(F_306(x), F_307(x) + F_308(x))
Eq(F_307(x), F_299(x) + F_53(x))
Eq(F_308(x), F_299(x))
Eq(F_309(x), F_24(x)*F_243(x))
Eq(F_310(x), F_0(x) + F_311(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_0(x)*F_313(x)*F_41(x))
Eq(F_313(x), F_24(x) + F_314(x))
Eq(F_314(x), F_2(x)*F_310(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_0(x)*F_317(x))
Eq(F_317(x), F_318(x))
Eq(F_318(x), F_0(x)*F_134(x)*F_41(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_321(x)*F_41(x))
Eq(F_321(x), F_322(x) - F_342(x))
Eq(F_322(x), F_323(x)/F_41(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_325(x) - F_340(x))
Eq(F_325(x), F_326(x) + F_327(x))
Eq(F_326(x), F_2(x)*F_45(x))
Eq(F_327(x), F_328(x) - F_339(x))
Eq(F_328(x), F_329(x)/(F_0(x)*F_41(x)))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_331(x) + F_332(x))
Eq(F_331(x), F_0(x)*F_5(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_334(x)*F_41(x))
Eq(F_334(x), F_335(x) + F_338(x))
Eq(F_335(x), F_181(x) + F_336(x))
Eq(F_336(x), F_224(x) + F_337(x))
Eq(F_337(x), F_0(x)*F_190(x))
Eq(F_338(x), F_224(x))
Eq(F_339(x), F_0(x)*F_45(x))
Eq(F_340(x), F_328(x) - F_341(x))
Eq(F_341(x), F_12(x) + F_168(x))
Eq(F_342(x), F_343(x) - F_345(x))
Eq(F_343(x), F_344(x)/F_41(x))
Eq(F_344(x), F_324(x))
Eq(F_345(x), F_346(x))
Eq(F_346(x), F_0(x)*F_347(x))
Eq(F_347(x), F_249(x) + F_348(x))
Eq(F_348(x), F_0(x)*F_229(x))
Eq(F_349(x), F_12(x) + F_28(x))
Eq(F_350(x), F_0(x)*F_2(x)**2)
Eq(F_351(x), F_352(x))
Eq(F_352(x), F_353(x)*F_41(x))
Eq(F_353(x), F_354(x) + F_355(x))
Eq(F_354(x), F_12(x)*F_4(x))
Eq(F_355(x), F_0(x)*F_19(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": 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[1, 2, 0], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [2, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [5, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [5, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [4, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [4, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [2, 1], [4, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [2, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [4, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [5, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [4, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [5, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [2, 1, 0], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[5, 1]]}]], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"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_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25057/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[39,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = -F[0,x]+F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[12,x]*F[4,x]
F[20,x] = F[0,x]*F[21,x]
F[21,x] = F[12,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[12,x]*F[13,x]
F[26,x] = F[27,x]*F[34,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[15,x]*F[29,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = 1/F[15,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[0,x]*F[15,x]*F[30,x]
F[34,x] = F[0,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[0,x]*F[15,x]*F[37,x]
F[37,x] = F[13,x]+F[38,x]
F[38,x] = F[2,x]*F[34,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[42,x]+F[57,x]
F[42,x] = F[43,x]+F[45,x]
F[43,x] = F[44,x]
F[44,x] = F[0,x]*F[30,x]*F[5,x]
F[45,x] = F[46,x]+F[52,x]
F[46,x] = F[0,x]*F[47,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[49,x]
F[49,x] = -F[0,x]+F[30,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]*F[15,x]*F[48,x]
F[52,x] = F[53,x]
F[53,x] = F[0,x]*F[32,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[15,x]*F[56,x]
F[56,x] = F[30,x]+F[48,x]
F[57,x] = F[52,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{39}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{34}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{57}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0}\! \left(x \right) F_{30}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{48}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_39(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), -F_0(x) + F_13(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_12(x)*F_4(x))
Eq(F_20(x), F_0(x)*F_21(x))
Eq(F_21(x), F_12(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_12(x)*F_13(x))
Eq(F_26(x), F_27(x)*F_34(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_15(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_31(x)/F_15(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_0(x)*F_15(x)*F_30(x))
Eq(F_34(x), F_0(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_0(x)*F_15(x)*F_37(x))
Eq(F_37(x), F_13(x) + F_38(x))
Eq(F_38(x), F_2(x)*F_34(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_57(x))
Eq(F_42(x), F_43(x) + F_45(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_0(x)*F_30(x)*F_5(x))
Eq(F_45(x), F_46(x) + F_52(x))
Eq(F_46(x), F_0(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), -F_0(x) + F_30(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)*F_15(x)*F_48(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_0(x)*F_32(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_15(x)*F_56(x))
Eq(F_56(x), F_30(x) + F_48(x))
Eq(F_57(x), F_52(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:
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0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 2], [3, 0], [3, 2], [3, 0], [3, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 2], [3, 0], [3, 3], [3, 0], [3, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 2], [3, 0], [3, 3], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 4], [3, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 4], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 2], [3, 0], [3, 2], [3, 0], [3, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25113/
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[13,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[13,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[278,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[15,x]+F[65,x]
F[15,x] = F[16,x]+F[53,x]
F[16,x] = F[17,x]+F[60,x]
F[17,x] = F[0,x]+F[18,x]
F[18,x] = F[19,x]+F[45,x]
F[19,x] = F[20,x]
F[20,x] = F[13,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[19,x]
F[23,x] = F[24,x]+F[31,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[24,x]
F[28,x] = F[13,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[13,x]*F[24,x]
F[31,x] = F[32,x]+F[33,x]+F[41,x]
F[32,x] = 0
F[33,x] = F[13,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[19,x]+F[31,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[38,x]
F[38,x] = F[13,x]*F[19,x]
F[39,x] = F[40,x]
F[40,x] = F[13,x]*F[31,x]
F[41,x] = F[13,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[13,x]+F[37,x]
F[44,x] = F[29,x]+F[39,x]
F[45,x] = F[46,x]
F[46,x] = F[13,x]*F[47,x]
F[47,x] = F[48,x]+F[53,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[2,x]*F[27,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]*F[27,x]*F[47,x]*F[52,x]
F[52,x] = F[1,x]+F[13,x]
F[53,x] = -F[60,x]+F[54,x]
F[54,x] = 1/F[13,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = -F[2,x]+F[57,x]
F[57,x] = -F[0,x]+F[58,x]
F[58,x] = 1/F[13,x]*F[59,x]
F[59,x] = F[2,x]
F[60,x] = F[61,x]
F[61,x] = F[13,x]*F[27,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[17,x]*F[52,x]
F[64,x] = F[18,x]
F[65,x] = -F[300,x]+F[66,x]
F[66,x] = 1/F[0,x]/F[13,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]+F[75,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[2,x]+F[56,x]
F[71,x] = F[72,x]
F[72,x] = F[13,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[0,x]*F[13,x]*F[15,x]
F[75,x] = F[76,x]
F[76,x] = F[13,x]*F[77,x]
F[77,x] = F[299,x]+F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[4,x]*F[70,x]
F[80,x] = F[0,x]*F[81,x]
F[81,x] = F[70,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[13,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[58,x]*F[70,x]
F[86,x] = F[249,x]*F[87,x]
F[87,x] = -F[298,x]+F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[2,x]^2
F[90,x] = -F[297,x]+F[91,x]
F[91,x] = -F[256,x]+F[92,x]
F[92,x] = -F[254,x]+F[93,x]
F[93,x] = 1/F[0,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = -F[158,x]+F[96,x]
F[96,x] = 1/F[13,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[0,x]*F[5,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[13,x]
F[102,x] = F[103,x]+F[119,x]
F[103,x] = F[104,x]+F[108,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[15,x]*F[2,x]
F[106,x] = F[107,x]
F[107,x] = F[0,x]*F[17,x]*F[6,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[0,x]*F[65,x]
F[110,x] = F[111,x]
F[111,x] = F[0,x]*F[112,x]*F[117,x]
F[112,x] = F[113,x]+F[2,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[13,x]
F[115,x] = F[116,x]+F[9,x]
F[116,x] = F[0,x]*F[70,x]
F[117,x] = F[118,x]
F[118,x] = F[0,x]*F[13,x]*F[17,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[156,x]
F[121,x] = F[122,x]*F[2,x]
F[122,x] = F[123,x]+F[154,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = F[125,x]+F[13,x]
F[125,x] = F[126,x]+F[153,x]+F[32,x]
F[126,x] = F[127,x]*F[13,x]
F[127,x] = F[124,x]+F[128,x]
F[128,x] = F[129,x]+F[139,x]
F[129,x] = F[130,x]+F[138,x]+F[32,x]
F[130,x] = F[13,x]*F[131,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[129,x]+F[13,x]
F[133,x] = F[134,x]+F[136,x]
F[134,x] = F[135,x]
F[135,x] = x^2
F[136,x] = F[137,x]
F[137,x] = F[129,x]*F[13,x]
F[138,x] = x^2
F[139,x] = F[140,x]+F[148,x]+F[152,x]+F[32,x]
F[140,x] = F[13,x]*F[141,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[125,x]+F[139,x]
F[143,x] = F[144,x]+F[146,x]
F[144,x] = F[145,x]
F[145,x] = F[125,x]*F[13,x]
F[146,x] = F[147,x]
F[147,x] = F[13,x]*F[139,x]
F[148,x] = F[13,x]*F[149,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[134,x]+F[144,x]
F[151,x] = F[136,x]+F[146,x]
F[152,x] = F[13,x]*F[29,x]
F[153,x] = F[13,x]*F[24,x]
F[154,x] = F[155,x]
F[155,x] = F[0,x]*F[13,x]*F[47,x]
F[156,x] = F[157,x]
F[157,x] = F[0,x]*F[113,x]*F[117,x]
F[158,x] = F[159,x]+F[162,x]
F[159,x] = F[160,x]+F[81,x]
F[160,x] = F[10,x]+F[161,x]
F[161,x] = F[0,x]*F[4,x]
F[162,x] = F[163,x]
F[163,x] = F[13,x]*F[164,x]
F[164,x] = 1/F[13,x]*F[165,x]
F[165,x] = F[166,x]
F[166,x] = -F[240,x]+F[167,x]
F[167,x] = 1/F[13,x]*F[168,x]
F[168,x] = F[169,x]
F[169,x] = F[170,x]+F[224,x]
F[170,x] = F[171,x]*F[2,x]
F[171,x] = F[172,x]+F[177,x]
F[172,x] = F[1,x]+F[173,x]
F[173,x] = F[174,x]
F[174,x] = F[13,x]*F[175,x]
F[175,x] = F[176,x]+F[52,x]
F[176,x] = F[13,x]
F[177,x] = F[178,x]+F[19,x]
F[178,x] = F[179,x]+F[220,x]+F[32,x]
F[179,x] = F[13,x]*F[180,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[173,x]+F[178,x]
F[182,x] = F[183,x]+F[196,x]
F[183,x] = F[184,x]+F[192,x]+F[32,x]
F[184,x] = F[13,x]*F[185,x]
F[185,x] = F[186,x]+F[187,x]
F[186,x] = F[173,x]+F[183,x]
F[187,x] = F[188,x]+F[190,x]
F[188,x] = F[189,x]
F[189,x] = F[13,x]*F[173,x]
F[190,x] = F[191,x]
F[191,x] = F[13,x]*F[183,x]
F[192,x] = F[13,x]*F[193,x]
F[193,x] = F[194,x]+F[195,x]
F[194,x] = F[13,x]+F[134,x]
F[195,x] = F[134,x]
F[196,x] = F[197,x]+F[205,x]+F[209,x]+F[32,x]
F[197,x] = F[13,x]*F[198,x]
F[198,x] = F[199,x]+F[200,x]
F[199,x] = F[178,x]+F[196,x]
F[200,x] = F[201,x]+F[203,x]
F[201,x] = F[202,x]
F[202,x] = F[13,x]*F[178,x]
F[203,x] = F[204,x]
F[204,x] = F[13,x]*F[196,x]
F[205,x] = F[13,x]*F[206,x]
F[206,x] = F[207,x]+F[208,x]
F[207,x] = F[188,x]+F[201,x]
F[208,x] = F[190,x]+F[203,x]
F[209,x] = F[13,x]*F[210,x]
F[210,x] = F[211,x]+F[219,x]
F[211,x] = F[212,x]+F[29,x]
F[212,x] = F[213,x]
F[213,x] = F[13,x]*F[214,x]
F[214,x] = F[215,x]
F[215,x] = F[13,x]*F[216,x]
F[216,x] = F[217,x]+F[218,x]
F[217,x] = F[13,x]+F[214,x]
F[218,x] = F[134,x]+F[212,x]
F[219,x] = F[212,x]
F[220,x] = F[13,x]*F[221,x]
F[221,x] = F[222,x]+F[223,x]
F[222,x] = F[214,x]+F[24,x]
F[223,x] = F[214,x]
F[224,x] = -F[228,x]+F[225,x]
F[225,x] = -F[170,x]+F[226,x]
F[226,x] = 1/F[13,x]*F[227,x]
F[227,x] = F[45,x]
F[228,x] = F[229,x]+F[230,x]
F[229,x] = F[2,x]+F[45,x]
F[230,x] = F[231,x]
F[231,x] = F[13,x]*F[232,x]
F[232,x] = F[233,x]+F[237,x]
F[233,x] = F[234,x]+F[47,x]
F[234,x] = F[235,x]+F[236,x]
F[235,x] = F[46,x]
F[236,x] = -F[64,x]+F[65,x]
F[237,x] = F[238,x]
F[238,x] = F[154,x]+F[239,x]
F[239,x] = F[124,x]*F[2,x]
F[240,x] = F[0,x]*F[241,x]
F[241,x] = F[242,x]+F[244,x]
F[242,x] = F[17,x]+F[243,x]
F[243,x] = F[181,x]+F[230,x]
F[244,x] = 1/F[249,x]*F[245,x]
F[245,x] = -F[248,x]+F[246,x]
F[246,x] = 1/F[13,x]*F[247,x]
F[247,x] = F[224,x]
F[248,x] = F[228,x]*F[58,x]
F[249,x] = F[0,x]+F[250,x]
F[250,x] = F[251,x]
F[251,x] = F[0,x]*F[13,x]*F[252,x]
F[252,x] = F[253,x]+F[58,x]
F[253,x] = F[2,x]*F[249,x]
F[254,x] = F[255,x]
F[255,x] = F[0,x]*F[13,x]*F[73,x]
F[256,x] = F[257,x]
F[257,x] = F[13,x]*F[258,x]
F[258,x] = -F[290,x]+F[259,x]
F[259,x] = 1/F[13,x]*F[260,x]
F[260,x] = F[261,x]
F[261,x] = -F[288,x]+F[262,x]
F[262,x] = F[263,x]+F[272,x]
F[263,x] = F[2,x]*F[264,x]
F[264,x] = F[265,x]+F[70,x]
F[265,x] = F[17,x]+F[266,x]
F[266,x] = F[267,x]
F[267,x] = F[13,x]*F[17,x]*F[268,x]
F[268,x] = F[269,x]+F[58,x]
F[269,x] = F[270,x]+F[71,x]
F[270,x] = F[271,x]
F[271,x] = F[0,x]^2*F[13,x]
F[272,x] = -F[287,x]+F[273,x]
F[273,x] = 1/F[0,x]/F[13,x]*F[274,x]
F[274,x] = F[275,x]
F[275,x] = F[276,x]+F[278,x]
F[276,x] = F[0,x]*F[277,x]
F[277,x] = F[2,x]+F[6,x]
F[278,x] = F[279,x]
F[279,x] = F[13,x]*F[280,x]
F[280,x] = F[281,x]+F[286,x]
F[281,x] = F[282,x]+F[284,x]
F[282,x] = F[283,x]
F[283,x] = F[0,x]*F[17,x]*F[277,x]
F[284,x] = F[110,x]+F[285,x]
F[285,x] = F[0,x]*F[122,x]
F[286,x] = F[110,x]
F[287,x] = F[0,x]*F[264,x]
F[288,x] = -F[289,x]+F[273,x]
F[289,x] = F[241,x]+F[70,x]
F[290,x] = -F[293,x]+F[291,x]
F[291,x] = 1/F[13,x]*F[292,x]
F[292,x] = F[261,x]
F[293,x] = F[294,x]
F[294,x] = F[0,x]*F[295,x]
F[295,x] = F[236,x]+F[296,x]
F[296,x] = F[0,x]*F[64,x]
F[297,x] = F[70,x]+F[89,x]
F[298,x] = F[2,x]^2*F[0,x]
F[299,x] = F[4,x]*F[71,x]
F[300,x] = F[15,x]+F[73,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_{13}\! \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_{13}\! \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_{278}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{53}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{60}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right) F_{31}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right)+F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right)+F_{39}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{47}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{2}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{17}\! \left(x \right) F_{52}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{300}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right)+F_{56}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{299}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{70}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{13}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{58}\! \left(x \right) F_{70}\! \left(x \right)
F_{86}\! \left(x \right) = F_{249}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{298}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{90}\! \left(x \right) = -F_{297}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{254}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{13}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{119}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{6}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right) F_{65}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{112}\! \left(x \right) F_{117}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{13}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{9}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right) F_{70}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{156}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{2}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{154}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{13}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{153}\! \left(x \right)+F_{32}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{13}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{139}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{138}\! \left(x \right)+F_{32}\! \left(x \right)
F_{130}\! \left(x \right) = F_{13}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{129}\! \left(x \right)+F_{13}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{136}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = x^{2}
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{129}\! \left(x \right) F_{13}\! \left(x \right)
F_{138}\! \left(x \right) = x^{2}
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{148}\! \left(x \right)+F_{152}\! \left(x \right)+F_{32}\! \left(x \right)
F_{140}\! \left(x \right) = F_{13}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{125}\! \left(x \right)+F_{139}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{146}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{125}\! \left(x \right) F_{13}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{13}\! \left(x \right) F_{139}\! \left(x \right)
F_{148}\! \left(x \right) = F_{13}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{134}\! \left(x \right)+F_{144}\! \left(x \right)
F_{151}\! \left(x \right) = F_{136}\! \left(x \right)+F_{146}\! \left(x \right)
F_{152}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{153}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{0}\! \left(x \right) F_{113}\! \left(x \right) F_{117}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{162}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{81}\! \left(x \right)
F_{160}\! \left(x \right) = F_{10}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{13}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = \frac{F_{165}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = -F_{240}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = \frac{F_{168}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{224}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{2}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{177}\! \left(x \right)
F_{172}\! \left(x \right) = F_{1}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{13}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{52}\! \left(x \right)
F_{176}\! \left(x \right) = F_{13}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{19}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{220}\! \left(x \right)+F_{32}\! \left(x \right)
F_{179}\! \left(x \right) = F_{13}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{173}\! \left(x \right)+F_{178}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{196}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{192}\! \left(x \right)+F_{32}\! \left(x \right)
F_{184}\! \left(x \right) = F_{13}\! \left(x \right) F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{187}\! \left(x \right)
F_{186}\! \left(x \right) = F_{173}\! \left(x \right)+F_{183}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{190}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{13}\! \left(x \right) F_{173}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{13}\! \left(x \right) F_{183}\! \left(x \right)
F_{192}\! \left(x \right) = F_{13}\! \left(x \right) F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{195}\! \left(x \right)
F_{194}\! \left(x \right) = F_{13}\! \left(x \right)+F_{134}\! \left(x \right)
F_{195}\! \left(x \right) = F_{134}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{205}\! \left(x \right)+F_{209}\! \left(x \right)+F_{32}\! \left(x \right)
F_{197}\! \left(x \right) = F_{13}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{200}\! \left(x \right)
F_{199}\! \left(x \right) = F_{178}\! \left(x \right)+F_{196}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{13}\! \left(x \right) F_{178}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{13}\! \left(x \right) F_{196}\! \left(x \right)
F_{205}\! \left(x \right) = F_{13}\! \left(x \right) F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{208}\! \left(x \right)
F_{207}\! \left(x \right) = F_{188}\! \left(x \right)+F_{201}\! \left(x \right)
F_{208}\! \left(x \right) = F_{190}\! \left(x \right)+F_{203}\! \left(x \right)
F_{209}\! \left(x \right) = F_{13}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{219}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{29}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{13}\! \left(x \right) F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{13}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{218}\! \left(x \right)
F_{217}\! \left(x \right) = F_{13}\! \left(x \right)+F_{214}\! \left(x \right)
F_{218}\! \left(x \right) = F_{134}\! \left(x \right)+F_{212}\! \left(x \right)
F_{219}\! \left(x \right) = F_{212}\! \left(x \right)
F_{220}\! \left(x \right) = F_{13}\! \left(x \right) F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)+F_{223}\! \left(x \right)
F_{222}\! \left(x \right) = F_{214}\! \left(x \right)+F_{24}\! \left(x \right)
F_{223}\! \left(x \right) = F_{214}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{228}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{170}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{227}\! \left(x \right) = F_{45}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{229}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{13}\! \left(x \right) F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{237}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{47}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{236}\! \left(x \right)
F_{235}\! \left(x \right) = F_{46}\! \left(x \right)
F_{236}\! \left(x \right) = -F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{154}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{124}\! \left(x \right) F_{2}\! \left(x \right)
F_{240}\! \left(x \right) = F_{0}\! \left(x \right) F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)
F_{242}\! \left(x \right) = F_{17}\! \left(x \right)+F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{181}\! \left(x \right)+F_{230}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{249}\! \left(x \right)}
F_{245}\! \left(x \right) = -F_{248}\! \left(x \right)+F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = \frac{F_{247}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{247}\! \left(x \right) = F_{224}\! \left(x \right)
F_{248}\! \left(x \right) = F_{228}\! \left(x \right) F_{58}\! \left(x \right)
F_{249}\! \left(x \right) = F_{0}\! \left(x \right)+F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{58}\! \left(x \right)
F_{253}\! \left(x \right) = F_{2}\! \left(x \right) F_{249}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{13}\! \left(x \right) F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = -F_{290}\! \left(x \right)+F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = \frac{F_{260}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{272}\! \left(x \right)
F_{263}\! \left(x \right) = F_{2}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)+F_{70}\! \left(x \right)
F_{265}\! \left(x \right) = F_{17}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right) F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{58}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)+F_{71}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{272}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = \frac{F_{274}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right)+F_{278}\! \left(x \right)
F_{276}\! \left(x \right) = F_{0}\! \left(x \right) F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{13}\! \left(x \right) F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{286}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{284}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{277}\! \left(x \right)
F_{284}\! \left(x \right) = F_{110}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{0}\! \left(x \right) F_{122}\! \left(x \right)
F_{286}\! \left(x \right) = F_{110}\! \left(x \right)
F_{287}\! \left(x \right) = F_{0}\! \left(x \right) F_{264}\! \left(x \right)
F_{288}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{273}\! \left(x \right)
F_{289}\! \left(x \right) = F_{241}\! \left(x \right)+F_{70}\! \left(x \right)
F_{290}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = \frac{F_{292}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{292}\! \left(x \right) = F_{261}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{0}\! \left(x \right) F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{236}\! \left(x \right)+F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{0}\! \left(x \right) F_{64}\! \left(x \right)
F_{297}\! \left(x \right) = F_{70}\! \left(x \right)+F_{89}\! \left(x \right)
F_{298}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{299}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{300}\! \left(x \right) = F_{15}\! \left(x \right)+F_{73}\! \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_13(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_13(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_278(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_65(x))
Eq(F_15(x), F_16(x) + F_53(x))
Eq(F_16(x), F_17(x) + F_60(x))
Eq(F_17(x), F_0(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_45(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_13(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_19(x))
Eq(F_23(x), F_24(x) + F_31(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_24(x))
Eq(F_28(x), F_13(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_13(x)*F_24(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_41(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_13(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_19(x) + F_31(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_13(x)*F_19(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_13(x)*F_31(x))
Eq(F_41(x), F_13(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_13(x) + F_37(x))
Eq(F_44(x), F_29(x) + F_39(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_13(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_53(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_2(x)*F_27(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)*F_27(x)*F_47(x)*F_52(x))
Eq(F_52(x), F_1(x) + F_13(x))
Eq(F_53(x), F_54(x) - F_60(x))
Eq(F_54(x), F_55(x)/F_13(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), -F_2(x) + F_57(x))
Eq(F_57(x), -F_0(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_13(x))
Eq(F_59(x), F_2(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_13(x)*F_27(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_17(x)*F_52(x))
Eq(F_64(x), F_18(x))
Eq(F_65(x), -F_300(x) + F_66(x))
Eq(F_66(x), F_67(x)/(F_0(x)*F_13(x)))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) + F_75(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_2(x) + F_56(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_13(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_0(x)*F_13(x)*F_15(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_13(x)*F_77(x))
Eq(F_77(x), F_299(x) + F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_4(x)*F_70(x))
Eq(F_80(x), F_0(x)*F_81(x))
Eq(F_81(x), F_70(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_13(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_58(x)*F_70(x))
Eq(F_86(x), F_249(x)*F_87(x))
Eq(F_87(x), -F_298(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_2(x)**2)
Eq(F_90(x), -F_297(x) + F_91(x))
Eq(F_91(x), -F_256(x) + F_92(x))
Eq(F_92(x), -F_254(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_0(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), -F_158(x) + F_96(x))
Eq(F_96(x), F_97(x)/F_13(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_0(x)*F_5(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_13(x))
Eq(F_102(x), F_103(x) + F_119(x))
Eq(F_103(x), F_104(x) + F_108(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_15(x)*F_2(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_0(x)*F_17(x)*F_6(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_0(x)*F_65(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_0(x)*F_112(x)*F_117(x))
Eq(F_112(x), F_113(x) + F_2(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_13(x))
Eq(F_115(x), F_116(x) + F_9(x))
Eq(F_116(x), F_0(x)*F_70(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_0(x)*F_13(x)*F_17(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_156(x))
Eq(F_121(x), F_122(x)*F_2(x))
Eq(F_122(x), F_123(x) + F_154(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), F_125(x) + F_13(x))
Eq(F_125(x), F_126(x) + F_153(x) + F_32(x))
Eq(F_126(x), F_127(x)*F_13(x))
Eq(F_127(x), F_124(x) + F_128(x))
Eq(F_128(x), F_129(x) + F_139(x))
Eq(F_129(x), F_130(x) + F_138(x) + F_32(x))
Eq(F_130(x), F_13(x)*F_131(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_129(x) + F_13(x))
Eq(F_133(x), F_134(x) + F_136(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), x**2)
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_129(x)*F_13(x))
Eq(F_138(x), x**2)
Eq(F_139(x), F_140(x) + F_148(x) + F_152(x) + F_32(x))
Eq(F_140(x), F_13(x)*F_141(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_125(x) + F_139(x))
Eq(F_143(x), F_144(x) + F_146(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_125(x)*F_13(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_13(x)*F_139(x))
Eq(F_148(x), F_13(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_134(x) + F_144(x))
Eq(F_151(x), F_136(x) + F_146(x))
Eq(F_152(x), F_13(x)*F_29(x))
Eq(F_153(x), F_13(x)*F_24(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_0(x)*F_13(x)*F_47(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_0(x)*F_113(x)*F_117(x))
Eq(F_158(x), F_159(x) + F_162(x))
Eq(F_159(x), F_160(x) + F_81(x))
Eq(F_160(x), F_10(x) + F_161(x))
Eq(F_161(x), F_0(x)*F_4(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_13(x)*F_164(x))
Eq(F_164(x), F_165(x)/F_13(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x) - F_240(x))
Eq(F_167(x), F_168(x)/F_13(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_170(x) + F_224(x))
Eq(F_170(x), F_171(x)*F_2(x))
Eq(F_171(x), F_172(x) + F_177(x))
Eq(F_172(x), F_1(x) + F_173(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_13(x)*F_175(x))
Eq(F_175(x), F_176(x) + F_52(x))
Eq(F_176(x), F_13(x))
Eq(F_177(x), F_178(x) + F_19(x))
Eq(F_178(x), F_179(x) + F_220(x) + F_32(x))
Eq(F_179(x), F_13(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_173(x) + F_178(x))
Eq(F_182(x), F_183(x) + F_196(x))
Eq(F_183(x), F_184(x) + F_192(x) + F_32(x))
Eq(F_184(x), F_13(x)*F_185(x))
Eq(F_185(x), F_186(x) + F_187(x))
Eq(F_186(x), F_173(x) + F_183(x))
Eq(F_187(x), F_188(x) + F_190(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_13(x)*F_173(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_13(x)*F_183(x))
Eq(F_192(x), F_13(x)*F_193(x))
Eq(F_193(x), F_194(x) + F_195(x))
Eq(F_194(x), F_13(x) + F_134(x))
Eq(F_195(x), F_134(x))
Eq(F_196(x), F_197(x) + F_205(x) + F_209(x) + F_32(x))
Eq(F_197(x), F_13(x)*F_198(x))
Eq(F_198(x), F_199(x) + F_200(x))
Eq(F_199(x), F_178(x) + F_196(x))
Eq(F_200(x), F_201(x) + F_203(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_13(x)*F_178(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_13(x)*F_196(x))
Eq(F_205(x), F_13(x)*F_206(x))
Eq(F_206(x), F_207(x) + F_208(x))
Eq(F_207(x), F_188(x) + F_201(x))
Eq(F_208(x), F_190(x) + F_203(x))
Eq(F_209(x), F_13(x)*F_210(x))
Eq(F_210(x), F_211(x) + F_219(x))
Eq(F_211(x), F_212(x) + F_29(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_13(x)*F_214(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_13(x)*F_216(x))
Eq(F_216(x), F_217(x) + F_218(x))
Eq(F_217(x), F_13(x) + F_214(x))
Eq(F_218(x), F_134(x) + F_212(x))
Eq(F_219(x), F_212(x))
Eq(F_220(x), F_13(x)*F_221(x))
Eq(F_221(x), F_222(x) + F_223(x))
Eq(F_222(x), F_214(x) + F_24(x))
Eq(F_223(x), F_214(x))
Eq(F_224(x), F_225(x) - F_228(x))
Eq(F_225(x), -F_170(x) + F_226(x))
Eq(F_226(x), F_227(x)/F_13(x))
Eq(F_227(x), F_45(x))
Eq(F_228(x), F_229(x) + F_230(x))
Eq(F_229(x), F_2(x) + F_45(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_13(x)*F_232(x))
Eq(F_232(x), F_233(x) + F_237(x))
Eq(F_233(x), F_234(x) + F_47(x))
Eq(F_234(x), F_235(x) + F_236(x))
Eq(F_235(x), F_46(x))
Eq(F_236(x), -F_64(x) + F_65(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_154(x) + F_239(x))
Eq(F_239(x), F_124(x)*F_2(x))
Eq(F_240(x), F_0(x)*F_241(x))
Eq(F_241(x), F_242(x) + F_244(x))
Eq(F_242(x), F_17(x) + F_243(x))
Eq(F_243(x), F_181(x) + F_230(x))
Eq(F_244(x), F_245(x)/F_249(x))
Eq(F_245(x), F_246(x) - F_248(x))
Eq(F_246(x), F_247(x)/F_13(x))
Eq(F_247(x), F_224(x))
Eq(F_248(x), F_228(x)*F_58(x))
Eq(F_249(x), F_0(x) + F_250(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_0(x)*F_13(x)*F_252(x))
Eq(F_252(x), F_253(x) + F_58(x))
Eq(F_253(x), F_2(x)*F_249(x))
Eq(F_254(x), F_255(x))
Eq(F_255(x), F_0(x)*F_13(x)*F_73(x))
Eq(F_256(x), F_257(x))
Eq(F_257(x), F_13(x)*F_258(x))
Eq(F_258(x), F_259(x) - F_290(x))
Eq(F_259(x), F_260(x)/F_13(x))
Eq(F_260(x), F_261(x))
Eq(F_261(x), F_262(x) - F_288(x))
Eq(F_262(x), F_263(x) + F_272(x))
Eq(F_263(x), F_2(x)*F_264(x))
Eq(F_264(x), F_265(x) + F_70(x))
Eq(F_265(x), F_17(x) + F_266(x))
Eq(F_266(x), F_267(x))
Eq(F_267(x), F_13(x)*F_17(x)*F_268(x))
Eq(F_268(x), F_269(x) + F_58(x))
Eq(F_269(x), F_270(x) + F_71(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_0(x)**2*F_13(x))
Eq(F_272(x), F_273(x) - F_287(x))
Eq(F_273(x), F_274(x)/(F_0(x)*F_13(x)))
Eq(F_274(x), F_275(x))
Eq(F_275(x), F_276(x) + F_278(x))
Eq(F_276(x), F_0(x)*F_277(x))
Eq(F_277(x), F_2(x) + F_6(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_13(x)*F_280(x))
Eq(F_280(x), F_281(x) + F_286(x))
Eq(F_281(x), F_282(x) + F_284(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_0(x)*F_17(x)*F_277(x))
Eq(F_284(x), F_110(x) + F_285(x))
Eq(F_285(x), F_0(x)*F_122(x))
Eq(F_286(x), F_110(x))
Eq(F_287(x), F_0(x)*F_264(x))
Eq(F_288(x), F_273(x) - F_289(x))
Eq(F_289(x), F_241(x) + F_70(x))
Eq(F_290(x), F_291(x) - F_293(x))
Eq(F_291(x), F_292(x)/F_13(x))
Eq(F_292(x), F_261(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_0(x)*F_295(x))
Eq(F_295(x), F_236(x) + F_296(x))
Eq(F_296(x), F_0(x)*F_64(x))
Eq(F_297(x), F_70(x) + F_89(x))
Eq(F_298(x), F_0(x)*F_2(x)**2)
Eq(F_299(x), F_4(x)*F_71(x))
Eq(F_300(x), F_15(x) + F_73(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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"rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "indices": [0, 0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "indices": [0, 0, 0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25140/
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[13,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[13,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[278,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[15,x]+F[65,x]
F[15,x] = F[16,x]+F[53,x]
F[16,x] = F[17,x]+F[60,x]
F[17,x] = F[0,x]+F[18,x]
F[18,x] = F[19,x]+F[45,x]
F[19,x] = F[20,x]
F[20,x] = F[13,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[19,x]
F[23,x] = F[24,x]+F[31,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[24,x]
F[28,x] = F[13,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[13,x]*F[24,x]
F[31,x] = F[32,x]+F[33,x]+F[41,x]
F[32,x] = 0
F[33,x] = F[13,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[19,x]+F[31,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[38,x]
F[38,x] = F[13,x]*F[19,x]
F[39,x] = F[40,x]
F[40,x] = F[13,x]*F[31,x]
F[41,x] = F[13,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[13,x]+F[37,x]
F[44,x] = F[29,x]+F[39,x]
F[45,x] = F[46,x]
F[46,x] = F[13,x]*F[47,x]
F[47,x] = F[48,x]+F[53,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[2,x]*F[27,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]*F[27,x]*F[47,x]*F[52,x]
F[52,x] = F[1,x]+F[13,x]
F[53,x] = -F[60,x]+F[54,x]
F[54,x] = 1/F[13,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = -F[2,x]+F[57,x]
F[57,x] = -F[0,x]+F[58,x]
F[58,x] = 1/F[13,x]*F[59,x]
F[59,x] = F[2,x]
F[60,x] = F[61,x]
F[61,x] = F[13,x]*F[27,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[17,x]*F[52,x]
F[64,x] = F[18,x]
F[65,x] = -F[300,x]+F[66,x]
F[66,x] = 1/F[0,x]/F[13,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]+F[75,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[2,x]+F[56,x]
F[71,x] = F[72,x]
F[72,x] = F[13,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[0,x]*F[13,x]*F[15,x]
F[75,x] = F[76,x]
F[76,x] = F[13,x]*F[77,x]
F[77,x] = F[299,x]+F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[4,x]*F[70,x]
F[80,x] = F[0,x]*F[81,x]
F[81,x] = F[70,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[13,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[58,x]*F[70,x]
F[86,x] = F[249,x]*F[87,x]
F[87,x] = -F[298,x]+F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[2,x]^2
F[90,x] = -F[297,x]+F[91,x]
F[91,x] = -F[256,x]+F[92,x]
F[92,x] = -F[254,x]+F[93,x]
F[93,x] = 1/F[0,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = -F[158,x]+F[96,x]
F[96,x] = 1/F[13,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[0,x]*F[5,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[13,x]
F[102,x] = F[103,x]+F[119,x]
F[103,x] = F[104,x]+F[108,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[15,x]*F[2,x]
F[106,x] = F[107,x]
F[107,x] = F[0,x]*F[17,x]*F[6,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[0,x]*F[65,x]
F[110,x] = F[111,x]
F[111,x] = F[0,x]*F[112,x]*F[117,x]
F[112,x] = F[113,x]+F[2,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[13,x]
F[115,x] = F[116,x]+F[9,x]
F[116,x] = F[0,x]*F[70,x]
F[117,x] = F[118,x]
F[118,x] = F[0,x]*F[13,x]*F[17,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[156,x]
F[121,x] = F[122,x]*F[2,x]
F[122,x] = F[123,x]+F[154,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = F[125,x]+F[13,x]
F[125,x] = F[126,x]+F[153,x]+F[32,x]
F[126,x] = F[127,x]*F[13,x]
F[127,x] = F[124,x]+F[128,x]
F[128,x] = F[129,x]+F[139,x]
F[129,x] = F[130,x]+F[138,x]+F[32,x]
F[130,x] = F[13,x]*F[131,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[129,x]+F[13,x]
F[133,x] = F[134,x]+F[136,x]
F[134,x] = F[135,x]
F[135,x] = x^2
F[136,x] = F[137,x]
F[137,x] = F[129,x]*F[13,x]
F[138,x] = x^2
F[139,x] = F[140,x]+F[148,x]+F[152,x]+F[32,x]
F[140,x] = F[13,x]*F[141,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[125,x]+F[139,x]
F[143,x] = F[144,x]+F[146,x]
F[144,x] = F[145,x]
F[145,x] = F[125,x]*F[13,x]
F[146,x] = F[147,x]
F[147,x] = F[13,x]*F[139,x]
F[148,x] = F[13,x]*F[149,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[134,x]+F[144,x]
F[151,x] = F[136,x]+F[146,x]
F[152,x] = F[13,x]*F[29,x]
F[153,x] = F[13,x]*F[24,x]
F[154,x] = F[155,x]
F[155,x] = F[0,x]*F[13,x]*F[47,x]
F[156,x] = F[157,x]
F[157,x] = F[0,x]*F[113,x]*F[117,x]
F[158,x] = F[159,x]+F[162,x]
F[159,x] = F[160,x]+F[81,x]
F[160,x] = F[10,x]+F[161,x]
F[161,x] = F[0,x]*F[4,x]
F[162,x] = F[163,x]
F[163,x] = F[13,x]*F[164,x]
F[164,x] = 1/F[13,x]*F[165,x]
F[165,x] = F[166,x]
F[166,x] = -F[240,x]+F[167,x]
F[167,x] = 1/F[13,x]*F[168,x]
F[168,x] = F[169,x]
F[169,x] = F[170,x]+F[224,x]
F[170,x] = F[171,x]*F[2,x]
F[171,x] = F[172,x]+F[177,x]
F[172,x] = F[1,x]+F[173,x]
F[173,x] = F[174,x]
F[174,x] = F[13,x]*F[175,x]
F[175,x] = F[176,x]+F[52,x]
F[176,x] = F[13,x]
F[177,x] = F[178,x]+F[19,x]
F[178,x] = F[179,x]+F[220,x]+F[32,x]
F[179,x] = F[13,x]*F[180,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[173,x]+F[178,x]
F[182,x] = F[183,x]+F[196,x]
F[183,x] = F[184,x]+F[192,x]+F[32,x]
F[184,x] = F[13,x]*F[185,x]
F[185,x] = F[186,x]+F[187,x]
F[186,x] = F[173,x]+F[183,x]
F[187,x] = F[188,x]+F[190,x]
F[188,x] = F[189,x]
F[189,x] = F[13,x]*F[173,x]
F[190,x] = F[191,x]
F[191,x] = F[13,x]*F[183,x]
F[192,x] = F[13,x]*F[193,x]
F[193,x] = F[194,x]+F[195,x]
F[194,x] = F[13,x]+F[134,x]
F[195,x] = F[134,x]
F[196,x] = F[197,x]+F[205,x]+F[209,x]+F[32,x]
F[197,x] = F[13,x]*F[198,x]
F[198,x] = F[199,x]+F[200,x]
F[199,x] = F[178,x]+F[196,x]
F[200,x] = F[201,x]+F[203,x]
F[201,x] = F[202,x]
F[202,x] = F[13,x]*F[178,x]
F[203,x] = F[204,x]
F[204,x] = F[13,x]*F[196,x]
F[205,x] = F[13,x]*F[206,x]
F[206,x] = F[207,x]+F[208,x]
F[207,x] = F[188,x]+F[201,x]
F[208,x] = F[190,x]+F[203,x]
F[209,x] = F[13,x]*F[210,x]
F[210,x] = F[211,x]+F[219,x]
F[211,x] = F[212,x]+F[29,x]
F[212,x] = F[213,x]
F[213,x] = F[13,x]*F[214,x]
F[214,x] = F[215,x]
F[215,x] = F[13,x]*F[216,x]
F[216,x] = F[217,x]+F[218,x]
F[217,x] = F[13,x]+F[214,x]
F[218,x] = F[134,x]+F[212,x]
F[219,x] = F[212,x]
F[220,x] = F[13,x]*F[221,x]
F[221,x] = F[222,x]+F[223,x]
F[222,x] = F[214,x]+F[24,x]
F[223,x] = F[214,x]
F[224,x] = -F[228,x]+F[225,x]
F[225,x] = -F[170,x]+F[226,x]
F[226,x] = 1/F[13,x]*F[227,x]
F[227,x] = F[45,x]
F[228,x] = F[229,x]+F[230,x]
F[229,x] = F[2,x]+F[45,x]
F[230,x] = F[231,x]
F[231,x] = F[13,x]*F[232,x]
F[232,x] = F[233,x]+F[237,x]
F[233,x] = F[234,x]+F[47,x]
F[234,x] = F[235,x]+F[236,x]
F[235,x] = F[46,x]
F[236,x] = -F[64,x]+F[65,x]
F[237,x] = F[238,x]
F[238,x] = F[154,x]+F[239,x]
F[239,x] = F[124,x]*F[2,x]
F[240,x] = F[0,x]*F[241,x]
F[241,x] = F[242,x]+F[244,x]
F[242,x] = F[17,x]+F[243,x]
F[243,x] = F[181,x]+F[230,x]
F[244,x] = 1/F[249,x]*F[245,x]
F[245,x] = -F[248,x]+F[246,x]
F[246,x] = 1/F[13,x]*F[247,x]
F[247,x] = F[224,x]
F[248,x] = F[228,x]*F[58,x]
F[249,x] = F[0,x]+F[250,x]
F[250,x] = F[251,x]
F[251,x] = F[0,x]*F[13,x]*F[252,x]
F[252,x] = F[253,x]+F[58,x]
F[253,x] = F[2,x]*F[249,x]
F[254,x] = F[255,x]
F[255,x] = F[0,x]*F[13,x]*F[73,x]
F[256,x] = F[257,x]
F[257,x] = F[13,x]*F[258,x]
F[258,x] = -F[290,x]+F[259,x]
F[259,x] = 1/F[13,x]*F[260,x]
F[260,x] = F[261,x]
F[261,x] = -F[288,x]+F[262,x]
F[262,x] = F[263,x]+F[272,x]
F[263,x] = F[2,x]*F[264,x]
F[264,x] = F[265,x]+F[70,x]
F[265,x] = F[17,x]+F[266,x]
F[266,x] = F[267,x]
F[267,x] = F[13,x]*F[17,x]*F[268,x]
F[268,x] = F[269,x]+F[58,x]
F[269,x] = F[270,x]+F[71,x]
F[270,x] = F[271,x]
F[271,x] = F[0,x]^2*F[13,x]
F[272,x] = -F[287,x]+F[273,x]
F[273,x] = 1/F[0,x]/F[13,x]*F[274,x]
F[274,x] = F[275,x]
F[275,x] = F[276,x]+F[278,x]
F[276,x] = F[0,x]*F[277,x]
F[277,x] = F[2,x]+F[6,x]
F[278,x] = F[279,x]
F[279,x] = F[13,x]*F[280,x]
F[280,x] = F[281,x]+F[286,x]
F[281,x] = F[282,x]+F[284,x]
F[282,x] = F[283,x]
F[283,x] = F[0,x]*F[17,x]*F[277,x]
F[284,x] = F[110,x]+F[285,x]
F[285,x] = F[0,x]*F[122,x]
F[286,x] = F[110,x]
F[287,x] = F[0,x]*F[264,x]
F[288,x] = -F[289,x]+F[273,x]
F[289,x] = F[241,x]+F[70,x]
F[290,x] = -F[293,x]+F[291,x]
F[291,x] = 1/F[13,x]*F[292,x]
F[292,x] = F[261,x]
F[293,x] = F[294,x]
F[294,x] = F[0,x]*F[295,x]
F[295,x] = F[236,x]+F[296,x]
F[296,x] = F[0,x]*F[64,x]
F[297,x] = F[70,x]+F[89,x]
F[298,x] = F[2,x]^2*F[0,x]
F[299,x] = F[4,x]*F[71,x]
F[300,x] = F[15,x]+F[73,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_{13}\! \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_{13}\! \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_{278}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{53}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{60}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right) F_{31}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right)+F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right)+F_{39}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right) F_{27}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{47}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{2}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{17}\! \left(x \right) F_{52}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{300}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right)+F_{56}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{299}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{70}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{13}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{58}\! \left(x \right) F_{70}\! \left(x \right)
F_{86}\! \left(x \right) = F_{249}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{298}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{90}\! \left(x \right) = -F_{297}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{254}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{13}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{119}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{6}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right) F_{65}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{112}\! \left(x \right) F_{117}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{13}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{9}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right) F_{70}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{156}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{2}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{154}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{13}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{153}\! \left(x \right)+F_{32}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{13}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{139}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{138}\! \left(x \right)+F_{32}\! \left(x \right)
F_{130}\! \left(x \right) = F_{13}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{129}\! \left(x \right)+F_{13}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{136}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = x^{2}
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{129}\! \left(x \right) F_{13}\! \left(x \right)
F_{138}\! \left(x \right) = x^{2}
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{148}\! \left(x \right)+F_{152}\! \left(x \right)+F_{32}\! \left(x \right)
F_{140}\! \left(x \right) = F_{13}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{125}\! \left(x \right)+F_{139}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{146}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{125}\! \left(x \right) F_{13}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{13}\! \left(x \right) F_{139}\! \left(x \right)
F_{148}\! \left(x \right) = F_{13}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{134}\! \left(x \right)+F_{144}\! \left(x \right)
F_{151}\! \left(x \right) = F_{136}\! \left(x \right)+F_{146}\! \left(x \right)
F_{152}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{153}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{0}\! \left(x \right) F_{113}\! \left(x \right) F_{117}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{162}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{81}\! \left(x \right)
F_{160}\! \left(x \right) = F_{10}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{13}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = \frac{F_{165}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = -F_{240}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = \frac{F_{168}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{224}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{2}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{177}\! \left(x \right)
F_{172}\! \left(x \right) = F_{1}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{13}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{52}\! \left(x \right)
F_{176}\! \left(x \right) = F_{13}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{19}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{220}\! \left(x \right)+F_{32}\! \left(x \right)
F_{179}\! \left(x \right) = F_{13}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{173}\! \left(x \right)+F_{178}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{196}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{192}\! \left(x \right)+F_{32}\! \left(x \right)
F_{184}\! \left(x \right) = F_{13}\! \left(x \right) F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{187}\! \left(x \right)
F_{186}\! \left(x \right) = F_{173}\! \left(x \right)+F_{183}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{190}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{13}\! \left(x \right) F_{173}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{13}\! \left(x \right) F_{183}\! \left(x \right)
F_{192}\! \left(x \right) = F_{13}\! \left(x \right) F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{195}\! \left(x \right)
F_{194}\! \left(x \right) = F_{13}\! \left(x \right)+F_{134}\! \left(x \right)
F_{195}\! \left(x \right) = F_{134}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{205}\! \left(x \right)+F_{209}\! \left(x \right)+F_{32}\! \left(x \right)
F_{197}\! \left(x \right) = F_{13}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{200}\! \left(x \right)
F_{199}\! \left(x \right) = F_{178}\! \left(x \right)+F_{196}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{13}\! \left(x \right) F_{178}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{13}\! \left(x \right) F_{196}\! \left(x \right)
F_{205}\! \left(x \right) = F_{13}\! \left(x \right) F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{208}\! \left(x \right)
F_{207}\! \left(x \right) = F_{188}\! \left(x \right)+F_{201}\! \left(x \right)
F_{208}\! \left(x \right) = F_{190}\! \left(x \right)+F_{203}\! \left(x \right)
F_{209}\! \left(x \right) = F_{13}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{219}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{29}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{13}\! \left(x \right) F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{13}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{218}\! \left(x \right)
F_{217}\! \left(x \right) = F_{13}\! \left(x \right)+F_{214}\! \left(x \right)
F_{218}\! \left(x \right) = F_{134}\! \left(x \right)+F_{212}\! \left(x \right)
F_{219}\! \left(x \right) = F_{212}\! \left(x \right)
F_{220}\! \left(x \right) = F_{13}\! \left(x \right) F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)+F_{223}\! \left(x \right)
F_{222}\! \left(x \right) = F_{214}\! \left(x \right)+F_{24}\! \left(x \right)
F_{223}\! \left(x \right) = F_{214}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{228}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{170}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{227}\! \left(x \right) = F_{45}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{229}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{13}\! \left(x \right) F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{237}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{47}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{236}\! \left(x \right)
F_{235}\! \left(x \right) = F_{46}\! \left(x \right)
F_{236}\! \left(x \right) = -F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{154}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{124}\! \left(x \right) F_{2}\! \left(x \right)
F_{240}\! \left(x \right) = F_{0}\! \left(x \right) F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)
F_{242}\! \left(x \right) = F_{17}\! \left(x \right)+F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{181}\! \left(x \right)+F_{230}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{249}\! \left(x \right)}
F_{245}\! \left(x \right) = -F_{248}\! \left(x \right)+F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = \frac{F_{247}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{247}\! \left(x \right) = F_{224}\! \left(x \right)
F_{248}\! \left(x \right) = F_{228}\! \left(x \right) F_{58}\! \left(x \right)
F_{249}\! \left(x \right) = F_{0}\! \left(x \right)+F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{58}\! \left(x \right)
F_{253}\! \left(x \right) = F_{2}\! \left(x \right) F_{249}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{13}\! \left(x \right) F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = -F_{290}\! \left(x \right)+F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = \frac{F_{260}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{272}\! \left(x \right)
F_{263}\! \left(x \right) = F_{2}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)+F_{70}\! \left(x \right)
F_{265}\! \left(x \right) = F_{17}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right) F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{58}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)+F_{71}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{272}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = \frac{F_{274}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right)+F_{278}\! \left(x \right)
F_{276}\! \left(x \right) = F_{0}\! \left(x \right) F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{13}\! \left(x \right) F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{286}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{284}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{277}\! \left(x \right)
F_{284}\! \left(x \right) = F_{110}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{0}\! \left(x \right) F_{122}\! \left(x \right)
F_{286}\! \left(x \right) = F_{110}\! \left(x \right)
F_{287}\! \left(x \right) = F_{0}\! \left(x \right) F_{264}\! \left(x \right)
F_{288}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{273}\! \left(x \right)
F_{289}\! \left(x \right) = F_{241}\! \left(x \right)+F_{70}\! \left(x \right)
F_{290}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = \frac{F_{292}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{292}\! \left(x \right) = F_{261}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{0}\! \left(x \right) F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{236}\! \left(x \right)+F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{0}\! \left(x \right) F_{64}\! \left(x \right)
F_{297}\! \left(x \right) = F_{70}\! \left(x \right)+F_{89}\! \left(x \right)
F_{298}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{299}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{300}\! \left(x \right) = F_{15}\! \left(x \right)+F_{73}\! \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_13(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_13(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_278(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_65(x))
Eq(F_15(x), F_16(x) + F_53(x))
Eq(F_16(x), F_17(x) + F_60(x))
Eq(F_17(x), F_0(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_45(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_13(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_19(x))
Eq(F_23(x), F_24(x) + F_31(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_24(x))
Eq(F_28(x), F_13(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_13(x)*F_24(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_41(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_13(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_19(x) + F_31(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_13(x)*F_19(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_13(x)*F_31(x))
Eq(F_41(x), F_13(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_13(x) + F_37(x))
Eq(F_44(x), F_29(x) + F_39(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_13(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_53(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_2(x)*F_27(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)*F_27(x)*F_47(x)*F_52(x))
Eq(F_52(x), F_1(x) + F_13(x))
Eq(F_53(x), F_54(x) - F_60(x))
Eq(F_54(x), F_55(x)/F_13(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), -F_2(x) + F_57(x))
Eq(F_57(x), -F_0(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_13(x))
Eq(F_59(x), F_2(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_13(x)*F_27(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_17(x)*F_52(x))
Eq(F_64(x), F_18(x))
Eq(F_65(x), -F_300(x) + F_66(x))
Eq(F_66(x), F_67(x)/(F_0(x)*F_13(x)))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) + F_75(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_2(x) + F_56(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_13(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_0(x)*F_13(x)*F_15(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_13(x)*F_77(x))
Eq(F_77(x), F_299(x) + F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_4(x)*F_70(x))
Eq(F_80(x), F_0(x)*F_81(x))
Eq(F_81(x), F_70(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_13(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_58(x)*F_70(x))
Eq(F_86(x), F_249(x)*F_87(x))
Eq(F_87(x), -F_298(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_2(x)**2)
Eq(F_90(x), -F_297(x) + F_91(x))
Eq(F_91(x), -F_256(x) + F_92(x))
Eq(F_92(x), -F_254(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_0(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), -F_158(x) + F_96(x))
Eq(F_96(x), F_97(x)/F_13(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_0(x)*F_5(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_13(x))
Eq(F_102(x), F_103(x) + F_119(x))
Eq(F_103(x), F_104(x) + F_108(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_15(x)*F_2(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_0(x)*F_17(x)*F_6(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_0(x)*F_65(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_0(x)*F_112(x)*F_117(x))
Eq(F_112(x), F_113(x) + F_2(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_13(x))
Eq(F_115(x), F_116(x) + F_9(x))
Eq(F_116(x), F_0(x)*F_70(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_0(x)*F_13(x)*F_17(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_156(x))
Eq(F_121(x), F_122(x)*F_2(x))
Eq(F_122(x), F_123(x) + F_154(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), F_125(x) + F_13(x))
Eq(F_125(x), F_126(x) + F_153(x) + F_32(x))
Eq(F_126(x), F_127(x)*F_13(x))
Eq(F_127(x), F_124(x) + F_128(x))
Eq(F_128(x), F_129(x) + F_139(x))
Eq(F_129(x), F_130(x) + F_138(x) + F_32(x))
Eq(F_130(x), F_13(x)*F_131(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_129(x) + F_13(x))
Eq(F_133(x), F_134(x) + F_136(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), x**2)
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_129(x)*F_13(x))
Eq(F_138(x), x**2)
Eq(F_139(x), F_140(x) + F_148(x) + F_152(x) + F_32(x))
Eq(F_140(x), F_13(x)*F_141(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_125(x) + F_139(x))
Eq(F_143(x), F_144(x) + F_146(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_125(x)*F_13(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_13(x)*F_139(x))
Eq(F_148(x), F_13(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_134(x) + F_144(x))
Eq(F_151(x), F_136(x) + F_146(x))
Eq(F_152(x), F_13(x)*F_29(x))
Eq(F_153(x), F_13(x)*F_24(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_0(x)*F_13(x)*F_47(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_0(x)*F_113(x)*F_117(x))
Eq(F_158(x), F_159(x) + F_162(x))
Eq(F_159(x), F_160(x) + F_81(x))
Eq(F_160(x), F_10(x) + F_161(x))
Eq(F_161(x), F_0(x)*F_4(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_13(x)*F_164(x))
Eq(F_164(x), F_165(x)/F_13(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x) - F_240(x))
Eq(F_167(x), F_168(x)/F_13(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_170(x) + F_224(x))
Eq(F_170(x), F_171(x)*F_2(x))
Eq(F_171(x), F_172(x) + F_177(x))
Eq(F_172(x), F_1(x) + F_173(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_13(x)*F_175(x))
Eq(F_175(x), F_176(x) + F_52(x))
Eq(F_176(x), F_13(x))
Eq(F_177(x), F_178(x) + F_19(x))
Eq(F_178(x), F_179(x) + F_220(x) + F_32(x))
Eq(F_179(x), F_13(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_173(x) + F_178(x))
Eq(F_182(x), F_183(x) + F_196(x))
Eq(F_183(x), F_184(x) + F_192(x) + F_32(x))
Eq(F_184(x), F_13(x)*F_185(x))
Eq(F_185(x), F_186(x) + F_187(x))
Eq(F_186(x), F_173(x) + F_183(x))
Eq(F_187(x), F_188(x) + F_190(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_13(x)*F_173(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_13(x)*F_183(x))
Eq(F_192(x), F_13(x)*F_193(x))
Eq(F_193(x), F_194(x) + F_195(x))
Eq(F_194(x), F_13(x) + F_134(x))
Eq(F_195(x), F_134(x))
Eq(F_196(x), F_197(x) + F_205(x) + F_209(x) + F_32(x))
Eq(F_197(x), F_13(x)*F_198(x))
Eq(F_198(x), F_199(x) + F_200(x))
Eq(F_199(x), F_178(x) + F_196(x))
Eq(F_200(x), F_201(x) + F_203(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_13(x)*F_178(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_13(x)*F_196(x))
Eq(F_205(x), F_13(x)*F_206(x))
Eq(F_206(x), F_207(x) + F_208(x))
Eq(F_207(x), F_188(x) + F_201(x))
Eq(F_208(x), F_190(x) + F_203(x))
Eq(F_209(x), F_13(x)*F_210(x))
Eq(F_210(x), F_211(x) + F_219(x))
Eq(F_211(x), F_212(x) + F_29(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_13(x)*F_214(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_13(x)*F_216(x))
Eq(F_216(x), F_217(x) + F_218(x))
Eq(F_217(x), F_13(x) + F_214(x))
Eq(F_218(x), F_134(x) + F_212(x))
Eq(F_219(x), F_212(x))
Eq(F_220(x), F_13(x)*F_221(x))
Eq(F_221(x), F_222(x) + F_223(x))
Eq(F_222(x), F_214(x) + F_24(x))
Eq(F_223(x), F_214(x))
Eq(F_224(x), F_225(x) - F_228(x))
Eq(F_225(x), -F_170(x) + F_226(x))
Eq(F_226(x), F_227(x)/F_13(x))
Eq(F_227(x), F_45(x))
Eq(F_228(x), F_229(x) + F_230(x))
Eq(F_229(x), F_2(x) + F_45(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_13(x)*F_232(x))
Eq(F_232(x), F_233(x) + F_237(x))
Eq(F_233(x), F_234(x) + F_47(x))
Eq(F_234(x), F_235(x) + F_236(x))
Eq(F_235(x), F_46(x))
Eq(F_236(x), -F_64(x) + F_65(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_154(x) + F_239(x))
Eq(F_239(x), F_124(x)*F_2(x))
Eq(F_240(x), F_0(x)*F_241(x))
Eq(F_241(x), F_242(x) + F_244(x))
Eq(F_242(x), F_17(x) + F_243(x))
Eq(F_243(x), F_181(x) + F_230(x))
Eq(F_244(x), F_245(x)/F_249(x))
Eq(F_245(x), F_246(x) - F_248(x))
Eq(F_246(x), F_247(x)/F_13(x))
Eq(F_247(x), F_224(x))
Eq(F_248(x), F_228(x)*F_58(x))
Eq(F_249(x), F_0(x) + F_250(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_0(x)*F_13(x)*F_252(x))
Eq(F_252(x), F_253(x) + F_58(x))
Eq(F_253(x), F_2(x)*F_249(x))
Eq(F_254(x), F_255(x))
Eq(F_255(x), F_0(x)*F_13(x)*F_73(x))
Eq(F_256(x), F_257(x))
Eq(F_257(x), F_13(x)*F_258(x))
Eq(F_258(x), F_259(x) - F_290(x))
Eq(F_259(x), F_260(x)/F_13(x))
Eq(F_260(x), F_261(x))
Eq(F_261(x), F_262(x) - F_288(x))
Eq(F_262(x), F_263(x) + F_272(x))
Eq(F_263(x), F_2(x)*F_264(x))
Eq(F_264(x), F_265(x) + F_70(x))
Eq(F_265(x), F_17(x) + F_266(x))
Eq(F_266(x), F_267(x))
Eq(F_267(x), F_13(x)*F_17(x)*F_268(x))
Eq(F_268(x), F_269(x) + F_58(x))
Eq(F_269(x), F_270(x) + F_71(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_0(x)**2*F_13(x))
Eq(F_272(x), F_273(x) - F_287(x))
Eq(F_273(x), F_274(x)/(F_0(x)*F_13(x)))
Eq(F_274(x), F_275(x))
Eq(F_275(x), F_276(x) + F_278(x))
Eq(F_276(x), F_0(x)*F_277(x))
Eq(F_277(x), F_2(x) + F_6(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_13(x)*F_280(x))
Eq(F_280(x), F_281(x) + F_286(x))
Eq(F_281(x), F_282(x) + F_284(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_0(x)*F_17(x)*F_277(x))
Eq(F_284(x), F_110(x) + F_285(x))
Eq(F_285(x), F_0(x)*F_122(x))
Eq(F_286(x), F_110(x))
Eq(F_287(x), F_0(x)*F_264(x))
Eq(F_288(x), F_273(x) - F_289(x))
Eq(F_289(x), F_241(x) + F_70(x))
Eq(F_290(x), F_291(x) - F_293(x))
Eq(F_291(x), F_292(x)/F_13(x))
Eq(F_292(x), F_261(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_0(x)*F_295(x))
Eq(F_295(x), F_236(x) + F_296(x))
Eq(F_296(x), F_0(x)*F_64(x))
Eq(F_297(x), F_70(x) + F_89(x))
Eq(F_298(x), F_0(x)*F_2(x)**2)
Eq(F_299(x), F_4(x)*F_71(x))
Eq(F_300(x), F_15(x) + F_73(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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"rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 2], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "indices": [0, 0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 3], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "indices": [0, 0, 0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 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": [], "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://permpal.com/tree/25163/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[41,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[332,x]
F[11,x] = F[12,x]+F[351,x]
F[12,x] = F[13,x]+F[2,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[41,x]
F[15,x] = F[16,x]+F[37,x]
F[16,x] = F[12,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[41,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[41,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[0,x]+F[12,x]
F[25,x] = F[26,x]*F[310,x]
F[26,x] = -F[350,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[2,x]^2
F[29,x] = -F[349,x]+F[30,x]
F[30,x] = -F[319,x]+F[31,x]
F[31,x] = 1/F[0,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[138,x]+F[34,x]
F[34,x] = 1/F[41,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[43,x]+F[37,x]
F[37,x] = -F[42,x]+F[38,x]
F[38,x] = 1/F[41,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[2,x]+F[6,x]
F[41,x] = x
F[42,x] = F[16,x]+F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[0,x]*F[41,x]*F[45,x]
F[45,x] = F[12,x]+F[46,x]
F[46,x] = F[126,x]+F[47,x]
F[47,x] = F[48,x]+F[74,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[41,x]*F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[53,x]+F[60,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[1,x]+F[53,x]
F[57,x] = F[41,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[41,x]*F[53,x]
F[60,x] = F[61,x]+F[62,x]+F[70,x]
F[61,x] = 0
F[62,x] = F[41,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[49,x]+F[60,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[67,x]
F[67,x] = F[41,x]*F[49,x]
F[68,x] = F[69,x]
F[69,x] = F[41,x]*F[60,x]
F[70,x] = F[41,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[41,x]+F[66,x]
F[73,x] = F[58,x]+F[68,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[41,x]*F[77,x]
F[77,x] = F[78,x]+F[85,x]
F[78,x] = F[74,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[41,x]*F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[78,x]*F[83,x]
F[83,x] = F[1,x]+F[41,x]
F[84,x] = F[76,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[41,x]*F[87,x]
F[87,x] = F[13,x]
F[88,x] = F[79,x]+F[89,x]
F[89,x] = F[53,x]+F[90,x]
F[90,x] = F[61,x]+F[91,x]+F[99,x]
F[91,x] = F[41,x]*F[92,x]
F[92,x] = F[89,x]+F[93,x]
F[93,x] = F[104,x]+F[94,x]
F[94,x] = F[61,x]+F[95,x]+F[99,x]
F[95,x] = F[41,x]*F[96,x]
F[96,x] = F[103,x]+F[97,x]
F[97,x] = F[53,x]+F[98,x]
F[98,x] = F[59,x]+F[61,x]+F[99,x]
F[99,x] = F[100,x]*F[41,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]+F[41,x]
F[102,x] = F[59,x]
F[103,x] = F[98,x]
F[104,x] = F[105,x]+F[110,x]+F[118,x]+F[61,x]
F[105,x] = F[106,x]*F[41,x]
F[106,x] = F[107,x]+F[123,x]
F[107,x] = F[108,x]+F[90,x]
F[108,x] = F[109,x]+F[110,x]+F[118,x]+F[61,x]
F[109,x] = F[41,x]*F[90,x]
F[110,x] = F[111,x]*F[41,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[108,x]+F[98,x]
F[113,x] = F[114,x]+F[119,x]
F[114,x] = F[115,x]+F[116,x]+F[118,x]+F[61,x]
F[115,x] = F[41,x]*F[98,x]
F[116,x] = F[117,x]*F[41,x]
F[117,x] = F[103,x]
F[118,x] = 0
F[119,x] = F[120,x]+F[121,x]+F[124,x]+F[125,x]+F[61,x]
F[120,x] = F[108,x]*F[41,x]
F[121,x] = F[122,x]*F[41,x]
F[122,x] = F[123,x]
F[123,x] = F[108,x]
F[124,x] = 0
F[125,x] = 0
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[41,x]*F[47,x]
F[128,x] = F[129,x]+F[24,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]
F[131,x] = F[0,x]^2*F[41,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]*F[41,x]
F[134,x] = F[135,x]
F[135,x] = F[0,x]*F[136,x]*F[41,x]
F[136,x] = F[137,x]+F[85,x]
F[137,x] = F[47,x]+F[88,x]
F[138,x] = -F[143,x]+F[139,x]
F[139,x] = 1/F[41,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]+F[36,x]
F[142,x] = F[17,x]+F[40,x]
F[143,x] = -F[147,x]+F[144,x]
F[144,x] = 1/F[41,x]*F[145,x]
F[145,x] = F[146,x]
F[146,x] = F[139,x]*F[41,x]
F[147,x] = F[148,x]+F[315,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[41,x]
F[150,x] = 1/F[41,x]*F[151,x]
F[151,x] = F[152,x]
F[152,x] = -F[167,x]+F[153,x]
F[153,x] = 1/F[41,x]*F[154,x]
F[154,x] = F[155,x]
F[155,x] = -F[158,x]+F[156,x]
F[156,x] = 1/F[41,x]*F[157,x]
F[157,x] = F[75,x]
F[158,x] = -F[161,x]+F[159,x]
F[159,x] = 1/F[41,x]*F[160,x]
F[160,x] = F[74,x]
F[161,x] = F[162,x]+F[47,x]
F[162,x] = -F[165,x]+F[163,x]
F[163,x] = 1/F[41,x]*F[164,x]
F[164,x] = F[6,x]
F[165,x] = F[16,x]+F[166,x]
F[166,x] = F[132,x]
F[167,x] = F[0,x]*F[168,x]
F[168,x] = F[169,x]+F[236,x]
F[169,x] = F[170,x]+F[47,x]
F[170,x] = -F[173,x]+F[171,x]
F[171,x] = 1/F[41,x]*F[172,x]
F[172,x] = F[6,x]
F[173,x] = F[174,x]+F[175,x]
F[174,x] = F[2,x]*F[47,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]*F[41,x]
F[177,x] = F[178,x]+F[233,x]
F[178,x] = F[179,x]+F[183,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[136,x]*F[2,x]
F[181,x] = F[182,x]
F[182,x] = F[0,x]*F[47,x]*F[5,x]
F[183,x] = F[184,x]+F[224,x]
F[184,x] = F[185,x]*F[2,x]
F[185,x] = F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[41,x]*F[188,x]
F[188,x] = F[170,x]
F[189,x] = F[136,x]+F[190,x]
F[190,x] = F[191,x]+F[222,x]
F[191,x] = F[0,x]*F[192,x]
F[192,x] = F[193,x]+F[41,x]
F[193,x] = F[194,x]+F[221,x]+F[61,x]
F[194,x] = F[195,x]*F[41,x]
F[195,x] = F[192,x]+F[196,x]
F[196,x] = F[197,x]+F[207,x]
F[197,x] = F[198,x]+F[206,x]+F[61,x]
F[198,x] = F[199,x]*F[41,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[197,x]+F[41,x]
F[201,x] = F[202,x]+F[204,x]
F[202,x] = F[203,x]
F[203,x] = x^2
F[204,x] = F[205,x]
F[205,x] = F[197,x]*F[41,x]
F[206,x] = x^2
F[207,x] = F[208,x]+F[216,x]+F[220,x]+F[61,x]
F[208,x] = F[209,x]*F[41,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[193,x]+F[207,x]
F[211,x] = F[212,x]+F[214,x]
F[212,x] = F[213,x]
F[213,x] = F[193,x]*F[41,x]
F[214,x] = F[215,x]
F[215,x] = F[207,x]*F[41,x]
F[216,x] = F[217,x]*F[41,x]
F[217,x] = F[218,x]+F[219,x]
F[218,x] = F[202,x]+F[212,x]
F[219,x] = F[204,x]+F[214,x]
F[220,x] = F[41,x]*F[58,x]
F[221,x] = F[41,x]*F[53,x]
F[222,x] = F[223,x]
F[223,x] = F[0,x]*F[41,x]*F[77,x]
F[224,x] = F[225,x]
F[225,x] = F[0,x]*F[226,x]*F[231,x]
F[226,x] = F[227,x]
F[227,x] = F[0,x]*F[228,x]*F[41,x]
F[228,x] = F[229,x]+F[47,x]
F[229,x] = F[230,x]
F[230,x] = F[49,x]+F[75,x]
F[231,x] = F[232,x]
F[232,x] = F[0,x]*F[41,x]*F[47,x]
F[233,x] = F[234,x]
F[234,x] = F[224,x]+F[235,x]
F[235,x] = F[190,x]*F[2,x]
F[236,x] = 1/F[310,x]*F[237,x]
F[237,x] = -F[309,x]+F[238,x]
F[238,x] = 1/F[41,x]*F[239,x]
F[239,x] = F[240,x]
F[240,x] = -F[243,x]+F[241,x]
F[241,x] = -F[255,x]+F[242,x]
F[242,x] = F[243,x]+F[253,x]
F[243,x] = F[244,x]+F[74,x]
F[244,x] = F[245,x]
F[245,x] = F[246,x]*F[41,x]
F[246,x] = F[247,x]+F[250,x]
F[247,x] = F[248,x]+F[77,x]
F[248,x] = F[249,x]+F[84,x]
F[249,x] = -F[229,x]+F[185,x]
F[250,x] = F[251,x]
F[251,x] = F[222,x]+F[252,x]
F[252,x] = F[192,x]*F[2,x]
F[253,x] = F[254,x]
F[254,x] = F[153,x]*F[41,x]
F[255,x] = F[2,x]*F[256,x]
F[256,x] = F[257,x]+F[262,x]
F[257,x] = F[1,x]+F[258,x]
F[258,x] = F[259,x]
F[259,x] = F[260,x]*F[41,x]
F[260,x] = F[261,x]+F[83,x]
F[261,x] = F[41,x]
F[262,x] = F[263,x]+F[49,x]
F[263,x] = F[264,x]+F[305,x]+F[61,x]
F[264,x] = F[265,x]*F[41,x]
F[265,x] = F[266,x]+F[267,x]
F[266,x] = F[258,x]+F[263,x]
F[267,x] = F[268,x]+F[281,x]
F[268,x] = F[269,x]+F[277,x]+F[61,x]
F[269,x] = F[270,x]*F[41,x]
F[270,x] = F[271,x]+F[272,x]
F[271,x] = F[258,x]+F[268,x]
F[272,x] = F[273,x]+F[275,x]
F[273,x] = F[274,x]
F[274,x] = F[258,x]*F[41,x]
F[275,x] = F[276,x]
F[276,x] = F[268,x]*F[41,x]
F[277,x] = F[278,x]*F[41,x]
F[278,x] = F[279,x]+F[280,x]
F[279,x] = F[202,x]+F[41,x]
F[280,x] = F[202,x]
F[281,x] = F[282,x]+F[290,x]+F[294,x]+F[61,x]
F[282,x] = F[283,x]*F[41,x]
F[283,x] = F[284,x]+F[285,x]
F[284,x] = F[263,x]+F[281,x]
F[285,x] = F[286,x]+F[288,x]
F[286,x] = F[287,x]
F[287,x] = F[263,x]*F[41,x]
F[288,x] = F[289,x]
F[289,x] = F[281,x]*F[41,x]
F[290,x] = F[291,x]*F[41,x]
F[291,x] = F[292,x]+F[293,x]
F[292,x] = F[273,x]+F[286,x]
F[293,x] = F[275,x]+F[288,x]
F[294,x] = F[295,x]*F[41,x]
F[295,x] = F[296,x]+F[304,x]
F[296,x] = F[297,x]+F[58,x]
F[297,x] = F[298,x]
F[298,x] = F[299,x]*F[41,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[41,x]
F[301,x] = F[302,x]+F[303,x]
F[302,x] = F[299,x]+F[41,x]
F[303,x] = F[202,x]+F[297,x]
F[304,x] = F[297,x]
F[305,x] = F[306,x]*F[41,x]
F[306,x] = F[307,x]+F[308,x]
F[307,x] = F[299,x]+F[53,x]
F[308,x] = F[299,x]
F[309,x] = F[24,x]*F[243,x]
F[310,x] = F[0,x]+F[311,x]
F[311,x] = F[312,x]
F[312,x] = F[0,x]*F[313,x]*F[41,x]
F[313,x] = F[24,x]+F[314,x]
F[314,x] = F[2,x]*F[310,x]
F[315,x] = F[316,x]
F[316,x] = F[0,x]*F[317,x]
F[317,x] = F[318,x]
F[318,x] = F[0,x]*F[134,x]*F[41,x]
F[319,x] = F[320,x]
F[320,x] = F[321,x]*F[41,x]
F[321,x] = -F[342,x]+F[322,x]
F[322,x] = 1/F[41,x]*F[323,x]
F[323,x] = F[324,x]
F[324,x] = -F[340,x]+F[325,x]
F[325,x] = F[326,x]+F[327,x]
F[326,x] = F[2,x]*F[45,x]
F[327,x] = -F[339,x]+F[328,x]
F[328,x] = 1/F[0,x]/F[41,x]*F[329,x]
F[329,x] = F[330,x]
F[330,x] = F[331,x]+F[332,x]
F[331,x] = F[0,x]*F[5,x]
F[332,x] = F[333,x]
F[333,x] = F[334,x]*F[41,x]
F[334,x] = F[335,x]+F[338,x]
F[335,x] = F[181,x]+F[336,x]
F[336,x] = F[224,x]+F[337,x]
F[337,x] = F[0,x]*F[190,x]
F[338,x] = F[224,x]
F[339,x] = F[0,x]*F[45,x]
F[340,x] = -F[341,x]+F[328,x]
F[341,x] = F[12,x]+F[168,x]
F[342,x] = -F[345,x]+F[343,x]
F[343,x] = 1/F[41,x]*F[344,x]
F[344,x] = F[324,x]
F[345,x] = F[346,x]
F[346,x] = F[0,x]*F[347,x]
F[347,x] = F[249,x]+F[348,x]
F[348,x] = F[0,x]*F[229,x]
F[349,x] = F[12,x]+F[28,x]
F[350,x] = F[2,x]^2*F[0,x]
F[351,x] = F[352,x]
F[352,x] = F[353,x]*F[41,x]
F[353,x] = F[354,x]+F[355,x]
F[354,x] = F[12,x]*F[4,x]
F[355,x] = F[0,x]*F[19,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{41}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{332}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{351}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{12}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{310}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{350}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{29}\! \left(x \right) = -F_{349}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{319}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{138}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = F_{16}\! \left(x \right)+F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{126}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{74}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{61}\! \left(x \right) = 0
F_{62}\! \left(x \right) = F_{41}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{49}\! \left(x \right)+F_{60}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{41}\! \left(x \right) F_{49}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{41}\! \left(x \right) F_{60}\! \left(x \right)
F_{70}\! \left(x \right) = F_{41}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{41}\! \left(x \right)+F_{66}\! \left(x \right)
F_{73}\! \left(x \right) = F_{58}\! \left(x \right)+F_{68}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{41}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{84}\! \left(x \right) = F_{76}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{13}\! \left(x \right)
F_{88}\! \left(x \right) = F_{79}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{53}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{61}\! \left(x \right)+F_{91}\! \left(x \right)+F_{99}\! \left(x \right)
F_{91}\! \left(x \right) = F_{41}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{104}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{61}\! \left(x \right)+F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{95}\! \left(x \right) = F_{41}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{53}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{41}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{41}\! \left(x \right)
F_{102}\! \left(x \right) = F_{59}\! \left(x \right)
F_{103}\! \left(x \right) = F_{98}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{110}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{41}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{123}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{90}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{109}\! \left(x \right) = F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{41}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)+F_{98}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{119}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{115}\! \left(x \right) = F_{41}\! \left(x \right) F_{98}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{41}\! \left(x \right)
F_{117}\! \left(x \right) = F_{103}\! \left(x \right)
F_{118}\! \left(x \right) = 0
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)+F_{124}\! \left(x \right)+F_{125}\! \left(x \right)+F_{61}\! \left(x \right)
F_{120}\! \left(x \right) = F_{108}\! \left(x \right) F_{41}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{41}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{108}\! \left(x \right)
F_{124}\! \left(x \right) = 0
F_{125}\! \left(x \right) = 0
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{41}\! \left(x \right) F_{47}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{24}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{41}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{41}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{0}\! \left(x \right) F_{136}\! \left(x \right) F_{41}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{85}\! \left(x \right)
F_{137}\! \left(x \right) = F_{47}\! \left(x \right)+F_{88}\! \left(x \right)
F_{138}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{36}\! \left(x \right)
F_{142}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{147}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = \frac{F_{145}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{139}\! \left(x \right) F_{41}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{315}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{41}\! \left(x \right)
F_{150}\! \left(x \right) = \frac{F_{151}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = -F_{167}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = \frac{F_{154}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = \frac{F_{157}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{157}\! \left(x \right) = F_{75}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{161}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = \frac{F_{160}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{160}\! \left(x \right) = F_{74}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{47}\! \left(x \right)
F_{162}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = \frac{F_{164}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{164}\! \left(x \right) = F_{6}\! \left(x \right)
F_{165}\! \left(x \right) = F_{16}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{132}\! \left(x \right)
F_{167}\! \left(x \right) = F_{0}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{236}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{47}\! \left(x \right)
F_{170}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = \frac{F_{172}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{172}\! \left(x \right) = F_{6}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{175}\! \left(x \right)
F_{174}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{41}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{233}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{183}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{136}\! \left(x \right) F_{2}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{0}\! \left(x \right) F_{47}\! \left(x \right) F_{5}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{224}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{2}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{170}\! \left(x \right)
F_{189}\! \left(x \right) = F_{136}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{222}\! \left(x \right)
F_{191}\! \left(x \right) = F_{0}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{41}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{221}\! \left(x \right)+F_{61}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{41}\! \left(x \right)
F_{195}\! \left(x \right) = F_{192}\! \left(x \right)+F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{207}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{206}\! \left(x \right)+F_{61}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{41}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{197}\! \left(x \right)+F_{41}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{204}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = x^{2}
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{197}\! \left(x \right) F_{41}\! \left(x \right)
F_{206}\! \left(x \right) = x^{2}
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{216}\! \left(x \right)+F_{220}\! \left(x \right)+F_{61}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{41}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{193}\! \left(x \right)+F_{207}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{214}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{193}\! \left(x \right) F_{41}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{207}\! \left(x \right) F_{41}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right) F_{41}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{219}\! \left(x \right)
F_{218}\! \left(x \right) = F_{202}\! \left(x \right)+F_{212}\! \left(x \right)
F_{219}\! \left(x \right) = F_{204}\! \left(x \right)+F_{214}\! \left(x \right)
F_{220}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{221}\! \left(x \right) = F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{77}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{0}\! \left(x \right) F_{226}\! \left(x \right) F_{231}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{0}\! \left(x \right) F_{228}\! \left(x \right) F_{41}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{47}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{49}\! \left(x \right)+F_{75}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right) F_{47}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{224}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{190}\! \left(x \right) F_{2}\! \left(x \right)
F_{236}\! \left(x \right) = \frac{F_{237}\! \left(x \right)}{F_{310}\! \left(x \right)}
F_{237}\! \left(x \right) = -F_{309}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = \frac{F_{239}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = -F_{243}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = -F_{255}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{253}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{74}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{41}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{250}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{77}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{84}\! \left(x \right)
F_{249}\! \left(x \right) = -F_{229}\! \left(x \right)+F_{185}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{222}\! \left(x \right)+F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{192}\! \left(x \right) F_{2}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{153}\! \left(x \right) F_{41}\! \left(x \right)
F_{255}\! \left(x \right) = F_{2}\! \left(x \right) F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{262}\! \left(x \right)
F_{257}\! \left(x \right) = F_{1}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right) F_{41}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{83}\! \left(x \right)
F_{261}\! \left(x \right) = F_{41}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)+F_{49}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{305}\! \left(x \right)+F_{61}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right) F_{41}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)+F_{267}\! \left(x \right)
F_{266}\! \left(x \right) = F_{258}\! \left(x \right)+F_{263}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{281}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{277}\! \left(x \right)+F_{61}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right) F_{41}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{272}\! \left(x \right)
F_{271}\! \left(x \right) = F_{258}\! \left(x \right)+F_{268}\! \left(x \right)
F_{272}\! \left(x \right) = F_{273}\! \left(x \right)+F_{275}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{258}\! \left(x \right) F_{41}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{268}\! \left(x \right) F_{41}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right) F_{41}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{280}\! \left(x \right)
F_{279}\! \left(x \right) = F_{202}\! \left(x \right)+F_{41}\! \left(x \right)
F_{280}\! \left(x \right) = F_{202}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{290}\! \left(x \right)+F_{294}\! \left(x \right)+F_{61}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right) F_{41}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)+F_{285}\! \left(x \right)
F_{284}\! \left(x \right) = F_{263}\! \left(x \right)+F_{281}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{288}\! \left(x \right)
F_{286}\! \left(x \right) = F_{287}\! \left(x \right)
F_{287}\! \left(x \right) = F_{263}\! \left(x \right) F_{41}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = F_{281}\! \left(x \right) F_{41}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{41}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{293}\! \left(x \right)
F_{292}\! \left(x \right) = F_{273}\! \left(x \right)+F_{286}\! \left(x \right)
F_{293}\! \left(x \right) = F_{275}\! \left(x \right)+F_{288}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{41}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)+F_{304}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{58}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{41}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{41}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)+F_{303}\! \left(x \right)
F_{302}\! \left(x \right) = F_{299}\! \left(x \right)+F_{41}\! \left(x \right)
F_{303}\! \left(x \right) = F_{202}\! \left(x \right)+F_{297}\! \left(x \right)
F_{304}\! \left(x \right) = F_{297}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right) F_{41}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)+F_{308}\! \left(x \right)
F_{307}\! \left(x \right) = F_{299}\! \left(x \right)+F_{53}\! \left(x \right)
F_{308}\! \left(x \right) = F_{299}\! \left(x \right)
F_{309}\! \left(x \right) = F_{24}\! \left(x \right) F_{243}\! \left(x \right)
F_{310}\! \left(x \right) = F_{0}\! \left(x \right)+F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{0}\! \left(x \right) F_{313}\! \left(x \right) F_{41}\! \left(x \right)
F_{313}\! \left(x \right) = F_{24}\! \left(x \right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{2}\! \left(x \right) F_{310}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{0}\! \left(x \right) F_{317}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)
F_{318}\! \left(x \right) = F_{0}\! \left(x \right) F_{134}\! \left(x \right) F_{41}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right) F_{41}\! \left(x \right)
F_{321}\! \left(x \right) = -F_{342}\! \left(x \right)+F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = \frac{F_{323}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = -F_{340}\! \left(x \right)+F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{327}\! \left(x \right)
F_{326}\! \left(x \right) = F_{2}\! \left(x \right) F_{45}\! \left(x \right)
F_{327}\! \left(x \right) = -F_{339}\! \left(x \right)+F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = \frac{F_{329}\! \left(x \right)}{F_{0}\! \left(x \right) F_{41}\! \left(x \right)}
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right)+F_{332}\! \left(x \right)
F_{331}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right) F_{41}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right)+F_{338}\! \left(x \right)
F_{335}\! \left(x \right) = F_{181}\! \left(x \right)+F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{224}\! \left(x \right)+F_{337}\! \left(x \right)
F_{337}\! \left(x \right) = F_{0}\! \left(x \right) F_{190}\! \left(x \right)
F_{338}\! \left(x \right) = F_{224}\! \left(x \right)
F_{339}\! \left(x \right) = F_{0}\! \left(x \right) F_{45}\! \left(x \right)
F_{340}\! \left(x \right) = -F_{341}\! \left(x \right)+F_{328}\! \left(x \right)
F_{341}\! \left(x \right) = F_{12}\! \left(x \right)+F_{168}\! \left(x \right)
F_{342}\! \left(x \right) = -F_{345}\! \left(x \right)+F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = \frac{F_{344}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{344}\! \left(x \right) = F_{324}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{0}\! \left(x \right) F_{347}\! \left(x \right)
F_{347}\! \left(x \right) = F_{249}\! \left(x \right)+F_{348}\! \left(x \right)
F_{348}\! \left(x \right) = F_{0}\! \left(x \right) F_{229}\! \left(x \right)
F_{349}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{350}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = F_{353}\! \left(x \right) F_{41}\! \left(x \right)
F_{353}\! \left(x \right) = F_{354}\! \left(x \right)+F_{355}\! \left(x \right)
F_{354}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{355}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_41(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_332(x))
Eq(F_11(x), F_12(x) + F_351(x))
Eq(F_12(x), F_13(x) + F_2(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_41(x))
Eq(F_15(x), F_16(x) + F_37(x))
Eq(F_16(x), F_12(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_41(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_41(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_0(x) + F_12(x))
Eq(F_25(x), F_26(x)*F_310(x))
Eq(F_26(x), F_27(x) - F_350(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_2(x)**2)
Eq(F_29(x), F_30(x) - F_349(x))
Eq(F_30(x), F_31(x) - F_319(x))
Eq(F_31(x), F_32(x)/F_0(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_138(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_41(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) - F_43(x))
Eq(F_37(x), F_38(x) - F_42(x))
Eq(F_38(x), F_39(x)/F_41(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_2(x) + F_6(x))
Eq(F_41(x), x)
Eq(F_42(x), F_16(x) + F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_0(x)*F_41(x)*F_45(x))
Eq(F_45(x), F_12(x) + F_46(x))
Eq(F_46(x), F_126(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_74(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_41(x)*F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_53(x) + F_60(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_1(x) + F_53(x))
Eq(F_57(x), F_41(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_41(x)*F_53(x))
Eq(F_60(x), F_61(x) + F_62(x) + F_70(x))
Eq(F_61(x), 0)
Eq(F_62(x), F_41(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_49(x) + F_60(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_41(x)*F_49(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_41(x)*F_60(x))
Eq(F_70(x), F_41(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_41(x) + F_66(x))
Eq(F_73(x), F_58(x) + F_68(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_41(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_85(x))
Eq(F_78(x), F_74(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_41(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_78(x)*F_83(x))
Eq(F_83(x), F_1(x) + F_41(x))
Eq(F_84(x), F_76(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_41(x))
Eq(F_87(x), F_13(x))
Eq(F_88(x), F_79(x) + F_89(x))
Eq(F_89(x), F_53(x) + F_90(x))
Eq(F_90(x), F_61(x) + F_91(x) + F_99(x))
Eq(F_91(x), F_41(x)*F_92(x))
Eq(F_92(x), F_89(x) + F_93(x))
Eq(F_93(x), F_104(x) + F_94(x))
Eq(F_94(x), F_61(x) + F_95(x) + F_99(x))
Eq(F_95(x), F_41(x)*F_96(x))
Eq(F_96(x), F_103(x) + F_97(x))
Eq(F_97(x), F_53(x) + F_98(x))
Eq(F_98(x), F_59(x) + F_61(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_41(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) + F_41(x))
Eq(F_102(x), F_59(x))
Eq(F_103(x), F_98(x))
Eq(F_104(x), F_105(x) + F_110(x) + F_118(x) + F_61(x))
Eq(F_105(x), F_106(x)*F_41(x))
Eq(F_106(x), F_107(x) + F_123(x))
Eq(F_107(x), F_108(x) + F_90(x))
Eq(F_108(x), F_109(x) + F_110(x) + F_118(x) + F_61(x))
Eq(F_109(x), F_41(x)*F_90(x))
Eq(F_110(x), F_111(x)*F_41(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_108(x) + F_98(x))
Eq(F_113(x), F_114(x) + F_119(x))
Eq(F_114(x), F_115(x) + F_116(x) + F_118(x) + F_61(x))
Eq(F_115(x), F_41(x)*F_98(x))
Eq(F_116(x), F_117(x)*F_41(x))
Eq(F_117(x), F_103(x))
Eq(F_118(x), 0)
Eq(F_119(x), F_120(x) + F_121(x) + F_124(x) + F_125(x) + F_61(x))
Eq(F_120(x), F_108(x)*F_41(x))
Eq(F_121(x), F_122(x)*F_41(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_108(x))
Eq(F_124(x), 0)
Eq(F_125(x), 0)
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_41(x)*F_47(x))
Eq(F_128(x), F_129(x) + F_24(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_0(x)**2*F_41(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x)*F_41(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_0(x)*F_136(x)*F_41(x))
Eq(F_136(x), F_137(x) + F_85(x))
Eq(F_137(x), F_47(x) + F_88(x))
Eq(F_138(x), F_139(x) - F_143(x))
Eq(F_139(x), F_140(x)/F_41(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x) + F_36(x))
Eq(F_142(x), F_17(x) + F_40(x))
Eq(F_143(x), F_144(x) - F_147(x))
Eq(F_144(x), F_145(x)/F_41(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_139(x)*F_41(x))
Eq(F_147(x), F_148(x) + F_315(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_41(x))
Eq(F_150(x), F_151(x)/F_41(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x) - F_167(x))
Eq(F_153(x), F_154(x)/F_41(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x) - F_158(x))
Eq(F_156(x), F_157(x)/F_41(x))
Eq(F_157(x), F_75(x))
Eq(F_158(x), F_159(x) - F_161(x))
Eq(F_159(x), F_160(x)/F_41(x))
Eq(F_160(x), F_74(x))
Eq(F_161(x), F_162(x) + F_47(x))
Eq(F_162(x), F_163(x) - F_165(x))
Eq(F_163(x), F_164(x)/F_41(x))
Eq(F_164(x), F_6(x))
Eq(F_165(x), F_16(x) + F_166(x))
Eq(F_166(x), F_132(x))
Eq(F_167(x), F_0(x)*F_168(x))
Eq(F_168(x), F_169(x) + F_236(x))
Eq(F_169(x), F_170(x) + F_47(x))
Eq(F_170(x), F_171(x) - F_173(x))
Eq(F_171(x), F_172(x)/F_41(x))
Eq(F_172(x), F_6(x))
Eq(F_173(x), F_174(x) + F_175(x))
Eq(F_174(x), F_2(x)*F_47(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x)*F_41(x))
Eq(F_177(x), F_178(x) + F_233(x))
Eq(F_178(x), F_179(x) + F_183(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_136(x)*F_2(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_0(x)*F_47(x)*F_5(x))
Eq(F_183(x), F_184(x) + F_224(x))
Eq(F_184(x), F_185(x)*F_2(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_41(x))
Eq(F_188(x), F_170(x))
Eq(F_189(x), F_136(x) + F_190(x))
Eq(F_190(x), F_191(x) + F_222(x))
Eq(F_191(x), F_0(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_41(x))
Eq(F_193(x), F_194(x) + F_221(x) + F_61(x))
Eq(F_194(x), F_195(x)*F_41(x))
Eq(F_195(x), F_192(x) + F_196(x))
Eq(F_196(x), F_197(x) + F_207(x))
Eq(F_197(x), F_198(x) + F_206(x) + F_61(x))
Eq(F_198(x), F_199(x)*F_41(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_197(x) + F_41(x))
Eq(F_201(x), F_202(x) + F_204(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), x**2)
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_197(x)*F_41(x))
Eq(F_206(x), x**2)
Eq(F_207(x), F_208(x) + F_216(x) + F_220(x) + F_61(x))
Eq(F_208(x), F_209(x)*F_41(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_193(x) + F_207(x))
Eq(F_211(x), F_212(x) + F_214(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_193(x)*F_41(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_207(x)*F_41(x))
Eq(F_216(x), F_217(x)*F_41(x))
Eq(F_217(x), F_218(x) + F_219(x))
Eq(F_218(x), F_202(x) + F_212(x))
Eq(F_219(x), F_204(x) + F_214(x))
Eq(F_220(x), F_41(x)*F_58(x))
Eq(F_221(x), F_41(x)*F_53(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_0(x)*F_41(x)*F_77(x))
Eq(F_224(x), F_225(x))
Eq(F_225(x), F_0(x)*F_226(x)*F_231(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_0(x)*F_228(x)*F_41(x))
Eq(F_228(x), F_229(x) + F_47(x))
Eq(F_229(x), F_230(x))
Eq(F_230(x), F_49(x) + F_75(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_0(x)*F_41(x)*F_47(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_224(x) + F_235(x))
Eq(F_235(x), F_190(x)*F_2(x))
Eq(F_236(x), F_237(x)/F_310(x))
Eq(F_237(x), F_238(x) - F_309(x))
Eq(F_238(x), F_239(x)/F_41(x))
Eq(F_239(x), F_240(x))
Eq(F_240(x), F_241(x) - F_243(x))
Eq(F_241(x), F_242(x) - F_255(x))
Eq(F_242(x), F_243(x) + F_253(x))
Eq(F_243(x), F_244(x) + F_74(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_246(x)*F_41(x))
Eq(F_246(x), F_247(x) + F_250(x))
Eq(F_247(x), F_248(x) + F_77(x))
Eq(F_248(x), F_249(x) + F_84(x))
Eq(F_249(x), F_185(x) - F_229(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_222(x) + F_252(x))
Eq(F_252(x), F_192(x)*F_2(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_153(x)*F_41(x))
Eq(F_255(x), F_2(x)*F_256(x))
Eq(F_256(x), F_257(x) + F_262(x))
Eq(F_257(x), F_1(x) + F_258(x))
Eq(F_258(x), F_259(x))
Eq(F_259(x), F_260(x)*F_41(x))
Eq(F_260(x), F_261(x) + F_83(x))
Eq(F_261(x), F_41(x))
Eq(F_262(x), F_263(x) + F_49(x))
Eq(F_263(x), F_264(x) + F_305(x) + F_61(x))
Eq(F_264(x), F_265(x)*F_41(x))
Eq(F_265(x), F_266(x) + F_267(x))
Eq(F_266(x), F_258(x) + F_263(x))
Eq(F_267(x), F_268(x) + F_281(x))
Eq(F_268(x), F_269(x) + F_277(x) + F_61(x))
Eq(F_269(x), F_270(x)*F_41(x))
Eq(F_270(x), F_271(x) + F_272(x))
Eq(F_271(x), F_258(x) + F_268(x))
Eq(F_272(x), F_273(x) + F_275(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_258(x)*F_41(x))
Eq(F_275(x), F_276(x))
Eq(F_276(x), F_268(x)*F_41(x))
Eq(F_277(x), F_278(x)*F_41(x))
Eq(F_278(x), F_279(x) + F_280(x))
Eq(F_279(x), F_202(x) + F_41(x))
Eq(F_280(x), F_202(x))
Eq(F_281(x), F_282(x) + F_290(x) + F_294(x) + F_61(x))
Eq(F_282(x), F_283(x)*F_41(x))
Eq(F_283(x), F_284(x) + F_285(x))
Eq(F_284(x), F_263(x) + F_281(x))
Eq(F_285(x), F_286(x) + F_288(x))
Eq(F_286(x), F_287(x))
Eq(F_287(x), F_263(x)*F_41(x))
Eq(F_288(x), F_289(x))
Eq(F_289(x), F_281(x)*F_41(x))
Eq(F_290(x), F_291(x)*F_41(x))
Eq(F_291(x), F_292(x) + F_293(x))
Eq(F_292(x), F_273(x) + F_286(x))
Eq(F_293(x), F_275(x) + F_288(x))
Eq(F_294(x), F_295(x)*F_41(x))
Eq(F_295(x), F_296(x) + F_304(x))
Eq(F_296(x), F_297(x) + F_58(x))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_299(x)*F_41(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_41(x))
Eq(F_301(x), F_302(x) + F_303(x))
Eq(F_302(x), F_299(x) + F_41(x))
Eq(F_303(x), F_202(x) + F_297(x))
Eq(F_304(x), F_297(x))
Eq(F_305(x), F_306(x)*F_41(x))
Eq(F_306(x), F_307(x) + F_308(x))
Eq(F_307(x), F_299(x) + F_53(x))
Eq(F_308(x), F_299(x))
Eq(F_309(x), F_24(x)*F_243(x))
Eq(F_310(x), F_0(x) + F_311(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_0(x)*F_313(x)*F_41(x))
Eq(F_313(x), F_24(x) + F_314(x))
Eq(F_314(x), F_2(x)*F_310(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_0(x)*F_317(x))
Eq(F_317(x), F_318(x))
Eq(F_318(x), F_0(x)*F_134(x)*F_41(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_321(x)*F_41(x))
Eq(F_321(x), F_322(x) - F_342(x))
Eq(F_322(x), F_323(x)/F_41(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_325(x) - F_340(x))
Eq(F_325(x), F_326(x) + F_327(x))
Eq(F_326(x), F_2(x)*F_45(x))
Eq(F_327(x), F_328(x) - F_339(x))
Eq(F_328(x), F_329(x)/(F_0(x)*F_41(x)))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_331(x) + F_332(x))
Eq(F_331(x), F_0(x)*F_5(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_334(x)*F_41(x))
Eq(F_334(x), F_335(x) + F_338(x))
Eq(F_335(x), F_181(x) + F_336(x))
Eq(F_336(x), F_224(x) + F_337(x))
Eq(F_337(x), F_0(x)*F_190(x))
Eq(F_338(x), F_224(x))
Eq(F_339(x), F_0(x)*F_45(x))
Eq(F_340(x), F_328(x) - F_341(x))
Eq(F_341(x), F_12(x) + F_168(x))
Eq(F_342(x), F_343(x) - F_345(x))
Eq(F_343(x), F_344(x)/F_41(x))
Eq(F_344(x), F_324(x))
Eq(F_345(x), F_346(x))
Eq(F_346(x), F_0(x)*F_347(x))
Eq(F_347(x), F_249(x) + F_348(x))
Eq(F_348(x), F_0(x)*F_229(x))
Eq(F_349(x), F_12(x) + F_28(x))
Eq(F_350(x), F_0(x)*F_2(x)**2)
Eq(F_351(x), F_352(x))
Eq(F_352(x), F_353(x)*F_41(x))
Eq(F_353(x), F_354(x) + F_355(x))
Eq(F_354(x), F_12(x)*F_4(x))
Eq(F_355(x), F_0(x)*F_19(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1], [3, 0, 2, 4, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 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, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 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, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 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