10243_10342_10432_20143_20341_20431_30142_30241

Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3035, 16838, 96189, 562676, 3356916, 20362850, 125287692, 780398094, 4913441262, 31229240680, 200161740988, 1292576829062, 8403454805199, 54967211523736, 361535419832333, 2389947199755618, 15872001924202212, 105856865458351580, 708772922521008784, 4762871495418671492, 32113740931587832751, 217205931109269779570, 1473397399954662005575, 10021971313320552266852, 68343439404117254465092, 467178816431250505135398, 3200739488323156151544178, 21975661569410929904374030, 151184175920749446435761195, 1042067825621875257674629184, 7195603148445961790925898653, 49771377743488289759497368126, 344822888779458511987740355921, 2392665215866096546211930886192, 16626665422948511637419189829467, 115700688754867010668416163722984, 806206940638498573390675729120948, 5624850968483046127287907362236266, 39292096532445331121621797480327188, 274793482049166548838650254997699774, 1923948603061437827270879254882068653, 13484858555127106181824532615428763820, 94612058930553182115130277284512651349, 664471173688319804906617926863833680566, 4671095589366562830162496646304606275442, 32866894581916612428021465677778612561752, 231462755109277130711600129566387985518868, 1631443829217281112211501845319452518603972, 11508493503552219578229336632441886107521300, 81247059838807269744448264584584764925782390, 574021008972554144764894115224314454355185044, 4058519307676996032080824297407620891238943096, 28715503957508116697873768196994953927155521131, 203312507742896257030248739802016544826996900446, 1440459012050432166219680530000093520494731354395, 10212161008509529187950286526301395864022707919696, 72444523963672515269739035779722317982487907644042, 514228640037517674067551912543883416299687475635202, 3652260588776032137457958561601934955679740860761624, 25954604694055633056113645261941960292353042606999490, 184546984220756213044760817586217871289436258148025497, 1312902220424045163260051181118328470348116745581752692, 9345101735772186343122134540526440161025720561276757783, 66551142026478580648609741701374542294589490155419281342, 474177227950310750787426096592402117217568094900241566927, 3380132335815680705739912464907932239620655351736324744240, 24106208527510428752876682743955514473900613001224814883169, 171997011639436799927965619517449043876266141613930416133388, 1227734575242898246454507021744365097498727968313192057317554, 8767477774915531590013282617145427699659124401536363946510782, 62636382006937723999639281074719187583493333307954225978933598, 447667784325828048335706196544178951659441938423869225869328758, 3200794305779093900132084509381577071416836602163106888739193772, 22894341549318489589522176322822843416897029644318968919691515516, 163818482018702903421909480089759829035251237678925271060460301754, 1172621935987308036874530435531186961542035614465085932467324623346, 8396720155808713264193506846938693130151717421874051674826549371047, 60147031722234712895836379925158005008279695519776893337247067677576, 430990811097097931692696611079125178473628348019380196995066419798985, 3089353976861220514334368718491740075672993048620168282394100263918842, 22151842806044107501548036140723486603116281601062297807591837342326922, 158888097693265402387768304084409768431022225962107717497041159331589408, 1140011106284074832176429875299578442456619408946109091872227956330424458, 8182010088842596808432781236856495776188413980321961137181256747098082524, 58740988064947544748757377895633942070037261260852429376680290787905258895, 421842161313959490960708749857822357626246970198024507744525919350744298646, 3030285164391450653576087627358923408387120878425002132148287783907741377191, 21774047339319960293106350330482093021588465446354320689509752097822655722672, 156500028977189701113081160051255101298631771853394920475849927023956360891601, 1125140626766895606137865567288169246219674346955482274615747793485389471487958, 8091218323444451384743383568285095999313510223129657244275927042496942370429705, 58201401016959855524822683264666224938768538278975490167321535997487318568736474, 418757994465974278069680158451763165574580565465876003160404486394487402820058120, 3013705079809260833347559808583493435882696780916174605367226945577743691711401692

Implicit equation for the generating function in Maple syntax:
16*x^6*(3*x-2)*F(x)^5-8*x^4*(14*x^3-40*x^2+53*x-22)*F(x)^4+4*x^2*(26*x^5-118*x^4+101*x^3+94*x^2-83*x+2)*F(x)^3-x*(48*x^6-276*x^5+106*x^4+644*x^3-212*x^2-163*x+10)*F(x)^2+(11*x^7-72*x^6+15*x^5+296*x^4+77*x^3-188*x^2-11*x+2)*F(x)-x^7+7*x^6-3*x^5-42*x^4-59*x^3+44*x^2+19*x-2 = 0

Implicit equation for the generating function in latex syntax:
16 x^{6} \left(3 x -2\right) F \! \left(x \right)^{5}-8 x^{4} \left(14 x^{3}-40 x^{2}+53 x -22\right) F \! \left(x \right)^{4}+4 x^{2} \left(26 x^{5}-118 x^{4}+101 x^{3}+94 x^{2}-83 x +2\right) F \! \left(x \right)^{3}-x \left(48 x^{6}-276 x^{5}+106 x^{4}+644 x^{3}-212 x^{2}-163 x +10\right) F \! \left(x \right)^{2}+\left(11 x^{7}-72 x^{6}+15 x^{5}+296 x^{4}+77 x^{3}-188 x^{2}-11 x +2\right) F \! \left(x \right)-x^{7}+7 x^{6}-3 x^{5}-42 x^{4}-59 x^{3}+44 x^{2}+19 x -2 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3035
a(8) = 16838
a(9) = 96189
a(10) = 562676
a(11) = 3356916
a(12) = 20362850
a(13) = 125287692
a(14) = 780398094
a(15) = 4913441262
a(16) = 31229240680
a(17) = 200161740988
a(18) = 1292576829062
a(19) = 8403454805199
a(20) = 54967211523736
a(21) = 361535419832333
a(22) = 2389947199755618
a(23) = 15872001924202212
a(24) = 105856865458351580
a(25) = 708772922521008784
a(26) = 4762871495418671492
a(27) = 32113740931587832751
a(28) = 217205931109269779570
a(29) = 1473397399954662005575
a(30) = 10021971313320552266852
a(31) = 68343439404117254465092
a(n+32) = 1/4795*(187799*n+5652356)/(n+34)*a(n+31)+3/19180*(20272371517*n^4+303008850210*n^3+1568687135000*n^2+3106616534010*n+1511089183668)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+4)-3/38360*(97881818833*n^4+1083961603645*n^3-807917955815*n^2-41877891298315*n-115195565564978)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+5)-1/76720*(24608635556546*n^4+689164507449490*n^3+7211646089705545*n^2+33418662141613685*n+57865858692346584)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+6)+1/15344*(43042866411828*n^4+1334987646612023*n^3+15488975107198161*n^2+79680008978016574*n+153355371033688464)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+7)-1/306880*(3630094555768813*n^4+125777357395720150*n^3+1630424078767905935*n^2+9372203643578247590*n+20159590975255169952)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+8)+3/30688*(348758848460025*n^4+13473898490178118*n^3+194862831505682819*n^2+1250484224896488702*n+3004789933576024184)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+9)-3/306880*(8311970392479087*n^4+358184160237272270*n^3+5783257171901472345*n^2+41471342990958094010*n+111456312396527578408)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+10)-1/19180*(11857573*n^2+701775051*n+10380571266)/(n+33)/(n+34)*a(n+30)+1/9590*(41286048*n^3+3599516147*n^2+104555141623*n+1011813233022)/(n+32)/(n+33)/(n+34)*a(n+29)+486/137*n*(4*n+5)*(2*n+1)*(4*n+3)/(n+34)/(n+33)/(n+32)/(n+31)*a(n)-1/76720*(26618997429*n^4+2947551130360*n^3+122398972740125*n^2+2259141023951330*n+15638267192350456)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+27)+1/76720*(298397903*n^4+34856043030*n^3+1529721987325*n^2+29895485662590*n+219525644715792)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+28)+1/153440*(22239237979515378*n^4+1781787882772912905*n^3+53500321880765244105*n^2+713516272442085562550*n+3566225797514236108752)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+19)-1/153440*(8203453158346531*n^4+689160780081403770*n^3+21697236331187442865*n^2+303409824761727229610*n+1590028885488112522744)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+20)+1/153440*(2346444074798034*n^4+206336302608874565*n^3+6799577923848594635*n^2+99519511107682276390*n+545834376055576028616)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+21)-1/153440*(490569636724889*n^4+45105655499918860*n^3+1553997881354981455*n^2+23775738003383202620*n+136296239562585047536)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+22)+1/153440*(62356958589842*n^4+6002622431234025*n^3+216422398002057725*n^2+3463655719313036550*n+20760175162395233488)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+23)+1/306880*(467173192609*n^4+23773802377110*n^3+116671112633175*n^2-9447577388591230*n-120143129964668264)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+24)-1/153440*(2125967030913*n^4+217491644300685*n^3+8346641978382150*n^2+142426417538856880*n+911873373949140752)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+25)+1/306880*(985676669069*n^4+105102141025710*n^3+4202865683437635*n^2+74703767191881170*n+498008922982644936)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+26)+27/685*(9842*n^4+69690*n^3+176140*n^2+182490*n+65583)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+1)+9/1918*(9927160*n^4+100105540*n^3+378144902*n^2+634907354*n+399967491)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+2)+3/19180*(137195804*n^4+5889775120*n^3+51832915870*n^2+167359634435*n+183315722331)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+3)+1/153440*(27113292379320764*n^4+1296511990275328095*n^3+23237801894900970545*n^2+185035479482980977570*n+552329845864650211136)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+11)-1/153440*(53099079041637489*n^4+2781830356304083870*n^3+54618207058495915195*n^2+476327067725085511030*n+1556891750600358316056)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+12)+1/153440*(88358984246516282*n^4+5006537159581866375*n^3+106297591010649121885*n^2+1002305540338833025970*n+3541494443405221672448)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+13)-1/30688*(24037746699829213*n^4+1459448697300486472*n^3+33202487660034853965*n^2+335450145595956207498*n+1269923832106391425216)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+14)+1/153440*(131862965169749994*n^4+8525006286182077605*n^3+206523326604132055205*n^2+2221944349090094873850*n+8957813130461353374296)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+15)-1/76720*(58283144035263622*n^4+3994225567747406830*n^3+102576435178103339765*n^2+1169967660787598845565*n+5000634353811311178118)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+16)+1/30688*(16638428888515354*n^4+1204485772279886699*n^3+32676565381434968557*n^2+393732550996529292874*n+1777907058352732193688)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+17)-1/76720*(23977381979274061*n^4+1828285231880450865*n^3+52245026510179543165*n^2+663114687876004329325*n+3154180897223740271764)/(n+34)/(n+33)/(n+32)/(n+31)*a(n+18), n >= 32

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3035
a(8) = 16838
a(9) = 96189
a(10) = 562676
a(11) = 3356916
a(12) = 20362850
a(13) = 125287692
a(14) = 780398094
a(15) = 4913441262
a(16) = 31229240680
a(17) = 200161740988
a(18) = 1292576829062
a(19) = 8403454805199
a(20) = 54967211523736
a(21) = 361535419832333
a(22) = 2389947199755618
a(23) = 15872001924202212
a(24) = 105856865458351580
a(25) = 708772922521008784
a(26) = 4762871495418671492
a(27) = 32113740931587832751
a(28) = 217205931109269779570
a(29) = 1473397399954662005575
a(30) = 10021971313320552266852
a(31) = 68343439404117254465092
a{\left(n + 32 \right)} = \frac{486 n \left(2 n + 1\right) \left(4 n + 3\right) \left(4 n + 5\right) a{\left(n \right)}}{137 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(187799 n + 5652356\right) a{\left(n + 31 \right)}}{4795 \left(n + 34\right)} - \frac{\left(11857573 n^{2} + 701775051 n + 10380571266\right) a{\left(n + 30 \right)}}{19180 \left(n + 33\right) \left(n + 34\right)} + \frac{\left(41286048 n^{3} + 3599516147 n^{2} + 104555141623 n + 1011813233022\right) a{\left(n + 29 \right)}}{9590 \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{27 \left(9842 n^{4} + 69690 n^{3} + 176140 n^{2} + 182490 n + 65583\right) a{\left(n + 1 \right)}}{685 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{9 \left(9927160 n^{4} + 100105540 n^{3} + 378144902 n^{2} + 634907354 n + 399967491\right) a{\left(n + 2 \right)}}{1918 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(137195804 n^{4} + 5889775120 n^{3} + 51832915870 n^{2} + 167359634435 n + 183315722331\right) a{\left(n + 3 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(298397903 n^{4} + 34856043030 n^{3} + 1529721987325 n^{2} + 29895485662590 n + 219525644715792\right) a{\left(n + 28 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(20272371517 n^{4} + 303008850210 n^{3} + 1568687135000 n^{2} + 3106616534010 n + 1511089183668\right) a{\left(n + 4 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(26618997429 n^{4} + 2947551130360 n^{3} + 122398972740125 n^{2} + 2259141023951330 n + 15638267192350456\right) a{\left(n + 27 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(97881818833 n^{4} + 1083961603645 n^{3} - 807917955815 n^{2} - 41877891298315 n - 115195565564978\right) a{\left(n + 5 \right)}}{38360 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(467173192609 n^{4} + 23773802377110 n^{3} + 116671112633175 n^{2} - 9447577388591230 n - 120143129964668264\right) a{\left(n + 24 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(985676669069 n^{4} + 105102141025710 n^{3} + 4202865683437635 n^{2} + 74703767191881170 n + 498008922982644936\right) a{\left(n + 26 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(2125967030913 n^{4} + 217491644300685 n^{3} + 8346641978382150 n^{2} + 142426417538856880 n + 911873373949140752\right) a{\left(n + 25 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24608635556546 n^{4} + 689164507449490 n^{3} + 7211646089705545 n^{2} + 33418662141613685 n + 57865858692346584\right) a{\left(n + 6 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(43042866411828 n^{4} + 1334987646612023 n^{3} + 15488975107198161 n^{2} + 79680008978016574 n + 153355371033688464\right) a{\left(n + 7 \right)}}{15344 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(62356958589842 n^{4} + 6002622431234025 n^{3} + 216422398002057725 n^{2} + 3463655719313036550 n + 20760175162395233488\right) a{\left(n + 23 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(348758848460025 n^{4} + 13473898490178118 n^{3} + 194862831505682819 n^{2} + 1250484224896488702 n + 3004789933576024184\right) a{\left(n + 9 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(490569636724889 n^{4} + 45105655499918860 n^{3} + 1553997881354981455 n^{2} + 23775738003383202620 n + 136296239562585047536\right) a{\left(n + 22 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(2346444074798034 n^{4} + 206336302608874565 n^{3} + 6799577923848594635 n^{2} + 99519511107682276390 n + 545834376055576028616\right) a{\left(n + 21 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(3630094555768813 n^{4} + 125777357395720150 n^{3} + 1630424078767905935 n^{2} + 9372203643578247590 n + 20159590975255169952\right) a{\left(n + 8 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(8203453158346531 n^{4} + 689160780081403770 n^{3} + 21697236331187442865 n^{2} + 303409824761727229610 n + 1590028885488112522744\right) a{\left(n + 20 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(8311970392479087 n^{4} + 358184160237272270 n^{3} + 5783257171901472345 n^{2} + 41471342990958094010 n + 111456312396527578408\right) a{\left(n + 10 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(16638428888515354 n^{4} + 1204485772279886699 n^{3} + 32676565381434968557 n^{2} + 393732550996529292874 n + 1777907058352732193688\right) a{\left(n + 17 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(22239237979515378 n^{4} + 1781787882772912905 n^{3} + 53500321880765244105 n^{2} + 713516272442085562550 n + 3566225797514236108752\right) a{\left(n + 19 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(23977381979274061 n^{4} + 1828285231880450865 n^{3} + 52245026510179543165 n^{2} + 663114687876004329325 n + 3154180897223740271764\right) a{\left(n + 18 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24037746699829213 n^{4} + 1459448697300486472 n^{3} + 33202487660034853965 n^{2} + 335450145595956207498 n + 1269923832106391425216\right) a{\left(n + 14 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(27113292379320764 n^{4} + 1296511990275328095 n^{3} + 23237801894900970545 n^{2} + 185035479482980977570 n + 552329845864650211136\right) a{\left(n + 11 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(53099079041637489 n^{4} + 2781830356304083870 n^{3} + 54618207058495915195 n^{2} + 476327067725085511030 n + 1556891750600358316056\right) a{\left(n + 12 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(58283144035263622 n^{4} + 3994225567747406830 n^{3} + 102576435178103339765 n^{2} + 1169967660787598845565 n + 5000634353811311178118\right) a{\left(n + 16 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(88358984246516282 n^{4} + 5006537159581866375 n^{3} + 106297591010649121885 n^{2} + 1002305540338833025970 n + 3541494443405221672448\right) a{\left(n + 13 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(131862965169749994 n^{4} + 8525006286182077605 n^{3} + 206523326604132055205 n^{2} + 2221944349090094873850 n + 8957813130461353374296\right) a{\left(n + 15 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)}, \quad n \geq 32

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24374/
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[30,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[30,x]*F[8,x]
F[8,x] = F[155,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[30,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]+F[153,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[30,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[23,x,k[0]]
F[17,x,k[0]] = F[151,x,k[0]]+F[16,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]*F[27,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[27,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[31,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[17,x,k[0]]*F[30,x]
F[30,x] = x
F[31,x,k[0]] = k[0]*F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[30,x]*F[35,x,k[0]]
F[36,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[19,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[30,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[144,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = -k[0]*(F[37,x,1]-F[37,x,k[0]])/(-1+k[0])
F[44,x,k[0]] = F[130,x,k[0]]+F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[48,x,k[0]]
F[45,x,k[0]] = F[2,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[13,x,k[0]]*F[27,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[30,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[126,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = -k[0]*(F[52,x,1]-F[52,x,k[0]])/(-1+k[0])
F[52,x,k[0]] = F[124,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[0,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[54,x,k[0]]+F[92,x]
F[55,x,k[0]] = F[13,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[30,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[91,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[72,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[63,x,k[0]] = F[23,x,k[0]]*F[64,x]
F[64,x] = F[1,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[30,x]*F[64,x]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[30,x]*F[55,x,k[0]]*F[64,x]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[30,x]*F[59,x,k[0]]*F[71,x]
F[71,x] = F[64,x]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[30,x]*F[61,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[4,x]+F[46,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[30,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[13,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[89,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[87,x,k[0]]
F[84,x,k[0]] = F[17,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[30,x]*F[71,x]*F[82,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[30,x]*F[74,x,k[0]]*F[84,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[24,x,k[0]]*F[30,x]*F[78,x,k[0]]
F[91,x,k[0]] = F[67,x,k[0]]
F[92,x] = F[93,x,1]
F[93,x,k[0]] = F[94,x]+F[99,x,k[0]]
F[94,x] = 1/F[30,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[0,x]+F[97,x]
F[97,x] = 1/F[30,x]*F[98,x]
F[98,x] = F[2,x]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[27,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[123,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[122,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[118,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[106,x,k[0]]
F[105,x,k[0]] = F[24,x,k[0]]*F[97,x]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[102,x,k[0]]*F[108,x,k[0]]*F[30,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[71,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[25,x,k[0]]
F[111,x,k[0]] = F[112,x]+F[113,x,k[0]]+F[117,x,k[0]]
F[112,x] = 0
F[113,x,k[0]] = F[114,x,k[0]]*F[27,x,k[0]]
F[114,x,k[0]] = F[111,x,k[0]]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[30,x]*F[71,x]
F[117,x,k[0]] = F[110,x,k[0]]*F[30,x]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[104,x,k[0]]*F[120,x]*F[30,x]
F[120,x] = F[121,x]+F[4,x]
F[121,x] = F[5,x]
F[122,x,k[0]] = F[24,x,k[0]]*F[96,x]
F[123,x,k[0]] = F[106,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[2,x]
F[13,x,k[0]] = F[125,x,k[0]]+F[94,x]
F[126,x,k[0]] = F[0,x]*F[127,x,k[0]]
F[128,x,k[0]] = F[127,x,k[0]]+F[143,x,k[0]]
F[129,x,k[0]] = F[128,x,k[0]]*F[30,x]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[27,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[139,x,k[0]]
F[133,x,k[0]] = (F[134,x,k[0]]-F[134,x,1])/(-1+k[0])
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[27,x,k[0]]
F[137,x,k[0]] = F[136,x,k[0]]*F[27,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[78,x,k[0]] = F[138,x,k[0]]+F[93,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = 1/(-1+k[0])*(F[141,x,k[0]]*k[0]-F[141,x,1])
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[101,x,k[0]]*F[30,x]
F[143,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]*F[27,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[147,x,k[0]] = F[21,x,k[0]]*F[74,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[24,x,k[0]]
F[150,x,k[0]] = k[0]*F[76,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[27,x,k[0]]*F[84,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[30,x]*F[81,x,k[0]]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[30,x]*F[97,x]
F[157,x] = F[158,x]+F[161,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[23,x,1]
F[160,x] = F[9,x]
F[161,x] = F[9,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_{30}\! \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_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{155}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x , y\right) = y F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{92}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{30}\! \left(x \right) F_{64}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{55}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{59}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{61}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{74}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{92}\! \left(x \right) = F_{93}\! \left(x , 1\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{2}\! \left(x \right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{97}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{108}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{71}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{112}\! \left(x \right) = 0
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{120}\! \left(x \right) F_{30}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{5}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{96}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{127}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = -\frac{-F_{134}\! \left(x , y\right)+F_{134}\! \left(x , 1\right)}{-1+y}
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = -\frac{-y F_{141}\! \left(x , y\right)+F_{141}\! \left(x , 1\right)}{-1+y}
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{143}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = y F_{76}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{30}\! \left(x \right) F_{97}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{161}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{160}\! \left(x \right) = F_{9}\! \left(x \right)
F_{161}\! \left(x \right) = F_{9}\! \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_30(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_30(x)*F_8(x))
Eq(F_8(x), F_155(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_30(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0) + F_153(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_30(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_23(x, k_0))
Eq(F_17(x, k_0), F_151(x, k_0) + F_16(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0)*F_27(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_27(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_31(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_17(x, k_0)*F_30(x))
Eq(F_30(x), x)
Eq(F_31(x, k_0), k_0*F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_30(x)*F_35(x, k_0))
Eq(F_36(x, k_0), F_27(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_19(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_144(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), -F_37(x, 1) + (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_130(x, k_0) + F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_48(x, k_0))
Eq(F_45(x, k_0), F_2(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_13(x, k_0)*F_27(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_30(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_126(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), -F_52(x, 1) + (k_0*F_52(x, k_0) - F_52(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_124(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_0(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_54(x, k_0) + F_92(x))
Eq(F_55(x, k_0), F_13(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_30(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_91(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_72(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_63(x, k_0), F_23(x, k_0)*F_64(x))
Eq(F_64(x), F_1(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_30(x)*F_64(x))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x)*F_55(x, k_0)*F_64(x))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_30(x)*F_59(x, k_0)*F_71(x))
Eq(F_71(x), F_64(x))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_30(x)*F_61(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_4(x) + F_46(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_30(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_13(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_89(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_87(x, k_0))
Eq(F_84(x, k_0), F_17(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_30(x)*F_71(x)*F_82(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_30(x)*F_74(x, k_0)*F_84(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_24(x, k_0)*F_30(x)*F_78(x, k_0))
Eq(F_91(x, k_0), F_67(x, k_0))
Eq(F_92(x), F_93(x, 1))
Eq(F_93(x, k_0), F_94(x) + F_99(x, k_0))
Eq(F_94(x), F_95(x)/F_30(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), -F_0(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_30(x))
Eq(F_98(x), F_2(x))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_27(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_123(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_122(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_118(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_106(x, k_0))
Eq(F_105(x, k_0), F_24(x, k_0)*F_97(x))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_102(x, k_0)*F_108(x, k_0)*F_30(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_71(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_25(x, k_0))
Eq(F_111(x, k_0), F_112(x) + F_113(x, k_0) + F_117(x, k_0))
Eq(F_112(x), 0)
Eq(F_113(x, k_0), F_114(x, k_0)*F_27(x, k_0))
Eq(F_114(x, k_0), F_111(x, k_0) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_30(x)*F_71(x))
Eq(F_117(x, k_0), F_110(x, k_0)*F_30(x))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_104(x, k_0)*F_120(x)*F_30(x))
Eq(F_120(x), F_121(x) + F_4(x))
Eq(F_121(x), F_5(x))
Eq(F_122(x, k_0), F_24(x, k_0)*F_96(x))
Eq(F_123(x, k_0), F_106(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_2(x))
Eq(F_13(x, k_0), F_125(x, k_0) + F_94(x))
Eq(F_126(x, k_0), F_0(x)*F_127(x, k_0))
Eq(F_128(x, k_0), F_127(x, k_0) + F_143(x, k_0))
Eq(F_129(x, k_0), F_128(x, k_0)*F_30(x))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_27(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_139(x, k_0))
Eq(F_133(x, k_0), -F_134(x, k_0) + (k_0*F_134(x, k_0) - F_134(x, 1))/(k_0 - 1))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_27(x, k_0))
Eq(F_137(x, k_0), F_136(x, k_0)*F_27(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_78(x, k_0), F_138(x, k_0) + F_93(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), (k_0*F_141(x, k_0) - F_141(x, 1))/(k_0 - 1))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_101(x, k_0)*F_30(x))
Eq(F_143(x, k_0), -F_54(x, 1) + (k_0*F_54(x, k_0) - F_54(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0)*F_27(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_147(x, k_0), F_21(x, k_0)*F_74(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_24(x, k_0))
Eq(F_150(x, k_0), k_0*F_76(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_27(x, k_0)*F_84(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_30(x)*F_81(x, k_0))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_30(x)*F_97(x))
Eq(F_157(x), F_158(x) + F_161(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_23(x, 1))
Eq(F_160(x), F_9(x))
Eq(F_161(x), F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "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]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "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]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 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1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[4, 1]]}]}}]}, {"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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24530/
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[30,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[30,x]*F[8,x]
F[8,x] = F[164,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[30,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]+F[162,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[30,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[23,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]+F[160,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]*F[27,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[27,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[31,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[17,x,k[0]]*F[30,x]
F[30,x] = x
F[31,x,k[0]] = k[0]*F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[30,x]*F[35,x,k[0]]
F[36,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[19,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[30,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[153,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = -k[0]*(F[37,x,1]-F[37,x,k[0]])/(-1+k[0])
F[44,x,k[0]] = F[139,x,k[0]]+F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[48,x,k[0]]
F[45,x,k[0]] = F[2,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[13,x,k[0]]*F[27,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[30,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[135,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = -k[0]*(F[52,x,1]-F[52,x,k[0]])/(-1+k[0])
F[52,x,k[0]] = F[133,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[0,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[54,x,k[0]]+F[95,x]
F[55,x,k[0]] = F[13,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[30,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[94,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[72,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[63,x,k[0]] = F[23,x,k[0]]*F[64,x]
F[64,x] = F[1,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[30,x]*F[64,x]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[30,x]*F[55,x,k[0]]*F[64,x]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[30,x]*F[59,x,k[0]]*F[71,x]
F[71,x] = F[64,x]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[30,x]*F[61,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[4,x]+F[46,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[30,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[13,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[92,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[89,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[17,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[30,x]*F[71,x]*F[82,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[30,x]*F[85,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[74,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[24,x,k[0]]*F[30,x]*F[78,x,k[0]]
F[94,x,k[0]] = F[67,x,k[0]]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = F[102,x,k[0]]+F[97,x]
F[97,x] = 1/F[30,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = -F[0,x]+F[100,x]
F[100,x] = 1/F[30,x]*F[101,x]
F[101,x] = F[2,x]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[27,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[132,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[131,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[127,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[111,x,k[0]]
F[110,x,k[0]] = F[100,x]*F[24,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[114,x,k[0]]*F[30,x]
F[113,x,k[0]] = F[105,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[119,x,k[0]]
F[115,x,k[0]] = F[1,x]+F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[115,x,k[0]]*F[118,x,k[0]]
F[118,x,k[0]] = k[0]*x
F[119,x,k[0]] = F[120,x]+F[122,x,k[0]]
F[120,x] = F[121,x]
F[121,x] = F[30,x]*F[71,x]
F[122,x,k[0]] = F[123,x]+F[124,x,k[0]]+F[126,x,k[0]]
F[123,x] = 0
F[124,x,k[0]] = F[125,x,k[0]]*F[30,x]
F[125,x,k[0]] = F[116,x,k[0]]+F[122,x,k[0]]
F[126,x,k[0]] = F[118,x,k[0]]*F[119,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[108,x,k[0]]*F[129,x]*F[30,x]
F[129,x] = F[130,x]+F[4,x]
F[130,x] = F[5,x]
F[131,x,k[0]] = F[24,x,k[0]]*F[99,x]
F[132,x,k[0]] = F[111,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[2,x]
F[13,x,k[0]] = F[134,x,k[0]]+F[97,x]
F[135,x,k[0]] = F[0,x]*F[136,x,k[0]]
F[137,x,k[0]] = F[136,x,k[0]]+F[152,x,k[0]]
F[138,x,k[0]] = F[137,x,k[0]]*F[30,x]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[27,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[148,x,k[0]]
F[142,x,k[0]] = (F[143,x,k[0]]-F[143,x,1])/(-1+k[0])
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]*F[27,x,k[0]]
F[146,x,k[0]] = F[145,x,k[0]]*F[27,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[78,x,k[0]] = F[147,x,k[0]]+F[96,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[150,x,k[0]]*k[0]-F[150,x,1])
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[104,x,k[0]]*F[30,x]
F[152,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[27,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[157,x,k[0]]
F[156,x,k[0]] = F[21,x,k[0]]*F[74,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[24,x,k[0]]
F[159,x,k[0]] = k[0]*F[76,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[27,x,k[0]]*F[86,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[30,x]*F[81,x,k[0]]
F[164,x] = F[165,x]
F[165,x] = F[100,x]*F[166,x]*F[30,x]
F[166,x] = F[167,x]+F[170,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[23,x,1]
F[169,x] = F[9,x]
F[170,x] = F[9,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_{30}\! \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_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{164}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x , y\right) = y F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{30}\! \left(x \right) F_{64}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{55}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{59}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{61}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{85}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{2}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{131}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{100}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{114}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = y x
F_{119}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{122}\! \left(x , y\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{123}\! \left(x \right) = 0
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{119}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{129}\! \left(x \right) F_{30}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{5}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{99}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{136}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = -\frac{-F_{143}\! \left(x , y\right)+F_{143}\! \left(x , 1\right)}{-1+y}
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{150}\! \left(x , y\right)+F_{150}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{152}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = y F_{76}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{100}\! \left(x \right) F_{166}\! \left(x \right) F_{30}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{170}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{9}\! \left(x \right)
F_{170}\! \left(x \right) = F_{9}\! \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_30(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_30(x)*F_8(x))
Eq(F_8(x), F_164(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_30(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0) + F_162(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_30(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_23(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0) + F_160(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0)*F_27(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_27(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_31(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_17(x, k_0)*F_30(x))
Eq(F_30(x), x)
Eq(F_31(x, k_0), k_0*F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_30(x)*F_35(x, k_0))
Eq(F_36(x, k_0), F_27(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_19(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_153(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), -F_37(x, 1) + (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_139(x, k_0) + F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_48(x, k_0))
Eq(F_45(x, k_0), F_2(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_13(x, k_0)*F_27(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_30(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_135(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), -F_52(x, 1) + (k_0*F_52(x, k_0) - F_52(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_133(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_0(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_54(x, k_0) + F_95(x))
Eq(F_55(x, k_0), F_13(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_30(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_94(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_72(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_63(x, k_0), F_23(x, k_0)*F_64(x))
Eq(F_64(x), F_1(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_30(x)*F_64(x))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x)*F_55(x, k_0)*F_64(x))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_30(x)*F_59(x, k_0)*F_71(x))
Eq(F_71(x), F_64(x))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_30(x)*F_61(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_4(x) + F_46(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_30(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_13(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_92(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_89(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_17(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_30(x)*F_71(x)*F_82(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_30(x)*F_85(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_74(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_24(x, k_0)*F_30(x)*F_78(x, k_0))
Eq(F_94(x, k_0), F_67(x, k_0))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), F_102(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x)/F_30(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), -F_0(x) + F_100(x))
Eq(F_100(x), F_101(x)/F_30(x))
Eq(F_101(x), F_2(x))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_27(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_132(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_131(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_127(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_111(x, k_0))
Eq(F_110(x, k_0), F_100(x)*F_24(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_114(x, k_0)*F_30(x))
Eq(F_113(x, k_0), F_105(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_119(x, k_0))
Eq(F_115(x, k_0), F_1(x) + F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_115(x, k_0)*F_118(x, k_0))
Eq(F_118(x, k_0), k_0*x)
Eq(F_119(x, k_0), F_120(x) + F_122(x, k_0))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_30(x)*F_71(x))
Eq(F_122(x, k_0), F_123(x) + F_124(x, k_0) + F_126(x, k_0))
Eq(F_123(x), 0)
Eq(F_124(x, k_0), F_125(x, k_0)*F_30(x))
Eq(F_125(x, k_0), F_116(x, k_0) + F_122(x, k_0))
Eq(F_126(x, k_0), F_118(x, k_0)*F_119(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_108(x, k_0)*F_129(x)*F_30(x))
Eq(F_129(x), F_130(x) + F_4(x))
Eq(F_130(x), F_5(x))
Eq(F_131(x, k_0), F_24(x, k_0)*F_99(x))
Eq(F_132(x, k_0), F_111(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_2(x))
Eq(F_13(x, k_0), F_134(x, k_0) + F_97(x))
Eq(F_135(x, k_0), F_0(x)*F_136(x, k_0))
Eq(F_137(x, k_0), F_136(x, k_0) + F_152(x, k_0))
Eq(F_138(x, k_0), F_137(x, k_0)*F_30(x))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_27(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_148(x, k_0))
Eq(F_142(x, k_0), -F_143(x, k_0) + (k_0*F_143(x, k_0) - F_143(x, 1))/(k_0 - 1))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0)*F_27(x, k_0))
Eq(F_146(x, k_0), F_145(x, k_0)*F_27(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_78(x, k_0), F_147(x, k_0) + F_96(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), (k_0*F_150(x, k_0) - F_150(x, 1))/(k_0 - 1))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_104(x, k_0)*F_30(x))
Eq(F_152(x, k_0), -F_54(x, 1) + (k_0*F_54(x, k_0) - F_54(x, 1))/(k_0 - 1))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_27(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_157(x, k_0))
Eq(F_156(x, k_0), F_21(x, k_0)*F_74(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_24(x, k_0))
Eq(F_159(x, k_0), k_0*F_76(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_27(x, k_0)*F_86(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_30(x)*F_81(x, k_0))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_100(x)*F_166(x)*F_30(x))
Eq(F_166(x), F_167(x) + F_170(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_23(x, 1))
Eq(F_169(x), F_9(x))
Eq(F_170(x), F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24804/
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[30,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[30,x]*F[8,x]
F[8,x] = F[164,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[30,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]+F[162,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[30,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[23,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]+F[160,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]*F[27,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[27,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[31,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[17,x,k[0]]*F[30,x]
F[30,x] = x
F[31,x,k[0]] = k[0]*F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[30,x]*F[35,x,k[0]]
F[36,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[19,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[30,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[153,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = -k[0]*(F[37,x,1]-F[37,x,k[0]])/(-1+k[0])
F[44,x,k[0]] = F[139,x,k[0]]+F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[48,x,k[0]]
F[45,x,k[0]] = F[2,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[13,x,k[0]]*F[27,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[30,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[135,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = -k[0]*(F[52,x,1]-F[52,x,k[0]])/(-1+k[0])
F[52,x,k[0]] = F[133,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[0,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[54,x,k[0]]+F[95,x]
F[55,x,k[0]] = F[13,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[30,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[94,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[72,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[63,x,k[0]] = F[23,x,k[0]]*F[64,x]
F[64,x] = F[1,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[30,x]*F[64,x]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[30,x]*F[55,x,k[0]]*F[64,x]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[30,x]*F[59,x,k[0]]*F[71,x]
F[71,x] = F[64,x]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[30,x]*F[61,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[4,x]+F[46,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[30,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[13,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[92,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[89,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[17,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[30,x]*F[71,x]*F[82,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[30,x]*F[85,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[74,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[24,x,k[0]]*F[30,x]*F[78,x,k[0]]
F[94,x,k[0]] = F[67,x,k[0]]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = F[102,x,k[0]]+F[97,x]
F[97,x] = 1/F[30,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = -F[0,x]+F[100,x]
F[100,x] = 1/F[30,x]*F[101,x]
F[101,x] = F[2,x]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[27,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[132,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[131,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[127,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[111,x,k[0]]
F[110,x,k[0]] = F[100,x]*F[24,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[114,x,k[0]]*F[30,x]
F[113,x,k[0]] = F[105,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[119,x,k[0]]
F[115,x,k[0]] = F[1,x]+F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[115,x,k[0]]*F[118,x,k[0]]
F[118,x,k[0]] = k[0]*x
F[119,x,k[0]] = F[120,x]+F[122,x,k[0]]
F[120,x] = F[121,x]
F[121,x] = F[30,x]*F[71,x]
F[122,x,k[0]] = F[123,x]+F[124,x,k[0]]+F[126,x,k[0]]
F[123,x] = 0
F[124,x,k[0]] = F[125,x,k[0]]*F[30,x]
F[125,x,k[0]] = F[116,x,k[0]]+F[122,x,k[0]]
F[126,x,k[0]] = F[118,x,k[0]]*F[119,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[108,x,k[0]]*F[129,x]*F[30,x]
F[129,x] = F[130,x]+F[4,x]
F[130,x] = F[5,x]
F[131,x,k[0]] = F[24,x,k[0]]*F[99,x]
F[132,x,k[0]] = F[111,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[2,x]
F[13,x,k[0]] = F[134,x,k[0]]+F[97,x]
F[135,x,k[0]] = F[0,x]*F[136,x,k[0]]
F[137,x,k[0]] = F[136,x,k[0]]+F[152,x,k[0]]
F[138,x,k[0]] = F[137,x,k[0]]*F[30,x]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[27,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[148,x,k[0]]
F[142,x,k[0]] = (F[143,x,k[0]]-F[143,x,1])/(-1+k[0])
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]*F[27,x,k[0]]
F[146,x,k[0]] = F[145,x,k[0]]*F[27,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[78,x,k[0]] = F[147,x,k[0]]+F[96,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[150,x,k[0]]*k[0]-F[150,x,1])
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[104,x,k[0]]*F[30,x]
F[152,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[27,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[157,x,k[0]]
F[156,x,k[0]] = F[21,x,k[0]]*F[74,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[24,x,k[0]]
F[159,x,k[0]] = k[0]*F[76,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[27,x,k[0]]*F[86,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[30,x]*F[81,x,k[0]]
F[164,x] = F[165,x]
F[165,x] = F[100,x]*F[166,x]*F[30,x]
F[166,x] = F[167,x]+F[170,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[23,x,1]
F[169,x] = F[9,x]
F[170,x] = F[9,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_{30}\! \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_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{164}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x , y\right) = y F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{30}\! \left(x \right) F_{64}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{55}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{59}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{61}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{85}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{2}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{131}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{100}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{114}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = y x
F_{119}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{122}\! \left(x , y\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{123}\! \left(x \right) = 0
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{119}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{129}\! \left(x \right) F_{30}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{5}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{99}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{136}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = -\frac{-F_{143}\! \left(x , y\right)+F_{143}\! \left(x , 1\right)}{-1+y}
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{150}\! \left(x , y\right)+F_{150}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{152}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = y F_{76}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{100}\! \left(x \right) F_{166}\! \left(x \right) F_{30}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{170}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{9}\! \left(x \right)
F_{170}\! \left(x \right) = F_{9}\! \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_30(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_30(x)*F_8(x))
Eq(F_8(x), F_164(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_30(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0) + F_162(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_30(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_23(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0) + F_160(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0)*F_27(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_27(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_31(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_17(x, k_0)*F_30(x))
Eq(F_30(x), x)
Eq(F_31(x, k_0), k_0*F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_30(x)*F_35(x, k_0))
Eq(F_36(x, k_0), F_27(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_19(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_30(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_153(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), -F_37(x, 1) + (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_139(x, k_0) + F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_48(x, k_0))
Eq(F_45(x, k_0), F_2(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_13(x, k_0)*F_27(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_30(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_135(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), -F_52(x, 1) + (k_0*F_52(x, k_0) - F_52(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_133(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_0(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_54(x, k_0) + F_95(x))
Eq(F_55(x, k_0), F_13(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_30(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_94(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_72(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_63(x, k_0), F_23(x, k_0)*F_64(x))
Eq(F_64(x), F_1(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_30(x)*F_64(x))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x)*F_55(x, k_0)*F_64(x))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_30(x)*F_59(x, k_0)*F_71(x))
Eq(F_71(x), F_64(x))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_30(x)*F_61(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_4(x) + F_46(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_30(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_13(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_92(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_89(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_17(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_30(x)*F_71(x)*F_82(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_30(x)*F_85(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_74(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_24(x, k_0)*F_30(x)*F_78(x, k_0))
Eq(F_94(x, k_0), F_67(x, k_0))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), F_102(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x)/F_30(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), -F_0(x) + F_100(x))
Eq(F_100(x), F_101(x)/F_30(x))
Eq(F_101(x), F_2(x))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_27(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_132(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_131(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_127(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_111(x, k_0))
Eq(F_110(x, k_0), F_100(x)*F_24(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_114(x, k_0)*F_30(x))
Eq(F_113(x, k_0), F_105(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_119(x, k_0))
Eq(F_115(x, k_0), F_1(x) + F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_115(x, k_0)*F_118(x, k_0))
Eq(F_118(x, k_0), k_0*x)
Eq(F_119(x, k_0), F_120(x) + F_122(x, k_0))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_30(x)*F_71(x))
Eq(F_122(x, k_0), F_123(x) + F_124(x, k_0) + F_126(x, k_0))
Eq(F_123(x), 0)
Eq(F_124(x, k_0), F_125(x, k_0)*F_30(x))
Eq(F_125(x, k_0), F_116(x, k_0) + F_122(x, k_0))
Eq(F_126(x, k_0), F_118(x, k_0)*F_119(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_108(x, k_0)*F_129(x)*F_30(x))
Eq(F_129(x), F_130(x) + F_4(x))
Eq(F_130(x), F_5(x))
Eq(F_131(x, k_0), F_24(x, k_0)*F_99(x))
Eq(F_132(x, k_0), F_111(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_2(x))
Eq(F_13(x, k_0), F_134(x, k_0) + F_97(x))
Eq(F_135(x, k_0), F_0(x)*F_136(x, k_0))
Eq(F_137(x, k_0), F_136(x, k_0) + F_152(x, k_0))
Eq(F_138(x, k_0), F_137(x, k_0)*F_30(x))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_27(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_148(x, k_0))
Eq(F_142(x, k_0), -F_143(x, k_0) + (k_0*F_143(x, k_0) - F_143(x, 1))/(k_0 - 1))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0)*F_27(x, k_0))
Eq(F_146(x, k_0), F_145(x, k_0)*F_27(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_78(x, k_0), F_147(x, k_0) + F_96(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), (k_0*F_150(x, k_0) - F_150(x, 1))/(k_0 - 1))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_104(x, k_0)*F_30(x))
Eq(F_152(x, k_0), -F_54(x, 1) + (k_0*F_54(x, k_0) - F_54(x, 1))/(k_0 - 1))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_27(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_157(x, k_0))
Eq(F_156(x, k_0), F_21(x, k_0)*F_74(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_24(x, k_0))
Eq(F_159(x, k_0), k_0*F_76(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_27(x, k_0)*F_86(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_30(x)*F_81(x, k_0))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_100(x)*F_166(x)*F_30(x))
Eq(F_166(x), F_167(x) + F_170(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_23(x, 1))
Eq(F_169(x), F_9(x))
Eq(F_170(x), F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "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]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 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"pos": [[0, 0], [1, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [2, 1]]}, {"patt": [1, 0, 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1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}], "strategy": 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"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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": 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"assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25529/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[54,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[28,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[13,x,k[0]]+F[6,x]
F[11,x,k[0]] = F[12,x]*F[9,x,k[0]]
F[12,x] = x
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]+F[20,x,k[0]]
F[15,x,k[0]] = F[12,x]*F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[26,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[12,x]*F[17,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[12,x]*F[24,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]*F[24,x,k[0]]
F[25,x,k[0]] = F[9,x,k[0]]
F[26,x,k[0]] = k[0]*F[27,x,k[0]]
F[27,x,k[0]] = F[23,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[12,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[42,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[12,x]*F[35,x,k[0]]*F[40,x]
F[35,x,k[0]] = -k[0]*(F[36,x,1]-F[36,x,k[0]])/(-1+k[0])
F[37,x,k[0]] = F[36,x,k[0]]+F[38,x]
F[37,x,k[0]] = F[17,x,k[0]]+F[27,x,k[0]]
F[38,x] = F[39,x]+F[4,x]
F[39,x] = F[5,x]
F[40,x] = 1/F[12,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x,k[0]] = F[43,x,k[0]]+F[45,x,k[0]]+F[6,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[12,x]*F[37,x,k[0]]*F[9,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[21,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[14,x,k[0]]*F[37,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[26,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[1,x]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[21,x,k[0]]*F[51,x,k[0]]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[4,x]*F[58,x]
F[58,x] = F[37,x,1]
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_{12}\! \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_{54}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{35}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{35}\! \left(x , y\right) = -\frac{y \left(F_{36}\! \left(x , 1\right)-F_{36}\! \left(x , y\right)\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{37}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x , 1\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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_54(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_28(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_13(x, k_0) + F_6(x))
Eq(F_11(x, k_0), F_12(x)*F_9(x, k_0))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0) + F_20(x, k_0))
Eq(F_15(x, k_0), F_12(x)*F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_26(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_12(x)*F_17(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_12(x)*F_24(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_24(x, k_0))
Eq(F_25(x, k_0), F_9(x, k_0))
Eq(F_26(x, k_0), k_0*F_27(x, k_0))
Eq(F_27(x, k_0), F_23(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_12(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_42(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_12(x)*F_35(x, k_0)*F_40(x))
Eq(F_35(x, k_0), -F_36(x, 1) + (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_36(x, k_0) + F_38(x))
Eq(F_37(x, k_0), F_17(x, k_0) + F_27(x, k_0))
Eq(F_38(x), F_39(x) + F_4(x))
Eq(F_39(x), F_5(x))
Eq(F_40(x), F_41(x)/F_12(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x, k_0), F_43(x, k_0) + F_45(x, k_0) + F_6(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_12(x)*F_37(x, k_0)*F_9(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_21(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_14(x, k_0)*F_37(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_26(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_1(x) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_21(x, k_0)*F_51(x, k_0))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_4(x)*F_58(x))
Eq(F_58(x), F_37(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "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]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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"comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25578/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[54,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[28,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[13,x,k[0]]+F[6,x]
F[11,x,k[0]] = F[12,x]*F[9,x,k[0]]
F[12,x] = x
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]+F[20,x,k[0]]
F[15,x,k[0]] = F[12,x]*F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[26,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[12,x]*F[17,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[12,x]*F[24,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]*F[24,x,k[0]]
F[25,x,k[0]] = F[9,x,k[0]]
F[26,x,k[0]] = k[0]*F[27,x,k[0]]
F[27,x,k[0]] = F[23,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[12,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[42,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[12,x]*F[35,x,k[0]]*F[40,x]
F[35,x,k[0]] = -k[0]*(F[36,x,1]-F[36,x,k[0]])/(-1+k[0])
F[37,x,k[0]] = F[36,x,k[0]]+F[38,x]
F[37,x,k[0]] = F[17,x,k[0]]+F[27,x,k[0]]
F[38,x] = F[39,x]+F[4,x]
F[39,x] = F[5,x]
F[40,x] = 1/F[12,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x,k[0]] = F[43,x,k[0]]+F[45,x,k[0]]+F[6,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[12,x]*F[37,x,k[0]]*F[9,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[21,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[14,x,k[0]]*F[37,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[26,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[1,x]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[21,x,k[0]]*F[51,x,k[0]]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[4,x]*F[58,x]
F[58,x] = F[37,x,1]
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_{12}\! \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_{54}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{35}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{35}\! \left(x , y\right) = -\frac{y \left(F_{36}\! \left(x , 1\right)-F_{36}\! \left(x , y\right)\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{37}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x , 1\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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_54(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_28(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_13(x, k_0) + F_6(x))
Eq(F_11(x, k_0), F_12(x)*F_9(x, k_0))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0) + F_20(x, k_0))
Eq(F_15(x, k_0), F_12(x)*F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_26(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_12(x)*F_17(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_12(x)*F_24(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_24(x, k_0))
Eq(F_25(x, k_0), F_9(x, k_0))
Eq(F_26(x, k_0), k_0*F_27(x, k_0))
Eq(F_27(x, k_0), F_23(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_12(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_42(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_12(x)*F_35(x, k_0)*F_40(x))
Eq(F_35(x, k_0), -F_36(x, 1) + (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_36(x, k_0) + F_38(x))
Eq(F_37(x, k_0), F_17(x, k_0) + F_27(x, k_0))
Eq(F_38(x), F_39(x) + F_4(x))
Eq(F_39(x), F_5(x))
Eq(F_40(x), F_41(x)/F_12(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x, k_0), F_43(x, k_0) + F_45(x, k_0) + F_6(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_12(x)*F_37(x, k_0)*F_9(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_21(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_14(x, k_0)*F_37(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_26(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_1(x) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_21(x, k_0)*F_51(x, k_0))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_4(x)*F_58(x))
Eq(F_58(x), F_37(x, 1))
Pack JSON:
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Specification JSON:
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