01342_10342_20341_30241
Counting sequence:
1, 1, 2, 6, 24, 116, 634, 3759, 23569, 153810, 1034041, 7112212, 49808121, 353935534, 2545458181, 18491921476, 135493249179, 1000126372718, 7429800334478, 55506586293332, 416750417952798, 3142945472515170, 23797349506568318, 180834906102671338, 1378645735410145164, 10541785683330664414, 80827154092933119269, 621278072762432007980, 4786475026915416599447, 36954866693666992840927, 285882003430924311859826, 2215652525468041980668009, 17201351332131025696075662, 133758463259998828592989409, 1041679436931590779662626233, 8123840669958478103072941908, 63440575649365412334829978158, 496041844640251766189256592350, 3883156099520194110010433903209, 30432599891923539664249229238482, 238756654116924018284507208681768, 1875040552736727796255402846718297, 14739505440210689322476121977584476, 115971731738600937703684613246031867, 913271118533233092285109398476599977, 7197941876105267896816479660518516491, 56775615141778844043955321943614237272, 448172513183539014949567992904831705458, 3540335220666017428032991245968412092847, 27986346027886212196945581326354220127768, 221379974046006263780452541431764620857437, 1752303044000347344685085759083932028718585, 13878674105857967516588472239680901701213822, 109987768377050771891422456817441216288573030, 872145240863205449169275092817212544535111518, 6919459338669008487981012651610851303792765979, 54926995553015586595174539407397887583161058748, 436236245194950694001343214543876778242530475889, 3466348206091329573271090675130310010151871375827, 27556869984979775434804938050857864193534158586547, 219173450833125149902017516876458057737940812861299, 1743973213067366321732384241178505859173354261204089, 13882869946995615992112123071791736018091282075123961, 110560593396497546847415932461481041645577808625968645, 880840940432291571545655429034305747019378086140092196, 7020455321665938364369064834515051146248287195612575451, 55975580543264932580760646702028620534626856569587215487, 446470314577973534693122248867327744105630912995922280667, 3562399014446903949364310039140420793897798716126015990947, 28434400172030936441581992494210612289707454104863300028494, 227035021283354113643546231009211292191922492407663794098381, 1813363349202737580445137420406949200758582468492424271395249, 14488255758539529313422455994283455652507954258983830472417538, 115793164496597493799856900343431659539039232170726227013963475, 925724382359911415386792672946031858270411480746316568931990575, 7403021328973562407874404547598708607003371899322287010474456937, 59219060353134599072407212609073772250628074601845388901469073705, 473844737972722037551868590230889532331869950403307426807316290589, 3792535020832698438584235618217409061092671076210666388590118726950, 30362616256550316472412852100627193973747423184473289748811374519150, 243143134692353891026858782979355615242495331432946384607457085743449, 1947580170780044867526271687575796183532748312422715375136873762141691, 15604022601688670955091733548565924944267788165166670156075027696913838, 125049848023805214563567646224954300375487813413606222208206834006847879, 1002380719169510078098571944129198764446996747532169614228521017167055278, 8036793929291804642279262993239001175073063337973508744471422514546673571, 64451241736080207197314416092616456451234190347996575263112943151560056600, 516982553046498123905551712008753626212359173686365576421435611866010272790, 4147768554538170797040080173554833116618720518514603060312857650783666994326, 33284737168703534236824631500768562442931617296878009567525831501745384225014, 267156512567461640495379146241433541835213125663576991358758461293849499890976, 2144739290160076646245844365306442540156806127838158156518110712346439546910923, 17221441971037078312945027489247206270518402683932845331543314984114231380889515, 138308538802310295851697415429216808334653317296844017935650810132949106562327336, 1110992735566335104804589141765918844312751249071101600908665831937510364481810317, 8925951341757034645397351215309819893093079959153547166381855653815995405258848049, 71726106471608426440949038103664888506748183891737127601382181132376100041509230483, 576471537641613246990286564663733940044402773495017971340724175120016552791768839463, 4633987175784518382149244543014395353533420348824396050064625552040153176119713692713, 37256894310722730789796653356318608568393864492611941155082017290672828259625141972680, 299593163863833409235355629943039503467984152536843330595826254338152449482375096936131
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25194/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[142,x]+F[9,x]
F[9,x] = F[10,x]+F[25,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]+F[2,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[7,x]
F[14,x] = F[15,x]+F[24,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[12,x]+F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]*F[7,x]
F[19,x] = F[20,x]
F[20,x] = F[7,x]*F[8,x]
F[21,x] = 1/F[23,x]/F[7,x]*F[22,x]
F[22,x] = F[15,x]
F[23,x] = F[0,x]+F[19,x]
F[24,x] = F[141,x]+F[25,x]
F[25,x] = F[19,x]+F[26,x]
F[26,x] = F[27,x,1]
F[28,x,k[0]] = F[11,x]+F[27,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[34,x,k[0]]
F[29,x,k[0]] = F[2,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[30,x,k[0]]^2*F[33,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[7,x]
F[36,x,k[0]] = F[140,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[7,x]
F[40,x,k[0]] = F[39,x,k[0]]*F[7,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[116,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[115,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[19,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[33,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[41,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[30,x,k[0]]*F[43,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[43,x,k[0]]*F[51,x,k[0]]*F[7,x]
F[51,x,k[0]] = F[37,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[60,x,k[0]]
F[53,x,k[0]] = F[4,x]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[33,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[30,x,k[0]]*F[53,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[51,x,k[0]]*F[53,x,k[0]]*F[7,x]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]*F[62,x,k[0]]
F[63,x,k[0]] = F[2,x]*F[62,x,k[0]]
F[64,x,k[0]] = F[113,x,k[0]]+F[63,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]*F[7,x]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]*F[7,x]
F[67,x,k[0]] = F[68,x,k[0]]+F[84,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[30,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[71,x]+F[79,x,k[0]]
F[71,x] = F[72,x]+F[78,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = (1+F[73,x])^2*x^3+(3*F[73,x]^2+14*F[73,x]+11)*x^2+(3*F[73,x]^2-14*F[73,x]-1)*x+F[73,x]^2+2*F[73,x]
F[74,x] = F[2,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]^2*F[7,x]
F[77,x] = F[1,x]+F[75,x]
F[78,x] = F[19,x]*F[75,x]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[70,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = F[71,x]*F[83,x,k[0]]
F[83,x,k[0]] = 1/(-1+k[0])*(F[30,x,k[0]]*k[0]-F[30,x,1])
F[85,x,k[0]] = F[109,x,k[0]]+F[84,x,k[0]]
F[85,x,k[0]] = F[101,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[104,x,k[0]]+F[87,x,k[0]]
F[88,x,k[0]] = F[33,x,k[0]]*F[87,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[90,x,k[0]] = F[0,x]+F[89,x,k[0]]
F[53,x,k[0]] = F[90,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[5,x]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[7,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[7,x]*F[95,x,k[0]]
F[96,x,k[0]] = F[44,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[33,x,k[0]]*F[99,x,k[0]]
F[100,x,k[0]] = F[7,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[102,x,k[0]] = F[101,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[33,x,k[0]]
F[103,x,k[0]] = F[44,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[30,x,k[0]]^2*F[19,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[19,x]*F[62,x,k[0]]*F[7,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[30,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[70,x,k[0]]
F[112,x,k[0]] = F[23,x]*F[30,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[7,x]*F[99,x,k[0]]
F[115,x,k[0]] = (F[27,x,k[0]]-F[27,x,1])/(-1+k[0])
F[116,x,k[0]] = (F[117,x,k[0]]-F[117,x,1])/(-1+k[0])
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[7,x]
F[120,x,k[0]] = F[119,x,k[0]]*F[7,x]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[124,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[2,x]*F[89,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]+F[27,x,k[0]]
F[126,x,k[0]] = F[125,x,k[0]]+F[138,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]+F[135,x]
F[127,x,k[0]] = F[128,x,k[0]]+F[129,x,k[0]]
F[128,x,k[0]] = F[28,x,k[0]]+F[90,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[7,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[30,x,k[0]]*F[8,x]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[51,x,k[0]]*F[7,x]*F[8,x]
F[135,x] = F[136,x]+F[4,x]
F[136,x] = F[137,x]
F[137,x] = F[21,x]*F[4,x]*F[7,x]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[0,x]*F[89,x,k[0]]
F[140,x,k[0]] = F[2,x]*F[51,x,k[0]]
F[141,x] = F[117,x,1]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[7,x]
F[144,x] = F[145,x]+F[152,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[77,x]*F[8,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[7,x]*F[8,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[52,x,1]
F[151,x] = F[37,x,1]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[182,x]*F[7,x]
F[154,x] = F[155,x]+F[156,x]
F[155,x] = 16*x+(1+x)^3*F[155,x]^2+(8*x^2-20*x)*F[155,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[7,x]
F[158,x] = F[159,x,1]
F[159,x,k[0]] = F[160,x,k[0]]+F[168,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]*F[30,x,k[0]]
F[161,x,k[0]] = F[155,x]+F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]+F[31,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[33,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[168,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[30,x,k[0]]
F[167,x,k[0]] = F[163,x,k[0]]+F[73,x]
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[161,x,k[0]]*F[170,x,k[0]]*F[7,x]
F[171,x,k[0]] = F[154,x]*F[170,x,k[0]]*F[7,x]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[180,x,k[0]]
F[173,x,k[0]] = F[167,x,k[0]]+F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]*F[7,x]
F[176,x,k[0]] = F[177,x,k[0]]+F[179,x,k[0]]
F[177,x,k[0]] = F[154,x]*F[178,x,k[0]]
F[178,x,k[0]] = (F[31,x,k[0]]-F[31,x,1])/(-1+k[0])
F[179,x,k[0]] = 1/(-1+k[0])*(F[172,x,k[0]]*k[0]-F[172,x,1])
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[156,x]*F[170,x,k[0]]*F[7,x]
F[182,x] = F[183,x,1]
F[184,x,k[0]] = F[155,x]*F[183,x,k[0]]*F[7,x]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]+F[209,x,k[0]]
F[186,x,k[0]] = F[115,x,k[0]]+F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[19,x]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[33,x,k[0]]
F[190,x,k[0]] = F[104,x,k[0]]+F[191,x,k[0]]
F[192,x,k[0]] = F[191,x,k[0]]+F[204,x,k[0]]
F[193,x,k[0]] = F[192,x,k[0]]*F[33,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[33,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[202,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[200,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[30,x,k[0]]
F[199,x,k[0]] = F[194,x,k[0]]+F[25,x]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[199,x,k[0]]*F[51,x,k[0]]*F[7,x]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[161,x,k[0]]*F[183,x,k[0]]*F[7,x]
F[204,x,k[0]] = F[205,x,k[0]]+F[207,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[30,x,k[0]]^2*F[25,x]
F[207,x,k[0]] = F[208,x,k[0]]
F[208,x,k[0]] = F[25,x]*F[62,x,k[0]]*F[7,x]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]*F[7,x]
F[211,x,k[0]] = F[212,x,k[0]]+F[213,x,k[0]]
F[212,x,k[0]] = (F[119,x,k[0]]-F[119,x,1])/(-1+k[0])
F[213,x,k[0]] = 1/(-1+k[0])*(F[214,x,k[0]]*k[0]-F[214,x,1])
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[154,x]*F[183,x,k[0]]*F[7,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{142}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right) F_{7}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{141}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = y x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{41}\! \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_{30}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{51}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{53}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = x^{3} F_{73} \left(x \right)^{2}+2 x^{3} F_{73}\! \left(x \right)+3 x^{2} F_{73} \left(x \right)^{2}+x^{3}+14 x^{2} F_{73}\! \left(x \right)+3 x F_{73} \left(x \right)^{2}+11 x^{2}-14 x F_{73}\! \left(x \right)+F_{73} \left(x \right)^{2}-x +2 F_{73}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{71}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{19}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{62}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{116}\! \left(x , y\right) = -\frac{-F_{117}\! \left(x , y\right)+F_{117}\! \left(x , 1\right)}{-1+y}
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{135}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{90}\! \left(x , y\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_{7}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{141}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{7}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{152}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{77}\! \left(x \right) F_{8}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{151}\! \left(x \right) = F_{37}\! \left(x , 1\right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{182}\! \left(x \right) F_{7}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{156}\! \left(x \right)
F_{155}\! \left(x \right) = x^{3} F_{155} \left(x \right)^{2}+3 x^{2} F_{155} \left(x \right)^{2}+8 x^{2} F_{155}\! \left(x \right)+3 x F_{155} \left(x \right)^{2}-20 x F_{155}\! \left(x \right)+F_{155} \left(x \right)^{2}+16 x
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{7}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x , 1\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{155}\! \left(x \right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = -\frac{-F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{179}\! \left(x , y\right) = -\frac{-y F_{172}\! \left(x , y\right)+F_{172}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{156}\! \left(x \right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x , 1\right)
F_{184}\! \left(x , y\right) = F_{155}\! \left(x \right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{25}\! \left(x \right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{51}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{25}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{62}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{-F_{119}\! \left(x , y\right)+F_{119}\! \left(x , 1\right)}{-1+y}
F_{213}\! \left(x , y\right) = -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_142(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_25(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x) + F_2(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_24(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_12(x) + F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x)*F_7(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_7(x)*F_8(x))
Eq(F_21(x), F_22(x)/(F_23(x)*F_7(x)))
Eq(F_22(x), F_15(x))
Eq(F_23(x), F_0(x) + F_19(x))
Eq(F_24(x), F_141(x) + F_25(x))
Eq(F_25(x), F_19(x) + F_26(x))
Eq(F_26(x), F_27(x, 1))
Eq(F_28(x, k_0), F_11(x) + F_27(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_34(x, k_0))
Eq(F_29(x, k_0), F_2(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_30(x, k_0)**2*F_33(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_7(x))
Eq(F_36(x, k_0), F_140(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_7(x))
Eq(F_40(x, k_0), F_39(x, k_0)*F_7(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_116(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_115(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_19(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_33(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_41(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_30(x, k_0)*F_43(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_43(x, k_0)*F_51(x, k_0)*F_7(x))
Eq(F_51(x, k_0), F_37(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_60(x, k_0))
Eq(F_53(x, k_0), F_4(x) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_33(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_30(x, k_0)*F_53(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_51(x, k_0)*F_53(x, k_0)*F_7(x))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0)*F_62(x, k_0))
Eq(F_63(x, k_0), F_2(x)*F_62(x, k_0))
Eq(F_64(x, k_0), F_113(x, k_0) + F_63(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0)*F_7(x))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0)*F_7(x))
Eq(F_67(x, k_0), F_68(x, k_0) + F_84(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_30(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x) + F_79(x, k_0))
Eq(F_71(x), F_72(x) + F_78(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), 16*x + (x + 1)**3*(F_73(x) + 1)**2 + (F_73(x) + 1)*(8*x**2 - 20*x - 1) + F_73(x))
Eq(F_74(x), F_2(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_7(x)*F_77(x)**2)
Eq(F_77(x), F_1(x) + F_75(x))
Eq(F_78(x), F_19(x)*F_75(x))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_30(x, k_0)*F_33(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_70(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), F_71(x)*F_83(x, k_0))
Eq(F_83(x, k_0), (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_85(x, k_0), F_109(x, k_0) + F_84(x, k_0))
Eq(F_85(x, k_0), F_101(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_104(x, k_0) + F_87(x, k_0))
Eq(F_88(x, k_0), F_33(x, k_0)*F_87(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_90(x, k_0), F_0(x) + F_89(x, k_0))
Eq(F_53(x, k_0), F_90(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_5(x) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_7(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_7(x)*F_95(x, k_0))
Eq(F_96(x, k_0), F_44(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_33(x, k_0)*F_99(x, k_0))
Eq(F_100(x, k_0), F_7(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_102(x, k_0), F_101(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_33(x, k_0))
Eq(F_103(x, k_0), F_44(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_107(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_19(x)*F_30(x, k_0)**2)
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_19(x)*F_62(x, k_0)*F_7(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_30(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_70(x, k_0))
Eq(F_112(x, k_0), F_23(x)*F_30(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_7(x)*F_99(x, k_0))
Eq(F_115(x, k_0), -F_27(x, k_0) + (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_116(x, k_0), -F_117(x, k_0) + (k_0*F_117(x, k_0) - F_117(x, 1))/(k_0 - 1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_7(x))
Eq(F_120(x, k_0), F_119(x, k_0)*F_7(x))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_124(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_2(x)*F_89(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0) + F_27(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0) + F_138(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0) + F_135(x))
Eq(F_127(x, k_0), F_128(x, k_0) + F_129(x, k_0))
Eq(F_128(x, k_0), F_28(x, k_0) + F_90(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_7(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_30(x, k_0)*F_8(x))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_51(x, k_0)*F_7(x)*F_8(x))
Eq(F_135(x), F_136(x) + F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_21(x)*F_4(x)*F_7(x))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_0(x)*F_89(x, k_0))
Eq(F_140(x, k_0), F_2(x)*F_51(x, k_0))
Eq(F_141(x), F_117(x, 1))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_7(x))
Eq(F_144(x), F_145(x) + F_152(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_77(x)*F_8(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_7(x)*F_8(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_52(x, 1))
Eq(F_151(x), F_37(x, 1))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_182(x)*F_7(x))
Eq(F_154(x), F_155(x) + F_156(x))
Eq(F_155(x), 16*x + (x + 1)**3*F_155(x)**2 + (8*x**2 - 20*x)*F_155(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_7(x))
Eq(F_158(x), F_159(x, 1))
Eq(F_159(x, k_0), F_160(x, k_0) + F_168(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0)*F_30(x, k_0))
Eq(F_161(x, k_0), F_155(x) + F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0) + F_31(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_33(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_168(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_30(x, k_0))
Eq(F_167(x, k_0), F_163(x, k_0) + F_73(x))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_161(x, k_0)*F_170(x, k_0)*F_7(x))
Eq(F_171(x, k_0), F_154(x)*F_170(x, k_0)*F_7(x))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_180(x, k_0))
Eq(F_173(x, k_0), F_167(x, k_0) + F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0)*F_7(x))
Eq(F_176(x, k_0), F_177(x, k_0) + F_179(x, k_0))
Eq(F_177(x, k_0), F_154(x)*F_178(x, k_0))
Eq(F_178(x, k_0), -F_31(x, k_0) + (k_0*F_31(x, k_0) - F_31(x, 1))/(k_0 - 1))
Eq(F_179(x, k_0), (k_0*F_172(x, k_0) - F_172(x, 1))/(k_0 - 1))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_156(x)*F_170(x, k_0)*F_7(x))
Eq(F_182(x), F_183(x, 1))
Eq(F_184(x, k_0), F_155(x)*F_183(x, k_0)*F_7(x))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0) + F_209(x, k_0))
Eq(F_186(x, k_0), F_115(x, k_0) + F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_19(x))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_33(x, k_0))
Eq(F_190(x, k_0), F_104(x, k_0) + F_191(x, k_0))
Eq(F_192(x, k_0), F_191(x, k_0) + F_204(x, k_0))
Eq(F_193(x, k_0), F_192(x, k_0)*F_33(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_33(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_202(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_200(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_30(x, k_0))
Eq(F_199(x, k_0), F_194(x, k_0) + F_25(x))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_199(x, k_0)*F_51(x, k_0)*F_7(x))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_161(x, k_0)*F_183(x, k_0)*F_7(x))
Eq(F_204(x, k_0), F_205(x, k_0) + F_207(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_25(x)*F_30(x, k_0)**2)
Eq(F_207(x, k_0), F_208(x, k_0))
Eq(F_208(x, k_0), F_25(x)*F_62(x, k_0)*F_7(x))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0)*F_7(x))
Eq(F_211(x, k_0), F_212(x, k_0) + F_213(x, k_0))
Eq(F_212(x, k_0), -F_119(x, k_0) + (k_0*F_119(x, k_0) - F_119(x, 1))/(k_0 - 1))
Eq(F_213(x, k_0), (k_0*F_214(x, k_0) - F_214(x, 1))/(k_0 - 1))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_154(x)*F_183(x, k_0)*F_7(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": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [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": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, 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"pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}}, {"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"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25411/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[142,x]+F[9,x]
F[9,x] = F[10,x]+F[25,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]+F[2,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[7,x]
F[14,x] = F[15,x]+F[24,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[12,x]+F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]*F[7,x]
F[19,x] = F[20,x]
F[20,x] = F[7,x]*F[8,x]
F[21,x] = 1/F[23,x]/F[7,x]*F[22,x]
F[22,x] = F[15,x]
F[23,x] = F[0,x]+F[19,x]
F[24,x] = F[141,x]+F[25,x]
F[25,x] = F[19,x]+F[26,x]
F[26,x] = F[27,x,1]
F[28,x,k[0]] = F[11,x]+F[27,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[34,x,k[0]]
F[29,x,k[0]] = F[2,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[30,x,k[0]]^2*F[33,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[7,x]
F[36,x,k[0]] = F[140,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[7,x]
F[40,x,k[0]] = F[39,x,k[0]]*F[7,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[116,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[115,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[19,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[33,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[41,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[30,x,k[0]]*F[43,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[43,x,k[0]]*F[51,x,k[0]]*F[7,x]
F[51,x,k[0]] = F[37,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[60,x,k[0]]
F[53,x,k[0]] = F[4,x]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[33,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[30,x,k[0]]*F[53,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[51,x,k[0]]*F[53,x,k[0]]*F[7,x]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]*F[62,x,k[0]]
F[63,x,k[0]] = F[2,x]*F[62,x,k[0]]
F[64,x,k[0]] = F[113,x,k[0]]+F[63,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]*F[7,x]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]*F[7,x]
F[67,x,k[0]] = F[68,x,k[0]]+F[84,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[30,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[71,x]+F[79,x,k[0]]
F[71,x] = F[72,x]+F[78,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = (1+F[73,x])^2*x^3+(3*F[73,x]^2+14*F[73,x]+11)*x^2+(3*F[73,x]^2-14*F[73,x]-1)*x+F[73,x]^2+2*F[73,x]
F[74,x] = F[2,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]^2*F[7,x]
F[77,x] = F[1,x]+F[75,x]
F[78,x] = F[19,x]*F[75,x]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[70,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = F[71,x]*F[83,x,k[0]]
F[83,x,k[0]] = 1/(-1+k[0])*(F[30,x,k[0]]*k[0]-F[30,x,1])
F[85,x,k[0]] = F[109,x,k[0]]+F[84,x,k[0]]
F[85,x,k[0]] = F[101,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[104,x,k[0]]+F[87,x,k[0]]
F[88,x,k[0]] = F[33,x,k[0]]*F[87,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[90,x,k[0]] = F[0,x]+F[89,x,k[0]]
F[53,x,k[0]] = F[90,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[5,x]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[7,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[7,x]*F[95,x,k[0]]
F[96,x,k[0]] = F[44,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[33,x,k[0]]*F[99,x,k[0]]
F[100,x,k[0]] = F[7,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[102,x,k[0]] = F[101,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[33,x,k[0]]
F[103,x,k[0]] = F[44,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[30,x,k[0]]^2*F[19,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[19,x]*F[62,x,k[0]]*F[7,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[30,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[70,x,k[0]]
F[112,x,k[0]] = F[23,x]*F[30,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[7,x]*F[99,x,k[0]]
F[115,x,k[0]] = (F[27,x,k[0]]-F[27,x,1])/(-1+k[0])
F[116,x,k[0]] = (F[117,x,k[0]]-F[117,x,1])/(-1+k[0])
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[7,x]
F[120,x,k[0]] = F[119,x,k[0]]*F[7,x]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[124,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[2,x]*F[89,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]+F[27,x,k[0]]
F[126,x,k[0]] = F[125,x,k[0]]+F[138,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]+F[135,x]
F[127,x,k[0]] = F[128,x,k[0]]+F[129,x,k[0]]
F[128,x,k[0]] = F[28,x,k[0]]+F[90,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[7,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[30,x,k[0]]*F[8,x]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[51,x,k[0]]*F[7,x]*F[8,x]
F[135,x] = F[136,x]+F[4,x]
F[136,x] = F[137,x]
F[137,x] = F[21,x]*F[4,x]*F[7,x]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[0,x]*F[89,x,k[0]]
F[140,x,k[0]] = F[2,x]*F[51,x,k[0]]
F[141,x] = F[117,x,1]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[7,x]
F[144,x] = F[145,x]+F[152,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[77,x]*F[8,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[7,x]*F[8,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[52,x,1]
F[151,x] = F[37,x,1]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[182,x]*F[7,x]
F[154,x] = F[155,x]+F[156,x]
F[155,x] = 16*x+(1+x)^3*F[155,x]^2+(8*x^2-20*x)*F[155,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[7,x]
F[158,x] = F[159,x,1]
F[159,x,k[0]] = F[160,x,k[0]]+F[168,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]*F[30,x,k[0]]
F[161,x,k[0]] = F[155,x]+F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]+F[31,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[33,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[168,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[30,x,k[0]]
F[167,x,k[0]] = F[163,x,k[0]]+F[73,x]
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[161,x,k[0]]*F[170,x,k[0]]*F[7,x]
F[171,x,k[0]] = F[154,x]*F[170,x,k[0]]*F[7,x]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[180,x,k[0]]
F[173,x,k[0]] = F[167,x,k[0]]+F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]*F[7,x]
F[176,x,k[0]] = F[177,x,k[0]]+F[179,x,k[0]]
F[177,x,k[0]] = F[154,x]*F[178,x,k[0]]
F[178,x,k[0]] = (F[31,x,k[0]]-F[31,x,1])/(-1+k[0])
F[179,x,k[0]] = 1/(-1+k[0])*(F[172,x,k[0]]*k[0]-F[172,x,1])
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[156,x]*F[170,x,k[0]]*F[7,x]
F[182,x] = F[183,x,1]
F[184,x,k[0]] = F[155,x]*F[183,x,k[0]]*F[7,x]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]+F[209,x,k[0]]
F[186,x,k[0]] = F[115,x,k[0]]+F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[19,x]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[33,x,k[0]]
F[190,x,k[0]] = F[104,x,k[0]]+F[191,x,k[0]]
F[192,x,k[0]] = F[191,x,k[0]]+F[204,x,k[0]]
F[193,x,k[0]] = F[192,x,k[0]]*F[33,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[33,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[202,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[200,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[30,x,k[0]]
F[199,x,k[0]] = F[194,x,k[0]]+F[25,x]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[199,x,k[0]]*F[51,x,k[0]]*F[7,x]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[161,x,k[0]]*F[183,x,k[0]]*F[7,x]
F[204,x,k[0]] = F[205,x,k[0]]+F[207,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[30,x,k[0]]^2*F[25,x]
F[207,x,k[0]] = F[208,x,k[0]]
F[208,x,k[0]] = F[25,x]*F[62,x,k[0]]*F[7,x]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]*F[7,x]
F[211,x,k[0]] = F[212,x,k[0]]+F[213,x,k[0]]
F[212,x,k[0]] = (F[119,x,k[0]]-F[119,x,1])/(-1+k[0])
F[213,x,k[0]] = 1/(-1+k[0])*(F[214,x,k[0]]*k[0]-F[214,x,1])
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[154,x]*F[183,x,k[0]]*F[7,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{142}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right) F_{7}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{141}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = y x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{41}\! \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_{30}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{51}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{53}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = x^{3} F_{73} \left(x \right)^{2}+2 x^{3} F_{73}\! \left(x \right)+3 x^{2} F_{73} \left(x \right)^{2}+x^{3}+14 x^{2} F_{73}\! \left(x \right)+3 x F_{73} \left(x \right)^{2}+11 x^{2}-14 x F_{73}\! \left(x \right)+F_{73} \left(x \right)^{2}-x +2 F_{73}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{71}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{19}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{62}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{116}\! \left(x , y\right) = -\frac{-F_{117}\! \left(x , y\right)+F_{117}\! \left(x , 1\right)}{-1+y}
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{135}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{90}\! \left(x , y\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_{7}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{141}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{7}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{152}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{77}\! \left(x \right) F_{8}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{151}\! \left(x \right) = F_{37}\! \left(x , 1\right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{182}\! \left(x \right) F_{7}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{156}\! \left(x \right)
F_{155}\! \left(x \right) = x^{3} F_{155} \left(x \right)^{2}+3 x^{2} F_{155} \left(x \right)^{2}+8 x^{2} F_{155}\! \left(x \right)+3 x F_{155} \left(x \right)^{2}-20 x F_{155}\! \left(x \right)+F_{155} \left(x \right)^{2}+16 x
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{7}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x , 1\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{155}\! \left(x \right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = -\frac{-F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{179}\! \left(x , y\right) = -\frac{-y F_{172}\! \left(x , y\right)+F_{172}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{156}\! \left(x \right) F_{170}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x , 1\right)
F_{184}\! \left(x , y\right) = F_{155}\! \left(x \right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{25}\! \left(x \right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{51}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{30}\! \left(x , y\right)^{2} F_{25}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{62}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{-F_{119}\! \left(x , y\right)+F_{119}\! \left(x , 1\right)}{-1+y}
F_{213}\! \left(x , y\right) = -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{154}\! \left(x \right) F_{183}\! \left(x , y\right) F_{7}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_142(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_25(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x) + F_2(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_24(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_12(x) + F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x)*F_7(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_7(x)*F_8(x))
Eq(F_21(x), F_22(x)/(F_23(x)*F_7(x)))
Eq(F_22(x), F_15(x))
Eq(F_23(x), F_0(x) + F_19(x))
Eq(F_24(x), F_141(x) + F_25(x))
Eq(F_25(x), F_19(x) + F_26(x))
Eq(F_26(x), F_27(x, 1))
Eq(F_28(x, k_0), F_11(x) + F_27(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_34(x, k_0))
Eq(F_29(x, k_0), F_2(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_30(x, k_0)**2*F_33(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_7(x))
Eq(F_36(x, k_0), F_140(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_7(x))
Eq(F_40(x, k_0), F_39(x, k_0)*F_7(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_116(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_115(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_19(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_33(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_41(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_30(x, k_0)*F_43(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_43(x, k_0)*F_51(x, k_0)*F_7(x))
Eq(F_51(x, k_0), F_37(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_60(x, k_0))
Eq(F_53(x, k_0), F_4(x) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_33(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_30(x, k_0)*F_53(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_51(x, k_0)*F_53(x, k_0)*F_7(x))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0)*F_62(x, k_0))
Eq(F_63(x, k_0), F_2(x)*F_62(x, k_0))
Eq(F_64(x, k_0), F_113(x, k_0) + F_63(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0)*F_7(x))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0)*F_7(x))
Eq(F_67(x, k_0), F_68(x, k_0) + F_84(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_30(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x) + F_79(x, k_0))
Eq(F_71(x), F_72(x) + F_78(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), 16*x + (x + 1)**3*(F_73(x) + 1)**2 + (F_73(x) + 1)*(8*x**2 - 20*x - 1) + F_73(x))
Eq(F_74(x), F_2(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_7(x)*F_77(x)**2)
Eq(F_77(x), F_1(x) + F_75(x))
Eq(F_78(x), F_19(x)*F_75(x))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_30(x, k_0)*F_33(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_70(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), F_71(x)*F_83(x, k_0))
Eq(F_83(x, k_0), (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_85(x, k_0), F_109(x, k_0) + F_84(x, k_0))
Eq(F_85(x, k_0), F_101(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_104(x, k_0) + F_87(x, k_0))
Eq(F_88(x, k_0), F_33(x, k_0)*F_87(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_90(x, k_0), F_0(x) + F_89(x, k_0))
Eq(F_53(x, k_0), F_90(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_5(x) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_7(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_7(x)*F_95(x, k_0))
Eq(F_96(x, k_0), F_44(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_33(x, k_0)*F_99(x, k_0))
Eq(F_100(x, k_0), F_7(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_102(x, k_0), F_101(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_33(x, k_0))
Eq(F_103(x, k_0), F_44(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_107(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_19(x)*F_30(x, k_0)**2)
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_19(x)*F_62(x, k_0)*F_7(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_30(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_70(x, k_0))
Eq(F_112(x, k_0), F_23(x)*F_30(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_7(x)*F_99(x, k_0))
Eq(F_115(x, k_0), -F_27(x, k_0) + (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_116(x, k_0), -F_117(x, k_0) + (k_0*F_117(x, k_0) - F_117(x, 1))/(k_0 - 1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_7(x))
Eq(F_120(x, k_0), F_119(x, k_0)*F_7(x))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_124(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_2(x)*F_89(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0) + F_27(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0) + F_138(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0) + F_135(x))
Eq(F_127(x, k_0), F_128(x, k_0) + F_129(x, k_0))
Eq(F_128(x, k_0), F_28(x, k_0) + F_90(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_7(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_30(x, k_0)*F_8(x))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_51(x, k_0)*F_7(x)*F_8(x))
Eq(F_135(x), F_136(x) + F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_21(x)*F_4(x)*F_7(x))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_0(x)*F_89(x, k_0))
Eq(F_140(x, k_0), F_2(x)*F_51(x, k_0))
Eq(F_141(x), F_117(x, 1))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_7(x))
Eq(F_144(x), F_145(x) + F_152(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_77(x)*F_8(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_7(x)*F_8(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_52(x, 1))
Eq(F_151(x), F_37(x, 1))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_182(x)*F_7(x))
Eq(F_154(x), F_155(x) + F_156(x))
Eq(F_155(x), 16*x + (x + 1)**3*F_155(x)**2 + (8*x**2 - 20*x)*F_155(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_7(x))
Eq(F_158(x), F_159(x, 1))
Eq(F_159(x, k_0), F_160(x, k_0) + F_168(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0)*F_30(x, k_0))
Eq(F_161(x, k_0), F_155(x) + F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0) + F_31(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_33(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_168(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_30(x, k_0))
Eq(F_167(x, k_0), F_163(x, k_0) + F_73(x))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_161(x, k_0)*F_170(x, k_0)*F_7(x))
Eq(F_171(x, k_0), F_154(x)*F_170(x, k_0)*F_7(x))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_180(x, k_0))
Eq(F_173(x, k_0), F_167(x, k_0) + F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0)*F_7(x))
Eq(F_176(x, k_0), F_177(x, k_0) + F_179(x, k_0))
Eq(F_177(x, k_0), F_154(x)*F_178(x, k_0))
Eq(F_178(x, k_0), -F_31(x, k_0) + (k_0*F_31(x, k_0) - F_31(x, 1))/(k_0 - 1))
Eq(F_179(x, k_0), (k_0*F_172(x, k_0) - F_172(x, 1))/(k_0 - 1))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_156(x)*F_170(x, k_0)*F_7(x))
Eq(F_182(x), F_183(x, 1))
Eq(F_184(x, k_0), F_155(x)*F_183(x, k_0)*F_7(x))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0) + F_209(x, k_0))
Eq(F_186(x, k_0), F_115(x, k_0) + F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_19(x))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_33(x, k_0))
Eq(F_190(x, k_0), F_104(x, k_0) + F_191(x, k_0))
Eq(F_192(x, k_0), F_191(x, k_0) + F_204(x, k_0))
Eq(F_193(x, k_0), F_192(x, k_0)*F_33(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_33(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_202(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_200(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_30(x, k_0))
Eq(F_199(x, k_0), F_194(x, k_0) + F_25(x))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_199(x, k_0)*F_51(x, k_0)*F_7(x))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_161(x, k_0)*F_183(x, k_0)*F_7(x))
Eq(F_204(x, k_0), F_205(x, k_0) + F_207(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_25(x)*F_30(x, k_0)**2)
Eq(F_207(x, k_0), F_208(x, k_0))
Eq(F_208(x, k_0), F_25(x)*F_62(x, k_0)*F_7(x))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0)*F_7(x))
Eq(F_211(x, k_0), F_212(x, k_0) + F_213(x, k_0))
Eq(F_212(x, k_0), -F_119(x, k_0) + (k_0*F_119(x, k_0) - F_119(x, 1))/(k_0 - 1))
Eq(F_213(x, k_0), (k_0*F_214(x, k_0) - F_214(x, 1))/(k_0 - 1))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_154(x)*F_183(x, k_0)*F_7(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": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [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": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
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[{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [1, 0, 3, 4, 2], [2, 0, 3, 4, 1], [3, 0, 2, 4, 1]], "symmetry": true}}, {"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"}}]}
Specification 3
Strategy pack name: insertion_point_row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25539/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,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[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[547,x]
F[10,x] = F[11,x]+F[546,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = (1+F[12,x])^2*x^3+(3*F[12,x]^2+14*F[12,x]+11)*x^2+(3*F[12,x]^2-14*F[12,x]-1)*x+F[12,x]^2+2*F[12,x]
F[13,x] = F[14,x]+F[2,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[542,x]
F[17,x] = F[13,x]+F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[12,x]*F[2,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[8,x]
F[22,x] = F[23,x]+F[535,x]
F[23,x] = F[24,x]*F[27,x]
F[24,x] = F[1,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[24,x]^2*F[8,x]
F[27,x] = F[172,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[36,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[38,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[37,x,k[0]]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[33,x,k[0]]^2*F[36,x,k[0]]
F[36,x,k[0]] = k[0]*x
F[37,x,k[0]] = F[2,x]+F[29,x,k[0]]
F[38,x,k[0]] = F[159,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]+F[41,x,k[0]]
F[40,x,k[0]] = F[2,x]*F[33,x,k[0]]
F[41,x,k[0]] = F[42,x]+F[54,x,k[0]]
F[42,x] = F[43,x]
F[43,x] = F[44,x]*F[8,x]
F[44,x] = F[45,x]+F[49,x]
F[45,x] = F[11,x]+F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[25,x]+F[48,x]
F[48,x] = F[2,x]+F[28,x]
F[49,x] = F[155,x]+F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[2,x]*F[25,x]
F[52,x] = F[42,x]+F[53,x]
F[53,x] = F[54,x,1]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[8,x]
F[56,x,k[0]] = F[146,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[138,x,k[0]]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[65,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[63,x,k[0]]
F[62,x,k[0]] = F[12,x]+F[59,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[64,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[65,x,k[0]] = F[29,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[36,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[75,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[71,x,k[0]]
F[70,x,k[0]] = F[14,x]+F[66,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[74,x,k[0]]
F[72,x,k[0]] = 1/(-1+k[0])*(F[73,x,k[0]]*k[0]-F[73,x,1])
F[73,x,k[0]] = F[12,x]*F[37,x,k[0]]
F[74,x,k[0]] = F[37,x,k[0]]*F[59,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[79,x,k[0]]
F[76,x,k[0]] = (F[77,x,k[0]]-F[77,x,1])/(-1+k[0])
F[77,x,k[0]] = F[54,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[2,x]*F[34,x,k[0]]
F[79,x,k[0]] = F[125,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = 1/(-1+k[0])*(F[81,x,k[0]]*k[0]-F[81,x,1])
F[81,x,k[0]] = F[82,x,k[0]]+F[83,x,k[0]]
F[82,x,k[0]] = F[14,x]*F[33,x,k[0]]
F[83,x,k[0]] = F[104,x,k[0]]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[8,x]*F[86,x]
F[86,x] = F[103,x]+F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = 1/F[8,x]*F[89,x]
F[89,x] = -F[90,x]-F[91,x]+F[42,x]
F[90,x] = 0
F[91,x] = F[8,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[2,x]+F[42,x]
F[94,x] = F[95,x]+F[97,x]
F[95,x] = F[96,x]
F[96,x] = F[2,x]^2
F[97,x] = F[98,x]
F[98,x] = F[8,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[2,x]*F[88,x]
F[101,x] = F[102,x]*F[6,x]
F[102,x] = F[4,x]+F[88,x]
F[103,x] = F[102,x]*F[14,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[8,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[124,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[12,x]
F[109,x,k[0]] = F[108,x,k[0]]*F[8,x]
F[54,x,k[0]] = F[109,x,k[0]]+F[110,x,k[0]]+F[90,x]
F[110,x,k[0]] = F[111,x,k[0]]*F[8,x]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[29,x,k[0]]+F[54,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[116,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[2,x]*F[29,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[8,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = F[108,x,k[0]]*F[2,x]
F[120,x,k[0]] = F[121,x,k[0]]*F[6,x]
F[121,x,k[0]] = F[108,x,k[0]]+F[122,x,k[0]]
F[123,x,k[0]] = F[122,x,k[0]]*F[8,x]
F[123,x,k[0]] = F[29,x,k[0]]
F[124,x,k[0]] = F[121,x,k[0]]*F[14,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[33,x,k[0]]*F[66,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[133,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[8,x]
F[130,x,k[0]] = F[131,x,k[0]]+F[132,x,k[0]]
F[131,x,k[0]] = F[59,x,k[0]]*F[88,x]
F[132,x,k[0]] = F[102,x]*F[66,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[8,x]
F[135,x,k[0]] = F[136,x,k[0]]+F[137,x,k[0]]
F[136,x,k[0]] = F[108,x,k[0]]*F[59,x,k[0]]
F[137,x,k[0]] = F[121,x,k[0]]*F[66,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]+F[145,x,k[0]]
F[139,x,k[0]] = (-F[140,x,1]*k[0]+F[140,x,k[0]])/(-1+k[0])
F[140,x,k[0]] = F[141,x,k[0]]*F[2,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[36,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[34,x,k[0]]
F[144,x,k[0]] = F[33,x,k[0]]*F[34,x,k[0]]
F[145,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[146,x,k[0]] = F[147,x,k[0]]+F[152,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[2,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[151,x,k[0]]
F[150,x,k[0]] = (-F[141,x,1]*k[0]+F[141,x,k[0]])/(-1+k[0])
F[151,x,k[0]] = -k[0]*(F[29,x,1]-F[29,x,k[0]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]+F[154,x,k[0]]
F[153,x,k[0]] = F[150,x,k[0]]*F[6,x]
F[154,x,k[0]] = -k[0]*(F[116,x,1]-F[116,x,k[0]])/(-1+k[0])
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[14,x]*F[25,x]
F[157,x] = F[158,x]+F[84,x]
F[158,x] = F[104,x,1]
F[159,x,k[0]] = F[160,x,k[0]]+F[161,x,k[0]]
F[160,x,k[0]] = F[29,x,k[0]]*F[33,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]+F[167,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[8,x]
F[164,x,k[0]] = F[165,x,k[0]]+F[166,x,k[0]]
F[165,x,k[0]] = F[34,x,k[0]]*F[88,x]
F[166,x,k[0]] = F[102,x]*F[29,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[8,x]
F[169,x,k[0]] = F[170,x,k[0]]+F[171,x,k[0]]
F[170,x,k[0]] = F[108,x,k[0]]*F[34,x,k[0]]
F[171,x,k[0]] = F[121,x,k[0]]*F[29,x,k[0]]
F[172,x] = F[14,x]+F[173,x]
F[173,x] = F[174,x,1]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]*F[36,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[327,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]+F[180,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]*F[33,x,k[0]]
F[179,x,k[0]] = F[14,x]+F[174,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]+F[300,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[73,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]+F[20,x]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[8,x]
F[185,x,k[0]] = F[186,x,k[0]]+F[193,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]+F[190,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[189,x,k[0]]
F[151,x,k[0]] = F[188,x,k[0]]+F[29,x,k[0]]
F[189,x,k[0]] = -k[0]*(F[174,x,1]-F[174,x,k[0]])/(-1+k[0])
F[190,x,k[0]] = F[191,x,k[0]]+F[192,x,k[0]]
F[191,x,k[0]] = F[12,x]*F[188,x,k[0]]
F[192,x,k[0]] = -k[0]*(F[183,x,1]-F[183,x,k[0]])/(-1+k[0])
F[193,x,k[0]] = F[194,x,k[0]]+F[196,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[12,x]*F[187,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[283,x,k[0]]
F[197,x,k[0]] = F[188,x,k[0]]*F[198,x]
F[198,x] = F[199,x]
F[199,x] = F[200,x]*F[8,x]
F[200,x] = F[201,x]+F[276,x]
F[201,x] = F[202,x]*F[24,x]
F[202,x] = F[203,x]+F[25,x]
F[203,x] = F[12,x]+F[204,x]
F[204,x] = F[205,x,1]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]*F[36,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[210,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]*F[33,x,k[0]]
F[209,x,k[0]] = F[12,x]+F[205,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]+F[246,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]+F[64,x,k[0]]
F[212,x,k[0]] = F[198,x]+F[213,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]*F[8,x]
F[215,x,k[0]] = F[216,x,k[0]]+F[223,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[219,x,k[0]]
F[217,x,k[0]] = F[150,x,k[0]]+F[218,x,k[0]]
F[218,x,k[0]] = -k[0]*(F[205,x,1]-F[205,x,k[0]])/(-1+k[0])
F[219,x,k[0]] = F[220,x,k[0]]+F[222,x,k[0]]
F[220,x,k[0]] = (-F[221,x,1]*k[0]+F[221,x,k[0]])/(-1+k[0])
F[221,x,k[0]] = F[12,x]*F[141,x,k[0]]
F[222,x,k[0]] = -k[0]*(F[213,x,1]-F[213,x,k[0]])/(-1+k[0])
F[223,x,k[0]] = F[224,x,k[0]]+F[226,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]
F[225,x,k[0]] = F[12,x]*F[217,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]+F[229,x,k[0]]
F[227,x,k[0]] = (-F[228,x,1]*k[0]+F[228,x,k[0]])/(-1+k[0])
F[228,x,k[0]] = F[141,x,k[0]]*F[198,x]
F[229,x,k[0]] = -k[0]*(F[230,x,1]-F[230,x,k[0]])/(-1+k[0])
F[230,x,k[0]] = F[231,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]*F[8,x]
F[232,x,k[0]] = F[233,x,k[0]]+F[242,x,k[0]]
F[233,x,k[0]] = F[12,x]*F[234,x,k[0]]
F[235,x,k[0]] = F[234,x,k[0]]*F[8,x]
F[213,x,k[0]] = F[235,x,k[0]]+F[236,x,k[0]]+F[90,x]
F[236,x,k[0]] = F[237,x,k[0]]*F[8,x]
F[237,x,k[0]] = F[238,x,k[0]]+F[239,x,k[0]]
F[238,x,k[0]] = F[205,x,k[0]]+F[213,x,k[0]]
F[239,x,k[0]] = F[230,x,k[0]]+F[240,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]
F[241,x,k[0]] = F[12,x]*F[205,x,k[0]]
F[242,x,k[0]] = F[198,x]*F[243,x,k[0]]
F[243,x,k[0]] = F[234,x,k[0]]+F[244,x,k[0]]
F[245,x,k[0]] = F[244,x,k[0]]*F[8,x]
F[245,x,k[0]] = F[205,x,k[0]]
F[246,x,k[0]] = F[247,x,k[0]]+F[248,x,k[0]]
F[247,x,k[0]] = F[205,x,k[0]]*F[33,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]+F[271,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]*F[8,x]
F[251,x,k[0]] = F[252,x,k[0]]+F[270,x,k[0]]
F[252,x,k[0]] = F[253,x]*F[34,x,k[0]]
F[253,x] = 1/F[8,x]*F[254,x]
F[254,x] = -F[255,x]-F[90,x]+F[198,x]
F[255,x] = F[256,x]*F[8,x]
F[256,x] = F[257,x]+F[258,x]
F[257,x] = F[12,x]+F[198,x]
F[258,x] = F[259,x]+F[261,x]
F[259,x] = F[260,x]
F[260,x] = F[12,x]^2
F[261,x] = F[262,x]
F[262,x] = F[263,x]*F[8,x]
F[263,x] = F[264,x]+F[265,x]
F[264,x] = F[12,x]*F[253,x]
F[265,x] = F[198,x]*F[266,x]
F[266,x] = F[253,x]+F[267,x]
F[267,x] = F[268,x]+F[269,x]
F[268,x] = 16*x+(1+x)^3*F[268,x]^2+(8*x^2-20*x)*F[268,x]
F[269,x] = F[12,x]+F[198,x]
F[270,x,k[0]] = F[205,x,k[0]]*F[266,x]
F[271,x,k[0]] = F[272,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0]]*F[8,x]
F[273,x,k[0]] = F[274,x,k[0]]+F[275,x,k[0]]
F[274,x,k[0]] = F[234,x,k[0]]*F[34,x,k[0]]
F[275,x,k[0]] = F[205,x,k[0]]*F[243,x,k[0]]
F[276,x] = F[277,x]+F[280,x]
F[277,x] = F[278,x]+F[279,x]
F[278,x] = F[12,x]*F[25,x]
F[279,x] = F[212,x,1]
F[280,x] = F[281,x]+F[282,x]
F[281,x] = F[204,x]*F[25,x]
F[282,x] = F[248,x,1]
F[283,x,k[0]] = -k[0]*(F[284,x,1]-F[284,x,k[0]])/(-1+k[0])
F[284,x,k[0]] = F[285,x,k[0]]
F[285,x,k[0]] = F[286,x,k[0]]*F[8,x]
F[286,x,k[0]] = F[287,x,k[0]]+F[296,x,k[0]]
F[287,x,k[0]] = F[12,x]*F[288,x,k[0]]
F[289,x,k[0]] = F[288,x,k[0]]*F[8,x]
F[183,x,k[0]] = F[289,x,k[0]]+F[290,x,k[0]]+F[90,x]
F[290,x,k[0]] = F[291,x,k[0]]*F[8,x]
F[291,x,k[0]] = F[292,x,k[0]]+F[293,x,k[0]]
F[292,x,k[0]] = F[174,x,k[0]]+F[183,x,k[0]]
F[293,x,k[0]] = F[284,x,k[0]]+F[294,x,k[0]]
F[294,x,k[0]] = F[295,x,k[0]]
F[295,x,k[0]] = F[12,x]*F[174,x,k[0]]
F[296,x,k[0]] = F[198,x]*F[297,x,k[0]]
F[297,x,k[0]] = F[288,x,k[0]]+F[298,x,k[0]]
F[299,x,k[0]] = F[298,x,k[0]]*F[8,x]
F[299,x,k[0]] = F[174,x,k[0]]
F[300,x,k[0]] = F[301,x,k[0]]+F[302,x,k[0]]
F[301,x,k[0]] = F[205,x,k[0]]*F[37,x,k[0]]
F[302,x,k[0]] = F[303,x,k[0]]+F[322,x,k[0]]
F[303,x,k[0]] = F[304,x,k[0]]
F[304,x,k[0]] = F[305,x,k[0]]*F[8,x]
F[305,x,k[0]] = F[306,x,k[0]]+F[321,x,k[0]]
F[306,x,k[0]] = F[307,x]*F[34,x,k[0]]
F[307,x] = 1/F[8,x]*F[308,x]
F[308,x] = -F[309,x]-F[90,x]+F[20,x]
F[309,x] = F[310,x]*F[8,x]
F[310,x] = F[311,x]+F[312,x]
F[311,x] = F[14,x]+F[20,x]
F[312,x] = F[313,x]+F[315,x]
F[313,x] = F[314,x]
F[314,x] = F[12,x]*F[14,x]
F[315,x] = F[316,x]
F[316,x] = F[317,x]*F[8,x]
F[317,x] = F[318,x]+F[319,x]
F[318,x] = F[12,x]*F[307,x]
F[319,x] = F[198,x]*F[320,x]
F[320,x] = F[16,x]+F[307,x]
F[321,x,k[0]] = F[205,x,k[0]]*F[320,x]
F[322,x,k[0]] = F[323,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]*F[8,x]
F[324,x,k[0]] = F[325,x,k[0]]+F[326,x,k[0]]
F[325,x,k[0]] = F[288,x,k[0]]*F[34,x,k[0]]
F[326,x,k[0]] = F[205,x,k[0]]*F[297,x,k[0]]
F[327,x,k[0]] = F[328,x,k[0]]+F[330,x,k[0]]
F[328,x,k[0]] = F[329,x,k[0]]
F[329,x,k[0]] = F[33,x,k[0]]*F[76,x,k[0]]
F[330,x,k[0]] = F[331,x,k[0]]+F[493,x,k[0]]
F[331,x,k[0]] = F[332,x,k[0]]+F[370,x,k[0]]
F[332,x,k[0]] = F[333,x,k[0]]+F[82,x,k[0]]
F[333,x,k[0]] = F[334,x]+F[349,x,k[0]]
F[334,x] = F[335,x]
F[335,x] = F[336,x]*F[8,x]
F[336,x] = F[337,x]+F[339,x]
F[337,x] = F[24,x]*F[338,x]
F[338,x] = F[14,x]+F[334,x]
F[339,x] = F[340,x]*F[347,x]
F[340,x] = F[12,x]+F[341,x]
F[341,x] = F[342,x]
F[342,x] = F[343,x]*F[8,x]
F[343,x] = F[344,x]+F[345,x]
F[344,x] = F[24,x]*F[340,x]
F[345,x] = F[340,x]*F[346,x]
F[346,x] = F[24,x]+F[340,x]
F[347,x] = F[338,x]+F[348,x]
F[348,x] = F[2,x]*F[24,x]
F[349,x,k[0]] = F[350,x,k[0]]+F[368,x,k[0]]+F[90,x]
F[350,x,k[0]] = F[351,x,k[0]]
F[351,x,k[0]] = F[352,x,k[0]]*F[8,x]
F[352,x,k[0]] = F[353,x,k[0]]+F[355,x,k[0]]
F[353,x,k[0]] = -k[0]*(F[354,x,1]-F[354,x,k[0]])/(-1+k[0])
F[354,x,k[0]] = F[338,x]*F[34,x,k[0]]
F[355,x,k[0]] = F[347,x]*F[356,x,k[0]]
F[356,x,k[0]] = F[357,x,k[0]]+F[358,x,k[0]]
F[357,x,k[0]] = F[12,x]*F[34,x,k[0]]
F[358,x,k[0]] = F[359,x,k[0]]+F[365,x,k[0]]+F[90,x]
F[359,x,k[0]] = F[360,x,k[0]]
F[360,x,k[0]] = F[361,x,k[0]]*F[8,x]
F[361,x,k[0]] = F[362,x,k[0]]+F[364,x,k[0]]
F[362,x,k[0]] = -k[0]*(F[363,x,1]-F[363,x,k[0]])/(-1+k[0])
F[363,x,k[0]] = F[34,x,k[0]]*F[340,x]
F[364,x,k[0]] = F[346,x]*F[356,x,k[0]]
F[365,x,k[0]] = F[366,x,k[0]]
F[366,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]*F[367,x,k[0]]
F[367,x,k[0]] = F[341,x]+F[358,x,k[0]]
F[368,x,k[0]] = F[369,x,k[0]]
F[369,x,k[0]] = F[33,x,k[0]]*F[333,x,k[0]]*F[36,x,k[0]]
F[370,x,k[0]] = F[371,x,k[0]]+F[83,x,k[0]]
F[371,x,k[0]] = F[372,x]+F[433,x,k[0]]
F[372,x] = F[373,x]+F[382,x]+F[90,x]
F[373,x] = F[374,x]
F[374,x] = F[375,x]*F[8,x]
F[375,x] = F[376,x]+F[379,x]
F[376,x] = F[28,x]*F[377,x]
F[377,x] = F[25,x]+F[378,x]
F[378,x] = F[59,x,1]
F[379,x] = F[380,x]+F[381,x]
F[380,x] = F[167,x,1]
F[381,x] = F[133,x,1]
F[382,x] = F[383,x]
F[383,x] = F[384,x]*F[8,x]
F[384,x] = F[385,x]+F[393,x]
F[385,x] = F[386,x]+F[388,x]
F[386,x] = F[387,x,1]
F[387,x,k[0]] = 1/(-1+k[0])*(F[54,x,k[0]]*k[0]-F[54,x,1])
F[388,x] = F[380,x]+F[389,x]
F[389,x] = F[390,x]
F[390,x] = F[25,x]*F[391,x]
F[391,x] = F[392,x,1]
F[392,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[393,x] = F[394,x]+F[396,x]
F[394,x] = F[158,x]+F[395,x]
F[395,x] = F[371,x,1]
F[396,x] = F[397,x]+F[403,x]
F[397,x] = F[398,x,1]
F[398,x,k[0]] = F[399,x,k[0]]
F[399,x,k[0]] = F[400,x,k[0]]*F[8,x]
F[400,x,k[0]] = F[401,x,k[0]]+F[402,x,k[0]]
F[401,x,k[0]] = F[108,x,k[0]]*F[205,x,k[0]]
F[402,x,k[0]] = F[121,x,k[0]]*F[174,x,k[0]]
F[403,x] = F[404,x,1]
F[404,x,k[0]] = F[405,x,k[0]]+F[427,x,k[0]]
F[405,x,k[0]] = F[406,x,k[0]]
F[406,x,k[0]] = F[407,x,k[0]]*F[8,x]
F[407,x,k[0]] = F[408,x,k[0]]+F[426,x,k[0]]
F[408,x,k[0]] = F[34,x,k[0]]*F[409,x]
F[409,x] = 1/F[8,x]*F[410,x]
F[410,x] = -F[411,x]-F[90,x]+F[372,x]
F[411,x] = F[412,x]*F[8,x]
F[412,x] = F[413,x]+F[414,x]
F[413,x] = F[372,x]+F[53,x]
F[414,x] = F[415,x]+F[417,x]
F[415,x] = F[416,x]
F[416,x] = F[12,x]*F[53,x]
F[417,x] = F[418,x]
F[418,x] = F[419,x]*F[8,x]
F[419,x] = F[420,x]+F[421,x]
F[420,x] = F[12,x]*F[409,x]
F[421,x] = F[198,x]*F[422,x]
F[422,x] = F[409,x]+F[423,x]
F[423,x] = F[424,x]
F[424,x] = 1/F[8,x]*F[425,x]
F[425,x] = F[53,x]
F[426,x,k[0]] = F[205,x,k[0]]*F[422,x]
F[427,x,k[0]] = F[428,x,k[0]]
F[428,x,k[0]] = F[429,x,k[0]]*F[8,x]
F[429,x,k[0]] = F[430,x,k[0]]+F[492,x,k[0]]
F[430,x,k[0]] = F[34,x,k[0]]*F[431,x,k[0]]
F[432,x,k[0]] = F[431,x,k[0]]*F[8,x]
F[433,x,k[0]] = F[432,x,k[0]]+F[481,x,k[0]]+F[90,x]
F[433,x,k[0]] = F[434,x,k[0]]+F[457,x,k[0]]+F[90,x]
F[434,x,k[0]] = F[435,x,k[0]]
F[436,x,k[0]] = F[435,x,k[0]]+F[438,x,k[0]]+F[90,x]
F[437,x,k[0]] = F[104,x,k[0]]+F[436,x,k[0]]
F[437,x,k[0]] = -k[0]*(F[104,x,1]-F[104,x,k[0]])/(-1+k[0])
F[438,x,k[0]] = F[439,x,k[0]]*F[8,x]
F[439,x,k[0]] = F[440,x,k[0]]+F[449,x,k[0]]
F[440,x,k[0]] = F[441,x,k[0]]+F[442,x,k[0]]
F[145,x,k[0]] = F[441,x,k[0]]+F[54,x,k[0]]
F[443,x,k[0]] = F[380,x]+F[442,x,k[0]]
F[443,x,k[0]] = (F[444,x,k[0]]-F[444,x,1])/(-1+k[0])
F[444,x,k[0]] = F[445,x,k[0]]
F[445,x,k[0]] = F[446,x,k[0]]*F[8,x]
F[446,x,k[0]] = F[447,x,k[0]]+F[448,x,k[0]]
F[447,x,k[0]] = F[108,x,k[0]]*F[25,x]
F[448,x,k[0]] = F[121,x,k[0]]*F[28,x]
F[449,x,k[0]] = F[436,x,k[0]]+F[450,x,k[0]]
F[451,x,k[0]] = F[397,x]+F[450,x,k[0]]
F[451,x,k[0]] = (F[452,x,k[0]]-F[452,x,1])/(-1+k[0])
F[452,x,k[0]] = F[453,x,k[0]]
F[453,x,k[0]] = F[454,x,k[0]]*F[8,x]
F[454,x,k[0]] = F[455,x,k[0]]+F[456,x,k[0]]
F[455,x,k[0]] = F[108,x,k[0]]*F[204,x]
F[456,x,k[0]] = F[121,x,k[0]]*F[173,x]
F[457,x,k[0]] = F[458,x,k[0]]
F[458,x,k[0]] = F[459,x,k[0]]*F[8,x]
F[459,x,k[0]] = F[460,x,k[0]]+F[467,x,k[0]]
F[460,x,k[0]] = F[461,x,k[0]]+F[463,x,k[0]]
F[461,x,k[0]] = F[441,x,k[0]]+F[462,x,k[0]]
F[462,x,k[0]] = -k[0]*(F[441,x,1]-F[441,x,k[0]])/(-1+k[0])
F[463,x,k[0]] = F[442,x,k[0]]+F[464,x,k[0]]
F[464,x,k[0]] = F[465,x,k[0]]
F[465,x,k[0]] = -k[0]*(F[466,x,1]-F[466,x,k[0]])/(-1+k[0])
F[466,x,k[0]] = F[25,x]*F[441,x,k[0]]
F[467,x,k[0]] = F[468,x,k[0]]+F[470,x,k[0]]
F[468,x,k[0]] = F[436,x,k[0]]+F[469,x,k[0]]
F[469,x,k[0]] = -k[0]*(F[433,x,1]-F[433,x,k[0]])/(-1+k[0])
F[470,x,k[0]] = F[450,x,k[0]]+F[471,x,k[0]]
F[471,x,k[0]] = -k[0]*(F[472,x,1]-F[472,x,k[0]])/(-1+k[0])
F[472,x,k[0]] = F[473,x,k[0]]
F[473,x,k[0]] = F[474,x,k[0]]*F[8,x]
F[474,x,k[0]] = F[475,x,k[0]]+F[476,x,k[0]]
F[475,x,k[0]] = F[25,x]*F[431,x,k[0]]
F[476,x,k[0]] = F[204,x]*F[477,x,k[0]]
F[477,x,k[0]] = F[431,x,k[0]]+F[478,x,k[0]]
F[478,x,k[0]] = F[479,x,k[0]]
F[480,x,k[0]] = F[479,x,k[0]]*F[8,x]
F[480,x,k[0]] = F[441,x,k[0]]
F[481,x,k[0]] = F[482,x,k[0]]*F[8,x]
F[482,x,k[0]] = F[483,x,k[0]]+F[484,x,k[0]]
F[483,x,k[0]] = F[433,x,k[0]]+F[441,x,k[0]]
F[484,x,k[0]] = F[485,x,k[0]]+F[487,x,k[0]]
F[485,x,k[0]] = F[486,x,k[0]]
F[486,x,k[0]] = F[12,x]*F[441,x,k[0]]
F[487,x,k[0]] = F[488,x,k[0]]
F[488,x,k[0]] = F[489,x,k[0]]*F[8,x]
F[489,x,k[0]] = F[490,x,k[0]]+F[491,x,k[0]]
F[490,x,k[0]] = F[12,x]*F[431,x,k[0]]
F[491,x,k[0]] = F[198,x]*F[477,x,k[0]]
F[492,x,k[0]] = F[205,x,k[0]]*F[477,x,k[0]]
F[493,x,k[0]] = F[494,x,k[0]]+F[528,x,k[0]]
F[494,x,k[0]] = F[495,x,k[0]]+F[496,x,k[0]]
F[495,x,k[0]] = F[174,x,k[0]]*F[33,x,k[0]]
F[496,x,k[0]] = F[497,x,k[0]]+F[508,x,k[0]]
F[497,x,k[0]] = F[498,x,k[0]]
F[498,x,k[0]] = F[499,x,k[0]]*F[8,x]
F[499,x,k[0]] = F[500,x,k[0]]+F[501,x,k[0]]
F[500,x,k[0]] = F[24,x]*F[338,x]*F[34,x,k[0]]
F[501,x,k[0]] = F[347,x]*F[502,x,k[0]]
F[502,x,k[0]] = F[205,x,k[0]]+F[503,x,k[0]]
F[503,x,k[0]] = F[504,x,k[0]]
F[504,x,k[0]] = F[505,x,k[0]]*F[8,x]
F[505,x,k[0]] = F[506,x,k[0]]+F[507,x,k[0]]
F[506,x,k[0]] = F[24,x]*F[34,x,k[0]]*F[340,x]
F[507,x,k[0]] = F[346,x]*F[502,x,k[0]]
F[508,x,k[0]] = F[509,x,k[0]]+F[526,x,k[0]]+F[90,x]
F[509,x,k[0]] = F[510,x,k[0]]
F[510,x,k[0]] = F[511,x,k[0]]*F[8,x]
F[511,x,k[0]] = F[512,x,k[0]]+F[514,x,k[0]]
F[512,x,k[0]] = F[338,x]*F[34,x,k[0]]*F[513,x,k[0]]
F[513,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
F[514,x,k[0]] = F[347,x]*F[515,x,k[0]]
F[515,x,k[0]] = F[516,x,k[0]]+F[517,x,k[0]]
F[516,x,k[0]] = F[205,x,k[0]]*F[34,x,k[0]]
F[517,x,k[0]] = F[518,x,k[0]]+F[523,x,k[0]]+F[90,x]
F[518,x,k[0]] = F[519,x,k[0]]
F[519,x,k[0]] = F[520,x,k[0]]*F[8,x]
F[520,x,k[0]] = F[521,x,k[0]]+F[522,x,k[0]]
F[521,x,k[0]] = F[34,x,k[0]]*F[340,x]*F[513,x,k[0]]
F[522,x,k[0]] = F[346,x]*F[515,x,k[0]]
F[523,x,k[0]] = F[524,x,k[0]]
F[524,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]*F[525,x,k[0]]
F[525,x,k[0]] = F[503,x,k[0]]+F[517,x,k[0]]
F[526,x,k[0]] = F[527,x,k[0]]
F[527,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]*F[496,x,k[0]]
F[528,x,k[0]] = F[404,x,k[0]]+F[529,x,k[0]]
F[529,x,k[0]] = F[398,x,k[0]]+F[530,x,k[0]]
F[530,x,k[0]] = F[531,x,k[0]]
F[531,x,k[0]] = F[532,x,k[0]]*F[8,x]
F[532,x,k[0]] = F[533,x,k[0]]+F[534,x,k[0]]
F[533,x,k[0]] = F[205,x,k[0]]*F[88,x]
F[534,x,k[0]] = F[102,x]*F[174,x,k[0]]
F[535,x] = F[536,x]+F[539,x]
F[536,x] = F[537,x]+F[538,x]
F[537,x] = F[12,x]*F[28,x]
F[538,x] = F[182,x,1]
F[539,x] = F[540,x]+F[541,x]
F[540,x] = F[204,x]*F[28,x]
F[541,x] = F[302,x,1]
F[542,x] = F[543,x]+F[544,x]
F[543,x] = F[348,x]+F[52,x]
F[544,x] = F[338,x]+F[545,x]
F[545,x] = F[372,x]+F[84,x]
F[546,x] = F[18,x]+F[198,x]
F[547,x] = F[50,x]+F[548,x]
F[548,x] = F[334,x]+F[545,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \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_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{547}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{546}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{3} F_{12} \left(x \right)^{2}+2 x^{3} F_{12}\! \left(x \right)+3 x^{2} F_{12} \left(x \right)^{2}+x^{3}+14 x^{2} F_{12}\! \left(x \right)+3 x F_{12} \left(x \right)^{2}+11 x^{2}-14 x F_{12}\! \left(x \right)+F_{12} \left(x \right)^{2}-x +2 F_{12}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{542}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{535}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{172}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{33}\! \left(x , y\right)^{2} F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = y x
F_{37}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{49}\! \left(x \right) = F_{155}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right)
F_{52}\! \left(x \right) = F_{42}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x , 1\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{-F_{64}\! \left(x , y\right) y +F_{64}\! \left(x , 1\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = -\frac{-F_{73}\! \left(x , y\right) y +F_{73}\! \left(x , 1\right)}{-1+y}
F_{73}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = -\frac{-F_{77}\! \left(x , y\right)+F_{77}\! \left(x , 1\right)}{-1+y}
F_{77}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = -\frac{-F_{81}\! \left(x , y\right) y +F_{81}\! \left(x , 1\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{8}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{103}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{89}\! \left(x \right) = -F_{90}\! \left(x \right)-F_{91}\! \left(x \right)+F_{42}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{8}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{8}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{2}\! \left(x \right) F_{88}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{6}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right)+F_{88}\! \left(x \right)
F_{103}\! \left(x \right) = F_{102}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{88}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = -\frac{F_{140}\! \left(x , 1\right) y -F_{140}\! \left(x , y\right)}{-1+y}
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = -\frac{F_{141}\! \left(x , 1\right) y -F_{141}\! \left(x , y\right)}{-1+y}
F_{151}\! \left(x , y\right) = -\frac{y \left(F_{29}\! \left(x , 1\right)-F_{29}\! \left(x , y\right)\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{154}\! \left(x , y\right) = -\frac{y \left(F_{116}\! \left(x , 1\right)-F_{116}\! \left(x , y\right)\right)}{-1+y}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{84}\! \left(x \right)
F_{158}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{88}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{172}\! \left(x \right) = F_{14}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x , 1\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{174}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{300}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{20}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = -\frac{y \left(F_{174}\! \left(x , 1\right)-F_{174}\! \left(x , y\right)\right)}{-1+y}
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = -\frac{y \left(F_{183}\! \left(x , 1\right)-F_{183}\! \left(x , y\right)\right)}{-1+y}
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{187}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{8}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{276}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right) F_{24}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{25}\! \left(x \right)
F_{203}\! \left(x \right) = F_{12}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x , 1\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{205}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{246}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{198}\! \left(x \right)+F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = -\frac{y \left(F_{205}\! \left(x , 1\right)-F_{205}\! \left(x , y\right)\right)}{-1+y}
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = -\frac{F_{221}\! \left(x , 1\right) y -F_{221}\! \left(x , y\right)}{-1+y}
F_{221}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = -\frac{y \left(F_{213}\! \left(x , 1\right)-F_{213}\! \left(x , y\right)\right)}{-1+y}
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = -\frac{F_{228}\! \left(x , 1\right) y -F_{228}\! \left(x , y\right)}{-1+y}
F_{228}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{198}\! \left(x \right)
F_{229}\! \left(x , y\right) = -\frac{y \left(F_{230}\! \left(x , 1\right)-F_{230}\! \left(x , y\right)\right)}{-1+y}
F_{230}\! \left(x , y\right) = F_{231}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right)+F_{242}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{234}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{234}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{213}\! \left(x , y\right) = F_{235}\! \left(x , y\right)+F_{236}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{198}\! \left(x \right) F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{244}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{245}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right)+F_{248}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)+F_{271}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{253}\! \left(x \right) = \frac{F_{254}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{254}\! \left(x \right) = -F_{255}\! \left(x \right)-F_{90}\! \left(x \right)+F_{198}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right) F_{8}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{258}\! \left(x \right)
F_{257}\! \left(x \right) = F_{12}\! \left(x \right)+F_{198}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)+F_{261}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{12} \left(x \right)^{2}
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{8}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{265}\! \left(x \right)
F_{264}\! \left(x \right) = F_{12}\! \left(x \right) F_{253}\! \left(x \right)
F_{265}\! \left(x \right) = F_{198}\! \left(x \right) F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{253}\! \left(x \right)+F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{269}\! \left(x \right)
F_{268}\! \left(x \right) = x^{3} F_{268} \left(x \right)^{2}+3 x^{2} F_{268} \left(x \right)^{2}+8 x^{2} F_{268}\! \left(x \right)+3 x F_{268} \left(x \right)^{2}-20 x F_{268}\! \left(x \right)+F_{268} \left(x \right)^{2}+16 x
F_{269}\! \left(x \right) = F_{12}\! \left(x \right)+F_{198}\! \left(x \right)
F_{270}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{266}\! \left(x \right)
F_{271}\! \left(x , y\right) = F_{272}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{273}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{234}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{243}\! \left(x , y\right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{280}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{279}\! \left(x \right)
F_{278}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{279}\! \left(x \right) = F_{212}\! \left(x , 1\right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{282}\! \left(x \right)
F_{281}\! \left(x \right) = F_{204}\! \left(x \right) F_{25}\! \left(x \right)
F_{282}\! \left(x \right) = F_{248}\! \left(x , 1\right)
F_{283}\! \left(x , y\right) = -\frac{y \left(F_{284}\! \left(x , 1\right)-F_{284}\! \left(x , y\right)\right)}{-1+y}
F_{284}\! \left(x , y\right) = F_{285}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{286}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{288}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{288}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{289}\! \left(x , y\right)+F_{290}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{290}\! \left(x , y\right) = F_{291}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{291}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{293}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{295}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{174}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{198}\! \left(x \right) F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{288}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{298}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{299}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right)+F_{302}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{303}\! \left(x , y\right)+F_{322}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{305}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{305}\! \left(x , y\right) = F_{306}\! \left(x , y\right)+F_{321}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{307}\! \left(x \right) = \frac{F_{308}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{308}\! \left(x \right) = -F_{309}\! \left(x \right)-F_{90}\! \left(x \right)+F_{20}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right) F_{8}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right)+F_{312}\! \left(x \right)
F_{311}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)+F_{315}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{8}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{319}\! \left(x \right)
F_{318}\! \left(x \right) = F_{12}\! \left(x \right) F_{307}\! \left(x \right)
F_{319}\! \left(x \right) = F_{198}\! \left(x \right) F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{16}\! \left(x \right)+F_{307}\! \left(x \right)
F_{321}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{320}\! \left(x \right)
F_{322}\! \left(x , y\right) = F_{323}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)+F_{326}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{288}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{297}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)+F_{330}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{329}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{331}\! \left(x , y\right)+F_{493}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{332}\! \left(x , y\right)+F_{370}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x \right)+F_{349}\! \left(x , y\right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right) F_{8}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x \right)+F_{339}\! \left(x \right)
F_{337}\! \left(x \right) = F_{24}\! \left(x \right) F_{338}\! \left(x \right)
F_{338}\! \left(x \right) = F_{14}\! \left(x \right)+F_{334}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right) F_{347}\! \left(x \right)
F_{340}\! \left(x \right) = F_{12}\! \left(x \right)+F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right) F_{8}\! \left(x \right)
F_{343}\! \left(x \right) = F_{344}\! \left(x \right)+F_{345}\! \left(x \right)
F_{344}\! \left(x \right) = F_{24}\! \left(x \right) F_{340}\! \left(x \right)
F_{345}\! \left(x \right) = F_{340}\! \left(x \right) F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{24}\! \left(x \right)+F_{340}\! \left(x \right)
F_{347}\! \left(x \right) = F_{338}\! \left(x \right)+F_{348}\! \left(x \right)
F_{348}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{349}\! \left(x , y\right) = F_{350}\! \left(x , y\right)+F_{368}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{350}\! \left(x , y\right) = F_{351}\! \left(x , y\right)
F_{351}\! \left(x , y\right) = F_{352}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{352}\! \left(x , y\right) = F_{353}\! \left(x , y\right)+F_{355}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = -\frac{y \left(F_{354}\! \left(x , 1\right)-F_{354}\! \left(x , y\right)\right)}{-1+y}
F_{354}\! \left(x , y\right) = F_{338}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{347}\! \left(x \right) F_{356}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{357}\! \left(x , y\right)+F_{358}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{359}\! \left(x , y\right)+F_{365}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{359}\! \left(x , y\right) = F_{360}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{361}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{361}\! \left(x , y\right) = F_{362}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = -\frac{y \left(F_{363}\! \left(x , 1\right)-F_{363}\! \left(x , y\right)\right)}{-1+y}
F_{363}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{340}\! \left(x \right)
F_{364}\! \left(x , y\right) = F_{346}\! \left(x \right) F_{356}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{366}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{367}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{341}\! \left(x \right)+F_{358}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{369}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{333}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{371}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{372}\! \left(x \right)+F_{433}\! \left(x , y\right)
F_{372}\! \left(x \right) = F_{373}\! \left(x \right)+F_{382}\! \left(x \right)+F_{90}\! \left(x \right)
F_{373}\! \left(x \right) = F_{374}\! \left(x \right)
F_{374}\! \left(x \right) = F_{375}\! \left(x \right) F_{8}\! \left(x \right)
F_{375}\! \left(x \right) = F_{376}\! \left(x \right)+F_{379}\! \left(x \right)
F_{376}\! \left(x \right) = F_{28}\! \left(x \right) F_{377}\! \left(x \right)
F_{377}\! \left(x \right) = F_{25}\! \left(x \right)+F_{378}\! \left(x \right)
F_{378}\! \left(x \right) = F_{59}\! \left(x , 1\right)
F_{379}\! \left(x \right) = F_{380}\! \left(x \right)+F_{381}\! \left(x \right)
F_{380}\! \left(x \right) = F_{167}\! \left(x , 1\right)
F_{381}\! \left(x \right) = F_{133}\! \left(x , 1\right)
F_{382}\! \left(x \right) = F_{383}\! \left(x \right)
F_{383}\! \left(x \right) = F_{384}\! \left(x \right) F_{8}\! \left(x \right)
F_{384}\! \left(x \right) = F_{385}\! \left(x \right)+F_{393}\! \left(x \right)
F_{385}\! \left(x \right) = F_{386}\! \left(x \right)+F_{388}\! \left(x \right)
F_{386}\! \left(x \right) = F_{387}\! \left(x , 1\right)
F_{387}\! \left(x , y\right) = -\frac{-y F_{54}\! \left(x , y\right)+F_{54}\! \left(x , 1\right)}{-1+y}
F_{388}\! \left(x \right) = F_{380}\! \left(x \right)+F_{389}\! \left(x \right)
F_{389}\! \left(x \right) = F_{390}\! \left(x \right)
F_{390}\! \left(x \right) = F_{25}\! \left(x \right) F_{391}\! \left(x \right)
F_{391}\! \left(x \right) = F_{392}\! \left(x , 1\right)
F_{392}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{393}\! \left(x \right) = F_{394}\! \left(x \right)+F_{396}\! \left(x \right)
F_{394}\! \left(x \right) = F_{158}\! \left(x \right)+F_{395}\! \left(x \right)
F_{395}\! \left(x \right) = F_{371}\! \left(x , 1\right)
F_{396}\! \left(x \right) = F_{397}\! \left(x \right)+F_{403}\! \left(x \right)
F_{397}\! \left(x \right) = F_{398}\! \left(x , 1\right)
F_{398}\! \left(x , y\right) = F_{399}\! \left(x , y\right)
F_{399}\! \left(x , y\right) = F_{400}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{400}\! \left(x , y\right) = F_{401}\! \left(x , y\right)+F_{402}\! \left(x , y\right)
F_{401}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{205}\! \left(x , y\right)
F_{402}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{174}\! \left(x , y\right)
F_{403}\! \left(x \right) = F_{404}\! \left(x , 1\right)
F_{404}\! \left(x , y\right) = F_{405}\! \left(x , y\right)+F_{427}\! \left(x , y\right)
F_{405}\! \left(x , y\right) = F_{406}\! \left(x , y\right)
F_{406}\! \left(x , y\right) = F_{407}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{407}\! \left(x , y\right) = F_{408}\! \left(x , y\right)+F_{426}\! \left(x , y\right)
F_{408}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{409}\! \left(x \right)
F_{409}\! \left(x \right) = \frac{F_{410}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{410}\! \left(x \right) = -F_{411}\! \left(x \right)-F_{90}\! \left(x \right)+F_{372}\! \left(x \right)
F_{411}\! \left(x \right) = F_{412}\! \left(x \right) F_{8}\! \left(x \right)
F_{412}\! \left(x \right) = F_{413}\! \left(x \right)+F_{414}\! \left(x \right)
F_{413}\! \left(x \right) = F_{372}\! \left(x \right)+F_{53}\! \left(x \right)
F_{414}\! \left(x \right) = F_{415}\! \left(x \right)+F_{417}\! \left(x \right)
F_{415}\! \left(x \right) = F_{416}\! \left(x \right)
F_{416}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{417}\! \left(x \right) = F_{418}\! \left(x \right)
F_{418}\! \left(x \right) = F_{419}\! \left(x \right) F_{8}\! \left(x \right)
F_{419}\! \left(x \right) = F_{420}\! \left(x \right)+F_{421}\! \left(x \right)
F_{420}\! \left(x \right) = F_{12}\! \left(x \right) F_{409}\! \left(x \right)
F_{421}\! \left(x \right) = F_{198}\! \left(x \right) F_{422}\! \left(x \right)
F_{422}\! \left(x \right) = F_{409}\! \left(x \right)+F_{423}\! \left(x \right)
F_{423}\! \left(x \right) = F_{424}\! \left(x \right)
F_{424}\! \left(x \right) = \frac{F_{425}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{425}\! \left(x \right) = F_{53}\! \left(x \right)
F_{426}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{422}\! \left(x \right)
F_{427}\! \left(x , y\right) = F_{428}\! \left(x , y\right)
F_{428}\! \left(x , y\right) = F_{429}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{429}\! \left(x , y\right) = F_{430}\! \left(x , y\right)+F_{492}\! \left(x , y\right)
F_{430}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{431}\! \left(x , y\right)
F_{432}\! \left(x , y\right) = F_{431}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{433}\! \left(x , y\right) = F_{432}\! \left(x , y\right)+F_{481}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{433}\! \left(x , y\right) = F_{434}\! \left(x , y\right)+F_{457}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{434}\! \left(x , y\right) = F_{435}\! \left(x , y\right)
F_{436}\! \left(x , y\right) = F_{435}\! \left(x , y\right)+F_{438}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{437}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{436}\! \left(x , y\right)
F_{437}\! \left(x , y\right) = -\frac{y \left(F_{104}\! \left(x , 1\right)-F_{104}\! \left(x , y\right)\right)}{-1+y}
F_{438}\! \left(x , y\right) = F_{439}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{439}\! \left(x , y\right) = F_{440}\! \left(x , y\right)+F_{449}\! \left(x , y\right)
F_{440}\! \left(x , y\right) = F_{441}\! \left(x , y\right)+F_{442}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{441}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{443}\! \left(x , y\right) = F_{380}\! \left(x \right)+F_{442}\! \left(x , y\right)
F_{443}\! \left(x , y\right) = -\frac{-F_{444}\! \left(x , y\right)+F_{444}\! \left(x , 1\right)}{-1+y}
F_{444}\! \left(x , y\right) = F_{445}\! \left(x , y\right)
F_{445}\! \left(x , y\right) = F_{446}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{446}\! \left(x , y\right) = F_{447}\! \left(x , y\right)+F_{448}\! \left(x , y\right)
F_{447}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{448}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{449}\! \left(x , y\right) = F_{436}\! \left(x , y\right)+F_{450}\! \left(x , y\right)
F_{451}\! \left(x , y\right) = F_{397}\! \left(x \right)+F_{450}\! \left(x , y\right)
F_{451}\! \left(x , y\right) = -\frac{-F_{452}\! \left(x , y\right)+F_{452}\! \left(x , 1\right)}{-1+y}
F_{452}\! \left(x , y\right) = F_{453}\! \left(x , y\right)
F_{453}\! \left(x , y\right) = F_{454}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{454}\! \left(x , y\right) = F_{455}\! \left(x , y\right)+F_{456}\! \left(x , y\right)
F_{455}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{204}\! \left(x \right)
F_{456}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{173}\! \left(x \right)
F_{457}\! \left(x , y\right) = F_{458}\! \left(x , y\right)
F_{458}\! \left(x , y\right) = F_{459}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{459}\! \left(x , y\right) = F_{460}\! \left(x , y\right)+F_{467}\! \left(x , y\right)
F_{460}\! \left(x , y\right) = F_{461}\! \left(x , y\right)+F_{463}\! \left(x , y\right)
F_{461}\! \left(x , y\right) = F_{441}\! \left(x , y\right)+F_{462}\! \left(x , y\right)
F_{462}\! \left(x , y\right) = -\frac{y \left(F_{441}\! \left(x , 1\right)-F_{441}\! \left(x , y\right)\right)}{-1+y}
F_{463}\! \left(x , y\right) = F_{442}\! \left(x , y\right)+F_{464}\! \left(x , y\right)
F_{464}\! \left(x , y\right) = F_{465}\! \left(x , y\right)
F_{465}\! \left(x , y\right) = -\frac{y \left(F_{466}\! \left(x , 1\right)-F_{466}\! \left(x , y\right)\right)}{-1+y}
F_{466}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{441}\! \left(x , y\right)
F_{467}\! \left(x , y\right) = F_{468}\! \left(x , y\right)+F_{470}\! \left(x , y\right)
F_{468}\! \left(x , y\right) = F_{436}\! \left(x , y\right)+F_{469}\! \left(x , y\right)
F_{469}\! \left(x , y\right) = -\frac{y \left(F_{433}\! \left(x , 1\right)-F_{433}\! \left(x , y\right)\right)}{-1+y}
F_{470}\! \left(x , y\right) = F_{450}\! \left(x , y\right)+F_{471}\! \left(x , y\right)
F_{471}\! \left(x , y\right) = -\frac{y \left(F_{472}\! \left(x , 1\right)-F_{472}\! \left(x , y\right)\right)}{-1+y}
F_{472}\! \left(x , y\right) = F_{473}\! \left(x , y\right)
F_{473}\! \left(x , y\right) = F_{474}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{474}\! \left(x , y\right) = F_{475}\! \left(x , y\right)+F_{476}\! \left(x , y\right)
F_{475}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{431}\! \left(x , y\right)
F_{476}\! \left(x , y\right) = F_{204}\! \left(x \right) F_{477}\! \left(x , y\right)
F_{477}\! \left(x , y\right) = F_{431}\! \left(x , y\right)+F_{478}\! \left(x , y\right)
F_{478}\! \left(x , y\right) = F_{479}\! \left(x , y\right)
F_{480}\! \left(x , y\right) = F_{479}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{480}\! \left(x , y\right) = F_{441}\! \left(x , y\right)
F_{481}\! \left(x , y\right) = F_{482}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{482}\! \left(x , y\right) = F_{483}\! \left(x , y\right)+F_{484}\! \left(x , y\right)
F_{483}\! \left(x , y\right) = F_{433}\! \left(x , y\right)+F_{441}\! \left(x , y\right)
F_{484}\! \left(x , y\right) = F_{485}\! \left(x , y\right)+F_{487}\! \left(x , y\right)
F_{485}\! \left(x , y\right) = F_{486}\! \left(x , y\right)
F_{486}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{441}\! \left(x , y\right)
F_{487}\! \left(x , y\right) = F_{488}\! \left(x , y\right)
F_{488}\! \left(x , y\right) = F_{489}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{489}\! \left(x , y\right) = F_{490}\! \left(x , y\right)+F_{491}\! \left(x , y\right)
F_{490}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{431}\! \left(x , y\right)
F_{491}\! \left(x , y\right) = F_{198}\! \left(x \right) F_{477}\! \left(x , y\right)
F_{492}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{477}\! \left(x , y\right)
F_{493}\! \left(x , y\right) = F_{494}\! \left(x , y\right)+F_{528}\! \left(x , y\right)
F_{494}\! \left(x , y\right) = F_{495}\! \left(x , y\right)+F_{496}\! \left(x , y\right)
F_{495}\! \left(x , y\right) = F_{174}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{496}\! \left(x , y\right) = F_{497}\! \left(x , y\right)+F_{508}\! \left(x , y\right)
F_{497}\! \left(x , y\right) = F_{498}\! \left(x , y\right)
F_{498}\! \left(x , y\right) = F_{499}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{499}\! \left(x , y\right) = F_{500}\! \left(x , y\right)+F_{501}\! \left(x , y\right)
F_{500}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{338}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{501}\! \left(x , y\right) = F_{347}\! \left(x \right) F_{502}\! \left(x , y\right)
F_{502}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{503}\! \left(x , y\right)
F_{503}\! \left(x , y\right) = F_{504}\! \left(x , y\right)
F_{504}\! \left(x , y\right) = F_{505}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{505}\! \left(x , y\right) = F_{506}\! \left(x , y\right)+F_{507}\! \left(x , y\right)
F_{506}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{34}\! \left(x , y\right) F_{340}\! \left(x \right)
F_{507}\! \left(x , y\right) = F_{346}\! \left(x \right) F_{502}\! \left(x , y\right)
F_{508}\! \left(x , y\right) = F_{509}\! \left(x , y\right)+F_{526}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{509}\! \left(x , y\right) = F_{510}\! \left(x , y\right)
F_{510}\! \left(x , y\right) = F_{511}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{511}\! \left(x , y\right) = F_{512}\! \left(x , y\right)+F_{514}\! \left(x , y\right)
F_{512}\! \left(x , y\right) = F_{338}\! \left(x \right) F_{34}\! \left(x , y\right) F_{513}\! \left(x , y\right)
F_{513}\! \left(x , y\right) = -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}
F_{514}\! \left(x , y\right) = F_{347}\! \left(x \right) F_{515}\! \left(x , y\right)
F_{515}\! \left(x , y\right) = F_{516}\! \left(x , y\right)+F_{517}\! \left(x , y\right)
F_{516}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{517}\! \left(x , y\right) = F_{518}\! \left(x , y\right)+F_{523}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{518}\! \left(x , y\right) = F_{519}\! \left(x , y\right)
F_{519}\! \left(x , y\right) = F_{520}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{520}\! \left(x , y\right) = F_{521}\! \left(x , y\right)+F_{522}\! \left(x , y\right)
F_{521}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{340}\! \left(x \right) F_{513}\! \left(x , y\right)
F_{522}\! \left(x , y\right) = F_{346}\! \left(x \right) F_{515}\! \left(x , y\right)
F_{523}\! \left(x , y\right) = F_{524}\! \left(x , y\right)
F_{524}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{525}\! \left(x , y\right)
F_{525}\! \left(x , y\right) = F_{503}\! \left(x , y\right)+F_{517}\! \left(x , y\right)
F_{526}\! \left(x , y\right) = F_{527}\! \left(x , y\right)
F_{527}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{496}\! \left(x , y\right)
F_{528}\! \left(x , y\right) = F_{404}\! \left(x , y\right)+F_{529}\! \left(x , y\right)
F_{529}\! \left(x , y\right) = F_{398}\! \left(x , y\right)+F_{530}\! \left(x , y\right)
F_{530}\! \left(x , y\right) = F_{531}\! \left(x , y\right)
F_{531}\! \left(x , y\right) = F_{532}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{532}\! \left(x , y\right) = F_{533}\! \left(x , y\right)+F_{534}\! \left(x , y\right)
F_{533}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{88}\! \left(x \right)
F_{534}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{174}\! \left(x , y\right)
F_{535}\! \left(x \right) = F_{536}\! \left(x \right)+F_{539}\! \left(x \right)
F_{536}\! \left(x \right) = F_{537}\! \left(x \right)+F_{538}\! \left(x \right)
F_{537}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{538}\! \left(x \right) = F_{182}\! \left(x , 1\right)
F_{539}\! \left(x \right) = F_{540}\! \left(x \right)+F_{541}\! \left(x \right)
F_{540}\! \left(x \right) = F_{204}\! \left(x \right) F_{28}\! \left(x \right)
F_{541}\! \left(x \right) = F_{302}\! \left(x , 1\right)
F_{542}\! \left(x \right) = F_{543}\! \left(x \right)+F_{544}\! \left(x \right)
F_{543}\! \left(x \right) = F_{348}\! \left(x \right)+F_{52}\! \left(x \right)
F_{544}\! \left(x \right) = F_{338}\! \left(x \right)+F_{545}\! \left(x \right)
F_{545}\! \left(x \right) = F_{372}\! \left(x \right)+F_{84}\! \left(x \right)
F_{546}\! \left(x \right) = F_{18}\! \left(x \right)+F_{198}\! \left(x \right)
F_{547}\! \left(x \right) = F_{50}\! \left(x \right)+F_{548}\! \left(x \right)
F_{548}\! \left(x \right) = F_{334}\! \left(x \right)+F_{545}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(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_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_547(x))
Eq(F_10(x), F_11(x) + F_546(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), 16*x + (x + 1)**3*(F_12(x) + 1)**2 + (F_12(x) + 1)*(8*x**2 - 20*x - 1) + F_12(x))
Eq(F_13(x), F_14(x) + F_2(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_542(x))
Eq(F_17(x), F_13(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_12(x)*F_2(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_8(x))
Eq(F_22(x), F_23(x) + F_535(x))
Eq(F_23(x), F_24(x)*F_27(x))
Eq(F_24(x), F_1(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_24(x)**2*F_8(x))
Eq(F_27(x), F_172(x) + F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_36(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_38(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_37(x, k_0))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_33(x, k_0)**2*F_36(x, k_0))
Eq(F_36(x, k_0), k_0*x)
Eq(F_37(x, k_0), F_2(x) + F_29(x, k_0))
Eq(F_38(x, k_0), F_159(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0) + F_41(x, k_0))
Eq(F_40(x, k_0), F_2(x)*F_33(x, k_0))
Eq(F_41(x, k_0), F_42(x) + F_54(x, k_0))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x)*F_8(x))
Eq(F_44(x), F_45(x) + F_49(x))
Eq(F_45(x), F_11(x) + F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_25(x) + F_48(x))
Eq(F_48(x), F_2(x) + F_28(x))
Eq(F_49(x), F_155(x) + F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_2(x)*F_25(x))
Eq(F_52(x), F_42(x) + F_53(x))
Eq(F_53(x), F_54(x, 1))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0)*F_8(x))
Eq(F_56(x, k_0), F_146(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_138(x, k_0) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_65(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_33(x, k_0)*F_36(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_63(x, k_0))
Eq(F_62(x, k_0), F_12(x) + F_59(x, k_0))
Eq(F_63(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_65(x, k_0), F_29(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_36(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_75(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_71(x, k_0))
Eq(F_70(x, k_0), F_14(x) + F_66(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_74(x, k_0))
Eq(F_72(x, k_0), (k_0*F_73(x, k_0) - F_73(x, 1))/(k_0 - 1))
Eq(F_73(x, k_0), F_12(x)*F_37(x, k_0))
Eq(F_74(x, k_0), F_37(x, k_0)*F_59(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_79(x, k_0))
Eq(F_76(x, k_0), -F_77(x, k_0) + (k_0*F_77(x, k_0) - F_77(x, 1))/(k_0 - 1))
Eq(F_77(x, k_0), F_54(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_2(x)*F_34(x, k_0))
Eq(F_79(x, k_0), F_125(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), (k_0*F_81(x, k_0) - F_81(x, 1))/(k_0 - 1))
Eq(F_81(x, k_0), F_82(x, k_0) + F_83(x, k_0))
Eq(F_82(x, k_0), F_14(x)*F_33(x, k_0))
Eq(F_83(x, k_0), F_104(x, k_0) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_8(x)*F_86(x))
Eq(F_86(x), F_103(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_8(x))
Eq(F_89(x), F_42(x) - F_90(x) - F_91(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_8(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_2(x) + F_42(x))
Eq(F_94(x), F_95(x) + F_97(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_2(x)**2)
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_8(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_2(x)*F_88(x))
Eq(F_101(x), F_102(x)*F_6(x))
Eq(F_102(x), F_4(x) + F_88(x))
Eq(F_103(x), F_102(x)*F_14(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_8(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_124(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_12(x))
Eq(F_109(x, k_0), F_108(x, k_0)*F_8(x))
Eq(F_54(x, k_0), F_109(x, k_0) + F_110(x, k_0) + F_90(x))
Eq(F_110(x, k_0), F_111(x, k_0)*F_8(x))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_29(x, k_0) + F_54(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_116(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_2(x)*F_29(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_8(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), F_108(x, k_0)*F_2(x))
Eq(F_120(x, k_0), F_121(x, k_0)*F_6(x))
Eq(F_121(x, k_0), F_108(x, k_0) + F_122(x, k_0))
Eq(F_123(x, k_0), F_122(x, k_0)*F_8(x))
Eq(F_123(x, k_0), F_29(x, k_0))
Eq(F_124(x, k_0), F_121(x, k_0)*F_14(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_33(x, k_0)*F_66(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_133(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_8(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_132(x, k_0))
Eq(F_131(x, k_0), F_59(x, k_0)*F_88(x))
Eq(F_132(x, k_0), F_102(x)*F_66(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_8(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_137(x, k_0))
Eq(F_136(x, k_0), F_108(x, k_0)*F_59(x, k_0))
Eq(F_137(x, k_0), F_121(x, k_0)*F_66(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0) + F_145(x, k_0))
Eq(F_139(x, k_0), -F_140(x, 1) - F_140(x, k_0) + (k_0*F_140(x, k_0) - F_140(x, 1))/(k_0 - 1))
Eq(F_140(x, k_0), F_141(x, k_0)*F_2(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_36(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_34(x, k_0))
Eq(F_144(x, k_0), F_33(x, k_0)*F_34(x, k_0))
Eq(F_145(x, k_0), -F_54(x, 1) + (k_0*F_54(x, k_0) - F_54(x, 1))/(k_0 - 1))
Eq(F_146(x, k_0), F_147(x, k_0) + F_152(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_2(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_151(x, k_0))
Eq(F_150(x, k_0), -F_141(x, 1) - F_141(x, k_0) + (k_0*F_141(x, k_0) - F_141(x, 1))/(k_0 - 1))
Eq(F_151(x, k_0), -F_29(x, 1) + (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_153(x, k_0) + F_154(x, k_0))
Eq(F_153(x, k_0), F_150(x, k_0)*F_6(x))
Eq(F_154(x, k_0), -F_116(x, 1) + (k_0*F_116(x, k_0) - F_116(x, 1))/(k_0 - 1))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_14(x)*F_25(x))
Eq(F_157(x), F_158(x) + F_84(x))
Eq(F_158(x), F_104(x, 1))
Eq(F_159(x, k_0), F_160(x, k_0) + F_161(x, k_0))
Eq(F_160(x, k_0), F_29(x, k_0)*F_33(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0) + F_167(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_8(x))
Eq(F_164(x, k_0), F_165(x, k_0) + F_166(x, k_0))
Eq(F_165(x, k_0), F_34(x, k_0)*F_88(x))
Eq(F_166(x, k_0), F_102(x)*F_29(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_8(x))
Eq(F_169(x, k_0), F_170(x, k_0) + F_171(x, k_0))
Eq(F_170(x, k_0), F_108(x, k_0)*F_34(x, k_0))
Eq(F_171(x, k_0), F_121(x, k_0)*F_29(x, k_0))
Eq(F_172(x), F_14(x) + F_173(x))
Eq(F_173(x), F_174(x, 1))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0)*F_36(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_327(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0) + F_180(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0)*F_33(x, k_0))
Eq(F_179(x, k_0), F_14(x) + F_174(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0) + F_300(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_73(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0) + F_20(x))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_8(x))
Eq(F_185(x, k_0), F_186(x, k_0) + F_193(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0) + F_190(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_189(x, k_0))
Eq(F_151(x, k_0), F_188(x, k_0) + F_29(x, k_0))
Eq(F_189(x, k_0), -F_174(x, 1) + (k_0*F_174(x, k_0) - F_174(x, 1))/(k_0 - 1))
Eq(F_190(x, k_0), F_191(x, k_0) + F_192(x, k_0))
Eq(F_191(x, k_0), F_12(x)*F_188(x, k_0))
Eq(F_192(x, k_0), -F_183(x, 1) + (k_0*F_183(x, k_0) - F_183(x, 1))/(k_0 - 1))
Eq(F_193(x, k_0), F_194(x, k_0) + F_196(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_12(x)*F_187(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_283(x, k_0))
Eq(F_197(x, k_0), F_188(x, k_0)*F_198(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x)*F_8(x))
Eq(F_200(x), F_201(x) + F_276(x))
Eq(F_201(x), F_202(x)*F_24(x))
Eq(F_202(x), F_203(x) + F_25(x))
Eq(F_203(x), F_12(x) + F_204(x))
Eq(F_204(x), F_205(x, 1))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0)*F_36(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_210(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0)*F_33(x, k_0))
Eq(F_209(x, k_0), F_12(x) + F_205(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0) + F_246(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0) + F_64(x, k_0))
Eq(F_212(x, k_0), F_198(x) + F_213(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0)*F_8(x))
Eq(F_215(x, k_0), F_216(x, k_0) + F_223(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_219(x, k_0))
Eq(F_217(x, k_0), F_150(x, k_0) + F_218(x, k_0))
Eq(F_218(x, k_0), -F_205(x, 1) + (k_0*F_205(x, k_0) - F_205(x, 1))/(k_0 - 1))
Eq(F_219(x, k_0), F_220(x, k_0) + F_222(x, k_0))
Eq(F_220(x, k_0), -F_221(x, 1) - F_221(x, k_0) + (k_0*F_221(x, k_0) - F_221(x, 1))/(k_0 - 1))
Eq(F_221(x, k_0), F_12(x)*F_141(x, k_0))
Eq(F_222(x, k_0), -F_213(x, 1) + (k_0*F_213(x, k_0) - F_213(x, 1))/(k_0 - 1))
Eq(F_223(x, k_0), F_224(x, k_0) + F_226(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0))
Eq(F_225(x, k_0), F_12(x)*F_217(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_229(x, k_0))
Eq(F_227(x, k_0), -F_228(x, 1) - F_228(x, k_0) + (k_0*F_228(x, k_0) - F_228(x, 1))/(k_0 - 1))
Eq(F_228(x, k_0), F_141(x, k_0)*F_198(x))
Eq(F_229(x, k_0), -F_230(x, 1) + (k_0*F_230(x, k_0) - F_230(x, 1))/(k_0 - 1))
Eq(F_230(x, k_0), F_231(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0)*F_8(x))
Eq(F_232(x, k_0), F_233(x, k_0) + F_242(x, k_0))
Eq(F_233(x, k_0), F_12(x)*F_234(x, k_0))
Eq(F_235(x, k_0), F_234(x, k_0)*F_8(x))
Eq(F_213(x, k_0), F_235(x, k_0) + F_236(x, k_0) + F_90(x))
Eq(F_236(x, k_0), F_237(x, k_0)*F_8(x))
Eq(F_237(x, k_0), F_238(x, k_0) + F_239(x, k_0))
Eq(F_238(x, k_0), F_205(x, k_0) + F_213(x, k_0))
Eq(F_239(x, k_0), F_230(x, k_0) + F_240(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0))
Eq(F_241(x, k_0), F_12(x)*F_205(x, k_0))
Eq(F_242(x, k_0), F_198(x)*F_243(x, k_0))
Eq(F_243(x, k_0), F_234(x, k_0) + F_244(x, k_0))
Eq(F_245(x, k_0), F_244(x, k_0)*F_8(x))
Eq(F_245(x, k_0), F_205(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0) + F_248(x, k_0))
Eq(F_247(x, k_0), F_205(x, k_0)*F_33(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_271(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0)*F_8(x))
Eq(F_251(x, k_0), F_252(x, k_0) + F_270(x, k_0))
Eq(F_252(x, k_0), F_253(x)*F_34(x, k_0))
Eq(F_253(x), F_254(x)/F_8(x))
Eq(F_254(x), F_198(x) - F_255(x) - F_90(x))
Eq(F_255(x), F_256(x)*F_8(x))
Eq(F_256(x), F_257(x) + F_258(x))
Eq(F_257(x), F_12(x) + F_198(x))
Eq(F_258(x), F_259(x) + F_261(x))
Eq(F_259(x), F_260(x))
Eq(F_260(x), F_12(x)**2)
Eq(F_261(x), F_262(x))
Eq(F_262(x), F_263(x)*F_8(x))
Eq(F_263(x), F_264(x) + F_265(x))
Eq(F_264(x), F_12(x)*F_253(x))
Eq(F_265(x), F_198(x)*F_266(x))
Eq(F_266(x), F_253(x) + F_267(x))
Eq(F_267(x), F_268(x) + F_269(x))
Eq(F_268(x), 16*x + (x + 1)**3*F_268(x)**2 + (8*x**2 - 20*x)*F_268(x))
Eq(F_269(x), F_12(x) + F_198(x))
Eq(F_270(x, k_0), F_205(x, k_0)*F_266(x))
Eq(F_271(x, k_0), F_272(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0)*F_8(x))
Eq(F_273(x, k_0), F_274(x, k_0) + F_275(x, k_0))
Eq(F_274(x, k_0), F_234(x, k_0)*F_34(x, k_0))
Eq(F_275(x, k_0), F_205(x, k_0)*F_243(x, k_0))
Eq(F_276(x), F_277(x) + F_280(x))
Eq(F_277(x), F_278(x) + F_279(x))
Eq(F_278(x), F_12(x)*F_25(x))
Eq(F_279(x), F_212(x, 1))
Eq(F_280(x), F_281(x) + F_282(x))
Eq(F_281(x), F_204(x)*F_25(x))
Eq(F_282(x), F_248(x, 1))
Eq(F_283(x, k_0), -F_284(x, 1) + (k_0*F_284(x, k_0) - F_284(x, 1))/(k_0 - 1))
Eq(F_284(x, k_0), F_285(x, k_0))
Eq(F_285(x, k_0), F_286(x, k_0)*F_8(x))
Eq(F_286(x, k_0), F_287(x, k_0) + F_296(x, k_0))
Eq(F_287(x, k_0), F_12(x)*F_288(x, k_0))
Eq(F_289(x, k_0), F_288(x, k_0)*F_8(x))
Eq(F_183(x, k_0), F_289(x, k_0) + F_290(x, k_0) + F_90(x))
Eq(F_290(x, k_0), F_291(x, k_0)*F_8(x))
Eq(F_291(x, k_0), F_292(x, k_0) + F_293(x, k_0))
Eq(F_292(x, k_0), F_174(x, k_0) + F_183(x, k_0))
Eq(F_293(x, k_0), F_284(x, k_0) + F_294(x, k_0))
Eq(F_294(x, k_0), F_295(x, k_0))
Eq(F_295(x, k_0), F_12(x)*F_174(x, k_0))
Eq(F_296(x, k_0), F_198(x)*F_297(x, k_0))
Eq(F_297(x, k_0), F_288(x, k_0) + F_298(x, k_0))
Eq(F_299(x, k_0), F_298(x, k_0)*F_8(x))
Eq(F_299(x, k_0), F_174(x, k_0))
Eq(F_300(x, k_0), F_301(x, k_0) + F_302(x, k_0))
Eq(F_301(x, k_0), F_205(x, k_0)*F_37(x, k_0))
Eq(F_302(x, k_0), F_303(x, k_0) + F_322(x, k_0))
Eq(F_303(x, k_0), F_304(x, k_0))
Eq(F_304(x, k_0), F_305(x, k_0)*F_8(x))
Eq(F_305(x, k_0), F_306(x, k_0) + F_321(x, k_0))
Eq(F_306(x, k_0), F_307(x)*F_34(x, k_0))
Eq(F_307(x), F_308(x)/F_8(x))
Eq(F_308(x), F_20(x) - F_309(x) - F_90(x))
Eq(F_309(x), F_310(x)*F_8(x))
Eq(F_310(x), F_311(x) + F_312(x))
Eq(F_311(x), F_14(x) + F_20(x))
Eq(F_312(x), F_313(x) + F_315(x))
Eq(F_313(x), F_314(x))
Eq(F_314(x), F_12(x)*F_14(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_317(x)*F_8(x))
Eq(F_317(x), F_318(x) + F_319(x))
Eq(F_318(x), F_12(x)*F_307(x))
Eq(F_319(x), F_198(x)*F_320(x))
Eq(F_320(x), F_16(x) + F_307(x))
Eq(F_321(x, k_0), F_205(x, k_0)*F_320(x))
Eq(F_322(x, k_0), F_323(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0)*F_8(x))
Eq(F_324(x, k_0), F_325(x, k_0) + F_326(x, k_0))
Eq(F_325(x, k_0), F_288(x, k_0)*F_34(x, k_0))
Eq(F_326(x, k_0), F_205(x, k_0)*F_297(x, k_0))
Eq(F_327(x, k_0), F_328(x, k_0) + F_330(x, k_0))
Eq(F_328(x, k_0), F_329(x, k_0))
Eq(F_329(x, k_0), F_33(x, k_0)*F_76(x, k_0))
Eq(F_330(x, k_0), F_331(x, k_0) + F_493(x, k_0))
Eq(F_331(x, k_0), F_332(x, k_0) + F_370(x, k_0))
Eq(F_332(x, k_0), F_333(x, k_0) + F_82(x, k_0))
Eq(F_333(x, k_0), F_334(x) + F_349(x, k_0))
Eq(F_334(x), F_335(x))
Eq(F_335(x), F_336(x)*F_8(x))
Eq(F_336(x), F_337(x) + F_339(x))
Eq(F_337(x), F_24(x)*F_338(x))
Eq(F_338(x), F_14(x) + F_334(x))
Eq(F_339(x), F_340(x)*F_347(x))
Eq(F_340(x), F_12(x) + F_341(x))
Eq(F_341(x), F_342(x))
Eq(F_342(x), F_343(x)*F_8(x))
Eq(F_343(x), F_344(x) + F_345(x))
Eq(F_344(x), F_24(x)*F_340(x))
Eq(F_345(x), F_340(x)*F_346(x))
Eq(F_346(x), F_24(x) + F_340(x))
Eq(F_347(x), F_338(x) + F_348(x))
Eq(F_348(x), F_2(x)*F_24(x))
Eq(F_349(x, k_0), F_350(x, k_0) + F_368(x, k_0) + F_90(x))
Eq(F_350(x, k_0), F_351(x, k_0))
Eq(F_351(x, k_0), F_352(x, k_0)*F_8(x))
Eq(F_352(x, k_0), F_353(x, k_0) + F_355(x, k_0))
Eq(F_353(x, k_0), -F_354(x, 1) + (k_0*F_354(x, k_0) - F_354(x, 1))/(k_0 - 1))
Eq(F_354(x, k_0), F_338(x)*F_34(x, k_0))
Eq(F_355(x, k_0), F_347(x)*F_356(x, k_0))
Eq(F_356(x, k_0), F_357(x, k_0) + F_358(x, k_0))
Eq(F_357(x, k_0), F_12(x)*F_34(x, k_0))
Eq(F_358(x, k_0), F_359(x, k_0) + F_365(x, k_0) + F_90(x))
Eq(F_359(x, k_0), F_360(x, k_0))
Eq(F_360(x, k_0), F_361(x, k_0)*F_8(x))
Eq(F_361(x, k_0), F_362(x, k_0) + F_364(x, k_0))
Eq(F_362(x, k_0), -F_363(x, 1) + (k_0*F_363(x, k_0) - F_363(x, 1))/(k_0 - 1))
Eq(F_363(x, k_0), F_34(x, k_0)*F_340(x))
Eq(F_364(x, k_0), F_346(x)*F_356(x, k_0))
Eq(F_365(x, k_0), F_366(x, k_0))
Eq(F_366(x, k_0), F_33(x, k_0)*F_36(x, k_0)*F_367(x, k_0))
Eq(F_367(x, k_0), F_341(x) + F_358(x, k_0))
Eq(F_368(x, k_0), F_369(x, k_0))
Eq(F_369(x, k_0), F_33(x, k_0)*F_333(x, k_0)*F_36(x, k_0))
Eq(F_370(x, k_0), F_371(x, k_0) + F_83(x, k_0))
Eq(F_371(x, k_0), F_372(x) + F_433(x, k_0))
Eq(F_372(x), F_373(x) + F_382(x) + F_90(x))
Eq(F_373(x), F_374(x))
Eq(F_374(x), F_375(x)*F_8(x))
Eq(F_375(x), F_376(x) + F_379(x))
Eq(F_376(x), F_28(x)*F_377(x))
Eq(F_377(x), F_25(x) + F_378(x))
Eq(F_378(x), F_59(x, 1))
Eq(F_379(x), F_380(x) + F_381(x))
Eq(F_380(x), F_167(x, 1))
Eq(F_381(x), F_133(x, 1))
Eq(F_382(x), F_383(x))
Eq(F_383(x), F_384(x)*F_8(x))
Eq(F_384(x), F_385(x) + F_393(x))
Eq(F_385(x), F_386(x) + F_388(x))
Eq(F_386(x), F_387(x, 1))
Eq(F_387(x, k_0), (-k_0*F_54(x, k_0) + F_54(x, 1))/(1 - k_0))
Eq(F_388(x), F_380(x) + F_389(x))
Eq(F_389(x), F_390(x))
Eq(F_390(x), F_25(x)*F_391(x))
Eq(F_391(x), F_392(x, 1))
Eq(F_392(x, k_0), -F_54(x, 1) + (-k_0*F_54(x, k_0) + F_54(x, 1))/(1 - k_0))
Eq(F_393(x), F_394(x) + F_396(x))
Eq(F_394(x), F_158(x) + F_395(x))
Eq(F_395(x), F_371(x, 1))
Eq(F_396(x), F_397(x) + F_403(x))
Eq(F_397(x), F_398(x, 1))
Eq(F_398(x, k_0), F_399(x, k_0))
Eq(F_399(x, k_0), F_400(x, k_0)*F_8(x))
Eq(F_400(x, k_0), F_401(x, k_0) + F_402(x, k_0))
Eq(F_401(x, k_0), F_108(x, k_0)*F_205(x, k_0))
Eq(F_402(x, k_0), F_121(x, k_0)*F_174(x, k_0))
Eq(F_403(x), F_404(x, 1))
Eq(F_404(x, k_0), F_405(x, k_0) + F_427(x, k_0))
Eq(F_405(x, k_0), F_406(x, k_0))
Eq(F_406(x, k_0), F_407(x, k_0)*F_8(x))
Eq(F_407(x, k_0), F_408(x, k_0) + F_426(x, k_0))
Eq(F_408(x, k_0), F_34(x, k_0)*F_409(x))
Eq(F_409(x), F_410(x)/F_8(x))
Eq(F_410(x), F_372(x) - F_411(x) - F_90(x))
Eq(F_411(x), F_412(x)*F_8(x))
Eq(F_412(x), F_413(x) + F_414(x))
Eq(F_413(x), F_372(x) + F_53(x))
Eq(F_414(x), F_415(x) + F_417(x))
Eq(F_415(x), F_416(x))
Eq(F_416(x), F_12(x)*F_53(x))
Eq(F_417(x), F_418(x))
Eq(F_418(x), F_419(x)*F_8(x))
Eq(F_419(x), F_420(x) + F_421(x))
Eq(F_420(x), F_12(x)*F_409(x))
Eq(F_421(x), F_198(x)*F_422(x))
Eq(F_422(x), F_409(x) + F_423(x))
Eq(F_423(x), F_424(x))
Eq(F_424(x), F_425(x)/F_8(x))
Eq(F_425(x), F_53(x))
Eq(F_426(x, k_0), F_205(x, k_0)*F_422(x))
Eq(F_427(x, k_0), F_428(x, k_0))
Eq(F_428(x, k_0), F_429(x, k_0)*F_8(x))
Eq(F_429(x, k_0), F_430(x, k_0) + F_492(x, k_0))
Eq(F_430(x, k_0), F_34(x, k_0)*F_431(x, k_0))
Eq(F_432(x, k_0), F_431(x, k_0)*F_8(x))
Eq(F_433(x, k_0), F_432(x, k_0) + F_481(x, k_0) + F_90(x))
Eq(F_433(x, k_0), F_434(x, k_0) + F_457(x, k_0) + F_90(x))
Eq(F_434(x, k_0), F_435(x, k_0))
Eq(F_436(x, k_0), F_435(x, k_0) + F_438(x, k_0) + F_90(x))
Eq(F_437(x, k_0), F_104(x, k_0) + F_436(x, k_0))
Eq(F_437(x, k_0), -F_104(x, 1) + (k_0*F_104(x, k_0) - F_104(x, 1))/(k_0 - 1))
Eq(F_438(x, k_0), F_439(x, k_0)*F_8(x))
Eq(F_439(x, k_0), F_440(x, k_0) + F_449(x, k_0))
Eq(F_440(x, k_0), F_441(x, k_0) + F_442(x, k_0))
Eq(F_145(x, k_0), F_441(x, k_0) + F_54(x, k_0))
Eq(F_443(x, k_0), F_380(x) + F_442(x, k_0))
Eq(F_443(x, k_0), -F_444(x, k_0) + (k_0*F_444(x, k_0) - F_444(x, 1))/(k_0 - 1))
Eq(F_444(x, k_0), F_445(x, k_0))
Eq(F_445(x, k_0), F_446(x, k_0)*F_8(x))
Eq(F_446(x, k_0), F_447(x, k_0) + F_448(x, k_0))
Eq(F_447(x, k_0), F_108(x, k_0)*F_25(x))
Eq(F_448(x, k_0), F_121(x, k_0)*F_28(x))
Eq(F_449(x, k_0), F_436(x, k_0) + F_450(x, k_0))
Eq(F_451(x, k_0), F_397(x) + F_450(x, k_0))
Eq(F_451(x, k_0), -F_452(x, k_0) + (k_0*F_452(x, k_0) - F_452(x, 1))/(k_0 - 1))
Eq(F_452(x, k_0), F_453(x, k_0))
Eq(F_453(x, k_0), F_454(x, k_0)*F_8(x))
Eq(F_454(x, k_0), F_455(x, k_0) + F_456(x, k_0))
Eq(F_455(x, k_0), F_108(x, k_0)*F_204(x))
Eq(F_456(x, k_0), F_121(x, k_0)*F_173(x))
Eq(F_457(x, k_0), F_458(x, k_0))
Eq(F_458(x, k_0), F_459(x, k_0)*F_8(x))
Eq(F_459(x, k_0), F_460(x, k_0) + F_467(x, k_0))
Eq(F_460(x, k_0), F_461(x, k_0) + F_463(x, k_0))
Eq(F_461(x, k_0), F_441(x, k_0) + F_462(x, k_0))
Eq(F_462(x, k_0), -F_441(x, 1) + (k_0*F_441(x, k_0) - F_441(x, 1))/(k_0 - 1))
Eq(F_463(x, k_0), F_442(x, k_0) + F_464(x, k_0))
Eq(F_464(x, k_0), F_465(x, k_0))
Eq(F_465(x, k_0), -F_466(x, 1) + (k_0*F_466(x, k_0) - F_466(x, 1))/(k_0 - 1))
Eq(F_466(x, k_0), F_25(x)*F_441(x, k_0))
Eq(F_467(x, k_0), F_468(x, k_0) + F_470(x, k_0))
Eq(F_468(x, k_0), F_436(x, k_0) + F_469(x, k_0))
Eq(F_469(x, k_0), -F_433(x, 1) + (k_0*F_433(x, k_0) - F_433(x, 1))/(k_0 - 1))
Eq(F_470(x, k_0), F_450(x, k_0) + F_471(x, k_0))
Eq(F_471(x, k_0), -F_472(x, 1) + (k_0*F_472(x, k_0) - F_472(x, 1))/(k_0 - 1))
Eq(F_472(x, k_0), F_473(x, k_0))
Eq(F_473(x, k_0), F_474(x, k_0)*F_8(x))
Eq(F_474(x, k_0), F_475(x, k_0) + F_476(x, k_0))
Eq(F_475(x, k_0), F_25(x)*F_431(x, k_0))
Eq(F_476(x, k_0), F_204(x)*F_477(x, k_0))
Eq(F_477(x, k_0), F_431(x, k_0) + F_478(x, k_0))
Eq(F_478(x, k_0), F_479(x, k_0))
Eq(F_480(x, k_0), F_479(x, k_0)*F_8(x))
Eq(F_480(x, k_0), F_441(x, k_0))
Eq(F_481(x, k_0), F_482(x, k_0)*F_8(x))
Eq(F_482(x, k_0), F_483(x, k_0) + F_484(x, k_0))
Eq(F_483(x, k_0), F_433(x, k_0) + F_441(x, k_0))
Eq(F_484(x, k_0), F_485(x, k_0) + F_487(x, k_0))
Eq(F_485(x, k_0), F_486(x, k_0))
Eq(F_486(x, k_0), F_12(x)*F_441(x, k_0))
Eq(F_487(x, k_0), F_488(x, k_0))
Eq(F_488(x, k_0), F_489(x, k_0)*F_8(x))
Eq(F_489(x, k_0), F_490(x, k_0) + F_491(x, k_0))
Eq(F_490(x, k_0), F_12(x)*F_431(x, k_0))
Eq(F_491(x, k_0), F_198(x)*F_477(x, k_0))
Eq(F_492(x, k_0), F_205(x, k_0)*F_477(x, k_0))
Eq(F_493(x, k_0), F_494(x, k_0) + F_528(x, k_0))
Eq(F_494(x, k_0), F_495(x, k_0) + F_496(x, k_0))
Eq(F_495(x, k_0), F_174(x, k_0)*F_33(x, k_0))
Eq(F_496(x, k_0), F_497(x, k_0) + F_508(x, k_0))
Eq(F_497(x, k_0), F_498(x, k_0))
Eq(F_498(x, k_0), F_499(x, k_0)*F_8(x))
Eq(F_499(x, k_0), F_500(x, k_0) + F_501(x, k_0))
Eq(F_500(x, k_0), F_24(x)*F_338(x)*F_34(x, k_0))
Eq(F_501(x, k_0), F_347(x)*F_502(x, k_0))
Eq(F_502(x, k_0), F_205(x, k_0) + F_503(x, k_0))
Eq(F_503(x, k_0), F_504(x, k_0))
Eq(F_504(x, k_0), F_505(x, k_0)*F_8(x))
Eq(F_505(x, k_0), F_506(x, k_0) + F_507(x, k_0))
Eq(F_506(x, k_0), F_24(x)*F_34(x, k_0)*F_340(x))
Eq(F_507(x, k_0), F_346(x)*F_502(x, k_0))
Eq(F_508(x, k_0), F_509(x, k_0) + F_526(x, k_0) + F_90(x))
Eq(F_509(x, k_0), F_510(x, k_0))
Eq(F_510(x, k_0), F_511(x, k_0)*F_8(x))
Eq(F_511(x, k_0), F_512(x, k_0) + F_514(x, k_0))
Eq(F_512(x, k_0), F_338(x)*F_34(x, k_0)*F_513(x, k_0))
Eq(F_513(x, k_0), -F_34(x, 1) + (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_514(x, k_0), F_347(x)*F_515(x, k_0))
Eq(F_515(x, k_0), F_516(x, k_0) + F_517(x, k_0))
Eq(F_516(x, k_0), F_205(x, k_0)*F_34(x, k_0))
Eq(F_517(x, k_0), F_518(x, k_0) + F_523(x, k_0) + F_90(x))
Eq(F_518(x, k_0), F_519(x, k_0))
Eq(F_519(x, k_0), F_520(x, k_0)*F_8(x))
Eq(F_520(x, k_0), F_521(x, k_0) + F_522(x, k_0))
Eq(F_521(x, k_0), F_34(x, k_0)*F_340(x)*F_513(x, k_0))
Eq(F_522(x, k_0), F_346(x)*F_515(x, k_0))
Eq(F_523(x, k_0), F_524(x, k_0))
Eq(F_524(x, k_0), F_33(x, k_0)*F_36(x, k_0)*F_525(x, k_0))
Eq(F_525(x, k_0), F_503(x, k_0) + F_517(x, k_0))
Eq(F_526(x, k_0), F_527(x, k_0))
Eq(F_527(x, k_0), F_33(x, k_0)*F_36(x, k_0)*F_496(x, k_0))
Eq(F_528(x, k_0), F_404(x, k_0) + F_529(x, k_0))
Eq(F_529(x, k_0), F_398(x, k_0) + F_530(x, k_0))
Eq(F_530(x, k_0), F_531(x, k_0))
Eq(F_531(x, k_0), F_532(x, k_0)*F_8(x))
Eq(F_532(x, k_0), F_533(x, k_0) + F_534(x, k_0))
Eq(F_533(x, k_0), F_205(x, k_0)*F_88(x))
Eq(F_534(x, k_0), F_102(x)*F_174(x, k_0))
Eq(F_535(x), F_536(x) + F_539(x))
Eq(F_536(x), F_537(x) + F_538(x))
Eq(F_537(x), F_12(x)*F_28(x))
Eq(F_538(x), F_182(x, 1))
Eq(F_539(x), F_540(x) + F_541(x))
Eq(F_540(x), F_204(x)*F_28(x))
Eq(F_541(x), F_302(x, 1))
Eq(F_542(x), F_543(x) + F_544(x))
Eq(F_543(x), F_348(x) + F_52(x))
Eq(F_544(x), F_338(x) + F_545(x))
Eq(F_545(x), F_372(x) + F_84(x))
Eq(F_546(x), F_18(x) + F_198(x))
Eq(F_547(x), F_50(x) + F_548(x))
Eq(F_548(x), F_334(x) + F_545(x))
Pack JSON:
{"name": "insertion_point_row_and_col_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.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}, {"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": [], "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_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}], [{"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": null}], "iterative": false}
Specification JSON:
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