01342_02341_03241_12340_13240_23140
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3296, 18885, 110815, 661352, 3997106, 24396054, 150083462, 929416530, 5788081456, 36223558683, 227685232561, 1436709982047, 9097698910552, 57794351439889, 368224944970180, 2352408958370889, 15065875074235209, 96711485339382411, 622146465450995468, 4010274553272905797, 25897909364281169364, 167537541309704101801, 1085597619955045206611, 7045172748331119166755, 45786861998768770855404, 297975370676356147552214, 1941676509503415278630467, 12667760321057708321108673, 82741060880082153260541916, 541021608212691960724605759, 3541248134525796480327894663, 23201925888432208119571576837, 152158755287894005857874667771, 998747840144582051392043362647, 6561193342114488673183682869881, 43138116762456152419554559903279, 283841099547376028912654583618691, 1869005285480296111295842675298387, 12315534076535445925791691428270495, 81206466361870052651395406574890707, 535809696288242147455064819074723838, 3537543487651827671132338914276487959, 23369725075213538852578090274338603703, 154474203029748854158761646635815600547, 1021643512838197012063930633870338342509, 6760439006459636603362384568668865182217, 44758347420236664893503340468319109174539, 296475490062079409719297477141633512078247, 1964769283602792375145216463367772228350457, 13026721611005951960752084881521328809113361, 86407745633077293475441876098015929597820155, 573400004367696448987293594910544134126439691, 3806659296125688218052900453760999603003104149, 25281669354697812595210312559957230519081462873, 167972161950463623190912666199398886514905631896, 1116434810363165116696608053530193815271577584657, 7423160179288040859466437453471489926013771924776, 49374060489941241885790809588214866214103798181120, 328517697434409529568173392684144901065442927885791, 2186573981131476245021896303372403562723613438022470, 14558305307534339456076577015915897844210450707990412, 96960457053528482772670703640284996415184331440064186, 645969159943722798239969600750342102586324079234102054, 4304854635466484710712978792125815061727651356081426220, 28696650262523990483165121874942326232942826101569629411, 191349134333248674869166893652277783325653332075544784664, 1276265692922087508787388230554685860544033199561235672802, 8514748573818938059598008039587955692601171841754298122820, 56821889158436964779724453337319850689804044253954332509340, 379288521312422314990839757288466117347916711464478361946830, 2532393069597610976694095528666703898233027862330988730589068, 16912087606290552191139324848811446143604211805584410541447124, 112970593552327077342749635553366998504595168802273511202551664, 754802248956541662202104291417568365957039420834826627265421040, 5044267759698349712652298938828787200622956108686248219863979948, 33717698509747316566686849323132630290073614978689121903980293772, 225429275715426431811958780605800541477566938610045619701318819588, 1507485503167087584927317517923818541887166006232590196919211287178, 10082873509742601241586569268884534914789675676222424086517174792088, 67453085547378508608266693864503888055460006756884779443624439845936, 451339869580629443176858545781127811595780394448909478986431477959618, 3020564188230256966686170452009711991577638436666364983293445288655662, 20218694397548143043513590614934965190756934557923216184491765720719768, 135362090468763383353544160438772709818882078513116313593261323729065152, 906396453284709837952626658862947227584201383053391116827737168635311054, 6070366196531288598639287761001559770703255042280933035987165033854674034, 40661700190705980010523450286338127596367479541084869826510201276079685764, 272413469783374530328501691824073917147899471564841858979658950956581952604, 1825334752391308794780848233451484475746781941004152806115583673294641904889, 12232801052291931685569464870301527756387647691538731953469475042043927390230, 81993106039977929156933482997196741503588721916878551544966227621884199758344, 549661643739862839946259872783452117266983146885942916961588760048701131279776, 3685351081716456245938871847578937441804352822831969390974718180234029243715596, 24713050378815543856681316903979260885314338824924035026061359944491228710641548
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25481/
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[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = (x^2*k[0]^2+4*x*k[0]-1)*F[8,x,k[0]]^2+(4*x^2*k[0]^2-5*x*k[0]+2)*F[8,x,k[0]]+4*k[0]^2*x^2-k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[2,x]+F[9,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[15,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[22,x,k[0]] = F[137,x,k[0]]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[19,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[25,x,k[0]]^2*F[15,x,k[0]]
F[28,x,k[0]] = F[136,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[135,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]+F[33,x,k[0]]
F[34,x,k[0]] = F[129,x,k[0]]+F[33,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[42,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[37,x,k[0]]
F[36,x,k[0]] = F[0,x]*F[26,x,k[0]]
F[37,x,k[0]] = F[38,x]*F[41,x,k[0]]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[38,x]*F[4,x]
F[41,x,k[0]] = -8*(-1/2+k[0]^2*(F[41,x,k[0]]+1)*x^3+1/2*k[0]*(k[0]+8*F[41,x,k[0]]-13)*x^2+(2*k[0]-F[41,x,k[0]]+3/2)*x)*x*(1-4*x)^(1/2)+8*k[0]^2*(F[41,x,k[0]]+1)^2*x^5+8*k[0]*(4*F[41,x,k[0]]^2+F[41,x,k[0]]*k[0]-13*F[41,x,k[0]]+8)*x^4+(4*k[0]^2+(32*F[41,x,k[0]]-84)*k[0]-8*F[41,x,k[0]]^2+24*F[41,x,k[0]]-16)*x^3+(16*k[0]-8*F[41,x,k[0]]+20)*x^2-4*x+F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[15,x,k[0]]*F[25,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[33,x,k[0]]*F[38,x]
F[46,x,k[0]] = F[47,x,k[0]]+F[48,x,k[0]]
F[47,x,k[0]] = F[25,x,k[0]]*F[35,x,k[0]]
F[48,x,k[0]] = F[38,x]*F[49,x,k[0]]*F[8,x,k[0]]
F[50,x,k[0]] = F[49,x,k[0]]*F[88,x,k[0]]
F[51,x,k[0]] = F[50,x,k[0]]+F[85,x,k[0]]
F[52,x,k[0]] = F[128,x,k[0]]+F[51,x,k[0]]
F[53,x,k[0]] = F[15,x,k[0]]*F[52,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[55,x,k[0]] = F[35,x,k[0]]+F[54,x,k[0]]
F[56,x,k[0]] = F[127,x,k[0]]+F[55,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[15,x,k[0]]*F[57,x,k[0]]
F[58,x,k[0]] = F[7,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[61,x,k[0]]
F[60,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[61,x,k[0]] = F[62,x]+F[96,x,k[0]]
F[62,x] = F[2,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[55,x,1]
F[67,x] = F[68,x,1]
F[69,x,k[0]] = F[68,x,k[0]]+F[71,x,k[0]]
F[70,x,k[0]] = F[15,x,k[0]]*F[69,x,k[0]]
F[70,x,k[0]] = F[9,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[75,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[74,x,k[0]]
F[73,x,k[0]] = F[2,x]*F[25,x,k[0]]
F[74,x,k[0]] = F[39,x]*F[41,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[9,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[15,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[26,x,k[0]]*F[69,x,k[0]]
F[80,x,k[0]] = F[28,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[95,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[4,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[32,x,k[0]]+F[82,x,k[0]]
F[86,x,k[0]] = F[49,x,k[0]]*F[87,x]
F[87,x] = F[88,x,1]
F[88,x,k[0]] = F[7,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[15,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[4,x]*F[93,x,k[0]]
F[93,x,k[0]] = 1/(-1+k[0])*(F[94,x,k[0]]*k[0]-F[94,x,1])
F[94,x,k[0]] = F[57,x,k[0]]+F[91,x,k[0]]
F[95,x,k[0]] = F[49,x,k[0]]*F[89,x,k[0]]
F[96,x,k[0]] = k[0]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[109,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]+F[2,x]
F[102,x] = F[103,x]+F[107,x]
F[103,x] = F[104,x]*F[2,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]^2*F[4,x]
F[106,x] = F[1,x]+F[104,x]
F[107,x] = F[108,x]*F[39,x]
F[108,x] = ((-8*F[108,x]-8)*x^4+(-32*F[108,x]+48)*x^3+(8*F[108,x]-28)*x^2+4*x)*(1-4*x)^(1/2)+8*(F[108,x]+1)^2*x^5+(32*F[108,x]^2-96*F[108,x]+64)*x^4+(-8*F[108,x]^2+56*F[108,x]-96)*x^3+(-8*F[108,x]+36)*x^2-4*x+F[108,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[99,x]
F[113,x] = F[114,x]+F[126,x]
F[114,x] = F[115,x,1]
F[115,x,k[0]] = F[116,x,k[0]]+F[121,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[7,x,k[0]]
F[118,x,k[0]] = -k[0]*(F[119,x,1]-F[119,x,k[0]])/(-1+k[0])
F[119,x,k[0]] = F[120,x,k[0]]+F[74,x,k[0]]
F[120,x,k[0]] = F[2,x]*F[26,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]*F[4,x]
F[123,x,k[0]] = -k[0]*(F[124,x,1]-F[124,x,k[0]])/(-1+k[0])
F[124,x,k[0]] = F[115,x,k[0]]+F[125,x,k[0]]
F[125,x,k[0]] = F[26,x,k[0]]*F[87,x]
F[126,x] = F[104,x]*F[87,x]
F[68,x,k[0]] = F[127,x,k[0]]+F[61,x,k[0]]
F[128,x,k[0]] = F[26,x,k[0]]*F[57,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[4,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[34,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[134,x]*F[25,x,k[0]]*F[26,x,k[0]]
F[134,x] = F[2,x]+F[63,x]
F[135,x,k[0]] = F[49,x,k[0]]*F[6,x]
F[136,x,k[0]] = F[49,x,k[0]]*F[9,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]+F[18,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[4,x]
F[140,x,k[0]] = F[141,x,k[0]]+F[612,x,k[0]]
F[141,x,k[0]] = F[138,x,k[0]]+F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]*F[4,x]
F[145,x,k[0]] = F[144,x,k[0]]*F[15,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]
F[147,x,k[0]] = F[146,x,k[0]]+F[611,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]+F[170,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[160,x]
F[149,x,k[0]] = F[1,x]+F[150,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[15,x,k[0]]*F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]+F[157,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[1,x]+F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[15,x,k[0]]*F[154,x,k[0]]
F[157,x,k[0]] = F[150,x,k[0]]+F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[15,x,k[0]]*F[157,x,k[0]]
F[160,x] = F[161,x]+F[162,x]
F[161,x] = -2+x^2+8*x+F[161,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[161,x]
F[162,x] = F[163,x,1]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[15,x,k[0]]*F[165,x,k[0]]*F[25,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[167,x,k[0]]
F[166,x,k[0]] = F[161,x]+F[163,x,k[0]]
F[167,x,k[0]] = F[168,x]*F[169,x,k[0]]
F[168,x] = (x^2+4*x-1)*F[168,x]^2+(4*x^2-5*x+2)*F[168,x]+4*x^2-x
F[169,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[15,x,k[0]]*F[172,x,k[0]]
F[173,x,k[0]] = F[172,x,k[0]]*F[4,x]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]+F[609,x,k[0]]
F[176,x,k[0]] = F[175,x,k[0]]+F[298,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]+F[212,x,k[0]]
F[178,x,k[0]] = F[177,x,k[0]]+F[185,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]+F[181,x,k[0]]
F[180,x,k[0]] = F[15,x,k[0]]*F[179,x,k[0]]
F[180,x,k[0]] = F[12,x,k[0]]
F[182,x,k[0]] = F[181,x,k[0]]+F[185,x,k[0]]
F[183,x,k[0]] = F[15,x,k[0]]*F[182,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[185,x,k[0]] = F[186,x,k[0]]+F[208,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]*F[203,x]
F[187,x,k[0]] = F[149,x,k[0]]+F[188,x,k[0]]
F[188,x,k[0]] = F[15,x,k[0]]+F[189,x,k[0]]
F[189,x,k[0]] = k[0]*F[190,x,k[0]]
F[190,x,k[0]] = F[191,x]+F[192,x,k[0]]+F[195,x,k[0]]
F[191,x] = 0
F[192,x,k[0]] = F[193,x,k[0]]*F[4,x]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[15,x,k[0]]*F[153,x,k[0]]
F[195,x,k[0]] = F[15,x,k[0]]*F[196,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[200,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[4,x]
F[198,x,k[0]] = F[199,x,k[0]]
F[199,x,k[0]] = F[15,x,k[0]]*F[197,x,k[0]]
F[200,x,k[0]] = F[190,x,k[0]]+F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]
F[202,x,k[0]] = F[15,x,k[0]]*F[200,x,k[0]]
F[203,x] = F[204,x]
F[204,x] = F[205,x]*F[4,x]
F[205,x] = F[206,x,1]
F[207,x,k[0]] = F[206,x,k[0]]*F[4,x]
F[207,x,k[0]] = F[19,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[149,x,k[0]]*F[153,x,k[0]]*F[211,x]*F[4,x]
F[211,x] = F[18,x,1]
F[212,x,k[0]] = F[213,x,k[0]]+F[605,x,k[0]]
F[214,x,k[0]] = F[213,x,k[0]]+F[550,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]+F[216,x,k[0]]
F[215,x,k[0]] = F[149,x,k[0]]*F[161,x]
F[217,x,k[0]] = F[216,x,k[0]]+F[604,x,k[0]]
F[218,x,k[0]] = F[15,x,k[0]]*F[217,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]
F[220,x,k[0]] = F[15,x,k[0]]*F[221,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]+F[488,x,k[0]]
F[223,x,k[0]] = F[222,x,k[0]]+F[596,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]+F[244,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]
F[225,x,k[0]] = F[161,x]*F[226,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]+F[228,x,k[0]]
F[227,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[228,x,k[0]] = F[229,x,k[0]]+F[238,x,k[0]]
F[229,x,k[0]] = F[230,x,k[0]]
F[230,x,k[0]] = F[15,x,k[0]]*F[231,x,k[0]]
F[231,x,k[0]] = F[227,x,k[0]]+F[232,x,k[0]]
F[232,x,k[0]] = F[193,x,k[0]]+F[233,x,k[0]]
F[233,x,k[0]] = k[0]*F[234,x,k[0]]
F[234,x,k[0]] = F[191,x]+F[235,x,k[0]]+F[237,x,k[0]]
F[235,x,k[0]] = F[15,x,k[0]]*F[236,x,k[0]]
F[236,x,k[0]] = F[234,x,k[0]]+F[4,x]
F[237,x,k[0]] = F[193,x,k[0]]*F[4,x]
F[238,x,k[0]] = k[0]*F[239,x,k[0]]
F[239,x,k[0]] = F[191,x]+F[237,x,k[0]]+F[240,x,k[0]]
F[240,x,k[0]] = F[15,x,k[0]]*F[241,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[243,x,k[0]]
F[242,x,k[0]] = F[4,x]
F[243,x,k[0]] = F[234,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]
F[245,x,k[0]] = F[15,x,k[0]]*F[246,x,k[0]]
F[246,x,k[0]] = F[247,x,k[0]]+F[267,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]+F[262,x,k[0]]
F[248,x,k[0]] = F[221,x,k[0]]+F[249,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]
F[250,x,k[0]] = F[15,x,k[0]]*F[251,x,k[0]]
F[251,x,k[0]] = F[247,x,k[0]]+F[252,x,k[0]]
F[252,x,k[0]] = F[253,x,k[0]]
F[253,x,k[0]] = F[15,x,k[0]]*F[153,x,k[0]]*F[254,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[256,x,k[0]]
F[255,x,k[0]] = F[153,x,k[0]]*F[161,x]
F[256,x,k[0]] = F[106,x]*F[257,x,k[0]]
F[258,x,k[0]] = F[149,x,k[0]]*F[257,x,k[0]]
F[259,x,k[0]] = F[216,x,k[0]]+F[258,x,k[0]]
F[260,x,k[0]] = F[15,x,k[0]]*F[259,x,k[0]]
F[260,x,k[0]] = F[261,x,k[0]]
F[219,x,k[0]] = F[150,x,k[0]]+F[261,x,k[0]]
F[262,x,k[0]] = F[263,x,k[0]]
F[263,x,k[0]] = F[153,x,k[0]]*F[264,x,k[0]]
F[264,x,k[0]] = k[0]*F[265,x,k[0]]
F[265,x,k[0]] = F[266,x,k[0]]
F[266,x,k[0]] = F[149,x,k[0]]*F[254,x,k[0]]*F[4,x]
F[267,x,k[0]] = F[268,x,k[0]]
F[268,x,k[0]] = F[161,x]*F[269,x,k[0]]
F[269,x,k[0]] = F[270,k[0]*x]
F[270,x] = 1/F[161,x]*F[271,x]
F[271,x] = F[272,x,1]
F[272,x,k[0]] = F[273,x,k[0]]
F[274,x,k[0]] = F[273,x,k[0]]+F[556,x,k[0]]
F[275,x,k[0]] = F[274,x,k[0]]*F[4,x]
F[275,x,k[0]] = F[276,x,k[0]]
F[277,x,k[0]] = F[276,x,k[0]]+F[552,x,k[0]]
F[277,x,k[0]] = F[278,x]+F[513,x,k[0]]
F[278,x] = F[279,x]+F[282,x]
F[279,x] = F[280,x]
F[280,x] = F[161,x]*F[281,x]
F[281,x] = F[1,x]+F[4,x]
F[282,x] = -F[486,x]+F[283,x]
F[283,x] = F[284,x,1]
F[285,x,k[0]] = F[284,x,k[0]]+F[382,x,k[0]]
F[286,x,k[0]] = F[285,x,k[0]]+F[365,x,k[0]]
F[286,x,k[0]] = F[287,x]+F[359,x,k[0]]
F[287,x] = F[288,x]+F[292,x]
F[288,x] = F[289,x]*F[5,x]
F[289,x] = F[1,x]+F[290,x]
F[290,x] = F[291,x]
F[291,x] = F[289,x]*F[38,x]*F[4,x]
F[292,x] = -F[353,x]+F[293,x]
F[293,x] = F[294,x]+F[306,x]
F[294,x] = 1/F[4,x]*F[295,x]
F[295,x] = F[296,x]
F[296,x] = -F[161,x]+F[297,x]
F[297,x] = F[298,x,1]
F[299,x,k[0]] = F[298,x,k[0]]+F[305,x,k[0]]
F[300,x,k[0]] = F[299,x,k[0]]+F[302,x,k[0]]
F[301,x,k[0]] = F[15,x,k[0]]*F[300,x,k[0]]
F[301,x,k[0]] = F[7,x,k[0]]
F[303,x,k[0]] = F[302,x,k[0]]+F[305,x,k[0]]
F[304,x,k[0]] = F[15,x,k[0]]*F[303,x,k[0]]
F[304,x,k[0]] = F[9,x,k[0]]
F[305,x,k[0]] = F[187,x,k[0]]*F[2,x]
F[306,x] = F[307,x]+F[352,x]
F[307,x] = F[289,x]*F[308,x]
F[308,x] = F[203,x]+F[309,x]
F[309,x] = F[310,x]
F[310,x] = F[311,x]*F[4,x]
F[311,x] = F[312,x]+F[314,x]
F[312,x] = F[313,x,1]
F[313,x,k[0]] = F[153,x,k[0]]*F[203,x]
F[314,x] = F[315,x]+F[349,x]
F[315,x] = F[316,x,1]
F[316,x,k[0]] = (F[317,x,k[0]]*k[0]-F[317,x,1])/(-1+k[0])
F[317,x,k[0]] = F[318,x,k[0]]
F[318,x,k[0]] = F[319,x,k[0]]*F[38,x]*F[4,x]
F[319,x,k[0]] = F[320,x,k[0]]+F[327,x,k[0]]
F[320,x,k[0]] = F[321,x,k[0]]
F[321,x,k[0]] = F[322,x,k[0]]*F[38,x]
F[322,x,k[0]] = F[323,x,k[0]]+F[325,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]*F[38,x]
F[324,x,k[0]] = -2+k[0]^2*x^2+F[324,x,k[0]]^2*(x^2*k[0]^2+4*x*k[0]-1)+(2*x^2*k[0]^2-13*x*k[0]+4)*F[324,x,k[0]]+8*k[0]*x
F[325,x,k[0]] = F[25,x,k[0]]*F[326,x]
F[326,x] = (x^4*F[326,x]^2+(-5*F[326,x]^2-F[326,x])*x^3+(9*F[326,x]^2+6*F[326,x]-1)*x^2+(-7*F[326,x]^2-10*F[326,x]+1)*x+2*F[326,x]^2+6*F[326,x])*x
F[327,x,k[0]] = F[25,x,k[0]]*F[328,x]
F[328,x] = F[329,x,1]
F[330,x,k[0]] = F[329,x,k[0]]+F[346,x,k[0]]
F[331,x,k[0]] = F[153,x,k[0]]*F[330,x,k[0]]*F[4,x]
F[331,x,k[0]] = F[332,x,k[0]]
F[332,x,k[0]] = F[2,x]+F[333,x,k[0]]
F[333,x,k[0]] = F[334,x,k[0]]
F[334,x,k[0]] = F[15,x,k[0]]*F[335,x,k[0]]
F[335,x,k[0]] = F[336,x,k[0]]+F[337,x,k[0]]
F[336,x,k[0]] = F[153,x,k[0]]*F[2,x]
F[337,x,k[0]] = F[338,x,k[0]]
F[338,x,k[0]] = F[153,x,k[0]]*F[339,x,k[0]]*F[4,x]
F[339,x,k[0]] = F[340,x,k[0]]+F[345,x,k[0]]
F[340,x,k[0]] = F[341,x,k[0]]
F[341,x,k[0]] = F[153,x,k[0]]*F[342,x]
F[342,x] = F[343,x]+F[344,x]
F[343,x] = F[161,x]*F[38,x]
F[344,x] = F[106,x]*F[326,x]
F[345,x,k[0]] = F[106,x]*F[329,x,k[0]]
F[346,x,k[0]] = F[347,x,k[0]]
F[347,x,k[0]] = F[153,x,k[0]]*F[348,x]
F[348,x] = -1+(x^2-2*x)*F[348,x]^2+(2+x)*F[348,x]
F[349,x] = F[106,x]*F[350,x]
F[350,x] = -F[351,x]+F[308,x]
F[351,x] = F[332,x,1]
F[352,x] = F[209,x,1]
F[353,x] = F[289,x]*F[354,x]
F[354,x] = F[308,x]+F[355,x]
F[355,x] = F[356,x,1]
F[356,x,k[0]] = F[161,x]+F[357,x,k[0]]
F[357,x,k[0]] = F[358,x,k[0]]
F[358,x,k[0]] = F[15,x,k[0]]*F[254,x,k[0]]
F[359,x,k[0]] = k[0]*F[360,x]
F[360,x] = F[361,x]+F[362,x]
F[361,x] = F[264,x,1]
F[362,x] = F[363,x]
F[363,x] = F[364,x,1]
F[364,x,k[0]] = F[188,x,k[0]]*F[203,x]
F[365,x,k[0]] = F[366,x,k[0]]+F[381,x,k[0]]
F[366,x,k[0]] = F[203,x]*F[367,x,k[0]]
F[367,x,k[0]] = F[289,x]+F[368,x,k[0]]
F[368,x,k[0]] = F[15,x,k[0]]+F[369,x,k[0]]
F[369,x,k[0]] = k[0]*F[370,x]
F[370,x] = F[371,x]
F[371,x] = F[191,x]+F[372,x]+F[373,x]
F[372,x] = F[39,x]*F[4,x]
F[373,x] = F[374,x]*F[4,x]
F[374,x] = F[375,x]+F[378,x]
F[375,x] = F[376,x]+F[4,x]
F[376,x] = F[377,x]
F[377,x] = F[375,x]*F[4,x]
F[378,x] = F[371,x]+F[379,x]
F[379,x] = F[380,x]
F[380,x] = F[378,x]*F[4,x]
F[381,x,k[0]] = F[352,x]
F[382,x,k[0]] = F[383,x,k[0]]
F[384,x,k[0]] = F[383,x,k[0]]+F[471,x,k[0]]
F[384,x,k[0]] = F[385,x]+F[418,x,k[0]]
F[385,x] = F[386,x]+F[389,x]
F[386,x] = F[161,x]+F[387,x]
F[387,x] = F[388,x]
F[388,x] = F[205,x]*F[4,x]
F[389,x] = F[390,x]
F[390,x] = F[391,x]*F[4,x]
F[391,x] = 1/F[4,x]*F[392,x]
F[392,x] = F[393,x]
F[393,x] = -F[396,x]+F[394,x]
F[394,x] = 1/F[4,x]*F[395,x]
F[395,x] = F[63,x]
F[396,x] = F[397,x]
F[397,x] = F[387,x]+F[398,x]
F[398,x] = -F[406,x]+F[399,x]
F[399,x] = F[400,x]
F[400,x] = F[4,x]*F[401,x]
F[401,x] = F[402,x,1]
F[402,x,k[0]] = F[206,x,k[0]]+F[403,x,k[0]]
F[403,x,k[0]] = F[404,x,k[0]]
F[404,x,k[0]] = F[4,x]*F[405,x,k[0]]
F[405,x,k[0]] = 1/(-1+k[0])*(F[402,x,k[0]]*k[0]-F[402,x,1])
F[406,x] = F[407,x]
F[407,x] = F[4,x]*F[408,x]
F[408,x] = F[409,x]+F[411,x]
F[409,x] = F[410,x,1]
F[410,x,k[0]] = (F[324,x,k[0]]*k[0]-F[324,x,1])/(-1+k[0])
F[411,x] = F[412,x]
F[412,x] = F[4,x]*F[413,x]
F[413,x] = F[414,x,1]
F[414,x,k[0]] = (F[415,x,k[0]]*k[0]-F[415,x,1])/(-1+k[0])
F[415,x,k[0]] = F[410,x,k[0]]+F[416,x,k[0]]
F[416,x,k[0]] = F[417,x,k[0]]
F[417,x,k[0]] = F[4,x]*F[414,x,k[0]]
F[418,x,k[0]] = F[15,x,k[0]]*F[419,x]
F[419,x] = 1/F[4,x]*F[420,x]
F[420,x] = -F[385,x]+F[421,x]
F[421,x] = F[422,x]+F[425,x]
F[422,x] = F[386,x]+F[423,x]
F[423,x] = F[4,x]*F[424,x]
F[424,x] = F[161,x]+F[406,x]
F[425,x] = F[426,x]
F[426,x] = F[389,x]+F[427,x]
F[427,x] = F[428,x]
F[428,x] = F[4,x]^2*F[429,x]
F[429,x] = F[430,x,1]
F[430,x,k[0]] = F[431,x,k[0]]+F[444,x,k[0]]
F[431,x,k[0]] = F[153,x,k[0]]*F[432,x]
F[432,x] = 1/F[39,x]*F[433,x]
F[433,x] = -F[443,x]+F[434,x]
F[434,x] = 1/F[38,x]/F[4,x]*F[435,x]
F[435,x] = F[436,x]
F[436,x] = F[437,x]+F[438,x]
F[437,x] = F[2,x]*F[38,x]
F[438,x] = F[439,x]
F[439,x] = F[38,x]*F[4,x]*F[440,x]
F[440,x] = F[441,x]+F[87,x]
F[441,x] = F[442,x]
F[442,x] = F[4,x]*F[434,x]
F[443,x] = F[386,x]+F[399,x]
F[444,x,k[0]] = F[445,x]*F[457,x,k[0]]
F[445,x] = F[446,x,1]
F[446,x,k[0]] = F[447,x,k[0]]+F[454,x,k[0]]
F[447,x,k[0]] = F[448,x,k[0]]
F[448,x,k[0]] = F[38,x]+F[449,x,k[0]]
F[449,x,k[0]] = F[193,x,k[0]]+F[450,x,k[0]]
F[450,x,k[0]] = F[191,x]+F[451,x,k[0]]+F[453,x,k[0]]
F[451,x,k[0]] = F[15,x,k[0]]*F[452,x,k[0]]
F[452,x,k[0]] = F[39,x]+F[450,x,k[0]]
F[453,x,k[0]] = F[4,x]*F[449,x,k[0]]
F[454,x,k[0]] = F[455,x,k[0]]
F[455,x,k[0]] = F[4,x]*F[447,x,k[0]]*F[456,x,k[0]]
F[456,x,k[0]] = (F[446,x,k[0]]*k[0]-F[446,x,1])/(-1+k[0])
F[457,x,k[0]] = F[168,x]+F[458,x,k[0]]
F[458,x,k[0]] = F[459,x,k[0]]
F[459,x,k[0]] = F[15,x,k[0]]*F[460,x,k[0]]
F[460,x,k[0]] = F[457,x,k[0]]+F[461,x,k[0]]
F[461,x,k[0]] = F[462,x]+F[464,x,k[0]]
F[462,x] = F[463,x,1]
F[463,x,k[0]] = -k[0]*(F[8,x,1]-F[8,x,k[0]])/(-1+k[0])
F[464,x,k[0]] = F[465,x,k[0]]
F[465,x,k[0]] = F[15,x,k[0]]*F[466,x,k[0]]
F[466,x,k[0]] = F[467,x,k[0],1]
F[467,x,k[0],k[1]] = -k[1]*(F[468,x,k[0],1]-F[468,x,k[0],k[1]])/(-1+k[1])
F[468,x,k[0],k[1]] = F[463,x,k[1]]+F[469,x,k[0],k[1]]
F[469,x,k[0],k[1]] = F[470,x,k[0],k[1]]
F[470,x,k[0],k[1]] = F[15,x,k[0]]*F[467,x,k[0],k[1]]
F[471,x,k[0]] = F[472,x]+F[481,x,k[0]]
F[472,x] = -F[477,x]+F[473,x]
F[473,x] = 1/F[4,x]*F[474,x]
F[474,x] = F[475,x]
F[475,x] = -F[476,x]+F[387,x]
F[476,x] = (x*F[476,x]+x-2*F[476,x])*(x*F[476,x]+x-1)
F[477,x] = -F[385,x]+F[478,x]
F[478,x] = 1/F[4,x]*F[479,x]
F[479,x] = F[480,x]
F[480,x] = F[168,x]+F[475,x]
F[481,x,k[0]] = F[15,x,k[0]]*F[482,x]
F[482,x] = -F[483,x]+F[419,x]
F[483,x] = F[484,x]
F[484,x] = F[161,x]+F[485,x]
F[485,x] = F[106,x]*F[168,x]
F[486,x] = -F[493,x]+F[487,x]
F[487,x] = F[488,x,1]
F[488,x,k[0]] = F[489,x,k[0]]
F[489,x,k[0]] = F[4,x]*F[490,x,k[0]]
F[491,x,k[0]] = F[15,x,k[0]]*F[490,x,k[0]]
F[491,x,k[0]] = F[492,x,k[0]]
F[492,x,k[0]] = -k[0]*(F[219,x,1]-F[219,x,k[0]])/(-1+k[0])
F[493,x] = F[494,x]
F[494,x] = F[495,x]+F[509,x]
F[495,x] = F[168,x]+F[496,x]
F[496,x] = F[497,x]
F[497,x] = F[4,x]*F[498,x]
F[498,x] = F[499,x]+F[501,x]
F[499,x] = F[104,x]*F[500,x]
F[500,x] = F[161,x]+F[495,x]
F[501,x] = F[502,x]+F[506,x]
F[502,x] = F[168,x]+F[503,x]
F[503,x] = F[504,x]
F[504,x] = F[106,x]*F[4,x]*F[505,x]
F[505,x] = F[485,x]+F[501,x]
F[506,x] = F[168,x]*F[507,x]
F[507,x] = F[508,x,1]
F[508,x,k[0]] = -k[0]*(F[26,x,1]-F[26,x,k[0]])/(-1+k[0])
F[509,x] = F[510,x]
F[510,x] = F[4,x]*F[511,x]
F[511,x] = F[168,x]+F[512,x]
F[512,x] = F[104,x]*F[168,x]
F[513,x,k[0]] = F[514,x,k[0]]
F[514,x,k[0]] = F[15,x,k[0]]*F[515,x,k[0]]
F[515,x,k[0]] = F[516,x,k[0]]+F[551,x,k[0]]
F[516,x,k[0]] = F[277,x,k[0]]+F[517,x,k[0]]
F[517,x,k[0]] = F[518,x,k[0]]
F[518,x,k[0]] = F[153,x,k[0]]*F[519,x]
F[519,x] = F[520,x,1]
F[521,x,k[0]] = F[520,x,k[0]]+F[550,x,k[0]]
F[522,x,k[0]] = F[521,x,k[0]]+F[547,x,k[0]]
F[522,x,k[0]] = F[523,x,k[0]]+F[526,x,k[0]]
F[523,x,k[0]] = F[0,x]*F[524,x,k[0]]
F[524,x,k[0]] = F[149,x,k[0]]+F[525,x,k[0]]
F[525,x,k[0]] = F[190,x,k[0]]+F[4,x]
F[526,x,k[0]] = F[527,x,k[0]]
F[527,x,k[0]] = F[4,x]*F[528,x,k[0]]
F[528,x,k[0]] = F[529,x,k[0]]+F[534,x,k[0]]
F[530,x,k[0]] = F[4,x]*F[529,x,k[0]]
F[530,x,k[0]] = F[531,x,k[0]]
F[531,x,k[0]] = F[532,x,k[0]]+F[533,x,k[0]]
F[532,x,k[0]] = F[168,x]+F[261,x,k[0]]
F[533,x,k[0]] = F[2,x]*F[525,x,k[0]]
F[535,x,k[0]] = F[106,x]*F[534,x,k[0]]
F[536,x,k[0]] = F[535,x,k[0]]+F[543,x,k[0]]
F[537,x,k[0]] = F[4,x]*F[536,x,k[0]]
F[537,x,k[0]] = F[538,x,k[0]]
F[538,x,k[0]] = F[539,x,k[0]]+F[542,x,k[0]]
F[540,x,k[0]] = F[539,x,k[0]]+F[541,x,k[0]]
F[540,x,k[0]] = F[214,x,k[0]]+F[265,x,k[0]]
F[541,x,k[0]] = F[161,x]*F[524,x,k[0]]
F[542,x,k[0]] = F[533,x,k[0]]
F[544,x,k[0]] = F[4,x]*F[543,x,k[0]]
F[544,x,k[0]] = F[545,x,k[0]]
F[545,x,k[0]] = F[216,x,k[0]]+F[546,x,k[0]]
F[546,x,k[0]] = F[533,x,k[0]]
F[547,x,k[0]] = F[2,x]*F[548,x,k[0]]
F[548,x,k[0]] = F[524,x,k[0]]+F[549,x,k[0]]
F[549,x,k[0]] = F[525,x,k[0]]
F[550,x,k[0]] = F[149,x,k[0]]+F[532,x,k[0]]
F[551,x,k[0]] = F[15,x,k[0]]*F[153,x,k[0]]*F[355,x]
F[552,x,k[0]] = F[553,x,k[0]]
F[553,x,k[0]] = F[161,x]*F[554,x,k[0]]
F[554,x,k[0]] = F[281,x]+F[555,x,k[0]]
F[555,x,k[0]] = F[229,x,k[0]]+F[239,x,k[0]]
F[557,x,k[0]] = F[556,x,k[0]]+F[572,x,k[0]]
F[558,x,k[0]] = F[15,x,k[0]]*F[557,x,k[0]]
F[558,x,k[0]] = F[559,x,k[0]]
F[560,x,k[0]] = F[559,x,k[0]]+F[575,x,k[0]]
F[560,x,k[0]] = F[561,x,k[0]]
F[561,x,k[0]] = F[15,x,k[0]]*F[562,x,k[0]]
F[562,x,k[0]] = F[563,x,k[0]]+F[572,x,k[0]]
F[563,x,k[0]] = F[564,x,k[0]]+F[570,x,k[0]]
F[564,x,k[0]] = F[560,x,k[0]]+F[565,x]
F[565,x] = F[566,x,1]
F[566,x,k[0]] = F[540,x,k[0]]+F[567,x,k[0]]
F[567,x,k[0]] = F[568,x,k[0]]+F[569,x,k[0]]
F[568,x,k[0]] = F[203,x]*F[524,x,k[0]]
F[569,x,k[0]] = F[209,x,k[0]]
F[570,x,k[0]] = F[571,x,k[0]]
F[571,x,k[0]] = F[153,x,k[0]]*F[360,x]
F[572,x,k[0]] = F[573,x,k[0]]
F[573,x,k[0]] = F[15,x,k[0]]*F[153,x,k[0]]*F[574,x]
F[574,x] = F[254,x,1]
F[575,x,k[0]] = F[576,x,k[0]]+F[594,x,k[0]]
F[576,x,k[0]] = F[203,x]*F[577,x,k[0]]
F[577,x,k[0]] = F[578,x,k[0]]
F[578,x,k[0]] = F[579,x,k[0]]+F[584,x,k[0]]
F[579,x,k[0]] = F[289,x]*F[580,x,k[0]]
F[580,x,k[0]] = F[581,x,k[0]]
F[581,x,k[0]] = F[582,x,k[0]]*F[583,x,k[0]]
F[582,x,k[0]] = F[1,x]+F[580,x,k[0]]
F[583,x,k[0]] = k[0]*x
F[584,x,k[0]] = F[585,x,k[0]]+F[589,x,k[0]]
F[585,x,k[0]] = F[191,x]+F[586,x,k[0]]+F[588,x,k[0]]
F[586,x,k[0]] = F[583,x,k[0]]*F[587,x,k[0]]
F[587,x,k[0]] = F[4,x]+F[585,x,k[0]]
F[588,x,k[0]] = F[4,x]*F[580,x,k[0]]
F[590,x,k[0]] = F[370,x]+F[589,x,k[0]]
F[590,x,k[0]] = F[591,x,k[0]]
F[591,x,k[0]] = F[153,x,k[0]]^2*F[4,x]*F[592,x]
F[592,x] = F[39,x]+F[593,x]
F[593,x] = F[290,x]*F[38,x]
F[594,x,k[0]] = F[595,x,k[0]]
F[595,x,k[0]] = F[193,x,k[0]]*F[352,x]
F[596,x,k[0]] = F[597,x,k[0]]
F[597,x,k[0]] = F[15,x,k[0]]*F[598,x,k[0]]
F[598,x,k[0]] = F[599,x,k[0]]+F[603,x,k[0]]
F[599,x,k[0]] = F[223,x,k[0]]+F[600,x,k[0]]
F[600,x,k[0]] = F[601,x,k[0]]
F[601,x,k[0]] = F[153,x,k[0]]*F[602,x,k[0]]
F[602,x,k[0]] = k[0]*F[520,x,k[0]]
F[603,x,k[0]] = F[15,x,k[0]]*F[153,x,k[0]]*F[356,x,k[0]]
F[604,x,k[0]] = F[149,x,k[0]]*F[356,x,k[0]]
F[605,x,k[0]] = k[0]*F[606,x,k[0]]
F[607,x,k[0]] = F[213,x,k[0]]+F[606,x,k[0]]
F[607,x,k[0]] = F[608,x,k[0]]
F[540,x,k[0]] = F[521,x,k[0]]+F[608,x,k[0]]
F[212,x,k[0]] = F[609,x,k[0]]+F[610,x,k[0]]
F[610,x,k[0]] = F[168,x]*F[187,x,k[0]]
F[611,x,k[0]] = 1/(-1+k[0])*(F[166,x,k[0]]*k[0]-F[166,x,1])
F[612,x,k[0]] = F[6,x]*F[613,x,k[0]]
F[613,x,k[0]] = F[614,x,1,k[0]]
F[614,x,k[0],k[1]] = (F[615,x,k[0]*k[1]]*k[0]-F[615,x,k[1]])/(-1+k[0])
F[615,x,k[0]] = (F[26,x,k[0]]-F[26,x,1])/(-1+k[0])
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = x^{2} F_{8}\! \left(x , y\right)^{2} y^{2}+4 x^{2} F_{8}\! \left(x , y\right) y^{2}+4 y^{2} x^{2}+4 x F_{8}\! \left(x , y\right)^{2} y -5 x F_{8}\! \left(x , y\right) y -y x -F_{8}\! \left(x , y\right)^{2}+2 F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{25}\! \left(x , y\right)^{2} F_{15}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{29}\! \left(x , y\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_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x , y\right) = -8 x^{3} F_{41}\! \left(x , y\right)^{2}-8 x^{2} F_{41}\! \left(x , y\right)+24 x^{3} F_{41}\! \left(x , y\right)+8 x^{5} y^{2}+64 x^{4} y +4 x^{3} y^{2}+16 x^{2} y -84 x^{3} y -32 \sqrt{1-4 x}\, x^{3} F_{41}\! \left(x , y\right) y -8 \sqrt{1-4 x}\, x^{4} F_{41}\! \left(x , y\right) y^{2}+F_{41}\! \left(x , y\right)+8 x^{5} F_{41}\! \left(x , y\right)^{2} y^{2}+32 x^{4} F_{41}\! \left(x , y\right)^{2} y +8 x^{4} F_{41}\! \left(x , y\right) y^{2}+32 x^{3} F_{41}\! \left(x , y\right) y +16 x^{5} F_{41}\! \left(x , y\right) y^{2}-104 x^{4} F_{41}\! \left(x , y\right) y +8 \sqrt{1-4 x}\, x^{2} F_{41}\! \left(x , y\right)-8 \sqrt{1-4 x}\, x^{4} y^{2}-4 \sqrt{1-4 x}\, x^{3} y^{2}+52 \sqrt{1-4 x}\, x^{3} y -16 \sqrt{1-4 x}\, x^{2} y -12 \sqrt{1-4 x}\, x^{2}+4 \sqrt{1-4 x}\, x -4 x +20 x^{2}-16 x^{3}
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{49}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{69}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x , 1\right)
F_{88}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = -\frac{-F_{94}\! \left(x , y\right) y +F_{94}\! \left(x , 1\right)}{-1+y}
F_{94}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = y F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{109}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{2}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{107}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{2}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{39}\! \left(x \right)
F_{108}\! \left(x \right) = 8 x^{5} F_{108} \left(x \right)^{2}-8 \sqrt{1-4 x}\, x^{4} F_{108}\! \left(x \right)+16 x^{5} F_{108}\! \left(x \right)+32 x^{4} F_{108} \left(x \right)^{2}-8 \sqrt{1-4 x}\, x^{4}-32 \sqrt{1-4 x}\, x^{3} F_{108}\! \left(x \right)+8 x^{5}-96 x^{4} F_{108}\! \left(x \right)-8 x^{3} F_{108} \left(x \right)^{2}+48 \sqrt{1-4 x}\, x^{3}+8 \sqrt{1-4 x}\, x^{2} F_{108}\! \left(x \right)+64 x^{4}+56 x^{3} F_{108}\! \left(x \right)-28 \sqrt{1-4 x}\, x^{2}-96 x^{3}-8 x^{2} F_{108}\! \left(x \right)+4 \sqrt{1-4 x}\, x +36 x^{2}-4 x +F_{108}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{99}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{126}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x , 1\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{121}\! \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_{7}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = -\frac{y \left(F_{119}\! \left(x , 1\right)-F_{119}\! \left(x , y\right)\right)}{-1+y}
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{123}\! \left(x , y\right) = -\frac{y \left(F_{124}\! \left(x , 1\right)-F_{124}\! \left(x , y\right)\right)}{-1+y}
F_{124}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{126}\! \left(x \right) = F_{104}\! \left(x \right) F_{87}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{57}\! \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_{4}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x \right) F_{25}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{612}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{611}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{160}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{154}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{157}\! \left(x , y\right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{162}\! \left(x \right)
F_{161}\! \left(x \right) = x^{2} F_{161} \left(x \right)^{2}+2 x^{2} F_{161}\! \left(x \right)+4 x F_{161} \left(x \right)^{2}+x^{2}-13 x F_{161}\! \left(x \right)-F_{161} \left(x \right)^{2}+8 x +4 F_{161}\! \left(x \right)-2
F_{162}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{165}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{161}\! \left(x \right)+F_{163}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x \right) F_{169}\! \left(x , y\right)
F_{168}\! \left(x \right) = x^{2} F_{168} \left(x \right)^{2}+4 x^{2} F_{168}\! \left(x \right)+4 x F_{168} \left(x \right)^{2}+4 x^{2}-5 x F_{168}\! \left(x \right)-F_{168} \left(x \right)^{2}-x +2 F_{168}\! \left(x \right)
F_{169}\! \left(x , y\right) = -\frac{-F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , 1\right)}{-1+y}
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{172}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{609}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{179}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{182}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{208}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{203}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = y F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{192}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{191}\! \left(x \right) = 0
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{153}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{197}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{200}\! \left(x , y\right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{4}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x , 1\right)
F_{207}\! \left(x , y\right) = F_{206}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{153}\! \left(x , y\right) F_{211}\! \left(x \right) F_{4}\! \left(x \right)
F_{211}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{605}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{550}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{161}\! \left(x \right)
F_{217}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{604}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{217}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{488}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{596}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{161}\! \left(x \right) F_{226}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{231}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = y F_{234}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{235}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{238}\! \left(x , y\right) = y F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{237}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{4}\! \left(x \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_{245}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right)+F_{267}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right)+F_{262}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{247}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{153}\! \left(x , y\right) F_{254}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{256}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{161}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{106}\! \left(x \right) F_{257}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{257}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{259}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{261}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{263}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = y F_{265}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{254}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{267}\! \left(x , y\right) = F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{161}\! \left(x \right) F_{269}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(y x \right)
F_{270}\! \left(x \right) = \frac{F_{271}\! \left(x \right)}{F_{161}\! \left(x \right)}
F_{271}\! \left(x \right) = F_{272}\! \left(x , 1\right)
F_{272}\! \left(x , y\right) = F_{273}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{273}\! \left(x , y\right)+F_{556}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{274}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{552}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{278}\! \left(x \right)+F_{513}\! \left(x , y\right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{282}\! \left(x \right)
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{161}\! \left(x \right) F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{282}\! \left(x \right) = -F_{486}\! \left(x \right)+F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x , 1\right)
F_{285}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{382}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{285}\! \left(x , y\right)+F_{365}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x \right)+F_{359}\! \left(x , y\right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)+F_{292}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right) F_{5}\! \left(x \right)
F_{289}\! \left(x \right) = F_{1}\! \left(x \right)+F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{289}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{353}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)+F_{306}\! \left(x \right)
F_{294}\! \left(x \right) = \frac{F_{295}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = -F_{161}\! \left(x \right)+F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x , 1\right)
F_{299}\! \left(x , y\right) = F_{298}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{299}\! \left(x , y\right)+F_{302}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{300}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{302}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{303}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)+F_{352}\! \left(x \right)
F_{307}\! \left(x \right) = F_{289}\! \left(x \right) F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{203}\! \left(x \right)+F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right) F_{4}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)+F_{314}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x , 1\right)
F_{313}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{203}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)+F_{349}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x , 1\right)
F_{316}\! \left(x , y\right) = -\frac{-F_{317}\! \left(x , y\right) y +F_{317}\! \left(x , 1\right)}{-1+y}
F_{317}\! \left(x , y\right) = F_{318}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{319}\! \left(x , y\right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{321}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{322}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{322}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{325}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{324}\! \left(x , y\right) = x^{2} F_{324}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{324}\! \left(x , y\right) y^{2}+y^{2} x^{2}+4 x F_{324}\! \left(x , y\right)^{2} y -13 x F_{324}\! \left(x , y\right) y +8 y x -F_{324}\! \left(x , y\right)^{2}+4 F_{324}\! \left(x , y\right)-2
F_{325}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{326}\! \left(x \right)
F_{326}\! \left(x \right) = x^{5} F_{326} \left(x \right)^{2}-5 x^{4} F_{326} \left(x \right)^{2}-x^{4} F_{326}\! \left(x \right)+9 x^{3} F_{326} \left(x \right)^{2}+6 x^{3} F_{326}\! \left(x \right)-7 x^{2} F_{326} \left(x \right)^{2}-x^{3}-10 x^{2} F_{326}\! \left(x \right)+2 x F_{326} \left(x \right)^{2}+x^{2}+6 F_{326}\! \left(x \right) x
F_{327}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x , 1\right)
F_{330}\! \left(x , y\right) = F_{329}\! \left(x , y\right)+F_{346}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{330}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{331}\! \left(x , y\right) = F_{332}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{335}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)+F_{337}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{337}\! \left(x , y\right) = F_{338}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{339}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{339}\! \left(x , y\right) = F_{340}\! \left(x , y\right)+F_{345}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{341}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right)+F_{344}\! \left(x \right)
F_{343}\! \left(x \right) = F_{161}\! \left(x \right) F_{38}\! \left(x \right)
F_{344}\! \left(x \right) = F_{106}\! \left(x \right) F_{326}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{106}\! \left(x \right) F_{329}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{347}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{348}\! \left(x \right)
F_{348}\! \left(x \right) = x^{2} F_{348} \left(x \right)^{2}-2 x F_{348} \left(x \right)^{2}+F_{348}\! \left(x \right) x +2 F_{348}\! \left(x \right)-1
F_{349}\! \left(x \right) = F_{106}\! \left(x \right) F_{350}\! \left(x \right)
F_{350}\! \left(x \right) = -F_{351}\! \left(x \right)+F_{308}\! \left(x \right)
F_{351}\! \left(x \right) = F_{332}\! \left(x , 1\right)
F_{352}\! \left(x \right) = F_{209}\! \left(x , 1\right)
F_{353}\! \left(x \right) = F_{289}\! \left(x \right) F_{354}\! \left(x \right)
F_{354}\! \left(x \right) = F_{308}\! \left(x \right)+F_{355}\! \left(x \right)
F_{355}\! \left(x \right) = F_{356}\! \left(x , 1\right)
F_{356}\! \left(x , y\right) = F_{161}\! \left(x \right)+F_{357}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{358}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{254}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = y F_{360}\! \left(x \right)
F_{360}\! \left(x \right) = F_{361}\! \left(x \right)+F_{362}\! \left(x \right)
F_{361}\! \left(x \right) = F_{264}\! \left(x , 1\right)
F_{362}\! \left(x \right) = F_{363}\! \left(x \right)
F_{363}\! \left(x \right) = F_{364}\! \left(x , 1\right)
F_{364}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{203}\! \left(x \right)
F_{365}\! \left(x , y\right) = F_{366}\! \left(x , y\right)+F_{381}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = F_{203}\! \left(x \right) F_{367}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{289}\! \left(x \right)+F_{368}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{369}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = y F_{370}\! \left(x \right)
F_{370}\! \left(x \right) = F_{371}\! \left(x \right)
F_{371}\! \left(x \right) = F_{191}\! \left(x \right)+F_{372}\! \left(x \right)+F_{373}\! \left(x \right)
F_{372}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{373}\! \left(x \right) = F_{374}\! \left(x \right) F_{4}\! \left(x \right)
F_{374}\! \left(x \right) = F_{375}\! \left(x \right)+F_{378}\! \left(x \right)
F_{375}\! \left(x \right) = F_{376}\! \left(x \right)+F_{4}\! \left(x \right)
F_{376}\! \left(x \right) = F_{377}\! \left(x \right)
F_{377}\! \left(x \right) = F_{375}\! \left(x \right) F_{4}\! \left(x \right)
F_{378}\! \left(x \right) = F_{371}\! \left(x \right)+F_{379}\! \left(x \right)
F_{379}\! \left(x \right) = F_{380}\! \left(x \right)
F_{380}\! \left(x \right) = F_{378}\! \left(x \right) F_{4}\! \left(x \right)
F_{381}\! \left(x , y\right) = F_{352}\! \left(x \right)
F_{382}\! \left(x , y\right) = F_{383}\! \left(x , y\right)
F_{384}\! \left(x , y\right) = F_{383}\! \left(x , y\right)+F_{471}\! \left(x , y\right)
F_{384}\! \left(x , y\right) = F_{385}\! \left(x \right)+F_{418}\! \left(x , y\right)
F_{385}\! \left(x \right) = F_{386}\! \left(x \right)+F_{389}\! \left(x \right)
F_{386}\! \left(x \right) = F_{161}\! \left(x \right)+F_{387}\! \left(x \right)
F_{387}\! \left(x \right) = F_{388}\! \left(x \right)
F_{388}\! \left(x \right) = F_{205}\! \left(x \right) F_{4}\! \left(x \right)
F_{389}\! \left(x \right) = F_{390}\! \left(x \right)
F_{390}\! \left(x \right) = F_{391}\! \left(x \right) F_{4}\! \left(x \right)
F_{391}\! \left(x \right) = \frac{F_{392}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{392}\! \left(x \right) = F_{393}\! \left(x \right)
F_{393}\! \left(x \right) = -F_{396}\! \left(x \right)+F_{394}\! \left(x \right)
F_{394}\! \left(x \right) = \frac{F_{395}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{395}\! \left(x \right) = F_{63}\! \left(x \right)
F_{396}\! \left(x \right) = F_{397}\! \left(x \right)
F_{397}\! \left(x \right) = F_{387}\! \left(x \right)+F_{398}\! \left(x \right)
F_{398}\! \left(x \right) = -F_{406}\! \left(x \right)+F_{399}\! \left(x \right)
F_{399}\! \left(x \right) = F_{400}\! \left(x \right)
F_{400}\! \left(x \right) = F_{4}\! \left(x \right) F_{401}\! \left(x \right)
F_{401}\! \left(x \right) = F_{402}\! \left(x , 1\right)
F_{402}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{403}\! \left(x , y\right)
F_{403}\! \left(x , y\right) = F_{404}\! \left(x , y\right)
F_{404}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{405}\! \left(x , y\right)
F_{405}\! \left(x , y\right) = -\frac{-F_{402}\! \left(x , y\right) y +F_{402}\! \left(x , 1\right)}{-1+y}
F_{406}\! \left(x \right) = F_{407}\! \left(x \right)
F_{407}\! \left(x \right) = F_{4}\! \left(x \right) F_{408}\! \left(x \right)
F_{408}\! \left(x \right) = F_{409}\! \left(x \right)+F_{411}\! \left(x \right)
F_{409}\! \left(x \right) = F_{410}\! \left(x , 1\right)
F_{410}\! \left(x , y\right) = -\frac{-F_{324}\! \left(x , y\right) y +F_{324}\! \left(x , 1\right)}{-1+y}
F_{411}\! \left(x \right) = F_{412}\! \left(x \right)
F_{412}\! \left(x \right) = F_{4}\! \left(x \right) F_{413}\! \left(x \right)
F_{413}\! \left(x \right) = F_{414}\! \left(x , 1\right)
F_{414}\! \left(x , y\right) = -\frac{-F_{415}\! \left(x , y\right) y +F_{415}\! \left(x , 1\right)}{-1+y}
F_{415}\! \left(x , y\right) = F_{410}\! \left(x , y\right)+F_{416}\! \left(x , y\right)
F_{416}\! \left(x , y\right) = F_{417}\! \left(x , y\right)
F_{417}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{414}\! \left(x , y\right)
F_{418}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{419}\! \left(x \right)
F_{419}\! \left(x \right) = \frac{F_{420}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{420}\! \left(x \right) = -F_{385}\! \left(x \right)+F_{421}\! \left(x \right)
F_{421}\! \left(x \right) = F_{422}\! \left(x \right)+F_{425}\! \left(x \right)
F_{422}\! \left(x \right) = F_{386}\! \left(x \right)+F_{423}\! \left(x \right)
F_{423}\! \left(x \right) = F_{4}\! \left(x \right) F_{424}\! \left(x \right)
F_{424}\! \left(x \right) = F_{161}\! \left(x \right)+F_{406}\! \left(x \right)
F_{425}\! \left(x \right) = F_{426}\! \left(x \right)
F_{426}\! \left(x \right) = F_{389}\! \left(x \right)+F_{427}\! \left(x \right)
F_{427}\! \left(x \right) = F_{428}\! \left(x \right)
F_{428}\! \left(x \right) = F_{4} \left(x \right)^{2} F_{429}\! \left(x \right)
F_{429}\! \left(x \right) = F_{430}\! \left(x , 1\right)
F_{430}\! \left(x , y\right) = F_{431}\! \left(x , y\right)+F_{444}\! \left(x , y\right)
F_{431}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{432}\! \left(x \right)
F_{432}\! \left(x \right) = \frac{F_{433}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{433}\! \left(x \right) = -F_{443}\! \left(x \right)+F_{434}\! \left(x \right)
F_{434}\! \left(x \right) = \frac{F_{435}\! \left(x \right)}{F_{38}\! \left(x \right) F_{4}\! \left(x \right)}
F_{435}\! \left(x \right) = F_{436}\! \left(x \right)
F_{436}\! \left(x \right) = F_{437}\! \left(x \right)+F_{438}\! \left(x \right)
F_{437}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \left(x \right)
F_{438}\! \left(x \right) = F_{439}\! \left(x \right)
F_{439}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{440}\! \left(x \right)
F_{440}\! \left(x \right) = F_{441}\! \left(x \right)+F_{87}\! \left(x \right)
F_{441}\! \left(x \right) = F_{442}\! \left(x \right)
F_{442}\! \left(x \right) = F_{4}\! \left(x \right) F_{434}\! \left(x \right)
F_{443}\! \left(x \right) = F_{386}\! \left(x \right)+F_{399}\! \left(x \right)
F_{444}\! \left(x , y\right) = F_{445}\! \left(x \right) F_{457}\! \left(x , y\right)
F_{445}\! \left(x \right) = F_{446}\! \left(x , 1\right)
F_{446}\! \left(x , y\right) = F_{447}\! \left(x , y\right)+F_{454}\! \left(x , y\right)
F_{447}\! \left(x , y\right) = F_{448}\! \left(x , y\right)
F_{448}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{449}\! \left(x , y\right)
F_{449}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{450}\! \left(x , y\right)
F_{450}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{451}\! \left(x , y\right)+F_{453}\! \left(x , y\right)
F_{451}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{452}\! \left(x , y\right)
F_{452}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{450}\! \left(x , y\right)
F_{453}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{449}\! \left(x , y\right)
F_{454}\! \left(x , y\right) = F_{455}\! \left(x , y\right)
F_{455}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{447}\! \left(x , y\right) F_{456}\! \left(x , y\right)
F_{456}\! \left(x , y\right) = -\frac{-F_{446}\! \left(x , y\right) y +F_{446}\! \left(x , 1\right)}{-1+y}
F_{457}\! \left(x , y\right) = F_{168}\! \left(x \right)+F_{458}\! \left(x , y\right)
F_{458}\! \left(x , y\right) = F_{459}\! \left(x , y\right)
F_{459}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{460}\! \left(x , y\right)
F_{460}\! \left(x , y\right) = F_{457}\! \left(x , y\right)+F_{461}\! \left(x , y\right)
F_{461}\! \left(x , y\right) = F_{462}\! \left(x \right)+F_{464}\! \left(x , y\right)
F_{462}\! \left(x \right) = F_{463}\! \left(x , 1\right)
F_{463}\! \left(x , y\right) = -\frac{y \left(F_{8}\! \left(x , 1\right)-F_{8}\! \left(x , y\right)\right)}{-1+y}
F_{464}\! \left(x , y\right) = F_{465}\! \left(x , y\right)
F_{465}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{466}\! \left(x , y\right)
F_{466}\! \left(x , y\right) = F_{467}\! \left(x , y , 1\right)
F_{467}\! \left(x , y , z\right) = -\frac{z \left(F_{468}\! \left(x , y , 1\right)-F_{468}\! \left(x , y , z\right)\right)}{-1+z}
F_{468}\! \left(x , y , z\right) = F_{463}\! \left(x , z\right)+F_{469}\! \left(x , y , z\right)
F_{469}\! \left(x , y , z\right) = F_{470}\! \left(x , y , z\right)
F_{470}\! \left(x , y , z\right) = F_{15}\! \left(x , y\right) F_{467}\! \left(x , y , z\right)
F_{471}\! \left(x , y\right) = F_{472}\! \left(x \right)+F_{481}\! \left(x , y\right)
F_{472}\! \left(x \right) = -F_{477}\! \left(x \right)+F_{473}\! \left(x \right)
F_{473}\! \left(x \right) = \frac{F_{474}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{474}\! \left(x \right) = F_{475}\! \left(x \right)
F_{475}\! \left(x \right) = -F_{476}\! \left(x \right)+F_{387}\! \left(x \right)
F_{476}\! \left(x \right) = x^{2} F_{476} \left(x \right)^{2}+2 x^{2} F_{476}\! \left(x \right)-2 x F_{476} \left(x \right)^{2}+x^{2}-3 x F_{476}\! \left(x \right)-x +2 F_{476}\! \left(x \right)
F_{477}\! \left(x \right) = -F_{385}\! \left(x \right)+F_{478}\! \left(x \right)
F_{478}\! \left(x \right) = \frac{F_{479}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{479}\! \left(x \right) = F_{480}\! \left(x \right)
F_{480}\! \left(x \right) = F_{168}\! \left(x \right)+F_{475}\! \left(x \right)
F_{481}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{482}\! \left(x \right)
F_{482}\! \left(x \right) = -F_{483}\! \left(x \right)+F_{419}\! \left(x \right)
F_{483}\! \left(x \right) = F_{484}\! \left(x \right)
F_{484}\! \left(x \right) = F_{161}\! \left(x \right)+F_{485}\! \left(x \right)
F_{485}\! \left(x \right) = F_{106}\! \left(x \right) F_{168}\! \left(x \right)
F_{486}\! \left(x \right) = -F_{493}\! \left(x \right)+F_{487}\! \left(x \right)
F_{487}\! \left(x \right) = F_{488}\! \left(x , 1\right)
F_{488}\! \left(x , y\right) = F_{489}\! \left(x , y\right)
F_{489}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{490}\! \left(x , y\right)
F_{491}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{490}\! \left(x , y\right)
F_{491}\! \left(x , y\right) = F_{492}\! \left(x , y\right)
F_{492}\! \left(x , y\right) = -\frac{y \left(F_{219}\! \left(x , 1\right)-F_{219}\! \left(x , y\right)\right)}{-1+y}
F_{493}\! \left(x \right) = F_{494}\! \left(x \right)
F_{494}\! \left(x \right) = F_{495}\! \left(x \right)+F_{509}\! \left(x \right)
F_{495}\! \left(x \right) = F_{168}\! \left(x \right)+F_{496}\! \left(x \right)
F_{496}\! \left(x \right) = F_{497}\! \left(x \right)
F_{497}\! \left(x \right) = F_{4}\! \left(x \right) F_{498}\! \left(x \right)
F_{498}\! \left(x \right) = F_{499}\! \left(x \right)+F_{501}\! \left(x \right)
F_{499}\! \left(x \right) = F_{104}\! \left(x \right) F_{500}\! \left(x \right)
F_{500}\! \left(x \right) = F_{161}\! \left(x \right)+F_{495}\! \left(x \right)
F_{501}\! \left(x \right) = F_{502}\! \left(x \right)+F_{506}\! \left(x \right)
F_{502}\! \left(x \right) = F_{168}\! \left(x \right)+F_{503}\! \left(x \right)
F_{503}\! \left(x \right) = F_{504}\! \left(x \right)
F_{504}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right) F_{505}\! \left(x \right)
F_{505}\! \left(x \right) = F_{485}\! \left(x \right)+F_{501}\! \left(x \right)
F_{506}\! \left(x \right) = F_{168}\! \left(x \right) F_{507}\! \left(x \right)
F_{507}\! \left(x \right) = F_{508}\! \left(x , 1\right)
F_{508}\! \left(x , y\right) = -\frac{y \left(F_{26}\! \left(x , 1\right)-F_{26}\! \left(x , y\right)\right)}{-1+y}
F_{509}\! \left(x \right) = F_{510}\! \left(x \right)
F_{510}\! \left(x \right) = F_{4}\! \left(x \right) F_{511}\! \left(x \right)
F_{511}\! \left(x \right) = F_{168}\! \left(x \right)+F_{512}\! \left(x \right)
F_{512}\! \left(x \right) = F_{104}\! \left(x \right) F_{168}\! \left(x \right)
F_{513}\! \left(x , y\right) = F_{514}\! \left(x , y\right)
F_{514}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{515}\! \left(x , y\right)
F_{515}\! \left(x , y\right) = F_{516}\! \left(x , y\right)+F_{551}\! \left(x , y\right)
F_{516}\! \left(x , y\right) = F_{277}\! \left(x , y\right)+F_{517}\! \left(x , y\right)
F_{517}\! \left(x , y\right) = F_{518}\! \left(x , y\right)
F_{518}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{519}\! \left(x \right)
F_{519}\! \left(x \right) = F_{520}\! \left(x , 1\right)
F_{521}\! \left(x , y\right) = F_{520}\! \left(x , y\right)+F_{550}\! \left(x , y\right)
F_{522}\! \left(x , y\right) = F_{521}\! \left(x , y\right)+F_{547}\! \left(x , y\right)
F_{522}\! \left(x , y\right) = F_{523}\! \left(x , y\right)+F_{526}\! \left(x , y\right)
F_{523}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{524}\! \left(x , y\right)
F_{524}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{525}\! \left(x , y\right)
F_{525}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{526}\! \left(x , y\right) = F_{527}\! \left(x , y\right)
F_{527}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{528}\! \left(x , y\right)
F_{528}\! \left(x , y\right) = F_{529}\! \left(x , y\right)+F_{534}\! \left(x , y\right)
F_{530}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{529}\! \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_{533}\! \left(x , y\right)
F_{532}\! \left(x , y\right) = F_{168}\! \left(x \right)+F_{261}\! \left(x , y\right)
F_{533}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{525}\! \left(x , y\right)
F_{535}\! \left(x , y\right) = F_{106}\! \left(x \right) F_{534}\! \left(x , y\right)
F_{536}\! \left(x , y\right) = F_{535}\! \left(x , y\right)+F_{543}\! \left(x , y\right)
F_{537}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{536}\! \left(x , y\right)
F_{537}\! \left(x , y\right) = F_{538}\! \left(x , y\right)
F_{538}\! \left(x , y\right) = F_{539}\! \left(x , y\right)+F_{542}\! \left(x , y\right)
F_{540}\! \left(x , y\right) = F_{539}\! \left(x , y\right)+F_{541}\! \left(x , y\right)
F_{540}\! \left(x , y\right) = F_{214}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{541}\! \left(x , y\right) = F_{161}\! \left(x \right) F_{524}\! \left(x , y\right)
F_{542}\! \left(x , y\right) = F_{533}\! \left(x , y\right)
F_{544}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{543}\! \left(x , y\right)
F_{544}\! \left(x , y\right) = F_{545}\! \left(x , y\right)
F_{545}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{546}\! \left(x , y\right)
F_{546}\! \left(x , y\right) = F_{533}\! \left(x , y\right)
F_{547}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{548}\! \left(x , y\right)
F_{548}\! \left(x , y\right) = F_{524}\! \left(x , y\right)+F_{549}\! \left(x , y\right)
F_{549}\! \left(x , y\right) = F_{525}\! \left(x , y\right)
F_{550}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{532}\! \left(x , y\right)
F_{551}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{153}\! \left(x , y\right) F_{355}\! \left(x \right)
F_{552}\! \left(x , y\right) = F_{553}\! \left(x , y\right)
F_{553}\! \left(x , y\right) = F_{161}\! \left(x \right) F_{554}\! \left(x , y\right)
F_{554}\! \left(x , y\right) = F_{281}\! \left(x \right)+F_{555}\! \left(x , y\right)
F_{555}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{557}\! \left(x , y\right) = F_{556}\! \left(x , y\right)+F_{572}\! \left(x , y\right)
F_{558}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{557}\! \left(x , y\right)
F_{558}\! \left(x , y\right) = F_{559}\! \left(x , y\right)
F_{560}\! \left(x , y\right) = F_{559}\! \left(x , y\right)+F_{575}\! \left(x , y\right)
F_{560}\! \left(x , y\right) = F_{561}\! \left(x , y\right)
F_{561}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{562}\! \left(x , y\right)
F_{562}\! \left(x , y\right) = F_{563}\! \left(x , y\right)+F_{572}\! \left(x , y\right)
F_{563}\! \left(x , y\right) = F_{564}\! \left(x , y\right)+F_{570}\! \left(x , y\right)
F_{564}\! \left(x , y\right) = F_{560}\! \left(x , y\right)+F_{565}\! \left(x \right)
F_{565}\! \left(x \right) = F_{566}\! \left(x , 1\right)
F_{566}\! \left(x , y\right) = F_{540}\! \left(x , y\right)+F_{567}\! \left(x , y\right)
F_{567}\! \left(x , y\right) = F_{568}\! \left(x , y\right)+F_{569}\! \left(x , y\right)
F_{568}\! \left(x , y\right) = F_{203}\! \left(x \right) F_{524}\! \left(x , y\right)
F_{569}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{570}\! \left(x , y\right) = F_{571}\! \left(x , y\right)
F_{571}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{360}\! \left(x \right)
F_{572}\! \left(x , y\right) = F_{573}\! \left(x , y\right)
F_{573}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{153}\! \left(x , y\right) F_{574}\! \left(x \right)
F_{574}\! \left(x \right) = F_{254}\! \left(x , 1\right)
F_{575}\! \left(x , y\right) = F_{576}\! \left(x , y\right)+F_{594}\! \left(x , y\right)
F_{576}\! \left(x , y\right) = F_{203}\! \left(x \right) F_{577}\! \left(x , y\right)
F_{577}\! \left(x , y\right) = F_{578}\! \left(x , y\right)
F_{578}\! \left(x , y\right) = F_{579}\! \left(x , y\right)+F_{584}\! \left(x , y\right)
F_{579}\! \left(x , y\right) = F_{289}\! \left(x \right) F_{580}\! \left(x , y\right)
F_{580}\! \left(x , y\right) = F_{581}\! \left(x , y\right)
F_{581}\! \left(x , y\right) = F_{582}\! \left(x , y\right) F_{583}\! \left(x , y\right)
F_{582}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{580}\! \left(x , y\right)
F_{583}\! \left(x , y\right) = y x
F_{584}\! \left(x , y\right) = F_{585}\! \left(x , y\right)+F_{589}\! \left(x , y\right)
F_{585}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{586}\! \left(x , y\right)+F_{588}\! \left(x , y\right)
F_{586}\! \left(x , y\right) = F_{583}\! \left(x , y\right) F_{587}\! \left(x , y\right)
F_{587}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{585}\! \left(x , y\right)
F_{588}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{580}\! \left(x , y\right)
F_{590}\! \left(x , y\right) = F_{370}\! \left(x \right)+F_{589}\! \left(x , y\right)
F_{590}\! \left(x , y\right) = F_{591}\! \left(x , y\right)
F_{591}\! \left(x , y\right) = F_{153}\! \left(x , y\right)^{2} F_{4}\! \left(x \right) F_{592}\! \left(x \right)
F_{592}\! \left(x \right) = F_{39}\! \left(x \right)+F_{593}\! \left(x \right)
F_{593}\! \left(x \right) = F_{290}\! \left(x \right) F_{38}\! \left(x \right)
F_{594}\! \left(x , y\right) = F_{595}\! \left(x , y\right)
F_{595}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{352}\! \left(x \right)
F_{596}\! \left(x , y\right) = F_{597}\! \left(x , y\right)
F_{597}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{598}\! \left(x , y\right)
F_{598}\! \left(x , y\right) = F_{599}\! \left(x , y\right)+F_{603}\! \left(x , y\right)
F_{599}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{600}\! \left(x , y\right)
F_{600}\! \left(x , y\right) = F_{601}\! \left(x , y\right)
F_{601}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{602}\! \left(x , y\right)
F_{602}\! \left(x , y\right) = y F_{520}\! \left(x , y\right)
F_{603}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{153}\! \left(x , y\right) F_{356}\! \left(x , y\right)
F_{604}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{356}\! \left(x , y\right)
F_{605}\! \left(x , y\right) = y F_{606}\! \left(x , y\right)
F_{607}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{606}\! \left(x , y\right)
F_{607}\! \left(x , y\right) = F_{608}\! \left(x , y\right)
F_{540}\! \left(x , y\right) = F_{521}\! \left(x , y\right)+F_{608}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{609}\! \left(x , y\right)+F_{610}\! \left(x , y\right)
F_{610}\! \left(x , y\right) = F_{168}\! \left(x \right) F_{187}\! \left(x , y\right)
F_{611}\! \left(x , y\right) = -\frac{-F_{166}\! \left(x , y\right) y +F_{166}\! \left(x , 1\right)}{-1+y}
F_{612}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{613}\! \left(x , y\right)
F_{613}\! \left(x , y\right) = F_{614}\! \left(x , 1, y\right)
F_{614}\! \left(x , y , z\right) = -\frac{-F_{615}\! \left(x , y z \right) y +F_{615}\! \left(x , z\right)}{-1+y}
F_{615}\! \left(x , y\right) = -\frac{F_{26}\! \left(x , 1\right)-F_{26}\! \left(x , y\right)}{-1+y}
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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0**2*x**2 + 8*k_0*x + (F_8(x, k_0) + 1)**2*(k_0**2*x**2 + 4*k_0*x - 1) + (F_8(x, k_0) + 1)*(2*k_0**2*x**2 - 13*k_0*x + 3) + F_8(x, k_0) - 2)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_2(x) + F_9(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_15(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_22(x, k_0), F_137(x, k_0) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_19(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_15(x, k_0)*F_25(x, k_0)**2)
Eq(F_28(x, k_0), F_136(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_135(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0) + F_33(x, k_0))
Eq(F_34(x, k_0), F_129(x, k_0) + F_33(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_42(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_37(x, k_0))
Eq(F_36(x, k_0), F_0(x)*F_26(x, k_0))
Eq(F_37(x, k_0), F_38(x)*F_41(x, k_0))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_38(x)*F_4(x))
Eq(F_41(x, k_0), 8*x**3*(k_0**2*x**2 + 8*k_0*x - 2) + 4*x**2*(2*k_0**2*x**2 - 13*k_0*x + 3)*(2*x*F_41(x, k_0) - sqrt(1 - 4*x) + 1) + 2*x*(k_0**2*x**2 + 4*k_0*x - 1)*(2*x*F_41(x, k_0) - sqrt(1 - 4*x) + 1)**2 + F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_15(x, k_0)*F_25(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_33(x, k_0)*F_38(x))
Eq(F_46(x, k_0), F_47(x, k_0) + F_48(x, k_0))
Eq(F_47(x, k_0), F_25(x, k_0)*F_35(x, k_0))
Eq(F_48(x, k_0), F_38(x)*F_49(x, k_0)*F_8(x, k_0))
Eq(F_50(x, k_0), F_49(x, k_0)*F_88(x, k_0))
Eq(F_51(x, k_0), F_50(x, k_0) + F_85(x, k_0))
Eq(F_52(x, k_0), F_128(x, k_0) + F_51(x, k_0))
Eq(F_53(x, k_0), F_15(x, k_0)*F_52(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_55(x, k_0), F_35(x, k_0) + F_54(x, k_0))
Eq(F_56(x, k_0), F_127(x, k_0) + F_55(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_15(x, k_0)*F_57(x, k_0))
Eq(F_58(x, k_0), F_7(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_61(x, k_0))
Eq(F_60(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_61(x, k_0), F_62(x) + F_96(x, k_0))
Eq(F_62(x), F_2(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_55(x, 1))
Eq(F_67(x), F_68(x, 1))
Eq(F_69(x, k_0), F_68(x, k_0) + F_71(x, k_0))
Eq(F_70(x, k_0), F_15(x, k_0)*F_69(x, k_0))
Eq(F_70(x, k_0), F_9(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_75(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_74(x, k_0))
Eq(F_73(x, k_0), F_2(x)*F_25(x, k_0))
Eq(F_74(x, k_0), F_39(x)*F_41(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_9(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_15(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_26(x, k_0)*F_69(x, k_0))
Eq(F_80(x, k_0), F_28(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_95(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_4(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_32(x, k_0) + F_82(x, k_0))
Eq(F_86(x, k_0), F_49(x, k_0)*F_87(x))
Eq(F_87(x), F_88(x, 1))
Eq(F_88(x, k_0), F_7(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_15(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_4(x)*F_93(x, k_0))
Eq(F_93(x, k_0), (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_94(x, k_0), F_57(x, k_0) + F_91(x, k_0))
Eq(F_95(x, k_0), F_49(x, k_0)*F_89(x, k_0))
Eq(F_96(x, k_0), k_0*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_109(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) + F_2(x))
Eq(F_102(x), F_103(x) + F_107(x))
Eq(F_103(x), F_104(x)*F_2(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)**2*F_4(x))
Eq(F_106(x), F_1(x) + F_104(x))
Eq(F_107(x), F_108(x)*F_39(x))
Eq(F_108(x), 8*x**3*(x**2 + 8*x - 2) + 4*x**2*(2*x**2 - 13*x + 3)*(2*x*F_108(x) - sqrt(1 - 4*x) + 1) + 2*x*(x**2 + 4*x - 1)*(2*x*F_108(x) - sqrt(1 - 4*x) + 1)**2 + F_108(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_99(x))
Eq(F_113(x), F_114(x) + F_126(x))
Eq(F_114(x), F_115(x, 1))
Eq(F_115(x, k_0), F_116(x, k_0) + F_121(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_7(x, k_0))
Eq(F_118(x, k_0), -F_119(x, 1) + (k_0*F_119(x, k_0) - F_119(x, 1))/(k_0 - 1))
Eq(F_119(x, k_0), F_120(x, k_0) + F_74(x, k_0))
Eq(F_120(x, k_0), F_2(x)*F_26(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_4(x))
Eq(F_123(x, k_0), -F_124(x, 1) + (k_0*F_124(x, k_0) - F_124(x, 1))/(k_0 - 1))
Eq(F_124(x, k_0), F_115(x, k_0) + F_125(x, k_0))
Eq(F_125(x, k_0), F_26(x, k_0)*F_87(x))
Eq(F_126(x), F_104(x)*F_87(x))
Eq(F_68(x, k_0), F_127(x, k_0) + F_61(x, k_0))
Eq(F_128(x, k_0), F_26(x, k_0)*F_57(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_4(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_34(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x)*F_25(x, k_0)*F_26(x, k_0))
Eq(F_134(x), F_2(x) + F_63(x))
Eq(F_135(x, k_0), F_49(x, k_0)*F_6(x))
Eq(F_136(x, k_0), F_49(x, k_0)*F_9(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_18(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_4(x))
Eq(F_140(x, k_0), F_141(x, k_0) + F_612(x, k_0))
Eq(F_141(x, k_0), F_138(x, k_0) + F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0)*F_4(x))
Eq(F_145(x, k_0), F_144(x, k_0)*F_15(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_147(x, k_0), F_146(x, k_0) + F_611(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + F_170(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_160(x))
Eq(F_149(x, k_0), F_1(x) + F_150(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_15(x, k_0)*F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_157(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_1(x) + F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_15(x, k_0)*F_154(x, k_0))
Eq(F_157(x, k_0), F_150(x, k_0) + F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_15(x, k_0)*F_157(x, k_0))
Eq(F_160(x), F_161(x) + F_162(x))
Eq(F_161(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_161(x)**2 + (2*x**2 - 13*x + 4)*F_161(x) - 2)
Eq(F_162(x), F_163(x, 1))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_15(x, k_0)*F_165(x, k_0)*F_25(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_167(x, k_0))
Eq(F_166(x, k_0), F_161(x) + F_163(x, k_0))
Eq(F_167(x, k_0), F_168(x)*F_169(x, k_0))
Eq(F_168(x), x**2 + 8*x + (F_168(x) + 1)**2*(x**2 + 4*x - 1) + (F_168(x) + 1)*(2*x**2 - 13*x + 3) + F_168(x) - 2)
Eq(F_169(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_15(x, k_0)*F_172(x, k_0))
Eq(F_173(x, k_0), F_172(x, k_0)*F_4(x))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0) + F_609(x, k_0))
Eq(F_176(x, k_0), F_175(x, k_0) + F_298(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0) + F_212(x, k_0))
Eq(F_178(x, k_0), F_177(x, k_0) + F_185(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0) + F_181(x, k_0))
Eq(F_180(x, k_0), F_15(x, k_0)*F_179(x, k_0))
Eq(F_180(x, k_0), F_12(x, k_0))
Eq(F_182(x, k_0), F_181(x, k_0) + F_185(x, k_0))
Eq(F_183(x, k_0), F_15(x, k_0)*F_182(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_185(x, k_0), F_186(x, k_0) + F_208(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0)*F_203(x))
Eq(F_187(x, k_0), F_149(x, k_0) + F_188(x, k_0))
Eq(F_188(x, k_0), F_15(x, k_0) + F_189(x, k_0))
Eq(F_189(x, k_0), k_0*F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x) + F_192(x, k_0) + F_195(x, k_0))
Eq(F_191(x), 0)
Eq(F_192(x, k_0), F_193(x, k_0)*F_4(x))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_15(x, k_0)*F_153(x, k_0))
Eq(F_195(x, k_0), F_15(x, k_0)*F_196(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_200(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_4(x))
Eq(F_198(x, k_0), F_199(x, k_0))
Eq(F_199(x, k_0), F_15(x, k_0)*F_197(x, k_0))
Eq(F_200(x, k_0), F_190(x, k_0) + F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0))
Eq(F_202(x, k_0), F_15(x, k_0)*F_200(x, k_0))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_205(x)*F_4(x))
Eq(F_205(x), F_206(x, 1))
Eq(F_207(x, k_0), F_206(x, k_0)*F_4(x))
Eq(F_207(x, k_0), F_19(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_149(x, k_0)*F_153(x, k_0)*F_211(x)*F_4(x))
Eq(F_211(x), F_18(x, 1))
Eq(F_212(x, k_0), F_213(x, k_0) + F_605(x, k_0))
Eq(F_214(x, k_0), F_213(x, k_0) + F_550(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0) + F_216(x, k_0))
Eq(F_215(x, k_0), F_149(x, k_0)*F_161(x))
Eq(F_217(x, k_0), F_216(x, k_0) + F_604(x, k_0))
Eq(F_218(x, k_0), F_15(x, k_0)*F_217(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0))
Eq(F_220(x, k_0), F_15(x, k_0)*F_221(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0) + F_488(x, k_0))
Eq(F_223(x, k_0), F_222(x, k_0) + F_596(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0) + F_244(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0))
Eq(F_225(x, k_0), F_161(x)*F_226(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_228(x, k_0))
Eq(F_227(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_228(x, k_0), F_229(x, k_0) + F_238(x, k_0))
Eq(F_229(x, k_0), F_230(x, k_0))
Eq(F_230(x, k_0), F_15(x, k_0)*F_231(x, k_0))
Eq(F_231(x, k_0), F_227(x, k_0) + F_232(x, k_0))
Eq(F_232(x, k_0), F_193(x, k_0) + F_233(x, k_0))
Eq(F_233(x, k_0), k_0*F_234(x, k_0))
Eq(F_234(x, k_0), F_191(x) + F_235(x, k_0) + F_237(x, k_0))
Eq(F_235(x, k_0), F_15(x, k_0)*F_236(x, k_0))
Eq(F_236(x, k_0), F_234(x, k_0) + F_4(x))
Eq(F_237(x, k_0), F_193(x, k_0)*F_4(x))
Eq(F_238(x, k_0), k_0*F_239(x, k_0))
Eq(F_239(x, k_0), F_191(x) + F_237(x, k_0) + F_240(x, k_0))
Eq(F_240(x, k_0), F_15(x, k_0)*F_241(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_243(x, k_0))
Eq(F_242(x, k_0), F_4(x))
Eq(F_243(x, k_0), F_234(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0))
Eq(F_245(x, k_0), F_15(x, k_0)*F_246(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0) + F_267(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0) + F_262(x, k_0))
Eq(F_248(x, k_0), F_221(x, k_0) + F_249(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0))
Eq(F_250(x, k_0), F_15(x, k_0)*F_251(x, k_0))
Eq(F_251(x, k_0), F_247(x, k_0) + F_252(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0))
Eq(F_253(x, k_0), F_15(x, k_0)*F_153(x, k_0)*F_254(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_256(x, k_0))
Eq(F_255(x, k_0), F_153(x, k_0)*F_161(x))
Eq(F_256(x, k_0), F_106(x)*F_257(x, k_0))
Eq(F_258(x, k_0), F_149(x, k_0)*F_257(x, k_0))
Eq(F_259(x, k_0), F_216(x, k_0) + F_258(x, k_0))
Eq(F_260(x, k_0), F_15(x, k_0)*F_259(x, k_0))
Eq(F_260(x, k_0), F_261(x, k_0))
Eq(F_219(x, k_0), F_150(x, k_0) + F_261(x, k_0))
Eq(F_262(x, k_0), F_263(x, k_0))
Eq(F_263(x, k_0), F_153(x, k_0)*F_264(x, k_0))
Eq(F_264(x, k_0), k_0*F_265(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0))
Eq(F_266(x, k_0), F_149(x, k_0)*F_254(x, k_0)*F_4(x))
Eq(F_267(x, k_0), F_268(x, k_0))
Eq(F_268(x, k_0), F_161(x)*F_269(x, k_0))
Eq(F_269(x, k_0), F_270(k_0*x))
Eq(F_270(x), F_271(x)/F_161(x))
Eq(F_271(x), F_272(x, 1))
Eq(F_272(x, k_0), F_273(x, k_0))
Eq(F_274(x, k_0), F_273(x, k_0) + F_556(x, k_0))
Eq(F_275(x, k_0), F_274(x, k_0)*F_4(x))
Eq(F_275(x, k_0), F_276(x, k_0))
Eq(F_277(x, k_0), F_276(x, k_0) + F_552(x, k_0))
Eq(F_277(x, k_0), F_278(x) + F_513(x, k_0))
Eq(F_278(x), F_279(x) + F_282(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_161(x)*F_281(x))
Eq(F_281(x), F_1(x) + F_4(x))
Eq(F_282(x), F_283(x) - F_486(x))
Eq(F_283(x), F_284(x, 1))
Eq(F_285(x, k_0), F_284(x, k_0) + F_382(x, k_0))
Eq(F_286(x, k_0), F_285(x, k_0) + F_365(x, k_0))
Eq(F_286(x, k_0), F_287(x) + F_359(x, k_0))
Eq(F_287(x), F_288(x) + F_292(x))
Eq(F_288(x), F_289(x)*F_5(x))
Eq(F_289(x), F_1(x) + F_290(x))
Eq(F_290(x), F_291(x))
Eq(F_291(x), F_289(x)*F_38(x)*F_4(x))
Eq(F_292(x), F_293(x) - F_353(x))
Eq(F_293(x), F_294(x) + F_306(x))
Eq(F_294(x), F_295(x)/F_4(x))
Eq(F_295(x), F_296(x))
Eq(F_296(x), -F_161(x) + F_297(x))
Eq(F_297(x), F_298(x, 1))
Eq(F_299(x, k_0), F_298(x, k_0) + F_305(x, k_0))
Eq(F_300(x, k_0), F_299(x, k_0) + F_302(x, k_0))
Eq(F_301(x, k_0), F_15(x, k_0)*F_300(x, k_0))
Eq(F_301(x, k_0), F_7(x, k_0))
Eq(F_303(x, k_0), F_302(x, k_0) + F_305(x, k_0))
Eq(F_304(x, k_0), F_15(x, k_0)*F_303(x, k_0))
Eq(F_304(x, k_0), F_9(x, k_0))
Eq(F_305(x, k_0), F_187(x, k_0)*F_2(x))
Eq(F_306(x), F_307(x) + F_352(x))
Eq(F_307(x), F_289(x)*F_308(x))
Eq(F_308(x), F_203(x) + F_309(x))
Eq(F_309(x), F_310(x))
Eq(F_310(x), F_311(x)*F_4(x))
Eq(F_311(x), F_312(x) + F_314(x))
Eq(F_312(x), F_313(x, 1))
Eq(F_313(x, k_0), F_153(x, k_0)*F_203(x))
Eq(F_314(x), F_315(x) + F_349(x))
Eq(F_315(x), F_316(x, 1))
Eq(F_316(x, k_0), (-k_0*F_317(x, k_0) + F_317(x, 1))/(1 - k_0))
Eq(F_317(x, k_0), F_318(x, k_0))
Eq(F_318(x, k_0), F_319(x, k_0)*F_38(x)*F_4(x))
Eq(F_319(x, k_0), F_320(x, k_0) + F_327(x, k_0))
Eq(F_320(x, k_0), F_321(x, k_0))
Eq(F_321(x, k_0), F_322(x, k_0)*F_38(x))
Eq(F_322(x, k_0), F_323(x, k_0) + F_325(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0)*F_38(x))
Eq(F_324(x, k_0), k_0**2*x**2 + 8*k_0*x + (k_0**2*x**2 + 4*k_0*x - 1)*F_324(x, k_0)**2 + (2*k_0**2*x**2 - 13*k_0*x + 4)*F_324(x, k_0) - 2)
Eq(F_325(x, k_0), F_25(x, k_0)*F_326(x))
Eq(F_326(x), x*(x - 2)*(x - 1)*((x - 1)*F_326(x) - 1)**2 - (x - 1)**3 + (x - 1)**2*(x + 1)*((x - 1)*F_326(x) - 1) + F_326(x))
Eq(F_327(x, k_0), F_25(x, k_0)*F_328(x))
Eq(F_328(x), F_329(x, 1))
Eq(F_330(x, k_0), F_329(x, k_0) + F_346(x, k_0))
Eq(F_331(x, k_0), F_153(x, k_0)*F_330(x, k_0)*F_4(x))
Eq(F_331(x, k_0), F_332(x, k_0))
Eq(F_332(x, k_0), F_2(x) + F_333(x, k_0))
Eq(F_333(x, k_0), F_334(x, k_0))
Eq(F_334(x, k_0), F_15(x, k_0)*F_335(x, k_0))
Eq(F_335(x, k_0), F_336(x, k_0) + F_337(x, k_0))
Eq(F_336(x, k_0), F_153(x, k_0)*F_2(x))
Eq(F_337(x, k_0), F_338(x, k_0))
Eq(F_338(x, k_0), F_153(x, k_0)*F_339(x, k_0)*F_4(x))
Eq(F_339(x, k_0), F_340(x, k_0) + F_345(x, k_0))
Eq(F_340(x, k_0), F_341(x, k_0))
Eq(F_341(x, k_0), F_153(x, k_0)*F_342(x))
Eq(F_342(x), F_343(x) + F_344(x))
Eq(F_343(x), F_161(x)*F_38(x))
Eq(F_344(x), F_106(x)*F_326(x))
Eq(F_345(x, k_0), F_106(x)*F_329(x, k_0))
Eq(F_346(x, k_0), F_347(x, k_0))
Eq(F_347(x, k_0), F_153(x, k_0)*F_348(x))
Eq(F_348(x), x*(x - 2)*F_348(x)**2 + (x + 2)*F_348(x) - 1)
Eq(F_349(x), F_106(x)*F_350(x))
Eq(F_350(x), F_308(x) - F_351(x))
Eq(F_351(x), F_332(x, 1))
Eq(F_352(x), F_209(x, 1))
Eq(F_353(x), F_289(x)*F_354(x))
Eq(F_354(x), F_308(x) + F_355(x))
Eq(F_355(x), F_356(x, 1))
Eq(F_356(x, k_0), F_161(x) + F_357(x, k_0))
Eq(F_357(x, k_0), F_358(x, k_0))
Eq(F_358(x, k_0), F_15(x, k_0)*F_254(x, k_0))
Eq(F_359(x, k_0), k_0*F_360(x))
Eq(F_360(x), F_361(x) + F_362(x))
Eq(F_361(x), F_264(x, 1))
Eq(F_362(x), F_363(x))
Eq(F_363(x), F_364(x, 1))
Eq(F_364(x, k_0), F_188(x, k_0)*F_203(x))
Eq(F_365(x, k_0), F_366(x, k_0) + F_381(x, k_0))
Eq(F_366(x, k_0), F_203(x)*F_367(x, k_0))
Eq(F_367(x, k_0), F_289(x) + F_368(x, k_0))
Eq(F_368(x, k_0), F_15(x, k_0) + F_369(x, k_0))
Eq(F_369(x, k_0), k_0*F_370(x))
Eq(F_370(x), F_371(x))
Eq(F_371(x), F_191(x) + F_372(x) + F_373(x))
Eq(F_372(x), F_39(x)*F_4(x))
Eq(F_373(x), F_374(x)*F_4(x))
Eq(F_374(x), F_375(x) + F_378(x))
Eq(F_375(x), F_376(x) + F_4(x))
Eq(F_376(x), F_377(x))
Eq(F_377(x), F_375(x)*F_4(x))
Eq(F_378(x), F_371(x) + F_379(x))
Eq(F_379(x), F_380(x))
Eq(F_380(x), F_378(x)*F_4(x))
Eq(F_381(x, k_0), F_352(x))
Eq(F_382(x, k_0), F_383(x, k_0))
Eq(F_384(x, k_0), F_383(x, k_0) + F_471(x, k_0))
Eq(F_384(x, k_0), F_385(x) + F_418(x, k_0))
Eq(F_385(x), F_386(x) + F_389(x))
Eq(F_386(x), F_161(x) + F_387(x))
Eq(F_387(x), F_388(x))
Eq(F_388(x), F_205(x)*F_4(x))
Eq(F_389(x), F_390(x))
Eq(F_390(x), F_391(x)*F_4(x))
Eq(F_391(x), F_392(x)/F_4(x))
Eq(F_392(x), F_393(x))
Eq(F_393(x), F_394(x) - F_396(x))
Eq(F_394(x), F_395(x)/F_4(x))
Eq(F_395(x), F_63(x))
Eq(F_396(x), F_397(x))
Eq(F_397(x), F_387(x) + F_398(x))
Eq(F_398(x), F_399(x) - F_406(x))
Eq(F_399(x), F_400(x))
Eq(F_400(x), F_4(x)*F_401(x))
Eq(F_401(x), F_402(x, 1))
Eq(F_402(x, k_0), F_206(x, k_0) + F_403(x, k_0))
Eq(F_403(x, k_0), F_404(x, k_0))
Eq(F_404(x, k_0), F_4(x)*F_405(x, k_0))
Eq(F_405(x, k_0), (k_0*F_402(x, k_0) - F_402(x, 1))/(k_0 - 1))
Eq(F_406(x), F_407(x))
Eq(F_407(x), F_4(x)*F_408(x))
Eq(F_408(x), F_409(x) + F_411(x))
Eq(F_409(x), F_410(x, 1))
Eq(F_410(x, k_0), (-k_0*F_324(x, k_0) + F_324(x, 1))/(1 - k_0))
Eq(F_411(x), F_412(x))
Eq(F_412(x), F_4(x)*F_413(x))
Eq(F_413(x), F_414(x, 1))
Eq(F_414(x, k_0), (-k_0*F_415(x, k_0) + F_415(x, 1))/(1 - k_0))
Eq(F_415(x, k_0), F_410(x, k_0) + F_416(x, k_0))
Eq(F_416(x, k_0), F_417(x, k_0))
Eq(F_417(x, k_0), F_4(x)*F_414(x, k_0))
Eq(F_418(x, k_0), F_15(x, k_0)*F_419(x))
Eq(F_419(x), F_420(x)/F_4(x))
Eq(F_420(x), -F_385(x) + F_421(x))
Eq(F_421(x), F_422(x) + F_425(x))
Eq(F_422(x), F_386(x) + F_423(x))
Eq(F_423(x), F_4(x)*F_424(x))
Eq(F_424(x), F_161(x) + F_406(x))
Eq(F_425(x), F_426(x))
Eq(F_426(x), F_389(x) + F_427(x))
Eq(F_427(x), F_428(x))
Eq(F_428(x), F_4(x)**2*F_429(x))
Eq(F_429(x), F_430(x, 1))
Eq(F_430(x, k_0), F_431(x, k_0) + F_444(x, k_0))
Eq(F_431(x, k_0), F_153(x, k_0)*F_432(x))
Eq(F_432(x), F_433(x)/F_39(x))
Eq(F_433(x), F_434(x) - F_443(x))
Eq(F_434(x), F_435(x)/(F_38(x)*F_4(x)))
Eq(F_435(x), F_436(x))
Eq(F_436(x), F_437(x) + F_438(x))
Eq(F_437(x), F_2(x)*F_38(x))
Eq(F_438(x), F_439(x))
Eq(F_439(x), F_38(x)*F_4(x)*F_440(x))
Eq(F_440(x), F_441(x) + F_87(x))
Eq(F_441(x), F_442(x))
Eq(F_442(x), F_4(x)*F_434(x))
Eq(F_443(x), F_386(x) + F_399(x))
Eq(F_444(x, k_0), F_445(x)*F_457(x, k_0))
Eq(F_445(x), F_446(x, 1))
Eq(F_446(x, k_0), F_447(x, k_0) + F_454(x, k_0))
Eq(F_447(x, k_0), F_448(x, k_0))
Eq(F_448(x, k_0), F_38(x) + F_449(x, k_0))
Eq(F_449(x, k_0), F_193(x, k_0) + F_450(x, k_0))
Eq(F_450(x, k_0), F_191(x) + F_451(x, k_0) + F_453(x, k_0))
Eq(F_451(x, k_0), F_15(x, k_0)*F_452(x, k_0))
Eq(F_452(x, k_0), F_39(x) + F_450(x, k_0))
Eq(F_453(x, k_0), F_4(x)*F_449(x, k_0))
Eq(F_454(x, k_0), F_455(x, k_0))
Eq(F_455(x, k_0), F_4(x)*F_447(x, k_0)*F_456(x, k_0))
Eq(F_456(x, k_0), (-k_0*F_446(x, k_0) + F_446(x, 1))/(1 - k_0))
Eq(F_457(x, k_0), F_168(x) + F_458(x, k_0))
Eq(F_458(x, k_0), F_459(x, k_0))
Eq(F_459(x, k_0), F_15(x, k_0)*F_460(x, k_0))
Eq(F_460(x, k_0), F_457(x, k_0) + F_461(x, k_0))
Eq(F_461(x, k_0), F_462(x) + F_464(x, k_0))
Eq(F_462(x), F_463(x, 1))
Eq(F_463(x, k_0), -F_8(x, 1) + (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_464(x, k_0), F_465(x, k_0))
Eq(F_465(x, k_0), F_15(x, k_0)*F_466(x, k_0))
Eq(F_466(x, k_0), F_467(x, k_0, 1))
Eq(F_467(x, k_0, k_1), -F_468(x, k_0, 1) + (-k_1*F_468(x, k_0, k_1) + F_468(x, k_0, 1))/(1 - k_1))
Eq(F_468(x, k_0, k_1), F_463(x, k_1) + F_469(x, k_0, k_1))
Eq(F_469(x, k_0, k_1), F_470(x, k_0, k_1))
Eq(F_470(x, k_0, k_1), F_15(x, k_0)*F_467(x, k_0, k_1))
Eq(F_471(x, k_0), F_472(x) + F_481(x, k_0))
Eq(F_472(x), F_473(x) - F_477(x))
Eq(F_473(x), F_474(x)/F_4(x))
Eq(F_474(x), F_475(x))
Eq(F_475(x), F_387(x) - F_476(x))
Eq(F_476(x), x*(x - 2)*(F_476(x) + 1)**2 + (x + 1)*(F_476(x) + 1) + F_476(x) - 1)
Eq(F_477(x), -F_385(x) + F_478(x))
Eq(F_478(x), F_479(x)/F_4(x))
Eq(F_479(x), F_480(x))
Eq(F_480(x), F_168(x) + F_475(x))
Eq(F_481(x, k_0), F_15(x, k_0)*F_482(x))
Eq(F_482(x), F_419(x) - F_483(x))
Eq(F_483(x), F_484(x))
Eq(F_484(x), F_161(x) + F_485(x))
Eq(F_485(x), F_106(x)*F_168(x))
Eq(F_486(x), F_487(x) - F_493(x))
Eq(F_487(x), F_488(x, 1))
Eq(F_488(x, k_0), F_489(x, k_0))
Eq(F_489(x, k_0), F_4(x)*F_490(x, k_0))
Eq(F_491(x, k_0), F_15(x, k_0)*F_490(x, k_0))
Eq(F_491(x, k_0), F_492(x, k_0))
Eq(F_492(x, k_0), -F_219(x, 1) + (k_0*F_219(x, k_0) - F_219(x, 1))/(k_0 - 1))
Eq(F_493(x), F_494(x))
Eq(F_494(x), F_495(x) + F_509(x))
Eq(F_495(x), F_168(x) + F_496(x))
Eq(F_496(x), F_497(x))
Eq(F_497(x), F_4(x)*F_498(x))
Eq(F_498(x), F_499(x) + F_501(x))
Eq(F_499(x), F_104(x)*F_500(x))
Eq(F_500(x), F_161(x) + F_495(x))
Eq(F_501(x), F_502(x) + F_506(x))
Eq(F_502(x), F_168(x) + F_503(x))
Eq(F_503(x), F_504(x))
Eq(F_504(x), F_106(x)*F_4(x)*F_505(x))
Eq(F_505(x), F_485(x) + F_501(x))
Eq(F_506(x), F_168(x)*F_507(x))
Eq(F_507(x), F_508(x, 1))
Eq(F_508(x, k_0), -F_26(x, 1) + (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_509(x), F_510(x))
Eq(F_510(x), F_4(x)*F_511(x))
Eq(F_511(x), F_168(x) + F_512(x))
Eq(F_512(x), F_104(x)*F_168(x))
Eq(F_513(x, k_0), F_514(x, k_0))
Eq(F_514(x, k_0), F_15(x, k_0)*F_515(x, k_0))
Eq(F_515(x, k_0), F_516(x, k_0) + F_551(x, k_0))
Eq(F_516(x, k_0), F_277(x, k_0) + F_517(x, k_0))
Eq(F_517(x, k_0), F_518(x, k_0))
Eq(F_518(x, k_0), F_153(x, k_0)*F_519(x))
Eq(F_519(x), F_520(x, 1))
Eq(F_521(x, k_0), F_520(x, k_0) + F_550(x, k_0))
Eq(F_522(x, k_0), F_521(x, k_0) + F_547(x, k_0))
Eq(F_522(x, k_0), F_523(x, k_0) + F_526(x, k_0))
Eq(F_523(x, k_0), F_0(x)*F_524(x, k_0))
Eq(F_524(x, k_0), F_149(x, k_0) + F_525(x, k_0))
Eq(F_525(x, k_0), F_190(x, k_0) + F_4(x))
Eq(F_526(x, k_0), F_527(x, k_0))
Eq(F_527(x, k_0), F_4(x)*F_528(x, k_0))
Eq(F_528(x, k_0), F_529(x, k_0) + F_534(x, k_0))
Eq(F_530(x, k_0), F_4(x)*F_529(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_533(x, k_0))
Eq(F_532(x, k_0), F_168(x) + F_261(x, k_0))
Eq(F_533(x, k_0), F_2(x)*F_525(x, k_0))
Eq(F_535(x, k_0), F_106(x)*F_534(x, k_0))
Eq(F_536(x, k_0), F_535(x, k_0) + F_543(x, k_0))
Eq(F_537(x, k_0), F_4(x)*F_536(x, k_0))
Eq(F_537(x, k_0), F_538(x, k_0))
Eq(F_538(x, k_0), F_539(x, k_0) + F_542(x, k_0))
Eq(F_540(x, k_0), F_539(x, k_0) + F_541(x, k_0))
Eq(F_540(x, k_0), F_214(x, k_0) + F_265(x, k_0))
Eq(F_541(x, k_0), F_161(x)*F_524(x, k_0))
Eq(F_542(x, k_0), F_533(x, k_0))
Eq(F_544(x, k_0), F_4(x)*F_543(x, k_0))
Eq(F_544(x, k_0), F_545(x, k_0))
Eq(F_545(x, k_0), F_216(x, k_0) + F_546(x, k_0))
Eq(F_546(x, k_0), F_533(x, k_0))
Eq(F_547(x, k_0), F_2(x)*F_548(x, k_0))
Eq(F_548(x, k_0), F_524(x, k_0) + F_549(x, k_0))
Eq(F_549(x, k_0), F_525(x, k_0))
Eq(F_550(x, k_0), F_149(x, k_0) + F_532(x, k_0))
Eq(F_551(x, k_0), F_15(x, k_0)*F_153(x, k_0)*F_355(x))
Eq(F_552(x, k_0), F_553(x, k_0))
Eq(F_553(x, k_0), F_161(x)*F_554(x, k_0))
Eq(F_554(x, k_0), F_281(x) + F_555(x, k_0))
Eq(F_555(x, k_0), F_229(x, k_0) + F_239(x, k_0))
Eq(F_557(x, k_0), F_556(x, k_0) + F_572(x, k_0))
Eq(F_558(x, k_0), F_15(x, k_0)*F_557(x, k_0))
Eq(F_558(x, k_0), F_559(x, k_0))
Eq(F_560(x, k_0), F_559(x, k_0) + F_575(x, k_0))
Eq(F_560(x, k_0), F_561(x, k_0))
Eq(F_561(x, k_0), F_15(x, k_0)*F_562(x, k_0))
Eq(F_562(x, k_0), F_563(x, k_0) + F_572(x, k_0))
Eq(F_563(x, k_0), F_564(x, k_0) + F_570(x, k_0))
Eq(F_564(x, k_0), F_560(x, k_0) + F_565(x))
Eq(F_565(x), F_566(x, 1))
Eq(F_566(x, k_0), F_540(x, k_0) + F_567(x, k_0))
Eq(F_567(x, k_0), F_568(x, k_0) + F_569(x, k_0))
Eq(F_568(x, k_0), F_203(x)*F_524(x, k_0))
Eq(F_569(x, k_0), F_209(x, k_0))
Eq(F_570(x, k_0), F_571(x, k_0))
Eq(F_571(x, k_0), F_153(x, k_0)*F_360(x))
Eq(F_572(x, k_0), F_573(x, k_0))
Eq(F_573(x, k_0), F_15(x, k_0)*F_153(x, k_0)*F_574(x))
Eq(F_574(x), F_254(x, 1))
Eq(F_575(x, k_0), F_576(x, k_0) + F_594(x, k_0))
Eq(F_576(x, k_0), F_203(x)*F_577(x, k_0))
Eq(F_577(x, k_0), F_578(x, k_0))
Eq(F_578(x, k_0), F_579(x, k_0) + F_584(x, k_0))
Eq(F_579(x, k_0), F_289(x)*F_580(x, k_0))
Eq(F_580(x, k_0), F_581(x, k_0))
Eq(F_581(x, k_0), F_582(x, k_0)*F_583(x, k_0))
Eq(F_582(x, k_0), F_1(x) + F_580(x, k_0))
Eq(F_583(x, k_0), k_0*x)
Eq(F_584(x, k_0), F_585(x, k_0) + F_589(x, k_0))
Eq(F_585(x, k_0), F_191(x) + F_586(x, k_0) + F_588(x, k_0))
Eq(F_586(x, k_0), F_583(x, k_0)*F_587(x, k_0))
Eq(F_587(x, k_0), F_4(x) + F_585(x, k_0))
Eq(F_588(x, k_0), F_4(x)*F_580(x, k_0))
Eq(F_590(x, k_0), F_370(x) + F_589(x, k_0))
Eq(F_590(x, k_0), F_591(x, k_0))
Eq(F_591(x, k_0), F_153(x, k_0)**2*F_4(x)*F_592(x))
Eq(F_592(x), F_39(x) + F_593(x))
Eq(F_593(x), F_290(x)*F_38(x))
Eq(F_594(x, k_0), F_595(x, k_0))
Eq(F_595(x, k_0), F_193(x, k_0)*F_352(x))
Eq(F_596(x, k_0), F_597(x, k_0))
Eq(F_597(x, k_0), F_15(x, k_0)*F_598(x, k_0))
Eq(F_598(x, k_0), F_599(x, k_0) + F_603(x, k_0))
Eq(F_599(x, k_0), F_223(x, k_0) + F_600(x, k_0))
Eq(F_600(x, k_0), F_601(x, k_0))
Eq(F_601(x, k_0), F_153(x, k_0)*F_602(x, k_0))
Eq(F_602(x, k_0), k_0*F_520(x, k_0))
Eq(F_603(x, k_0), F_15(x, k_0)*F_153(x, k_0)*F_356(x, k_0))
Eq(F_604(x, k_0), F_149(x, k_0)*F_356(x, k_0))
Eq(F_605(x, k_0), k_0*F_606(x, k_0))
Eq(F_607(x, k_0), F_213(x, k_0) + F_606(x, k_0))
Eq(F_607(x, k_0), F_608(x, k_0))
Eq(F_540(x, k_0), F_521(x, k_0) + F_608(x, k_0))
Eq(F_212(x, k_0), F_609(x, k_0) + F_610(x, k_0))
Eq(F_610(x, k_0), F_168(x)*F_187(x, k_0))
Eq(F_611(x, k_0), (k_0*F_166(x, k_0) - F_166(x, 1))/(k_0 - 1))
Eq(F_612(x, k_0), F_6(x)*F_613(x, k_0))
Eq(F_613(x, k_0), F_614(x, 1, k_0))
Eq(F_614(x, k_0, k_1), (-k_0*k_1*F_615(x, k_0*k_1) + k_1*F_615(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_615(x, k_0), -F_26(x, k_0) + (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
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], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "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], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": 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