02314_02341_02431_03124_03214_03241
Counting sequence:
1, 1, 2, 6, 24, 114, 598, 3342, 19506, 117475, 724363, 4548909, 28985592, 186898643, 1217033483, 7991019462, 52842581156, 351588611308, 2351914079263, 15807804546593, 106698745704897, 722928446087001, 4914948371662040, 33519132115863068, 229244012752879278, 1571923275898282010, 10804439538598535776, 74427056689303113484, 513743485574043483558, 3552921098728037552819, 24614556317499837806994, 170810602903648814008033, 1187156824867268828505818, 8262856604169556007142875, 57589508769767254421215591, 401895442535472695400980912, 2808069160676877986977614803, 19642583666109203074149959255, 137549474045532886206632351337, 964193666619375037262466344055, 6765377198129072498280710804571, 47513959961499570085236887015435, 333989262532933660346829384858960, 2349675133900834899827190235320298, 16543614422021426246904640013468995, 116569411114969317089647752633868673, 821969737130347116920173977534690544, 5800032430983870734627085171567405716, 40953931132751411043095624600056569061, 289360573110434221810921773703386952436, 2045740011249480638497925355211506197860, 14471656789895778228955852919477255176464, 102431333918767844338097572906738908316646, 725412043055551376188006682754138813278009, 5140024410113036285618310092831675554531539, 36438937662914086776467543582961545461816868, 258451115415475177430530121783060398274121178, 1833985033587188072552300753340714325922111324, 13019992184191349536666899644640701847134109255, 92473324753157381958268105815065239957851069002, 657062417740850855782185345364968290265353512828, 4670626083915234611267704842520016276472770390195, 33213611443953509965619924895575554132260321049194, 236278451478379594365302617788298571591358514013234, 1681488473169424734450821295794334504701058724532511, 11970724322488700028836116653891316426908979035531663, 85250894219216206597389613271728063489506250092002431, 607330195108923773869935934585418203137664518260208080, 4328065877920971581907652414180367707768348976127176349, 30853308488946695069487582690104643143955942261567535537, 220011064663689353617989583383347216316759163571018080540, 1569344854544217365601796304730161040049087995301372126814, 11197464106798986558655670462541235438630504594439314426041, 79918052039023517984089685451338475729237489823015544149880, 570545988569884413064679663339081278632283764727512593972927, 4074307006183843792968831549070394480085711387133385823926071, 29102551959671622990407597310463313782492317734178223654482344, 207931193114090886815297691871912113648299629040155854351459894, 1485992455444863831351326286983416154923901096338674966105732390, 10622315493511100141543269000247365001519097699266793109548178108, 75949474107832086191455725048000506858739378507170376335018922020, 543163749502768275622263857671663627190825758297763577635466564629, 3885391257210623873443803413292117418631292201317556239427395998983, 27799331081622549462505491762490897297763040850117972915700925063810, 198942355781936296979600055557990112661121919625131838043733982679686, 1424004257867464138737317922798418724304973426946212123095076423415099, 10194931580116500997896075349797161344606199817706501945074238345609197, 73003601855450618696397457105655747537548928552663409178288527975058282, 522864581429304702222919971733450990281332291848152211775834686015157120, 3745563891565776953015459170508557891045765459685295652765502807857581436, 26836532146620499421485525399036373452505396316269769954901072994858594409, 192315811279771286879591377468264093816494144111776774402374788811988949172, 1378419056020140031317917906570634743776310804962923961791589686672435428976, 9881515407876169699080249612914163447717350542854252924405247063634548158507, 70850059950102028622218645361492891781932935156875191807451025825986913095502, 508077203071557804099929277323052052666041541348036898758847099094044195062351, 3644101734912871602087257617850198951813139356334286939373766520531146762270555, 26140934040729005472915726537848138717675057048498896852815856725247402608938453, 187551311922133763224721587772524634327636525548850039620038335052988207849512439, 1345817354127640526054270924200508546239750209785155025413938349192485719427187594, 9658680764712931377637820949458352735020645482373357767699943778905389093995920995
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25323/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 1+(F[5,x]^3-F[5,x]^2+F[5,x])*x
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[35,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = F[14,x]
F[14,x] = F[5,x]^2*F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[1,x]+F[16,x]
F[20,x] = F[16,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[30,x]
F[22,x] = 0
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[16,x]
F[30,x] = F[15,x]*F[31,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[15,x]*F[34,x]
F[34,x] = F[16,x]
F[35,x] = F[36,x,1]
F[37,x,k[0]] = F[214,x,k[0]]+F[36,x,k[0]]
F[37,x,k[0]] = F[128,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[211,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[0,x]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]*F[69,x,k[0]]
F[42,x,k[0]] = F[43,x,1,k[0]]
F[43,x,k[0],k[1]] = F[44,x,k[0]*k[1],k[1]]
F[44,x,k[0],k[1]] = F[38,x,k[0]]+F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[47,x,k[0],k[1]]*F[69,x,k[1]]
F[47,x,k[0],k[1]] = F[205,x,k[0],k[1]]+F[48,x,k[0],k[1]]
F[48,x,k[0],k[1]] = F[201,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = F[50,x,1,k[0],k[1]]
F[50,x,k[0],k[1],k[2]] = F[198,x,k[0],k[1],k[2]]+F[51,x,k[1],k[2]]
F[51,x,k[0],k[1]] = F[38,x,k[1]]+F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[54,x,k[0],k[1]]*F[69,x,k[0]]
F[54,x,k[0],k[1]] = F[160,x,k[0],k[1]]+F[55,x,k[0]]
F[56,x,k[0]] = F[125,x,k[0]]+F[55,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]*F[69,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = (F[58,x,k[0]]-F[58,x,1])/(-1+k[0])
F[60,x,k[0]] = F[36,x,k[0]]+F[59,x,k[0]]
F[60,x,k[0]] = F[124,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[16,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[110,x,k[0]]+F[22,x]+F[64,x,k[0]]
F[64,x,k[0]] = F[15,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[86,x,k[0]]
F[66,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]*F[70,x,k[0]]
F[69,x,k[0]] = k[0]*x
F[70,x,k[0]] = F[71,x,k[0]]+F[72,x,k[0]]
F[71,x,k[0]] = F[1,x]+F[67,x,k[0]]
F[72,x,k[0]] = F[67,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[22,x]+F[74,x,k[0]]+F[81,x,k[0]]
F[74,x,k[0]] = F[69,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[67,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[69,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[67,x,k[0]]
F[81,x,k[0]] = F[69,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[69,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[67,x,k[0]]
F[86,x,k[0]] = F[100,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[22,x]+F[88,x,k[0]]+F[95,x,k[0]]
F[88,x,k[0]] = F[15,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[67,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[69,x,k[0]]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[16,x]
F[95,x,k[0]] = F[69,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[15,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[67,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]+F[104,x,k[0]]+F[22,x]
F[101,x,k[0]] = F[102,x,k[0]]*F[15,x]
F[102,x,k[0]] = F[63,x,k[0]]
F[103,x,k[0]] = 0
F[104,x,k[0]] = F[105,x,k[0]]*F[69,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[107,x,k[0]]
F[106,x,k[0]] = F[33,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[15,x]
F[109,x,k[0]] = F[63,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[69,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[16,x]+F[87,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[63,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[121,x,k[0]]+F[122,x,k[0]]+F[22,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[15,x]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[77,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[69,x,k[0]]
F[120,x,k[0]] = F[63,x,k[0]]
F[121,x,k[0]] = 0
F[122,x,k[0]] = F[123,x,k[0]]*F[69,x,k[0]]
F[123,x,k[0]] = F[63,x,k[0]]
F[124,x,k[0]] = 1/(-1+k[0])*(F[36,x,k[0]]*k[0]-F[36,x,1])
F[126,x,k[0]] = F[125,x,k[0]]*F[69,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[128,x,k[0]] = F[127,x,k[0]]+F[154,x]
F[128,x,k[0]] = F[129,x,1,k[0]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]*F[69,x,k[0]]
F[131,x,k[0],k[1]] = F[132,x,k[0],1,k[1]]
F[132,x,k[0],k[1],k[2]] = F[133,x,k[0],k[1],k[2]]+F[145,x,k[0],k[1],k[2]]
F[133,x,k[0],k[1],k[2]] = F[134,x,k[0],k[1],k[2]]+F[137,x,k[0],k[1],k[2]]
F[134,x,k[0],k[1],k[2]] = F[135,x,k[0],k[1],k[2]]
F[135,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[51,x,k[1],k[2]]
F[136,x,k[0]] = 1+x*F[136,x,k[0]]*(F[136,x,k[0]]^2-F[136,x,k[0]]+1)*k[0]
F[137,x,k[0],k[1],k[2]] = F[138,x,k[0],k[1],k[2]]
F[138,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[139,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[139,x,k[0],k[1],k[2]] = F[140,x,k[0],k[1],k[2]]+F[144,x,k[0],k[1],k[2]]
F[140,x,k[0],k[1],k[2]] = F[141,x,k[0],k[1],k[2]]+F[142,x,k[0],k[1],k[2]]
F[141,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[133,x,k[0],k[1],k[2]]*k[1]-F[133,x,k[0],1,k[2]])
F[142,x,k[0],k[1],k[2]] = F[133,x,k[0],k[1],k[2]]*F[143,x,k[0]]
F[143,x,k[0]] = k[0]*x*(1+F[143,x,k[0]])*(F[143,x,k[0]]^2+F[143,x,k[0]]+1)
F[144,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[145,x,k[0],k[1],k[2]]*k[1]-F[145,x,k[0],1,k[2]])
F[145,x,k[0],k[1],k[2]] = F[146,x,k[0],k[1],k[2]]+F[152,x,k[0],k[1],k[2]]
F[146,x,k[0],k[1],k[2]] = F[147,x,k[0],k[1],k[2]]
F[147,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[148,x,k[1],k[2]]
F[148,x,k[0],k[1]] = F[149,x,k[0],k[1]]
F[149,x,k[0],k[1]] = F[15,x]*F[150,x,k[0],k[1]]
F[150,x,k[0],k[1]] = F[151,x,k[0],k[1]]+F[37,x,k[1]]
F[151,x,k[0],k[1]] = F[58,x,k[0]]
F[152,x,k[0],k[1],k[2]] = F[153,x,k[0],k[1],k[2]]
F[153,x,k[0],k[1],k[2]] = F[136,x,k[0]]^2*F[145,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[154,x] = F[155,x]+F[157,x]
F[155,x] = F[156,x]
F[156,x] = -F[5,x]+F[12,x]
F[157,x] = -F[6,x]+F[158,x]
F[158,x] = -F[159,x]+F[9,x]
F[159,x] = F[58,x,1]
F[160,x,k[0],k[1]] = F[161,x,k[1]]
F[161,x,k[0]] = F[162,x,k[0]]*F[69,x,k[0]]
F[162,x,k[0]] = F[163,x,1,k[0]]
F[163,x,k[0],k[1]] = (F[164,x,k[0],k[1]]*k[0]-F[164,x,1,k[1]])/(-1+k[0])
F[165,x,k[0],k[1]] = F[164,x,k[0],k[1]]*F[69,x,k[1]]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]
F[166,x,k[0],k[1]] = F[167,x,k[0],k[1]]*F[69,x,k[1]]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]+F[169,x,k[0],k[1]]
F[168,x,k[0],k[1]] = F[129,x,k[0],k[1]]+F[38,x,k[1]]
F[169,x,k[0],k[1]] = F[170,x,k[0],k[1]]+F[175,x,k[0],k[1]]
F[170,x,k[0],k[1]] = F[171,x,k[0]]*F[174,x,k[1]]
F[171,x,k[0]] = F[136,x,k[0]]+F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[136,x,k[0]]^2*F[11,x]*F[15,x]
F[174,x,k[0]] = F[72,x,k[0]]
F[175,x,k[0],k[1]] = F[176,x,k[0],k[1]]
F[176,x,k[0],k[1]] = F[15,x]*F[171,x,k[0]]*F[177,x,k[1]]
F[177,x,k[0]] = F[178,x,k[0],1]
F[178,x,k[0],k[1]] = F[179,x,k[0]*k[1],k[0]]
F[180,x,k[0],k[1]] = F[15,x]*F[179,x,k[0],k[1]]*F[5,x]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[181,x,k[0],k[1]]+F[182,x,k[0],k[1]]
F[182,x,k[0],k[1]] = F[183,x,k[0],k[1]]*F[5,x]
F[183,x,k[0],k[1]] = F[184,x,k[1],k[0]]
F[184,x,k[0],k[1]] = F[185,x,k[0],k[1]]+F[67,x,k[0]]
F[185,x,k[0],k[1]] = F[186,x,k[0],k[1]]+F[193,x,k[1],k[0]]+F[22,x]
F[186,x,k[0],k[1]] = F[187,x,k[0],k[1]]*F[69,x,k[0]]
F[187,x,k[0],k[1]] = F[188,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[67,x,k[1]]
F[189,x,k[0],k[1]] = F[190,x,k[1],k[0]]
F[190,x,k[0],k[1]] = F[191,x,k[1],k[0]]*F[69,x,k[0]]
F[191,x,k[0],k[1]] = F[192,x,k[0],k[1]]
F[192,x,k[0],k[1]] = F[67,x,k[0]]
F[193,x,k[0],k[1]] = F[194,x,k[1],k[0]]*F[69,x,k[0]]
F[194,x,k[0],k[1]] = F[192,x,k[0],k[1]]+F[195,x,k[0],k[1]]
F[195,x,k[0],k[1]] = F[196,x,k[0],k[1]]
F[196,x,k[0],k[1]] = F[197,x,k[0],k[1]]*F[69,x,k[0]]
F[197,x,k[0],k[1]] = F[67,x,k[1]]
F[198,x,k[0],k[1],k[2]] = F[199,x,k[0],k[1],k[2]]
F[199,x,k[0],k[1],k[2]] = F[200,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[200,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[132,x,k[0],k[1],k[2]]*k[1]-F[132,x,k[0],1,k[2]])
F[201,x,k[0],k[1]] = F[202,x,k[1]]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[204,x,1,k[0]]
F[204,x,k[0],k[1]] = F[169,x,k[0],k[1]]
F[205,x,k[0],k[1]] = k[0]*F[206,x,k[0],k[1]]
F[206,x,k[0],k[1]] = F[207,x,k[0],k[1]]
F[207,x,k[0],k[1]] = F[15,x]*F[208,x,k[0],k[1]]*F[5,x]
F[208,x,k[0],k[1]] = F[209,x,k[1]]+F[210,x,k[0],k[1]]
F[209,x,k[0]] = F[202,x,k[0]]+F[37,x,k[0]]
F[210,x,k[0],k[1]] = F[58,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]
F[212,x,k[0]] = F[15,x]*F[213,x,k[0]]
F[213,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[214,x,k[0]] = F[11,x]*F[71,x,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x F_{5} \left(x \right)^{3}-x F_{5} \left(x \right)^{2}+x F_{5}\! \left(x \right)+1
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{35}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x , 1\right)
F_{37}\! \left(x , y_{0}\right) = F_{214}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = F_{211}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{205}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{201}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{50}\! \left(x , 1, y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{198}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{51}\! \left(x , y_{1}, y_{2}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{54}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{125}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = -\frac{-F_{58}\! \left(x , y_{0}\right)+F_{58}\! \left(x , 1\right)}{-1+y_{0}}
F_{60}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)+F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)+F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{70}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = y_{0} x
F_{70}\! \left(x , y_{0}\right) = F_{71}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{67}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{73}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{22}\! \left(x \right)+F_{74}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{80}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{85}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{22}\! \left(x \right)+F_{88}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)
F_{95}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{103}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{102}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = 0
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)+F_{107}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{33}\! \left(x \right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{109}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{113}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)+F_{87}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}\right) = F_{114}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}\right) = F_{115}\! \left(x , y_{0}\right)+F_{121}\! \left(x , y_{0}\right)+F_{122}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{116}\! \left(x , y_{0}\right) = F_{117}\! \left(x , y_{0}\right)
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{119}\! \left(x , y_{0}\right)
F_{119}\! \left(x , y_{0}\right) = F_{120}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}\right) = 0
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{123}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{124}\! \left(x , y_{0}\right) = -\frac{-F_{36}\! \left(x , y_{0}\right) y_{0}+F_{36}\! \left(x , 1\right)}{-1+y_{0}}
F_{126}\! \left(x , y_{0}\right) = F_{125}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)+F_{154}\! \left(x \right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , 1, y_{0}\right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right)
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{0}, 1, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}, y_{2}\right)
F_{136}\! \left(x , y_{0}\right) = x F_{136}\! \left(x , y_{0}\right)^{3} y_{0}-x F_{136}\! \left(x , y_{0}\right)^{2} y_{0}+x F_{136}\! \left(x , y_{0}\right) y_{0}+1
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{133}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{143}\! \left(x , y_{0}\right)
F_{143}\! \left(x , y_{0}\right) = x F_{143}\! \left(x , y_{0}\right)^{3} y_{0}+2 x F_{143}\! \left(x , y_{0}\right)^{2} y_{0}+2 x F_{143}\! \left(x , y_{0}\right) y_{0}+y_{0} x
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{145}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{148}\! \left(x , y_{1}, y_{2}\right)
F_{148}\! \left(x , y_{0}, y_{1}\right) = F_{149}\! \left(x , y_{0}, y_{1}\right)
F_{149}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{150}\! \left(x , y_{0}, y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}\right) = F_{151}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{1}\right)
F_{151}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}\right)
F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right)^{2} F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{157}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{12}\! \left(x \right)
F_{157}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{159}\! \left(x \right)+F_{9}\! \left(x \right)
F_{159}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{160}\! \left(x , y_{0}, y_{1}\right) = F_{161}\! \left(x , y_{1}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{163}\! \left(x , 1, y_{0}\right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{164}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{164}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = F_{167}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{0}, y_{1}\right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{129}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{0}, y_{1}\right)+F_{175}\! \left(x , y_{0}, y_{1}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{171}\! \left(x , y_{0}\right) F_{174}\! \left(x , y_{1}\right)
F_{171}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)+F_{172}\! \left(x , y_{0}\right)
F_{172}\! \left(x , y_{0}\right) = F_{173}\! \left(x , y_{0}\right)
F_{173}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)^{2} F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{174}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}\right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{171}\! \left(x , y_{0}\right) F_{177}\! \left(x , y_{1}\right)
F_{177}\! \left(x , y_{0}\right) = F_{178}\! \left(x , y_{0}, 1\right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{179}\! \left(x , y_{0} y_{1}, y_{0}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{179}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}, y_{1}\right) = F_{183}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{183}\! \left(x , y_{0}, y_{1}\right) = F_{184}\! \left(x , y_{1}, y_{0}\right)
F_{184}\! \left(x , y_{0}, y_{1}\right) = F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{0}\right)
F_{185}\! \left(x , y_{0}, y_{1}\right) = F_{186}\! \left(x , y_{0}, y_{1}\right)+F_{193}\! \left(x , y_{1}, y_{0}\right)+F_{22}\! \left(x \right)
F_{186}\! \left(x , y_{0}, y_{1}\right) = F_{187}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{187}\! \left(x , y_{0}, y_{1}\right) = F_{188}\! \left(x , y_{0}, y_{1}\right)
F_{188}\! \left(x , y_{0}, y_{1}\right) = F_{189}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}\right)
F_{189}\! \left(x , y_{0}, y_{1}\right) = F_{190}\! \left(x , y_{1}, y_{0}\right)
F_{190}\! \left(x , y_{0}, y_{1}\right) = F_{191}\! \left(x , y_{1}, y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{191}\! \left(x , y_{0}, y_{1}\right) = F_{192}\! \left(x , y_{0}, y_{1}\right)
F_{192}\! \left(x , y_{0}, y_{1}\right) = F_{67}\! \left(x , y_{0}\right)
F_{193}\! \left(x , y_{0}, y_{1}\right) = F_{194}\! \left(x , y_{1}, y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{194}\! \left(x , y_{0}, y_{1}\right) = F_{192}\! \left(x , y_{0}, y_{1}\right)+F_{195}\! \left(x , y_{0}, y_{1}\right)
F_{195}\! \left(x , y_{0}, y_{1}\right) = F_{196}\! \left(x , y_{0}, y_{1}\right)
F_{196}\! \left(x , y_{0}, y_{1}\right) = F_{197}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{197}\! \left(x , y_{0}, y_{1}\right) = F_{67}\! \left(x , y_{1}\right)
F_{198}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{199}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{199}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{200}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{200}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{132}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{201}\! \left(x , y_{0}, y_{1}\right) = F_{202}\! \left(x , y_{1}\right)
F_{202}\! \left(x , y_{0}\right) = F_{203}\! \left(x , y_{0}\right)
F_{203}\! \left(x , y_{0}\right) = F_{204}\! \left(x , 1, y_{0}\right)
F_{204}\! \left(x , y_{0}, y_{1}\right) = F_{169}\! \left(x , y_{0}, y_{1}\right)
F_{205}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{206}\! \left(x , y_{0}, y_{1}\right)
F_{206}\! \left(x , y_{0}, y_{1}\right) = F_{207}\! \left(x , y_{0}, y_{1}\right)
F_{207}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{208}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{208}\! \left(x , y_{0}, y_{1}\right) = F_{209}\! \left(x , y_{1}\right)+F_{210}\! \left(x , y_{0}, y_{1}\right)
F_{209}\! \left(x , y_{0}\right) = F_{202}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{210}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}\right)
F_{211}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)
F_{212}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{213}\! \left(x , y_{0}\right)
F_{213}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{37}\! \left(x , y_{0}\right)+F_{37}\! \left(x , 1\right)}{-1+y_{0}}
F_{214}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{71}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x*F_5(x)**3 - x*F_5(x)**2 + x*F_5(x) + 1)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_35(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x) + F_5(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x)*F_5(x)**2)
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_1(x) + F_16(x))
Eq(F_20(x), F_16(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_30(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_16(x))
Eq(F_30(x), F_15(x)*F_31(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_15(x)*F_34(x))
Eq(F_34(x), F_16(x))
Eq(F_35(x), F_36(x, 1))
Eq(F_37(x, k_0), F_214(x, k_0) + F_36(x, k_0))
Eq(F_37(x, k_0), F_128(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_211(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_0(x) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0)*F_69(x, k_0))
Eq(F_42(x, k_0), F_43(x, 1, k_0))
Eq(F_43(x, k_0, k_1), F_44(x, k_0*k_1, k_1))
Eq(F_44(x, k_0, k_1), F_38(x, k_0) + F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_47(x, k_0, k_1)*F_69(x, k_1))
Eq(F_47(x, k_0, k_1), F_205(x, k_0, k_1) + F_48(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), F_201(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), F_50(x, 1, k_0, k_1))
Eq(F_50(x, k_0, k_1, k_2), F_198(x, k_0, k_1, k_2) + F_51(x, k_1, k_2))
Eq(F_51(x, k_0, k_1), F_38(x, k_1) + F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_54(x, k_0, k_1)*F_69(x, k_0))
Eq(F_54(x, k_0, k_1), F_160(x, k_0, k_1) + F_55(x, k_0))
Eq(F_56(x, k_0), F_125(x, k_0) + F_55(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0)*F_69(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), -F_58(x, k_0) + (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_36(x, k_0) + F_59(x, k_0))
Eq(F_60(x, k_0), F_124(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_110(x, k_0) + F_22(x) + F_64(x, k_0))
Eq(F_64(x, k_0), F_15(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_86(x, k_0))
Eq(F_66(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0)*F_70(x, k_0))
Eq(F_69(x, k_0), k_0*x)
Eq(F_70(x, k_0), F_71(x, k_0) + F_72(x, k_0))
Eq(F_71(x, k_0), F_1(x) + F_67(x, k_0))
Eq(F_72(x, k_0), F_67(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_22(x) + F_74(x, k_0) + F_81(x, k_0))
Eq(F_74(x, k_0), F_69(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_67(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_69(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_67(x, k_0))
Eq(F_81(x, k_0), F_69(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_69(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_67(x, k_0))
Eq(F_86(x, k_0), F_100(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_22(x) + F_88(x, k_0) + F_95(x, k_0))
Eq(F_88(x, k_0), F_15(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_67(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_69(x, k_0)*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_16(x))
Eq(F_95(x, k_0), F_69(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_15(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_67(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + F_104(x, k_0) + F_22(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_15(x))
Eq(F_102(x, k_0), F_63(x, k_0))
Eq(F_103(x, k_0), 0)
Eq(F_104(x, k_0), F_105(x, k_0)*F_69(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_107(x, k_0))
Eq(F_106(x, k_0), F_33(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_15(x))
Eq(F_109(x, k_0), F_63(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_69(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_16(x) + F_87(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_63(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_121(x, k_0) + F_122(x, k_0) + F_22(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_15(x))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_77(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0)*F_69(x, k_0))
Eq(F_120(x, k_0), F_63(x, k_0))
Eq(F_121(x, k_0), 0)
Eq(F_122(x, k_0), F_123(x, k_0)*F_69(x, k_0))
Eq(F_123(x, k_0), F_63(x, k_0))
Eq(F_124(x, k_0), (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_126(x, k_0), F_125(x, k_0)*F_69(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_128(x, k_0), F_127(x, k_0) + F_154(x))
Eq(F_128(x, k_0), F_129(x, 1, k_0))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1)*F_69(x, k_0))
Eq(F_131(x, k_0, k_1), F_132(x, k_0, 1, k_1))
Eq(F_132(x, k_0, k_1, k_2), F_133(x, k_0, k_1, k_2) + F_145(x, k_0, k_1, k_2))
Eq(F_133(x, k_0, k_1, k_2), F_134(x, k_0, k_1, k_2) + F_137(x, k_0, k_1, k_2))
Eq(F_134(x, k_0, k_1, k_2), F_135(x, k_0, k_1, k_2))
Eq(F_135(x, k_0, k_1, k_2), F_136(x, k_0)*F_51(x, k_1, k_2))
Eq(F_136(x, k_0), k_0*x*F_136(x, k_0)**3 - k_0*x*F_136(x, k_0)**2 + k_0*x*F_136(x, k_0) + 1)
Eq(F_137(x, k_0, k_1, k_2), F_138(x, k_0, k_1, k_2))
Eq(F_138(x, k_0, k_1, k_2), F_136(x, k_0)*F_139(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_139(x, k_0, k_1, k_2), F_140(x, k_0, k_1, k_2) + F_144(x, k_0, k_1, k_2))
Eq(F_140(x, k_0, k_1, k_2), F_141(x, k_0, k_1, k_2) + F_142(x, k_0, k_1, k_2))
Eq(F_141(x, k_0, k_1, k_2), (k_1*F_133(x, k_0, k_1, k_2) - F_133(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_142(x, k_0, k_1, k_2), F_133(x, k_0, k_1, k_2)*F_143(x, k_0))
Eq(F_143(x, k_0), k_0*x*(F_143(x, k_0) + 1)**3 - k_0*x*(F_143(x, k_0) + 1)**2 + (k_0*x - 1)*(F_143(x, k_0) + 1) + F_143(x, k_0) + 1)
Eq(F_144(x, k_0, k_1, k_2), (k_1*F_145(x, k_0, k_1, k_2) - F_145(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_145(x, k_0, k_1, k_2), F_146(x, k_0, k_1, k_2) + F_152(x, k_0, k_1, k_2))
Eq(F_146(x, k_0, k_1, k_2), F_147(x, k_0, k_1, k_2))
Eq(F_147(x, k_0, k_1, k_2), F_136(x, k_0)*F_148(x, k_1, k_2))
Eq(F_148(x, k_0, k_1), F_149(x, k_0, k_1))
Eq(F_149(x, k_0, k_1), F_15(x)*F_150(x, k_0, k_1))
Eq(F_150(x, k_0, k_1), F_151(x, k_0, k_1) + F_37(x, k_1))
Eq(F_151(x, k_0, k_1), F_58(x, k_0))
Eq(F_152(x, k_0, k_1, k_2), F_153(x, k_0, k_1, k_2))
Eq(F_153(x, k_0, k_1, k_2), F_136(x, k_0)**2*F_145(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_154(x), F_155(x) + F_157(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_12(x) - F_5(x))
Eq(F_157(x), F_158(x) - F_6(x))
Eq(F_158(x), -F_159(x) + F_9(x))
Eq(F_159(x), F_58(x, 1))
Eq(F_160(x, k_0, k_1), F_161(x, k_1))
Eq(F_161(x, k_0), F_162(x, k_0)*F_69(x, k_0))
Eq(F_162(x, k_0), F_163(x, 1, k_0))
Eq(F_163(x, k_0, k_1), (-k_0*F_164(x, k_0, k_1) + F_164(x, 1, k_1))/(1 - k_0))
Eq(F_165(x, k_0, k_1), F_164(x, k_0, k_1)*F_69(x, k_1))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1))
Eq(F_166(x, k_0, k_1), F_167(x, k_0, k_1)*F_69(x, k_1))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1) + F_169(x, k_0, k_1))
Eq(F_168(x, k_0, k_1), F_129(x, k_0, k_1) + F_38(x, k_1))
Eq(F_169(x, k_0, k_1), F_170(x, k_0, k_1) + F_175(x, k_0, k_1))
Eq(F_170(x, k_0, k_1), F_171(x, k_0)*F_174(x, k_1))
Eq(F_171(x, k_0), F_136(x, k_0) + F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_11(x)*F_136(x, k_0)**2*F_15(x))
Eq(F_174(x, k_0), F_72(x, k_0))
Eq(F_175(x, k_0, k_1), F_176(x, k_0, k_1))
Eq(F_176(x, k_0, k_1), F_15(x)*F_171(x, k_0)*F_177(x, k_1))
Eq(F_177(x, k_0), F_178(x, k_0, 1))
Eq(F_178(x, k_0, k_1), F_179(x, k_0*k_1, k_0))
Eq(F_180(x, k_0, k_1), F_15(x)*F_179(x, k_0, k_1)*F_5(x))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_181(x, k_0, k_1) + F_182(x, k_0, k_1))
Eq(F_182(x, k_0, k_1), F_183(x, k_0, k_1)*F_5(x))
Eq(F_183(x, k_0, k_1), F_184(x, k_1, k_0))
Eq(F_184(x, k_0, k_1), F_185(x, k_0, k_1) + F_67(x, k_0))
Eq(F_185(x, k_0, k_1), F_186(x, k_0, k_1) + F_193(x, k_1, k_0) + F_22(x))
Eq(F_186(x, k_0, k_1), F_187(x, k_0, k_1)*F_69(x, k_0))
Eq(F_187(x, k_0, k_1), F_188(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1) + F_67(x, k_1))
Eq(F_189(x, k_0, k_1), F_190(x, k_1, k_0))
Eq(F_190(x, k_0, k_1), F_191(x, k_1, k_0)*F_69(x, k_0))
Eq(F_191(x, k_0, k_1), F_192(x, k_0, k_1))
Eq(F_192(x, k_0, k_1), F_67(x, k_0))
Eq(F_193(x, k_0, k_1), F_194(x, k_1, k_0)*F_69(x, k_0))
Eq(F_194(x, k_0, k_1), F_192(x, k_0, k_1) + F_195(x, k_0, k_1))
Eq(F_195(x, k_0, k_1), F_196(x, k_0, k_1))
Eq(F_196(x, k_0, k_1), F_197(x, k_0, k_1)*F_69(x, k_0))
Eq(F_197(x, k_0, k_1), F_67(x, k_1))
Eq(F_198(x, k_0, k_1, k_2), F_199(x, k_0, k_1, k_2))
Eq(F_199(x, k_0, k_1, k_2), F_200(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_200(x, k_0, k_1, k_2), (k_1*F_132(x, k_0, k_1, k_2) - F_132(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_201(x, k_0, k_1), F_202(x, k_1))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_204(x, 1, k_0))
Eq(F_204(x, k_0, k_1), F_169(x, k_0, k_1))
Eq(F_205(x, k_0, k_1), k_0*F_206(x, k_0, k_1))
Eq(F_206(x, k_0, k_1), F_207(x, k_0, k_1))
Eq(F_207(x, k_0, k_1), F_15(x)*F_208(x, k_0, k_1)*F_5(x))
Eq(F_208(x, k_0, k_1), F_209(x, k_1) + F_210(x, k_0, k_1))
Eq(F_209(x, k_0), F_202(x, k_0) + F_37(x, k_0))
Eq(F_210(x, k_0, k_1), F_58(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0))
Eq(F_212(x, k_0), F_15(x)*F_213(x, k_0))
Eq(F_213(x, k_0), (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_214(x, k_0), F_11(x)*F_71(x, k_0))
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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 1], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [2, 1], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": 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"pos": [[0, 0], [1, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], 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3, 0], "pos": [[1, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 1], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 1], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, 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3, 2, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 1], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 2], [1, 1], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25950/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 1+(F[5,x]^3-F[5,x]^2+F[5,x])*x
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[35,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = F[14,x]
F[14,x] = F[5,x]^2*F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[1,x]+F[16,x]
F[20,x] = F[16,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[30,x]
F[22,x] = 0
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[16,x]
F[30,x] = F[15,x]*F[31,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[15,x]*F[34,x]
F[34,x] = F[16,x]
F[35,x] = F[36,x,1]
F[37,x,k[0]] = F[214,x,k[0]]+F[36,x,k[0]]
F[37,x,k[0]] = F[128,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[211,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[0,x]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]*F[69,x,k[0]]
F[42,x,k[0]] = F[43,x,1,k[0]]
F[43,x,k[0],k[1]] = F[44,x,k[0]*k[1],k[1]]
F[44,x,k[0],k[1]] = F[38,x,k[0]]+F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[47,x,k[0],k[1]]*F[69,x,k[1]]
F[47,x,k[0],k[1]] = F[205,x,k[0],k[1]]+F[48,x,k[0],k[1]]
F[48,x,k[0],k[1]] = F[201,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = F[50,x,1,k[0],k[1]]
F[50,x,k[0],k[1],k[2]] = F[198,x,k[0],k[1],k[2]]+F[51,x,k[1],k[2]]
F[51,x,k[0],k[1]] = F[38,x,k[1]]+F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[54,x,k[0],k[1]]*F[69,x,k[0]]
F[54,x,k[0],k[1]] = F[160,x,k[0],k[1]]+F[55,x,k[0]]
F[56,x,k[0]] = F[125,x,k[0]]+F[55,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]*F[69,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = (F[58,x,k[0]]-F[58,x,1])/(-1+k[0])
F[60,x,k[0]] = F[36,x,k[0]]+F[59,x,k[0]]
F[60,x,k[0]] = F[124,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[16,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[110,x,k[0]]+F[22,x]+F[64,x,k[0]]
F[64,x,k[0]] = F[15,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[86,x,k[0]]
F[66,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]*F[70,x,k[0]]
F[69,x,k[0]] = k[0]*x
F[70,x,k[0]] = F[71,x,k[0]]+F[72,x,k[0]]
F[71,x,k[0]] = F[1,x]+F[67,x,k[0]]
F[72,x,k[0]] = F[67,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[22,x]+F[74,x,k[0]]+F[81,x,k[0]]
F[74,x,k[0]] = F[69,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[67,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[69,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[67,x,k[0]]
F[81,x,k[0]] = F[69,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[69,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[67,x,k[0]]
F[86,x,k[0]] = F[100,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[22,x]+F[88,x,k[0]]+F[95,x,k[0]]
F[88,x,k[0]] = F[15,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[67,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[69,x,k[0]]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[16,x]
F[95,x,k[0]] = F[69,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[15,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[67,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]+F[104,x,k[0]]+F[22,x]
F[101,x,k[0]] = F[102,x,k[0]]*F[15,x]
F[102,x,k[0]] = F[63,x,k[0]]
F[103,x,k[0]] = 0
F[104,x,k[0]] = F[105,x,k[0]]*F[69,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[107,x,k[0]]
F[106,x,k[0]] = F[33,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[15,x]
F[109,x,k[0]] = F[63,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[69,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[16,x]+F[87,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[63,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[121,x,k[0]]+F[122,x,k[0]]+F[22,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[15,x]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[77,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[69,x,k[0]]
F[120,x,k[0]] = F[63,x,k[0]]
F[121,x,k[0]] = 0
F[122,x,k[0]] = F[123,x,k[0]]*F[69,x,k[0]]
F[123,x,k[0]] = F[63,x,k[0]]
F[124,x,k[0]] = 1/(-1+k[0])*(F[36,x,k[0]]*k[0]-F[36,x,1])
F[126,x,k[0]] = F[125,x,k[0]]*F[69,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[128,x,k[0]] = F[127,x,k[0]]+F[154,x]
F[128,x,k[0]] = F[129,x,1,k[0]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]*F[69,x,k[0]]
F[131,x,k[0],k[1]] = F[132,x,k[0],1,k[1]]
F[132,x,k[0],k[1],k[2]] = F[133,x,k[0],k[1],k[2]]+F[145,x,k[0],k[1],k[2]]
F[133,x,k[0],k[1],k[2]] = F[134,x,k[0],k[1],k[2]]+F[137,x,k[0],k[1],k[2]]
F[134,x,k[0],k[1],k[2]] = F[135,x,k[0],k[1],k[2]]
F[135,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[51,x,k[1],k[2]]
F[136,x,k[0]] = 1+x*F[136,x,k[0]]*(F[136,x,k[0]]^2-F[136,x,k[0]]+1)*k[0]
F[137,x,k[0],k[1],k[2]] = F[138,x,k[0],k[1],k[2]]
F[138,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[139,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[139,x,k[0],k[1],k[2]] = F[140,x,k[0],k[1],k[2]]+F[144,x,k[0],k[1],k[2]]
F[140,x,k[0],k[1],k[2]] = F[141,x,k[0],k[1],k[2]]+F[142,x,k[0],k[1],k[2]]
F[141,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[133,x,k[0],k[1],k[2]]*k[1]-F[133,x,k[0],1,k[2]])
F[142,x,k[0],k[1],k[2]] = F[133,x,k[0],k[1],k[2]]*F[143,x,k[0]]
F[143,x,k[0]] = k[0]*x*(1+F[143,x,k[0]])*(F[143,x,k[0]]^2+F[143,x,k[0]]+1)
F[144,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[145,x,k[0],k[1],k[2]]*k[1]-F[145,x,k[0],1,k[2]])
F[145,x,k[0],k[1],k[2]] = F[146,x,k[0],k[1],k[2]]+F[152,x,k[0],k[1],k[2]]
F[146,x,k[0],k[1],k[2]] = F[147,x,k[0],k[1],k[2]]
F[147,x,k[0],k[1],k[2]] = F[136,x,k[0]]*F[148,x,k[1],k[2]]
F[148,x,k[0],k[1]] = F[149,x,k[0],k[1]]
F[149,x,k[0],k[1]] = F[15,x]*F[150,x,k[0],k[1]]
F[150,x,k[0],k[1]] = F[151,x,k[0],k[1]]+F[37,x,k[1]]
F[151,x,k[0],k[1]] = F[58,x,k[0]]
F[152,x,k[0],k[1],k[2]] = F[153,x,k[0],k[1],k[2]]
F[153,x,k[0],k[1],k[2]] = F[136,x,k[0]]^2*F[145,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[154,x] = F[155,x]+F[157,x]
F[155,x] = F[156,x]
F[156,x] = -F[5,x]+F[12,x]
F[157,x] = -F[6,x]+F[158,x]
F[158,x] = -F[159,x]+F[9,x]
F[159,x] = F[58,x,1]
F[160,x,k[0],k[1]] = F[161,x,k[1]]
F[161,x,k[0]] = F[162,x,k[0]]*F[69,x,k[0]]
F[162,x,k[0]] = F[163,x,1,k[0]]
F[163,x,k[0],k[1]] = (F[164,x,k[0],k[1]]*k[0]-F[164,x,1,k[1]])/(-1+k[0])
F[165,x,k[0],k[1]] = F[164,x,k[0],k[1]]*F[69,x,k[1]]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]
F[166,x,k[0],k[1]] = F[167,x,k[0],k[1]]*F[69,x,k[1]]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]+F[169,x,k[0],k[1]]
F[168,x,k[0],k[1]] = F[129,x,k[0],k[1]]+F[38,x,k[1]]
F[169,x,k[0],k[1]] = F[170,x,k[0],k[1]]+F[175,x,k[0],k[1]]
F[170,x,k[0],k[1]] = F[171,x,k[0]]*F[174,x,k[1]]
F[171,x,k[0]] = F[136,x,k[0]]+F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[136,x,k[0]]^2*F[11,x]*F[15,x]
F[174,x,k[0]] = F[72,x,k[0]]
F[175,x,k[0],k[1]] = F[176,x,k[0],k[1]]
F[176,x,k[0],k[1]] = F[15,x]*F[171,x,k[0]]*F[177,x,k[1]]
F[177,x,k[0]] = F[178,x,k[0],1]
F[178,x,k[0],k[1]] = F[179,x,k[0]*k[1],k[0]]
F[180,x,k[0],k[1]] = F[15,x]*F[179,x,k[0],k[1]]*F[5,x]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[181,x,k[0],k[1]]+F[182,x,k[0],k[1]]
F[182,x,k[0],k[1]] = F[183,x,k[0],k[1]]*F[5,x]
F[183,x,k[0],k[1]] = F[184,x,k[1],k[0]]
F[184,x,k[0],k[1]] = F[185,x,k[0],k[1]]+F[67,x,k[0]]
F[185,x,k[0],k[1]] = F[186,x,k[0],k[1]]+F[193,x,k[1],k[0]]+F[22,x]
F[186,x,k[0],k[1]] = F[187,x,k[0],k[1]]*F[69,x,k[0]]
F[187,x,k[0],k[1]] = F[188,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[67,x,k[1]]
F[189,x,k[0],k[1]] = F[190,x,k[1],k[0]]
F[190,x,k[0],k[1]] = F[191,x,k[1],k[0]]*F[69,x,k[0]]
F[191,x,k[0],k[1]] = F[192,x,k[0],k[1]]
F[192,x,k[0],k[1]] = F[67,x,k[0]]
F[193,x,k[0],k[1]] = F[194,x,k[1],k[0]]*F[69,x,k[0]]
F[194,x,k[0],k[1]] = F[192,x,k[0],k[1]]+F[195,x,k[0],k[1]]
F[195,x,k[0],k[1]] = F[196,x,k[0],k[1]]
F[196,x,k[0],k[1]] = F[197,x,k[0],k[1]]*F[69,x,k[0]]
F[197,x,k[0],k[1]] = F[67,x,k[1]]
F[198,x,k[0],k[1],k[2]] = F[199,x,k[0],k[1],k[2]]
F[199,x,k[0],k[1],k[2]] = F[200,x,k[0],k[1],k[2]]*F[69,x,k[0]]
F[200,x,k[0],k[1],k[2]] = 1/(-1+k[1])*(F[132,x,k[0],k[1],k[2]]*k[1]-F[132,x,k[0],1,k[2]])
F[201,x,k[0],k[1]] = F[202,x,k[1]]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[204,x,1,k[0]]
F[204,x,k[0],k[1]] = F[169,x,k[0],k[1]]
F[205,x,k[0],k[1]] = k[0]*F[206,x,k[0],k[1]]
F[206,x,k[0],k[1]] = F[207,x,k[0],k[1]]
F[207,x,k[0],k[1]] = F[15,x]*F[208,x,k[0],k[1]]*F[5,x]
F[208,x,k[0],k[1]] = F[209,x,k[1]]+F[210,x,k[0],k[1]]
F[209,x,k[0]] = F[202,x,k[0]]+F[37,x,k[0]]
F[210,x,k[0],k[1]] = F[58,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]
F[212,x,k[0]] = F[15,x]*F[213,x,k[0]]
F[213,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[214,x,k[0]] = F[11,x]*F[71,x,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x F_{5} \left(x \right)^{3}-x F_{5} \left(x \right)^{2}+x F_{5}\! \left(x \right)+1
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{35}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x , 1\right)
F_{37}\! \left(x , y_{0}\right) = F_{214}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = F_{211}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{205}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{201}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{50}\! \left(x , 1, y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{198}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{51}\! \left(x , y_{1}, y_{2}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{54}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{125}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = -\frac{-F_{58}\! \left(x , y_{0}\right)+F_{58}\! \left(x , 1\right)}{-1+y_{0}}
F_{60}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)+F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)+F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{70}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = y_{0} x
F_{70}\! \left(x , y_{0}\right) = F_{71}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{67}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{73}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{22}\! \left(x \right)+F_{74}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{80}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{85}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{22}\! \left(x \right)+F_{88}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)
F_{95}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right) F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{103}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{102}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = 0
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)+F_{107}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{33}\! \left(x \right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{109}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{113}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{16}\! \left(x \right)+F_{87}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}\right) = F_{114}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}\right) = F_{115}\! \left(x , y_{0}\right)+F_{121}\! \left(x , y_{0}\right)+F_{122}\! \left(x , y_{0}\right)+F_{22}\! \left(x \right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right) F_{15}\! \left(x \right)
F_{116}\! \left(x , y_{0}\right) = F_{117}\! \left(x , y_{0}\right)
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{119}\! \left(x , y_{0}\right)
F_{119}\! \left(x , y_{0}\right) = F_{120}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}\right) = 0
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{123}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{124}\! \left(x , y_{0}\right) = -\frac{-F_{36}\! \left(x , y_{0}\right) y_{0}+F_{36}\! \left(x , 1\right)}{-1+y_{0}}
F_{126}\! \left(x , y_{0}\right) = F_{125}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)+F_{154}\! \left(x \right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , 1, y_{0}\right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right)
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{0}, 1, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}, y_{2}\right)
F_{136}\! \left(x , y_{0}\right) = x F_{136}\! \left(x , y_{0}\right)^{3} y_{0}-x F_{136}\! \left(x , y_{0}\right)^{2} y_{0}+x F_{136}\! \left(x , y_{0}\right) y_{0}+1
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{133}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{143}\! \left(x , y_{0}\right)
F_{143}\! \left(x , y_{0}\right) = x F_{143}\! \left(x , y_{0}\right)^{3} y_{0}+2 x F_{143}\! \left(x , y_{0}\right)^{2} y_{0}+2 x F_{143}\! \left(x , y_{0}\right) y_{0}+y_{0} x
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{145}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right) F_{148}\! \left(x , y_{1}, y_{2}\right)
F_{148}\! \left(x , y_{0}, y_{1}\right) = F_{149}\! \left(x , y_{0}, y_{1}\right)
F_{149}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{150}\! \left(x , y_{0}, y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}\right) = F_{151}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{1}\right)
F_{151}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}\right)
F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}\right)^{2} F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{157}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{12}\! \left(x \right)
F_{157}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{159}\! \left(x \right)+F_{9}\! \left(x \right)
F_{159}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{160}\! \left(x , y_{0}, y_{1}\right) = F_{161}\! \left(x , y_{1}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{163}\! \left(x , 1, y_{0}\right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{164}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{164}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = F_{167}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{1}\right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{0}, y_{1}\right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{129}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{0}, y_{1}\right)+F_{175}\! \left(x , y_{0}, y_{1}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{171}\! \left(x , y_{0}\right) F_{174}\! \left(x , y_{1}\right)
F_{171}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)+F_{172}\! \left(x , y_{0}\right)
F_{172}\! \left(x , y_{0}\right) = F_{173}\! \left(x , y_{0}\right)
F_{173}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)^{2} F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{174}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}\right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{171}\! \left(x , y_{0}\right) F_{177}\! \left(x , y_{1}\right)
F_{177}\! \left(x , y_{0}\right) = F_{178}\! \left(x , y_{0}, 1\right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{179}\! \left(x , y_{0} y_{1}, y_{0}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{179}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}, y_{1}\right) = F_{183}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{183}\! \left(x , y_{0}, y_{1}\right) = F_{184}\! \left(x , y_{1}, y_{0}\right)
F_{184}\! \left(x , y_{0}, y_{1}\right) = F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{0}\right)
F_{185}\! \left(x , y_{0}, y_{1}\right) = F_{186}\! \left(x , y_{0}, y_{1}\right)+F_{193}\! \left(x , y_{1}, y_{0}\right)+F_{22}\! \left(x \right)
F_{186}\! \left(x , y_{0}, y_{1}\right) = F_{187}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{187}\! \left(x , y_{0}, y_{1}\right) = F_{188}\! \left(x , y_{0}, y_{1}\right)
F_{188}\! \left(x , y_{0}, y_{1}\right) = F_{189}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}\right)
F_{189}\! \left(x , y_{0}, y_{1}\right) = F_{190}\! \left(x , y_{1}, y_{0}\right)
F_{190}\! \left(x , y_{0}, y_{1}\right) = F_{191}\! \left(x , y_{1}, y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{191}\! \left(x , y_{0}, y_{1}\right) = F_{192}\! \left(x , y_{0}, y_{1}\right)
F_{192}\! \left(x , y_{0}, y_{1}\right) = F_{67}\! \left(x , y_{0}\right)
F_{193}\! \left(x , y_{0}, y_{1}\right) = F_{194}\! \left(x , y_{1}, y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{194}\! \left(x , y_{0}, y_{1}\right) = F_{192}\! \left(x , y_{0}, y_{1}\right)+F_{195}\! \left(x , y_{0}, y_{1}\right)
F_{195}\! \left(x , y_{0}, y_{1}\right) = F_{196}\! \left(x , y_{0}, y_{1}\right)
F_{196}\! \left(x , y_{0}, y_{1}\right) = F_{197}\! \left(x , y_{0}, y_{1}\right) F_{69}\! \left(x , y_{0}\right)
F_{197}\! \left(x , y_{0}, y_{1}\right) = F_{67}\! \left(x , y_{1}\right)
F_{198}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{199}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{199}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{200}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{69}\! \left(x , y_{0}\right)
F_{200}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{132}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{201}\! \left(x , y_{0}, y_{1}\right) = F_{202}\! \left(x , y_{1}\right)
F_{202}\! \left(x , y_{0}\right) = F_{203}\! \left(x , y_{0}\right)
F_{203}\! \left(x , y_{0}\right) = F_{204}\! \left(x , 1, y_{0}\right)
F_{204}\! \left(x , y_{0}, y_{1}\right) = F_{169}\! \left(x , y_{0}, y_{1}\right)
F_{205}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{206}\! \left(x , y_{0}, y_{1}\right)
F_{206}\! \left(x , y_{0}, y_{1}\right) = F_{207}\! \left(x , y_{0}, y_{1}\right)
F_{207}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x \right) F_{208}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{208}\! \left(x , y_{0}, y_{1}\right) = F_{209}\! \left(x , y_{1}\right)+F_{210}\! \left(x , y_{0}, y_{1}\right)
F_{209}\! \left(x , y_{0}\right) = F_{202}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{210}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}\right)
F_{211}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)
F_{212}\! \left(x , y_{0}\right) = F_{15}\! \left(x \right) F_{213}\! \left(x , y_{0}\right)
F_{213}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{37}\! \left(x , y_{0}\right)+F_{37}\! \left(x , 1\right)}{-1+y_{0}}
F_{214}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{71}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x*F_5(x)**3 - x*F_5(x)**2 + x*F_5(x) + 1)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_35(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x) + F_5(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x)*F_5(x)**2)
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_1(x) + F_16(x))
Eq(F_20(x), F_16(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_30(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_16(x))
Eq(F_30(x), F_15(x)*F_31(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_15(x)*F_34(x))
Eq(F_34(x), F_16(x))
Eq(F_35(x), F_36(x, 1))
Eq(F_37(x, k_0), F_214(x, k_0) + F_36(x, k_0))
Eq(F_37(x, k_0), F_128(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_211(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_0(x) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0)*F_69(x, k_0))
Eq(F_42(x, k_0), F_43(x, 1, k_0))
Eq(F_43(x, k_0, k_1), F_44(x, k_0*k_1, k_1))
Eq(F_44(x, k_0, k_1), F_38(x, k_0) + F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_47(x, k_0, k_1)*F_69(x, k_1))
Eq(F_47(x, k_0, k_1), F_205(x, k_0, k_1) + F_48(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), F_201(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), F_50(x, 1, k_0, k_1))
Eq(F_50(x, k_0, k_1, k_2), F_198(x, k_0, k_1, k_2) + F_51(x, k_1, k_2))
Eq(F_51(x, k_0, k_1), F_38(x, k_1) + F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_54(x, k_0, k_1)*F_69(x, k_0))
Eq(F_54(x, k_0, k_1), F_160(x, k_0, k_1) + F_55(x, k_0))
Eq(F_56(x, k_0), F_125(x, k_0) + F_55(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0)*F_69(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), -F_58(x, k_0) + (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_36(x, k_0) + F_59(x, k_0))
Eq(F_60(x, k_0), F_124(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_110(x, k_0) + F_22(x) + F_64(x, k_0))
Eq(F_64(x, k_0), F_15(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_86(x, k_0))
Eq(F_66(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0)*F_70(x, k_0))
Eq(F_69(x, k_0), k_0*x)
Eq(F_70(x, k_0), F_71(x, k_0) + F_72(x, k_0))
Eq(F_71(x, k_0), F_1(x) + F_67(x, k_0))
Eq(F_72(x, k_0), F_67(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_22(x) + F_74(x, k_0) + F_81(x, k_0))
Eq(F_74(x, k_0), F_69(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_67(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_69(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_67(x, k_0))
Eq(F_81(x, k_0), F_69(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_69(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_67(x, k_0))
Eq(F_86(x, k_0), F_100(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_22(x) + F_88(x, k_0) + F_95(x, k_0))
Eq(F_88(x, k_0), F_15(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_67(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_69(x, k_0)*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_16(x))
Eq(F_95(x, k_0), F_69(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_15(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_67(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + F_104(x, k_0) + F_22(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_15(x))
Eq(F_102(x, k_0), F_63(x, k_0))
Eq(F_103(x, k_0), 0)
Eq(F_104(x, k_0), F_105(x, k_0)*F_69(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_107(x, k_0))
Eq(F_106(x, k_0), F_33(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_15(x))
Eq(F_109(x, k_0), F_63(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_69(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_16(x) + F_87(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_63(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_121(x, k_0) + F_122(x, k_0) + F_22(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_15(x))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_77(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0)*F_69(x, k_0))
Eq(F_120(x, k_0), F_63(x, k_0))
Eq(F_121(x, k_0), 0)
Eq(F_122(x, k_0), F_123(x, k_0)*F_69(x, k_0))
Eq(F_123(x, k_0), F_63(x, k_0))
Eq(F_124(x, k_0), (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_126(x, k_0), F_125(x, k_0)*F_69(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_128(x, k_0), F_127(x, k_0) + F_154(x))
Eq(F_128(x, k_0), F_129(x, 1, k_0))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1)*F_69(x, k_0))
Eq(F_131(x, k_0, k_1), F_132(x, k_0, 1, k_1))
Eq(F_132(x, k_0, k_1, k_2), F_133(x, k_0, k_1, k_2) + F_145(x, k_0, k_1, k_2))
Eq(F_133(x, k_0, k_1, k_2), F_134(x, k_0, k_1, k_2) + F_137(x, k_0, k_1, k_2))
Eq(F_134(x, k_0, k_1, k_2), F_135(x, k_0, k_1, k_2))
Eq(F_135(x, k_0, k_1, k_2), F_136(x, k_0)*F_51(x, k_1, k_2))
Eq(F_136(x, k_0), k_0*x*F_136(x, k_0)**3 - k_0*x*F_136(x, k_0)**2 + k_0*x*F_136(x, k_0) + 1)
Eq(F_137(x, k_0, k_1, k_2), F_138(x, k_0, k_1, k_2))
Eq(F_138(x, k_0, k_1, k_2), F_136(x, k_0)*F_139(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_139(x, k_0, k_1, k_2), F_140(x, k_0, k_1, k_2) + F_144(x, k_0, k_1, k_2))
Eq(F_140(x, k_0, k_1, k_2), F_141(x, k_0, k_1, k_2) + F_142(x, k_0, k_1, k_2))
Eq(F_141(x, k_0, k_1, k_2), (k_1*F_133(x, k_0, k_1, k_2) - F_133(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_142(x, k_0, k_1, k_2), F_133(x, k_0, k_1, k_2)*F_143(x, k_0))
Eq(F_143(x, k_0), k_0*x*(F_143(x, k_0) + 1)**3 - k_0*x*(F_143(x, k_0) + 1)**2 + (k_0*x - 1)*(F_143(x, k_0) + 1) + F_143(x, k_0) + 1)
Eq(F_144(x, k_0, k_1, k_2), (k_1*F_145(x, k_0, k_1, k_2) - F_145(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_145(x, k_0, k_1, k_2), F_146(x, k_0, k_1, k_2) + F_152(x, k_0, k_1, k_2))
Eq(F_146(x, k_0, k_1, k_2), F_147(x, k_0, k_1, k_2))
Eq(F_147(x, k_0, k_1, k_2), F_136(x, k_0)*F_148(x, k_1, k_2))
Eq(F_148(x, k_0, k_1), F_149(x, k_0, k_1))
Eq(F_149(x, k_0, k_1), F_15(x)*F_150(x, k_0, k_1))
Eq(F_150(x, k_0, k_1), F_151(x, k_0, k_1) + F_37(x, k_1))
Eq(F_151(x, k_0, k_1), F_58(x, k_0))
Eq(F_152(x, k_0, k_1, k_2), F_153(x, k_0, k_1, k_2))
Eq(F_153(x, k_0, k_1, k_2), F_136(x, k_0)**2*F_145(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_154(x), F_155(x) + F_157(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_12(x) - F_5(x))
Eq(F_157(x), F_158(x) - F_6(x))
Eq(F_158(x), -F_159(x) + F_9(x))
Eq(F_159(x), F_58(x, 1))
Eq(F_160(x, k_0, k_1), F_161(x, k_1))
Eq(F_161(x, k_0), F_162(x, k_0)*F_69(x, k_0))
Eq(F_162(x, k_0), F_163(x, 1, k_0))
Eq(F_163(x, k_0, k_1), (-k_0*F_164(x, k_0, k_1) + F_164(x, 1, k_1))/(1 - k_0))
Eq(F_165(x, k_0, k_1), F_164(x, k_0, k_1)*F_69(x, k_1))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1))
Eq(F_166(x, k_0, k_1), F_167(x, k_0, k_1)*F_69(x, k_1))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1) + F_169(x, k_0, k_1))
Eq(F_168(x, k_0, k_1), F_129(x, k_0, k_1) + F_38(x, k_1))
Eq(F_169(x, k_0, k_1), F_170(x, k_0, k_1) + F_175(x, k_0, k_1))
Eq(F_170(x, k_0, k_1), F_171(x, k_0)*F_174(x, k_1))
Eq(F_171(x, k_0), F_136(x, k_0) + F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_11(x)*F_136(x, k_0)**2*F_15(x))
Eq(F_174(x, k_0), F_72(x, k_0))
Eq(F_175(x, k_0, k_1), F_176(x, k_0, k_1))
Eq(F_176(x, k_0, k_1), F_15(x)*F_171(x, k_0)*F_177(x, k_1))
Eq(F_177(x, k_0), F_178(x, k_0, 1))
Eq(F_178(x, k_0, k_1), F_179(x, k_0*k_1, k_0))
Eq(F_180(x, k_0, k_1), F_15(x)*F_179(x, k_0, k_1)*F_5(x))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_181(x, k_0, k_1) + F_182(x, k_0, k_1))
Eq(F_182(x, k_0, k_1), F_183(x, k_0, k_1)*F_5(x))
Eq(F_183(x, k_0, k_1), F_184(x, k_1, k_0))
Eq(F_184(x, k_0, k_1), F_185(x, k_0, k_1) + F_67(x, k_0))
Eq(F_185(x, k_0, k_1), F_186(x, k_0, k_1) + F_193(x, k_1, k_0) + F_22(x))
Eq(F_186(x, k_0, k_1), F_187(x, k_0, k_1)*F_69(x, k_0))
Eq(F_187(x, k_0, k_1), F_188(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1) + F_67(x, k_1))
Eq(F_189(x, k_0, k_1), F_190(x, k_1, k_0))
Eq(F_190(x, k_0, k_1), F_191(x, k_1, k_0)*F_69(x, k_0))
Eq(F_191(x, k_0, k_1), F_192(x, k_0, k_1))
Eq(F_192(x, k_0, k_1), F_67(x, k_0))
Eq(F_193(x, k_0, k_1), F_194(x, k_1, k_0)*F_69(x, k_0))
Eq(F_194(x, k_0, k_1), F_192(x, k_0, k_1) + F_195(x, k_0, k_1))
Eq(F_195(x, k_0, k_1), F_196(x, k_0, k_1))
Eq(F_196(x, k_0, k_1), F_197(x, k_0, k_1)*F_69(x, k_0))
Eq(F_197(x, k_0, k_1), F_67(x, k_1))
Eq(F_198(x, k_0, k_1, k_2), F_199(x, k_0, k_1, k_2))
Eq(F_199(x, k_0, k_1, k_2), F_200(x, k_0, k_1, k_2)*F_69(x, k_0))
Eq(F_200(x, k_0, k_1, k_2), (k_1*F_132(x, k_0, k_1, k_2) - F_132(x, k_0, 1, k_2))/(k_1 - 1))
Eq(F_201(x, k_0, k_1), F_202(x, k_1))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_204(x, 1, k_0))
Eq(F_204(x, k_0, k_1), F_169(x, k_0, k_1))
Eq(F_205(x, k_0, k_1), k_0*F_206(x, k_0, k_1))
Eq(F_206(x, k_0, k_1), F_207(x, k_0, k_1))
Eq(F_207(x, k_0, k_1), F_15(x)*F_208(x, k_0, k_1)*F_5(x))
Eq(F_208(x, k_0, k_1), F_209(x, k_1) + F_210(x, k_0, k_1))
Eq(F_209(x, k_0), F_202(x, k_0) + F_37(x, k_0))
Eq(F_210(x, k_0, k_1), F_58(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0))
Eq(F_212(x, k_0), F_15(x)*F_213(x, k_0))
Eq(F_213(x, k_0), (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_214(x, k_0), F_11(x)*F_71(x, k_0))
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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1]]}], "iterative": false}
Specification JSON:
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