02413_03412_12403_13402_21403_23401_31402_32401
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3031, 16754, 95080, 550800, 3243854, 19363200, 116879680, 712143338, 4373676576, 27044808342, 168220846101, 1051737239086, 6605345691021, 41650354192632, 263564177882141, 1673158631014734, 10652042774773760, 67991562930724356, 435011510456276350, 2789206410089055654, 17919112773969965557, 115329257492973523178, 743513502941778894378, 4800767502385200652756, 31042515022316961102500, 200994686784507813008268, 1303032187293423282609601, 8457341487035194473615548, 54952740960515711075564026, 357431784790905429442042886, 2327123494200191964657717468, 15165074844600306071478500764, 98911546246314086629955243909, 645664589332179443749373014442, 4217997661164211461221925510618, 27575815681375973330294642524404, 180408765046291471859950476501950, 1181081470955108136173635562167590, 7737163994669215154030153121338360, 50716722572950599758918038229407942, 332641595668083039738464002028489976, 2182967471044947426025631816029238286, 14333536310371323934690471256237259745, 94164130722256513630097814056803014838, 618920673196352929262448607718608840133, 4069992644897844776019471856630649962968, 26776493890761848486239595225543975560023, 176241427315287531733166032282884651752768, 1160512092783435566531493154087685607124285, 7644908152213859872934718895267154798560010, 50381340238242706400332405227752528374175511, 332151517015010341438843009811370576661756124, 2190616650577177678582333713115928458121328523, 14452899085474479924106693453474873615299704442, 95388733211970928691921238444671718455808678561, 629778809216738893379152072763812805983881952546, 4159330294486898620234530518442132952180609509803, 27478874623741008464179123730739334115257434850126, 181597808889229064828558922157030241432479591393187, 1200478922456518240551494817751041783020973001141196, 7938291927991766647708340800146862402057193045931653, 52507901716809298638297260975734033487826697553302496, 347411319054941129793543016074092400443717239418072321, 2299226421742805972816535186854557172761855531898173352, 15220709748801017294969240582409000798654893905466332058, 100786064463917466744554559413746046022919819392759300524, 667537462699665348168429423209027980334663695617413924134, 4422396119954406994234927612965035644256456567490234484496, 29305143296691617380882746301586582465998600080599634356403, 194236902310836923052741530756408073270485459950933526405320, 1287712435824780592139893564804733478653893693225361151255685, 8538920031331702375364202220043342296715382925148562074963958, 56634576267773879380219943081466196364722627690433665549428525, 375710074846212115258482149174451232318632590387316772721035382, 2492954793749897545865761042342492525764682090604085121861453768, 16544906439140331184997666255576462846897982600441137975869259184, 109824850530679587645864988288535543121107112122808176705410070647, 729157635705662592044112441212588178873341114277561316682809264570, 4842001382278688945870397584550213425064156489933203121868650571067, 32159500589593735659445614267309913651366310196502830961194716390468, 213635232539200166924820566865168071155228491029340786118897560556346, 1419430060913409151657066095115188549277981522953909294363354285565814, 9432592103591499043821006149447749696153635088257655681812942304527811, 62693496514571012490758138963684828493095355934934038122563178699875070, 416760743683585025540222147089181304535846311704907623187437444453317662, 2770910713415829124164047543829193786668216357660614566153451036246415696, 18425880818917854720559969293958299033487191071444086493725079192719135880, 122546978468378646301437726587140545776832070203564415274051871423224196232, 815162603044326121993458874615079754258355653178386283488926764600283246394, 5423153304876170925515199986877915498793766084473061927708919953676710761348, 36084795748276114964686071346807938362521371590446784539296384515606326088872, 240137582588624323288733958910638187279892704418100803582851666867517132307268, 1598300156361600332851723662690956997924472054741026386545152563566590041969668, 10639414247333761858902630362617697890772333812544640819913228703725078141704076
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24461/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[63,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[116,x]*F[12,x]*F[4,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]+F[21,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[13,x,k[0]]*F[15,x,k[0]]*F[4,x]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[379,x,k[0]]
F[24,x,k[0]] = F[15,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[188,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[51,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]
F[29,x] = (-1+x^3*F[29,x]^2+6*x^2*F[29,x]+(-11*F[29,x]+9)*x)*(x*F[29,x]-1)
F[30,x,k[0]] = F[16,x,k[0]]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[34,x,k[0]]+F[50,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[35,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[29,x]*F[38,x]*F[4,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = F[28,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]+F[43,x,k[0]]
F[41,x,k[0]] = F[31,x,k[0]]+F[42,x]
F[42,x] = ((1+F[42,x])^3*x^3+5*(1+F[42,x])^2*x^2+(-11*F[42,x]^2-19*F[42,x]-8)*x+10*F[42,x]+1)*x
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[4,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]+F[47,x,k[0]]
F[46,x,k[0]] = F[39,x,k[0]]*F[41,x,k[0]]
F[47,x,k[0]] = F[29,x]*F[48,x,k[0]]
F[48,x,k[0]] = (F[49,x,k[0]]-F[49,x,1])/(-1+k[0])
F[39,x,k[0]] = F[35,x]+F[49,x,k[0]]
F[50,x,k[0]] = F[15,x,k[0]]*F[49,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[4,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[186,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[81,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[26,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[4,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[63,x]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[55,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[10,x]
F[63,x] = F[64,x]+F[72,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[36,x]
F[66,x] = F[67,x]
F[67,x] = F[29,x]*F[4,x]*F[68,x]*F[69,x]
F[68,x] = F[38,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[1,x]+F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[71,x]*F[74,x]
F[74,x] = F[75,x]+F[95,x]
F[75,x] = F[76,x]
F[76,x] = F[29,x]*F[4,x]*F[77,x]
F[77,x] = F[78,x,1]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[59,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[55,x,k[0]]*F[83,x,k[0]]*F[87,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[89,x,k[0]]
F[84,x,k[0]] = F[1,x]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[84,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = k[0]*x
F[89,x,k[0]] = F[69,x]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x]+F[92,x,k[0]]+F[94,x,k[0]]
F[91,x] = 0
F[92,x,k[0]] = F[4,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[85,x,k[0]]+F[90,x,k[0]]
F[94,x,k[0]] = F[87,x,k[0]]*F[89,x,k[0]]
F[95,x] = F[96,x]
F[96,x] = F[107,x]*F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[29,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[29,x]*F[4,x]
F[101,x] = F[102,x]+F[71,x]
F[102,x] = F[103,x]+F[69,x]
F[103,x] = F[104,x]+F[106,x]+F[91,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[103,x]+F[69,x]
F[106,x] = F[102,x]*F[4,x]
F[107,x] = F[108,x,1]
F[109,x,k[0]] = F[108,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x]+F[168,x,k[0]]
F[111,x] = F[112,x]+F[150,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[148,x]
F[115,x] = F[116,x]+F[119,x]
F[116,x] = F[117,x,1]
F[117,x,k[0]] = (F[118,x,k[0]]*k[0]-F[118,x,1])/(-1+k[0])
F[118,x,k[0]] = (x*F[118,x,k[0]]*k[0]-1)*(-1+x^3*F[118,x,k[0]]^2*k[0]^3+6*x^2*F[118,x,k[0]]*k[0]^2+(-11*F[118,x,k[0]]+9)*x*k[0])
F[119,x] = F[120,x]
F[120,x] = F[116,x]*F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[125,x]
F[122,x] = F[123,x]+F[71,x]
F[123,x] = F[124,x]
F[124,x] = F[121,x]*F[4,x]*F[71,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[147,x]
F[128,x] = F[129,x]+F[8,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[4,x]*F[71,x]
F[132,x] = F[133,x]+F[141,x]
F[133,x] = F[134,x]*F[71,x]
F[134,x] = F[1,x]+F[135,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[71,x]
F[138,x] = F[135,x]+F[139,x]
F[139,x] = F[140,x]
F[140,x] = F[138,x]*F[4,x]
F[141,x] = F[142,x]
F[142,x] = F[134,x]*F[143,x]*F[4,x]*F[71,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[130,x]+F[5,x]
F[145,x] = F[146,x]
F[146,x] = F[101,x]*F[144,x]*F[4,x]
F[147,x] = F[145,x]
F[148,x] = F[149,x]
F[149,x] = F[127,x]*F[29,x]*F[4,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[156,x]
F[153,x] = F[154,x]*F[29,x]
F[154,x] = F[155,x]
F[155,x] = F[107,x]*F[4,x]
F[156,x] = -F[166,x]+F[157,x]
F[157,x] = 1/F[4,x]/F[71,x]*F[158,x]
F[158,x] = F[159,x]
F[159,x] = -F[163,x]+F[160,x]
F[160,x] = 1/F[4,x]*F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[4,x]*F[8,x]
F[163,x] = F[164,x]+F[5,x]
F[164,x] = F[165,x]
F[165,x] = F[114,x]*F[4,x]*F[71,x]
F[166,x] = F[167,x]*F[29,x]
F[167,x] = F[154,x]+F[68,x]
F[168,x,k[0]] = F[169,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]+F[183,x]
F[171,x,k[0]] = F[15,x,k[0]]*F[170,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]
F[23,x,k[0]] = F[172,x,k[0]]+F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[176,x,k[0]]
F[174,x,k[0]] = F[15,x,k[0]]*F[175,x,k[0]]
F[175,x,k[0]] = F[39,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[181,x,k[0]]
F[178,x,k[0]] = F[177,x,k[0]]+F[180,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]*F[4,x]
F[179,x,k[0]] = F[19,x,k[0]]
F[180,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]
F[182,x,k[0]] = F[15,x,k[0]]*F[66,x]
F[183,x] = F[111,x]+F[184,x]
F[184,x] = F[185,x]
F[185,x] = F[183,x]*F[4,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[108,x,k[0]]*F[4,x]*F[83,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[4,x]
F[190,x,k[0]] = F[191,x,k[0]]+F[361,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]+F[197,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]*F[194,x,k[0]]
F[193,x,k[0]] = F[26,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[196,x,k[0]] = F[15,x,k[0]]*F[195,x,k[0]]*F[4,x]
F[196,x,k[0]] = F[41,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[4,x]
F[199,x,k[0]] = F[200,x,k[0]]+F[351,x,k[0]]
F[200,x,k[0]] = F[193,x,k[0]]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[273,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[259,x,k[0]]
F[204,x,k[0]] = F[203,x,k[0]]*F[258,x,k[0]]
F[205,x,k[0]] = F[204,x,k[0]]+F[257,x,k[0]]
F[206,x,k[0]] = F[205,x,k[0]]*F[4,x]
F[206,x,k[0]] = F[207,x,k[0]]
F[208,x,k[0]] = F[207,x,k[0]]+F[254,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]+F[215,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[213,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]*F[84,x,k[0]]
F[212,x,k[0]] = F[28,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]
F[214,x,k[0]] = F[4,x]*F[53,x,k[0]]*F[84,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]*F[218,x,k[0]]*F[4,x]
F[217,x,k[0]] = F[13,x,k[0]]
F[219,x,k[0]] = F[218,x,k[0]]*F[4,x]
F[219,x,k[0]] = F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]*F[4,x]
F[221,x,k[0]] = F[222,x,k[0]]
F[223,x,k[0]] = F[222,x,k[0]]*F[4,x]
F[223,x,k[0]] = F[224,x,k[0]]
F[225,x,k[0]] = F[224,x,k[0]]+F[28,x,k[0]]
F[225,x,k[0]] = F[226,x,k[0]]+F[231,x,k[0]]
F[226,x,k[0]] = F[15,x,k[0]]+F[227,x,k[0]]
F[227,x,k[0]] = F[228,x,k[0]]+F[4,x]
F[228,x,k[0]] = F[229,x,k[0]]+F[230,x,k[0]]+F[91,x]
F[229,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[230,x,k[0]] = F[18,x,k[0]]*F[227,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]
F[232,x,k[0]] = F[233,x,k[0]]*F[4,x]
F[233,x,k[0]] = F[234,x,k[0]]+F[253,x,k[0]]
F[234,x,k[0]] = F[15,x,k[0]]*F[235,x,k[0]]
F[235,x,k[0]] = F[225,x,k[0]]+F[236,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]*F[4,x]
F[238,x,k[0]] = F[239,x,k[0]]+F[245,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[243,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]*F[29,x]
F[241,x,k[0]] = (F[242,x,k[0]]*k[0]-F[242,x,1])/(-1+k[0])
F[242,x,k[0]] = F[235,x,k[0]]
F[243,x,k[0]] = F[242,x,k[0]]*F[244,x,k[0]]
F[244,x,k[0]] = F[30,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]+F[249,x,k[0]]
F[246,x,k[0]] = F[247,x,k[0]]*F[248,x,k[0]]
F[247,x,k[0]] = F[224,x,k[0]]
F[248,x,k[0]] = F[39,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]
F[250,x,k[0]] = F[251,x]*F[48,x,k[0]]
F[251,x] = F[252,x]
F[252,x] = F[116,x]*F[4,x]
F[253,x,k[0]] = F[227,x,k[0]]*F[39,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]*F[256,x,k[0]]
F[255,x,k[0]] = F[14,x,k[0]]
F[256,x,k[0]] = F[212,x,k[0]]
F[257,x,k[0]] = F[53,x,k[0]]*F[84,x,k[0]]
F[258,x,k[0]] = F[19,x,k[0]]
F[259,x,k[0]] = F[260,x]
F[260,x] = F[261,x]*F[4,x]*F[71,x]
F[261,x] = 1/F[4,x]*F[262,x]
F[262,x] = F[263,x]
F[263,x] = 1/F[68,x]*F[264,x]
F[264,x] = -F[265,x]+F[152,x]
F[265,x] = F[153,x]+F[266,x]
F[266,x] = F[267,x]
F[267,x] = F[268,x]*F[4,x]
F[268,x] = F[269,x]+F[270,x]
F[269,x] = F[154,x]*F[261,x]
F[270,x] = F[271,x]
F[271,x] = F[272,x]*F[71,x]
F[272,x] = F[265,x]
F[273,x,k[0]] = F[274,x]
F[274,x] = -F[345,x]+F[275,x]
F[275,x] = 1/F[2,x]*F[276,x]
F[276,x] = -F[339,x]+F[277,x]
F[277,x] = 1/F[4,x]*F[278,x]
F[278,x] = F[279,x]
F[279,x] = -F[338,x]+F[280,x]
F[280,x] = F[281,x]+F[332,x]
F[281,x] = -F[288,x]+F[282,x]
F[282,x] = 1/F[4,x]*F[283,x]
F[283,x] = F[284,x]
F[284,x] = -F[2,x]+F[285,x]
F[285,x] = -F[0,x]+F[286,x]
F[286,x] = 1/F[4,x]*F[287,x]
F[287,x] = F[2,x]
F[288,x] = -F[292,x]+F[289,x]
F[289,x] = 1/F[4,x]*F[290,x]
F[290,x] = F[291,x]
F[291,x] = F[2,x]+F[284,x]
F[292,x] = -F[296,x]+F[293,x]
F[293,x] = 1/F[4,x]*F[294,x]
F[294,x] = F[295,x]
F[295,x] = F[289,x]*F[4,x]
F[296,x] = F[297,x]+F[332,x]
F[297,x] = F[298,x]+F[331,x]
F[298,x] = F[299,x]+F[42,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[4,x]
F[301,x] = F[111,x]+F[302,x]
F[302,x] = F[303,x,1]
F[303,x,k[0]] = F[304,x,k[0]]+F[312,x,k[0]]
F[304,x,k[0]] = F[305,x,k[0]]*F[311,x]
F[305,x,k[0]] = F[306,x,k[0]]
F[306,x,k[0]] = F[18,x,k[0]]*F[307,x,k[0]]
F[307,x,k[0]] = F[15,x,k[0]]+F[308,x,k[0]]
F[308,x,k[0]] = F[305,x,k[0]]+F[309,x,k[0]]
F[309,x,k[0]] = F[310,x,k[0]]
F[310,x,k[0]] = F[18,x,k[0]]*F[308,x,k[0]]
F[311,x] = F[35,x]
F[312,x,k[0]] = F[313,x,k[0]]
F[313,x,k[0]] = F[18,x,k[0]]*F[314,x,k[0]]
F[314,x,k[0]] = F[315,x,k[0]]+F[329,x,k[0]]
F[315,x,k[0]] = F[111,x]*F[316,x,k[0]]
F[316,x,k[0]] = F[317,x,k[0]]+F[318,x,k[0]]
F[317,x,k[0]] = F[1,x]+F[305,x,k[0]]
F[318,x,k[0]] = F[18,x,k[0]]+F[319,x,k[0]]
F[319,x,k[0]] = k[0]*F[320,x,k[0]]
F[320,x,k[0]] = F[229,x,k[0]]+F[321,x,k[0]]+F[91,x]
F[321,x,k[0]] = F[18,x,k[0]]*F[322,x,k[0]]
F[322,x,k[0]] = F[323,x,k[0]]+F[326,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]+F[4,x]
F[324,x,k[0]] = F[325,x,k[0]]
F[325,x,k[0]] = F[18,x,k[0]]*F[323,x,k[0]]
F[326,x,k[0]] = F[320,x,k[0]]+F[327,x,k[0]]
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[18,x,k[0]]*F[326,x,k[0]]
F[329,x,k[0]] = F[330,x,k[0]]
F[330,x,k[0]] = F[111,x]+F[312,x,k[0]]
F[331,x] = F[299,x]
F[332,x] = F[333,x]
F[333,x] = F[2,x]*F[334,x]*F[4,x]
F[334,x] = F[335,x]+F[337,x]
F[335,x] = F[29,x]*F[336,x]
F[336,x] = F[235,x,1]
F[337,x] = F[251,x]*F[38,x]
F[338,x] = F[2,x]*F[35,x]
F[339,x] = -F[344,x]+F[340,x]
F[340,x] = 1/F[4,x]*F[341,x]
F[341,x] = F[342,x]
F[342,x] = -F[343,x]+F[281,x]
F[343,x] = F[2,x]*F[29,x]
F[344,x] = F[2,x]*F[261,x]
F[345,x] = F[346,x]+F[350,x]
F[346,x] = F[347,x]
F[347,x] = F[348,x,1]
F[348,x,k[0]] = (F[349,x,k[0]]*k[0]-F[349,x,1])/(-1+k[0])
F[349,x,k[0]] = F[311,k[0]*x]
F[350,x] = F[260,x]
F[351,x,k[0]] = F[352,x,k[0]]
F[352,x,k[0]] = F[353,x,k[0]]*F[71,x]
F[353,x,k[0]] = F[354,x,k[0]]
F[354,x,k[0]] = F[355,x,k[0]]+F[356,x,k[0]]
F[355,x,k[0]] = F[29,x]*F[51,x,k[0]]
F[356,x,k[0]] = F[357,x,k[0]]
F[357,x,k[0]] = F[358,x,k[0]]*F[4,x]
F[358,x,k[0]] = F[359,x,k[0]]+F[360,x,k[0]]
F[359,x,k[0]] = F[261,x]*F[51,x,k[0]]
F[360,x,k[0]] = F[352,x,k[0]]
F[361,x,k[0]] = F[362,x,k[0]]
F[362,x,k[0]] = F[363,x,k[0]]*F[4,x]
F[364,x,k[0]] = F[363,x,k[0]]*F[4,x]
F[364,x,k[0]] = F[365,x,k[0]]
F[365,x,k[0]] = (F[366,x,k[0]]-F[366,x,1])/(-1+k[0])
F[366,x,k[0]] = F[367,x,k[0]]+F[370,x,k[0]]
F[367,x,k[0]] = F[368,x]*F[369,x,k[0]]
F[368,x] = F[263,x]+F[29,x]
F[369,x,k[0]] = F[49,x,k[0]]
F[370,x,k[0]] = F[371,x,k[0]]+F[372,x,k[0]]
F[371,x,k[0]] = F[168,x,k[0]]*F[29,x]
F[372,x,k[0]] = F[373,x,k[0]]
F[373,x,k[0]] = F[374,x,k[0]]*F[4,x]
F[374,x,k[0]] = F[375,x,k[0]]+F[376,x,k[0]]
F[375,x,k[0]] = F[168,x,k[0]]*F[261,x]
F[376,x,k[0]] = F[377,x,k[0]]
F[377,x,k[0]] = F[378,x,k[0]]*F[71,x]
F[378,x,k[0]] = F[370,x,k[0]]
F[379,x,k[0]] = F[176,x,k[0]]+F[380,x,k[0]]
F[380,x,k[0]] = F[381,x,k[0]]
F[381,x,k[0]] = F[15,x,k[0]]*F[184,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{63}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{379}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x \right) = x^{4} F_{29} \left(x \right)^{3}+5 x^{3} F_{29} \left(x \right)^{2}-11 x^{2} F_{29} \left(x \right)^{2}+3 x^{2} F_{29}\! \left(x \right)+10 x F_{29}\! \left(x \right)-9 x +1
F_{30}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{29}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = x^{4} F_{42} \left(x \right)^{3}+3 x^{4} F_{42} \left(x \right)^{2}+3 x^{4} F_{42}\! \left(x \right)+5 x^{3} F_{42} \left(x \right)^{2}+x^{4}+10 x^{3} F_{42}\! \left(x \right)-11 x^{2} F_{42} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{42}\! \left(x \right)-8 x^{2}+10 x F_{42}\! \left(x \right)+x
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{-F_{49}\! \left(x , y\right)+F_{49}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{10}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{36}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right) F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{95}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = y x
F_{89}\! \left(x , y\right) = F_{69}\! \left(x \right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{91}\! \left(x \right) = 0
F_{92}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{29}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{71}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{69}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)+F_{91}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{69}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x , 1\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{168}\! \left(x , y\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{150}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{148}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = -\frac{-F_{118}\! \left(x , y\right) y +F_{118}\! \left(x , 1\right)}{-1+y}
F_{118}\! \left(x , y\right) = y^{4} x^{4} F_{118}\! \left(x , y\right)^{3}+5 x^{3} F_{118}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{118}\! \left(x , y\right)^{2}+3 x^{2} F_{118}\! \left(x , y\right) y^{2}+10 x F_{118}\! \left(x , y\right) y -9 y x +1
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{125}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{71}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{147}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{8}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{141}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{71}\! \left(x \right)
F_{134}\! \left(x \right) = F_{1}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{71}\! \left(x \right)
F_{138}\! \left(x \right) = F_{135}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{134}\! \left(x \right) F_{143}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{130}\! \left(x \right)+F_{5}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{101}\! \left(x \right) F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{127}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{156}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{29}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{166}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = \frac{F_{158}\! \left(x \right)}{F_{4}\! \left(x \right) F_{71}\! \left(x \right)}
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{5}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{29}\! \left(x \right)
F_{167}\! \left(x \right) = F_{154}\! \left(x \right)+F_{68}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{183}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{170}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{66}\! \left(x \right)
F_{183}\! \left(x \right) = F_{111}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{195}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{196}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{351}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{259}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{258}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{53}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right) F_{218}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{217}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{222}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{228}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{230}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{230}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{227}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{233}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right) F_{29}\! \left(x \right)
F_{241}\! \left(x , y\right) = -\frac{-F_{242}\! \left(x , y\right) y +F_{242}\! \left(x , 1\right)}{-1+y}
F_{242}\! \left(x , y\right) = F_{235}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{242}\! \left(x , y\right) F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right) F_{248}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{253}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right) F_{256}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{212}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{261}\! \left(x \right) = \frac{F_{262}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = \frac{F_{264}\! \left(x \right)}{F_{68}\! \left(x \right)}
F_{264}\! \left(x \right) = -F_{265}\! \left(x \right)+F_{152}\! \left(x \right)
F_{265}\! \left(x \right) = F_{153}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right) F_{4}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{270}\! \left(x \right)
F_{269}\! \left(x \right) = F_{154}\! \left(x \right) F_{261}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right) F_{71}\! \left(x \right)
F_{272}\! \left(x \right) = F_{265}\! \left(x \right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = -F_{345}\! \left(x \right)+F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = \frac{F_{276}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{276}\! \left(x \right) = -F_{339}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = \frac{F_{278}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{332}\! \left(x \right)
F_{281}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = \frac{F_{283}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = \frac{F_{287}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{287}\! \left(x \right) = F_{2}\! \left(x \right)
F_{288}\! \left(x \right) = -F_{292}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = \frac{F_{290}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{290}\! \left(x \right) = F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{2}\! \left(x \right)+F_{284}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{296}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = \frac{F_{294}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{289}\! \left(x \right) F_{4}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{332}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)+F_{331}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{42}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{4}\! \left(x \right)
F_{301}\! \left(x \right) = F_{111}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x , 1\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)+F_{312}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{305}\! \left(x , y\right) F_{311}\! \left(x \right)
F_{305}\! \left(x , y\right) = F_{306}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{307}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{308}\! \left(x , y\right)
F_{308}\! \left(x , y\right) = F_{305}\! \left(x , y\right)+F_{309}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{310}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{308}\! \left(x , y\right)
F_{311}\! \left(x \right) = F_{35}\! \left(x \right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{314}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{315}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{111}\! \left(x \right) F_{316}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{317}\! \left(x , y\right)+F_{318}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{305}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{319}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = y F_{320}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{321}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{321}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{326}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{323}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{326}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{312}\! \left(x , y\right)
F_{331}\! \left(x \right) = F_{299}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{2}\! \left(x \right) F_{334}\! \left(x \right) F_{4}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right)+F_{337}\! \left(x \right)
F_{335}\! \left(x \right) = F_{29}\! \left(x \right) F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{235}\! \left(x , 1\right)
F_{337}\! \left(x \right) = F_{251}\! \left(x \right) F_{38}\! \left(x \right)
F_{338}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{339}\! \left(x \right) = -F_{344}\! \left(x \right)+F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = \frac{F_{341}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{341}\! \left(x \right) = F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = -F_{343}\! \left(x \right)+F_{281}\! \left(x \right)
F_{343}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right)
F_{344}\! \left(x \right) = F_{2}\! \left(x \right) F_{261}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)+F_{350}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right)
F_{347}\! \left(x \right) = F_{348}\! \left(x , 1\right)
F_{348}\! \left(x , y\right) = -\frac{-y F_{349}\! \left(x , y\right)+F_{349}\! \left(x , 1\right)}{-1+y}
F_{349}\! \left(x , y\right) = F_{311}\! \left(y x \right)
F_{350}\! \left(x \right) = F_{260}\! \left(x \right)
F_{351}\! \left(x , y\right) = F_{352}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{353}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{353}\! \left(x , y\right) = F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{355}\! \left(x , y\right)+F_{356}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{357}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{358}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{358}\! \left(x , y\right) = F_{359}\! \left(x , y\right)+F_{360}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{261}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{352}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = F_{362}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{363}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{364}\! \left(x , y\right) = F_{363}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{364}\! \left(x , y\right) = F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = -\frac{-F_{366}\! \left(x , y\right)+F_{366}\! \left(x , 1\right)}{-1+y}
F_{366}\! \left(x , y\right) = F_{367}\! \left(x , y\right)+F_{370}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{368}\! \left(x \right) F_{369}\! \left(x , y\right)
F_{368}\! \left(x \right) = F_{263}\! \left(x \right)+F_{29}\! \left(x \right)
F_{369}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{371}\! \left(x , y\right)+F_{372}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{29}\! \left(x \right)
F_{372}\! \left(x , y\right) = F_{373}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{374}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{374}\! \left(x , y\right) = F_{375}\! \left(x , y\right)+F_{376}\! \left(x , y\right)
F_{375}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{261}\! \left(x \right)
F_{376}\! \left(x , y\right) = F_{377}\! \left(x , y\right)
F_{377}\! \left(x , y\right) = F_{378}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{378}\! \left(x , y\right) = F_{370}\! \left(x , y\right)
F_{379}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{380}\! \left(x , y\right)
F_{380}\! \left(x , y\right) = F_{381}\! \left(x , y\right)
F_{381}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{184}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_63(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_116(x)*F_12(x)*F_4(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0) + F_21(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_13(x, k_0)*F_15(x, k_0)*F_4(x))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_379(x, k_0))
Eq(F_24(x, k_0), F_15(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_188(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_51(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0))
Eq(F_29(x), x**4*F_29(x)**3 + x**2*(5*x - 11)*F_29(x)**2 - 9*x + (3*x**2 + 10*x)*F_29(x) + 1)
Eq(F_30(x, k_0), F_16(x, k_0) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_34(x, k_0) + F_50(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_35(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_29(x)*F_38(x)*F_4(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), F_28(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0) + F_43(x, k_0))
Eq(F_41(x, k_0), F_31(x, k_0) + F_42(x))
Eq(F_42(x), x**4*(F_42(x) + 1)**3 + x**2*(5*x - 11)*(F_42(x) + 1)**2 - 9*x + (F_42(x) + 1)*(3*x**2 + 10*x - 1) + F_42(x) + 1)
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_4(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0) + F_47(x, k_0))
Eq(F_46(x, k_0), F_39(x, k_0)*F_41(x, k_0))
Eq(F_47(x, k_0), F_29(x)*F_48(x, k_0))
Eq(F_48(x, k_0), -F_49(x, k_0) + (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), F_35(x) + F_49(x, k_0))
Eq(F_50(x, k_0), F_15(x, k_0)*F_49(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_4(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_186(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_81(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_26(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_4(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_63(x))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_55(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_10(x))
Eq(F_63(x), F_64(x) + F_72(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_36(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_29(x)*F_4(x)*F_68(x)*F_69(x))
Eq(F_68(x), F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_1(x) + F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_71(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_95(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_29(x)*F_4(x)*F_77(x))
Eq(F_77(x), F_78(x, 1))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_59(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_55(x, k_0)*F_83(x, k_0)*F_87(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_89(x, k_0))
Eq(F_84(x, k_0), F_1(x) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_84(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), k_0*x)
Eq(F_89(x, k_0), F_69(x) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_91(x), 0)
Eq(F_92(x, k_0), F_4(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_85(x, k_0) + F_90(x, k_0))
Eq(F_94(x, k_0), F_87(x, k_0)*F_89(x, k_0))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_107(x)*F_4(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_29(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_29(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_71(x))
Eq(F_102(x), F_103(x) + F_69(x))
Eq(F_103(x), F_104(x) + F_106(x) + F_91(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_103(x) + F_69(x))
Eq(F_106(x), F_102(x)*F_4(x))
Eq(F_107(x), F_108(x, 1))
Eq(F_109(x, k_0), F_108(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x) + F_168(x, k_0))
Eq(F_111(x), F_112(x) + F_150(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_148(x))
Eq(F_115(x), F_116(x) + F_119(x))
Eq(F_116(x), F_117(x, 1))
Eq(F_117(x, k_0), (-k_0*F_118(x, k_0) + F_118(x, 1))/(1 - k_0))
Eq(F_118(x, k_0), k_0**4*x**4*F_118(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_118(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_118(x, k_0) + 1)
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_116(x)*F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_125(x))
Eq(F_122(x), F_123(x) + F_71(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_121(x)*F_4(x)*F_71(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_147(x))
Eq(F_128(x), F_129(x) + F_8(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_4(x)*F_71(x))
Eq(F_132(x), F_133(x) + F_141(x))
Eq(F_133(x), F_134(x)*F_71(x))
Eq(F_134(x), F_1(x) + F_135(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_71(x))
Eq(F_138(x), F_135(x) + F_139(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_138(x)*F_4(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_134(x)*F_143(x)*F_4(x)*F_71(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_130(x) + F_5(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_101(x)*F_144(x)*F_4(x))
Eq(F_147(x), F_145(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_127(x)*F_29(x)*F_4(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_156(x))
Eq(F_153(x), F_154(x)*F_29(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_107(x)*F_4(x))
Eq(F_156(x), F_157(x) - F_166(x))
Eq(F_157(x), F_158(x)/(F_4(x)*F_71(x)))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x) - F_163(x))
Eq(F_160(x), F_161(x)/F_4(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_4(x)*F_8(x))
Eq(F_163(x), F_164(x) + F_5(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_114(x)*F_4(x)*F_71(x))
Eq(F_166(x), F_167(x)*F_29(x))
Eq(F_167(x), F_154(x) + F_68(x))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0) + F_183(x))
Eq(F_171(x, k_0), F_15(x, k_0)*F_170(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_23(x, k_0), F_172(x, k_0) + F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_176(x, k_0))
Eq(F_174(x, k_0), F_15(x, k_0)*F_175(x, k_0))
Eq(F_175(x, k_0), F_39(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_181(x, k_0))
Eq(F_178(x, k_0), F_177(x, k_0) + F_180(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0)*F_4(x))
Eq(F_179(x, k_0), F_19(x, k_0))
Eq(F_180(x, k_0), F_15(x, k_0)*F_27(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0))
Eq(F_182(x, k_0), F_15(x, k_0)*F_66(x))
Eq(F_183(x), F_111(x) + F_184(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_183(x)*F_4(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_108(x, k_0)*F_4(x)*F_83(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_4(x))
Eq(F_190(x, k_0), F_191(x, k_0) + F_361(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0) + F_197(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0)*F_194(x, k_0))
Eq(F_193(x, k_0), F_26(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_196(x, k_0), F_15(x, k_0)*F_195(x, k_0)*F_4(x))
Eq(F_196(x, k_0), F_41(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_4(x))
Eq(F_199(x, k_0), F_200(x, k_0) + F_351(x, k_0))
Eq(F_200(x, k_0), F_193(x, k_0)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_273(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_259(x, k_0))
Eq(F_204(x, k_0), F_203(x, k_0)*F_258(x, k_0))
Eq(F_205(x, k_0), F_204(x, k_0) + F_257(x, k_0))
Eq(F_206(x, k_0), F_205(x, k_0)*F_4(x))
Eq(F_206(x, k_0), F_207(x, k_0))
Eq(F_208(x, k_0), F_207(x, k_0) + F_254(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_215(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_213(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0)*F_84(x, k_0))
Eq(F_212(x, k_0), F_28(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0))
Eq(F_214(x, k_0), F_4(x)*F_53(x, k_0)*F_84(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0)*F_218(x, k_0)*F_4(x))
Eq(F_217(x, k_0), F_13(x, k_0))
Eq(F_219(x, k_0), F_218(x, k_0)*F_4(x))
Eq(F_219(x, k_0), F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0)*F_4(x))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_223(x, k_0), F_222(x, k_0)*F_4(x))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_225(x, k_0), F_224(x, k_0) + F_28(x, k_0))
Eq(F_225(x, k_0), F_226(x, k_0) + F_231(x, k_0))
Eq(F_226(x, k_0), F_15(x, k_0) + F_227(x, k_0))
Eq(F_227(x, k_0), F_228(x, k_0) + F_4(x))
Eq(F_228(x, k_0), F_229(x, k_0) + F_230(x, k_0) + F_91(x))
Eq(F_229(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_230(x, k_0), F_18(x, k_0)*F_227(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0))
Eq(F_232(x, k_0), F_233(x, k_0)*F_4(x))
Eq(F_233(x, k_0), F_234(x, k_0) + F_253(x, k_0))
Eq(F_234(x, k_0), F_15(x, k_0)*F_235(x, k_0))
Eq(F_235(x, k_0), F_225(x, k_0) + F_236(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0)*F_4(x))
Eq(F_238(x, k_0), F_239(x, k_0) + F_245(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_243(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0)*F_29(x))
Eq(F_241(x, k_0), (-k_0*F_242(x, k_0) + F_242(x, 1))/(1 - k_0))
Eq(F_242(x, k_0), F_235(x, k_0))
Eq(F_243(x, k_0), F_242(x, k_0)*F_244(x, k_0))
Eq(F_244(x, k_0), F_30(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0) + F_249(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0)*F_248(x, k_0))
Eq(F_247(x, k_0), F_224(x, k_0))
Eq(F_248(x, k_0), F_39(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x)*F_48(x, k_0))
Eq(F_251(x), F_252(x))
Eq(F_252(x), F_116(x)*F_4(x))
Eq(F_253(x, k_0), F_227(x, k_0)*F_39(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0)*F_256(x, k_0))
Eq(F_255(x, k_0), F_14(x, k_0))
Eq(F_256(x, k_0), F_212(x, k_0))
Eq(F_257(x, k_0), F_53(x, k_0)*F_84(x, k_0))
Eq(F_258(x, k_0), F_19(x, k_0))
Eq(F_259(x, k_0), F_260(x))
Eq(F_260(x), F_261(x)*F_4(x)*F_71(x))
Eq(F_261(x), F_262(x)/F_4(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_264(x)/F_68(x))
Eq(F_264(x), F_152(x) - F_265(x))
Eq(F_265(x), F_153(x) + F_266(x))
Eq(F_266(x), F_267(x))
Eq(F_267(x), F_268(x)*F_4(x))
Eq(F_268(x), F_269(x) + F_270(x))
Eq(F_269(x), F_154(x)*F_261(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_272(x)*F_71(x))
Eq(F_272(x), F_265(x))
Eq(F_273(x, k_0), F_274(x))
Eq(F_274(x), F_275(x) - F_345(x))
Eq(F_275(x), F_276(x)/F_2(x))
Eq(F_276(x), F_277(x) - F_339(x))
Eq(F_277(x), F_278(x)/F_4(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_280(x) - F_338(x))
Eq(F_280(x), F_281(x) + F_332(x))
Eq(F_281(x), F_282(x) - F_288(x))
Eq(F_282(x), F_283(x)/F_4(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), -F_2(x) + F_285(x))
Eq(F_285(x), -F_0(x) + F_286(x))
Eq(F_286(x), F_287(x)/F_4(x))
Eq(F_287(x), F_2(x))
Eq(F_288(x), F_289(x) - F_292(x))
Eq(F_289(x), F_290(x)/F_4(x))
Eq(F_290(x), F_291(x))
Eq(F_291(x), F_2(x) + F_284(x))
Eq(F_292(x), F_293(x) - F_296(x))
Eq(F_293(x), F_294(x)/F_4(x))
Eq(F_294(x), F_295(x))
Eq(F_295(x), F_289(x)*F_4(x))
Eq(F_296(x), F_297(x) + F_332(x))
Eq(F_297(x), F_298(x) + F_331(x))
Eq(F_298(x), F_299(x) + F_42(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_4(x))
Eq(F_301(x), F_111(x) + F_302(x))
Eq(F_302(x), F_303(x, 1))
Eq(F_303(x, k_0), F_304(x, k_0) + F_312(x, k_0))
Eq(F_304(x, k_0), F_305(x, k_0)*F_311(x))
Eq(F_305(x, k_0), F_306(x, k_0))
Eq(F_306(x, k_0), F_18(x, k_0)*F_307(x, k_0))
Eq(F_307(x, k_0), F_15(x, k_0) + F_308(x, k_0))
Eq(F_308(x, k_0), F_305(x, k_0) + F_309(x, k_0))
Eq(F_309(x, k_0), F_310(x, k_0))
Eq(F_310(x, k_0), F_18(x, k_0)*F_308(x, k_0))
Eq(F_311(x), F_35(x))
Eq(F_312(x, k_0), F_313(x, k_0))
Eq(F_313(x, k_0), F_18(x, k_0)*F_314(x, k_0))
Eq(F_314(x, k_0), F_315(x, k_0) + F_329(x, k_0))
Eq(F_315(x, k_0), F_111(x)*F_316(x, k_0))
Eq(F_316(x, k_0), F_317(x, k_0) + F_318(x, k_0))
Eq(F_317(x, k_0), F_1(x) + F_305(x, k_0))
Eq(F_318(x, k_0), F_18(x, k_0) + F_319(x, k_0))
Eq(F_319(x, k_0), k_0*F_320(x, k_0))
Eq(F_320(x, k_0), F_229(x, k_0) + F_321(x, k_0) + F_91(x))
Eq(F_321(x, k_0), F_18(x, k_0)*F_322(x, k_0))
Eq(F_322(x, k_0), F_323(x, k_0) + F_326(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0) + F_4(x))
Eq(F_324(x, k_0), F_325(x, k_0))
Eq(F_325(x, k_0), F_18(x, k_0)*F_323(x, k_0))
Eq(F_326(x, k_0), F_320(x, k_0) + F_327(x, k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_18(x, k_0)*F_326(x, k_0))
Eq(F_329(x, k_0), F_330(x, k_0))
Eq(F_330(x, k_0), F_111(x) + F_312(x, k_0))
Eq(F_331(x), F_299(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_2(x)*F_334(x)*F_4(x))
Eq(F_334(x), F_335(x) + F_337(x))
Eq(F_335(x), F_29(x)*F_336(x))
Eq(F_336(x), F_235(x, 1))
Eq(F_337(x), F_251(x)*F_38(x))
Eq(F_338(x), F_2(x)*F_35(x))
Eq(F_339(x), F_340(x) - F_344(x))
Eq(F_340(x), F_341(x)/F_4(x))
Eq(F_341(x), F_342(x))
Eq(F_342(x), F_281(x) - F_343(x))
Eq(F_343(x), F_2(x)*F_29(x))
Eq(F_344(x), F_2(x)*F_261(x))
Eq(F_345(x), F_346(x) + F_350(x))
Eq(F_346(x), F_347(x))
Eq(F_347(x), F_348(x, 1))
Eq(F_348(x, k_0), (-k_0*F_349(x, k_0) + F_349(x, 1))/(1 - k_0))
Eq(F_349(x, k_0), F_311(k_0*x))
Eq(F_350(x), F_260(x))
Eq(F_351(x, k_0), F_352(x, k_0))
Eq(F_352(x, k_0), F_353(x, k_0)*F_71(x))
Eq(F_353(x, k_0), F_354(x, k_0))
Eq(F_354(x, k_0), F_355(x, k_0) + F_356(x, k_0))
Eq(F_355(x, k_0), F_29(x)*F_51(x, k_0))
Eq(F_356(x, k_0), F_357(x, k_0))
Eq(F_357(x, k_0), F_358(x, k_0)*F_4(x))
Eq(F_358(x, k_0), F_359(x, k_0) + F_360(x, k_0))
Eq(F_359(x, k_0), F_261(x)*F_51(x, k_0))
Eq(F_360(x, k_0), F_352(x, k_0))
Eq(F_361(x, k_0), F_362(x, k_0))
Eq(F_362(x, k_0), F_363(x, k_0)*F_4(x))
Eq(F_364(x, k_0), F_363(x, k_0)*F_4(x))
Eq(F_364(x, k_0), F_365(x, k_0))
Eq(F_365(x, k_0), -F_366(x, k_0) + (k_0*F_366(x, k_0) - F_366(x, 1))/(k_0 - 1))
Eq(F_366(x, k_0), F_367(x, k_0) + F_370(x, k_0))
Eq(F_367(x, k_0), F_368(x)*F_369(x, k_0))
Eq(F_368(x), F_263(x) + F_29(x))
Eq(F_369(x, k_0), F_49(x, k_0))
Eq(F_370(x, k_0), F_371(x, k_0) + F_372(x, k_0))
Eq(F_371(x, k_0), F_168(x, k_0)*F_29(x))
Eq(F_372(x, k_0), F_373(x, k_0))
Eq(F_373(x, k_0), F_374(x, k_0)*F_4(x))
Eq(F_374(x, k_0), F_375(x, k_0) + F_376(x, k_0))
Eq(F_375(x, k_0), F_168(x, k_0)*F_261(x))
Eq(F_376(x, k_0), F_377(x, k_0))
Eq(F_377(x, k_0), F_378(x, k_0)*F_71(x))
Eq(F_378(x, k_0), F_370(x, k_0))
Eq(F_379(x, k_0), F_176(x, k_0) + F_380(x, k_0))
Eq(F_380(x, k_0), F_381(x, k_0))
Eq(F_381(x, k_0), F_15(x, k_0)*F_184(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 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, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, 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"requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": 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[0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24532/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[318,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[21,x]*F[8,x]
F[8,x] = F[123,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[21,x]*F[35,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]+F[22,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[13,x,k[0]]*F[15,x,k[0]]*F[21,x]
F[21,x] = x
F[22,x,k[0]] = F[23,x,k[0]]+F[316,x,k[0]]+F[317,x,k[0]]+F[6,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[145,x,k[0]]+F[146,x,k[0]]+F[235,x,k[0]]+F[25,x,k[0]]
F[25,x,k[0]] = F[21,x]*F[26,x,k[0]]
F[27,x,k[0]] = F[21,x]*F[26,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[144,x,k[0]]+F[27,x,k[0]]+F[66,x,k[0]]+F[68,x,k[0]]
F[28,x,k[0]] = F[142,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[14,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[36,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[35,x]
F[34,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[35,x] = (x*F[35,x]-1)*(-1+x^3*F[35,x]^2+6*x^2*F[35,x]+(-11*F[35,x]+9)*x)
F[36,x,k[0]] = F[13,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[140,x,k[0]]+F[38,x,k[0]]+F[6,x]
F[38,x,k[0]] = F[21,x]*F[39,x,k[0]]
F[40,x,k[0]] = F[136,x]+F[39,x,k[0]]
F[41,x,k[0]] = F[13,x,k[0]]*F[21,x]*F[40,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[44,x,k[0]] = F[29,x,k[0]]+F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[50,x,k[0]]
F[45,x,k[0]] = F[14,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = 2*F[6,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[47,x,k[0]] = F[21,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[13,x,k[0]]+F[42,x,k[0]]
F[49,x,k[0]] = F[18,x,k[0]]*F[46,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[21,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[58,x,k[0]]
F[54,x,k[0]] = F[48,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]+F[6,x]
F[56,x,k[0]] = F[21,x]*F[40,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[55,x,k[0]]
F[58,x,k[0]] = F[35,x]*F[59,x,k[0]]
F[60,x,k[0]] = F[48,x,k[0]]+F[59,x,k[0]]
F[60,x,k[0]] = F[1,x]+F[130,x,k[0]]+F[134,x]+F[135,x,k[0]]+F[61,x,k[0]]+F[66,x,k[0]]
F[62,x,k[0]] = F[1,x]+F[129,x,k[0]]+F[27,x,k[0]]+F[61,x,k[0]]+F[66,x,k[0]]+F[68,x,k[0]]
F[62,x,k[0]] = F[28,x,k[0]]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[13,x,k[0]]*F[21,x]*F[65,x,k[0]]
F[65,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[66,x,k[0]] = F[21,x]*F[67,x,k[0]]
F[67,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[68,x,k[0]] = F[21,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[122,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[121,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[75,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[35,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[37,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[118,x,k[0]]+F[120,x,k[0]]+F[6,x]+F[77,x,k[0]]+F[78,x,k[0]]
F[77,x,k[0]] = F[21,x]*F[71,x,k[0]]
F[78,x,k[0]] = F[21,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[76,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[21,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[113,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x]
F[84,x] = F[111,x]+F[6,x]+F[85,x]+F[91,x]
F[85,x] = F[86,x]
F[86,x] = F[21,x]*F[35,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[40,x,1]
F[89,x] = F[90,x,1]
F[24,x,k[0]] = F[40,x,k[0]]+F[90,x,k[0]]
F[91,x] = F[21,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[109,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[105,x]+F[107,x]+F[6,x]+F[96,x]+F[98,x]
F[96,x] = F[21,x]*F[35,x]*F[97,x]
F[97,x] = F[71,x,1]
F[98,x] = F[21,x]*F[35,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]+F[103,x]
F[101,x] = F[102,x]
F[102,x] = F[75,x,1]
F[103,x] = F[104,x]
F[104,x] = F[80,x,k[0]]
F[105,x] = F[106,x]*F[21,x]*F[35,x]
F[106,x] = F[89,x]
F[107,x] = F[108,x]
F[108,x] = F[21,x]*F[95,x]
F[109,x] = F[110,x]
F[110,x] = F[104,x]*F[35,x]
F[111,x] = F[112,x]
F[112,x] = F[21,x]*F[84,x]
F[113,x,k[0]] = F[114,x]
F[114,x] = F[115,x]*F[12,x]*F[21,x]
F[115,x] = F[116,x,1]
F[116,x,k[0]] = (F[117,x,k[0]]*k[0]-F[117,x,1])/(-1+k[0])
F[117,x,k[0]] = (-1+x^3*F[117,x,k[0]]^2*k[0]^3+6*x^2*F[117,x,k[0]]*k[0]^2+(-11*F[117,x,k[0]]+9)*x*k[0])*(x*F[117,x,k[0]]*k[0]-1)
F[118,x,k[0]] = F[119,x,k[0]]*F[21,x]
F[119,x,k[0]] = F[90,x,k[0]]
F[120,x,k[0]] = F[18,x,k[0]]*F[76,x,k[0]]
F[121,x,k[0]] = F[10,x]
F[122,x,k[0]] = F[123,x]
F[123,x] = F[124,x]+F[125,x]+F[127,x]+F[6,x]
F[124,x] = F[21,x]*F[87,x]
F[125,x] = F[126,x]*F[21,x]
F[126,x] = F[100,x]
F[127,x] = F[128,x]
F[128,x] = F[123,x]*F[21,x]
F[129,x,k[0]] = F[18,x,k[0]]*F[62,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[21,x]
F[131,x,k[0]] = 1/(-1+k[0])*(F[132,x,k[0]]*k[0]-F[132,x,1])
F[132,x,k[0]] = F[133,x,k[0]]+F[71,x,k[0]]
F[133,x,k[0]] = F[79,x,k[0]]
F[134,x] = F[12,x]*F[21,x]
F[135,x,k[0]] = F[18,x,k[0]]*F[60,x,k[0]]
F[136,x] = F[137,x]+F[35,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[21,x]*F[35,x]
F[139,x] = F[88,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[18,x,k[0]]*F[73,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[144,x,k[0]] = F[18,x,k[0]]*F[28,x,k[0]]
F[145,x,k[0]] = F[21,x]*F[67,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[21,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[24,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[21,x]
F[150,x,k[0]] = F[151,x,k[0]]+F[264,x,k[0]]
F[152,x,k[0]] = F[151,x,k[0]]*F[21,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]*F[21,x]
F[155,x,k[0]] = F[154,x,k[0]]+F[254,x,k[0]]+F[261,x,k[0]]+F[263,x,k[0]]+F[6,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[240,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[160,x,k[0]]+F[239,x,k[0]]+F[6,x]
F[157,x,k[0]] = F[158,x,k[0]]*F[21,x]
F[158,x,k[0]] = F[159,x,k[0]]+F[45,x,k[0]]
F[159,x,k[0]] = F[22,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]*F[21,x]
F[161,x,k[0]] = F[162,x,k[0]]+F[236,x,k[0]]+F[237,x,k[0]]+F[238,x,k[0]]+F[6,x]
F[162,x,k[0]] = F[163,x,k[0]]*F[21,x]
F[164,x,k[0]] = F[163,x,k[0]]*F[21,x]
F[165,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[223,x,k[0]]+F[227,x,k[0]]+F[235,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[71,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]*F[21,x]*F[71,x,k[0]]
F[168,x,k[0]] = F[1,x]+F[169,x,k[0]]+F[182,x,k[0]]+F[216,x,k[0]]+F[222,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]*F[21,x]
F[170,x,k[0]] = F[1,x]+F[171,x,k[0]]+F[174,x,k[0]]+F[181,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[21,x]
F[172,x,k[0]] = F[170,x,k[0]]+F[173,x,k[0]]
F[173,x,k[0]] = F[137,x]
F[174,x,k[0]] = F[175,x,k[0]]*F[21,x]
F[176,x,k[0]] = F[175,x,k[0]]*F[21,x]
F[40,x,k[0]] = F[1,x]+F[176,x,k[0]]+F[177,x,k[0]]+F[178,x,k[0]]
F[177,x,k[0]] = F[172,x,k[0]]*F[21,x]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[18,x,k[0]]*F[180,x,k[0]]
F[180,x,k[0]] = F[40,x,k[0]]
F[181,x,k[0]] = F[170,x,k[0]]*F[18,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[183,x,k[0]] = F[168,x,k[0]]+F[184,x,k[0]]
F[184,x,k[0]] = F[185,x]
F[185,x] = F[186,x]*F[21,x]
F[186,x] = F[187,x]+F[215,x]
F[187,x] = F[188,x]*F[35,x]
F[188,x] = F[189,x,1]
F[189,x,k[0]] = F[190,x,k[0]]+F[40,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]*F[21,x]
F[192,x,k[0]] = F[193,x,k[0]]
F[194,x,k[0]] = F[193,x,k[0]]*F[21,x]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]+F[200,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[198,x,k[0]]+F[199,x,k[0]]+F[6,x]
F[197,x,k[0]] = F[21,x]*F[73,x,k[0]]
F[198,x,k[0]] = F[18,x,k[0]]*F[196,x,k[0]]
F[199,x,k[0]] = F[195,x,k[0]]*F[21,x]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[21,x]
F[202,x,k[0]] = F[203,x,k[0]]+F[210,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]+F[205,x,k[0]]
F[204,x,k[0]] = F[180,x,k[0]]*F[196,x,k[0]]
F[205,x,k[0]] = F[206,x]*F[208,x,k[0]]
F[206,x] = F[207,x]
F[207,x] = F[115,x]*F[21,x]
F[208,x,k[0]] = F[209,x,k[0]]
F[209,x,k[0]] = (F[39,x,k[0]]-F[39,x,1])/(-1+k[0])
F[210,x,k[0]] = F[211,x,k[0]]+F[212,x,k[0]]
F[211,x,k[0]] = F[195,x,k[0]]*F[73,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]*F[35,x]
F[214,x,k[0]] = F[195,x,k[0]]+F[213,x,k[0]]
F[214,x,k[0]] = (F[195,x,k[0]]*k[0]-F[195,x,1])/(-1+k[0])
F[215,x] = F[206,x]*F[88,x]
F[216,x,k[0]] = F[21,x]*F[217,x,k[0]]
F[218,x,k[0]] = F[21,x]*F[217,x,k[0]]
F[189,x,k[0]] = F[1,x]+F[218,x,k[0]]+F[219,x,k[0]]+F[220,x,k[0]]+F[221,x,k[0]]
F[219,x,k[0]] = F[21,x]*F[40,x,k[0]]
F[220,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[221,x,k[0]] = F[18,x,k[0]]*F[189,x,k[0]]
F[222,x,k[0]] = F[168,x,k[0]]*F[18,x,k[0]]
F[223,x,k[0]] = F[21,x]*F[224,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]+F[234,x,k[0]]
F[225,x,k[0]] = F[1,x]+F[226,x,k[0]]+F[227,x,k[0]]+F[228,x,k[0]]+F[233,x,k[0]]
F[226,x,k[0]] = F[132,x,k[0]]*F[21,x]
F[227,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[228,x,k[0]] = F[21,x]*F[229,x,k[0]]
F[230,x,k[0]] = F[21,x]*F[229,x,k[0]]
F[48,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[230,x,k[0]]+F[231,x,k[0]]+F[232,x,k[0]]
F[231,x,k[0]] = F[132,x,k[0]]*F[21,x]
F[232,x,k[0]] = F[18,x,k[0]]*F[48,x,k[0]]
F[233,x,k[0]] = F[18,x,k[0]]*F[225,x,k[0]]
F[234,x,k[0]] = F[133,x,k[0]]
F[235,x,k[0]] = F[165,x,k[0]]*F[18,x,k[0]]
F[236,x,k[0]] = F[119,x,k[0]]*F[21,x]
F[237,x,k[0]] = F[21,x]*F[79,x,k[0]]
F[238,x,k[0]] = F[161,x,k[0]]*F[18,x,k[0]]
F[239,x,k[0]] = F[156,x,k[0]]*F[18,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]
F[241,x,k[0]] = F[21,x]*F[242,x,k[0]]
F[242,x,k[0]] = F[243,x,k[0]]+F[247,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]*F[246,x,k[0]]
F[245,x,k[0]] = F[161,x,k[0]]
F[246,x,k[0]] = F[73,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]*F[253,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[251,x,k[0]]+F[252,x,k[0]]+F[6,x]
F[250,x,k[0]] = F[21,x]*F[72,x,k[0]]
F[251,x,k[0]] = F[190,x,k[0]]*F[21,x]
F[252,x,k[0]] = F[18,x,k[0]]*F[249,x,k[0]]
F[253,x,k[0]] = F[48,x,k[0]]
F[254,x,k[0]] = F[21,x]*F[255,x,k[0]]
F[255,x,k[0]] = F[165,x,k[0]]+F[256,x,k[0]]
F[256,x,k[0]] = F[257,x,k[0]]
F[165,x,k[0]] = F[257,x,k[0]]+F[258,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[72,x,k[0]]
F[259,x,k[0]] = F[260,x,k[0]]
F[260,x,k[0]] = F[170,x,k[0]]*F[21,x]*F[72,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]
F[262,x,k[0]] = F[21,x]*F[76,x,k[0]]
F[263,x,k[0]] = F[155,x,k[0]]*F[18,x,k[0]]
F[264,x,k[0]] = (F[265,x,k[0]]-F[265,x,1])/(-1+k[0])
F[265,x,k[0]] = F[266,x,k[0]]+F[312,x,k[0]]
F[266,x,k[0]] = F[267,x,k[0]]*F[35,x]
F[163,x,k[0]] = F[267,x,k[0]]+F[268,x]
F[268,x] = 1/F[21,x]*F[269,x]
F[269,x] = -F[1,x]-F[295,x]-F[307,x]+F[270,x]
F[270,x] = F[271,x]+F[296,x]
F[271,x] = F[1,x]+F[272,x]+F[295,x]
F[272,x] = F[21,x]*F[273,x]
F[273,x] = 1/F[21,x]*F[274,x]
F[274,x] = -F[1,x]-F[275,x]+F[4,x]
F[275,x] = F[21,x]*F[276,x]
F[276,x] = F[1,x]+F[277,x]+F[281,x]+F[287,x]
F[277,x] = F[21,x]*F[278,x]
F[278,x] = F[126,x]+F[279,x]
F[279,x] = F[1,x]+F[280,x]+F[281,x]+F[282,x]
F[280,x] = F[226,x,1]
F[281,x] = F[21,x]*F[87,x]
F[282,x] = F[21,x]*F[283,x]
F[283,x] = F[279,x]+F[284,x]
F[284,x] = F[285,x]
F[285,x] = F[21,x]*F[286,x]*F[35,x]
F[286,x] = F[229,x,1]
F[287,x] = F[21,x]*F[288,x]
F[288,x] = F[276,x]+F[289,x]
F[289,x] = F[290,x]
F[290,x] = F[21,x]*F[291,x]
F[291,x] = F[292,x]+F[294,x]
F[292,x] = F[293,x]*F[35,x]
F[293,x] = F[163,x,1]
F[294,x] = F[206,x]*F[286,x]
F[295,x] = F[21,x]*F[276,x]
F[296,x] = F[297,x]
F[297,x] = F[21,x]*F[271,x]*F[298,x]
F[298,x] = F[299,x]+F[300,x]
F[299,x] = F[206,x]+F[35,x]
F[300,x] = F[301,x]
F[301,x] = F[21,x]*F[302,x]
F[302,x] = F[303,x]+F[306,x]
F[303,x] = F[304,x]*F[35,x]
F[304,x] = F[305,x,1]
F[305,x,k[0]] = F[180,x,k[0]]+F[195,x,k[0]]
F[306,x] = F[139,x]*F[206,x]
F[307,x] = F[308,x]
F[308,x] = F[21,x]*F[309,x]
F[309,x] = F[273,x]+F[310,x]
F[310,x] = F[271,x]*F[311,x]
F[311,x] = x*((1+F[311,x])^3*x^3+5*(1+F[311,x])^2*x^2+(-11*F[311,x]^2-19*F[311,x]-8)*x+10*F[311,x]+1)
F[312,x,k[0]] = F[206,x]*F[313,x,k[0]]
F[229,x,k[0]] = F[313,x,k[0]]+F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[136,x]*F[271,x]
F[316,x,k[0]] = F[133,x,k[0]]*F[21,x]
F[317,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[318,x] = F[21,x]*F[319,x]
F[319,x] = F[320,x]+F[5,x]
F[320,x] = F[321,x]
F[321,x] = F[21,x]*F[322,x]
F[322,x] = F[323,x]+F[331,x]
F[323,x] = F[324,x]+F[326,x]+F[328,x]+F[329,x]+F[6,x]
F[324,x] = F[325,x]
F[325,x] = F[21,x]*F[293,x]*F[35,x]
F[326,x] = F[327,x]
F[327,x] = F[106,x]*F[21,x]*F[35,x]
F[328,x] = F[21,x]*F[93,x]
F[329,x] = F[330,x]
F[330,x] = F[21,x]*F[323,x]
F[331,x] = F[332,x]
F[332,x] = F[115,x]*F[21,x]*F[333,x]
F[333,x] = F[48,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{318}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{123}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{316}\! \left(x , y\right)+F_{317}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{146}\! \left(x , y\right)+F_{235}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{34}\! \left(x , y\right) = -\frac{-F_{13}\! \left(x , y\right) y +F_{13}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x \right) = x^{4} F_{35} \left(x \right)^{3}+5 x^{3} F_{35} \left(x \right)^{2}-11 x^{2} F_{35} \left(x \right)^{2}+3 x^{2} F_{35}\! \left(x \right)+10 x F_{35}\! \left(x \right)-9 x +1
F_{36}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{35}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{134}\! \left(x \right)+F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{66}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{111}\! \left(x \right)+F_{6}\! \left(x \right)+F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{89}\! \left(x \right) = F_{90}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{109}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{6}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{98}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{103}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{75}\! \left(x , 1\right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{80}\! \left(x , y\right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{106}\! \left(x \right) = F_{89}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{21}\! \left(x \right) F_{95}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{104}\! \left(x \right) F_{35}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x , 1\right)
F_{116}\! \left(x , y\right) = -\frac{-F_{117}\! \left(x , y\right) y +F_{117}\! \left(x , 1\right)}{-1+y}
F_{117}\! \left(x , y\right) = y^{4} x^{4} F_{117}\! \left(x , y\right)^{3}+5 x^{3} F_{117}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{117}\! \left(x , y\right)^{2}+3 x^{2} F_{117}\! \left(x , y\right) y^{2}+10 x F_{117}\! \left(x , y\right) y -9 y x +1
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{10}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)+F_{6}\! \left(x \right)
F_{124}\! \left(x \right) = F_{21}\! \left(x \right) F_{87}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{21}\! \left(x \right)
F_{126}\! \left(x \right) = F_{100}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right) F_{21}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{131}\! \left(x , y\right) = -\frac{-F_{132}\! \left(x , y\right) y +F_{132}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{35}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{139}\! \left(x \right) = F_{88}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{264}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{254}\! \left(x , y\right)+F_{261}\! \left(x , y\right)+F_{263}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{239}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{236}\! \left(x , y\right)+F_{237}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{223}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{235}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{21}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{169}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{216}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{171}\! \left(x , y\right)+F_{174}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{137}\! \left(x \right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{21}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{215}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{35}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x , 1\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{198}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{115}\! \left(x \right) F_{21}\! \left(x \right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = -\frac{-F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = -\frac{-y F_{195}\! \left(x , y\right)+F_{195}\! \left(x , 1\right)}{-1+y}
F_{215}\! \left(x \right) = F_{206}\! \left(x \right) F_{88}\! \left(x \right)
F_{216}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{218}\! \left(x , y\right)+F_{219}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{189}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{226}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{227}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{230}\! \left(x , y\right)+F_{231}\! \left(x , y\right)+F_{232}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{232}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{225}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{242}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{243}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right) F_{246}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right) F_{253}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)+F_{252}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{250}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{249}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{257}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{21}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = -\frac{-F_{265}\! \left(x , y\right)+F_{265}\! \left(x , 1\right)}{-1+y}
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{312}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{267}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{267}\! \left(x , y\right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = \frac{F_{269}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{269}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{295}\! \left(x \right)-F_{307}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{296}\! \left(x \right)
F_{271}\! \left(x \right) = F_{1}\! \left(x \right)+F_{272}\! \left(x \right)+F_{295}\! \left(x \right)
F_{272}\! \left(x \right) = F_{21}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = \frac{F_{274}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{274}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{275}\! \left(x \right)+F_{4}\! \left(x \right)
F_{275}\! \left(x \right) = F_{21}\! \left(x \right) F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{1}\! \left(x \right)+F_{277}\! \left(x \right)+F_{281}\! \left(x \right)+F_{287}\! \left(x \right)
F_{277}\! \left(x \right) = F_{21}\! \left(x \right) F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = F_{126}\! \left(x \right)+F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{1}\! \left(x \right)+F_{280}\! \left(x \right)+F_{281}\! \left(x \right)+F_{282}\! \left(x \right)
F_{280}\! \left(x \right) = F_{226}\! \left(x , 1\right)
F_{281}\! \left(x \right) = F_{21}\! \left(x \right) F_{87}\! \left(x \right)
F_{282}\! \left(x \right) = F_{21}\! \left(x \right) F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{279}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{21}\! \left(x \right) F_{286}\! \left(x \right) F_{35}\! \left(x \right)
F_{286}\! \left(x \right) = F_{229}\! \left(x , 1\right)
F_{287}\! \left(x \right) = F_{21}\! \left(x \right) F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{276}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{21}\! \left(x \right) F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{294}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x \right) F_{35}\! \left(x \right)
F_{293}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{294}\! \left(x \right) = F_{206}\! \left(x \right) F_{286}\! \left(x \right)
F_{295}\! \left(x \right) = F_{21}\! \left(x \right) F_{276}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{21}\! \left(x \right) F_{271}\! \left(x \right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{300}\! \left(x \right)
F_{299}\! \left(x \right) = F_{206}\! \left(x \right)+F_{35}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{21}\! \left(x \right) F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)+F_{306}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right) F_{35}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x , 1\right)
F_{305}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{306}\! \left(x \right) = F_{139}\! \left(x \right) F_{206}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{21}\! \left(x \right) F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{273}\! \left(x \right)+F_{310}\! \left(x \right)
F_{310}\! \left(x \right) = F_{271}\! \left(x \right) F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = x^{4} F_{311} \left(x \right)^{3}+3 x^{4} F_{311} \left(x \right)^{2}+3 x^{4} F_{311}\! \left(x \right)+5 x^{3} F_{311} \left(x \right)^{2}+x^{4}+10 x^{3} F_{311}\! \left(x \right)-11 x^{2} F_{311} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{311}\! \left(x \right)-8 x^{2}+10 x F_{311}\! \left(x \right)+x
F_{312}\! \left(x , y\right) = F_{206}\! \left(x \right) F_{313}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{313}\! \left(x , y\right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{136}\! \left(x \right) F_{271}\! \left(x \right)
F_{316}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{317}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{318}\! \left(x \right) = F_{21}\! \left(x \right) F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)+F_{5}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{21}\! \left(x \right) F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right)+F_{331}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)+F_{326}\! \left(x \right)+F_{328}\! \left(x \right)+F_{329}\! \left(x \right)+F_{6}\! \left(x \right)
F_{324}\! \left(x \right) = F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{21}\! \left(x \right) F_{293}\! \left(x \right) F_{35}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{106}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{328}\! \left(x \right) = F_{21}\! \left(x \right) F_{93}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{21}\! \left(x \right) F_{323}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{115}\! \left(x \right) F_{21}\! \left(x \right) F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{48}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_318(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_21(x)*F_8(x))
Eq(F_8(x), F_123(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_21(x)*F_35(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0) + F_22(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_13(x, k_0)*F_15(x, k_0)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_23(x, k_0) + F_316(x, k_0) + F_317(x, k_0) + F_6(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_145(x, k_0) + F_146(x, k_0) + F_235(x, k_0) + F_25(x, k_0))
Eq(F_25(x, k_0), F_21(x)*F_26(x, k_0))
Eq(F_27(x, k_0), F_21(x)*F_26(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_144(x, k_0) + F_27(x, k_0) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_28(x, k_0), F_142(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_14(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_36(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_35(x))
Eq(F_34(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_35(x), x**4*F_35(x)**3 + x**2*(5*x - 11)*F_35(x)**2 - 9*x + (3*x**2 + 10*x)*F_35(x) + 1)
Eq(F_36(x, k_0), F_13(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_140(x, k_0) + F_38(x, k_0) + F_6(x))
Eq(F_38(x, k_0), F_21(x)*F_39(x, k_0))
Eq(F_40(x, k_0), F_136(x) + F_39(x, k_0))
Eq(F_41(x, k_0), F_13(x, k_0)*F_21(x)*F_40(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_44(x, k_0), F_29(x, k_0) + F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_50(x, k_0))
Eq(F_45(x, k_0), F_14(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_49(x, k_0) + 2*F_6(x))
Eq(F_47(x, k_0), F_21(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_13(x, k_0) + F_42(x, k_0))
Eq(F_49(x, k_0), F_18(x, k_0)*F_46(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_21(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_58(x, k_0))
Eq(F_54(x, k_0), F_48(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_57(x, k_0) + F_6(x))
Eq(F_56(x, k_0), F_21(x)*F_40(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_55(x, k_0))
Eq(F_58(x, k_0), F_35(x)*F_59(x, k_0))
Eq(F_60(x, k_0), F_48(x, k_0) + F_59(x, k_0))
Eq(F_60(x, k_0), F_1(x) + F_130(x, k_0) + F_134(x) + F_135(x, k_0) + F_61(x, k_0) + F_66(x, k_0))
Eq(F_62(x, k_0), F_1(x) + F_129(x, k_0) + F_27(x, k_0) + F_61(x, k_0) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_62(x, k_0), F_28(x, k_0) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_13(x, k_0)*F_21(x)*F_65(x, k_0))
Eq(F_65(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_66(x, k_0), F_21(x)*F_67(x, k_0))
Eq(F_67(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_21(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_122(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_121(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_75(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_35(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_37(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_118(x, k_0) + F_120(x, k_0) + F_6(x) + F_77(x, k_0) + F_78(x, k_0))
Eq(F_77(x, k_0), F_21(x)*F_71(x, k_0))
Eq(F_78(x, k_0), F_21(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_76(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_21(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_113(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x))
Eq(F_84(x), F_111(x) + F_6(x) + F_85(x) + F_91(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_21(x)*F_35(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_40(x, 1))
Eq(F_89(x), F_90(x, 1))
Eq(F_24(x, k_0), F_40(x, k_0) + F_90(x, k_0))
Eq(F_91(x), F_21(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_109(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_105(x) + F_107(x) + F_6(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_21(x)*F_35(x)*F_97(x))
Eq(F_97(x), F_71(x, 1))
Eq(F_98(x), F_21(x)*F_35(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) + F_103(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_75(x, 1))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_80(x, k_0))
Eq(F_105(x), F_106(x)*F_21(x)*F_35(x))
Eq(F_106(x), F_89(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_21(x)*F_95(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_104(x)*F_35(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_21(x)*F_84(x))
Eq(F_113(x, k_0), F_114(x))
Eq(F_114(x), F_115(x)*F_12(x)*F_21(x))
Eq(F_115(x), F_116(x, 1))
Eq(F_116(x, k_0), (-k_0*F_117(x, k_0) + F_117(x, 1))/(1 - k_0))
Eq(F_117(x, k_0), k_0**4*x**4*F_117(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_117(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_117(x, k_0) + 1)
Eq(F_118(x, k_0), F_119(x, k_0)*F_21(x))
Eq(F_119(x, k_0), F_90(x, k_0))
Eq(F_120(x, k_0), F_18(x, k_0)*F_76(x, k_0))
Eq(F_121(x, k_0), F_10(x))
Eq(F_122(x, k_0), F_123(x))
Eq(F_123(x), F_124(x) + F_125(x) + F_127(x) + F_6(x))
Eq(F_124(x), F_21(x)*F_87(x))
Eq(F_125(x), F_126(x)*F_21(x))
Eq(F_126(x), F_100(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_123(x)*F_21(x))
Eq(F_129(x, k_0), F_18(x, k_0)*F_62(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_21(x))
Eq(F_131(x, k_0), (k_0*F_132(x, k_0) - F_132(x, 1))/(k_0 - 1))
Eq(F_132(x, k_0), F_133(x, k_0) + F_71(x, k_0))
Eq(F_133(x, k_0), F_79(x, k_0))
Eq(F_134(x), F_12(x)*F_21(x))
Eq(F_135(x, k_0), F_18(x, k_0)*F_60(x, k_0))
Eq(F_136(x), F_137(x) + F_35(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_21(x)*F_35(x))
Eq(F_139(x), F_88(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_18(x, k_0)*F_73(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), F_18(x, k_0)*F_28(x, k_0))
Eq(F_145(x, k_0), F_21(x)*F_67(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_21(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_24(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_21(x))
Eq(F_150(x, k_0), F_151(x, k_0) + F_264(x, k_0))
Eq(F_152(x, k_0), F_151(x, k_0)*F_21(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0)*F_21(x))
Eq(F_155(x, k_0), F_154(x, k_0) + F_254(x, k_0) + F_261(x, k_0) + F_263(x, k_0) + F_6(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_240(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_160(x, k_0) + F_239(x, k_0) + F_6(x))
Eq(F_157(x, k_0), F_158(x, k_0)*F_21(x))
Eq(F_158(x, k_0), F_159(x, k_0) + F_45(x, k_0))
Eq(F_159(x, k_0), F_22(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0)*F_21(x))
Eq(F_161(x, k_0), F_162(x, k_0) + F_236(x, k_0) + F_237(x, k_0) + F_238(x, k_0) + F_6(x))
Eq(F_162(x, k_0), F_163(x, k_0)*F_21(x))
Eq(F_164(x, k_0), F_163(x, k_0)*F_21(x))
Eq(F_165(x, k_0), F_1(x) + F_164(x, k_0) + F_223(x, k_0) + F_227(x, k_0) + F_235(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_71(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0)*F_21(x)*F_71(x, k_0))
Eq(F_168(x, k_0), F_1(x) + F_169(x, k_0) + F_182(x, k_0) + F_216(x, k_0) + F_222(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0)*F_21(x))
Eq(F_170(x, k_0), F_1(x) + F_171(x, k_0) + F_174(x, k_0) + F_181(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_21(x))
Eq(F_172(x, k_0), F_170(x, k_0) + F_173(x, k_0))
Eq(F_173(x, k_0), F_137(x))
Eq(F_174(x, k_0), F_175(x, k_0)*F_21(x))
Eq(F_176(x, k_0), F_175(x, k_0)*F_21(x))
Eq(F_40(x, k_0), F_1(x) + F_176(x, k_0) + F_177(x, k_0) + F_178(x, k_0))
Eq(F_177(x, k_0), F_172(x, k_0)*F_21(x))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_18(x, k_0)*F_180(x, k_0))
Eq(F_180(x, k_0), F_40(x, k_0))
Eq(F_181(x, k_0), F_170(x, k_0)*F_18(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_183(x, k_0), F_168(x, k_0) + F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x))
Eq(F_185(x), F_186(x)*F_21(x))
Eq(F_186(x), F_187(x) + F_215(x))
Eq(F_187(x), F_188(x)*F_35(x))
Eq(F_188(x), F_189(x, 1))
Eq(F_189(x, k_0), F_190(x, k_0) + F_40(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0)*F_21(x))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_194(x, k_0), F_193(x, k_0)*F_21(x))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0) + F_200(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_198(x, k_0) + F_199(x, k_0) + F_6(x))
Eq(F_197(x, k_0), F_21(x)*F_73(x, k_0))
Eq(F_198(x, k_0), F_18(x, k_0)*F_196(x, k_0))
Eq(F_199(x, k_0), F_195(x, k_0)*F_21(x))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0)*F_21(x))
Eq(F_202(x, k_0), F_203(x, k_0) + F_210(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_205(x, k_0))
Eq(F_204(x, k_0), F_180(x, k_0)*F_196(x, k_0))
Eq(F_205(x, k_0), F_206(x)*F_208(x, k_0))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_115(x)*F_21(x))
Eq(F_208(x, k_0), F_209(x, k_0))
Eq(F_209(x, k_0), -F_39(x, k_0) + (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_210(x, k_0), F_211(x, k_0) + F_212(x, k_0))
Eq(F_211(x, k_0), F_195(x, k_0)*F_73(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0)*F_35(x))
Eq(F_214(x, k_0), F_195(x, k_0) + F_213(x, k_0))
Eq(F_214(x, k_0), (-k_0*F_195(x, k_0) + F_195(x, 1))/(1 - k_0))
Eq(F_215(x), F_206(x)*F_88(x))
Eq(F_216(x, k_0), F_21(x)*F_217(x, k_0))
Eq(F_218(x, k_0), F_21(x)*F_217(x, k_0))
Eq(F_189(x, k_0), F_1(x) + F_218(x, k_0) + F_219(x, k_0) + F_220(x, k_0) + F_221(x, k_0))
Eq(F_219(x, k_0), F_21(x)*F_40(x, k_0))
Eq(F_220(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_221(x, k_0), F_18(x, k_0)*F_189(x, k_0))
Eq(F_222(x, k_0), F_168(x, k_0)*F_18(x, k_0))
Eq(F_223(x, k_0), F_21(x)*F_224(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0) + F_234(x, k_0))
Eq(F_225(x, k_0), F_1(x) + F_226(x, k_0) + F_227(x, k_0) + F_228(x, k_0) + F_233(x, k_0))
Eq(F_226(x, k_0), F_132(x, k_0)*F_21(x))
Eq(F_227(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_228(x, k_0), F_21(x)*F_229(x, k_0))
Eq(F_230(x, k_0), F_21(x)*F_229(x, k_0))
Eq(F_48(x, k_0), F_1(x) + F_23(x, k_0) + F_230(x, k_0) + F_231(x, k_0) + F_232(x, k_0))
Eq(F_231(x, k_0), F_132(x, k_0)*F_21(x))
Eq(F_232(x, k_0), F_18(x, k_0)*F_48(x, k_0))
Eq(F_233(x, k_0), F_18(x, k_0)*F_225(x, k_0))
Eq(F_234(x, k_0), F_133(x, k_0))
Eq(F_235(x, k_0), F_165(x, k_0)*F_18(x, k_0))
Eq(F_236(x, k_0), F_119(x, k_0)*F_21(x))
Eq(F_237(x, k_0), F_21(x)*F_79(x, k_0))
Eq(F_238(x, k_0), F_161(x, k_0)*F_18(x, k_0))
Eq(F_239(x, k_0), F_156(x, k_0)*F_18(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0))
Eq(F_241(x, k_0), F_21(x)*F_242(x, k_0))
Eq(F_242(x, k_0), F_243(x, k_0) + F_247(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0)*F_246(x, k_0))
Eq(F_245(x, k_0), F_161(x, k_0))
Eq(F_246(x, k_0), F_73(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0)*F_253(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_251(x, k_0) + F_252(x, k_0) + F_6(x))
Eq(F_250(x, k_0), F_21(x)*F_72(x, k_0))
Eq(F_251(x, k_0), F_190(x, k_0)*F_21(x))
Eq(F_252(x, k_0), F_18(x, k_0)*F_249(x, k_0))
Eq(F_253(x, k_0), F_48(x, k_0))
Eq(F_254(x, k_0), F_21(x)*F_255(x, k_0))
Eq(F_255(x, k_0), F_165(x, k_0) + F_256(x, k_0))
Eq(F_256(x, k_0), F_257(x, k_0))
Eq(F_165(x, k_0), F_257(x, k_0) + F_258(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_72(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0))
Eq(F_260(x, k_0), F_170(x, k_0)*F_21(x)*F_72(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0))
Eq(F_262(x, k_0), F_21(x)*F_76(x, k_0))
Eq(F_263(x, k_0), F_155(x, k_0)*F_18(x, k_0))
Eq(F_264(x, k_0), -F_265(x, k_0) + (k_0*F_265(x, k_0) - F_265(x, 1))/(k_0 - 1))
Eq(F_265(x, k_0), F_266(x, k_0) + F_312(x, k_0))
Eq(F_266(x, k_0), F_267(x, k_0)*F_35(x))
Eq(F_163(x, k_0), F_267(x, k_0) + F_268(x))
Eq(F_268(x), F_269(x)/F_21(x))
Eq(F_269(x), -F_1(x) + F_270(x) - F_295(x) - F_307(x))
Eq(F_270(x), F_271(x) + F_296(x))
Eq(F_271(x), F_1(x) + F_272(x) + F_295(x))
Eq(F_272(x), F_21(x)*F_273(x))
Eq(F_273(x), F_274(x)/F_21(x))
Eq(F_274(x), -F_1(x) - F_275(x) + F_4(x))
Eq(F_275(x), F_21(x)*F_276(x))
Eq(F_276(x), F_1(x) + F_277(x) + F_281(x) + F_287(x))
Eq(F_277(x), F_21(x)*F_278(x))
Eq(F_278(x), F_126(x) + F_279(x))
Eq(F_279(x), F_1(x) + F_280(x) + F_281(x) + F_282(x))
Eq(F_280(x), F_226(x, 1))
Eq(F_281(x), F_21(x)*F_87(x))
Eq(F_282(x), F_21(x)*F_283(x))
Eq(F_283(x), F_279(x) + F_284(x))
Eq(F_284(x), F_285(x))
Eq(F_285(x), F_21(x)*F_286(x)*F_35(x))
Eq(F_286(x), F_229(x, 1))
Eq(F_287(x), F_21(x)*F_288(x))
Eq(F_288(x), F_276(x) + F_289(x))
Eq(F_289(x), F_290(x))
Eq(F_290(x), F_21(x)*F_291(x))
Eq(F_291(x), F_292(x) + F_294(x))
Eq(F_292(x), F_293(x)*F_35(x))
Eq(F_293(x), F_163(x, 1))
Eq(F_294(x), F_206(x)*F_286(x))
Eq(F_295(x), F_21(x)*F_276(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), F_21(x)*F_271(x)*F_298(x))
Eq(F_298(x), F_299(x) + F_300(x))
Eq(F_299(x), F_206(x) + F_35(x))
Eq(F_300(x), F_301(x))
Eq(F_301(x), F_21(x)*F_302(x))
Eq(F_302(x), F_303(x) + F_306(x))
Eq(F_303(x), F_304(x)*F_35(x))
Eq(F_304(x), F_305(x, 1))
Eq(F_305(x, k_0), F_180(x, k_0) + F_195(x, k_0))
Eq(F_306(x), F_139(x)*F_206(x))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_21(x)*F_309(x))
Eq(F_309(x), F_273(x) + F_310(x))
Eq(F_310(x), F_271(x)*F_311(x))
Eq(F_311(x), x**4*(F_311(x) + 1)**3 + x**2*(5*x - 11)*(F_311(x) + 1)**2 - 9*x + (F_311(x) + 1)*(3*x**2 + 10*x - 1) + F_311(x) + 1)
Eq(F_312(x, k_0), F_206(x)*F_313(x, k_0))
Eq(F_229(x, k_0), F_313(x, k_0) + F_314(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_136(x)*F_271(x))
Eq(F_316(x, k_0), F_133(x, k_0)*F_21(x))
Eq(F_317(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_318(x), F_21(x)*F_319(x))
Eq(F_319(x), F_320(x) + F_5(x))
Eq(F_320(x), F_321(x))
Eq(F_321(x), F_21(x)*F_322(x))
Eq(F_322(x), F_323(x) + F_331(x))
Eq(F_323(x), F_324(x) + F_326(x) + F_328(x) + F_329(x) + F_6(x))
Eq(F_324(x), F_325(x))
Eq(F_325(x), F_21(x)*F_293(x)*F_35(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_106(x)*F_21(x)*F_35(x))
Eq(F_328(x), F_21(x)*F_93(x))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_21(x)*F_323(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_115(x)*F_21(x)*F_333(x))
Eq(F_333(x), F_48(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]]}], "iterative": false}
Specification JSON:
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0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25403/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[318,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[21,x]*F[8,x]
F[8,x] = F[123,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[21,x]*F[35,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]+F[22,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[13,x,k[0]]*F[15,x,k[0]]*F[21,x]
F[21,x] = x
F[22,x,k[0]] = F[23,x,k[0]]+F[316,x,k[0]]+F[317,x,k[0]]+F[6,x]
F[23,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[145,x,k[0]]+F[146,x,k[0]]+F[235,x,k[0]]+F[25,x,k[0]]
F[25,x,k[0]] = F[21,x]*F[26,x,k[0]]
F[27,x,k[0]] = F[21,x]*F[26,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[144,x,k[0]]+F[27,x,k[0]]+F[66,x,k[0]]+F[68,x,k[0]]
F[28,x,k[0]] = F[142,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[14,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[36,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[35,x]
F[34,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[35,x] = (x*F[35,x]-1)*(-1+x^3*F[35,x]^2+6*x^2*F[35,x]+(-11*F[35,x]+9)*x)
F[36,x,k[0]] = F[13,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[140,x,k[0]]+F[38,x,k[0]]+F[6,x]
F[38,x,k[0]] = F[21,x]*F[39,x,k[0]]
F[40,x,k[0]] = F[136,x]+F[39,x,k[0]]
F[41,x,k[0]] = F[13,x,k[0]]*F[21,x]*F[40,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[44,x,k[0]] = F[29,x,k[0]]+F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[50,x,k[0]]
F[45,x,k[0]] = F[14,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = 2*F[6,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[47,x,k[0]] = F[21,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[13,x,k[0]]+F[42,x,k[0]]
F[49,x,k[0]] = F[18,x,k[0]]*F[46,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[21,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[58,x,k[0]]
F[54,x,k[0]] = F[48,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]+F[6,x]
F[56,x,k[0]] = F[21,x]*F[40,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[55,x,k[0]]
F[58,x,k[0]] = F[35,x]*F[59,x,k[0]]
F[60,x,k[0]] = F[48,x,k[0]]+F[59,x,k[0]]
F[60,x,k[0]] = F[1,x]+F[130,x,k[0]]+F[134,x]+F[135,x,k[0]]+F[61,x,k[0]]+F[66,x,k[0]]
F[62,x,k[0]] = F[1,x]+F[129,x,k[0]]+F[27,x,k[0]]+F[61,x,k[0]]+F[66,x,k[0]]+F[68,x,k[0]]
F[62,x,k[0]] = F[28,x,k[0]]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[13,x,k[0]]*F[21,x]*F[65,x,k[0]]
F[65,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[66,x,k[0]] = F[21,x]*F[67,x,k[0]]
F[67,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[68,x,k[0]] = F[21,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[122,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[121,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[75,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[35,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[37,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[118,x,k[0]]+F[120,x,k[0]]+F[6,x]+F[77,x,k[0]]+F[78,x,k[0]]
F[77,x,k[0]] = F[21,x]*F[71,x,k[0]]
F[78,x,k[0]] = F[21,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[76,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[21,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[113,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x]
F[84,x] = F[111,x]+F[6,x]+F[85,x]+F[91,x]
F[85,x] = F[86,x]
F[86,x] = F[21,x]*F[35,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[40,x,1]
F[89,x] = F[90,x,1]
F[24,x,k[0]] = F[40,x,k[0]]+F[90,x,k[0]]
F[91,x] = F[21,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[109,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[105,x]+F[107,x]+F[6,x]+F[96,x]+F[98,x]
F[96,x] = F[21,x]*F[35,x]*F[97,x]
F[97,x] = F[71,x,1]
F[98,x] = F[21,x]*F[35,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]+F[103,x]
F[101,x] = F[102,x]
F[102,x] = F[75,x,1]
F[103,x] = F[104,x]
F[104,x] = F[80,x,k[0]]
F[105,x] = F[106,x]*F[21,x]*F[35,x]
F[106,x] = F[89,x]
F[107,x] = F[108,x]
F[108,x] = F[21,x]*F[95,x]
F[109,x] = F[110,x]
F[110,x] = F[104,x]*F[35,x]
F[111,x] = F[112,x]
F[112,x] = F[21,x]*F[84,x]
F[113,x,k[0]] = F[114,x]
F[114,x] = F[115,x]*F[12,x]*F[21,x]
F[115,x] = F[116,x,1]
F[116,x,k[0]] = (F[117,x,k[0]]*k[0]-F[117,x,1])/(-1+k[0])
F[117,x,k[0]] = (x*F[117,x,k[0]]*k[0]-1)*(-1+x^3*F[117,x,k[0]]^2*k[0]^3+6*x^2*F[117,x,k[0]]*k[0]^2+(-11*F[117,x,k[0]]+9)*x*k[0])
F[118,x,k[0]] = F[119,x,k[0]]*F[21,x]
F[119,x,k[0]] = F[90,x,k[0]]
F[120,x,k[0]] = F[18,x,k[0]]*F[76,x,k[0]]
F[121,x,k[0]] = F[10,x]
F[122,x,k[0]] = F[123,x]
F[123,x] = F[124,x]+F[125,x]+F[127,x]+F[6,x]
F[124,x] = F[21,x]*F[87,x]
F[125,x] = F[126,x]*F[21,x]
F[126,x] = F[100,x]
F[127,x] = F[128,x]
F[128,x] = F[123,x]*F[21,x]
F[129,x,k[0]] = F[18,x,k[0]]*F[62,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[21,x]
F[131,x,k[0]] = 1/(-1+k[0])*(F[132,x,k[0]]*k[0]-F[132,x,1])
F[132,x,k[0]] = F[133,x,k[0]]+F[71,x,k[0]]
F[133,x,k[0]] = F[79,x,k[0]]
F[134,x] = F[12,x]*F[21,x]
F[135,x,k[0]] = F[18,x,k[0]]*F[60,x,k[0]]
F[136,x] = F[137,x]+F[35,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[21,x]*F[35,x]
F[139,x] = F[88,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[18,x,k[0]]*F[73,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[144,x,k[0]] = F[18,x,k[0]]*F[28,x,k[0]]
F[145,x,k[0]] = F[21,x]*F[67,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[21,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[24,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[21,x]
F[150,x,k[0]] = F[151,x,k[0]]+F[264,x,k[0]]
F[152,x,k[0]] = F[151,x,k[0]]*F[21,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]*F[21,x]
F[155,x,k[0]] = F[154,x,k[0]]+F[254,x,k[0]]+F[261,x,k[0]]+F[263,x,k[0]]+F[6,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[240,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[160,x,k[0]]+F[239,x,k[0]]+F[6,x]
F[157,x,k[0]] = F[158,x,k[0]]*F[21,x]
F[158,x,k[0]] = F[159,x,k[0]]+F[45,x,k[0]]
F[159,x,k[0]] = F[22,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]*F[21,x]
F[161,x,k[0]] = F[162,x,k[0]]+F[236,x,k[0]]+F[237,x,k[0]]+F[238,x,k[0]]+F[6,x]
F[162,x,k[0]] = F[163,x,k[0]]*F[21,x]
F[164,x,k[0]] = F[163,x,k[0]]*F[21,x]
F[165,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[223,x,k[0]]+F[227,x,k[0]]+F[235,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[71,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]*F[21,x]*F[71,x,k[0]]
F[168,x,k[0]] = F[1,x]+F[169,x,k[0]]+F[182,x,k[0]]+F[216,x,k[0]]+F[222,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]*F[21,x]
F[170,x,k[0]] = F[1,x]+F[171,x,k[0]]+F[174,x,k[0]]+F[181,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[21,x]
F[172,x,k[0]] = F[170,x,k[0]]+F[173,x,k[0]]
F[173,x,k[0]] = F[137,x]
F[174,x,k[0]] = F[175,x,k[0]]*F[21,x]
F[176,x,k[0]] = F[175,x,k[0]]*F[21,x]
F[40,x,k[0]] = F[1,x]+F[176,x,k[0]]+F[177,x,k[0]]+F[178,x,k[0]]
F[177,x,k[0]] = F[172,x,k[0]]*F[21,x]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[18,x,k[0]]*F[180,x,k[0]]
F[180,x,k[0]] = F[40,x,k[0]]
F[181,x,k[0]] = F[170,x,k[0]]*F[18,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[183,x,k[0]] = F[168,x,k[0]]+F[184,x,k[0]]
F[184,x,k[0]] = F[185,x]
F[185,x] = F[186,x]*F[21,x]
F[186,x] = F[187,x]+F[215,x]
F[187,x] = F[188,x]*F[35,x]
F[188,x] = F[189,x,1]
F[189,x,k[0]] = F[190,x,k[0]]+F[40,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]*F[21,x]
F[192,x,k[0]] = F[193,x,k[0]]
F[194,x,k[0]] = F[193,x,k[0]]*F[21,x]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]+F[200,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[198,x,k[0]]+F[199,x,k[0]]+F[6,x]
F[197,x,k[0]] = F[21,x]*F[73,x,k[0]]
F[198,x,k[0]] = F[18,x,k[0]]*F[196,x,k[0]]
F[199,x,k[0]] = F[195,x,k[0]]*F[21,x]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[21,x]
F[202,x,k[0]] = F[203,x,k[0]]+F[210,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]+F[205,x,k[0]]
F[204,x,k[0]] = F[180,x,k[0]]*F[196,x,k[0]]
F[205,x,k[0]] = F[206,x]*F[208,x,k[0]]
F[206,x] = F[207,x]
F[207,x] = F[115,x]*F[21,x]
F[208,x,k[0]] = F[209,x,k[0]]
F[209,x,k[0]] = (F[39,x,k[0]]-F[39,x,1])/(-1+k[0])
F[210,x,k[0]] = F[211,x,k[0]]+F[212,x,k[0]]
F[211,x,k[0]] = F[195,x,k[0]]*F[73,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]*F[35,x]
F[214,x,k[0]] = F[195,x,k[0]]+F[213,x,k[0]]
F[214,x,k[0]] = (F[195,x,k[0]]*k[0]-F[195,x,1])/(-1+k[0])
F[215,x] = F[206,x]*F[88,x]
F[216,x,k[0]] = F[21,x]*F[217,x,k[0]]
F[218,x,k[0]] = F[21,x]*F[217,x,k[0]]
F[189,x,k[0]] = F[1,x]+F[218,x,k[0]]+F[219,x,k[0]]+F[220,x,k[0]]+F[221,x,k[0]]
F[219,x,k[0]] = F[21,x]*F[40,x,k[0]]
F[220,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[221,x,k[0]] = F[18,x,k[0]]*F[189,x,k[0]]
F[222,x,k[0]] = F[168,x,k[0]]*F[18,x,k[0]]
F[223,x,k[0]] = F[21,x]*F[224,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]+F[234,x,k[0]]
F[225,x,k[0]] = F[1,x]+F[226,x,k[0]]+F[227,x,k[0]]+F[228,x,k[0]]+F[233,x,k[0]]
F[226,x,k[0]] = F[132,x,k[0]]*F[21,x]
F[227,x,k[0]] = F[21,x]*F[24,x,k[0]]
F[228,x,k[0]] = F[21,x]*F[229,x,k[0]]
F[230,x,k[0]] = F[21,x]*F[229,x,k[0]]
F[48,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[230,x,k[0]]+F[231,x,k[0]]+F[232,x,k[0]]
F[231,x,k[0]] = F[132,x,k[0]]*F[21,x]
F[232,x,k[0]] = F[18,x,k[0]]*F[48,x,k[0]]
F[233,x,k[0]] = F[18,x,k[0]]*F[225,x,k[0]]
F[234,x,k[0]] = F[133,x,k[0]]
F[235,x,k[0]] = F[165,x,k[0]]*F[18,x,k[0]]
F[236,x,k[0]] = F[119,x,k[0]]*F[21,x]
F[237,x,k[0]] = F[21,x]*F[79,x,k[0]]
F[238,x,k[0]] = F[161,x,k[0]]*F[18,x,k[0]]
F[239,x,k[0]] = F[156,x,k[0]]*F[18,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]
F[241,x,k[0]] = F[21,x]*F[242,x,k[0]]
F[242,x,k[0]] = F[243,x,k[0]]+F[247,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]*F[246,x,k[0]]
F[245,x,k[0]] = F[161,x,k[0]]
F[246,x,k[0]] = F[73,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]*F[253,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[251,x,k[0]]+F[252,x,k[0]]+F[6,x]
F[250,x,k[0]] = F[21,x]*F[72,x,k[0]]
F[251,x,k[0]] = F[190,x,k[0]]*F[21,x]
F[252,x,k[0]] = F[18,x,k[0]]*F[249,x,k[0]]
F[253,x,k[0]] = F[48,x,k[0]]
F[254,x,k[0]] = F[21,x]*F[255,x,k[0]]
F[255,x,k[0]] = F[165,x,k[0]]+F[256,x,k[0]]
F[256,x,k[0]] = F[257,x,k[0]]
F[165,x,k[0]] = F[257,x,k[0]]+F[258,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[72,x,k[0]]
F[259,x,k[0]] = F[260,x,k[0]]
F[260,x,k[0]] = F[170,x,k[0]]*F[21,x]*F[72,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]
F[262,x,k[0]] = F[21,x]*F[76,x,k[0]]
F[263,x,k[0]] = F[155,x,k[0]]*F[18,x,k[0]]
F[264,x,k[0]] = (F[265,x,k[0]]-F[265,x,1])/(-1+k[0])
F[265,x,k[0]] = F[266,x,k[0]]+F[312,x,k[0]]
F[266,x,k[0]] = F[267,x,k[0]]*F[35,x]
F[163,x,k[0]] = F[267,x,k[0]]+F[268,x]
F[268,x] = 1/F[21,x]*F[269,x]
F[269,x] = -F[1,x]-F[295,x]-F[307,x]+F[270,x]
F[270,x] = F[271,x]+F[296,x]
F[271,x] = F[1,x]+F[272,x]+F[295,x]
F[272,x] = F[21,x]*F[273,x]
F[273,x] = 1/F[21,x]*F[274,x]
F[274,x] = -F[1,x]-F[275,x]+F[4,x]
F[275,x] = F[21,x]*F[276,x]
F[276,x] = F[1,x]+F[277,x]+F[281,x]+F[287,x]
F[277,x] = F[21,x]*F[278,x]
F[278,x] = F[126,x]+F[279,x]
F[279,x] = F[1,x]+F[280,x]+F[281,x]+F[282,x]
F[280,x] = F[226,x,1]
F[281,x] = F[21,x]*F[87,x]
F[282,x] = F[21,x]*F[283,x]
F[283,x] = F[279,x]+F[284,x]
F[284,x] = F[285,x]
F[285,x] = F[21,x]*F[286,x]*F[35,x]
F[286,x] = F[229,x,1]
F[287,x] = F[21,x]*F[288,x]
F[288,x] = F[276,x]+F[289,x]
F[289,x] = F[290,x]
F[290,x] = F[21,x]*F[291,x]
F[291,x] = F[292,x]+F[294,x]
F[292,x] = F[293,x]*F[35,x]
F[293,x] = F[163,x,1]
F[294,x] = F[206,x]*F[286,x]
F[295,x] = F[21,x]*F[276,x]
F[296,x] = F[297,x]
F[297,x] = F[21,x]*F[271,x]*F[298,x]
F[298,x] = F[299,x]+F[300,x]
F[299,x] = F[206,x]+F[35,x]
F[300,x] = F[301,x]
F[301,x] = F[21,x]*F[302,x]
F[302,x] = F[303,x]+F[306,x]
F[303,x] = F[304,x]*F[35,x]
F[304,x] = F[305,x,1]
F[305,x,k[0]] = F[180,x,k[0]]+F[195,x,k[0]]
F[306,x] = F[139,x]*F[206,x]
F[307,x] = F[308,x]
F[308,x] = F[21,x]*F[309,x]
F[309,x] = F[273,x]+F[310,x]
F[310,x] = F[271,x]*F[311,x]
F[311,x] = x*((1+F[311,x])^3*x^3+5*(1+F[311,x])^2*x^2+(-11*F[311,x]^2-19*F[311,x]-8)*x+10*F[311,x]+1)
F[312,x,k[0]] = F[206,x]*F[313,x,k[0]]
F[229,x,k[0]] = F[313,x,k[0]]+F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[136,x]*F[271,x]
F[316,x,k[0]] = F[133,x,k[0]]*F[21,x]
F[317,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[318,x] = F[21,x]*F[319,x]
F[319,x] = F[320,x]+F[5,x]
F[320,x] = F[321,x]
F[321,x] = F[21,x]*F[322,x]
F[322,x] = F[323,x]+F[331,x]
F[323,x] = F[324,x]+F[326,x]+F[328,x]+F[329,x]+F[6,x]
F[324,x] = F[325,x]
F[325,x] = F[21,x]*F[293,x]*F[35,x]
F[326,x] = F[327,x]
F[327,x] = F[106,x]*F[21,x]*F[35,x]
F[328,x] = F[21,x]*F[93,x]
F[329,x] = F[330,x]
F[330,x] = F[21,x]*F[323,x]
F[331,x] = F[332,x]
F[332,x] = F[115,x]*F[21,x]*F[333,x]
F[333,x] = F[48,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{318}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{123}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{316}\! \left(x , y\right)+F_{317}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{146}\! \left(x , y\right)+F_{235}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{34}\! \left(x , y\right) = -\frac{-F_{13}\! \left(x , y\right) y +F_{13}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x \right) = x^{4} F_{35} \left(x \right)^{3}+5 x^{3} F_{35} \left(x \right)^{2}-11 x^{2} F_{35} \left(x \right)^{2}+3 x^{2} F_{35}\! \left(x \right)+10 x F_{35}\! \left(x \right)-9 x +1
F_{36}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{35}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{134}\! \left(x \right)+F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{66}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{111}\! \left(x \right)+F_{6}\! \left(x \right)+F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{89}\! \left(x \right) = F_{90}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{109}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{6}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{98}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{103}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{75}\! \left(x , 1\right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{80}\! \left(x , y\right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{106}\! \left(x \right) = F_{89}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{21}\! \left(x \right) F_{95}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{104}\! \left(x \right) F_{35}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x , 1\right)
F_{116}\! \left(x , y\right) = -\frac{-F_{117}\! \left(x , y\right) y +F_{117}\! \left(x , 1\right)}{-1+y}
F_{117}\! \left(x , y\right) = y^{4} x^{4} F_{117}\! \left(x , y\right)^{3}+5 x^{3} F_{117}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{117}\! \left(x , y\right)^{2}+3 x^{2} F_{117}\! \left(x , y\right) y^{2}+10 x F_{117}\! \left(x , y\right) y -9 y x +1
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{10}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)+F_{6}\! \left(x \right)
F_{124}\! \left(x \right) = F_{21}\! \left(x \right) F_{87}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{21}\! \left(x \right)
F_{126}\! \left(x \right) = F_{100}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right) F_{21}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{131}\! \left(x , y\right) = -\frac{-F_{132}\! \left(x , y\right) y +F_{132}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{35}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{139}\! \left(x \right) = F_{88}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{264}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{254}\! \left(x , y\right)+F_{261}\! \left(x , y\right)+F_{263}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{239}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{236}\! \left(x , y\right)+F_{237}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{223}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{235}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{21}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{169}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{216}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{171}\! \left(x , y\right)+F_{174}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{137}\! \left(x \right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{21}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{215}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{35}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x , 1\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{198}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{115}\! \left(x \right) F_{21}\! \left(x \right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = -\frac{-F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = -\frac{-y F_{195}\! \left(x , y\right)+F_{195}\! \left(x , 1\right)}{-1+y}
F_{215}\! \left(x \right) = F_{206}\! \left(x \right) F_{88}\! \left(x \right)
F_{216}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{218}\! \left(x , y\right)+F_{219}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{189}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{226}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{227}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{230}\! \left(x , y\right)+F_{231}\! \left(x , y\right)+F_{232}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{232}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{225}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{242}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{243}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right) F_{246}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right) F_{253}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)+F_{252}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{250}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{249}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{257}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{21}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = -\frac{-F_{265}\! \left(x , y\right)+F_{265}\! \left(x , 1\right)}{-1+y}
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{312}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{267}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{267}\! \left(x , y\right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = \frac{F_{269}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{269}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{295}\! \left(x \right)-F_{307}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{296}\! \left(x \right)
F_{271}\! \left(x \right) = F_{1}\! \left(x \right)+F_{272}\! \left(x \right)+F_{295}\! \left(x \right)
F_{272}\! \left(x \right) = F_{21}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = \frac{F_{274}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{274}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{275}\! \left(x \right)+F_{4}\! \left(x \right)
F_{275}\! \left(x \right) = F_{21}\! \left(x \right) F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{1}\! \left(x \right)+F_{277}\! \left(x \right)+F_{281}\! \left(x \right)+F_{287}\! \left(x \right)
F_{277}\! \left(x \right) = F_{21}\! \left(x \right) F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = F_{126}\! \left(x \right)+F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{1}\! \left(x \right)+F_{280}\! \left(x \right)+F_{281}\! \left(x \right)+F_{282}\! \left(x \right)
F_{280}\! \left(x \right) = F_{226}\! \left(x , 1\right)
F_{281}\! \left(x \right) = F_{21}\! \left(x \right) F_{87}\! \left(x \right)
F_{282}\! \left(x \right) = F_{21}\! \left(x \right) F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{279}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{21}\! \left(x \right) F_{286}\! \left(x \right) F_{35}\! \left(x \right)
F_{286}\! \left(x \right) = F_{229}\! \left(x , 1\right)
F_{287}\! \left(x \right) = F_{21}\! \left(x \right) F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{276}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{21}\! \left(x \right) F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{294}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x \right) F_{35}\! \left(x \right)
F_{293}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{294}\! \left(x \right) = F_{206}\! \left(x \right) F_{286}\! \left(x \right)
F_{295}\! \left(x \right) = F_{21}\! \left(x \right) F_{276}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{21}\! \left(x \right) F_{271}\! \left(x \right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{300}\! \left(x \right)
F_{299}\! \left(x \right) = F_{206}\! \left(x \right)+F_{35}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{21}\! \left(x \right) F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)+F_{306}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right) F_{35}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x , 1\right)
F_{305}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{306}\! \left(x \right) = F_{139}\! \left(x \right) F_{206}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{21}\! \left(x \right) F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{273}\! \left(x \right)+F_{310}\! \left(x \right)
F_{310}\! \left(x \right) = F_{271}\! \left(x \right) F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = x^{4} F_{311} \left(x \right)^{3}+3 x^{4} F_{311} \left(x \right)^{2}+3 x^{4} F_{311}\! \left(x \right)+5 x^{3} F_{311} \left(x \right)^{2}+x^{4}+10 x^{3} F_{311}\! \left(x \right)-11 x^{2} F_{311} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{311}\! \left(x \right)-8 x^{2}+10 x F_{311}\! \left(x \right)+x
F_{312}\! \left(x , y\right) = F_{206}\! \left(x \right) F_{313}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{313}\! \left(x , y\right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{136}\! \left(x \right) F_{271}\! \left(x \right)
F_{316}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{317}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{318}\! \left(x \right) = F_{21}\! \left(x \right) F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)+F_{5}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{21}\! \left(x \right) F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right)+F_{331}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)+F_{326}\! \left(x \right)+F_{328}\! \left(x \right)+F_{329}\! \left(x \right)+F_{6}\! \left(x \right)
F_{324}\! \left(x \right) = F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{21}\! \left(x \right) F_{293}\! \left(x \right) F_{35}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{106}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{328}\! \left(x \right) = F_{21}\! \left(x \right) F_{93}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{21}\! \left(x \right) F_{323}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{115}\! \left(x \right) F_{21}\! \left(x \right) F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{48}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_318(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_21(x)*F_8(x))
Eq(F_8(x), F_123(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_21(x)*F_35(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0) + F_22(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_13(x, k_0)*F_15(x, k_0)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_23(x, k_0) + F_316(x, k_0) + F_317(x, k_0) + F_6(x))
Eq(F_23(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_145(x, k_0) + F_146(x, k_0) + F_235(x, k_0) + F_25(x, k_0))
Eq(F_25(x, k_0), F_21(x)*F_26(x, k_0))
Eq(F_27(x, k_0), F_21(x)*F_26(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_144(x, k_0) + F_27(x, k_0) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_28(x, k_0), F_142(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_14(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_36(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_35(x))
Eq(F_34(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_35(x), x**4*F_35(x)**3 + x**2*(5*x - 11)*F_35(x)**2 - 9*x + (3*x**2 + 10*x)*F_35(x) + 1)
Eq(F_36(x, k_0), F_13(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_140(x, k_0) + F_38(x, k_0) + F_6(x))
Eq(F_38(x, k_0), F_21(x)*F_39(x, k_0))
Eq(F_40(x, k_0), F_136(x) + F_39(x, k_0))
Eq(F_41(x, k_0), F_13(x, k_0)*F_21(x)*F_40(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_44(x, k_0), F_29(x, k_0) + F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_50(x, k_0))
Eq(F_45(x, k_0), F_14(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_49(x, k_0) + 2*F_6(x))
Eq(F_47(x, k_0), F_21(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_13(x, k_0) + F_42(x, k_0))
Eq(F_49(x, k_0), F_18(x, k_0)*F_46(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_21(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_58(x, k_0))
Eq(F_54(x, k_0), F_48(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_57(x, k_0) + F_6(x))
Eq(F_56(x, k_0), F_21(x)*F_40(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_55(x, k_0))
Eq(F_58(x, k_0), F_35(x)*F_59(x, k_0))
Eq(F_60(x, k_0), F_48(x, k_0) + F_59(x, k_0))
Eq(F_60(x, k_0), F_1(x) + F_130(x, k_0) + F_134(x) + F_135(x, k_0) + F_61(x, k_0) + F_66(x, k_0))
Eq(F_62(x, k_0), F_1(x) + F_129(x, k_0) + F_27(x, k_0) + F_61(x, k_0) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_62(x, k_0), F_28(x, k_0) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_13(x, k_0)*F_21(x)*F_65(x, k_0))
Eq(F_65(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_66(x, k_0), F_21(x)*F_67(x, k_0))
Eq(F_67(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_21(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_122(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_121(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_75(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_35(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_37(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_118(x, k_0) + F_120(x, k_0) + F_6(x) + F_77(x, k_0) + F_78(x, k_0))
Eq(F_77(x, k_0), F_21(x)*F_71(x, k_0))
Eq(F_78(x, k_0), F_21(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_76(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_21(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_113(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x))
Eq(F_84(x), F_111(x) + F_6(x) + F_85(x) + F_91(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_21(x)*F_35(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_40(x, 1))
Eq(F_89(x), F_90(x, 1))
Eq(F_24(x, k_0), F_40(x, k_0) + F_90(x, k_0))
Eq(F_91(x), F_21(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_109(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_105(x) + F_107(x) + F_6(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_21(x)*F_35(x)*F_97(x))
Eq(F_97(x), F_71(x, 1))
Eq(F_98(x), F_21(x)*F_35(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) + F_103(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_75(x, 1))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_80(x, k_0))
Eq(F_105(x), F_106(x)*F_21(x)*F_35(x))
Eq(F_106(x), F_89(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_21(x)*F_95(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_104(x)*F_35(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_21(x)*F_84(x))
Eq(F_113(x, k_0), F_114(x))
Eq(F_114(x), F_115(x)*F_12(x)*F_21(x))
Eq(F_115(x), F_116(x, 1))
Eq(F_116(x, k_0), (-k_0*F_117(x, k_0) + F_117(x, 1))/(1 - k_0))
Eq(F_117(x, k_0), k_0**4*x**4*F_117(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_117(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_117(x, k_0) + 1)
Eq(F_118(x, k_0), F_119(x, k_0)*F_21(x))
Eq(F_119(x, k_0), F_90(x, k_0))
Eq(F_120(x, k_0), F_18(x, k_0)*F_76(x, k_0))
Eq(F_121(x, k_0), F_10(x))
Eq(F_122(x, k_0), F_123(x))
Eq(F_123(x), F_124(x) + F_125(x) + F_127(x) + F_6(x))
Eq(F_124(x), F_21(x)*F_87(x))
Eq(F_125(x), F_126(x)*F_21(x))
Eq(F_126(x), F_100(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_123(x)*F_21(x))
Eq(F_129(x, k_0), F_18(x, k_0)*F_62(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_21(x))
Eq(F_131(x, k_0), (k_0*F_132(x, k_0) - F_132(x, 1))/(k_0 - 1))
Eq(F_132(x, k_0), F_133(x, k_0) + F_71(x, k_0))
Eq(F_133(x, k_0), F_79(x, k_0))
Eq(F_134(x), F_12(x)*F_21(x))
Eq(F_135(x, k_0), F_18(x, k_0)*F_60(x, k_0))
Eq(F_136(x), F_137(x) + F_35(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_21(x)*F_35(x))
Eq(F_139(x), F_88(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_18(x, k_0)*F_73(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), F_18(x, k_0)*F_28(x, k_0))
Eq(F_145(x, k_0), F_21(x)*F_67(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_21(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_24(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_21(x))
Eq(F_150(x, k_0), F_151(x, k_0) + F_264(x, k_0))
Eq(F_152(x, k_0), F_151(x, k_0)*F_21(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0)*F_21(x))
Eq(F_155(x, k_0), F_154(x, k_0) + F_254(x, k_0) + F_261(x, k_0) + F_263(x, k_0) + F_6(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_240(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_160(x, k_0) + F_239(x, k_0) + F_6(x))
Eq(F_157(x, k_0), F_158(x, k_0)*F_21(x))
Eq(F_158(x, k_0), F_159(x, k_0) + F_45(x, k_0))
Eq(F_159(x, k_0), F_22(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0)*F_21(x))
Eq(F_161(x, k_0), F_162(x, k_0) + F_236(x, k_0) + F_237(x, k_0) + F_238(x, k_0) + F_6(x))
Eq(F_162(x, k_0), F_163(x, k_0)*F_21(x))
Eq(F_164(x, k_0), F_163(x, k_0)*F_21(x))
Eq(F_165(x, k_0), F_1(x) + F_164(x, k_0) + F_223(x, k_0) + F_227(x, k_0) + F_235(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_71(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0)*F_21(x)*F_71(x, k_0))
Eq(F_168(x, k_0), F_1(x) + F_169(x, k_0) + F_182(x, k_0) + F_216(x, k_0) + F_222(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0)*F_21(x))
Eq(F_170(x, k_0), F_1(x) + F_171(x, k_0) + F_174(x, k_0) + F_181(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_21(x))
Eq(F_172(x, k_0), F_170(x, k_0) + F_173(x, k_0))
Eq(F_173(x, k_0), F_137(x))
Eq(F_174(x, k_0), F_175(x, k_0)*F_21(x))
Eq(F_176(x, k_0), F_175(x, k_0)*F_21(x))
Eq(F_40(x, k_0), F_1(x) + F_176(x, k_0) + F_177(x, k_0) + F_178(x, k_0))
Eq(F_177(x, k_0), F_172(x, k_0)*F_21(x))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_18(x, k_0)*F_180(x, k_0))
Eq(F_180(x, k_0), F_40(x, k_0))
Eq(F_181(x, k_0), F_170(x, k_0)*F_18(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_183(x, k_0), F_168(x, k_0) + F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x))
Eq(F_185(x), F_186(x)*F_21(x))
Eq(F_186(x), F_187(x) + F_215(x))
Eq(F_187(x), F_188(x)*F_35(x))
Eq(F_188(x), F_189(x, 1))
Eq(F_189(x, k_0), F_190(x, k_0) + F_40(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0)*F_21(x))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_194(x, k_0), F_193(x, k_0)*F_21(x))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0) + F_200(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_198(x, k_0) + F_199(x, k_0) + F_6(x))
Eq(F_197(x, k_0), F_21(x)*F_73(x, k_0))
Eq(F_198(x, k_0), F_18(x, k_0)*F_196(x, k_0))
Eq(F_199(x, k_0), F_195(x, k_0)*F_21(x))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0)*F_21(x))
Eq(F_202(x, k_0), F_203(x, k_0) + F_210(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_205(x, k_0))
Eq(F_204(x, k_0), F_180(x, k_0)*F_196(x, k_0))
Eq(F_205(x, k_0), F_206(x)*F_208(x, k_0))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_115(x)*F_21(x))
Eq(F_208(x, k_0), F_209(x, k_0))
Eq(F_209(x, k_0), -F_39(x, k_0) + (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_210(x, k_0), F_211(x, k_0) + F_212(x, k_0))
Eq(F_211(x, k_0), F_195(x, k_0)*F_73(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0)*F_35(x))
Eq(F_214(x, k_0), F_195(x, k_0) + F_213(x, k_0))
Eq(F_214(x, k_0), (-k_0*F_195(x, k_0) + F_195(x, 1))/(1 - k_0))
Eq(F_215(x), F_206(x)*F_88(x))
Eq(F_216(x, k_0), F_21(x)*F_217(x, k_0))
Eq(F_218(x, k_0), F_21(x)*F_217(x, k_0))
Eq(F_189(x, k_0), F_1(x) + F_218(x, k_0) + F_219(x, k_0) + F_220(x, k_0) + F_221(x, k_0))
Eq(F_219(x, k_0), F_21(x)*F_40(x, k_0))
Eq(F_220(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_221(x, k_0), F_18(x, k_0)*F_189(x, k_0))
Eq(F_222(x, k_0), F_168(x, k_0)*F_18(x, k_0))
Eq(F_223(x, k_0), F_21(x)*F_224(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0) + F_234(x, k_0))
Eq(F_225(x, k_0), F_1(x) + F_226(x, k_0) + F_227(x, k_0) + F_228(x, k_0) + F_233(x, k_0))
Eq(F_226(x, k_0), F_132(x, k_0)*F_21(x))
Eq(F_227(x, k_0), F_21(x)*F_24(x, k_0))
Eq(F_228(x, k_0), F_21(x)*F_229(x, k_0))
Eq(F_230(x, k_0), F_21(x)*F_229(x, k_0))
Eq(F_48(x, k_0), F_1(x) + F_23(x, k_0) + F_230(x, k_0) + F_231(x, k_0) + F_232(x, k_0))
Eq(F_231(x, k_0), F_132(x, k_0)*F_21(x))
Eq(F_232(x, k_0), F_18(x, k_0)*F_48(x, k_0))
Eq(F_233(x, k_0), F_18(x, k_0)*F_225(x, k_0))
Eq(F_234(x, k_0), F_133(x, k_0))
Eq(F_235(x, k_0), F_165(x, k_0)*F_18(x, k_0))
Eq(F_236(x, k_0), F_119(x, k_0)*F_21(x))
Eq(F_237(x, k_0), F_21(x)*F_79(x, k_0))
Eq(F_238(x, k_0), F_161(x, k_0)*F_18(x, k_0))
Eq(F_239(x, k_0), F_156(x, k_0)*F_18(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0))
Eq(F_241(x, k_0), F_21(x)*F_242(x, k_0))
Eq(F_242(x, k_0), F_243(x, k_0) + F_247(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0)*F_246(x, k_0))
Eq(F_245(x, k_0), F_161(x, k_0))
Eq(F_246(x, k_0), F_73(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0)*F_253(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_251(x, k_0) + F_252(x, k_0) + F_6(x))
Eq(F_250(x, k_0), F_21(x)*F_72(x, k_0))
Eq(F_251(x, k_0), F_190(x, k_0)*F_21(x))
Eq(F_252(x, k_0), F_18(x, k_0)*F_249(x, k_0))
Eq(F_253(x, k_0), F_48(x, k_0))
Eq(F_254(x, k_0), F_21(x)*F_255(x, k_0))
Eq(F_255(x, k_0), F_165(x, k_0) + F_256(x, k_0))
Eq(F_256(x, k_0), F_257(x, k_0))
Eq(F_165(x, k_0), F_257(x, k_0) + F_258(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_72(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0))
Eq(F_260(x, k_0), F_170(x, k_0)*F_21(x)*F_72(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0))
Eq(F_262(x, k_0), F_21(x)*F_76(x, k_0))
Eq(F_263(x, k_0), F_155(x, k_0)*F_18(x, k_0))
Eq(F_264(x, k_0), -F_265(x, k_0) + (k_0*F_265(x, k_0) - F_265(x, 1))/(k_0 - 1))
Eq(F_265(x, k_0), F_266(x, k_0) + F_312(x, k_0))
Eq(F_266(x, k_0), F_267(x, k_0)*F_35(x))
Eq(F_163(x, k_0), F_267(x, k_0) + F_268(x))
Eq(F_268(x), F_269(x)/F_21(x))
Eq(F_269(x), -F_1(x) + F_270(x) - F_295(x) - F_307(x))
Eq(F_270(x), F_271(x) + F_296(x))
Eq(F_271(x), F_1(x) + F_272(x) + F_295(x))
Eq(F_272(x), F_21(x)*F_273(x))
Eq(F_273(x), F_274(x)/F_21(x))
Eq(F_274(x), -F_1(x) - F_275(x) + F_4(x))
Eq(F_275(x), F_21(x)*F_276(x))
Eq(F_276(x), F_1(x) + F_277(x) + F_281(x) + F_287(x))
Eq(F_277(x), F_21(x)*F_278(x))
Eq(F_278(x), F_126(x) + F_279(x))
Eq(F_279(x), F_1(x) + F_280(x) + F_281(x) + F_282(x))
Eq(F_280(x), F_226(x, 1))
Eq(F_281(x), F_21(x)*F_87(x))
Eq(F_282(x), F_21(x)*F_283(x))
Eq(F_283(x), F_279(x) + F_284(x))
Eq(F_284(x), F_285(x))
Eq(F_285(x), F_21(x)*F_286(x)*F_35(x))
Eq(F_286(x), F_229(x, 1))
Eq(F_287(x), F_21(x)*F_288(x))
Eq(F_288(x), F_276(x) + F_289(x))
Eq(F_289(x), F_290(x))
Eq(F_290(x), F_21(x)*F_291(x))
Eq(F_291(x), F_292(x) + F_294(x))
Eq(F_292(x), F_293(x)*F_35(x))
Eq(F_293(x), F_163(x, 1))
Eq(F_294(x), F_206(x)*F_286(x))
Eq(F_295(x), F_21(x)*F_276(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), F_21(x)*F_271(x)*F_298(x))
Eq(F_298(x), F_299(x) + F_300(x))
Eq(F_299(x), F_206(x) + F_35(x))
Eq(F_300(x), F_301(x))
Eq(F_301(x), F_21(x)*F_302(x))
Eq(F_302(x), F_303(x) + F_306(x))
Eq(F_303(x), F_304(x)*F_35(x))
Eq(F_304(x), F_305(x, 1))
Eq(F_305(x, k_0), F_180(x, k_0) + F_195(x, k_0))
Eq(F_306(x), F_139(x)*F_206(x))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_21(x)*F_309(x))
Eq(F_309(x), F_273(x) + F_310(x))
Eq(F_310(x), F_271(x)*F_311(x))
Eq(F_311(x), x**4*(F_311(x) + 1)**3 + x**2*(5*x - 11)*(F_311(x) + 1)**2 - 9*x + (F_311(x) + 1)*(3*x**2 + 10*x - 1) + F_311(x) + 1)
Eq(F_312(x, k_0), F_206(x)*F_313(x, k_0))
Eq(F_229(x, k_0), F_313(x, k_0) + F_314(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_136(x)*F_271(x))
Eq(F_316(x, k_0), F_133(x, k_0)*F_21(x))
Eq(F_317(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_318(x), F_21(x)*F_319(x))
Eq(F_319(x), F_320(x) + F_5(x))
Eq(F_320(x), F_321(x))
Eq(F_321(x), F_21(x)*F_322(x))
Eq(F_322(x), F_323(x) + F_331(x))
Eq(F_323(x), F_324(x) + F_326(x) + F_328(x) + F_329(x) + F_6(x))
Eq(F_324(x), F_325(x))
Eq(F_325(x), F_21(x)*F_293(x)*F_35(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_106(x)*F_21(x)*F_35(x))
Eq(F_328(x), F_21(x)*F_93(x))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_21(x)*F_323(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_115(x)*F_21(x)*F_333(x))
Eq(F_333(x), F_48(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]]}], "iterative": false}
Specification JSON:
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0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 1, 3], [0, 3, 4, 1, 2], [1, 2, 4, 0, 3], [1, 3, 4, 0, 2], [2, 1, 4, 0, 3], [2, 3, 4, 0, 1], [3, 1, 4, 0, 2], [3, 2, 4, 0, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25642/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[63,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[116,x]*F[12,x]*F[4,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]+F[21,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[13,x,k[0]]*F[15,x,k[0]]*F[4,x]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[379,x,k[0]]
F[24,x,k[0]] = F[15,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[188,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[51,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]
F[29,x] = (-1+x^3*F[29,x]^2+6*x^2*F[29,x]+(-11*F[29,x]+9)*x)*(x*F[29,x]-1)
F[30,x,k[0]] = F[16,x,k[0]]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[34,x,k[0]]+F[50,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[35,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[29,x]*F[38,x]*F[4,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = F[28,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]+F[43,x,k[0]]
F[41,x,k[0]] = F[31,x,k[0]]+F[42,x]
F[42,x] = ((1+F[42,x])^3*x^3+5*(1+F[42,x])^2*x^2+(-11*F[42,x]^2-19*F[42,x]-8)*x+10*F[42,x]+1)*x
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[4,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]+F[47,x,k[0]]
F[46,x,k[0]] = F[39,x,k[0]]*F[41,x,k[0]]
F[47,x,k[0]] = F[29,x]*F[48,x,k[0]]
F[48,x,k[0]] = (F[49,x,k[0]]-F[49,x,1])/(-1+k[0])
F[39,x,k[0]] = F[35,x]+F[49,x,k[0]]
F[50,x,k[0]] = F[15,x,k[0]]*F[49,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[4,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[186,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[81,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[26,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[4,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[63,x]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[55,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[10,x]
F[63,x] = F[64,x]+F[72,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[36,x]
F[66,x] = F[67,x]
F[67,x] = F[29,x]*F[4,x]*F[68,x]*F[69,x]
F[68,x] = F[38,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[1,x]+F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[71,x]*F[74,x]
F[74,x] = F[75,x]+F[95,x]
F[75,x] = F[76,x]
F[76,x] = F[29,x]*F[4,x]*F[77,x]
F[77,x] = F[78,x,1]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[59,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[55,x,k[0]]*F[83,x,k[0]]*F[87,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[89,x,k[0]]
F[84,x,k[0]] = F[1,x]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[84,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = k[0]*x
F[89,x,k[0]] = F[69,x]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x]+F[92,x,k[0]]+F[94,x,k[0]]
F[91,x] = 0
F[92,x,k[0]] = F[4,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[85,x,k[0]]+F[90,x,k[0]]
F[94,x,k[0]] = F[87,x,k[0]]*F[89,x,k[0]]
F[95,x] = F[96,x]
F[96,x] = F[107,x]*F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[29,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[29,x]*F[4,x]
F[101,x] = F[102,x]+F[71,x]
F[102,x] = F[103,x]+F[69,x]
F[103,x] = F[104,x]+F[106,x]+F[91,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[103,x]+F[69,x]
F[106,x] = F[102,x]*F[4,x]
F[107,x] = F[108,x,1]
F[109,x,k[0]] = F[108,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x]+F[168,x,k[0]]
F[111,x] = F[112,x]+F[150,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[148,x]
F[115,x] = F[116,x]+F[119,x]
F[116,x] = F[117,x,1]
F[117,x,k[0]] = (F[118,x,k[0]]*k[0]-F[118,x,1])/(-1+k[0])
F[118,x,k[0]] = (-1+x^3*F[118,x,k[0]]^2*k[0]^3+6*x^2*F[118,x,k[0]]*k[0]^2+(-11*F[118,x,k[0]]+9)*x*k[0])*(x*F[118,x,k[0]]*k[0]-1)
F[119,x] = F[120,x]
F[120,x] = F[116,x]*F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[125,x]
F[122,x] = F[123,x]+F[71,x]
F[123,x] = F[124,x]
F[124,x] = F[121,x]*F[4,x]*F[71,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[147,x]
F[128,x] = F[129,x]+F[8,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[4,x]*F[71,x]
F[132,x] = F[133,x]+F[141,x]
F[133,x] = F[134,x]*F[71,x]
F[134,x] = F[1,x]+F[135,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[71,x]
F[138,x] = F[135,x]+F[139,x]
F[139,x] = F[140,x]
F[140,x] = F[138,x]*F[4,x]
F[141,x] = F[142,x]
F[142,x] = F[134,x]*F[143,x]*F[4,x]*F[71,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[130,x]+F[5,x]
F[145,x] = F[146,x]
F[146,x] = F[101,x]*F[144,x]*F[4,x]
F[147,x] = F[145,x]
F[148,x] = F[149,x]
F[149,x] = F[127,x]*F[29,x]*F[4,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[156,x]
F[153,x] = F[154,x]*F[29,x]
F[154,x] = F[155,x]
F[155,x] = F[107,x]*F[4,x]
F[156,x] = -F[166,x]+F[157,x]
F[157,x] = 1/F[4,x]/F[71,x]*F[158,x]
F[158,x] = F[159,x]
F[159,x] = -F[163,x]+F[160,x]
F[160,x] = 1/F[4,x]*F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[4,x]*F[8,x]
F[163,x] = F[164,x]+F[5,x]
F[164,x] = F[165,x]
F[165,x] = F[114,x]*F[4,x]*F[71,x]
F[166,x] = F[167,x]*F[29,x]
F[167,x] = F[154,x]+F[68,x]
F[168,x,k[0]] = F[169,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]+F[183,x]
F[171,x,k[0]] = F[15,x,k[0]]*F[170,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]
F[23,x,k[0]] = F[172,x,k[0]]+F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[176,x,k[0]]
F[174,x,k[0]] = F[15,x,k[0]]*F[175,x,k[0]]
F[175,x,k[0]] = F[39,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[181,x,k[0]]
F[178,x,k[0]] = F[177,x,k[0]]+F[180,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]*F[4,x]
F[179,x,k[0]] = F[19,x,k[0]]
F[180,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]
F[182,x,k[0]] = F[15,x,k[0]]*F[66,x]
F[183,x] = F[111,x]+F[184,x]
F[184,x] = F[185,x]
F[185,x] = F[183,x]*F[4,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[108,x,k[0]]*F[4,x]*F[83,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[4,x]
F[190,x,k[0]] = F[191,x,k[0]]+F[361,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]+F[197,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]*F[194,x,k[0]]
F[193,x,k[0]] = F[26,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[196,x,k[0]] = F[15,x,k[0]]*F[195,x,k[0]]*F[4,x]
F[196,x,k[0]] = F[41,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[4,x]
F[199,x,k[0]] = F[200,x,k[0]]+F[351,x,k[0]]
F[200,x,k[0]] = F[193,x,k[0]]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[273,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[259,x,k[0]]
F[204,x,k[0]] = F[203,x,k[0]]*F[258,x,k[0]]
F[205,x,k[0]] = F[204,x,k[0]]+F[257,x,k[0]]
F[206,x,k[0]] = F[205,x,k[0]]*F[4,x]
F[206,x,k[0]] = F[207,x,k[0]]
F[208,x,k[0]] = F[207,x,k[0]]+F[254,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]+F[215,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[213,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]*F[84,x,k[0]]
F[212,x,k[0]] = F[28,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]
F[214,x,k[0]] = F[4,x]*F[53,x,k[0]]*F[84,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]*F[218,x,k[0]]*F[4,x]
F[217,x,k[0]] = F[13,x,k[0]]
F[219,x,k[0]] = F[218,x,k[0]]*F[4,x]
F[219,x,k[0]] = F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]*F[4,x]
F[221,x,k[0]] = F[222,x,k[0]]
F[223,x,k[0]] = F[222,x,k[0]]*F[4,x]
F[223,x,k[0]] = F[224,x,k[0]]
F[225,x,k[0]] = F[224,x,k[0]]+F[28,x,k[0]]
F[225,x,k[0]] = F[226,x,k[0]]+F[231,x,k[0]]
F[226,x,k[0]] = F[15,x,k[0]]+F[227,x,k[0]]
F[227,x,k[0]] = F[228,x,k[0]]+F[4,x]
F[228,x,k[0]] = F[229,x,k[0]]+F[230,x,k[0]]+F[91,x]
F[229,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[230,x,k[0]] = F[18,x,k[0]]*F[227,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]
F[232,x,k[0]] = F[233,x,k[0]]*F[4,x]
F[233,x,k[0]] = F[234,x,k[0]]+F[253,x,k[0]]
F[234,x,k[0]] = F[15,x,k[0]]*F[235,x,k[0]]
F[235,x,k[0]] = F[225,x,k[0]]+F[236,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]*F[4,x]
F[238,x,k[0]] = F[239,x,k[0]]+F[245,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[243,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]*F[29,x]
F[241,x,k[0]] = (F[242,x,k[0]]*k[0]-F[242,x,1])/(-1+k[0])
F[242,x,k[0]] = F[235,x,k[0]]
F[243,x,k[0]] = F[242,x,k[0]]*F[244,x,k[0]]
F[244,x,k[0]] = F[30,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]+F[249,x,k[0]]
F[246,x,k[0]] = F[247,x,k[0]]*F[248,x,k[0]]
F[247,x,k[0]] = F[224,x,k[0]]
F[248,x,k[0]] = F[39,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]
F[250,x,k[0]] = F[251,x]*F[48,x,k[0]]
F[251,x] = F[252,x]
F[252,x] = F[116,x]*F[4,x]
F[253,x,k[0]] = F[227,x,k[0]]*F[39,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]*F[256,x,k[0]]
F[255,x,k[0]] = F[14,x,k[0]]
F[256,x,k[0]] = F[212,x,k[0]]
F[257,x,k[0]] = F[53,x,k[0]]*F[84,x,k[0]]
F[258,x,k[0]] = F[19,x,k[0]]
F[259,x,k[0]] = F[260,x]
F[260,x] = F[261,x]*F[4,x]*F[71,x]
F[261,x] = 1/F[4,x]*F[262,x]
F[262,x] = F[263,x]
F[263,x] = 1/F[68,x]*F[264,x]
F[264,x] = -F[265,x]+F[152,x]
F[265,x] = F[153,x]+F[266,x]
F[266,x] = F[267,x]
F[267,x] = F[268,x]*F[4,x]
F[268,x] = F[269,x]+F[270,x]
F[269,x] = F[154,x]*F[261,x]
F[270,x] = F[271,x]
F[271,x] = F[272,x]*F[71,x]
F[272,x] = F[265,x]
F[273,x,k[0]] = F[274,x]
F[274,x] = -F[345,x]+F[275,x]
F[275,x] = 1/F[2,x]*F[276,x]
F[276,x] = -F[339,x]+F[277,x]
F[277,x] = 1/F[4,x]*F[278,x]
F[278,x] = F[279,x]
F[279,x] = -F[338,x]+F[280,x]
F[280,x] = F[281,x]+F[332,x]
F[281,x] = -F[288,x]+F[282,x]
F[282,x] = 1/F[4,x]*F[283,x]
F[283,x] = F[284,x]
F[284,x] = -F[2,x]+F[285,x]
F[285,x] = -F[0,x]+F[286,x]
F[286,x] = 1/F[4,x]*F[287,x]
F[287,x] = F[2,x]
F[288,x] = -F[292,x]+F[289,x]
F[289,x] = 1/F[4,x]*F[290,x]
F[290,x] = F[291,x]
F[291,x] = F[2,x]+F[284,x]
F[292,x] = -F[296,x]+F[293,x]
F[293,x] = 1/F[4,x]*F[294,x]
F[294,x] = F[295,x]
F[295,x] = F[289,x]*F[4,x]
F[296,x] = F[297,x]+F[332,x]
F[297,x] = F[298,x]+F[331,x]
F[298,x] = F[299,x]+F[42,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[4,x]
F[301,x] = F[111,x]+F[302,x]
F[302,x] = F[303,x,1]
F[303,x,k[0]] = F[304,x,k[0]]+F[312,x,k[0]]
F[304,x,k[0]] = F[305,x,k[0]]*F[311,x]
F[305,x,k[0]] = F[306,x,k[0]]
F[306,x,k[0]] = F[18,x,k[0]]*F[307,x,k[0]]
F[307,x,k[0]] = F[15,x,k[0]]+F[308,x,k[0]]
F[308,x,k[0]] = F[305,x,k[0]]+F[309,x,k[0]]
F[309,x,k[0]] = F[310,x,k[0]]
F[310,x,k[0]] = F[18,x,k[0]]*F[308,x,k[0]]
F[311,x] = F[35,x]
F[312,x,k[0]] = F[313,x,k[0]]
F[313,x,k[0]] = F[18,x,k[0]]*F[314,x,k[0]]
F[314,x,k[0]] = F[315,x,k[0]]+F[329,x,k[0]]
F[315,x,k[0]] = F[111,x]*F[316,x,k[0]]
F[316,x,k[0]] = F[317,x,k[0]]+F[318,x,k[0]]
F[317,x,k[0]] = F[1,x]+F[305,x,k[0]]
F[318,x,k[0]] = F[18,x,k[0]]+F[319,x,k[0]]
F[319,x,k[0]] = k[0]*F[320,x,k[0]]
F[320,x,k[0]] = F[229,x,k[0]]+F[321,x,k[0]]+F[91,x]
F[321,x,k[0]] = F[18,x,k[0]]*F[322,x,k[0]]
F[322,x,k[0]] = F[323,x,k[0]]+F[326,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]+F[4,x]
F[324,x,k[0]] = F[325,x,k[0]]
F[325,x,k[0]] = F[18,x,k[0]]*F[323,x,k[0]]
F[326,x,k[0]] = F[320,x,k[0]]+F[327,x,k[0]]
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[18,x,k[0]]*F[326,x,k[0]]
F[329,x,k[0]] = F[330,x,k[0]]
F[330,x,k[0]] = F[111,x]+F[312,x,k[0]]
F[331,x] = F[299,x]
F[332,x] = F[333,x]
F[333,x] = F[2,x]*F[334,x]*F[4,x]
F[334,x] = F[335,x]+F[337,x]
F[335,x] = F[29,x]*F[336,x]
F[336,x] = F[235,x,1]
F[337,x] = F[251,x]*F[38,x]
F[338,x] = F[2,x]*F[35,x]
F[339,x] = -F[344,x]+F[340,x]
F[340,x] = 1/F[4,x]*F[341,x]
F[341,x] = F[342,x]
F[342,x] = -F[343,x]+F[281,x]
F[343,x] = F[2,x]*F[29,x]
F[344,x] = F[2,x]*F[261,x]
F[345,x] = F[346,x]+F[350,x]
F[346,x] = F[347,x]
F[347,x] = F[348,x,1]
F[348,x,k[0]] = (F[349,x,k[0]]*k[0]-F[349,x,1])/(-1+k[0])
F[349,x,k[0]] = F[311,k[0]*x]
F[350,x] = F[260,x]
F[351,x,k[0]] = F[352,x,k[0]]
F[352,x,k[0]] = F[353,x,k[0]]*F[71,x]
F[353,x,k[0]] = F[354,x,k[0]]
F[354,x,k[0]] = F[355,x,k[0]]+F[356,x,k[0]]
F[355,x,k[0]] = F[29,x]*F[51,x,k[0]]
F[356,x,k[0]] = F[357,x,k[0]]
F[357,x,k[0]] = F[358,x,k[0]]*F[4,x]
F[358,x,k[0]] = F[359,x,k[0]]+F[360,x,k[0]]
F[359,x,k[0]] = F[261,x]*F[51,x,k[0]]
F[360,x,k[0]] = F[352,x,k[0]]
F[361,x,k[0]] = F[362,x,k[0]]
F[362,x,k[0]] = F[363,x,k[0]]*F[4,x]
F[364,x,k[0]] = F[363,x,k[0]]*F[4,x]
F[364,x,k[0]] = F[365,x,k[0]]
F[365,x,k[0]] = (F[366,x,k[0]]-F[366,x,1])/(-1+k[0])
F[366,x,k[0]] = F[367,x,k[0]]+F[370,x,k[0]]
F[367,x,k[0]] = F[368,x]*F[369,x,k[0]]
F[368,x] = F[263,x]+F[29,x]
F[369,x,k[0]] = F[49,x,k[0]]
F[370,x,k[0]] = F[371,x,k[0]]+F[372,x,k[0]]
F[371,x,k[0]] = F[168,x,k[0]]*F[29,x]
F[372,x,k[0]] = F[373,x,k[0]]
F[373,x,k[0]] = F[374,x,k[0]]*F[4,x]
F[374,x,k[0]] = F[375,x,k[0]]+F[376,x,k[0]]
F[375,x,k[0]] = F[168,x,k[0]]*F[261,x]
F[376,x,k[0]] = F[377,x,k[0]]
F[377,x,k[0]] = F[378,x,k[0]]*F[71,x]
F[378,x,k[0]] = F[370,x,k[0]]
F[379,x,k[0]] = F[176,x,k[0]]+F[380,x,k[0]]
F[380,x,k[0]] = F[381,x,k[0]]
F[381,x,k[0]] = F[15,x,k[0]]*F[184,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{63}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{379}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x \right) = x^{4} F_{29} \left(x \right)^{3}+5 x^{3} F_{29} \left(x \right)^{2}-11 x^{2} F_{29} \left(x \right)^{2}+3 x^{2} F_{29}\! \left(x \right)+10 x F_{29}\! \left(x \right)-9 x +1
F_{30}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{29}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = x^{4} F_{42} \left(x \right)^{3}+3 x^{4} F_{42} \left(x \right)^{2}+3 x^{4} F_{42}\! \left(x \right)+5 x^{3} F_{42} \left(x \right)^{2}+x^{4}+10 x^{3} F_{42}\! \left(x \right)-11 x^{2} F_{42} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{42}\! \left(x \right)-8 x^{2}+10 x F_{42}\! \left(x \right)+x
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{-F_{49}\! \left(x , y\right)+F_{49}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{10}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{36}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right) F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{95}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = y x
F_{89}\! \left(x , y\right) = F_{69}\! \left(x \right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{91}\! \left(x \right) = 0
F_{92}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{29}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{71}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{69}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)+F_{91}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{69}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x , 1\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{168}\! \left(x , y\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{150}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{148}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = -\frac{-F_{118}\! \left(x , y\right) y +F_{118}\! \left(x , 1\right)}{-1+y}
F_{118}\! \left(x , y\right) = y^{4} x^{4} F_{118}\! \left(x , y\right)^{3}+5 x^{3} F_{118}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{118}\! \left(x , y\right)^{2}+3 x^{2} F_{118}\! \left(x , y\right) y^{2}+10 x F_{118}\! \left(x , y\right) y -9 y x +1
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{125}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{71}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{147}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{8}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{141}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{71}\! \left(x \right)
F_{134}\! \left(x \right) = F_{1}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{71}\! \left(x \right)
F_{138}\! \left(x \right) = F_{135}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{134}\! \left(x \right) F_{143}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{130}\! \left(x \right)+F_{5}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{101}\! \left(x \right) F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{127}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{156}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{29}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{166}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = \frac{F_{158}\! \left(x \right)}{F_{4}\! \left(x \right) F_{71}\! \left(x \right)}
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{5}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{29}\! \left(x \right)
F_{167}\! \left(x \right) = F_{154}\! \left(x \right)+F_{68}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{183}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{170}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{66}\! \left(x \right)
F_{183}\! \left(x \right) = F_{111}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{195}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{196}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{351}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{259}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{258}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{53}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right) F_{218}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{217}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{222}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{228}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{230}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{230}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{227}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{233}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right) F_{29}\! \left(x \right)
F_{241}\! \left(x , y\right) = -\frac{-F_{242}\! \left(x , y\right) y +F_{242}\! \left(x , 1\right)}{-1+y}
F_{242}\! \left(x , y\right) = F_{235}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{242}\! \left(x , y\right) F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right) F_{248}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{253}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right) F_{256}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{212}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{261}\! \left(x \right) = \frac{F_{262}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = \frac{F_{264}\! \left(x \right)}{F_{68}\! \left(x \right)}
F_{264}\! \left(x \right) = -F_{265}\! \left(x \right)+F_{152}\! \left(x \right)
F_{265}\! \left(x \right) = F_{153}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right) F_{4}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{270}\! \left(x \right)
F_{269}\! \left(x \right) = F_{154}\! \left(x \right) F_{261}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right) F_{71}\! \left(x \right)
F_{272}\! \left(x \right) = F_{265}\! \left(x \right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = -F_{345}\! \left(x \right)+F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = \frac{F_{276}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{276}\! \left(x \right) = -F_{339}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = \frac{F_{278}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{332}\! \left(x \right)
F_{281}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = \frac{F_{283}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = \frac{F_{287}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{287}\! \left(x \right) = F_{2}\! \left(x \right)
F_{288}\! \left(x \right) = -F_{292}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = \frac{F_{290}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{290}\! \left(x \right) = F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{2}\! \left(x \right)+F_{284}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{296}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = \frac{F_{294}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{289}\! \left(x \right) F_{4}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{332}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)+F_{331}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{42}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{4}\! \left(x \right)
F_{301}\! \left(x \right) = F_{111}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x , 1\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)+F_{312}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{305}\! \left(x , y\right) F_{311}\! \left(x \right)
F_{305}\! \left(x , y\right) = F_{306}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{307}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{308}\! \left(x , y\right)
F_{308}\! \left(x , y\right) = F_{305}\! \left(x , y\right)+F_{309}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{310}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{308}\! \left(x , y\right)
F_{311}\! \left(x \right) = F_{35}\! \left(x \right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{314}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{315}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{111}\! \left(x \right) F_{316}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{317}\! \left(x , y\right)+F_{318}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{305}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{319}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = y F_{320}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{229}\! \left(x , y\right)+F_{321}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{321}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{326}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{323}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{326}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{312}\! \left(x , y\right)
F_{331}\! \left(x \right) = F_{299}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{2}\! \left(x \right) F_{334}\! \left(x \right) F_{4}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right)+F_{337}\! \left(x \right)
F_{335}\! \left(x \right) = F_{29}\! \left(x \right) F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{235}\! \left(x , 1\right)
F_{337}\! \left(x \right) = F_{251}\! \left(x \right) F_{38}\! \left(x \right)
F_{338}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{339}\! \left(x \right) = -F_{344}\! \left(x \right)+F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = \frac{F_{341}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{341}\! \left(x \right) = F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = -F_{343}\! \left(x \right)+F_{281}\! \left(x \right)
F_{343}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right)
F_{344}\! \left(x \right) = F_{2}\! \left(x \right) F_{261}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)+F_{350}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right)
F_{347}\! \left(x \right) = F_{348}\! \left(x , 1\right)
F_{348}\! \left(x , y\right) = -\frac{-y F_{349}\! \left(x , y\right)+F_{349}\! \left(x , 1\right)}{-1+y}
F_{349}\! \left(x , y\right) = F_{311}\! \left(y x \right)
F_{350}\! \left(x \right) = F_{260}\! \left(x \right)
F_{351}\! \left(x , y\right) = F_{352}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{353}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{353}\! \left(x , y\right) = F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{355}\! \left(x , y\right)+F_{356}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{357}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{358}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{358}\! \left(x , y\right) = F_{359}\! \left(x , y\right)+F_{360}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{261}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{352}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = F_{362}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{363}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{364}\! \left(x , y\right) = F_{363}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{364}\! \left(x , y\right) = F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = -\frac{-F_{366}\! \left(x , y\right)+F_{366}\! \left(x , 1\right)}{-1+y}
F_{366}\! \left(x , y\right) = F_{367}\! \left(x , y\right)+F_{370}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{368}\! \left(x \right) F_{369}\! \left(x , y\right)
F_{368}\! \left(x \right) = F_{263}\! \left(x \right)+F_{29}\! \left(x \right)
F_{369}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{371}\! \left(x , y\right)+F_{372}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{29}\! \left(x \right)
F_{372}\! \left(x , y\right) = F_{373}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{374}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{374}\! \left(x , y\right) = F_{375}\! \left(x , y\right)+F_{376}\! \left(x , y\right)
F_{375}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{261}\! \left(x \right)
F_{376}\! \left(x , y\right) = F_{377}\! \left(x , y\right)
F_{377}\! \left(x , y\right) = F_{378}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{378}\! \left(x , y\right) = F_{370}\! \left(x , y\right)
F_{379}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{380}\! \left(x , y\right)
F_{380}\! \left(x , y\right) = F_{381}\! \left(x , y\right)
F_{381}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{184}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_63(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_116(x)*F_12(x)*F_4(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0) + F_21(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_13(x, k_0)*F_15(x, k_0)*F_4(x))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_379(x, k_0))
Eq(F_24(x, k_0), F_15(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_188(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_51(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0))
Eq(F_29(x), x**4*F_29(x)**3 + x**2*(5*x - 11)*F_29(x)**2 - 9*x + (3*x**2 + 10*x)*F_29(x) + 1)
Eq(F_30(x, k_0), F_16(x, k_0) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_34(x, k_0) + F_50(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_35(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_29(x)*F_38(x)*F_4(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), F_28(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0) + F_43(x, k_0))
Eq(F_41(x, k_0), F_31(x, k_0) + F_42(x))
Eq(F_42(x), x**4*(F_42(x) + 1)**3 + x**2*(5*x - 11)*(F_42(x) + 1)**2 - 9*x + (F_42(x) + 1)*(3*x**2 + 10*x - 1) + F_42(x) + 1)
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_4(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0) + F_47(x, k_0))
Eq(F_46(x, k_0), F_39(x, k_0)*F_41(x, k_0))
Eq(F_47(x, k_0), F_29(x)*F_48(x, k_0))
Eq(F_48(x, k_0), -F_49(x, k_0) + (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), F_35(x) + F_49(x, k_0))
Eq(F_50(x, k_0), F_15(x, k_0)*F_49(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_4(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_186(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_81(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_26(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_4(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_63(x))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_55(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_10(x))
Eq(F_63(x), F_64(x) + F_72(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_36(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_29(x)*F_4(x)*F_68(x)*F_69(x))
Eq(F_68(x), F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_1(x) + F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_71(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_95(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_29(x)*F_4(x)*F_77(x))
Eq(F_77(x), F_78(x, 1))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_59(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_55(x, k_0)*F_83(x, k_0)*F_87(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_89(x, k_0))
Eq(F_84(x, k_0), F_1(x) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_84(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), k_0*x)
Eq(F_89(x, k_0), F_69(x) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_91(x), 0)
Eq(F_92(x, k_0), F_4(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_85(x, k_0) + F_90(x, k_0))
Eq(F_94(x, k_0), F_87(x, k_0)*F_89(x, k_0))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_107(x)*F_4(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_29(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_29(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_71(x))
Eq(F_102(x), F_103(x) + F_69(x))
Eq(F_103(x), F_104(x) + F_106(x) + F_91(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_103(x) + F_69(x))
Eq(F_106(x), F_102(x)*F_4(x))
Eq(F_107(x), F_108(x, 1))
Eq(F_109(x, k_0), F_108(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x) + F_168(x, k_0))
Eq(F_111(x), F_112(x) + F_150(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_148(x))
Eq(F_115(x), F_116(x) + F_119(x))
Eq(F_116(x), F_117(x, 1))
Eq(F_117(x, k_0), (-k_0*F_118(x, k_0) + F_118(x, 1))/(1 - k_0))
Eq(F_118(x, k_0), k_0**4*x**4*F_118(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_118(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_118(x, k_0) + 1)
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_116(x)*F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_125(x))
Eq(F_122(x), F_123(x) + F_71(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_121(x)*F_4(x)*F_71(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_147(x))
Eq(F_128(x), F_129(x) + F_8(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_4(x)*F_71(x))
Eq(F_132(x), F_133(x) + F_141(x))
Eq(F_133(x), F_134(x)*F_71(x))
Eq(F_134(x), F_1(x) + F_135(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_71(x))
Eq(F_138(x), F_135(x) + F_139(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_138(x)*F_4(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_134(x)*F_143(x)*F_4(x)*F_71(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_130(x) + F_5(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_101(x)*F_144(x)*F_4(x))
Eq(F_147(x), F_145(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_127(x)*F_29(x)*F_4(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_156(x))
Eq(F_153(x), F_154(x)*F_29(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_107(x)*F_4(x))
Eq(F_156(x), F_157(x) - F_166(x))
Eq(F_157(x), F_158(x)/(F_4(x)*F_71(x)))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x) - F_163(x))
Eq(F_160(x), F_161(x)/F_4(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_4(x)*F_8(x))
Eq(F_163(x), F_164(x) + F_5(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_114(x)*F_4(x)*F_71(x))
Eq(F_166(x), F_167(x)*F_29(x))
Eq(F_167(x), F_154(x) + F_68(x))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0) + F_183(x))
Eq(F_171(x, k_0), F_15(x, k_0)*F_170(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_23(x, k_0), F_172(x, k_0) + F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_176(x, k_0))
Eq(F_174(x, k_0), F_15(x, k_0)*F_175(x, k_0))
Eq(F_175(x, k_0), F_39(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_181(x, k_0))
Eq(F_178(x, k_0), F_177(x, k_0) + F_180(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0)*F_4(x))
Eq(F_179(x, k_0), F_19(x, k_0))
Eq(F_180(x, k_0), F_15(x, k_0)*F_27(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0))
Eq(F_182(x, k_0), F_15(x, k_0)*F_66(x))
Eq(F_183(x), F_111(x) + F_184(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_183(x)*F_4(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_108(x, k_0)*F_4(x)*F_83(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_4(x))
Eq(F_190(x, k_0), F_191(x, k_0) + F_361(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0) + F_197(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0)*F_194(x, k_0))
Eq(F_193(x, k_0), F_26(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_196(x, k_0), F_15(x, k_0)*F_195(x, k_0)*F_4(x))
Eq(F_196(x, k_0), F_41(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_4(x))
Eq(F_199(x, k_0), F_200(x, k_0) + F_351(x, k_0))
Eq(F_200(x, k_0), F_193(x, k_0)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_273(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_259(x, k_0))
Eq(F_204(x, k_0), F_203(x, k_0)*F_258(x, k_0))
Eq(F_205(x, k_0), F_204(x, k_0) + F_257(x, k_0))
Eq(F_206(x, k_0), F_205(x, k_0)*F_4(x))
Eq(F_206(x, k_0), F_207(x, k_0))
Eq(F_208(x, k_0), F_207(x, k_0) + F_254(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_215(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_213(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0)*F_84(x, k_0))
Eq(F_212(x, k_0), F_28(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0))
Eq(F_214(x, k_0), F_4(x)*F_53(x, k_0)*F_84(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0)*F_218(x, k_0)*F_4(x))
Eq(F_217(x, k_0), F_13(x, k_0))
Eq(F_219(x, k_0), F_218(x, k_0)*F_4(x))
Eq(F_219(x, k_0), F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0)*F_4(x))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_223(x, k_0), F_222(x, k_0)*F_4(x))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_225(x, k_0), F_224(x, k_0) + F_28(x, k_0))
Eq(F_225(x, k_0), F_226(x, k_0) + F_231(x, k_0))
Eq(F_226(x, k_0), F_15(x, k_0) + F_227(x, k_0))
Eq(F_227(x, k_0), F_228(x, k_0) + F_4(x))
Eq(F_228(x, k_0), F_229(x, k_0) + F_230(x, k_0) + F_91(x))
Eq(F_229(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_230(x, k_0), F_18(x, k_0)*F_227(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0))
Eq(F_232(x, k_0), F_233(x, k_0)*F_4(x))
Eq(F_233(x, k_0), F_234(x, k_0) + F_253(x, k_0))
Eq(F_234(x, k_0), F_15(x, k_0)*F_235(x, k_0))
Eq(F_235(x, k_0), F_225(x, k_0) + F_236(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0)*F_4(x))
Eq(F_238(x, k_0), F_239(x, k_0) + F_245(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_243(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0)*F_29(x))
Eq(F_241(x, k_0), (-k_0*F_242(x, k_0) + F_242(x, 1))/(1 - k_0))
Eq(F_242(x, k_0), F_235(x, k_0))
Eq(F_243(x, k_0), F_242(x, k_0)*F_244(x, k_0))
Eq(F_244(x, k_0), F_30(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0) + F_249(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0)*F_248(x, k_0))
Eq(F_247(x, k_0), F_224(x, k_0))
Eq(F_248(x, k_0), F_39(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x)*F_48(x, k_0))
Eq(F_251(x), F_252(x))
Eq(F_252(x), F_116(x)*F_4(x))
Eq(F_253(x, k_0), F_227(x, k_0)*F_39(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0)*F_256(x, k_0))
Eq(F_255(x, k_0), F_14(x, k_0))
Eq(F_256(x, k_0), F_212(x, k_0))
Eq(F_257(x, k_0), F_53(x, k_0)*F_84(x, k_0))
Eq(F_258(x, k_0), F_19(x, k_0))
Eq(F_259(x, k_0), F_260(x))
Eq(F_260(x), F_261(x)*F_4(x)*F_71(x))
Eq(F_261(x), F_262(x)/F_4(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_264(x)/F_68(x))
Eq(F_264(x), F_152(x) - F_265(x))
Eq(F_265(x), F_153(x) + F_266(x))
Eq(F_266(x), F_267(x))
Eq(F_267(x), F_268(x)*F_4(x))
Eq(F_268(x), F_269(x) + F_270(x))
Eq(F_269(x), F_154(x)*F_261(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_272(x)*F_71(x))
Eq(F_272(x), F_265(x))
Eq(F_273(x, k_0), F_274(x))
Eq(F_274(x), F_275(x) - F_345(x))
Eq(F_275(x), F_276(x)/F_2(x))
Eq(F_276(x), F_277(x) - F_339(x))
Eq(F_277(x), F_278(x)/F_4(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_280(x) - F_338(x))
Eq(F_280(x), F_281(x) + F_332(x))
Eq(F_281(x), F_282(x) - F_288(x))
Eq(F_282(x), F_283(x)/F_4(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), -F_2(x) + F_285(x))
Eq(F_285(x), -F_0(x) + F_286(x))
Eq(F_286(x), F_287(x)/F_4(x))
Eq(F_287(x), F_2(x))
Eq(F_288(x), F_289(x) - F_292(x))
Eq(F_289(x), F_290(x)/F_4(x))
Eq(F_290(x), F_291(x))
Eq(F_291(x), F_2(x) + F_284(x))
Eq(F_292(x), F_293(x) - F_296(x))
Eq(F_293(x), F_294(x)/F_4(x))
Eq(F_294(x), F_295(x))
Eq(F_295(x), F_289(x)*F_4(x))
Eq(F_296(x), F_297(x) + F_332(x))
Eq(F_297(x), F_298(x) + F_331(x))
Eq(F_298(x), F_299(x) + F_42(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_4(x))
Eq(F_301(x), F_111(x) + F_302(x))
Eq(F_302(x), F_303(x, 1))
Eq(F_303(x, k_0), F_304(x, k_0) + F_312(x, k_0))
Eq(F_304(x, k_0), F_305(x, k_0)*F_311(x))
Eq(F_305(x, k_0), F_306(x, k_0))
Eq(F_306(x, k_0), F_18(x, k_0)*F_307(x, k_0))
Eq(F_307(x, k_0), F_15(x, k_0) + F_308(x, k_0))
Eq(F_308(x, k_0), F_305(x, k_0) + F_309(x, k_0))
Eq(F_309(x, k_0), F_310(x, k_0))
Eq(F_310(x, k_0), F_18(x, k_0)*F_308(x, k_0))
Eq(F_311(x), F_35(x))
Eq(F_312(x, k_0), F_313(x, k_0))
Eq(F_313(x, k_0), F_18(x, k_0)*F_314(x, k_0))
Eq(F_314(x, k_0), F_315(x, k_0) + F_329(x, k_0))
Eq(F_315(x, k_0), F_111(x)*F_316(x, k_0))
Eq(F_316(x, k_0), F_317(x, k_0) + F_318(x, k_0))
Eq(F_317(x, k_0), F_1(x) + F_305(x, k_0))
Eq(F_318(x, k_0), F_18(x, k_0) + F_319(x, k_0))
Eq(F_319(x, k_0), k_0*F_320(x, k_0))
Eq(F_320(x, k_0), F_229(x, k_0) + F_321(x, k_0) + F_91(x))
Eq(F_321(x, k_0), F_18(x, k_0)*F_322(x, k_0))
Eq(F_322(x, k_0), F_323(x, k_0) + F_326(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0) + F_4(x))
Eq(F_324(x, k_0), F_325(x, k_0))
Eq(F_325(x, k_0), F_18(x, k_0)*F_323(x, k_0))
Eq(F_326(x, k_0), F_320(x, k_0) + F_327(x, k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_18(x, k_0)*F_326(x, k_0))
Eq(F_329(x, k_0), F_330(x, k_0))
Eq(F_330(x, k_0), F_111(x) + F_312(x, k_0))
Eq(F_331(x), F_299(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_2(x)*F_334(x)*F_4(x))
Eq(F_334(x), F_335(x) + F_337(x))
Eq(F_335(x), F_29(x)*F_336(x))
Eq(F_336(x), F_235(x, 1))
Eq(F_337(x), F_251(x)*F_38(x))
Eq(F_338(x), F_2(x)*F_35(x))
Eq(F_339(x), F_340(x) - F_344(x))
Eq(F_340(x), F_341(x)/F_4(x))
Eq(F_341(x), F_342(x))
Eq(F_342(x), F_281(x) - F_343(x))
Eq(F_343(x), F_2(x)*F_29(x))
Eq(F_344(x), F_2(x)*F_261(x))
Eq(F_345(x), F_346(x) + F_350(x))
Eq(F_346(x), F_347(x))
Eq(F_347(x), F_348(x, 1))
Eq(F_348(x, k_0), (-k_0*F_349(x, k_0) + F_349(x, 1))/(1 - k_0))
Eq(F_349(x, k_0), F_311(k_0*x))
Eq(F_350(x), F_260(x))
Eq(F_351(x, k_0), F_352(x, k_0))
Eq(F_352(x, k_0), F_353(x, k_0)*F_71(x))
Eq(F_353(x, k_0), F_354(x, k_0))
Eq(F_354(x, k_0), F_355(x, k_0) + F_356(x, k_0))
Eq(F_355(x, k_0), F_29(x)*F_51(x, k_0))
Eq(F_356(x, k_0), F_357(x, k_0))
Eq(F_357(x, k_0), F_358(x, k_0)*F_4(x))
Eq(F_358(x, k_0), F_359(x, k_0) + F_360(x, k_0))
Eq(F_359(x, k_0), F_261(x)*F_51(x, k_0))
Eq(F_360(x, k_0), F_352(x, k_0))
Eq(F_361(x, k_0), F_362(x, k_0))
Eq(F_362(x, k_0), F_363(x, k_0)*F_4(x))
Eq(F_364(x, k_0), F_363(x, k_0)*F_4(x))
Eq(F_364(x, k_0), F_365(x, k_0))
Eq(F_365(x, k_0), -F_366(x, k_0) + (k_0*F_366(x, k_0) - F_366(x, 1))/(k_0 - 1))
Eq(F_366(x, k_0), F_367(x, k_0) + F_370(x, k_0))
Eq(F_367(x, k_0), F_368(x)*F_369(x, k_0))
Eq(F_368(x), F_263(x) + F_29(x))
Eq(F_369(x, k_0), F_49(x, k_0))
Eq(F_370(x, k_0), F_371(x, k_0) + F_372(x, k_0))
Eq(F_371(x, k_0), F_168(x, k_0)*F_29(x))
Eq(F_372(x, k_0), F_373(x, k_0))
Eq(F_373(x, k_0), F_374(x, k_0)*F_4(x))
Eq(F_374(x, k_0), F_375(x, k_0) + F_376(x, k_0))
Eq(F_375(x, k_0), F_168(x, k_0)*F_261(x))
Eq(F_376(x, k_0), F_377(x, k_0))
Eq(F_377(x, k_0), F_378(x, k_0)*F_71(x))
Eq(F_378(x, k_0), F_370(x, k_0))
Eq(F_379(x, k_0), F_176(x, k_0) + F_380(x, k_0))
Eq(F_380(x, k_0), F_381(x, k_0))
Eq(F_381(x, k_0), F_15(x, k_0)*F_184(x))
Pack JSON:
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Specification JSON:
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