01234_01324_01342_03124_03142_03412_30124_30142_30412
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2756, 14071, 72224, 371650, 1914624, 9867763, 50859778, 262097703, 1350332142, 6954833736, 35809294670, 184318817495, 948450854045, 4879100671701, 25093080026219, 129022965562663, 663266790955110, 3408995916865277, 17518215899555585, 90008996974429549, 462403839659895731, 2375212969294292877, 12199297826343880369, 62650312087684743058, 321715678418450753601, 1651907728286507984636, 8481398761223524790783, 43543216673708752048395, 223536123703434170346790, 1147497253297382257795164, 5890261937191937362695128, 30234209576101663715369656, 155183491248255723957293498, 796483798071712784735693858, 4087844566655575006266150783, 20979692792646859434626001887, 107669422725926500772312516898, 552554630219831245906807503572, 2835623715299729582979477767926, 14551688284192226226223630711974, 74674161264833459642097550717980, 383195337431036248830511599955846, 1966362614268722336903741250829451, 10090230952275571651459350285277368, 51776564708652612183882148771610184, 265680975670151198768893869342800387, 1363274183315829596014678556618684456, 6995228087477994638129578276606712494, 35893583421442955096754235592953459975, 184174010892022037723737282381244191247, 945010764161896513030749562225190022722, 4848889766744991560129825786880669211506, 24879706624961121124358125917172054767740, 127657344816233384184588218725290721418439, 655004326346354634394788932350169072853064, 3360783391925067997891943810042613439825760, 17243881749181407369073486599842262193114379, 88476485347670606050897831918656609941883511, 453961624187264040394001591553853369190417878, 2329211900644014869261471256300324766157169865, 11950815921805755796938487614129863075190232122, 61317567558818244157913450795942895766189214996, 314609028953531960126084119766904904928225109110, 1614196640365774168114679669938294793669158629309, 8282105744677877251980526793094003787136358230063, 42493671319850639657716404182903733728934686250731, 218025332820423676402483265520463218005813121602387, 1118636397988606768109251116172836213211339803759276, 5739450006191209146510542215558687554872610092735326, 29447674582020452786640926881832696129998188499892154, 151088419944613382710219661299073051454637138456478909, 775194790627452989267867659429067302246183016407064330, 3977315524609448065368902291684897000974525848248019536, 20406513810955540191432065185593768664622366794102130299, 104700124281779165590647839325271720097556336015259438880, 537186657496010323669584527310996158075212253322706094398, 2756150366750986658296582613236039800189415937459088705167, 14141005654907530637182668448492222037211857632352511478787, 72553339616732906729453767108476369393237199072175826011524, 372249622850909921265492638486647315894596179062696508649914, 1909901164890739852457474960686339250736773123677971526833111, 9799125260545536124214529904649516268767537086389572828504001, 50276325765313316168477410733551988759081308327182482043859416, 257952402779767461393180244843564378945012982171867808089996165, 1323474149214155510561121401981424559600118131905483573292473845, 6790335016172257379759068844784925213285098846072402075612683690, 34839090372704136162244932410653607939634366821814459929996694776, 178748453043610055790187757385884921214504608544692254746257164886, 917102055378398467714371870724238748885074994127828902552874396176, 4705360930751536131554775253378825129345566898712695312114052421634, 24141715498882099053397710106768397098026456187880154979822116700937, 123863466990940408327388338067533469970445979666287013949487408313782, 635503963020655209498384522284136179323983935819868924568287189180357, 3260567750851590471911703251285314558134765346614745278534382623383605
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25203/
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[11,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[7,x,k[0]] = (F[6,x,k[0]]-F[6,x,1])/(-1+k[0])
F[7,x,k[0]] = F[12,x,k[0]]+F[220,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]*F[57,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[11,x]*F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[219,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[54,x,k[0]]
F[18,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x]+F[215,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[214,x]+F[23,x]
F[23,x] = F[24,x]*F[69,x]
F[24,x] = F[0,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[136,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[24,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[120,x,k[0]]+F[31,x,k[0]]+F[8,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[212,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = -k[0]*(F[35,x,1]-F[35,x,k[0]])/(-1+k[0])
F[35,x,k[0]] = F[36,x,k[0]]+F[6,x,k[0]]
F[37,x,k[0]] = F[25,x]+F[36,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[39,x,k[0]] = F[136,x]+F[40,x,k[0]]
F[41,x,k[0]] = (F[40,x,k[0]]*k[0]-F[40,x,1])/(-1+k[0])
F[41,x,k[0]] = F[42,x]+F[47,x,k[0]]
F[42,x] = F[28,x]+F[43,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[19,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[11,x]*F[46,x,k[0]]
F[46,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[57,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[58,x,k[0]]
F[50,x,k[0]] = F[51,x]*F[54,x,k[0]]
F[51,x] = F[52,x,1]
F[53,x,k[0]] = F[11,x]*F[52,x,k[0]]
F[53,x,k[0]] = F[44,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = k[0]*x
F[58,x,k[0]] = F[103,x,k[0]]*F[59,x]*F[69,x]
F[59,x] = F[60,x,1]
F[61,x,k[0]] = F[129,x]*F[60,x,k[0]]*F[69,x]
F[62,x,k[0]] = F[135,x,k[0]]+F[61,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[133,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[11,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[72,x,k[0]]
F[68,x,k[0]] = F[17,x,k[0]]*F[69,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[69,x]
F[72,x,k[0]] = F[129,x]*F[69,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[79,x,k[0]]
F[74,x,k[0]] = F[54,x,k[0]]*F[75,x]
F[75,x] = F[0,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[78,x]
F[78,x] = F[73,x,1]
F[80,x,k[0]] = F[125,x,k[0]]+F[79,x,k[0]]
F[81,x,k[0]] = F[11,x]*F[69,x]*F[80,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[83,x,k[0]] = F[124,x,k[0]]+F[8,x]+F[82,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = F[19,x,k[0]]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[11,x]*F[85,x,k[0]]
F[85,x,k[0]] = 1/(-1+k[0])*(F[83,x,k[0]]*k[0]-F[83,x,1])
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]*F[70,x]*F[73,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[11,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[92,x,k[0]] = F[118,x,k[0]]+F[91,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[94,x,k[0]] = F[107,x,k[0]]+F[93,x,k[0]]+F[95,x]+F[96,x,k[0]]
F[94,x,k[0]] = F[29,x,k[0]]+F[44,x,k[0]]
F[95,x] = -1+x^2+4*x+F[95,x]^2*(-1+4*x)+(3-8*x)*F[95,x]
F[96,x,k[0]] = F[57,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[94,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[57,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[102,x,k[0]]
F[101,x,k[0]] = F[52,x,k[0]]*F[54,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[60,x,k[0]]*F[69,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[57,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[106,x,k[0]]+F[8,x]
F[105,x,k[0]] = F[55,x,k[0]]*F[57,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]*F[57,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[69,x]^2*F[109,x]*F[11,x]*F[54,x,k[0]]
F[109,x] = F[0,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[0,x]*F[11,x]*F[112,x]
F[112,x] = F[113,x]+F[69,x]
F[113,x] = F[114,x]+F[70,x]
F[114,x] = F[115,x]+F[117,x]+F[8,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[70,x]
F[117,x] = F[11,x]*F[113,x]
F[119,x,k[0]] = F[11,x]*F[118,x,k[0]]
F[29,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]+F[95,x]
F[120,x,k[0]] = F[121,x,k[0]]*F[57,x,k[0]]
F[97,x,k[0]] = F[121,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[124,x,k[0]] = F[122,x,k[0]]*F[57,x,k[0]]
F[125,x,k[0]] = F[126,x]*F[54,x,k[0]]
F[126,x] = F[127,x,1]
F[127,x,k[0]] = F[128,x,k[0]]+F[75,x]
F[128,x,k[0]] = F[109,x]*F[55,x,k[0]]
F[129,x] = F[11,x]+F[130,x]
F[130,x] = F[131,x]+F[132,x]+F[8,x]
F[131,x] = F[11,x]*F[70,x]
F[132,x] = F[11,x]*F[129,x]
F[133,x,k[0]] = F[11,x]*F[134,x,k[0]]
F[134,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[135,x,k[0]] = F[52,x,k[0]]*F[69,x]
F[136,x] = F[137,x]+F[159,x]+F[209,x]
F[137,x] = F[138,x,1]
F[138,x,k[0]] = F[139,x,k[0]]+F[156,x,k[0]]+F[8,x]
F[139,x,k[0]] = F[11,x]*F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[150,x,k[0]]+F[152,x,k[0]]+F[8,x]
F[141,x,k[0]] = F[11,x]*F[142,x,k[0]]
F[142,x,k[0]] = -k[0]*(F[143,x,1]-F[143,x,k[0]])/(-1+k[0])
F[143,x,k[0]] = -k[0]*(F[144,x,1]-F[144,x,k[0]])/(-1+k[0])
F[144,x,k[0]] = F[145,x,k[0]]+F[146,x,k[0]]+F[8,x]
F[145,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[57,x,k[0]]
F[147,x,k[0]] = F[144,x,k[0]]+F[148,x]
F[148,x] = F[149,x,1]
F[149,x,k[0]] = x*F[149,x,k[0]]^2*k[0]+1
F[150,x,k[0]] = F[11,x]*F[151,x,k[0]]
F[151,x,k[0]] = -k[0]*(F[140,x,1]-F[140,x,k[0]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]*F[57,x,k[0]]
F[153,x,k[0]] = F[140,x,k[0]]+F[154,x]
F[154,x] = F[155,x,1]
F[155,x,k[0]] = (F[149,x,k[0]]*k[0]-F[149,x,1])/(-1+k[0])
F[156,x,k[0]] = F[157,x,k[0]]*F[57,x,k[0]]
F[157,x,k[0]] = F[158,x,1,k[0]]
F[158,x,k[0],k[1]] = (F[147,x,k[0]*k[1]]*k[0]-F[147,x,k[1]])/(-1+k[0])
F[159,x] = F[160,x]
F[160,x] = F[161,x,1]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[11,x]*F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]+F[171,x,k[0]]+F[173,x,k[0]]+F[8,x]
F[164,x,k[0]] = F[165,x,k[0]]
F[165,x,k[0]] = F[11,x]*F[166,x,k[0]]
F[166,x,k[0]] = -k[0]*(F[167,x,1]-F[167,x,k[0]])/(-1+k[0])
F[167,x,k[0]] = F[168,x,k[0]]+F[170,x,k[0]]
F[168,x,k[0]] = -k[0]*(F[169,x,1]-F[169,x,k[0]])/(-1+k[0])
F[169,x,k[0]] = F[138,x,k[0]]+F[161,x,k[0]]
F[170,x,k[0]] = F[11,x]*F[166,x,k[0]]
F[171,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[172,x,k[0]] = -k[0]*(F[163,x,1]-F[163,x,k[0]])/(-1+k[0])
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[57,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[189,x,k[0]]
F[176,x,k[0]] = F[163,x,k[0]]+F[177,x]
F[177,x] = F[178,x]+F[184,x]+F[4,x]
F[178,x] = F[179,x]
F[179,x] = F[11,x]*F[180,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[39,x,1]
F[182,x] = F[183,x]
F[183,x] = F[167,x,1]
F[184,x] = F[185,x]
F[185,x] = F[11,x]*F[186,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[118,x,1]
F[188,x] = F[163,x,1]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]*F[57,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]+F[206,x,k[0]]+F[208,x,k[0]]+F[4,x]
F[192,x,k[0]] = F[193,x,k[0]]
F[193,x,k[0]] = F[11,x]*F[194,x,k[0]]
F[194,x,k[0]] = 1/(-1+k[0])*(F[195,x,k[0]]*k[0]-F[195,x,1])
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[203,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = 1/(-1+k[0])*(F[199,x,k[0]]*k[0]-F[199,x,1])
F[199,x,k[0]] = F[0,x]+F[200,x,k[0]]+F[202,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[11,x]*F[195,x,k[0]]
F[202,x,k[0]] = F[199,x,k[0]]*F[57,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]
F[204,x,k[0]] = F[11,x]*F[205,x,k[0]]
F[205,x,k[0]] = F[194,x,k[0]]
F[206,x,k[0]] = F[11,x]*F[207,x,k[0]]
F[207,x,k[0]] = 1/(-1+k[0])*(F[191,x,k[0]]*k[0]-F[191,x,1])
F[208,x,k[0]] = F[191,x,k[0]]*F[57,x,k[0]]
F[209,x] = F[210,x]
F[210,x] = F[11,x]*F[211,x]
F[211,x] = F[136,x]+F[182,x]
F[212,x,k[0]] = F[11,x]*F[213,x,k[0]]
F[213,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[214,x] = F[129,x]*F[75,x]
F[215,x,k[0]] = F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]*F[57,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[83,x,k[0]]
F[218,x,k[0]] = F[18,x,k[0]]
F[219,x,k[0]] = F[103,x,k[0]]*F[69,x]*F[73,x,k[0]]
F[220,x,k[0]] = F[11,x]*F[221,x,k[0]]
F[221,x,k[0]] = (F[222,x,k[0]]*k[0]-F[222,x,1])/(-1+k[0])
F[222,x,k[0]] = F[19,x,k[0]]+F[5,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{215}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{214}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{69}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{136}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{y \left(F_{35}\! \left(x , 1\right)-F_{35}\! \left(x , y\right)\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = y x
F_{58}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{59}\! \left(x \right) F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{61}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{0}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x , 1\right)
F_{80}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{-F_{83}\! \left(x , y\right) y +F_{83}\! \left(x , 1\right)}{-1+y}
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right) F_{70}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{95}\! \left(x \right) = 4 F_{95} \left(x \right)^{2} x +x^{2}-8 F_{95}\! \left(x \right) x -F_{95} \left(x \right)^{2}+4 x +3 F_{95}\! \left(x \right)-1
F_{96}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{69} \left(x \right)^{2} F_{109}\! \left(x \right) F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{69}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)+F_{8}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{113}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{118}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{126}\! \left(x \right) = F_{127}\! \left(x , 1\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{75}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{109}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{129}\! \left(x \right) = F_{11}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{132}\! \left(x \right) = F_{11}\! \left(x \right) F_{129}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = -\frac{-F_{64}\! \left(x , y\right) y +F_{64}\! \left(x , 1\right)}{-1+y}
F_{135}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{159}\! \left(x \right)+F_{209}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x , 1\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{156}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = -\frac{y \left(F_{143}\! \left(x , 1\right)-F_{143}\! \left(x , y\right)\right)}{-1+y}
F_{143}\! \left(x , y\right) = -\frac{y \left(F_{144}\! \left(x , 1\right)-F_{144}\! \left(x , y\right)\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{146}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x , 1\right)
F_{149}\! \left(x , y\right) = x F_{149}\! \left(x , y\right)^{2} y +1
F_{150}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = -\frac{y \left(F_{140}\! \left(x , 1\right)-F_{140}\! \left(x , y\right)\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x , 1\right)
F_{155}\! \left(x , y\right) = -\frac{-F_{149}\! \left(x , y\right) y +F_{149}\! \left(x , 1\right)}{-1+y}
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , 1, y\right)
F_{158}\! \left(x , y , z\right) = -\frac{-F_{147}\! \left(x , y z \right) y +F_{147}\! \left(x , z\right)}{-1+y}
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x , 1\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{173}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = -\frac{y \left(F_{167}\! \left(x , 1\right)-F_{167}\! \left(x , y\right)\right)}{-1+y}
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = -\frac{y \left(F_{169}\! \left(x , 1\right)-F_{169}\! \left(x , y\right)\right)}{-1+y}
F_{169}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{166}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = -\frac{y \left(F_{163}\! \left(x , 1\right)-F_{163}\! \left(x , y\right)\right)}{-1+y}
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{184}\! \left(x \right)+F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{11}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{167}\! \left(x , 1\right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{11}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{118}\! \left(x , 1\right)
F_{188}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{206}\! \left(x , y\right)+F_{208}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = -\frac{-F_{195}\! \left(x , y\right) y +F_{195}\! \left(x , 1\right)}{-1+y}
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = -\frac{-F_{199}\! \left(x , y\right) y +F_{199}\! \left(x , 1\right)}{-1+y}
F_{199}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{195}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = -\frac{-F_{191}\! \left(x , y\right) y +F_{191}\! \left(x , 1\right)}{-1+y}
F_{208}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{11}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{136}\! \left(x \right)+F_{182}\! \left(x \right)
F_{212}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{214}\! \left(x \right) = F_{129}\! \left(x \right) F_{75}\! \left(x \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_{57}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = -\frac{-y F_{222}\! \left(x , y\right)+F_{222}\! \left(x , 1\right)}{-1+y}
F_{222}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{5}\! \left(x , y\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_11(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_7(x, k_0), -F_6(x, k_0) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_7(x, k_0), F_12(x, k_0) + F_220(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0)*F_57(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_11(x)*F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_219(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_54(x, k_0))
Eq(F_18(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x) + F_215(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_214(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_69(x))
Eq(F_24(x), F_0(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_136(x) + F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_24(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_120(x, k_0) + F_31(x, k_0) + F_8(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_212(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), -F_35(x, 1) + (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_6(x, k_0))
Eq(F_37(x, k_0), F_25(x) + F_36(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_39(x, k_0), F_136(x) + F_40(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_40(x, k_0) + F_40(x, 1))/(1 - k_0))
Eq(F_41(x, k_0), F_42(x) + F_47(x, k_0))
Eq(F_42(x), F_28(x) + F_43(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_19(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_11(x)*F_46(x, k_0))
Eq(F_46(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_57(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_58(x, k_0))
Eq(F_50(x, k_0), F_51(x)*F_54(x, k_0))
Eq(F_51(x), F_52(x, 1))
Eq(F_53(x, k_0), F_11(x)*F_52(x, k_0))
Eq(F_53(x, k_0), F_44(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_54(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x)
Eq(F_58(x, k_0), F_103(x, k_0)*F_59(x)*F_69(x))
Eq(F_59(x), F_60(x, 1))
Eq(F_61(x, k_0), F_129(x)*F_60(x, k_0)*F_69(x))
Eq(F_62(x, k_0), F_135(x, k_0) + F_61(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_133(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_11(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_72(x, k_0))
Eq(F_68(x, k_0), F_17(x, k_0)*F_69(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_69(x))
Eq(F_72(x, k_0), F_129(x)*F_69(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_79(x, k_0))
Eq(F_74(x, k_0), F_54(x, k_0)*F_75(x))
Eq(F_75(x), F_0(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_78(x))
Eq(F_78(x), F_73(x, 1))
Eq(F_80(x, k_0), F_125(x, k_0) + F_79(x, k_0))
Eq(F_81(x, k_0), F_11(x)*F_69(x)*F_80(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_83(x, k_0), F_124(x, k_0) + F_8(x) + F_82(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), F_19(x, k_0) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_11(x)*F_85(x, k_0))
Eq(F_85(x, k_0), (k_0*F_83(x, k_0) - F_83(x, 1))/(k_0 - 1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_54(x, k_0)*F_57(x, k_0)*F_70(x)*F_73(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_11(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_92(x, k_0), F_118(x, k_0) + F_91(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_94(x, k_0), F_107(x, k_0) + F_93(x, k_0) + F_95(x) + F_96(x, k_0))
Eq(F_94(x, k_0), F_29(x, k_0) + F_44(x, k_0))
Eq(F_95(x), x**2 + 4*x + (3 - 8*x)*F_95(x) + (4*x - 1)*F_95(x)**2 - 1)
Eq(F_96(x, k_0), F_57(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_94(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_57(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_102(x, k_0))
Eq(F_101(x, k_0), F_52(x, k_0)*F_54(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_60(x, k_0)*F_69(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_57(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_106(x, k_0) + F_8(x))
Eq(F_105(x, k_0), F_55(x, k_0)*F_57(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0)*F_57(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x)*F_11(x)*F_54(x, k_0)*F_69(x)**2)
Eq(F_109(x), F_0(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_0(x)*F_11(x)*F_112(x))
Eq(F_112(x), F_113(x) + F_69(x))
Eq(F_113(x), F_114(x) + F_70(x))
Eq(F_114(x), F_115(x) + F_117(x) + F_8(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_70(x))
Eq(F_117(x), F_11(x)*F_113(x))
Eq(F_119(x, k_0), F_11(x)*F_118(x, k_0))
Eq(F_29(x, k_0), F_119(x, k_0) + F_120(x, k_0) + F_95(x))
Eq(F_120(x, k_0), F_121(x, k_0)*F_57(x, k_0))
Eq(F_97(x, k_0), F_121(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_124(x, k_0), F_122(x, k_0)*F_57(x, k_0))
Eq(F_125(x, k_0), F_126(x)*F_54(x, k_0))
Eq(F_126(x), F_127(x, 1))
Eq(F_127(x, k_0), F_128(x, k_0) + F_75(x))
Eq(F_128(x, k_0), F_109(x)*F_55(x, k_0))
Eq(F_129(x), F_11(x) + F_130(x))
Eq(F_130(x), F_131(x) + F_132(x) + F_8(x))
Eq(F_131(x), F_11(x)*F_70(x))
Eq(F_132(x), F_11(x)*F_129(x))
Eq(F_133(x, k_0), F_11(x)*F_134(x, k_0))
Eq(F_134(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_135(x, k_0), F_52(x, k_0)*F_69(x))
Eq(F_136(x), F_137(x) + F_159(x) + F_209(x))
Eq(F_137(x), F_138(x, 1))
Eq(F_138(x, k_0), F_139(x, k_0) + F_156(x, k_0) + F_8(x))
Eq(F_139(x, k_0), F_11(x)*F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_150(x, k_0) + F_152(x, k_0) + F_8(x))
Eq(F_141(x, k_0), F_11(x)*F_142(x, k_0))
Eq(F_142(x, k_0), -F_143(x, 1) + (k_0*F_143(x, k_0) - F_143(x, 1))/(k_0 - 1))
Eq(F_143(x, k_0), -F_144(x, 1) + (k_0*F_144(x, k_0) - F_144(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), F_145(x, k_0) + F_146(x, k_0) + F_8(x))
Eq(F_145(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_57(x, k_0))
Eq(F_147(x, k_0), F_144(x, k_0) + F_148(x))
Eq(F_148(x), F_149(x, 1))
Eq(F_149(x, k_0), k_0*x*F_149(x, k_0)**2 + 1)
Eq(F_150(x, k_0), F_11(x)*F_151(x, k_0))
Eq(F_151(x, k_0), -F_140(x, 1) + (k_0*F_140(x, k_0) - F_140(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_153(x, k_0)*F_57(x, k_0))
Eq(F_153(x, k_0), F_140(x, k_0) + F_154(x))
Eq(F_154(x), F_155(x, 1))
Eq(F_155(x, k_0), (-k_0*F_149(x, k_0) + F_149(x, 1))/(1 - k_0))
Eq(F_156(x, k_0), F_157(x, k_0)*F_57(x, k_0))
Eq(F_157(x, k_0), F_158(x, 1, k_0))
Eq(F_158(x, k_0, k_1), (-k_0*k_1*F_147(x, k_0*k_1) + k_1*F_147(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x, 1))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_11(x)*F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0) + F_171(x, k_0) + F_173(x, k_0) + F_8(x))
Eq(F_164(x, k_0), F_165(x, k_0))
Eq(F_165(x, k_0), F_11(x)*F_166(x, k_0))
Eq(F_166(x, k_0), -F_167(x, 1) + (k_0*F_167(x, k_0) - F_167(x, 1))/(k_0 - 1))
Eq(F_167(x, k_0), F_168(x, k_0) + F_170(x, k_0))
Eq(F_168(x, k_0), -F_169(x, 1) + (k_0*F_169(x, k_0) - F_169(x, 1))/(k_0 - 1))
Eq(F_169(x, k_0), F_138(x, k_0) + F_161(x, k_0))
Eq(F_170(x, k_0), F_11(x)*F_166(x, k_0))
Eq(F_171(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_172(x, k_0), -F_163(x, 1) + (k_0*F_163(x, k_0) - F_163(x, 1))/(k_0 - 1))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_57(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_189(x, k_0))
Eq(F_176(x, k_0), F_163(x, k_0) + F_177(x))
Eq(F_177(x), F_178(x) + F_184(x) + F_4(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_11(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_39(x, 1))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_167(x, 1))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_11(x)*F_186(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_118(x, 1))
Eq(F_188(x), F_163(x, 1))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0)*F_57(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0) + F_206(x, k_0) + F_208(x, k_0) + F_4(x))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_193(x, k_0), F_11(x)*F_194(x, k_0))
Eq(F_194(x, k_0), (k_0*F_195(x, k_0) - F_195(x, 1))/(k_0 - 1))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_203(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), (k_0*F_199(x, k_0) - F_199(x, 1))/(k_0 - 1))
Eq(F_199(x, k_0), F_0(x) + F_200(x, k_0) + F_202(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_11(x)*F_195(x, k_0))
Eq(F_202(x, k_0), F_199(x, k_0)*F_57(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0))
Eq(F_204(x, k_0), F_11(x)*F_205(x, k_0))
Eq(F_205(x, k_0), F_194(x, k_0))
Eq(F_206(x, k_0), F_11(x)*F_207(x, k_0))
Eq(F_207(x, k_0), (k_0*F_191(x, k_0) - F_191(x, 1))/(k_0 - 1))
Eq(F_208(x, k_0), F_191(x, k_0)*F_57(x, k_0))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_11(x)*F_211(x))
Eq(F_211(x), F_136(x) + F_182(x))
Eq(F_212(x, k_0), F_11(x)*F_213(x, k_0))
Eq(F_213(x, k_0), -F_33(x, 1) + (k_0*F_33(x, k_0) - F_33(x, 1))/(k_0 - 1))
Eq(F_214(x), F_129(x)*F_75(x))
Eq(F_215(x, k_0), F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0)*F_57(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_83(x, k_0))
Eq(F_218(x, k_0), F_18(x, k_0))
Eq(F_219(x, k_0), F_103(x, k_0)*F_69(x)*F_73(x, k_0))
Eq(F_220(x, k_0), F_11(x)*F_221(x, k_0))
Eq(F_221(x, k_0), (-k_0*F_222(x, k_0) + F_222(x, 1))/(1 - k_0))
Eq(F_222(x, k_0), F_19(x, k_0) + F_5(x, k_0))
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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "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": null}], "iterative": false}
Specification JSON:
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3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [3, 3], [3, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "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": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"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": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "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": [0, 1, 2], "pos": [[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, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[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": null, "col_idx": 0, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25267/
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[11,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[7,x,k[0]] = (F[6,x,k[0]]-F[6,x,1])/(-1+k[0])
F[7,x,k[0]] = F[12,x,k[0]]+F[219,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]*F[57,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[11,x]*F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[218,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[54,x,k[0]]
F[18,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x]+F[214,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[213,x]+F[23,x]
F[23,x] = F[24,x]*F[69,x]
F[24,x] = F[0,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[136,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[24,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[120,x,k[0]]+F[31,x,k[0]]+F[8,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[211,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = -k[0]*(F[35,x,1]-F[35,x,k[0]])/(-1+k[0])
F[35,x,k[0]] = F[36,x,k[0]]+F[6,x,k[0]]
F[37,x,k[0]] = F[25,x]+F[36,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[39,x,k[0]] = F[136,x]+F[40,x,k[0]]
F[41,x,k[0]] = (F[40,x,k[0]]*k[0]-F[40,x,1])/(-1+k[0])
F[41,x,k[0]] = F[42,x]+F[47,x,k[0]]
F[42,x] = F[28,x]+F[43,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[19,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[11,x]*F[46,x,k[0]]
F[46,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[57,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[58,x,k[0]]
F[50,x,k[0]] = F[51,x]*F[54,x,k[0]]
F[51,x] = F[52,x,1]
F[53,x,k[0]] = F[11,x]*F[52,x,k[0]]
F[53,x,k[0]] = F[44,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = k[0]*x
F[58,x,k[0]] = F[103,x,k[0]]*F[59,x]*F[69,x]
F[59,x] = F[60,x,1]
F[61,x,k[0]] = F[129,x]*F[60,x,k[0]]*F[69,x]
F[62,x,k[0]] = F[135,x,k[0]]+F[61,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[133,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[11,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[72,x,k[0]]
F[68,x,k[0]] = F[17,x,k[0]]*F[69,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[69,x]
F[72,x,k[0]] = F[129,x]*F[69,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[79,x,k[0]]
F[74,x,k[0]] = F[54,x,k[0]]*F[75,x]
F[75,x] = F[0,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[78,x]
F[78,x] = F[73,x,1]
F[80,x,k[0]] = F[125,x,k[0]]+F[79,x,k[0]]
F[81,x,k[0]] = F[11,x]*F[69,x]*F[80,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[83,x,k[0]] = F[124,x,k[0]]+F[8,x]+F[82,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = F[19,x,k[0]]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[11,x]*F[85,x,k[0]]
F[85,x,k[0]] = 1/(-1+k[0])*(F[83,x,k[0]]*k[0]-F[83,x,1])
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]*F[70,x]*F[73,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[11,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[92,x,k[0]] = F[118,x,k[0]]+F[91,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[94,x,k[0]] = F[107,x,k[0]]+F[93,x,k[0]]+F[95,x]+F[96,x,k[0]]
F[94,x,k[0]] = F[29,x,k[0]]+F[44,x,k[0]]
F[95,x] = -1+x^2+4*x+F[95,x]^2*(-1+4*x)+(3-8*x)*F[95,x]
F[96,x,k[0]] = F[57,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[94,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[57,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[102,x,k[0]]
F[101,x,k[0]] = F[52,x,k[0]]*F[54,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[60,x,k[0]]*F[69,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[57,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[106,x,k[0]]+F[8,x]
F[105,x,k[0]] = F[55,x,k[0]]*F[57,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]*F[57,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[69,x]^2*F[109,x]*F[11,x]*F[54,x,k[0]]
F[109,x] = F[0,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[0,x]*F[11,x]*F[112,x]
F[112,x] = F[113,x]+F[69,x]
F[113,x] = F[114,x]+F[70,x]
F[114,x] = F[115,x]+F[117,x]+F[8,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[70,x]
F[117,x] = F[11,x]*F[113,x]
F[119,x,k[0]] = F[11,x]*F[118,x,k[0]]
F[29,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]+F[95,x]
F[120,x,k[0]] = F[121,x,k[0]]*F[57,x,k[0]]
F[97,x,k[0]] = F[121,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[124,x,k[0]] = F[122,x,k[0]]*F[57,x,k[0]]
F[125,x,k[0]] = F[126,x]*F[54,x,k[0]]
F[126,x] = F[127,x,1]
F[127,x,k[0]] = F[128,x,k[0]]+F[75,x]
F[128,x,k[0]] = F[109,x]*F[55,x,k[0]]
F[129,x] = F[11,x]+F[130,x]
F[130,x] = F[131,x]+F[132,x]+F[8,x]
F[131,x] = F[11,x]*F[70,x]
F[132,x] = F[11,x]*F[129,x]
F[133,x,k[0]] = F[11,x]*F[134,x,k[0]]
F[134,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[135,x,k[0]] = F[52,x,k[0]]*F[69,x]
F[136,x] = F[137,x]+F[154,x]+F[208,x]
F[137,x] = -F[95,x]+F[138,x]
F[138,x] = F[1,x]+F[139,x]+F[151,x]
F[139,x] = F[11,x]*F[140,x]
F[140,x] = F[141,x,1]
F[141,x,k[0]] = F[1,x]+F[142,x,k[0]]+F[148,x,k[0]]+F[150,x,k[0]]
F[142,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[143,x,k[0]] = 1/(-1+k[0])*(F[144,x,k[0]]*k[0]-F[144,x,1])
F[144,x,k[0]] = 1/(-1+k[0])*(F[145,x,k[0]]*k[0]-F[145,x,1])
F[145,x,k[0]] = F[1,x]+F[146,x,k[0]]+F[147,x,k[0]]
F[146,x,k[0]] = F[11,x]*F[144,x,k[0]]
F[147,x,k[0]] = F[145,x,k[0]]*F[57,x,k[0]]
F[148,x,k[0]] = F[11,x]*F[149,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[141,x,k[0]]*k[0]-F[141,x,1])
F[150,x,k[0]] = F[141,x,k[0]]*F[57,x,k[0]]
F[151,x] = F[11,x]*F[152,x]
F[152,x] = F[153,x,1]
F[153,x,k[0]] = 1/(-1+k[0])*(F[145,x,k[0]]*k[0]-F[145,x,1])
F[154,x] = F[155,x]
F[155,x] = F[156,x,1]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[11,x]*F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[182,x,k[0]]+F[184,x,k[0]]+F[8,x]
F[159,x,k[0]] = F[160,x,k[0]]
F[160,x,k[0]] = F[11,x]*F[161,x,k[0]]
F[161,x,k[0]] = -k[0]*(F[162,x,1]-F[162,x,k[0]])/(-1+k[0])
F[162,x,k[0]] = F[163,x,k[0]]+F[181,x,k[0]]
F[163,x,k[0]] = -k[0]*(F[164,x,1]-F[164,x,k[0]])/(-1+k[0])
F[164,x,k[0]] = F[165,x,k[0]]+F[167,x,k[0]]+F[8,x]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[11,x]*F[162,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[57,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]+F[171,x,k[0]]
F[170,x,k[0]] = F[164,x,k[0]]+F[24,x]
F[171,x,k[0]] = F[172,x,k[0]]*F[57,x,k[0]]
F[172,x,k[0]] = F[0,x]+F[173,x,k[0]]+F[180,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[11,x]*F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[177,x,k[0]]
F[176,x,k[0]] = 1/(-1+k[0])*(F[172,x,k[0]]*k[0]-F[172,x,1])
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[11,x]*F[179,x,k[0]]
F[179,x,k[0]] = 1/(-1+k[0])*(F[175,x,k[0]]*k[0]-F[175,x,1])
F[180,x,k[0]] = F[172,x,k[0]]*F[57,x,k[0]]
F[181,x,k[0]] = F[11,x]*F[161,x,k[0]]
F[182,x,k[0]] = F[11,x]*F[183,x,k[0]]
F[183,x,k[0]] = -k[0]*(F[158,x,1]-F[158,x,k[0]])/(-1+k[0])
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[57,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]+F[200,x,k[0]]
F[187,x,k[0]] = F[158,x,k[0]]+F[188,x]
F[188,x] = F[189,x]+F[195,x]+F[4,x]
F[189,x] = F[190,x]
F[190,x] = F[11,x]*F[191,x]
F[191,x] = F[192,x]+F[193,x]
F[192,x] = F[39,x,1]
F[193,x] = F[194,x]
F[194,x] = F[162,x,1]
F[195,x] = F[196,x]
F[196,x] = F[11,x]*F[197,x]
F[197,x] = F[198,x]+F[199,x]
F[198,x] = F[118,x,1]
F[199,x] = F[158,x,1]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[57,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[205,x,k[0]]+F[207,x,k[0]]+F[4,x]
F[203,x,k[0]] = F[204,x,k[0]]
F[204,x,k[0]] = F[11,x]*F[179,x,k[0]]
F[205,x,k[0]] = F[11,x]*F[206,x,k[0]]
F[206,x,k[0]] = 1/(-1+k[0])*(F[202,x,k[0]]*k[0]-F[202,x,1])
F[207,x,k[0]] = F[202,x,k[0]]*F[57,x,k[0]]
F[208,x] = F[209,x]
F[209,x] = F[11,x]*F[210,x]
F[210,x] = F[136,x]+F[193,x]
F[211,x,k[0]] = F[11,x]*F[212,x,k[0]]
F[212,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[213,x] = F[129,x]*F[75,x]
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[57,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[83,x,k[0]]
F[217,x,k[0]] = F[18,x,k[0]]
F[218,x,k[0]] = F[103,x,k[0]]*F[69,x]*F[73,x,k[0]]
F[219,x,k[0]] = F[11,x]*F[220,x,k[0]]
F[220,x,k[0]] = (F[221,x,k[0]]*k[0]-F[221,x,1])/(-1+k[0])
F[221,x,k[0]] = F[19,x,k[0]]+F[5,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{219}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{214}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{213}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{69}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{136}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{y \left(F_{35}\! \left(x , 1\right)-F_{35}\! \left(x , y\right)\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = y x
F_{58}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{59}\! \left(x \right) F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{61}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{0}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x , 1\right)
F_{80}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{-F_{83}\! \left(x , y\right) y +F_{83}\! \left(x , 1\right)}{-1+y}
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right) F_{70}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{95}\! \left(x \right) = 4 F_{95} \left(x \right)^{2} x +x^{2}-8 F_{95}\! \left(x \right) x -F_{95} \left(x \right)^{2}+4 x +3 F_{95}\! \left(x \right)-1
F_{96}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{69} \left(x \right)^{2} F_{109}\! \left(x \right) F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{69}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)+F_{8}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{113}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{118}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{126}\! \left(x \right) = F_{127}\! \left(x , 1\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{75}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{109}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{129}\! \left(x \right) = F_{11}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{132}\! \left(x \right) = F_{11}\! \left(x \right) F_{129}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = -\frac{-F_{64}\! \left(x , y\right) y +F_{64}\! \left(x , 1\right)}{-1+y}
F_{135}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{154}\! \left(x \right)+F_{208}\! \left(x \right)
F_{137}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{1}\! \left(x \right)+F_{139}\! \left(x \right)+F_{151}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x , 1\right)
F_{141}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = -\frac{-F_{144}\! \left(x , y\right) y +F_{144}\! \left(x , 1\right)}{-1+y}
F_{144}\! \left(x , y\right) = -\frac{-F_{145}\! \left(x , y\right) y +F_{145}\! \left(x , 1\right)}{-1+y}
F_{145}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{146}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-F_{141}\! \left(x , y\right) y +F_{141}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x , 1\right)
F_{153}\! \left(x , y\right) = -\frac{-F_{145}\! \left(x , y\right) y +F_{145}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = -\frac{y \left(F_{162}\! \left(x , 1\right)-F_{162}\! \left(x , y\right)\right)}{-1+y}
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = -\frac{y \left(F_{164}\! \left(x , 1\right)-F_{164}\! \left(x , y\right)\right)}{-1+y}
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = -\frac{-F_{172}\! \left(x , y\right) y +F_{172}\! \left(x , 1\right)}{-1+y}
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = -\frac{-F_{175}\! \left(x , y\right) y +F_{175}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = -\frac{y \left(F_{158}\! \left(x , 1\right)-F_{158}\! \left(x , y\right)\right)}{-1+y}
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{195}\! \left(x \right)+F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{11}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{193}\! \left(x \right)
F_{192}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{162}\! \left(x , 1\right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{11}\! \left(x \right) F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{199}\! \left(x \right)
F_{198}\! \left(x \right) = F_{118}\! \left(x , 1\right)
F_{199}\! \left(x \right) = F_{158}\! \left(x , 1\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_{57}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = -\frac{-F_{202}\! \left(x , y\right) y +F_{202}\! \left(x , 1\right)}{-1+y}
F_{207}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{11}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{136}\! \left(x \right)+F_{193}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{213}\! \left(x \right) = F_{129}\! \left(x \right) F_{75}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = -\frac{-y F_{221}\! \left(x , y\right)+F_{221}\! \left(x , 1\right)}{-1+y}
F_{221}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{5}\! \left(x , y\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_11(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_7(x, k_0), -F_6(x, k_0) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_7(x, k_0), F_12(x, k_0) + F_219(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0)*F_57(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_11(x)*F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_218(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_54(x, k_0))
Eq(F_18(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x) + F_214(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_213(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_69(x))
Eq(F_24(x), F_0(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_136(x) + F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_24(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_120(x, k_0) + F_31(x, k_0) + F_8(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_211(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), -F_35(x, 1) + (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_6(x, k_0))
Eq(F_37(x, k_0), F_25(x) + F_36(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_39(x, k_0), F_136(x) + F_40(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_40(x, k_0) + F_40(x, 1))/(1 - k_0))
Eq(F_41(x, k_0), F_42(x) + F_47(x, k_0))
Eq(F_42(x), F_28(x) + F_43(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_19(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_11(x)*F_46(x, k_0))
Eq(F_46(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_57(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_58(x, k_0))
Eq(F_50(x, k_0), F_51(x)*F_54(x, k_0))
Eq(F_51(x), F_52(x, 1))
Eq(F_53(x, k_0), F_11(x)*F_52(x, k_0))
Eq(F_53(x, k_0), F_44(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_54(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x)
Eq(F_58(x, k_0), F_103(x, k_0)*F_59(x)*F_69(x))
Eq(F_59(x), F_60(x, 1))
Eq(F_61(x, k_0), F_129(x)*F_60(x, k_0)*F_69(x))
Eq(F_62(x, k_0), F_135(x, k_0) + F_61(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_133(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_11(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_72(x, k_0))
Eq(F_68(x, k_0), F_17(x, k_0)*F_69(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_69(x))
Eq(F_72(x, k_0), F_129(x)*F_69(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_79(x, k_0))
Eq(F_74(x, k_0), F_54(x, k_0)*F_75(x))
Eq(F_75(x), F_0(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_78(x))
Eq(F_78(x), F_73(x, 1))
Eq(F_80(x, k_0), F_125(x, k_0) + F_79(x, k_0))
Eq(F_81(x, k_0), F_11(x)*F_69(x)*F_80(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_83(x, k_0), F_124(x, k_0) + F_8(x) + F_82(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), F_19(x, k_0) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_11(x)*F_85(x, k_0))
Eq(F_85(x, k_0), (k_0*F_83(x, k_0) - F_83(x, 1))/(k_0 - 1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_54(x, k_0)*F_57(x, k_0)*F_70(x)*F_73(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_11(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_92(x, k_0), F_118(x, k_0) + F_91(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_94(x, k_0), F_107(x, k_0) + F_93(x, k_0) + F_95(x) + F_96(x, k_0))
Eq(F_94(x, k_0), F_29(x, k_0) + F_44(x, k_0))
Eq(F_95(x), x**2 + 4*x + (3 - 8*x)*F_95(x) + (4*x - 1)*F_95(x)**2 - 1)
Eq(F_96(x, k_0), F_57(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_94(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_57(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_102(x, k_0))
Eq(F_101(x, k_0), F_52(x, k_0)*F_54(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_60(x, k_0)*F_69(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_57(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_106(x, k_0) + F_8(x))
Eq(F_105(x, k_0), F_55(x, k_0)*F_57(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0)*F_57(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x)*F_11(x)*F_54(x, k_0)*F_69(x)**2)
Eq(F_109(x), F_0(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_0(x)*F_11(x)*F_112(x))
Eq(F_112(x), F_113(x) + F_69(x))
Eq(F_113(x), F_114(x) + F_70(x))
Eq(F_114(x), F_115(x) + F_117(x) + F_8(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_70(x))
Eq(F_117(x), F_11(x)*F_113(x))
Eq(F_119(x, k_0), F_11(x)*F_118(x, k_0))
Eq(F_29(x, k_0), F_119(x, k_0) + F_120(x, k_0) + F_95(x))
Eq(F_120(x, k_0), F_121(x, k_0)*F_57(x, k_0))
Eq(F_97(x, k_0), F_121(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_124(x, k_0), F_122(x, k_0)*F_57(x, k_0))
Eq(F_125(x, k_0), F_126(x)*F_54(x, k_0))
Eq(F_126(x), F_127(x, 1))
Eq(F_127(x, k_0), F_128(x, k_0) + F_75(x))
Eq(F_128(x, k_0), F_109(x)*F_55(x, k_0))
Eq(F_129(x), F_11(x) + F_130(x))
Eq(F_130(x), F_131(x) + F_132(x) + F_8(x))
Eq(F_131(x), F_11(x)*F_70(x))
Eq(F_132(x), F_11(x)*F_129(x))
Eq(F_133(x, k_0), F_11(x)*F_134(x, k_0))
Eq(F_134(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_135(x, k_0), F_52(x, k_0)*F_69(x))
Eq(F_136(x), F_137(x) + F_154(x) + F_208(x))
Eq(F_137(x), F_138(x) - F_95(x))
Eq(F_138(x), F_1(x) + F_139(x) + F_151(x))
Eq(F_139(x), F_11(x)*F_140(x))
Eq(F_140(x), F_141(x, 1))
Eq(F_141(x, k_0), F_1(x) + F_142(x, k_0) + F_148(x, k_0) + F_150(x, k_0))
Eq(F_142(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_143(x, k_0), (k_0*F_144(x, k_0) - F_144(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), (k_0*F_145(x, k_0) - F_145(x, 1))/(k_0 - 1))
Eq(F_145(x, k_0), F_1(x) + F_146(x, k_0) + F_147(x, k_0))
Eq(F_146(x, k_0), F_11(x)*F_144(x, k_0))
Eq(F_147(x, k_0), F_145(x, k_0)*F_57(x, k_0))
Eq(F_148(x, k_0), F_11(x)*F_149(x, k_0))
Eq(F_149(x, k_0), (k_0*F_141(x, k_0) - F_141(x, 1))/(k_0 - 1))
Eq(F_150(x, k_0), F_141(x, k_0)*F_57(x, k_0))
Eq(F_151(x), F_11(x)*F_152(x))
Eq(F_152(x), F_153(x, 1))
Eq(F_153(x, k_0), (-k_0*F_145(x, k_0) + F_145(x, 1))/(1 - k_0))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x, 1))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_11(x)*F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_182(x, k_0) + F_184(x, k_0) + F_8(x))
Eq(F_159(x, k_0), F_160(x, k_0))
Eq(F_160(x, k_0), F_11(x)*F_161(x, k_0))
Eq(F_161(x, k_0), -F_162(x, 1) + (k_0*F_162(x, k_0) - F_162(x, 1))/(k_0 - 1))
Eq(F_162(x, k_0), F_163(x, k_0) + F_181(x, k_0))
Eq(F_163(x, k_0), -F_164(x, 1) + (k_0*F_164(x, k_0) - F_164(x, 1))/(k_0 - 1))
Eq(F_164(x, k_0), F_165(x, k_0) + F_167(x, k_0) + F_8(x))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_11(x)*F_162(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_57(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_171(x, k_0))
Eq(F_170(x, k_0), F_164(x, k_0) + F_24(x))
Eq(F_171(x, k_0), F_172(x, k_0)*F_57(x, k_0))
Eq(F_172(x, k_0), F_0(x) + F_173(x, k_0) + F_180(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_11(x)*F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_177(x, k_0))
Eq(F_176(x, k_0), (k_0*F_172(x, k_0) - F_172(x, 1))/(k_0 - 1))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_11(x)*F_179(x, k_0))
Eq(F_179(x, k_0), (k_0*F_175(x, k_0) - F_175(x, 1))/(k_0 - 1))
Eq(F_180(x, k_0), F_172(x, k_0)*F_57(x, k_0))
Eq(F_181(x, k_0), F_11(x)*F_161(x, k_0))
Eq(F_182(x, k_0), F_11(x)*F_183(x, k_0))
Eq(F_183(x, k_0), -F_158(x, 1) + (k_0*F_158(x, k_0) - F_158(x, 1))/(k_0 - 1))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_57(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0) + F_200(x, k_0))
Eq(F_187(x, k_0), F_158(x, k_0) + F_188(x))
Eq(F_188(x), F_189(x) + F_195(x) + F_4(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_11(x)*F_191(x))
Eq(F_191(x), F_192(x) + F_193(x))
Eq(F_192(x), F_39(x, 1))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_162(x, 1))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_11(x)*F_197(x))
Eq(F_197(x), F_198(x) + F_199(x))
Eq(F_198(x), F_118(x, 1))
Eq(F_199(x), F_158(x, 1))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0)*F_57(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_205(x, k_0) + F_207(x, k_0) + F_4(x))
Eq(F_203(x, k_0), F_204(x, k_0))
Eq(F_204(x, k_0), F_11(x)*F_179(x, k_0))
Eq(F_205(x, k_0), F_11(x)*F_206(x, k_0))
Eq(F_206(x, k_0), (k_0*F_202(x, k_0) - F_202(x, 1))/(k_0 - 1))
Eq(F_207(x, k_0), F_202(x, k_0)*F_57(x, k_0))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_11(x)*F_210(x))
Eq(F_210(x), F_136(x) + F_193(x))
Eq(F_211(x, k_0), F_11(x)*F_212(x, k_0))
Eq(F_212(x, k_0), -F_33(x, 1) + (k_0*F_33(x, k_0) - F_33(x, 1))/(k_0 - 1))
Eq(F_213(x), F_129(x)*F_75(x))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_57(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_83(x, k_0))
Eq(F_217(x, k_0), F_18(x, k_0))
Eq(F_218(x, k_0), F_103(x, k_0)*F_69(x)*F_73(x, k_0))
Eq(F_219(x, k_0), F_11(x)*F_220(x, k_0))
Eq(F_220(x, k_0), (-k_0*F_221(x, k_0) + F_221(x, 1))/(1 - k_0))
Eq(F_221(x, k_0), F_19(x, k_0) + F_5(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}], "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, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 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{"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "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": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "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": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25822/
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[11,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[7,x,k[0]] = (F[6,x,k[0]]-F[6,x,1])/(-1+k[0])
F[7,x,k[0]] = F[12,x,k[0]]+F[219,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]*F[57,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[11,x]*F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[218,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[54,x,k[0]]
F[18,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x]+F[214,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[213,x]+F[23,x]
F[23,x] = F[24,x]*F[69,x]
F[24,x] = F[0,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[136,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[24,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[120,x,k[0]]+F[31,x,k[0]]+F[8,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[211,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = -k[0]*(F[35,x,1]-F[35,x,k[0]])/(-1+k[0])
F[35,x,k[0]] = F[36,x,k[0]]+F[6,x,k[0]]
F[37,x,k[0]] = F[25,x]+F[36,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[39,x,k[0]] = F[136,x]+F[40,x,k[0]]
F[41,x,k[0]] = (F[40,x,k[0]]*k[0]-F[40,x,1])/(-1+k[0])
F[41,x,k[0]] = F[42,x]+F[47,x,k[0]]
F[42,x] = F[28,x]+F[43,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[19,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[11,x]*F[46,x,k[0]]
F[46,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[57,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[58,x,k[0]]
F[50,x,k[0]] = F[51,x]*F[54,x,k[0]]
F[51,x] = F[52,x,1]
F[53,x,k[0]] = F[11,x]*F[52,x,k[0]]
F[53,x,k[0]] = F[44,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = k[0]*x
F[58,x,k[0]] = F[103,x,k[0]]*F[59,x]*F[69,x]
F[59,x] = F[60,x,1]
F[61,x,k[0]] = F[129,x]*F[60,x,k[0]]*F[69,x]
F[62,x,k[0]] = F[135,x,k[0]]+F[61,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[133,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[11,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[72,x,k[0]]
F[68,x,k[0]] = F[17,x,k[0]]*F[69,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[69,x]
F[72,x,k[0]] = F[129,x]*F[69,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[79,x,k[0]]
F[74,x,k[0]] = F[54,x,k[0]]*F[75,x]
F[75,x] = F[0,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[78,x]
F[78,x] = F[73,x,1]
F[80,x,k[0]] = F[125,x,k[0]]+F[79,x,k[0]]
F[81,x,k[0]] = F[11,x]*F[69,x]*F[80,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[83,x,k[0]] = F[124,x,k[0]]+F[8,x]+F[82,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = F[19,x,k[0]]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[11,x]*F[85,x,k[0]]
F[85,x,k[0]] = 1/(-1+k[0])*(F[83,x,k[0]]*k[0]-F[83,x,1])
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]*F[70,x]*F[73,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[11,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[92,x,k[0]] = F[118,x,k[0]]+F[91,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[94,x,k[0]] = F[107,x,k[0]]+F[93,x,k[0]]+F[95,x]+F[96,x,k[0]]
F[94,x,k[0]] = F[29,x,k[0]]+F[44,x,k[0]]
F[95,x] = -1+x^2+4*x+F[95,x]^2*(-1+4*x)+(3-8*x)*F[95,x]
F[96,x,k[0]] = F[57,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[94,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[57,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[102,x,k[0]]
F[101,x,k[0]] = F[52,x,k[0]]*F[54,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[60,x,k[0]]*F[69,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[57,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[106,x,k[0]]+F[8,x]
F[105,x,k[0]] = F[55,x,k[0]]*F[57,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]*F[57,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[69,x]^2*F[109,x]*F[11,x]*F[54,x,k[0]]
F[109,x] = F[0,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[0,x]*F[11,x]*F[112,x]
F[112,x] = F[113,x]+F[69,x]
F[113,x] = F[114,x]+F[70,x]
F[114,x] = F[115,x]+F[117,x]+F[8,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[70,x]
F[117,x] = F[11,x]*F[113,x]
F[119,x,k[0]] = F[11,x]*F[118,x,k[0]]
F[29,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]+F[95,x]
F[120,x,k[0]] = F[121,x,k[0]]*F[57,x,k[0]]
F[97,x,k[0]] = F[121,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[124,x,k[0]] = F[122,x,k[0]]*F[57,x,k[0]]
F[125,x,k[0]] = F[126,x]*F[54,x,k[0]]
F[126,x] = F[127,x,1]
F[127,x,k[0]] = F[128,x,k[0]]+F[75,x]
F[128,x,k[0]] = F[109,x]*F[55,x,k[0]]
F[129,x] = F[11,x]+F[130,x]
F[130,x] = F[131,x]+F[132,x]+F[8,x]
F[131,x] = F[11,x]*F[70,x]
F[132,x] = F[11,x]*F[129,x]
F[133,x,k[0]] = F[11,x]*F[134,x,k[0]]
F[134,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[135,x,k[0]] = F[52,x,k[0]]*F[69,x]
F[136,x] = F[137,x]+F[154,x]+F[208,x]
F[137,x] = -F[95,x]+F[138,x]
F[138,x] = F[1,x]+F[139,x]+F[151,x]
F[139,x] = F[11,x]*F[140,x]
F[140,x] = F[141,x,1]
F[141,x,k[0]] = F[1,x]+F[142,x,k[0]]+F[148,x,k[0]]+F[150,x,k[0]]
F[142,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[143,x,k[0]] = 1/(-1+k[0])*(F[144,x,k[0]]*k[0]-F[144,x,1])
F[144,x,k[0]] = 1/(-1+k[0])*(F[145,x,k[0]]*k[0]-F[145,x,1])
F[145,x,k[0]] = F[1,x]+F[146,x,k[0]]+F[147,x,k[0]]
F[146,x,k[0]] = F[11,x]*F[144,x,k[0]]
F[147,x,k[0]] = F[145,x,k[0]]*F[57,x,k[0]]
F[148,x,k[0]] = F[11,x]*F[149,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[141,x,k[0]]*k[0]-F[141,x,1])
F[150,x,k[0]] = F[141,x,k[0]]*F[57,x,k[0]]
F[151,x] = F[11,x]*F[152,x]
F[152,x] = F[153,x,1]
F[153,x,k[0]] = 1/(-1+k[0])*(F[145,x,k[0]]*k[0]-F[145,x,1])
F[154,x] = F[155,x]
F[155,x] = F[156,x,1]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[11,x]*F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[182,x,k[0]]+F[184,x,k[0]]+F[8,x]
F[159,x,k[0]] = F[160,x,k[0]]
F[160,x,k[0]] = F[11,x]*F[161,x,k[0]]
F[161,x,k[0]] = -k[0]*(F[162,x,1]-F[162,x,k[0]])/(-1+k[0])
F[162,x,k[0]] = F[163,x,k[0]]+F[181,x,k[0]]
F[163,x,k[0]] = -k[0]*(F[164,x,1]-F[164,x,k[0]])/(-1+k[0])
F[164,x,k[0]] = F[165,x,k[0]]+F[167,x,k[0]]+F[8,x]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[11,x]*F[162,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[57,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]+F[171,x,k[0]]
F[170,x,k[0]] = F[164,x,k[0]]+F[24,x]
F[171,x,k[0]] = F[172,x,k[0]]*F[57,x,k[0]]
F[172,x,k[0]] = F[0,x]+F[173,x,k[0]]+F[180,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[11,x]*F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[177,x,k[0]]
F[176,x,k[0]] = 1/(-1+k[0])*(F[172,x,k[0]]*k[0]-F[172,x,1])
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[11,x]*F[179,x,k[0]]
F[179,x,k[0]] = 1/(-1+k[0])*(F[175,x,k[0]]*k[0]-F[175,x,1])
F[180,x,k[0]] = F[172,x,k[0]]*F[57,x,k[0]]
F[181,x,k[0]] = F[11,x]*F[161,x,k[0]]
F[182,x,k[0]] = F[11,x]*F[183,x,k[0]]
F[183,x,k[0]] = -k[0]*(F[158,x,1]-F[158,x,k[0]])/(-1+k[0])
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[57,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]+F[200,x,k[0]]
F[187,x,k[0]] = F[158,x,k[0]]+F[188,x]
F[188,x] = F[189,x]+F[195,x]+F[4,x]
F[189,x] = F[190,x]
F[190,x] = F[11,x]*F[191,x]
F[191,x] = F[192,x]+F[193,x]
F[192,x] = F[39,x,1]
F[193,x] = F[194,x]
F[194,x] = F[162,x,1]
F[195,x] = F[196,x]
F[196,x] = F[11,x]*F[197,x]
F[197,x] = F[198,x]+F[199,x]
F[198,x] = F[118,x,1]
F[199,x] = F[158,x,1]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[57,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[205,x,k[0]]+F[207,x,k[0]]+F[4,x]
F[203,x,k[0]] = F[204,x,k[0]]
F[204,x,k[0]] = F[11,x]*F[179,x,k[0]]
F[205,x,k[0]] = F[11,x]*F[206,x,k[0]]
F[206,x,k[0]] = 1/(-1+k[0])*(F[202,x,k[0]]*k[0]-F[202,x,1])
F[207,x,k[0]] = F[202,x,k[0]]*F[57,x,k[0]]
F[208,x] = F[209,x]
F[209,x] = F[11,x]*F[210,x]
F[210,x] = F[136,x]+F[193,x]
F[211,x,k[0]] = F[11,x]*F[212,x,k[0]]
F[212,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[213,x] = F[129,x]*F[75,x]
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[57,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[83,x,k[0]]
F[217,x,k[0]] = F[18,x,k[0]]
F[218,x,k[0]] = F[103,x,k[0]]*F[69,x]*F[73,x,k[0]]
F[219,x,k[0]] = F[11,x]*F[220,x,k[0]]
F[220,x,k[0]] = (F[221,x,k[0]]*k[0]-F[221,x,1])/(-1+k[0])
F[221,x,k[0]] = F[19,x,k[0]]+F[5,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{219}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{214}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{213}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{69}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{136}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{y \left(F_{35}\! \left(x , 1\right)-F_{35}\! \left(x , y\right)\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = y x
F_{58}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{59}\! \left(x \right) F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{61}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{0}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x , 1\right)
F_{80}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{-F_{83}\! \left(x , y\right) y +F_{83}\! \left(x , 1\right)}{-1+y}
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right) F_{70}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{95}\! \left(x \right) = 4 F_{95} \left(x \right)^{2} x +x^{2}-8 F_{95}\! \left(x \right) x -F_{95} \left(x \right)^{2}+4 x +3 F_{95}\! \left(x \right)-1
F_{96}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{60}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{69} \left(x \right)^{2} F_{109}\! \left(x \right) F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{69}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)+F_{8}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{70}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{113}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{118}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{126}\! \left(x \right) = F_{127}\! \left(x , 1\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{75}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{109}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{129}\! \left(x \right) = F_{11}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{132}\! \left(x \right) = F_{11}\! \left(x \right) F_{129}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = -\frac{-F_{64}\! \left(x , y\right) y +F_{64}\! \left(x , 1\right)}{-1+y}
F_{135}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{154}\! \left(x \right)+F_{208}\! \left(x \right)
F_{137}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{1}\! \left(x \right)+F_{139}\! \left(x \right)+F_{151}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x , 1\right)
F_{141}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = -\frac{-F_{144}\! \left(x , y\right) y +F_{144}\! \left(x , 1\right)}{-1+y}
F_{144}\! \left(x , y\right) = -\frac{-F_{145}\! \left(x , y\right) y +F_{145}\! \left(x , 1\right)}{-1+y}
F_{145}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{146}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-F_{141}\! \left(x , y\right) y +F_{141}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x , 1\right)
F_{153}\! \left(x , y\right) = -\frac{-F_{145}\! \left(x , y\right) y +F_{145}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = -\frac{y \left(F_{162}\! \left(x , 1\right)-F_{162}\! \left(x , y\right)\right)}{-1+y}
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = -\frac{y \left(F_{164}\! \left(x , 1\right)-F_{164}\! \left(x , y\right)\right)}{-1+y}
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = -\frac{-F_{172}\! \left(x , y\right) y +F_{172}\! \left(x , 1\right)}{-1+y}
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = -\frac{-F_{175}\! \left(x , y\right) y +F_{175}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = -\frac{y \left(F_{158}\! \left(x , 1\right)-F_{158}\! \left(x , y\right)\right)}{-1+y}
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{195}\! \left(x \right)+F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{11}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{193}\! \left(x \right)
F_{192}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{162}\! \left(x , 1\right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{11}\! \left(x \right) F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{199}\! \left(x \right)
F_{198}\! \left(x \right) = F_{118}\! \left(x , 1\right)
F_{199}\! \left(x \right) = F_{158}\! \left(x , 1\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_{57}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = -\frac{-F_{202}\! \left(x , y\right) y +F_{202}\! \left(x , 1\right)}{-1+y}
F_{207}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{11}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{136}\! \left(x \right)+F_{193}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{213}\! \left(x \right) = F_{129}\! \left(x \right) F_{75}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{69}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = -\frac{-y F_{221}\! \left(x , y\right)+F_{221}\! \left(x , 1\right)}{-1+y}
F_{221}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{5}\! \left(x , y\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_11(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_7(x, k_0), -F_6(x, k_0) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_7(x, k_0), F_12(x, k_0) + F_219(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0)*F_57(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_11(x)*F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_218(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_54(x, k_0))
Eq(F_18(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x) + F_214(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_213(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_69(x))
Eq(F_24(x), F_0(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_136(x) + F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_24(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_120(x, k_0) + F_31(x, k_0) + F_8(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_211(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), -F_35(x, 1) + (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_6(x, k_0))
Eq(F_37(x, k_0), F_25(x) + F_36(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_39(x, k_0), F_136(x) + F_40(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_40(x, k_0) + F_40(x, 1))/(1 - k_0))
Eq(F_41(x, k_0), F_42(x) + F_47(x, k_0))
Eq(F_42(x), F_28(x) + F_43(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_19(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_11(x)*F_46(x, k_0))
Eq(F_46(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_57(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_58(x, k_0))
Eq(F_50(x, k_0), F_51(x)*F_54(x, k_0))
Eq(F_51(x), F_52(x, 1))
Eq(F_53(x, k_0), F_11(x)*F_52(x, k_0))
Eq(F_53(x, k_0), F_44(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_54(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x)
Eq(F_58(x, k_0), F_103(x, k_0)*F_59(x)*F_69(x))
Eq(F_59(x), F_60(x, 1))
Eq(F_61(x, k_0), F_129(x)*F_60(x, k_0)*F_69(x))
Eq(F_62(x, k_0), F_135(x, k_0) + F_61(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_133(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_11(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_72(x, k_0))
Eq(F_68(x, k_0), F_17(x, k_0)*F_69(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_69(x))
Eq(F_72(x, k_0), F_129(x)*F_69(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_79(x, k_0))
Eq(F_74(x, k_0), F_54(x, k_0)*F_75(x))
Eq(F_75(x), F_0(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_78(x))
Eq(F_78(x), F_73(x, 1))
Eq(F_80(x, k_0), F_125(x, k_0) + F_79(x, k_0))
Eq(F_81(x, k_0), F_11(x)*F_69(x)*F_80(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_83(x, k_0), F_124(x, k_0) + F_8(x) + F_82(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), F_19(x, k_0) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_11(x)*F_85(x, k_0))
Eq(F_85(x, k_0), (k_0*F_83(x, k_0) - F_83(x, 1))/(k_0 - 1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_54(x, k_0)*F_57(x, k_0)*F_70(x)*F_73(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_11(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_92(x, k_0), F_118(x, k_0) + F_91(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_94(x, k_0), F_107(x, k_0) + F_93(x, k_0) + F_95(x) + F_96(x, k_0))
Eq(F_94(x, k_0), F_29(x, k_0) + F_44(x, k_0))
Eq(F_95(x), x**2 + 4*x + (3 - 8*x)*F_95(x) + (4*x - 1)*F_95(x)**2 - 1)
Eq(F_96(x, k_0), F_57(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_94(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_57(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_102(x, k_0))
Eq(F_101(x, k_0), F_52(x, k_0)*F_54(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_60(x, k_0)*F_69(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_57(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_106(x, k_0) + F_8(x))
Eq(F_105(x, k_0), F_55(x, k_0)*F_57(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0)*F_57(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x)*F_11(x)*F_54(x, k_0)*F_69(x)**2)
Eq(F_109(x), F_0(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_0(x)*F_11(x)*F_112(x))
Eq(F_112(x), F_113(x) + F_69(x))
Eq(F_113(x), F_114(x) + F_70(x))
Eq(F_114(x), F_115(x) + F_117(x) + F_8(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_70(x))
Eq(F_117(x), F_11(x)*F_113(x))
Eq(F_119(x, k_0), F_11(x)*F_118(x, k_0))
Eq(F_29(x, k_0), F_119(x, k_0) + F_120(x, k_0) + F_95(x))
Eq(F_120(x, k_0), F_121(x, k_0)*F_57(x, k_0))
Eq(F_97(x, k_0), F_121(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_124(x, k_0), F_122(x, k_0)*F_57(x, k_0))
Eq(F_125(x, k_0), F_126(x)*F_54(x, k_0))
Eq(F_126(x), F_127(x, 1))
Eq(F_127(x, k_0), F_128(x, k_0) + F_75(x))
Eq(F_128(x, k_0), F_109(x)*F_55(x, k_0))
Eq(F_129(x), F_11(x) + F_130(x))
Eq(F_130(x), F_131(x) + F_132(x) + F_8(x))
Eq(F_131(x), F_11(x)*F_70(x))
Eq(F_132(x), F_11(x)*F_129(x))
Eq(F_133(x, k_0), F_11(x)*F_134(x, k_0))
Eq(F_134(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_135(x, k_0), F_52(x, k_0)*F_69(x))
Eq(F_136(x), F_137(x) + F_154(x) + F_208(x))
Eq(F_137(x), F_138(x) - F_95(x))
Eq(F_138(x), F_1(x) + F_139(x) + F_151(x))
Eq(F_139(x), F_11(x)*F_140(x))
Eq(F_140(x), F_141(x, 1))
Eq(F_141(x, k_0), F_1(x) + F_142(x, k_0) + F_148(x, k_0) + F_150(x, k_0))
Eq(F_142(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_143(x, k_0), (k_0*F_144(x, k_0) - F_144(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), (k_0*F_145(x, k_0) - F_145(x, 1))/(k_0 - 1))
Eq(F_145(x, k_0), F_1(x) + F_146(x, k_0) + F_147(x, k_0))
Eq(F_146(x, k_0), F_11(x)*F_144(x, k_0))
Eq(F_147(x, k_0), F_145(x, k_0)*F_57(x, k_0))
Eq(F_148(x, k_0), F_11(x)*F_149(x, k_0))
Eq(F_149(x, k_0), (k_0*F_141(x, k_0) - F_141(x, 1))/(k_0 - 1))
Eq(F_150(x, k_0), F_141(x, k_0)*F_57(x, k_0))
Eq(F_151(x), F_11(x)*F_152(x))
Eq(F_152(x), F_153(x, 1))
Eq(F_153(x, k_0), (-k_0*F_145(x, k_0) + F_145(x, 1))/(1 - k_0))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x, 1))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_11(x)*F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_182(x, k_0) + F_184(x, k_0) + F_8(x))
Eq(F_159(x, k_0), F_160(x, k_0))
Eq(F_160(x, k_0), F_11(x)*F_161(x, k_0))
Eq(F_161(x, k_0), -F_162(x, 1) + (k_0*F_162(x, k_0) - F_162(x, 1))/(k_0 - 1))
Eq(F_162(x, k_0), F_163(x, k_0) + F_181(x, k_0))
Eq(F_163(x, k_0), -F_164(x, 1) + (k_0*F_164(x, k_0) - F_164(x, 1))/(k_0 - 1))
Eq(F_164(x, k_0), F_165(x, k_0) + F_167(x, k_0) + F_8(x))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_11(x)*F_162(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_57(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_171(x, k_0))
Eq(F_170(x, k_0), F_164(x, k_0) + F_24(x))
Eq(F_171(x, k_0), F_172(x, k_0)*F_57(x, k_0))
Eq(F_172(x, k_0), F_0(x) + F_173(x, k_0) + F_180(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_11(x)*F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_177(x, k_0))
Eq(F_176(x, k_0), (k_0*F_172(x, k_0) - F_172(x, 1))/(k_0 - 1))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_11(x)*F_179(x, k_0))
Eq(F_179(x, k_0), (k_0*F_175(x, k_0) - F_175(x, 1))/(k_0 - 1))
Eq(F_180(x, k_0), F_172(x, k_0)*F_57(x, k_0))
Eq(F_181(x, k_0), F_11(x)*F_161(x, k_0))
Eq(F_182(x, k_0), F_11(x)*F_183(x, k_0))
Eq(F_183(x, k_0), -F_158(x, 1) + (k_0*F_158(x, k_0) - F_158(x, 1))/(k_0 - 1))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_57(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0) + F_200(x, k_0))
Eq(F_187(x, k_0), F_158(x, k_0) + F_188(x))
Eq(F_188(x), F_189(x) + F_195(x) + F_4(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_11(x)*F_191(x))
Eq(F_191(x), F_192(x) + F_193(x))
Eq(F_192(x), F_39(x, 1))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_162(x, 1))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_11(x)*F_197(x))
Eq(F_197(x), F_198(x) + F_199(x))
Eq(F_198(x), F_118(x, 1))
Eq(F_199(x), F_158(x, 1))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0)*F_57(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_205(x, k_0) + F_207(x, k_0) + F_4(x))
Eq(F_203(x, k_0), F_204(x, k_0))
Eq(F_204(x, k_0), F_11(x)*F_179(x, k_0))
Eq(F_205(x, k_0), F_11(x)*F_206(x, k_0))
Eq(F_206(x, k_0), (k_0*F_202(x, k_0) - F_202(x, 1))/(k_0 - 1))
Eq(F_207(x, k_0), F_202(x, k_0)*F_57(x, k_0))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_11(x)*F_210(x))
Eq(F_210(x), F_136(x) + F_193(x))
Eq(F_211(x, k_0), F_11(x)*F_212(x, k_0))
Eq(F_212(x, k_0), -F_33(x, 1) + (k_0*F_33(x, k_0) - F_33(x, 1))/(k_0 - 1))
Eq(F_213(x), F_129(x)*F_75(x))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_57(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_83(x, k_0))
Eq(F_217(x, k_0), F_18(x, k_0))
Eq(F_218(x, k_0), F_103(x, k_0)*F_69(x)*F_73(x, k_0))
Eq(F_219(x, k_0), F_11(x)*F_220(x, k_0))
Eq(F_220(x, k_0), (-k_0*F_221(x, k_0) + F_221(x, 1))/(1 - k_0))
Eq(F_221(x, k_0), F_19(x, k_0) + F_5(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}], "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, 1, 2, 3, 4], [0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], 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