02413_02431_03412_03421_04312_04321_021534_021543_240513_240531_250413_250431_2430615_2430651_3560214_3560241_3650214_3650241_35470216_35470261
Counting sequence:
1, 1, 2, 6, 24, 114, 592, 3216, 17904, 101198, 578208, 3332136, 19343408, 113017332, 664168160, 3923729280, 23291913440, 138872375958, 831321465408, 4994806458040, 30111586314800, 182094123983660, 1104331746746208, 6715050373394528, 40931670125150624, 250065092876686924, 1530948705125205952, 9391164635349135184, 57712883173474920672, 355278672452949923560, 2190593493657993981120, 13527207348811788869504, 83650648836665975778240, 517976091727838401128166, 3211417140000833544987776, 19934270554398083221073496, 123877656936166895073944112, 770635729960102081516035068, 4798939374666976163156157536, 29912969335586894114714389920, 186625796812041641097897113120, 1165367452189729784504046559140, 7283089113217920933785333553344, 45552639243713249344904920179504, 285128989647080791357190264674720, 1786013888917022500332882502088280, 11195165895557022603116936448221760, 70220825218631387592396864972349440, 440736713767579767576463367255054400, 2767957057040814525355061607346790268, 17393855080190387374094396630975000448, 109365133507026059165384524080374165296, 688017021377838344130245097733220567264, 4330598895441826345475618649106173204408, 27271996070021852751216389994455887713216, 171829696796744744714708266021178358552256, 1083139548298086613138407631973222614494272, 6830750714268676951760491527400106384671832, 43096657832575127799649888948872379901930880, 272021676761010605119307648868273645451238048, 1717679555893446120510630470303540765575119808, 10850599393346162313388632142523005221037965776, 68569782752779398845464471820218691718415930752, 433484972816157489047271349775531815678759936256, 2741400948399872791796877163787255192633871228800, 17342972869655148106533821276511461806198817446790, 109754529788636630052642595161499901742371506407680, 694808198078416458784874786194226049385407138577304, 4399940710877292126834251888507050696861068220576304, 27871743758015182455768642325063639802905443041792540, 176609095729736181653655997197886785922422359043382880, 1119411969150975481037706301779550800313107699964502560, 7097269093342356609543367618090478894305995800570012448, 45010483581457051844797358039389667203001891614156527028, 285531441023597845237471130115361241809502639821776470720, 1811794527807107987302297250653521909626489262764207807600, 11499414175104951904705651574173435633011077825420544706080, 73004795311017721839623829459488923981926329738145184357112, 463589081768776574998249248025024318059030145030675802481472, 2944547031807351987441839670839580337821009953273562108926720, 18707024707521029804479312861957183339637705013106923341652800, 118874693121232239783888217069366780476514337601393582869224980, 755562139979964935352794826178086792520930166633454895167811968, 4803355914936035359685773771533564540368029550374335207879901328, 30542947065165419131386189884542473544804371884937635126799387040, 194252479618025632833174353104264649131999350534487460016877038760, 1235690207039278850064307558193227951649179924459224598837675750720, 7862090746550962788831771224701628685830093993246966362577133422912, 50032245209166727321602171661362762908650682867935510702233499520192, 318451697496443054379696579887262191023864430236864251915407824222120, 2027295162002683017567625570851135853765994950444942374804834844680320, 12908283717359266254277107673336445451121597375847772371029449972908640, 82204660933836882438845173058037186325308772214093633387514693395574848, 523599443552200432465717992639289321741070003785135519473942267225375408, 3335608932959169763377348108384354375826223763996530548773385478532065920, 21253123761307611635782963817903362184007194193931674668779433412641322240, 135438029229269498676709715430728744342286786466147546200909939016253719680, 863231455594726263969688777977133420134696124014488960353490779234187544540, 5502768917047942502534607710963309281953927769339237086006417774363839635200, 35083372196888682630972327260311225189938528122731882101626767786562793473520, 223710369254739685383518685393247501479949774964895335343769527441000112347360
Specification 1
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24340/
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[33,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[33,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[181,x,k[0]]+F[183,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]+F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]
F[13,x,k[0]] = F[12,x,k[0]]*F[33,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[16,x,k[0]]+F[180,x,k[0]]
F[15,x] = 0
F[16,x,k[0]] = F[17,x,k[0]]*F[33,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[36,x,k[0]]
F[20,x,k[0]] = F[178,x,k[0]]+F[19,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]*F[33,x]
F[22,x,k[0]] = F[176,x,k[0]]+F[21,x,k[0]]+F[83,x,k[0]]
F[22,x,k[0]] = F[174,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[172,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[48,x,k[0]]
F[25,x,k[0]] = F[26,x]*F[45,x,k[0]]
F[26,x] = F[0,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[33,x]*F[37,x]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = F[31,x]+F[34,x,k[0]]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[29,x]*F[33,x]
F[33,x] = x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[30,x,k[0]]*F[31,x]*F[36,x,k[0]]
F[36,x,k[0]] = k[0]*x
F[37,x] = 1/F[29,x]/F[33,x]/F[40,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[33,x]*F[40,x]*F[41,x]
F[40,x] = F[12,x,1]
F[41,x] = F[42,x,1]
F[42,x,k[0]] = F[30,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[30,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[36,x,k[0]]*F[45,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[12,x,k[0]]*F[33,x]*F[50,x]
F[50,x] = 1/F[33,x]/F[40,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[170,x]+F[53,x]+F[55,x]
F[53,x] = F[54,x]
F[54,x] = F[10,x,1]
F[55,x] = F[33,x]*F[56,x]
F[56,x] = F[57,x]+F[63,x]
F[57,x] = F[15,x]+F[58,x]+F[62,x]
F[58,x] = F[33,x]*F[41,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[33,x]*F[59,x]
F[62,x] = F[33,x]*F[57,x]
F[63,x] = 1/F[33,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[15,x]-F[76,x]+F[66,x]
F[66,x] = -F[67,x]+F[7,x]
F[67,x] = F[4,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[33,x]*F[70,x]
F[70,x] = F[57,x]+F[71,x]
F[71,x] = F[59,x]*F[72,x]
F[72,x] = F[4,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x,1]
F[75,x,k[0]] = F[43,x,k[0]]
F[76,x] = F[77,x,1]
F[77,x,k[0]] = F[33,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]+F[79,x,k[0]]+F[85,x,k[0]]
F[80,x,k[0]] = F[33,x]*F[79,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[80,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[36,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[84,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]+F[45,x,k[0]]
F[84,x,k[0]] = F[11,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[33,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[92,x,k[0]]
F[88,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[89,x,k[0]] = F[19,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[29,x]*F[33,x]*F[41,x]*F[83,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[36,x,k[0]]*F[83,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]+F[99,x,k[0]]
F[95,x,k[0]] = F[41,x]*F[96,x,k[0]]
F[97,x,k[0]] = F[33,x]*F[96,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[97,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[30,x,k[0]]*F[36,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[30,x,k[0]]
F[100,x,k[0]] = -k[0]*(F[101,x,1]-F[101,x,k[0]])/(-1+k[0])
F[102,x,k[0]] = F[101,x,k[0]]+F[29,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[29,x]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[102,x,k[0]]*F[30,x,k[0]]*F[36,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[33,x]
F[106,x,k[0]] = 1/(-1+k[0])*(F[78,x,k[0]]*k[0]-F[78,x,1])
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[36,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]*F[33,x]
F[111,x,k[0]] = F[110,x,k[0]]+F[153,x,k[0]]+F[159,x,k[0]]+F[161,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[151,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[8,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[36,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]*F[36,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]+F[12,x,k[0]]+F[149,x,k[0]]
F[119,x,k[0]] = F[118,x,k[0]]*F[33,x]
F[119,x,k[0]] = F[120,x,k[0]]
F[121,x,k[0]] = F[120,x,k[0]]+F[144,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[142,x,k[0]]
F[122,x,k[0]] = F[0,x]+F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[36,x,k[0]]
F[126,x,k[0]] = F[125,x,k[0]]+F[140,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[138,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[26,x]*F[45,x,k[0]]
F[129,x,k[0]] = F[1,x]+F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[36,x,k[0]]
F[132,x,k[0]] = F[129,x,k[0]]+F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[36,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[136,x,k[0]]+F[15,x]
F[135,x,k[0]] = F[130,x,k[0]]*F[36,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[36,x,k[0]]
F[137,x,k[0]] = F[133,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[118,x,k[0]]*F[33,x]*F[50,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[121,x,k[0]]*F[29,x]*F[33,x]*F[37,x]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[125,x,k[0]]*F[36,x,k[0]]
F[144,x,k[0]] = F[129,x,k[0]]+F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[46,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]*F[36,x,k[0]]
F[148,x,k[0]] = F[130,x,k[0]]+F[146,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]
F[150,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[157,x,k[0]]
F[154,x,k[0]] = F[0,x]+F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[36,x,k[0]]*F[8,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[118,x,k[0]]*F[36,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]
F[160,x,k[0]] = F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[36,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]+F[169,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[168,x,k[0]]
F[166,x,k[0]] = F[165,x,k[0]]*F[36,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]
F[8,x,k[0]] = F[154,x,k[0]]+F[167,x,k[0]]+F[77,x,k[0]]
F[168,x,k[0]] = F[113,x,k[0]]
F[169,x,k[0]] = F[152,x,k[0]]
F[170,x] = F[171,x]
F[171,x] = F[33,x]*F[41,x]*F[53,x]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[29,x]*F[33,x]*F[37,x]*F[83,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[31,x]*F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[102,x,k[0]]*F[30,x,k[0]]*F[36,x,k[0]]*F[83,x,k[0]]
F[180,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[33,x]
F[182,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[111,x,k[0]]*F[36,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_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{33}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = y x
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right) F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{33}\! \left(x \right) F_{40}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{170}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{55}\! \left(x \right) = F_{33}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{33}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{33}\! \left(x \right) F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{15}\! \left(x \right)-F_{76}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{7}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{33}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{57}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{59}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x , 1\right)
F_{75}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{76}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{89}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = -\frac{y \left(F_{101}\! \left(x , 1\right)-F_{101}\! \left(x , y\right)\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{106}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{159}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{182}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{36}\! \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_33(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_33(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_181(x, k_0) + F_183(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x) + F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_36(x, k_0))
Eq(F_13(x, k_0), F_12(x, k_0)*F_33(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_16(x, k_0) + F_180(x, k_0))
Eq(F_15(x), 0)
Eq(F_16(x, k_0), F_17(x, k_0)*F_33(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_36(x, k_0))
Eq(F_20(x, k_0), F_178(x, k_0) + F_19(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0)*F_33(x))
Eq(F_22(x, k_0), F_176(x, k_0) + F_21(x, k_0) + F_83(x, k_0))
Eq(F_22(x, k_0), F_174(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_172(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_48(x, k_0))
Eq(F_25(x, k_0), F_26(x)*F_45(x, k_0))
Eq(F_26(x), F_0(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_33(x)*F_37(x))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), F_31(x) + F_34(x, k_0))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_29(x)*F_33(x))
Eq(F_33(x), x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_30(x, k_0)*F_31(x)*F_36(x, k_0))
Eq(F_36(x, k_0), k_0*x)
Eq(F_37(x), F_38(x)/(F_29(x)*F_33(x)*F_40(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_33(x)*F_40(x)*F_41(x))
Eq(F_40(x), F_12(x, 1))
Eq(F_41(x), F_42(x, 1))
Eq(F_42(x, k_0), F_30(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_30(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_36(x, k_0)*F_45(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_12(x, k_0)*F_33(x)*F_50(x))
Eq(F_50(x), F_51(x)/(F_33(x)*F_40(x)))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_170(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_10(x, 1))
Eq(F_55(x), F_33(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_63(x))
Eq(F_57(x), F_15(x) + F_58(x) + F_62(x))
Eq(F_58(x), F_33(x)*F_41(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_33(x)*F_59(x))
Eq(F_62(x), F_33(x)*F_57(x))
Eq(F_63(x), F_64(x)/F_33(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_15(x) + F_66(x) - F_76(x))
Eq(F_66(x), -F_67(x) + F_7(x))
Eq(F_67(x), F_4(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_33(x)*F_70(x))
Eq(F_70(x), F_57(x) + F_71(x))
Eq(F_71(x), F_59(x)*F_72(x))
Eq(F_72(x), F_4(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x, 1))
Eq(F_75(x, k_0), F_43(x, k_0))
Eq(F_76(x), F_77(x, 1))
Eq(F_77(x, k_0), F_33(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_105(x, k_0) + F_107(x, k_0) + F_79(x, k_0) + F_85(x, k_0))
Eq(F_80(x, k_0), F_33(x)*F_79(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_80(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_36(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_84(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0) + F_45(x, k_0))
Eq(F_84(x, k_0), F_11(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_33(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_92(x, k_0))
Eq(F_88(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_89(x, k_0), F_19(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_29(x)*F_33(x)*F_41(x)*F_83(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_36(x, k_0)*F_83(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0) + F_99(x, k_0))
Eq(F_95(x, k_0), F_41(x)*F_96(x, k_0))
Eq(F_97(x, k_0), F_33(x)*F_96(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_97(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_30(x, k_0)*F_36(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_30(x, k_0))
Eq(F_100(x, k_0), -F_101(x, 1) + (k_0*F_101(x, k_0) - F_101(x, 1))/(k_0 - 1))
Eq(F_102(x, k_0), F_101(x, k_0) + F_29(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_29(x))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_102(x, k_0)*F_30(x, k_0)*F_36(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_33(x))
Eq(F_106(x, k_0), (k_0*F_78(x, k_0) - F_78(x, 1))/(k_0 - 1))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_36(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0)*F_33(x))
Eq(F_111(x, k_0), F_110(x, k_0) + F_153(x, k_0) + F_159(x, k_0) + F_161(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_151(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_8(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_36(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0)*F_36(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_118(x, k_0), F_117(x, k_0) + F_12(x, k_0) + F_149(x, k_0))
Eq(F_119(x, k_0), F_118(x, k_0)*F_33(x))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_121(x, k_0), F_120(x, k_0) + F_144(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_142(x, k_0))
Eq(F_122(x, k_0), F_0(x) + F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_36(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0) + F_140(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_138(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_26(x)*F_45(x, k_0))
Eq(F_129(x, k_0), F_1(x) + F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_36(x, k_0))
Eq(F_132(x, k_0), F_129(x, k_0) + F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_36(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_136(x, k_0) + F_15(x))
Eq(F_135(x, k_0), F_130(x, k_0)*F_36(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_36(x, k_0))
Eq(F_137(x, k_0), F_133(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_118(x, k_0)*F_33(x)*F_50(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_121(x, k_0)*F_29(x)*F_33(x)*F_37(x))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_125(x, k_0)*F_36(x, k_0))
Eq(F_144(x, k_0), F_129(x, k_0) + F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_46(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0)*F_36(x, k_0))
Eq(F_148(x, k_0), F_130(x, k_0) + F_146(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0))
Eq(F_150(x, k_0), F_12(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_12(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_157(x, k_0))
Eq(F_154(x, k_0), F_0(x) + F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_36(x, k_0)*F_8(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_118(x, k_0)*F_36(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0))
Eq(F_160(x, k_0), F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_36(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0) + F_169(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_168(x, k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_36(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_8(x, k_0), F_154(x, k_0) + F_167(x, k_0) + F_77(x, k_0))
Eq(F_168(x, k_0), F_113(x, k_0))
Eq(F_169(x, k_0), F_152(x, k_0))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_33(x)*F_41(x)*F_53(x))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_29(x)*F_33(x)*F_37(x)*F_83(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_31(x)*F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_102(x, k_0)*F_30(x, k_0)*F_36(x, k_0)*F_83(x, k_0))
Eq(F_180(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_33(x))
Eq(F_182(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_111(x, k_0)*F_36(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 5, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 5, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 5, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 6, 1, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 6, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 6, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 6, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 6, 5, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 6, 5, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 7, 0, 2, 1, 6], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 7, 0, 2, 6, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 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[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1], [2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 2
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24360/
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[33,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[33,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[181,x,k[0]]+F[183,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]+F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]
F[13,x,k[0]] = F[12,x,k[0]]*F[33,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[16,x,k[0]]+F[180,x,k[0]]
F[15,x] = 0
F[16,x,k[0]] = F[17,x,k[0]]*F[33,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[36,x,k[0]]
F[20,x,k[0]] = F[178,x,k[0]]+F[19,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]*F[33,x]
F[22,x,k[0]] = F[176,x,k[0]]+F[21,x,k[0]]+F[83,x,k[0]]
F[22,x,k[0]] = F[174,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[172,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[48,x,k[0]]
F[25,x,k[0]] = F[26,x]*F[45,x,k[0]]
F[26,x] = F[0,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[33,x]*F[37,x]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = F[31,x]+F[34,x,k[0]]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[29,x]*F[33,x]
F[33,x] = x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[30,x,k[0]]*F[31,x]*F[36,x,k[0]]
F[36,x,k[0]] = k[0]*x
F[37,x] = 1/F[29,x]/F[33,x]/F[40,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[33,x]*F[40,x]*F[41,x]
F[40,x] = F[12,x,1]
F[41,x] = F[42,x,1]
F[42,x,k[0]] = F[30,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[30,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[36,x,k[0]]*F[45,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[12,x,k[0]]*F[33,x]*F[50,x]
F[50,x] = 1/F[33,x]/F[40,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[170,x]+F[53,x]+F[55,x]
F[53,x] = F[54,x]
F[54,x] = F[10,x,1]
F[55,x] = F[33,x]*F[56,x]
F[56,x] = F[57,x]+F[63,x]
F[57,x] = F[15,x]+F[58,x]+F[62,x]
F[58,x] = F[33,x]*F[41,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[33,x]*F[59,x]
F[62,x] = F[33,x]*F[57,x]
F[63,x] = 1/F[33,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[15,x]-F[76,x]+F[66,x]
F[66,x] = -F[67,x]+F[7,x]
F[67,x] = F[4,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[33,x]*F[70,x]
F[70,x] = F[57,x]+F[71,x]
F[71,x] = F[59,x]*F[72,x]
F[72,x] = F[4,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x,1]
F[75,x,k[0]] = F[43,x,k[0]]
F[76,x] = F[77,x,1]
F[77,x,k[0]] = F[33,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]+F[79,x,k[0]]+F[85,x,k[0]]
F[80,x,k[0]] = F[33,x]*F[79,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[80,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[36,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[84,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]+F[45,x,k[0]]
F[84,x,k[0]] = F[11,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[33,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[92,x,k[0]]
F[88,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[89,x,k[0]] = F[19,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[29,x]*F[33,x]*F[41,x]*F[83,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[36,x,k[0]]*F[83,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]+F[99,x,k[0]]
F[95,x,k[0]] = F[41,x]*F[96,x,k[0]]
F[97,x,k[0]] = F[33,x]*F[96,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[97,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[30,x,k[0]]*F[36,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[30,x,k[0]]
F[100,x,k[0]] = -k[0]*(F[101,x,1]-F[101,x,k[0]])/(-1+k[0])
F[102,x,k[0]] = F[101,x,k[0]]+F[29,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[29,x]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[102,x,k[0]]*F[30,x,k[0]]*F[36,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[33,x]
F[106,x,k[0]] = 1/(-1+k[0])*(F[78,x,k[0]]*k[0]-F[78,x,1])
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[36,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]*F[33,x]
F[111,x,k[0]] = F[110,x,k[0]]+F[153,x,k[0]]+F[159,x,k[0]]+F[161,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[151,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[8,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[36,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]*F[36,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]+F[12,x,k[0]]+F[149,x,k[0]]
F[119,x,k[0]] = F[118,x,k[0]]*F[33,x]
F[119,x,k[0]] = F[120,x,k[0]]
F[121,x,k[0]] = F[120,x,k[0]]+F[144,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[142,x,k[0]]
F[122,x,k[0]] = F[0,x]+F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[36,x,k[0]]
F[126,x,k[0]] = F[125,x,k[0]]+F[140,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[138,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[26,x]*F[45,x,k[0]]
F[129,x,k[0]] = F[1,x]+F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[36,x,k[0]]
F[132,x,k[0]] = F[129,x,k[0]]+F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[36,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[136,x,k[0]]+F[15,x]
F[135,x,k[0]] = F[130,x,k[0]]*F[36,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[36,x,k[0]]
F[137,x,k[0]] = F[133,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[118,x,k[0]]*F[33,x]*F[50,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[121,x,k[0]]*F[29,x]*F[33,x]*F[37,x]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[125,x,k[0]]*F[36,x,k[0]]
F[144,x,k[0]] = F[129,x,k[0]]+F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[46,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]*F[36,x,k[0]]
F[148,x,k[0]] = F[130,x,k[0]]+F[146,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]
F[150,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[12,x,k[0]]*F[36,x,k[0]]*F[42,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[157,x,k[0]]
F[154,x,k[0]] = F[0,x]+F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[36,x,k[0]]*F[8,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[118,x,k[0]]*F[36,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]
F[160,x,k[0]] = F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[36,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]+F[169,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[168,x,k[0]]
F[166,x,k[0]] = F[165,x,k[0]]*F[36,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]
F[8,x,k[0]] = F[154,x,k[0]]+F[167,x,k[0]]+F[77,x,k[0]]
F[168,x,k[0]] = F[113,x,k[0]]
F[169,x,k[0]] = F[152,x,k[0]]
F[170,x] = F[171,x]
F[171,x] = F[33,x]*F[41,x]*F[53,x]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[29,x]*F[33,x]*F[37,x]*F[83,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[31,x]*F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[36,x,k[0]]*F[42,x,k[0]]*F[83,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[102,x,k[0]]*F[30,x,k[0]]*F[36,x,k[0]]*F[83,x,k[0]]
F[180,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[33,x]
F[182,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[111,x,k[0]]*F[36,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_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{33}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = y x
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right) F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{33}\! \left(x \right) F_{40}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{170}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{55}\! \left(x \right) = F_{33}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{33}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{33}\! \left(x \right) F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{15}\! \left(x \right)-F_{76}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{7}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{33}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{57}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{59}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x , 1\right)
F_{75}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{76}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{89}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = -\frac{y \left(F_{101}\! \left(x , 1\right)-F_{101}\! \left(x , y\right)\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{106}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{159}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{53}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{182}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{36}\! \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_33(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_33(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_181(x, k_0) + F_183(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x) + F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_36(x, k_0))
Eq(F_13(x, k_0), F_12(x, k_0)*F_33(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_16(x, k_0) + F_180(x, k_0))
Eq(F_15(x), 0)
Eq(F_16(x, k_0), F_17(x, k_0)*F_33(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_36(x, k_0))
Eq(F_20(x, k_0), F_178(x, k_0) + F_19(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0)*F_33(x))
Eq(F_22(x, k_0), F_176(x, k_0) + F_21(x, k_0) + F_83(x, k_0))
Eq(F_22(x, k_0), F_174(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_172(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_48(x, k_0))
Eq(F_25(x, k_0), F_26(x)*F_45(x, k_0))
Eq(F_26(x), F_0(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_33(x)*F_37(x))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), F_31(x) + F_34(x, k_0))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_29(x)*F_33(x))
Eq(F_33(x), x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_30(x, k_0)*F_31(x)*F_36(x, k_0))
Eq(F_36(x, k_0), k_0*x)
Eq(F_37(x), F_38(x)/(F_29(x)*F_33(x)*F_40(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_33(x)*F_40(x)*F_41(x))
Eq(F_40(x), F_12(x, 1))
Eq(F_41(x), F_42(x, 1))
Eq(F_42(x, k_0), F_30(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_30(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_36(x, k_0)*F_45(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_12(x, k_0)*F_33(x)*F_50(x))
Eq(F_50(x), F_51(x)/(F_33(x)*F_40(x)))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_170(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_10(x, 1))
Eq(F_55(x), F_33(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_63(x))
Eq(F_57(x), F_15(x) + F_58(x) + F_62(x))
Eq(F_58(x), F_33(x)*F_41(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_33(x)*F_59(x))
Eq(F_62(x), F_33(x)*F_57(x))
Eq(F_63(x), F_64(x)/F_33(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_15(x) + F_66(x) - F_76(x))
Eq(F_66(x), -F_67(x) + F_7(x))
Eq(F_67(x), F_4(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_33(x)*F_70(x))
Eq(F_70(x), F_57(x) + F_71(x))
Eq(F_71(x), F_59(x)*F_72(x))
Eq(F_72(x), F_4(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x, 1))
Eq(F_75(x, k_0), F_43(x, k_0))
Eq(F_76(x), F_77(x, 1))
Eq(F_77(x, k_0), F_33(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_105(x, k_0) + F_107(x, k_0) + F_79(x, k_0) + F_85(x, k_0))
Eq(F_80(x, k_0), F_33(x)*F_79(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_80(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_36(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_84(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0) + F_45(x, k_0))
Eq(F_84(x, k_0), F_11(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_33(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_92(x, k_0))
Eq(F_88(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_89(x, k_0), F_19(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_29(x)*F_33(x)*F_41(x)*F_83(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_36(x, k_0)*F_83(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0) + F_99(x, k_0))
Eq(F_95(x, k_0), F_41(x)*F_96(x, k_0))
Eq(F_97(x, k_0), F_33(x)*F_96(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_97(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_30(x, k_0)*F_36(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_30(x, k_0))
Eq(F_100(x, k_0), -F_101(x, 1) + (k_0*F_101(x, k_0) - F_101(x, 1))/(k_0 - 1))
Eq(F_102(x, k_0), F_101(x, k_0) + F_29(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_29(x))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_102(x, k_0)*F_30(x, k_0)*F_36(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_33(x))
Eq(F_106(x, k_0), (k_0*F_78(x, k_0) - F_78(x, 1))/(k_0 - 1))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_36(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0)*F_33(x))
Eq(F_111(x, k_0), F_110(x, k_0) + F_153(x, k_0) + F_159(x, k_0) + F_161(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_151(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_8(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_36(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0)*F_36(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_118(x, k_0), F_117(x, k_0) + F_12(x, k_0) + F_149(x, k_0))
Eq(F_119(x, k_0), F_118(x, k_0)*F_33(x))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_121(x, k_0), F_120(x, k_0) + F_144(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_142(x, k_0))
Eq(F_122(x, k_0), F_0(x) + F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_36(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0) + F_140(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_138(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_26(x)*F_45(x, k_0))
Eq(F_129(x, k_0), F_1(x) + F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_36(x, k_0))
Eq(F_132(x, k_0), F_129(x, k_0) + F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_36(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_136(x, k_0) + F_15(x))
Eq(F_135(x, k_0), F_130(x, k_0)*F_36(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_36(x, k_0))
Eq(F_137(x, k_0), F_133(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_118(x, k_0)*F_33(x)*F_50(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_121(x, k_0)*F_29(x)*F_33(x)*F_37(x))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_125(x, k_0)*F_36(x, k_0))
Eq(F_144(x, k_0), F_129(x, k_0) + F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_46(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0)*F_36(x, k_0))
Eq(F_148(x, k_0), F_130(x, k_0) + F_146(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0))
Eq(F_150(x, k_0), F_12(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_12(x, k_0)*F_36(x, k_0)*F_42(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_157(x, k_0))
Eq(F_154(x, k_0), F_0(x) + F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_36(x, k_0)*F_8(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_118(x, k_0)*F_36(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0))
Eq(F_160(x, k_0), F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_36(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0) + F_169(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_168(x, k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_36(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_8(x, k_0), F_154(x, k_0) + F_167(x, k_0) + F_77(x, k_0))
Eq(F_168(x, k_0), F_113(x, k_0))
Eq(F_169(x, k_0), F_152(x, k_0))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_33(x)*F_41(x)*F_53(x))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_29(x)*F_33(x)*F_37(x)*F_83(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_31(x)*F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_36(x, k_0)*F_42(x, k_0)*F_83(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_102(x, k_0)*F_30(x, k_0)*F_36(x, k_0)*F_83(x, k_0))
Eq(F_180(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_33(x))
Eq(F_182(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_111(x, k_0)*F_36(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1], [2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 3
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob_NOT_EXPANDED
Tree: http://permpal.com/tree/24361/
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[34,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[34,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[182,x,k[0]]+F[184,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]+F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[37,x,k[0]]
F[13,x,k[0]] = F[12,x,k[0]]*F[34,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[16,x,k[0]]+F[181,x,k[0]]
F[15,x] = 0
F[16,x,k[0]] = F[17,x,k[0]]*F[34,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[37,x,k[0]]
F[20,x,k[0]] = F[179,x,k[0]]+F[19,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]*F[34,x]
F[22,x,k[0]] = F[177,x,k[0]]+F[21,x,k[0]]+F[84,x,k[0]]
F[22,x,k[0]] = F[175,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[173,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[49,x,k[0]]
F[25,x,k[0]] = F[26,x]*F[46,x,k[0]]
F[26,x] = F[0,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[34,x]*F[38,x]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = F[31,x]+F[35,x,k[0]]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]^2*F[34,x]
F[34,x] = x
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[30,x,k[0]]*F[31,x]*F[37,x,k[0]]
F[37,x,k[0]] = k[0]*x
F[38,x] = 1/F[29,x]/F[34,x]/F[41,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[31,x]*F[34,x]*F[41,x]*F[42,x]
F[41,x] = F[12,x,1]
F[42,x] = F[43,x,1]
F[43,x,k[0]] = F[30,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[30,x,k[0]]*F[37,x,k[0]]*F[43,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[37,x,k[0]]*F[46,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[12,x,k[0]]*F[34,x]*F[51,x]
F[51,x] = 1/F[34,x]/F[41,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[171,x]+F[54,x]+F[56,x]
F[54,x] = F[55,x]
F[55,x] = F[10,x,1]
F[56,x] = F[34,x]*F[57,x]
F[57,x] = F[58,x]+F[64,x]
F[58,x] = F[15,x]+F[59,x]+F[63,x]
F[59,x] = F[34,x]*F[42,x]*F[60,x]
F[60,x] = F[1,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[34,x]*F[60,x]
F[63,x] = F[34,x]*F[58,x]
F[64,x] = 1/F[34,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = -F[15,x]-F[77,x]+F[67,x]
F[67,x] = -F[68,x]+F[7,x]
F[68,x] = F[4,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[34,x]*F[71,x]
F[71,x] = F[58,x]+F[72,x]
F[72,x] = F[60,x]*F[73,x]
F[73,x] = F[4,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[44,x,k[0]]
F[77,x] = F[78,x,1]
F[78,x,k[0]] = F[34,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[106,x,k[0]]+F[108,x,k[0]]+F[80,x,k[0]]+F[86,x,k[0]]
F[81,x,k[0]] = F[34,x]*F[80,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[81,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = F[37,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[85,x,k[0]]
F[84,x,k[0]] = F[14,x,k[0]]+F[46,x,k[0]]
F[85,x,k[0]] = F[11,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[34,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[93,x,k[0]]
F[89,x,k[0]] = 1/(-1+k[0])*(F[90,x,k[0]]*k[0]-F[90,x,1])
F[90,x,k[0]] = F[19,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[29,x]*F[34,x]*F[42,x]*F[84,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[37,x,k[0]]*F[84,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[100,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[42,x]*F[97,x,k[0]]
F[98,x,k[0]] = F[34,x]*F[97,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[98,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[30,x,k[0]]*F[37,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[30,x,k[0]]
F[101,x,k[0]] = -k[0]*(F[102,x,1]-F[102,x,k[0]])/(-1+k[0])
F[103,x,k[0]] = F[102,x,k[0]]+F[29,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[29,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[103,x,k[0]]*F[30,x,k[0]]*F[37,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[34,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[79,x,k[0]]*k[0]-F[79,x,1])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[37,x,k[0]]
F[111,x,k[0]] = F[110,x,k[0]]*F[34,x]
F[112,x,k[0]] = F[111,x,k[0]]+F[154,x,k[0]]+F[160,x,k[0]]+F[162,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[152,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[8,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[37,x,k[0]]
F[117,x,k[0]] = F[116,x,k[0]]*F[37,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]
F[119,x,k[0]] = F[118,x,k[0]]+F[12,x,k[0]]+F[150,x,k[0]]
F[120,x,k[0]] = F[119,x,k[0]]*F[34,x]
F[120,x,k[0]] = F[121,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]+F[145,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[143,x,k[0]]
F[123,x,k[0]] = F[0,x]+F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[37,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]+F[141,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[139,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[26,x]*F[46,x,k[0]]
F[130,x,k[0]] = F[1,x]+F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]*F[37,x,k[0]]
F[133,x,k[0]] = F[130,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[37,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]+F[137,x,k[0]]+F[15,x]
F[136,x,k[0]] = F[131,x,k[0]]*F[37,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]*F[37,x,k[0]]
F[138,x,k[0]] = F[134,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[119,x,k[0]]*F[34,x]*F[51,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[122,x,k[0]]*F[29,x]*F[34,x]*F[38,x]
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[126,x,k[0]]*F[37,x,k[0]]
F[145,x,k[0]] = F[130,x,k[0]]+F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]+F[47,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[37,x,k[0]]
F[149,x,k[0]] = F[131,x,k[0]]+F[147,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[12,x,k[0]]*F[37,x,k[0]]*F[43,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[12,x,k[0]]*F[37,x,k[0]]*F[43,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[158,x,k[0]]
F[155,x,k[0]] = F[0,x]+F[156,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[37,x,k[0]]*F[8,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[119,x,k[0]]*F[37,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[37,x,k[0]]*F[43,x,k[0]]*F[84,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[37,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[170,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[169,x,k[0]]
F[167,x,k[0]] = F[166,x,k[0]]*F[37,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]
F[8,x,k[0]] = F[155,x,k[0]]+F[168,x,k[0]]+F[78,x,k[0]]
F[169,x,k[0]] = F[114,x,k[0]]
F[170,x,k[0]] = F[153,x,k[0]]
F[171,x] = F[172,x]
F[172,x] = F[34,x]*F[42,x]*F[54,x]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[29,x]*F[34,x]*F[38,x]*F[84,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]
F[176,x,k[0]] = F[31,x]*F[37,x,k[0]]*F[43,x,k[0]]*F[84,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[37,x,k[0]]*F[43,x,k[0]]*F[84,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]
F[180,x,k[0]] = F[103,x,k[0]]*F[30,x,k[0]]*F[37,x,k[0]]*F[84,x,k[0]]
F[181,x,k[0]] = F[14,x,k[0]]*F[37,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]*F[34,x]
F[183,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[112,x,k[0]]*F[37,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_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{35}\! \left(x , y\right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31} \left(x \right)^{2} F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = x
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = y x
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{41}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{41}\! \left(x \right) F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{42}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{34}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{34}\! \left(x \right) F_{41}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{171}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{56}\! \left(x \right) = F_{34}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{1}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{34}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{34}\! \left(x \right) F_{58}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{34}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{15}\! \left(x \right)-F_{77}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{34}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{58}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{60}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{77}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{78}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = -\frac{-y F_{90}\! \left(x , y\right)+F_{90}\! \left(x , 1\right)}{-1+y}
F_{90}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{84}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{42}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{98}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = -\frac{y \left(F_{102}\! \left(x , 1\right)-F_{102}\! \left(x , y\right)\right)}{-1+y}
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-y F_{79}\! \left(x , y\right)+F_{79}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{26}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{34}\! \left(x \right) F_{51}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{54}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{183}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{37}\! \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_34(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_34(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_182(x, k_0) + F_184(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x) + F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_37(x, k_0))
Eq(F_13(x, k_0), F_12(x, k_0)*F_34(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_16(x, k_0) + F_181(x, k_0))
Eq(F_15(x), 0)
Eq(F_16(x, k_0), F_17(x, k_0)*F_34(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_37(x, k_0))
Eq(F_20(x, k_0), F_179(x, k_0) + F_19(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0)*F_34(x))
Eq(F_22(x, k_0), F_177(x, k_0) + F_21(x, k_0) + F_84(x, k_0))
Eq(F_22(x, k_0), F_175(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_173(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_49(x, k_0))
Eq(F_25(x, k_0), F_26(x)*F_46(x, k_0))
Eq(F_26(x), F_0(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_34(x)*F_38(x))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), F_31(x) + F_35(x, k_0))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)**2*F_34(x))
Eq(F_34(x), x)
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_30(x, k_0)*F_31(x)*F_37(x, k_0))
Eq(F_37(x, k_0), k_0*x)
Eq(F_38(x), F_39(x)/(F_29(x)*F_34(x)*F_41(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_31(x)*F_34(x)*F_41(x)*F_42(x))
Eq(F_41(x), F_12(x, 1))
Eq(F_42(x), F_43(x, 1))
Eq(F_43(x, k_0), F_30(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_30(x, k_0)*F_37(x, k_0)*F_43(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_37(x, k_0)*F_46(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_12(x, k_0)*F_34(x)*F_51(x))
Eq(F_51(x), F_52(x)/(F_34(x)*F_41(x)))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_171(x) + F_54(x) + F_56(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_10(x, 1))
Eq(F_56(x), F_34(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_64(x))
Eq(F_58(x), F_15(x) + F_59(x) + F_63(x))
Eq(F_59(x), F_34(x)*F_42(x)*F_60(x))
Eq(F_60(x), F_1(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_34(x)*F_60(x))
Eq(F_63(x), F_34(x)*F_58(x))
Eq(F_64(x), F_65(x)/F_34(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), -F_15(x) + F_67(x) - F_77(x))
Eq(F_67(x), -F_68(x) + F_7(x))
Eq(F_68(x), F_4(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_34(x)*F_71(x))
Eq(F_71(x), F_58(x) + F_72(x))
Eq(F_72(x), F_60(x)*F_73(x))
Eq(F_73(x), F_4(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_44(x, k_0))
Eq(F_77(x), F_78(x, 1))
Eq(F_78(x, k_0), F_34(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_106(x, k_0) + F_108(x, k_0) + F_80(x, k_0) + F_86(x, k_0))
Eq(F_81(x, k_0), F_34(x)*F_80(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_81(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), F_37(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_85(x, k_0))
Eq(F_84(x, k_0), F_14(x, k_0) + F_46(x, k_0))
Eq(F_85(x, k_0), F_11(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_34(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_93(x, k_0))
Eq(F_89(x, k_0), (k_0*F_90(x, k_0) - F_90(x, 1))/(k_0 - 1))
Eq(F_90(x, k_0), F_19(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_29(x)*F_34(x)*F_42(x)*F_84(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_37(x, k_0)*F_84(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_100(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_42(x)*F_97(x, k_0))
Eq(F_98(x, k_0), F_34(x)*F_97(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_98(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_30(x, k_0)*F_37(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_30(x, k_0))
Eq(F_101(x, k_0), -F_102(x, 1) + (k_0*F_102(x, k_0) - F_102(x, 1))/(k_0 - 1))
Eq(F_103(x, k_0), F_102(x, k_0) + F_29(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_29(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_103(x, k_0)*F_30(x, k_0)*F_37(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_34(x))
Eq(F_107(x, k_0), (k_0*F_79(x, k_0) - F_79(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_37(x, k_0))
Eq(F_111(x, k_0), F_110(x, k_0)*F_34(x))
Eq(F_112(x, k_0), F_111(x, k_0) + F_154(x, k_0) + F_160(x, k_0) + F_162(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_152(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_8(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_37(x, k_0))
Eq(F_117(x, k_0), F_116(x, k_0)*F_37(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_119(x, k_0), F_118(x, k_0) + F_12(x, k_0) + F_150(x, k_0))
Eq(F_120(x, k_0), F_119(x, k_0)*F_34(x))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0) + F_145(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_143(x, k_0))
Eq(F_123(x, k_0), F_0(x) + F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_37(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0) + F_141(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_139(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_26(x)*F_46(x, k_0))
Eq(F_130(x, k_0), F_1(x) + F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0)*F_37(x, k_0))
Eq(F_133(x, k_0), F_130(x, k_0) + F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_37(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_137(x, k_0) + F_15(x))
Eq(F_136(x, k_0), F_131(x, k_0)*F_37(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0)*F_37(x, k_0))
Eq(F_138(x, k_0), F_134(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_119(x, k_0)*F_34(x)*F_51(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_122(x, k_0)*F_29(x)*F_34(x)*F_38(x))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_126(x, k_0)*F_37(x, k_0))
Eq(F_145(x, k_0), F_130(x, k_0) + F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0) + F_47(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_37(x, k_0))
Eq(F_149(x, k_0), F_131(x, k_0) + F_147(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_12(x, k_0)*F_37(x, k_0)*F_43(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_12(x, k_0)*F_37(x, k_0)*F_43(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_158(x, k_0))
Eq(F_155(x, k_0), F_0(x) + F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_37(x, k_0)*F_8(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_119(x, k_0)*F_37(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_37(x, k_0)*F_43(x, k_0)*F_84(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_37(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_170(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_169(x, k_0))
Eq(F_167(x, k_0), F_166(x, k_0)*F_37(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_8(x, k_0), F_155(x, k_0) + F_168(x, k_0) + F_78(x, k_0))
Eq(F_169(x, k_0), F_114(x, k_0))
Eq(F_170(x, k_0), F_153(x, k_0))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_34(x)*F_42(x)*F_54(x))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_29(x)*F_34(x)*F_38(x)*F_84(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_176(x, k_0), F_31(x)*F_37(x, k_0)*F_43(x, k_0)*F_84(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_37(x, k_0)*F_43(x, k_0)*F_84(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_180(x, k_0), F_103(x, k_0)*F_30(x, k_0)*F_37(x, k_0)*F_84(x, k_0))
Eq(F_181(x, k_0), F_14(x, k_0)*F_37(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0)*F_34(x))
Eq(F_183(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_112(x, k_0)*F_37(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob_NOT_EXPANDED", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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