02314_02341_20314_20341_23014_23041_23104
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3116, 17162, 95874, 540190, 3060318, 17402163, 99222951, 566921455, 3244624023, 18596165940, 106713979164, 613056321172, 3525461009371, 20292314175319, 116900535710088, 673974762270734, 3888559097923792, 22450684788139045, 129701784238844628, 749754274523615684, 4336417844989873982, 25093788933005067367, 145281136727030307141, 841484442640683504758, 4876001601088441794488, 28265094064250570700791, 163905952489449104802466, 950793905834034482999432, 5517163776988702177275885, 32023909918078179338164991, 185931795506611174267367777, 1079807283356767224185718420, 6272564651125446508673625394, 36445498365071859309392074849, 211805155195266947522330113576, 1231168580884522242312357070785, 7157836497609206619908815082079, 41622152915045829137989373414283, 242070258300795492674187036084180, 1408083406583894272235205138888520, 8191842622471281746618640033876154, 47664778480352316223585546505915541, 277378662187804738501127012859332647, 1614377028550069302197360456007128205, 9397027660766253483620577131599420564, 54704999004560158444894498865114238204, 318501901976404618602968918107466219115, 1854570073393655272484005831616045948557, 10799869580126090425414330192757318611809, 62897850368760796610119032987965527911693, 366347500760079377331114913879661879130166, 2133973530564045787997100193549507349664315, 12431442453624691246846927666763051208857042, 72425108812569953037062683091191125384214906, 421978627053706183925944234125223602403825432, 2458804700575488799928695150784814263022447716, 14328099598350093072629196134643049905067371576, 83499311766321902862273423370851204032852178189, 486637739574830651493347312336982318011571647651, 2836326130055498156310118087421583395012018464231, 16532289379461010509254464119715198065800146878633, 96368545182582908497680455773121951825471720696700, 561774665287410188704490348873036393472715569765048, 3275010213464506826502557288975154661947017213041445, 19093519752437905976321277708005998166978690197334881, 111322093552939613841671187946549600298114741827227894, 649079685030379419671473248950796833787430011253986446, 3784732883196045122902744821763022225223633761020907350, 22069491886881487150389359748355546797102689347463305615, 128697073324091295363881195360188188319914521374422010245, 750522341753308590998721934477807029920287510084647669371, 4377000616502246432637707746779573759388222011936489014818, 25527427841493684285139313371292367172260381341269040626383, 148886196972225371397793808481583010371587290356854691289647, 868396838825027512128410272168339025315711542890793010677150, 5065215864080402374492669993981612955493974034585220363563164, 29545622304130068307853775168370723686362362230279781936858098, 172346844063557527701344803337381777004869802637049076255671745, 1005375063605013634334344283158129520369715748199059354392250866, 5864986974066491699118711578098364834391014345569224350151943372, 34215254014466516565417947994118170465120995959939482735499651855, 199611648072493969249414783276040079632733544846408109565137765461, 1164568459495182475353707674416373006796880335388004742495342457210, 6794489775908591622113801164407546737885730412447983312280005603507, 39642498819312841581439604697185497971317921063216166846885305281023, 231300844521631279664216665875066280406928482088060712277909347101305, 1349600183607035354677255900397524891221304755997918924231303020588931, 7874889233089661037387634689555518464319790966932571968643972348049284, 45950993554571481405062218275072100666662349364916618611685459023686605, 268136668193688128245542130678917529416955245117081916126667004415603817, 1564689232956304429006527291229512711752999193667438087156834371490570563, 9130831006113779194372625420627066519130401414361085857443951019361249993, 53284708299181354041302760755845473353840123965971671639473900411753096512, 310960135868875733924582296223098465127364788891708970801793665647006011273
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24786/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[49,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]+F[165,x,k[0]]+F[5,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]+F[97,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[1]]+F[96,x,k[0],k[1]]
F[16,x,k[0]] = F[17,x,k[0]]+F[93,x,k[0]]
F[9,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x]+F[20,x,k[0]]+F[83,x,k[0]]
F[19,x] = 0
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[8,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]+F[9,x,k[1]]
F[26,x,k[0],k[1]] = F[19,x]+F[27,x,k[0],k[1]]+F[50,x,k[0],k[1]]+F[55,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[8,x,k[0]]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[17,x,k[1]]+F[26,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[0,x]*F[33,x,k[0]]*F[41,x,k[0],k[1]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]*F[8,x,k[0]]
F[35,x,k[0]] = F[36,x,1,k[0]]
F[36,x,k[0],k[1]] = F[37,x,k[0]*k[1],k[1]]
F[37,x,k[0],k[1]] = F[1,x]+F[38,x,k[0],k[1]]+F[39,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[37,x,k[0],k[1]]*F[8,x,k[0]]
F[39,x,k[0],k[1]] = F[40,x,k[0],k[1]]*F[8,x,k[1]]
F[40,x,k[0],k[1]] = (-F[36,x,1,k[1]]*k[1]+F[36,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[42,x,k[0],k[1]] = F[41,x,k[0],k[0]*k[1]]
F[42,x,k[0],k[1]] = (F[43,x,k[0]*k[1]]*k[1]-F[43,x,k[0]])/(k[1]-1)
F[43,x,k[0]] = F[1,x]+F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[43,x,k[0]]*F[46,x,k[0]]*F[8,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[49,x]
F[48,x,k[0]] = (F[43,x,k[0]]*k[0]-F[43,x,1])/(-1+k[0])
F[49,x] = x
F[50,x,k[0],k[1]] = F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[0,x]*F[43,x,k[1]]*F[52,x,k[0],k[1]]*F[8,x,k[1]]
F[53,x,k[0],k[1]] = F[52,x,k[0]*k[1],k[1]]
F[53,x,k[0],k[1]] = F[54,k[1]*x,k[0]]
F[54,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[55,x,k[0],k[1]] = F[49,x]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(k[1]-1)
F[58,x,k[0],k[1]] = F[57,x,k[0],k[1]]+F[77,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[58,x,k[0],k[1]]*F[8,x,k[1]]
F[59,x,k[0],k[1]] = F[60,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[60,x,k[0],k[1]]+F[63,x,k[0]]
F[61,x,k[0],k[1]] = F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x,k[0]]
F[64,x,k[0]] = F[0,x]+F[63,x,k[0]]
F[65,x,k[0],k[1]] = F[64,x,k[0]]+F[67,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[66,x,k[0],k[0]*k[1]]
F[66,x,k[0],k[1]] = F[5,x,k[1]]+F[61,x,k[0],k[1]]
F[68,x,k[0],k[1]] = k[1]*(F[67,x,k[0],1]-F[67,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[69,x,k[0],k[1]] = F[68,x,k[0],k[1]]*F[8,x,k[0]]
F[70,x,k[0],k[1]] = F[19,x]+F[69,x,k[0],k[1]]+F[71,x,k[0],k[1]]+F[74,x,k[0],k[1]]
F[70,x,k[0],k[1]] = k[1]*(F[6,x,k[0]]-F[6,x,k[1]])/(-k[1]+k[0])
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]*F[8,x,k[1]]
F[72,x,k[0],k[1]] = (-F[73,x,1,k[1]]*k[1]+F[73,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[73,x,k[0],k[1]] = F[66,x,k[0]*k[1],k[1]]
F[74,x,k[0],k[1]] = F[49,x]*F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = k[1]*(F[76,x,k[0]]-F[76,x,k[1]])/(-k[1]+k[0])
F[76,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[77,x,k[0],k[1]] = F[78,x,k[0],k[1]]
F[78,x,k[0],k[1]] = F[79,x,k[0],k[1]]*F[8,x,k[0]]
F[79,x,k[0],k[1]] = F[17,x,k[1]]+F[80,x,k[0],k[1]]+F[81,x,k[0],k[1]]
F[80,x,k[0],k[1]] = F[79,x,k[0],k[1]]*F[8,x,k[0]]
F[81,x,k[0],k[1]] = F[82,x,k[0],k[1]]
F[82,x,k[0],k[1]] = F[0,x]*F[35,x,k[0]]*F[43,x,k[1]]*F[46,x,k[0]]*F[8,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[49,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = -k[0]*(F[87,x,1]-F[87,x,k[0]])/(-1+k[0])
F[87,x,k[0]] = F[6,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[49,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[57,x,k[0],1]
F[91,x,k[0]] = F[49,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[85,x,1]-F[85,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[8,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,1,k[0]]
F[95,x,k[0],k[1]] = F[30,x,k[0]*k[1],k[1]]
F[96,x,k[0],k[1]] = F[61,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[98,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[8,x,k[0]]*F[99,x,k[0],k[1]]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[158,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[101,x,k[0],k[1]]*F[46,x,k[0]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[97,x,k[0],k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[1]]+F[154,x,k[0],k[1]]
F[103,x,k[0]] = F[104,x,k[0]]+F[150,x,k[0]]
F[104,x,k[0]] = F[0,x]+F[105,x,k[0]]+F[148,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[8,x,k[0]]
F[106,x,k[0]] = F[107,x,1,k[0]]
F[107,x,k[0],k[1]] = F[0,x]+F[108,x,k[0],k[1]]+F[109,x,k[0],k[1]]+F[111,x,k[0],k[1]]
F[108,x,k[0],k[1]] = F[107,x,k[0],k[1]]*F[8,x,k[1]]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1]]*F[8,x,k[1]]
F[110,x,k[0],k[1]] = (F[107,x,k[0],k[1]]*k[0]-F[107,x,1,k[1]])/(-1+k[0])
F[111,x,k[0],k[1]] = F[112,x,k[0],k[1]]
F[112,x,k[0],k[1]] = F[113,x,k[0],k[1]]*F[49,x]
F[113,x,k[0],k[1]] = (F[114,x,k[0]*k[1]]*k[0]-F[114,x,k[1]])/(-1+k[0])
F[114,x,k[0]] = F[115,x,k[0]]+F[144,x,k[0]]
F[115,x,k[0]] = F[0,x]+F[116,x,k[0]]+F[117,x,k[0]]+F[119,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]*F[8,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[49,x]
F[118,x,k[0]] = (F[115,x,k[0]]*k[0]-F[115,x,1])/(-1+k[0])
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[49,x]
F[121,x,k[0]] = (F[122,x,k[0]]*k[0]-F[122,x,1])/(-1+k[0])
F[122,x,k[0]] = F[123,x,k[0]]+F[124,x,k[0]]
F[123,x,k[0]] = F[107,x,k[0],1]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[0,x]*F[126,x,k[0]]*F[49,x]
F[126,x,k[0]] = F[127,x,k[0],1]
F[127,x,k[0],k[1]] = (F[128,x,k[0],k[1]]*k[1]-F[128,x,k[0],1])/(k[1]-1)
F[128,x,k[0],k[1]] = F[1,x]+F[129,x,k[0],k[1]]+F[130,x,k[0],k[1]]+F[133,x,k[0],k[1]]
F[129,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[8,x,k[0]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]*F[8,x,k[1]]
F[131,x,k[0],k[1]] = (-F[132,x,1,k[1]]*k[1]+F[132,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[132,x,k[0],k[1]] = F[128,x,k[0]*k[1],k[1]]
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]*F[49,x]
F[134,x,k[0],k[1]] = (F[135,x,k[0]]*k[0]-F[135,x,k[1]]*k[1])/(-k[1]+k[0])
F[135,x,k[0]] = F[136,x,k[0],1]
F[136,x,k[0],k[1]] = F[137,x,k[0]*k[1],k[1]]
F[137,x,k[0],k[1]] = F[1,x]+F[138,x,k[0],k[1]]+F[139,x,k[0],k[1]]+F[141,x,k[0],k[1]]
F[138,x,k[0],k[1]] = F[137,x,k[0],k[1]]*F[8,x,k[0]]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]*F[8,x,k[1]]
F[140,x,k[0],k[1]] = (-F[136,x,1,k[1]]*k[1]+F[136,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]*F[49,x]
F[142,x,k[0],k[1]] = (F[143,x,k[0]]*k[0]-F[143,x,k[1]]*k[1])/(-k[1]+k[0])
F[143,x,k[0]] = F[132,x,k[0],1]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[0,x]*F[146,x,k[0]]*F[49,x]
F[146,x,k[0]] = F[147,x,k[0],1]
F[147,x,k[0],k[1]] = (F[137,x,k[0],k[1]]*k[1]-F[137,x,k[0],1])/(k[1]-1)
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[114,x,k[0]]*F[49,x]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[0,x]*F[152,x,k[0]]*F[8,x,k[0]]
F[152,x,k[0]] = F[153,x,1,k[0]]
F[153,x,k[0],k[1]] = (F[43,x,k[0]*k[1]]*k[0]-F[43,x,k[1]])/(-1+k[0])
F[154,x,k[0],k[1]] = F[155,x,k[0],k[1]]*F[8,x,k[0]]
F[155,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[156,x,k[0],k[1]]
F[156,x,k[0],k[1]] = F[157,x,k[0],k[1]]
F[157,x,k[0],k[1]] = F[8,x,k[0]]*F[99,x,k[0],k[1]]
F[158,x,k[0],k[1]] = F[159,x,k[0],k[1]]
F[159,x,k[0],k[1]] = F[46,x,k[0]]^2*F[0,x]*F[160,x,k[0]]*F[43,x,k[1]]
F[160,x,k[0]] = k[0]*F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[49,x]
F[163,x,k[0]] = F[164,x,1,k[0]]
F[164,x,k[0],k[1]] = (F[46,x,k[0]*k[1]]*k[0]-F[46,x,k[1]])/(-1+k[0])
F[165,x,k[0]] = F[166,x,k[0]]*F[49,x]
F[166,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{5}\! \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_{8}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , 1, y\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y z , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right)+F_{96}\! \left(x , y , z\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y , 1\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , y z \right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right)+F_{9}\! \left(x , z\right)
F_{26}\! \left(x , y , z\right) = F_{19}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{50}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right)+F_{26}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{33}\! \left(x , y\right) F_{41}\! \left(x , y , z\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , 1, y\right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , y z , z\right)
F_{37}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y , z\right)+F_{39}\! \left(x , y , z\right)
F_{38}\! \left(x , y , z\right) = F_{37}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{39}\! \left(x , y , z\right) = F_{40}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{40}\! \left(x , y , z\right) = -\frac{F_{36}\! \left(x , 1, z\right) z -F_{36}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{42}\! \left(x , y , z\right) = F_{41}\! \left(x , y , y z \right)
F_{42}\! \left(x , y , z\right) = -\frac{-F_{43}\! \left(x , y z \right) z +F_{43}\! \left(x , y\right)}{z -1}
F_{43}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{48}\! \left(x , y\right) = -\frac{-F_{43}\! \left(x , y\right) y +F_{43}\! \left(x , 1\right)}{-1+y}
F_{49}\! \left(x \right) = x
F_{50}\! \left(x , y , z\right) = F_{51}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{43}\! \left(x , z\right) F_{52}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{53}\! \left(x , y , z\right) = F_{52}\! \left(x , y z , z\right)
F_{53}\! \left(x , y , z\right) = F_{54}\! \left(z x , y\right)
F_{54}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{55}\! \left(x , y , z\right) = F_{49}\! \left(x \right) F_{56}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{z -1}
F_{58}\! \left(x , y , z\right) = F_{57}\! \left(x , y , z\right)+F_{77}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y , z\right)
F_{61}\! \left(x , y , z\right) = F_{60}\! \left(x , y , z\right)+F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y , z\right) = F_{62}\! \left(x , y , z\right)
F_{62}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{65}\! \left(x , y , z\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y , z\right)
F_{65}\! \left(x , y , z\right) = F_{66}\! \left(x , y , y z \right)
F_{66}\! \left(x , y , z\right) = F_{5}\! \left(x , z\right)+F_{61}\! \left(x , y , z\right)
F_{68}\! \left(x , y , z\right) = \frac{z \left(F_{67}\! \left(x , y , 1\right)-F_{67}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{69}\! \left(x , y , z\right) = F_{68}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{70}\! \left(x , y , z\right) = F_{19}\! \left(x \right)+F_{69}\! \left(x , y , z\right)+F_{71}\! \left(x , y , z\right)+F_{74}\! \left(x , y , z\right)
F_{70}\! \left(x , y , z\right) = \frac{z \left(F_{6}\! \left(x , y\right)-F_{6}\! \left(x , z\right)\right)}{-z +y}
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{72}\! \left(x , y , z\right) = -\frac{F_{73}\! \left(x , 1, z\right) z -F_{73}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{73}\! \left(x , y , z\right) = F_{66}\! \left(x , y z , z\right)
F_{74}\! \left(x , y , z\right) = F_{49}\! \left(x \right) F_{75}\! \left(x , y , z\right)
F_{75}\! \left(x , y , z\right) = \frac{z \left(F_{76}\! \left(x , y\right)-F_{76}\! \left(x , z\right)\right)}{-z +y}
F_{76}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y , z\right)
F_{78}\! \left(x , y , z\right) = F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{79}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right)+F_{80}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)
F_{80}\! \left(x , y , z\right) = F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{81}\! \left(x , y , z\right) = F_{82}\! \left(x , y , z\right)
F_{82}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{35}\! \left(x , y\right) F_{43}\! \left(x , z\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = -\frac{y \left(F_{87}\! \left(x , 1\right)-F_{87}\! \left(x , y\right)\right)}{-1+y}
F_{87}\! \left(x , y\right) = F_{6}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{57}\! \left(x , y , 1\right)
F_{91}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , 1, y\right)
F_{95}\! \left(x , y , z\right) = F_{30}\! \left(x , y z , z\right)
F_{96}\! \left(x , y , z\right) = F_{61}\! \left(x , y , z\right)
F_{97}\! \left(x , y , z\right) = F_{98}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)
F_{99}\! \left(x , y , z\right) = F_{100}\! \left(x , y , z\right)+F_{158}\! \left(x , y , z\right)
F_{100}\! \left(x , y , z\right) = F_{101}\! \left(x , y , z\right) F_{46}\! \left(x , y\right)
F_{101}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)
F_{102}\! \left(x , y , z\right) = F_{103}\! \left(x , z\right)+F_{154}\! \left(x , y , z\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , 1, y\right)
F_{107}\! \left(x , y , z\right) = F_{0}\! \left(x \right)+F_{108}\! \left(x , y , z\right)+F_{109}\! \left(x , y , z\right)+F_{111}\! \left(x , y , z\right)
F_{108}\! \left(x , y , z\right) = F_{107}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{109}\! \left(x , y , z\right) = F_{110}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{110}\! \left(x , y , z\right) = -\frac{-F_{107}\! \left(x , y , z\right) y +F_{107}\! \left(x , 1, z\right)}{-1+y}
F_{111}\! \left(x , y , z\right) = F_{112}\! \left(x , y , z\right)
F_{112}\! \left(x , y , z\right) = F_{113}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{113}\! \left(x , y , z\right) = -\frac{-F_{114}\! \left(x , y z \right) y +F_{114}\! \left(x , z\right)}{-1+y}
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{118}\! \left(x , y\right) = -\frac{-F_{115}\! \left(x , y\right) y +F_{115}\! \left(x , 1\right)}{-1+y}
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{121}\! \left(x , y\right) = -\frac{-F_{122}\! \left(x , y\right) y +F_{122}\! \left(x , 1\right)}{-1+y}
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{107}\! \left(x , y , 1\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{126}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y , 1\right)
F_{127}\! \left(x , y , z\right) = -\frac{-F_{128}\! \left(x , y , z\right) z +F_{128}\! \left(x , y , 1\right)}{z -1}
F_{128}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{129}\! \left(x , y , z\right)+F_{130}\! \left(x , y , z\right)+F_{133}\! \left(x , y , z\right)
F_{129}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{130}\! \left(x , y , z\right) = F_{131}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{131}\! \left(x , y , z\right) = -\frac{F_{132}\! \left(x , 1, z\right) z -F_{132}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{132}\! \left(x , y , z\right) = F_{128}\! \left(x , y z , z\right)
F_{133}\! \left(x , y , z\right) = F_{134}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{134}\! \left(x , y , z\right) = \frac{F_{135}\! \left(x , y\right) y -F_{135}\! \left(x , z\right) z}{-z +y}
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y , 1\right)
F_{136}\! \left(x , y , z\right) = F_{137}\! \left(x , y z , z\right)
F_{137}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{138}\! \left(x , y , z\right)+F_{139}\! \left(x , y , z\right)+F_{141}\! \left(x , y , z\right)
F_{138}\! \left(x , y , z\right) = F_{137}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{139}\! \left(x , y , z\right) = F_{140}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{140}\! \left(x , y , z\right) = -\frac{F_{136}\! \left(x , 1, z\right) z -F_{136}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{141}\! \left(x , y , z\right) = F_{142}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{142}\! \left(x , y , z\right) = \frac{F_{143}\! \left(x , y\right) y -F_{143}\! \left(x , z\right) z}{-z +y}
F_{143}\! \left(x , y\right) = F_{132}\! \left(x , y , 1\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{146}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y , 1\right)
F_{147}\! \left(x , y , z\right) = -\frac{-F_{137}\! \left(x , y , z\right) z +F_{137}\! \left(x , y , 1\right)}{z -1}
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{152}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , 1, y\right)
F_{153}\! \left(x , y , z\right) = -\frac{-F_{43}\! \left(x , y z \right) y +F_{43}\! \left(x , z\right)}{-1+y}
F_{154}\! \left(x , y , z\right) = F_{155}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{155}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{156}\! \left(x , y , z\right)
F_{156}\! \left(x , y , z\right) = F_{157}\! \left(x , y , z\right)
F_{157}\! \left(x , y , z\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)
F_{158}\! \left(x , y , z\right) = F_{159}\! \left(x , y , z\right)
F_{159}\! \left(x , y , z\right) = F_{46}\! \left(x , y\right)^{2} F_{0}\! \left(x \right) F_{160}\! \left(x , y\right) F_{43}\! \left(x , z\right)
F_{160}\! \left(x , y\right) = y F_{161}\! \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_{49}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , 1, y\right)
F_{164}\! \left(x , y , z\right) = -\frac{-F_{46}\! \left(x , y z \right) y +F_{46}\! \left(x , z\right)}{-1+y}
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{166}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_49(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0) + F_165(x, k_0) + F_5(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_8(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1) + F_97(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_1) + F_96(x, k_0, k_1))
Eq(F_16(x, k_0), F_17(x, k_0) + F_93(x, k_0))
Eq(F_9(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x) + F_20(x, k_0) + F_83(x, k_0))
Eq(F_19(x), 0)
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_8(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1) + F_9(x, k_1))
Eq(F_26(x, k_0, k_1), F_19(x) + F_27(x, k_0, k_1) + F_50(x, k_0, k_1) + F_55(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_8(x, k_0))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_1) + F_31(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_17(x, k_1) + F_26(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_0(x)*F_33(x, k_0)*F_41(x, k_0, k_1))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0)*F_8(x, k_0))
Eq(F_35(x, k_0), F_36(x, 1, k_0))
Eq(F_36(x, k_0, k_1), F_37(x, k_0*k_1, k_1))
Eq(F_37(x, k_0, k_1), F_1(x) + F_38(x, k_0, k_1) + F_39(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_37(x, k_0, k_1)*F_8(x, k_0))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, k_1)*F_8(x, k_1))
Eq(F_40(x, k_0, k_1), (-k_0*F_36(x, k_0/k_1, k_1) + k_1*F_36(x, 1, k_1))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1), F_41(x, k_0, k_0*k_1))
Eq(F_42(x, k_0, k_1), (k_0*k_1*F_43(x, k_0*k_1) - k_0*F_43(x, k_0))/(k_0*k_1 - k_0))
Eq(F_43(x, k_0), F_1(x) + F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_43(x, k_0)*F_46(x, k_0)*F_8(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_49(x))
Eq(F_48(x, k_0), (-k_0*F_43(x, k_0) + F_43(x, 1))/(1 - k_0))
Eq(F_49(x), x)
Eq(F_50(x, k_0, k_1), F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_0(x)*F_43(x, k_1)*F_52(x, k_0, k_1)*F_8(x, k_1))
Eq(F_53(x, k_0, k_1), F_52(x, k_0*k_1, k_1))
Eq(F_53(x, k_0, k_1), F_54(k_1*x, k_0))
Eq(F_54(x, k_0), -F_33(x, 1) + (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_55(x, k_0, k_1), F_49(x)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_58(x, k_0, k_1), F_57(x, k_0, k_1) + F_77(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_58(x, k_0, k_1)*F_8(x, k_1))
Eq(F_59(x, k_0, k_1), F_60(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_60(x, k_0, k_1) + F_63(x, k_0))
Eq(F_61(x, k_0, k_1), F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x, k_0))
Eq(F_64(x, k_0), F_0(x) + F_63(x, k_0))
Eq(F_65(x, k_0, k_1), F_64(x, k_0) + F_67(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_66(x, k_0, k_0*k_1))
Eq(F_66(x, k_0, k_1), F_5(x, k_1) + F_61(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), -F_67(x, k_0, 1) + (-k_0*F_67(x, k_0, 1) + k_1*F_67(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_69(x, k_0, k_1), F_68(x, k_0, k_1)*F_8(x, k_0))
Eq(F_70(x, k_0, k_1), F_19(x) + F_69(x, k_0, k_1) + F_71(x, k_0, k_1) + F_74(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), -F_6(x, k_0) + (-k_0*F_6(x, k_0) + k_1*F_6(x, k_1))/(-k_0 + k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1)*F_8(x, k_1))
Eq(F_72(x, k_0, k_1), (-k_0*F_73(x, k_0/k_1, k_1) + k_1*F_73(x, 1, k_1))/(-k_0 + k_1))
Eq(F_73(x, k_0, k_1), F_66(x, k_0*k_1, k_1))
Eq(F_74(x, k_0, k_1), F_49(x)*F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), -F_76(x, k_0) + (-k_0*F_76(x, k_0) + k_1*F_76(x, k_1))/(-k_0 + k_1))
Eq(F_76(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_77(x, k_0, k_1), F_78(x, k_0, k_1))
Eq(F_78(x, k_0, k_1), F_79(x, k_0, k_1)*F_8(x, k_0))
Eq(F_79(x, k_0, k_1), F_17(x, k_1) + F_80(x, k_0, k_1) + F_81(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), F_79(x, k_0, k_1)*F_8(x, k_0))
Eq(F_81(x, k_0, k_1), F_82(x, k_0, k_1))
Eq(F_82(x, k_0, k_1), F_0(x)*F_35(x, k_0)*F_43(x, k_1)*F_46(x, k_0)*F_8(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_49(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), -F_87(x, 1) + (-k_0*F_87(x, k_0) + F_87(x, 1))/(1 - k_0))
Eq(F_87(x, k_0), F_6(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_49(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_57(x, k_0, 1))
Eq(F_91(x, k_0), F_49(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_85(x, 1) + (-k_0*F_85(x, k_0) + F_85(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_8(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, 1, k_0))
Eq(F_95(x, k_0, k_1), F_30(x, k_0*k_1, k_1))
Eq(F_96(x, k_0, k_1), F_61(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_98(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_8(x, k_0)*F_99(x, k_0, k_1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1) + F_158(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_101(x, k_0, k_1)*F_46(x, k_0))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1) + F_97(x, k_0, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_1) + F_154(x, k_0, k_1))
Eq(F_103(x, k_0), F_104(x, k_0) + F_150(x, k_0))
Eq(F_104(x, k_0), F_0(x) + F_105(x, k_0) + F_148(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_8(x, k_0))
Eq(F_106(x, k_0), F_107(x, 1, k_0))
Eq(F_107(x, k_0, k_1), F_0(x) + F_108(x, k_0, k_1) + F_109(x, k_0, k_1) + F_111(x, k_0, k_1))
Eq(F_108(x, k_0, k_1), F_107(x, k_0, k_1)*F_8(x, k_1))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1)*F_8(x, k_1))
Eq(F_110(x, k_0, k_1), (-k_0*F_107(x, k_0, k_1) + F_107(x, 1, k_1))/(1 - k_0))
Eq(F_111(x, k_0, k_1), F_112(x, k_0, k_1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0, k_1)*F_49(x))
Eq(F_113(x, k_0, k_1), (-k_0*k_1*F_114(x, k_0*k_1) + k_1*F_114(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_114(x, k_0), F_115(x, k_0) + F_144(x, k_0))
Eq(F_115(x, k_0), F_0(x) + F_116(x, k_0) + F_117(x, k_0) + F_119(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0)*F_8(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_49(x))
Eq(F_118(x, k_0), (-k_0*F_115(x, k_0) + F_115(x, 1))/(1 - k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_49(x))
Eq(F_121(x, k_0), (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_124(x, k_0))
Eq(F_123(x, k_0), F_107(x, k_0, 1))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_0(x)*F_126(x, k_0)*F_49(x))
Eq(F_126(x, k_0), F_127(x, k_0, 1))
Eq(F_127(x, k_0, k_1), (-k_1*F_128(x, k_0, k_1) + F_128(x, k_0, 1))/(1 - k_1))
Eq(F_128(x, k_0, k_1), F_1(x) + F_129(x, k_0, k_1) + F_130(x, k_0, k_1) + F_133(x, k_0, k_1))
Eq(F_129(x, k_0, k_1), F_128(x, k_0, k_1)*F_8(x, k_0))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1)*F_8(x, k_1))
Eq(F_131(x, k_0, k_1), (-k_0*F_132(x, k_0/k_1, k_1) + k_1*F_132(x, 1, k_1))/(-k_0 + k_1))
Eq(F_132(x, k_0, k_1), F_128(x, k_0*k_1, k_1))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1)*F_49(x))
Eq(F_134(x, k_0, k_1), (-k_0*F_135(x, k_0) + k_1*F_135(x, k_1))/(-k_0 + k_1))
Eq(F_135(x, k_0), F_136(x, k_0, 1))
Eq(F_136(x, k_0, k_1), F_137(x, k_0*k_1, k_1))
Eq(F_137(x, k_0, k_1), F_1(x) + F_138(x, k_0, k_1) + F_139(x, k_0, k_1) + F_141(x, k_0, k_1))
Eq(F_138(x, k_0, k_1), F_137(x, k_0, k_1)*F_8(x, k_0))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1)*F_8(x, k_1))
Eq(F_140(x, k_0, k_1), (-k_0*F_136(x, k_0/k_1, k_1) + k_1*F_136(x, 1, k_1))/(-k_0 + k_1))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1)*F_49(x))
Eq(F_142(x, k_0, k_1), (-k_0*F_143(x, k_0) + k_1*F_143(x, k_1))/(-k_0 + k_1))
Eq(F_143(x, k_0), F_132(x, k_0, 1))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_0(x)*F_146(x, k_0)*F_49(x))
Eq(F_146(x, k_0), F_147(x, k_0, 1))
Eq(F_147(x, k_0, k_1), (-k_1*F_137(x, k_0, k_1) + F_137(x, k_0, 1))/(1 - k_1))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_114(x, k_0)*F_49(x))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_0(x)*F_152(x, k_0)*F_8(x, k_0))
Eq(F_152(x, k_0), F_153(x, 1, k_0))
Eq(F_153(x, k_0, k_1), (-k_0*k_1*F_43(x, k_0*k_1) + k_1*F_43(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_154(x, k_0, k_1), F_155(x, k_0, k_1)*F_8(x, k_0))
Eq(F_155(x, k_0, k_1), F_102(x, k_0, k_1) + F_156(x, k_0, k_1))
Eq(F_156(x, k_0, k_1), F_157(x, k_0, k_1))
Eq(F_157(x, k_0, k_1), F_8(x, k_0)*F_99(x, k_0, k_1))
Eq(F_158(x, k_0, k_1), F_159(x, k_0, k_1))
Eq(F_159(x, k_0, k_1), F_0(x)*F_160(x, k_0)*F_43(x, k_1)*F_46(x, k_0)**2)
Eq(F_160(x, k_0), k_0*F_161(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_49(x))
Eq(F_163(x, k_0), F_164(x, 1, k_0))
Eq(F_164(x, k_0, k_1), (-k_0*k_1*F_46(x, k_0*k_1) + k_1*F_46(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_165(x, k_0), F_166(x, k_0)*F_49(x))
Eq(F_166(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 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0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25596/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[49,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]+F[165,x,k[0]]+F[5,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]+F[97,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[1]]+F[96,x,k[0],k[1]]
F[16,x,k[0]] = F[17,x,k[0]]+F[93,x,k[0]]
F[9,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x]+F[20,x,k[0]]+F[83,x,k[0]]
F[19,x] = 0
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[8,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]+F[9,x,k[1]]
F[26,x,k[0],k[1]] = F[19,x]+F[27,x,k[0],k[1]]+F[50,x,k[0],k[1]]+F[55,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[8,x,k[0]]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[17,x,k[1]]+F[26,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[0,x]*F[33,x,k[0]]*F[41,x,k[0],k[1]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]*F[8,x,k[0]]
F[35,x,k[0]] = F[36,x,1,k[0]]
F[36,x,k[0],k[1]] = F[37,x,k[0]*k[1],k[1]]
F[37,x,k[0],k[1]] = F[1,x]+F[38,x,k[0],k[1]]+F[39,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[37,x,k[0],k[1]]*F[8,x,k[0]]
F[39,x,k[0],k[1]] = F[40,x,k[0],k[1]]*F[8,x,k[1]]
F[40,x,k[0],k[1]] = (-F[36,x,1,k[1]]*k[1]+F[36,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[42,x,k[0],k[1]] = F[41,x,k[0],k[0]*k[1]]
F[42,x,k[0],k[1]] = (F[43,x,k[0]*k[1]]*k[1]-F[43,x,k[0]])/(k[1]-1)
F[43,x,k[0]] = F[1,x]+F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[43,x,k[0]]*F[46,x,k[0]]*F[8,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[49,x]
F[48,x,k[0]] = (F[43,x,k[0]]*k[0]-F[43,x,1])/(-1+k[0])
F[49,x] = x
F[50,x,k[0],k[1]] = F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[0,x]*F[43,x,k[1]]*F[52,x,k[0],k[1]]*F[8,x,k[1]]
F[53,x,k[0],k[1]] = F[52,x,k[0]*k[1],k[1]]
F[53,x,k[0],k[1]] = F[54,k[1]*x,k[0]]
F[54,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[55,x,k[0],k[1]] = F[49,x]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[1]-F[26,x,k[0],1])/(k[1]-1)
F[58,x,k[0],k[1]] = F[57,x,k[0],k[1]]+F[77,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[58,x,k[0],k[1]]*F[8,x,k[1]]
F[59,x,k[0],k[1]] = F[60,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[60,x,k[0],k[1]]+F[63,x,k[0]]
F[61,x,k[0],k[1]] = F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x,k[0]]
F[64,x,k[0]] = F[0,x]+F[63,x,k[0]]
F[65,x,k[0],k[1]] = F[64,x,k[0]]+F[67,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[66,x,k[0],k[0]*k[1]]
F[66,x,k[0],k[1]] = F[5,x,k[1]]+F[61,x,k[0],k[1]]
F[68,x,k[0],k[1]] = k[1]*(F[67,x,k[0],1]-F[67,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[69,x,k[0],k[1]] = F[68,x,k[0],k[1]]*F[8,x,k[0]]
F[70,x,k[0],k[1]] = F[19,x]+F[69,x,k[0],k[1]]+F[71,x,k[0],k[1]]+F[74,x,k[0],k[1]]
F[70,x,k[0],k[1]] = k[1]*(F[6,x,k[0]]-F[6,x,k[1]])/(-k[1]+k[0])
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]*F[8,x,k[1]]
F[72,x,k[0],k[1]] = (-F[73,x,1,k[1]]*k[1]+F[73,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[73,x,k[0],k[1]] = F[66,x,k[0]*k[1],k[1]]
F[74,x,k[0],k[1]] = F[49,x]*F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = k[1]*(F[76,x,k[0]]-F[76,x,k[1]])/(-k[1]+k[0])
F[76,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[77,x,k[0],k[1]] = F[78,x,k[0],k[1]]
F[78,x,k[0],k[1]] = F[79,x,k[0],k[1]]*F[8,x,k[0]]
F[79,x,k[0],k[1]] = F[17,x,k[1]]+F[80,x,k[0],k[1]]+F[81,x,k[0],k[1]]
F[80,x,k[0],k[1]] = F[79,x,k[0],k[1]]*F[8,x,k[0]]
F[81,x,k[0],k[1]] = F[82,x,k[0],k[1]]
F[82,x,k[0],k[1]] = F[0,x]*F[35,x,k[0]]*F[43,x,k[1]]*F[46,x,k[0]]*F[8,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[49,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = -k[0]*(F[87,x,1]-F[87,x,k[0]])/(-1+k[0])
F[87,x,k[0]] = F[6,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[49,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[57,x,k[0],1]
F[91,x,k[0]] = F[49,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[85,x,1]-F[85,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[8,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,1,k[0]]
F[95,x,k[0],k[1]] = F[30,x,k[0]*k[1],k[1]]
F[96,x,k[0],k[1]] = F[61,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[98,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[8,x,k[0]]*F[99,x,k[0],k[1]]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[158,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[101,x,k[0],k[1]]*F[46,x,k[0]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[97,x,k[0],k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[1]]+F[154,x,k[0],k[1]]
F[103,x,k[0]] = F[104,x,k[0]]+F[150,x,k[0]]
F[104,x,k[0]] = F[0,x]+F[105,x,k[0]]+F[148,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[8,x,k[0]]
F[106,x,k[0]] = F[107,x,1,k[0]]
F[107,x,k[0],k[1]] = F[0,x]+F[108,x,k[0],k[1]]+F[109,x,k[0],k[1]]+F[111,x,k[0],k[1]]
F[108,x,k[0],k[1]] = F[107,x,k[0],k[1]]*F[8,x,k[1]]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1]]*F[8,x,k[1]]
F[110,x,k[0],k[1]] = (F[107,x,k[0],k[1]]*k[0]-F[107,x,1,k[1]])/(-1+k[0])
F[111,x,k[0],k[1]] = F[112,x,k[0],k[1]]
F[112,x,k[0],k[1]] = F[113,x,k[0],k[1]]*F[49,x]
F[113,x,k[0],k[1]] = (F[114,x,k[0]*k[1]]*k[0]-F[114,x,k[1]])/(-1+k[0])
F[114,x,k[0]] = F[115,x,k[0]]+F[144,x,k[0]]
F[115,x,k[0]] = F[0,x]+F[116,x,k[0]]+F[117,x,k[0]]+F[119,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]*F[8,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[49,x]
F[118,x,k[0]] = (F[115,x,k[0]]*k[0]-F[115,x,1])/(-1+k[0])
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[49,x]
F[121,x,k[0]] = (F[122,x,k[0]]*k[0]-F[122,x,1])/(-1+k[0])
F[122,x,k[0]] = F[123,x,k[0]]+F[124,x,k[0]]
F[123,x,k[0]] = F[107,x,k[0],1]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[0,x]*F[126,x,k[0]]*F[49,x]
F[126,x,k[0]] = F[127,x,k[0],1]
F[127,x,k[0],k[1]] = (F[128,x,k[0],k[1]]*k[1]-F[128,x,k[0],1])/(k[1]-1)
F[128,x,k[0],k[1]] = F[1,x]+F[129,x,k[0],k[1]]+F[130,x,k[0],k[1]]+F[133,x,k[0],k[1]]
F[129,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[8,x,k[0]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]*F[8,x,k[1]]
F[131,x,k[0],k[1]] = (-F[132,x,1,k[1]]*k[1]+F[132,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[132,x,k[0],k[1]] = F[128,x,k[0]*k[1],k[1]]
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]*F[49,x]
F[134,x,k[0],k[1]] = (F[135,x,k[0]]*k[0]-F[135,x,k[1]]*k[1])/(-k[1]+k[0])
F[135,x,k[0]] = F[136,x,k[0],1]
F[136,x,k[0],k[1]] = F[137,x,k[0]*k[1],k[1]]
F[137,x,k[0],k[1]] = F[1,x]+F[138,x,k[0],k[1]]+F[139,x,k[0],k[1]]+F[141,x,k[0],k[1]]
F[138,x,k[0],k[1]] = F[137,x,k[0],k[1]]*F[8,x,k[0]]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]*F[8,x,k[1]]
F[140,x,k[0],k[1]] = (-F[136,x,1,k[1]]*k[1]+F[136,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]*F[49,x]
F[142,x,k[0],k[1]] = (F[143,x,k[0]]*k[0]-F[143,x,k[1]]*k[1])/(-k[1]+k[0])
F[143,x,k[0]] = F[132,x,k[0],1]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[0,x]*F[146,x,k[0]]*F[49,x]
F[146,x,k[0]] = F[147,x,k[0],1]
F[147,x,k[0],k[1]] = (F[137,x,k[0],k[1]]*k[1]-F[137,x,k[0],1])/(k[1]-1)
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[114,x,k[0]]*F[49,x]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[0,x]*F[152,x,k[0]]*F[8,x,k[0]]
F[152,x,k[0]] = F[153,x,1,k[0]]
F[153,x,k[0],k[1]] = (F[43,x,k[0]*k[1]]*k[0]-F[43,x,k[1]])/(-1+k[0])
F[154,x,k[0],k[1]] = F[155,x,k[0],k[1]]*F[8,x,k[0]]
F[155,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[156,x,k[0],k[1]]
F[156,x,k[0],k[1]] = F[157,x,k[0],k[1]]
F[157,x,k[0],k[1]] = F[8,x,k[0]]*F[99,x,k[0],k[1]]
F[158,x,k[0],k[1]] = F[159,x,k[0],k[1]]
F[159,x,k[0],k[1]] = F[46,x,k[0]]^2*F[0,x]*F[160,x,k[0]]*F[43,x,k[1]]
F[160,x,k[0]] = k[0]*F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[49,x]
F[163,x,k[0]] = F[164,x,1,k[0]]
F[164,x,k[0],k[1]] = (F[46,x,k[0]*k[1]]*k[0]-F[46,x,k[1]])/(-1+k[0])
F[165,x,k[0]] = F[166,x,k[0]]*F[49,x]
F[166,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{5}\! \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_{8}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , 1, y\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y z , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right)+F_{96}\! \left(x , y , z\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y , 1\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , y z \right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right)+F_{9}\! \left(x , z\right)
F_{26}\! \left(x , y , z\right) = F_{19}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{50}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right)+F_{26}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{33}\! \left(x , y\right) F_{41}\! \left(x , y , z\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , 1, y\right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , y z , z\right)
F_{37}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y , z\right)+F_{39}\! \left(x , y , z\right)
F_{38}\! \left(x , y , z\right) = F_{37}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{39}\! \left(x , y , z\right) = F_{40}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{40}\! \left(x , y , z\right) = -\frac{F_{36}\! \left(x , 1, z\right) z -F_{36}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{42}\! \left(x , y , z\right) = F_{41}\! \left(x , y , y z \right)
F_{42}\! \left(x , y , z\right) = -\frac{-F_{43}\! \left(x , y z \right) z +F_{43}\! \left(x , y\right)}{z -1}
F_{43}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{48}\! \left(x , y\right) = -\frac{-F_{43}\! \left(x , y\right) y +F_{43}\! \left(x , 1\right)}{-1+y}
F_{49}\! \left(x \right) = x
F_{50}\! \left(x , y , z\right) = F_{51}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{43}\! \left(x , z\right) F_{52}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{53}\! \left(x , y , z\right) = F_{52}\! \left(x , y z , z\right)
F_{53}\! \left(x , y , z\right) = F_{54}\! \left(z x , y\right)
F_{54}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{55}\! \left(x , y , z\right) = F_{49}\! \left(x \right) F_{56}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{z -1}
F_{58}\! \left(x , y , z\right) = F_{57}\! \left(x , y , z\right)+F_{77}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y , z\right)
F_{61}\! \left(x , y , z\right) = F_{60}\! \left(x , y , z\right)+F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y , z\right) = F_{62}\! \left(x , y , z\right)
F_{62}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{65}\! \left(x , y , z\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y , z\right)
F_{65}\! \left(x , y , z\right) = F_{66}\! \left(x , y , y z \right)
F_{66}\! \left(x , y , z\right) = F_{5}\! \left(x , z\right)+F_{61}\! \left(x , y , z\right)
F_{68}\! \left(x , y , z\right) = \frac{z \left(F_{67}\! \left(x , y , 1\right)-F_{67}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{69}\! \left(x , y , z\right) = F_{68}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{70}\! \left(x , y , z\right) = F_{19}\! \left(x \right)+F_{69}\! \left(x , y , z\right)+F_{71}\! \left(x , y , z\right)+F_{74}\! \left(x , y , z\right)
F_{70}\! \left(x , y , z\right) = \frac{z \left(F_{6}\! \left(x , y\right)-F_{6}\! \left(x , z\right)\right)}{-z +y}
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{72}\! \left(x , y , z\right) = -\frac{F_{73}\! \left(x , 1, z\right) z -F_{73}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{73}\! \left(x , y , z\right) = F_{66}\! \left(x , y z , z\right)
F_{74}\! \left(x , y , z\right) = F_{49}\! \left(x \right) F_{75}\! \left(x , y , z\right)
F_{75}\! \left(x , y , z\right) = \frac{z \left(F_{76}\! \left(x , y\right)-F_{76}\! \left(x , z\right)\right)}{-z +y}
F_{76}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y , z\right)
F_{78}\! \left(x , y , z\right) = F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{79}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right)+F_{80}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)
F_{80}\! \left(x , y , z\right) = F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{81}\! \left(x , y , z\right) = F_{82}\! \left(x , y , z\right)
F_{82}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{35}\! \left(x , y\right) F_{43}\! \left(x , z\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = -\frac{y \left(F_{87}\! \left(x , 1\right)-F_{87}\! \left(x , y\right)\right)}{-1+y}
F_{87}\! \left(x , y\right) = F_{6}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{57}\! \left(x , y , 1\right)
F_{91}\! \left(x , y\right) = F_{49}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , 1, y\right)
F_{95}\! \left(x , y , z\right) = F_{30}\! \left(x , y z , z\right)
F_{96}\! \left(x , y , z\right) = F_{61}\! \left(x , y , z\right)
F_{97}\! \left(x , y , z\right) = F_{98}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)
F_{99}\! \left(x , y , z\right) = F_{100}\! \left(x , y , z\right)+F_{158}\! \left(x , y , z\right)
F_{100}\! \left(x , y , z\right) = F_{101}\! \left(x , y , z\right) F_{46}\! \left(x , y\right)
F_{101}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)
F_{102}\! \left(x , y , z\right) = F_{103}\! \left(x , z\right)+F_{154}\! \left(x , y , z\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , 1, y\right)
F_{107}\! \left(x , y , z\right) = F_{0}\! \left(x \right)+F_{108}\! \left(x , y , z\right)+F_{109}\! \left(x , y , z\right)+F_{111}\! \left(x , y , z\right)
F_{108}\! \left(x , y , z\right) = F_{107}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{109}\! \left(x , y , z\right) = F_{110}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{110}\! \left(x , y , z\right) = -\frac{-F_{107}\! \left(x , y , z\right) y +F_{107}\! \left(x , 1, z\right)}{-1+y}
F_{111}\! \left(x , y , z\right) = F_{112}\! \left(x , y , z\right)
F_{112}\! \left(x , y , z\right) = F_{113}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{113}\! \left(x , y , z\right) = -\frac{-F_{114}\! \left(x , y z \right) y +F_{114}\! \left(x , z\right)}{-1+y}
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{118}\! \left(x , y\right) = -\frac{-F_{115}\! \left(x , y\right) y +F_{115}\! \left(x , 1\right)}{-1+y}
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{121}\! \left(x , y\right) = -\frac{-F_{122}\! \left(x , y\right) y +F_{122}\! \left(x , 1\right)}{-1+y}
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{107}\! \left(x , y , 1\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{126}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y , 1\right)
F_{127}\! \left(x , y , z\right) = -\frac{-F_{128}\! \left(x , y , z\right) z +F_{128}\! \left(x , y , 1\right)}{z -1}
F_{128}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{129}\! \left(x , y , z\right)+F_{130}\! \left(x , y , z\right)+F_{133}\! \left(x , y , z\right)
F_{129}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{130}\! \left(x , y , z\right) = F_{131}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{131}\! \left(x , y , z\right) = -\frac{F_{132}\! \left(x , 1, z\right) z -F_{132}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{132}\! \left(x , y , z\right) = F_{128}\! \left(x , y z , z\right)
F_{133}\! \left(x , y , z\right) = F_{134}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{134}\! \left(x , y , z\right) = \frac{F_{135}\! \left(x , y\right) y -F_{135}\! \left(x , z\right) z}{-z +y}
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y , 1\right)
F_{136}\! \left(x , y , z\right) = F_{137}\! \left(x , y z , z\right)
F_{137}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{138}\! \left(x , y , z\right)+F_{139}\! \left(x , y , z\right)+F_{141}\! \left(x , y , z\right)
F_{138}\! \left(x , y , z\right) = F_{137}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{139}\! \left(x , y , z\right) = F_{140}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)
F_{140}\! \left(x , y , z\right) = -\frac{F_{136}\! \left(x , 1, z\right) z -F_{136}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{141}\! \left(x , y , z\right) = F_{142}\! \left(x , y , z\right) F_{49}\! \left(x \right)
F_{142}\! \left(x , y , z\right) = \frac{F_{143}\! \left(x , y\right) y -F_{143}\! \left(x , z\right) z}{-z +y}
F_{143}\! \left(x , y\right) = F_{132}\! \left(x , y , 1\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{146}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y , 1\right)
F_{147}\! \left(x , y , z\right) = -\frac{-F_{137}\! \left(x , y , z\right) z +F_{137}\! \left(x , y , 1\right)}{z -1}
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{152}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , 1, y\right)
F_{153}\! \left(x , y , z\right) = -\frac{-F_{43}\! \left(x , y z \right) y +F_{43}\! \left(x , z\right)}{-1+y}
F_{154}\! \left(x , y , z\right) = F_{155}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)
F_{155}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{156}\! \left(x , y , z\right)
F_{156}\! \left(x , y , z\right) = F_{157}\! \left(x , y , z\right)
F_{157}\! \left(x , y , z\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)
F_{158}\! \left(x , y , z\right) = F_{159}\! \left(x , y , z\right)
F_{159}\! \left(x , y , z\right) = F_{46}\! \left(x , y\right)^{2} F_{0}\! \left(x \right) F_{160}\! \left(x , y\right) F_{43}\! \left(x , z\right)
F_{160}\! \left(x , y\right) = y F_{161}\! \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_{49}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , 1, y\right)
F_{164}\! \left(x , y , z\right) = -\frac{-F_{46}\! \left(x , y z \right) y +F_{46}\! \left(x , z\right)}{-1+y}
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{166}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_49(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0) + F_165(x, k_0) + F_5(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_8(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1) + F_97(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_1) + F_96(x, k_0, k_1))
Eq(F_16(x, k_0), F_17(x, k_0) + F_93(x, k_0))
Eq(F_9(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x) + F_20(x, k_0) + F_83(x, k_0))
Eq(F_19(x), 0)
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_8(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1) + F_9(x, k_1))
Eq(F_26(x, k_0, k_1), F_19(x) + F_27(x, k_0, k_1) + F_50(x, k_0, k_1) + F_55(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_8(x, k_0))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_1) + F_31(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_17(x, k_1) + F_26(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_0(x)*F_33(x, k_0)*F_41(x, k_0, k_1))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0)*F_8(x, k_0))
Eq(F_35(x, k_0), F_36(x, 1, k_0))
Eq(F_36(x, k_0, k_1), F_37(x, k_0*k_1, k_1))
Eq(F_37(x, k_0, k_1), F_1(x) + F_38(x, k_0, k_1) + F_39(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_37(x, k_0, k_1)*F_8(x, k_0))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, k_1)*F_8(x, k_1))
Eq(F_40(x, k_0, k_1), (-k_0*F_36(x, k_0/k_1, k_1) + k_1*F_36(x, 1, k_1))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1), F_41(x, k_0, k_0*k_1))
Eq(F_42(x, k_0, k_1), (k_0*k_1*F_43(x, k_0*k_1) - k_0*F_43(x, k_0))/(k_0*k_1 - k_0))
Eq(F_43(x, k_0), F_1(x) + F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_43(x, k_0)*F_46(x, k_0)*F_8(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_49(x))
Eq(F_48(x, k_0), (-k_0*F_43(x, k_0) + F_43(x, 1))/(1 - k_0))
Eq(F_49(x), x)
Eq(F_50(x, k_0, k_1), F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_0(x)*F_43(x, k_1)*F_52(x, k_0, k_1)*F_8(x, k_1))
Eq(F_53(x, k_0, k_1), F_52(x, k_0*k_1, k_1))
Eq(F_53(x, k_0, k_1), F_54(k_1*x, k_0))
Eq(F_54(x, k_0), -F_33(x, 1) + (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_55(x, k_0, k_1), F_49(x)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (-k_1*F_26(x, k_0, k_1) + F_26(x, k_0, 1))/(1 - k_1))
Eq(F_58(x, k_0, k_1), F_57(x, k_0, k_1) + F_77(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_58(x, k_0, k_1)*F_8(x, k_1))
Eq(F_59(x, k_0, k_1), F_60(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_60(x, k_0, k_1) + F_63(x, k_0))
Eq(F_61(x, k_0, k_1), F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x, k_0))
Eq(F_64(x, k_0), F_0(x) + F_63(x, k_0))
Eq(F_65(x, k_0, k_1), F_64(x, k_0) + F_67(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_66(x, k_0, k_0*k_1))
Eq(F_66(x, k_0, k_1), F_5(x, k_1) + F_61(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), -F_67(x, k_0, 1) + (-k_0*F_67(x, k_0, 1) + k_1*F_67(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_69(x, k_0, k_1), F_68(x, k_0, k_1)*F_8(x, k_0))
Eq(F_70(x, k_0, k_1), F_19(x) + F_69(x, k_0, k_1) + F_71(x, k_0, k_1) + F_74(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), -F_6(x, k_0) + (-k_0*F_6(x, k_0) + k_1*F_6(x, k_1))/(-k_0 + k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1)*F_8(x, k_1))
Eq(F_72(x, k_0, k_1), (-k_0*F_73(x, k_0/k_1, k_1) + k_1*F_73(x, 1, k_1))/(-k_0 + k_1))
Eq(F_73(x, k_0, k_1), F_66(x, k_0*k_1, k_1))
Eq(F_74(x, k_0, k_1), F_49(x)*F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), -F_76(x, k_0) + (-k_0*F_76(x, k_0) + k_1*F_76(x, k_1))/(-k_0 + k_1))
Eq(F_76(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_77(x, k_0, k_1), F_78(x, k_0, k_1))
Eq(F_78(x, k_0, k_1), F_79(x, k_0, k_1)*F_8(x, k_0))
Eq(F_79(x, k_0, k_1), F_17(x, k_1) + F_80(x, k_0, k_1) + F_81(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), F_79(x, k_0, k_1)*F_8(x, k_0))
Eq(F_81(x, k_0, k_1), F_82(x, k_0, k_1))
Eq(F_82(x, k_0, k_1), F_0(x)*F_35(x, k_0)*F_43(x, k_1)*F_46(x, k_0)*F_8(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_49(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), -F_87(x, 1) + (-k_0*F_87(x, k_0) + F_87(x, 1))/(1 - k_0))
Eq(F_87(x, k_0), F_6(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_49(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_57(x, k_0, 1))
Eq(F_91(x, k_0), F_49(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_85(x, 1) + (-k_0*F_85(x, k_0) + F_85(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_8(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, 1, k_0))
Eq(F_95(x, k_0, k_1), F_30(x, k_0*k_1, k_1))
Eq(F_96(x, k_0, k_1), F_61(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_98(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_8(x, k_0)*F_99(x, k_0, k_1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1) + F_158(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_101(x, k_0, k_1)*F_46(x, k_0))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1) + F_97(x, k_0, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_1) + F_154(x, k_0, k_1))
Eq(F_103(x, k_0), F_104(x, k_0) + F_150(x, k_0))
Eq(F_104(x, k_0), F_0(x) + F_105(x, k_0) + F_148(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_8(x, k_0))
Eq(F_106(x, k_0), F_107(x, 1, k_0))
Eq(F_107(x, k_0, k_1), F_0(x) + F_108(x, k_0, k_1) + F_109(x, k_0, k_1) + F_111(x, k_0, k_1))
Eq(F_108(x, k_0, k_1), F_107(x, k_0, k_1)*F_8(x, k_1))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1)*F_8(x, k_1))
Eq(F_110(x, k_0, k_1), (-k_0*F_107(x, k_0, k_1) + F_107(x, 1, k_1))/(1 - k_0))
Eq(F_111(x, k_0, k_1), F_112(x, k_0, k_1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0, k_1)*F_49(x))
Eq(F_113(x, k_0, k_1), (-k_0*k_1*F_114(x, k_0*k_1) + k_1*F_114(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_114(x, k_0), F_115(x, k_0) + F_144(x, k_0))
Eq(F_115(x, k_0), F_0(x) + F_116(x, k_0) + F_117(x, k_0) + F_119(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0)*F_8(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_49(x))
Eq(F_118(x, k_0), (-k_0*F_115(x, k_0) + F_115(x, 1))/(1 - k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_49(x))
Eq(F_121(x, k_0), (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_124(x, k_0))
Eq(F_123(x, k_0), F_107(x, k_0, 1))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_0(x)*F_126(x, k_0)*F_49(x))
Eq(F_126(x, k_0), F_127(x, k_0, 1))
Eq(F_127(x, k_0, k_1), (-k_1*F_128(x, k_0, k_1) + F_128(x, k_0, 1))/(1 - k_1))
Eq(F_128(x, k_0, k_1), F_1(x) + F_129(x, k_0, k_1) + F_130(x, k_0, k_1) + F_133(x, k_0, k_1))
Eq(F_129(x, k_0, k_1), F_128(x, k_0, k_1)*F_8(x, k_0))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1)*F_8(x, k_1))
Eq(F_131(x, k_0, k_1), (-k_0*F_132(x, k_0/k_1, k_1) + k_1*F_132(x, 1, k_1))/(-k_0 + k_1))
Eq(F_132(x, k_0, k_1), F_128(x, k_0*k_1, k_1))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1)*F_49(x))
Eq(F_134(x, k_0, k_1), (-k_0*F_135(x, k_0) + k_1*F_135(x, k_1))/(-k_0 + k_1))
Eq(F_135(x, k_0), F_136(x, k_0, 1))
Eq(F_136(x, k_0, k_1), F_137(x, k_0*k_1, k_1))
Eq(F_137(x, k_0, k_1), F_1(x) + F_138(x, k_0, k_1) + F_139(x, k_0, k_1) + F_141(x, k_0, k_1))
Eq(F_138(x, k_0, k_1), F_137(x, k_0, k_1)*F_8(x, k_0))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1)*F_8(x, k_1))
Eq(F_140(x, k_0, k_1), (-k_0*F_136(x, k_0/k_1, k_1) + k_1*F_136(x, 1, k_1))/(-k_0 + k_1))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1)*F_49(x))
Eq(F_142(x, k_0, k_1), (-k_0*F_143(x, k_0) + k_1*F_143(x, k_1))/(-k_0 + k_1))
Eq(F_143(x, k_0), F_132(x, k_0, 1))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_0(x)*F_146(x, k_0)*F_49(x))
Eq(F_146(x, k_0), F_147(x, k_0, 1))
Eq(F_147(x, k_0, k_1), (-k_1*F_137(x, k_0, k_1) + F_137(x, k_0, 1))/(1 - k_1))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_114(x, k_0)*F_49(x))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_0(x)*F_152(x, k_0)*F_8(x, k_0))
Eq(F_152(x, k_0), F_153(x, 1, k_0))
Eq(F_153(x, k_0, k_1), (-k_0*k_1*F_43(x, k_0*k_1) + k_1*F_43(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_154(x, k_0, k_1), F_155(x, k_0, k_1)*F_8(x, k_0))
Eq(F_155(x, k_0, k_1), F_102(x, k_0, k_1) + F_156(x, k_0, k_1))
Eq(F_156(x, k_0, k_1), F_157(x, k_0, k_1))
Eq(F_157(x, k_0, k_1), F_8(x, k_0)*F_99(x, k_0, k_1))
Eq(F_158(x, k_0, k_1), F_159(x, k_0, k_1))
Eq(F_159(x, k_0, k_1), F_0(x)*F_160(x, k_0)*F_43(x, k_1)*F_46(x, k_0)**2)
Eq(F_160(x, k_0), k_0*F_161(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_49(x))
Eq(F_163(x, k_0), F_164(x, 1, k_0))
Eq(F_164(x, k_0, k_1), (-k_0*k_1*F_46(x, k_0*k_1) + k_1*F_46(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_165(x, k_0), F_166(x, k_0)*F_49(x))
Eq(F_166(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 1, 0, 4]]}], "iterative": false}
Specification JSON:
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