0213_1230_13042
Counting sequence:
1, 1, 2, 6, 22, 86, 343, 1374, 5497, 21926, 87176, 345612, 1366960, 5396604, 21275618, 83793268, 329791425, 1297428774, 5103039279, 20069815052, 78936685887, 310509337760, 1221686293926, 4807894697586, 18926706307263, 74529761736076, 293579002631157, 1156815016422286, 4559817353074664, 17979387808806340, 70916030094268643, 279803591461965176, 1104328313262472836, 4359889552589461382, 17217939831128612241, 68016021859298665406, 268758053615943678794, 1062252722497513104232, 4199583949879536152215, 16607060259158728338272, 65687612401944802780617, 259881088671489612048700, 1028401644505442787591946, 4070467276688513395247826, 16114464151696156251589043, 63807889388824773754909248, 252706696605718399791645085, 1001013802694655330841173054, 3965897973961525734117983504, 15715148950030476424494771852, 62282840936246259435593772511, 246881668480650942062584691436, 978762832096541401601511310997, 3880896592373866470762951838596, 15390422064000416482169229996622, 61042290260090838786118062650106, 242142489159212360095249201681373, 960658933244004471661485512044104, 3811743918841923565721327798743447, 15126302350303485023009094741213246, 60033654772100435605376443019574926, 238291295860957180764435761784368292, 945957167333534270722635586281088675, 3755633745537271389992314235788397244, 14912212681803839705363807435428124498, 59217044093645343403660655342439008838, 235177558480947833334350065665232265575, 934089160333762732375504992784900621314, 3710418733828378068446851450659676575314, 14740035579060953464650232645731005876592, 58561754264833137988783812413213143696657, 232685073918080932096259725744259036962800, 924614876132812178142031807884266841966011, 3674431625149792094866687817148914863276716, 14603450444984377330260389313428727924640618, 58043810760633476402764459816224281723294478, 230722856136923975795508530357341137060180545, 917188830495322267326159920625503457318319584, 3646359898273101134659666456546660731158227579, 14497468379259556235593950065262801476492060202, 57644241304494859494771997561113671105885642132, 229218720310281261554844678938296200463151143860, 911536246677610196536600525704958214971282894461, 3625157105960424078406848917426993883658971760636, 14418102312706693586822064327784161417469379550043, 57347847944328610789183381980383880270118305191388, 228114709281709034262795292271269059584242720473190, 907436010982096261363216404192550740247617403801494, 3609979317608066085775334025007331896546464857128679, 14362129868515002268529131596816408812137087904899352, 57142321745813113087676210626275611750830143897817737, 227363786525784250195734690788901805557921020472715050, 904708312173358926155123516376780919273551230734373886, 3600138892700617275208044148274877937826636442284794636, 14326920382459781284978506329327773358190776653021273033, 57017595129618240212407955833571323295291169296293453468, 226927409816425275126695447031435107587661207437258241025, 903205546602371232277107430226143187648744780633386085164, 3595070370452691403323778168721482158672628939019239423284, 14310306901101663388908691984760743380334697085651726176482, 56965361271786940357560870015261121480675070710370869330257
Generating function in Maple syntax:
1/8*((4*x^5-25*x^4+54*x^3-54*x^2+22*x-3)*(1-4*x)^(1/2)-20*x^5+69*x^4-72*x^3+38*x^2-10*x+1)/(x^2-3*x+1)^2/(x-1/4)
Generating function in latex syntax:
\frac{\left(4 x^{5}-25 x^{4}+54 x^{3}-54 x^{2}+22 x -3\right) \sqrt{1-4 x}-20 x^{5}+69 x^{4}-72 x^{3}+38 x^{2}-10 x +1}{8 \left(x^{2}-3 x +1\right)^{2} \left(x -\frac{1}{4}\right)}
Generating function in sympy syntax:
(-5*x**5/2 + 69*x**4/8 - 9*x**3 + 19*x**2/4 - 5*x/4 + sqrt(1 - 4*x)*(4*x**5 - 25*x**4 + 54*x**3 - 54*x**2 + 22*x - 3)/8 + 1/8)/((x - 1/4)*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(4*x-1)*(x^2-3*x+1)^4*F(x)^2+(4*x-1)*(5*x^4-16*x^3+14*x^2-6*x+1)*(x^2-3*x+1)^2*F(x)+4*x^10-25*x^9+98*x^8-347*x^7+841*x^6-1214*x^5+1061*x^4-561*x^3+174*x^2-29*x+2 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) \left(x^{2}-3 x +1\right)^{4} F \! \left(x \right)^{2}+\left(4 x -1\right) \left(5 x^{4}-16 x^{3}+14 x^{2}-6 x +1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+4 x^{10}-25 x^{9}+98 x^{8}-347 x^{7}+841 x^{6}-1214 x^{5}+1061 x^{4}-561 x^{3}+174 x^{2}-29 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 86
a(6) = 343
a(7) = 1374
a(8) = 5497
a(9) = 21926
a(10) = 87176
a(n+10) = -8/3*(-1+2*n)/(n+10)*a(n)+2/3*(51+100*n)/(n+10)*a(n+1)-1/3*(1618+1041*n)/(n+10)*a(n+2)+2/3*(3921+1478*n)/(n+10)*a(n+3)-1/3*(19166+5053*n)/(n+10)*a(n+4)+2/3*(13312+2703*n)/(n+10)*a(n+5)-22/3*(992+165*n)/(n+10)*a(n+6)+2/3*(5339+757*n)/(n+10)*a(n+7)-1/3*(3054+379*n)/(n+10)*a(n+8)+2/3*(235+26*n)/(n+10)*a(n+9), n >= 11
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 86
a \! \left(6\right) = 343
a \! \left(7\right) = 1374
a \! \left(8\right) = 5497
a \! \left(9\right) = 21926
a \! \left(10\right) = 87176
a \! \left(n +10\right) = -\frac{8 \left(-1+2 n \right) a \! \left(n \right)}{3 \left(n +10\right)}+\frac{2 \left(51+100 n \right) a \! \left(n +1\right)}{3 \left(n +10\right)}-\frac{\left(1618+1041 n \right) a \! \left(n +2\right)}{3 \left(n +10\right)}+\frac{2 \left(3921+1478 n \right) a \! \left(n +3\right)}{3 \left(n +10\right)}-\frac{\left(19166+5053 n \right) a \! \left(n +4\right)}{3 \left(n +10\right)}+\frac{2 \left(13312+2703 n \right) a \! \left(n +5\right)}{3 \left(n +10\right)}-\frac{22 \left(992+165 n \right) a \! \left(n +6\right)}{3 \left(n +10\right)}+\frac{2 \left(5339+757 n \right) a \! \left(n +7\right)}{3 \left(n +10\right)}-\frac{\left(3054+379 n \right) a \! \left(n +8\right)}{3 \left(n +10\right)}+\frac{2 \left(235+26 n \right) a \! \left(n +9\right)}{3 \left(n +10\right)}, \quad n \geq 11
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23974/
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[8,x]
F[4,x] = F[16,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[6,x]
F[15,x] = F[11,x]
F[16,x] = F[17,x]+F[28,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[8,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[21,x]+F[22,x,k[0]]
F[21,x] = F[1,x]+F[18,x]
F[22,x,k[0]] = F[23,x]+F[24,x,k[0]]+F[26,x,k[0]]
F[23,x] = 0
F[24,x,k[0]] = F[25,x,k[0]]*F[8,x]
F[25,x,k[0]] = -k[0]*(F[22,x,1]-F[22,x,k[0]])/(-1+k[0])
F[26,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[19,x]*F[6,x]
F[32,x] = F[33,x,1]
F[33,x,k[0]] = F[108,x,k[0]]+F[34,x,k[0]]
F[35,x,k[0]] = F[20,x,k[0]]+F[34,x,k[0]]
F[35,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[38,x,k[0]]+F[73,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[8,x]
F[37,x,k[0]] = 1/(-1+k[0])*(F[35,x,k[0]]*k[0]-F[35,x,1])
F[38,x,k[0]] = F[27,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[4,x]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]+F[46,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[5,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[27,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[43,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[8,x]
F[48,x,k[0]] = F[106,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = -k[0]*(F[51,x,1]-F[51,x,k[0]])/(-1+k[0])
F[51,x,k[0]] = F[23,x]+F[52,x,k[0]]+F[54,x,k[0]]+F[55,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[50,x,k[0]]*F[8,x]
F[54,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]*F[5,x]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]*F[8,x]
F[58,x,k[0]] = F[57,x,k[0]]+F[82,x]
F[59,x,k[0]] = F[58,x,k[0]]*F[8,x]
F[59,x,k[0]] = F[60,x,k[0]]
F[61,x,k[0]] = F[5,x]+F[60,x,k[0]]+F[63,x,k[0]]+F[65,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[20,x,k[0]]*F[5,x]
F[63,x,k[0]] = F[64,x,k[0]]*F[8,x]
F[64,x,k[0]] = 1/(-1+k[0])*(F[61,x,k[0]]*k[0]-F[61,x,1])
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[27,x,k[0]]*F[67,x,k[0]]
F[67,x,k[0]] = F[62,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]*F[79,x]
F[70,x,k[0]] = F[27,x,k[0]]*F[69,x,k[0]]
F[34,x,k[0]] = F[23,x]+F[70,x,k[0]]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]*F[8,x]
F[72,x,k[0]] = 1/(-1+k[0])*(F[34,x,k[0]]*k[0]-F[34,x,1])
F[39,x,k[0]] = F[1,x]+F[26,x,k[0]]+F[73,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]*F[8,x]
F[75,x,k[0]] = F[76,x]+F[77,x,k[0]]
F[76,x] = F[35,x,1]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = -k[0]*(F[40,x,1]-F[40,x,k[0]])/(-1+k[0])
F[79,x] = F[1,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[79,x]*F[8,x]
F[82,x] = 1/F[8,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[105,x]-F[5,x]+F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[21,x]*F[5,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[28,x]+F[6,x]
F[89,x] = F[90,x]
F[90,x] = F[8,x]*F[91,x]
F[91,x] = F[87,x]+F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[51,x,1]
F[94,x] = F[95,x]
F[95,x] = F[101,x]*F[5,x]*F[8,x]*F[96,x]
F[96,x] = F[104,x]+F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[22,x,1]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[8,x]*F[96,x]
F[101,x] = F[1,x]+F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[101,x]*F[8,x]
F[104,x] = F[25,x,1]
F[105,x] = F[16,x]
F[106,x,k[0]] = F[107,x,k[0]]*F[43,x,k[0]]*F[5,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[8,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[33,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[114,x,k[0]]
F[113,x,k[0]] = (F[51,x,k[0]]-F[51,x,1])/(-1+k[0])
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[101,x]*F[116,x,k[0]]*F[5,x]*F[8,x]
F[116,x,k[0]] = F[117,x,k[0]]+F[121,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = (F[22,x,k[0]]-F[22,x,1])/(-1+k[0])
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[101,x]*F[116,x,k[0]]*F[8,x]
F[121,x,k[0]] = (F[118,x,k[0]]*k[0]-F[118,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{6}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{28}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{y \left(F_{22}\! \left(x , 1\right)-F_{22}\! \left(x , y\right)\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right) F_{6}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{33}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{37}\! \left(x , y\right) = -\frac{-y F_{35}\! \left(x , y\right)+F_{35}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = -\frac{y \left(F_{51}\! \left(x , 1\right)-F_{51}\! \left(x , y\right)\right)}{-1+y}
F_{51}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{64}\! \left(x , y\right) = -\frac{-y F_{61}\! \left(x , y\right)+F_{61}\! \left(x , 1\right)}{-1+y}
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{79}\! \left(x \right)
F_{70}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{72}\! \left(x , y\right) = -\frac{-y F_{34}\! \left(x , y\right)+F_{34}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{76}\! \left(x \right) = F_{35}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = -\frac{y \left(F_{40}\! \left(x , 1\right)-F_{40}\! \left(x , y\right)\right)}{-1+y}
F_{79}\! \left(x \right) = F_{1}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{79}\! \left(x \right) F_{8}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{105}\! \left(x \right)-F_{5}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{28}\! \left(x \right)+F_{6}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{8}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{104}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right) F_{8}\! \left(x \right)
F_{104}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{105}\! \left(x \right) = F_{16}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \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_{8}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = -\frac{F_{51}\! \left(x , 1\right)-F_{51}\! \left(x , y\right)}{-1+y}
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{101}\! \left(x \right) F_{116}\! \left(x , y\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{121}\! \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) = -\frac{F_{22}\! \left(x , 1\right)-F_{22}\! \left(x , y\right)}{-1+y}
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{101}\! \left(x \right) F_{116}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{121}\! \left(x , y\right) = -\frac{-y F_{118}\! \left(x , y\right)+F_{118}\! \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_8(x))
Eq(F_4(x), F_16(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_6(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), F_17(x) + F_28(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_8(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_21(x) + F_22(x, k_0))
Eq(F_21(x), F_1(x) + F_18(x))
Eq(F_22(x, k_0), F_23(x) + F_24(x, k_0) + F_26(x, k_0))
Eq(F_23(x), 0)
Eq(F_24(x, k_0), F_25(x, k_0)*F_8(x))
Eq(F_25(x, k_0), -F_22(x, 1) + (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_19(x)*F_6(x))
Eq(F_32(x), F_33(x, 1))
Eq(F_33(x, k_0), F_108(x, k_0) + F_34(x, k_0))
Eq(F_35(x, k_0), F_20(x, k_0) + F_34(x, k_0))
Eq(F_35(x, k_0), F_1(x) + F_36(x, k_0) + F_38(x, k_0) + F_73(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_8(x))
Eq(F_37(x, k_0), (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_27(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_4(x) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0) + F_46(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_5(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_27(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_43(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_8(x))
Eq(F_48(x, k_0), F_106(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), -F_51(x, 1) + (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_51(x, k_0), F_23(x) + F_52(x, k_0) + F_54(x, k_0) + F_55(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_50(x, k_0)*F_8(x))
Eq(F_54(x, k_0), F_20(x, k_0)*F_27(x, k_0)*F_5(x))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0)*F_8(x))
Eq(F_58(x, k_0), F_57(x, k_0) + F_82(x))
Eq(F_59(x, k_0), F_58(x, k_0)*F_8(x))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_61(x, k_0), F_5(x) + F_60(x, k_0) + F_63(x, k_0) + F_65(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_20(x, k_0)*F_5(x))
Eq(F_63(x, k_0), F_64(x, k_0)*F_8(x))
Eq(F_64(x, k_0), (k_0*F_61(x, k_0) - F_61(x, 1))/(k_0 - 1))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_27(x, k_0)*F_67(x, k_0))
Eq(F_67(x, k_0), F_62(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0)*F_79(x))
Eq(F_70(x, k_0), F_27(x, k_0)*F_69(x, k_0))
Eq(F_34(x, k_0), F_23(x) + F_70(x, k_0) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0)*F_8(x))
Eq(F_72(x, k_0), (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_1(x) + F_26(x, k_0) + F_73(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0)*F_8(x))
Eq(F_75(x, k_0), F_76(x) + F_77(x, k_0))
Eq(F_76(x), F_35(x, 1))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), -F_40(x, 1) + (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_79(x), F_1(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_79(x)*F_8(x))
Eq(F_82(x), F_83(x)/F_8(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), -F_105(x) - F_5(x) + F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_21(x)*F_5(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_28(x) + F_6(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_8(x)*F_91(x))
Eq(F_91(x), F_87(x) + F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_51(x, 1))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_101(x)*F_5(x)*F_8(x)*F_96(x))
Eq(F_96(x), F_104(x) + F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_22(x, 1))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_8(x)*F_96(x))
Eq(F_101(x), F_1(x) + F_102(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_101(x)*F_8(x))
Eq(F_104(x), F_25(x, 1))
Eq(F_105(x), F_16(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_43(x, k_0)*F_5(x))
Eq(F_107(x, k_0), (k_0*F_20(x, k_0) - F_20(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_8(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_33(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_114(x, k_0))
Eq(F_113(x, k_0), -F_51(x, k_0) + (-k_0*F_51(x, k_0) + F_51(x, 1))/(1 - k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_101(x)*F_116(x, k_0)*F_5(x)*F_8(x))
Eq(F_116(x, k_0), F_117(x, k_0) + F_121(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), -F_22(x, k_0) + (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_101(x)*F_116(x, k_0)*F_8(x))
Eq(F_121(x, k_0), (-k_0*F_118(x, k_0) + F_118(x, 1))/(1 - 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": false, "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_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 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": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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"BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23975/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[11,x]*F[4,x]
F[4,x] = F[1,x]+F[115,x]+F[5,x]
F[5,x] = F[11,x]*F[6,x]
F[6,x] = F[39,x]+F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[1,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[8,x]
F[11,x] = x
F[12,x] = F[13,x]+F[25,x]
F[13,x] = F[14,x]
F[14,x] = F[11,x]*F[15,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[1,x]+F[11,x]
F[17,x] = F[13,x]+F[18,x]
F[18,x] = F[19,x]+F[20,x]+F[24,x]
F[19,x] = 0
F[20,x] = F[11,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[11,x]
F[23,x] = F[18,x]
F[24,x] = F[11,x]*F[13,x]
F[25,x] = F[19,x]+F[26,x]+F[38,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]+F[9,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[9,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = 2*F[19,x]+F[33,x]+F[37,x]
F[33,x] = F[11,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[11,x]*F[25,x]
F[38,x] = F[11,x]*F[12,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[41,x]*F[7,x]
F[41,x] = F[1,x]+F[42,x]+F[43,x]+F[61,x]+F[70,x]
F[42,x] = F[11,x]*F[41,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[45,x]*F[51,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[11,x]*F[45,x]*F[48,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[48,x]
F[51,x] = F[1,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[51,x]+F[55,x]
F[55,x] = F[52,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[52,x]
F[60,x] = F[56,x]
F[61,x] = F[11,x]*F[62,x]
F[62,x] = F[63,x,1]
F[63,x,k[0]] = (F[64,x,k[0]]*k[0]-F[64,x,1])/(-1+k[0])
F[64,x,k[0]] = F[1,x]+F[65,x,k[0]]+F[66,x,k[0]]+F[69,x,k[0]]+F[70,x]
F[65,x,k[0]] = F[11,x]*F[64,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[45,x]*F[51,x]*F[68,x,k[0]]
F[68,x,k[0]] = k[0]*x
F[69,x,k[0]] = F[11,x]*F[63,x,k[0]]
F[70,x] = F[71,x,1]
F[71,x,k[0]] = F[11,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[1,x]+F[73,x,k[0]]+F[74,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[68,x,k[0]]*F[72,x,k[0]]
F[74,x,k[0]] = F[11,x]*F[72,x,k[0]]
F[75,x,k[0]] = F[11,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[80,x,k[0]]
F[77,x,k[0]] = F[1,x]+F[71,x,k[0]]+F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[68,x,k[0]]*F[77,x,k[0]]
F[79,x,k[0]] = F[11,x]*F[76,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[51,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x]+F[94,x,k[0]]
F[83,x] = F[11,x]+F[84,x]
F[84,x] = F[19,x]+F[85,x]+F[86,x]
F[85,x] = F[11,x]*F[49,x]
F[86,x] = F[11,x]*F[87,x]
F[87,x] = F[88,x]+F[91,x]
F[88,x] = F[11,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[11,x]*F[88,x]
F[91,x] = F[84,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[11,x]*F[91,x]
F[94,x,k[0]] = F[100,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[11,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[68,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[97,x,k[0]]
F[100,x,k[0]] = 2*F[19,x]+F[101,x,k[0]]+F[107,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[105,x,k[0]]+F[19,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[68,x,k[0]]
F[104,x,k[0]] = F[102,x,k[0]]+F[49,x]
F[105,x,k[0]] = F[106,x,k[0]]*F[11,x]
F[106,x,k[0]] = F[102,x,k[0]]+F[97,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[11,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[112,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[95,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[109,x,k[0]]*F[11,x]
F[112,x,k[0]] = F[100,x,k[0]]+F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[11,x]*F[112,x,k[0]]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[117,x,1]
F[117,x,k[0]] = F[1,x]+F[118,x,k[0]]+F[129,x,k[0]]+F[177,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[68,x,k[0]]
F[119,x,k[0]] = F[1,x]+F[118,x,k[0]]+F[120,x,k[0]]+F[125,x,k[0]]
F[120,x,k[0]] = F[11,x]*F[121,x,k[0]]
F[121,x,k[0]] = F[1,x]+F[122,x,k[0]]+F[123,x,k[0]]+F[125,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]*F[68,x,k[0]]
F[123,x,k[0]] = F[11,x]*F[124,x,k[0]]
F[124,x,k[0]] = F[106,x,k[0]]+F[48,x]
F[125,x,k[0]] = F[11,x]*F[126,x,k[0]]
F[126,x,k[0]] = F[1,x]+F[127,x,k[0]]+F[128,x,k[0]]+F[71,x,k[0]]+F[79,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]*F[68,x,k[0]]
F[128,x,k[0]] = F[11,x]*F[126,x,k[0]]
F[129,x,k[0]] = F[11,x]*F[130,x,k[0]]
F[130,x,k[0]] = F[1,x]+F[131,x,k[0]]+F[141,x,k[0]]+F[157,x,k[0]]+F[168,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[68,x,k[0]]
F[132,x,k[0]] = F[119,x,k[0]]+F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[135,x,k[0]]+F[136,x,k[0]]+F[137,x,k[0]]+F[19,x]
F[134,x,k[0]] = F[133,x,k[0]]*F[68,x,k[0]]
F[135,x,k[0]] = F[11,x]*F[133,x,k[0]]
F[136,x,k[0]] = F[11,x]*F[119,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[11,x]*F[139,x,k[0]]
F[139,x,k[0]] = 3*F[19,x]+F[140,x,k[0]]+F[74,x,k[0]]
F[140,x,k[0]] = F[139,x,k[0]]*F[68,x,k[0]]
F[141,x,k[0]] = F[11,x]*F[142,x,k[0]]
F[142,x,k[0]] = F[130,x,k[0]]+F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[145,x,k[0]]+F[147,x,k[0]]+F[149,x,k[0]]+F[151,x,k[0]]+F[19,x]
F[144,x,k[0]] = F[143,x,k[0]]*F[68,x,k[0]]
F[145,x,k[0]] = F[11,x]*F[146,x,k[0]]
F[146,x,k[0]] = (F[143,x,k[0]]*k[0]-F[143,x,1])/(-1+k[0])
F[147,x,k[0]] = F[11,x]*F[148,x,k[0]]
F[148,x,k[0]] = (F[133,x,k[0]]*k[0]-F[133,x,1])/(-1+k[0])
F[149,x,k[0]] = F[11,x]*F[150,x,k[0]]
F[150,x,k[0]] = (F[119,x,k[0]]*k[0]-F[119,x,1])/(-1+k[0])
F[151,x,k[0]] = F[152,x,k[0]]
F[153,x,k[0]] = F[149,x,k[0]]+F[152,x,k[0]]+F[154,x,k[0]]+F[155,x,k[0]]+F[19,x]
F[130,x,k[0]] = F[117,x,k[0]]+F[153,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]*F[68,x,k[0]]
F[155,x,k[0]] = F[11,x]*F[156,x,k[0]]
F[156,x,k[0]] = (F[153,x,k[0]]*k[0]-F[153,x,1])/(-1+k[0])
F[157,x,k[0]] = F[11,x]*F[158,x,k[0]]
F[158,x,k[0]] = F[1,x]+F[159,x,k[0]]+F[160,x,k[0]]+F[162,x,k[0]]+F[164,x,k[0]]
F[159,x,k[0]] = F[158,x,k[0]]*F[68,x,k[0]]
F[160,x,k[0]] = F[11,x]*F[161,x,k[0]]
F[161,x,k[0]] = (F[158,x,k[0]]*k[0]-F[158,x,1])/(-1+k[0])
F[162,x,k[0]] = F[11,x]*F[163,x,k[0]]
F[163,x,k[0]] = (F[121,x,k[0]]*k[0]-F[121,x,1])/(-1+k[0])
F[117,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[165,x,k[0]]+F[166,x,k[0]]
F[165,x,k[0]] = F[117,x,k[0]]*F[68,x,k[0]]
F[166,x,k[0]] = F[11,x]*F[167,x,k[0]]
F[167,x,k[0]] = (F[117,x,k[0]]*k[0]-F[117,x,1])/(-1+k[0])
F[168,x,k[0]] = F[11,x]*F[169,x,k[0]]
F[169,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[170,x,k[0]]+F[171,x,k[0]]+F[173,x,k[0]]+F[175,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[68,x,k[0]]
F[171,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[172,x,k[0]] = (F[169,x,k[0]]*k[0]-F[169,x,1])/(-1+k[0])
F[173,x,k[0]] = F[11,x]*F[174,x,k[0]]
F[174,x,k[0]] = (F[126,x,k[0]]*k[0]-F[126,x,1])/(-1+k[0])
F[175,x,k[0]] = F[11,x]*F[176,x,k[0]]
F[176,x,k[0]] = (F[76,x,k[0]]*k[0]-F[76,x,1])/(-1+k[0])
F[177,x,k[0]] = F[11,x]*F[178,x,k[0]]
F[178,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[175,x,k[0]]+F[179,x,k[0]]+F[180,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]*F[68,x,k[0]]
F[180,x,k[0]] = F[11,x]*F[181,x,k[0]]
F[181,x,k[0]] = (F[178,x,k[0]]*k[0]-F[178,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_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{11}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{39}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{25}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)+F_{38}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{61}\! \left(x \right)+F_{70}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{41}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right) F_{51}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{52}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x , 1\right)
F_{63}\! \left(x , y\right) = -\frac{-y F_{64}\! \left(x , y\right)+F_{64}\! \left(x , 1\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{69}\! \left(x , y\right)+F_{70}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{45}\! \left(x \right) F_{51}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = y x
F_{69}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{70}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{71}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{51}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right)+F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right) F_{91}\! \left(x \right)
F_{94}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{49}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{112}\! \left(x , y\right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{118}\! \left(x , y\right)+F_{129}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{122}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{127}\! \left(x , y\right)+F_{128}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{126}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{141}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{133}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{119}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = 3 F_{19}\! \left(x \right)+F_{140}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{145}\! \left(x , y\right)+F_{147}\! \left(x , y\right)+F_{149}\! \left(x , y\right)+F_{151}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = -\frac{-y F_{143}\! \left(x , y\right)+F_{143}\! \left(x , 1\right)}{-1+y}
F_{147}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = -\frac{-y F_{133}\! \left(x , y\right)+F_{133}\! \left(x , 1\right)}{-1+y}
F_{149}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = -\frac{-y F_{119}\! \left(x , y\right)+F_{119}\! \left(x , 1\right)}{-1+y}
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{152}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = -\frac{-y F_{153}\! \left(x , y\right)+F_{153}\! \left(x , 1\right)}{-1+y}
F_{157}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{159}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{162}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = -\frac{-y F_{158}\! \left(x , y\right)+F_{158}\! \left(x , 1\right)}{-1+y}
F_{162}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = -\frac{-y F_{121}\! \left(x , y\right)+F_{121}\! \left(x , 1\right)}{-1+y}
F_{117}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = -\frac{-y F_{117}\! \left(x , y\right)+F_{117}\! \left(x , 1\right)}{-1+y}
F_{168}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{173}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = -\frac{-y F_{169}\! \left(x , y\right)+F_{169}\! \left(x , 1\right)}{-1+y}
F_{173}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = -\frac{-y F_{126}\! \left(x , y\right)+F_{126}\! \left(x , 1\right)}{-1+y}
F_{175}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}
F_{177}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{175}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = -\frac{-y F_{178}\! \left(x , y\right)+F_{178}\! \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_11(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_115(x) + F_5(x))
Eq(F_5(x), F_11(x)*F_6(x))
Eq(F_6(x), F_39(x) + F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_1(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_8(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_25(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_11(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_1(x) + F_11(x))
Eq(F_17(x), F_13(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_24(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_11(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_11(x))
Eq(F_23(x), F_18(x))
Eq(F_24(x), F_11(x)*F_13(x))
Eq(F_25(x), F_19(x) + F_26(x) + F_38(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_29(x) + F_9(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_9(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), 2*F_19(x) + F_33(x) + F_37(x))
Eq(F_33(x), F_11(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_11(x)*F_25(x))
Eq(F_38(x), F_11(x)*F_12(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_41(x)*F_7(x))
Eq(F_41(x), F_1(x) + F_42(x) + F_43(x) + F_61(x) + F_70(x))
Eq(F_42(x), F_11(x)*F_41(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_45(x)*F_51(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_11(x)*F_45(x)*F_48(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_48(x))
Eq(F_51(x), F_1(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_51(x) + F_55(x))
Eq(F_55(x), F_52(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_52(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_11(x)*F_62(x))
Eq(F_62(x), F_63(x, 1))
Eq(F_63(x, k_0), (-k_0*F_64(x, k_0) + F_64(x, 1))/(1 - k_0))
Eq(F_64(x, k_0), F_1(x) + F_65(x, k_0) + F_66(x, k_0) + F_69(x, k_0) + F_70(x))
Eq(F_65(x, k_0), F_11(x)*F_64(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_45(x)*F_51(x)*F_68(x, k_0))
Eq(F_68(x, k_0), k_0*x)
Eq(F_69(x, k_0), F_11(x)*F_63(x, k_0))
Eq(F_70(x), F_71(x, 1))
Eq(F_71(x, k_0), F_11(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_1(x) + F_73(x, k_0) + F_74(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_68(x, k_0)*F_72(x, k_0))
Eq(F_74(x, k_0), F_11(x)*F_72(x, k_0))
Eq(F_75(x, k_0), F_11(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_80(x, k_0))
Eq(F_77(x, k_0), F_1(x) + F_71(x, k_0) + F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_68(x, k_0)*F_77(x, k_0))
Eq(F_79(x, k_0), F_11(x)*F_76(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_51(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x) + F_94(x, k_0))
Eq(F_83(x), F_11(x) + F_84(x))
Eq(F_84(x), F_19(x) + F_85(x) + F_86(x))
Eq(F_85(x), F_11(x)*F_49(x))
Eq(F_86(x), F_11(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_91(x))
Eq(F_88(x), F_11(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_11(x)*F_88(x))
Eq(F_91(x), F_84(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_11(x)*F_91(x))
Eq(F_94(x, k_0), F_100(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_11(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_68(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_107(x, k_0) + 2*F_19(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_105(x, k_0) + F_19(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_68(x, k_0))
Eq(F_104(x, k_0), F_102(x, k_0) + F_49(x))
Eq(F_105(x, k_0), F_106(x, k_0)*F_11(x))
Eq(F_106(x, k_0), F_102(x, k_0) + F_97(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_11(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_112(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_95(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_109(x, k_0)*F_11(x))
Eq(F_112(x, k_0), F_100(x, k_0) + F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_11(x)*F_112(x, k_0))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_117(x, 1))
Eq(F_117(x, k_0), F_1(x) + F_118(x, k_0) + F_129(x, k_0) + F_177(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_68(x, k_0))
Eq(F_119(x, k_0), F_1(x) + F_118(x, k_0) + F_120(x, k_0) + F_125(x, k_0))
Eq(F_120(x, k_0), F_11(x)*F_121(x, k_0))
Eq(F_121(x, k_0), F_1(x) + F_122(x, k_0) + F_123(x, k_0) + F_125(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0)*F_68(x, k_0))
Eq(F_123(x, k_0), F_11(x)*F_124(x, k_0))
Eq(F_124(x, k_0), F_106(x, k_0) + F_48(x))
Eq(F_125(x, k_0), F_11(x)*F_126(x, k_0))
Eq(F_126(x, k_0), F_1(x) + F_127(x, k_0) + F_128(x, k_0) + F_71(x, k_0) + F_79(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0)*F_68(x, k_0))
Eq(F_128(x, k_0), F_11(x)*F_126(x, k_0))
Eq(F_129(x, k_0), F_11(x)*F_130(x, k_0))
Eq(F_130(x, k_0), F_1(x) + F_131(x, k_0) + F_141(x, k_0) + F_157(x, k_0) + F_168(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_68(x, k_0))
Eq(F_132(x, k_0), F_119(x, k_0) + F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_135(x, k_0) + F_136(x, k_0) + F_137(x, k_0) + F_19(x))
Eq(F_134(x, k_0), F_133(x, k_0)*F_68(x, k_0))
Eq(F_135(x, k_0), F_11(x)*F_133(x, k_0))
Eq(F_136(x, k_0), F_11(x)*F_119(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_11(x)*F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0) + 3*F_19(x) + F_74(x, k_0))
Eq(F_140(x, k_0), F_139(x, k_0)*F_68(x, k_0))
Eq(F_141(x, k_0), F_11(x)*F_142(x, k_0))
Eq(F_142(x, k_0), F_130(x, k_0) + F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_145(x, k_0) + F_147(x, k_0) + F_149(x, k_0) + F_151(x, k_0) + F_19(x))
Eq(F_144(x, k_0), F_143(x, k_0)*F_68(x, k_0))
Eq(F_145(x, k_0), F_11(x)*F_146(x, k_0))
Eq(F_146(x, k_0), (-k_0*F_143(x, k_0) + F_143(x, 1))/(1 - k_0))
Eq(F_147(x, k_0), F_11(x)*F_148(x, k_0))
Eq(F_148(x, k_0), (-k_0*F_133(x, k_0) + F_133(x, 1))/(1 - k_0))
Eq(F_149(x, k_0), F_11(x)*F_150(x, k_0))
Eq(F_150(x, k_0), (-k_0*F_119(x, k_0) + F_119(x, 1))/(1 - k_0))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_153(x, k_0), F_149(x, k_0) + F_152(x, k_0) + F_154(x, k_0) + F_155(x, k_0) + F_19(x))
Eq(F_130(x, k_0), F_117(x, k_0) + F_153(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0)*F_68(x, k_0))
Eq(F_155(x, k_0), F_11(x)*F_156(x, k_0))
Eq(F_156(x, k_0), (-k_0*F_153(x, k_0) + F_153(x, 1))/(1 - k_0))
Eq(F_157(x, k_0), F_11(x)*F_158(x, k_0))
Eq(F_158(x, k_0), F_1(x) + F_159(x, k_0) + F_160(x, k_0) + F_162(x, k_0) + F_164(x, k_0))
Eq(F_159(x, k_0), F_158(x, k_0)*F_68(x, k_0))
Eq(F_160(x, k_0), F_11(x)*F_161(x, k_0))
Eq(F_161(x, k_0), (-k_0*F_158(x, k_0) + F_158(x, 1))/(1 - k_0))
Eq(F_162(x, k_0), F_11(x)*F_163(x, k_0))
Eq(F_163(x, k_0), (-k_0*F_121(x, k_0) + F_121(x, 1))/(1 - k_0))
Eq(F_117(x, k_0), F_1(x) + F_164(x, k_0) + F_165(x, k_0) + F_166(x, k_0))
Eq(F_165(x, k_0), F_117(x, k_0)*F_68(x, k_0))
Eq(F_166(x, k_0), F_11(x)*F_167(x, k_0))
Eq(F_167(x, k_0), (-k_0*F_117(x, k_0) + F_117(x, 1))/(1 - k_0))
Eq(F_168(x, k_0), F_11(x)*F_169(x, k_0))
Eq(F_169(x, k_0), F_1(x) + F_164(x, k_0) + F_170(x, k_0) + F_171(x, k_0) + F_173(x, k_0) + F_175(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_68(x, k_0))
Eq(F_171(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_172(x, k_0), (-k_0*F_169(x, k_0) + F_169(x, 1))/(1 - k_0))
Eq(F_173(x, k_0), F_11(x)*F_174(x, k_0))
Eq(F_174(x, k_0), (-k_0*F_126(x, k_0) + F_126(x, 1))/(1 - k_0))
Eq(F_175(x, k_0), F_11(x)*F_176(x, k_0))
Eq(F_176(x, k_0), (-k_0*F_76(x, k_0) + F_76(x, 1))/(1 - k_0))
Eq(F_177(x, k_0), F_11(x)*F_178(x, k_0))
Eq(F_178(x, k_0), F_1(x) + F_164(x, k_0) + F_175(x, k_0) + F_179(x, k_0) + F_180(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0)*F_68(x, k_0))
Eq(F_180(x, k_0), F_11(x)*F_181(x, k_0))
Eq(F_181(x, k_0), (-k_0*F_178(x, k_0) + F_178(x, 1))/(1 - 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": false, "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}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 3, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 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], [2, 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": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], 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1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[4, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[2, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23976/
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[12,x]*F[4,x]
F[4,x] = F[40,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[12,x]
F[24,x] = F[19,x]
F[25,x] = F[12,x]*F[14,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[10,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[12,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = 2*F[20,x]+F[34,x]+F[38,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[12,x]*F[26,x]
F[39,x] = F[12,x]*F[13,x]
F[40,x] = F[41,x]+F[52,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[1,x]+F[44,x]+F[45,x]
F[44,x] = F[12,x]*F[43,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x,1]
F[47,x,k[0]] = (F[48,x,k[0]]*k[0]-F[48,x,1])/(-1+k[0])
F[48,x,k[0]] = F[1,x]+F[49,x,k[0]]+F[51,x,k[0]]
F[49,x,k[0]] = F[48,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = k[0]*x
F[51,x,k[0]] = F[12,x]*F[47,x,k[0]]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[214,x]+F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[52,x]+F[6,x]
F[57,x] = F[58,x,1]
F[59,x,k[0]] = F[56,x]+F[58,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[67,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[5,x]*F[62,x,k[0]]*F[65,x]*F[66,x,k[0]]
F[62,x,k[0]] = F[1,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[50,x,k[0]]*F[62,x,k[0]]
F[65,x] = F[1,x]+F[14,x]
F[66,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[193,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[72,x,k[0]]
F[71,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[72,x,k[0]] = F[50,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = F[55,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = -k[0]*(F[76,x,1]-F[76,x,k[0]])/(-1+k[0])
F[77,x,k[0]] = F[76,x,k[0]]+F[82,x]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[191,x,k[0]]+F[80,x]
F[80,x] = 1/F[12,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = -F[85,x]+F[83,x]
F[83,x] = 1/F[12,x]*F[84,x]
F[84,x] = F[52,x]
F[85,x] = F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[183,x]+F[88,x]
F[88,x] = 1/F[12,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[40,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[177,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = -k[0]*(F[97,x,1]-F[97,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[50,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[113,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[5,x]
F[102,x,k[0]] = F[101,x,k[0]]*F[50,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[63,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[12,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[111,x,k[0]]
F[107,x,k[0]] = F[108,x]*F[63,x,k[0]]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[1,x]+F[42,x]
F[110,x] = F[103,x,1]
F[111,x,k[0]] = F[112,x,k[0]]*F[62,x,k[0]]
F[112,x,k[0]] = -k[0]*(F[103,x,1]-F[103,x,k[0]])/(-1+k[0])
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[12,x]
F[116,x,k[0]] = F[115,x,k[0]]*F[50,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]+F[151,x,k[0]]
F[119,x,k[0]] = F[118,x,k[0]]*F[12,x]
F[119,x,k[0]] = F[120,x,k[0]]
F[121,x,k[0]] = F[120,x,k[0]]+F[138,x]
F[121,x,k[0]] = F[122,x,k[0]]+F[59,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[12,x]*F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[132,x,k[0]]
F[125,x,k[0]] = F[121,x,k[0]]+F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]*F[129,x]*F[6,x]
F[128,x,k[0]] = (F[103,x,k[0]]-F[103,x,1])/(-1+k[0])
F[129,x] = F[1,x]+F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[12,x]*F[129,x]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = (F[134,x,k[0]]-F[134,x,1])/(-1+k[0])
F[134,x,k[0]] = F[135,x,k[0]]+F[97,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[129,x]*F[137,x,k[0]]*F[6,x]
F[137,x,k[0]] = -k[0]*(F[103,x,1]-F[103,x,k[0]])/(-1+k[0])
F[138,x] = -F[147,x]+F[139,x]
F[139,x] = F[140,x]+F[82,x]
F[140,x] = F[141,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[146,x]
F[143,x] = F[139,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[110,x]*F[129,x]*F[6,x]
F[146,x] = F[134,x,1]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = -F[56,x]+F[82,x]
F[149,x] = F[150,x]
F[150,x] = F[12,x]*F[147,x]
F[151,x,k[0]] = F[152,x,k[0]]*F[9,x]
F[153,x,k[0]] = F[152,x,k[0]]+F[155,x,k[0]]
F[154,x,k[0]] = F[12,x]*F[153,x,k[0]]
F[154,x,k[0]] = F[58,x,k[0]]
F[156,x,k[0]] = F[155,x,k[0]]+F[172,x]
F[156,x,k[0]] = F[157,x,k[0]]+F[166,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]*F[159,x]
F[158,x,k[0]] = F[103,x,k[0]]+F[109,x]
F[159,x] = F[160,x]+F[5,x]
F[160,x] = F[161,x]
F[161,x] = F[12,x]*F[162,x]*F[9,x]
F[162,x] = F[163,x]+F[164,x]
F[163,x] = F[129,x]*F[5,x]
F[164,x] = F[165,x]
F[165,x] = F[12,x]*F[129,x]*F[160,x]
F[166,x,k[0]] = F[167,x,k[0]]
F[167,x,k[0]] = F[12,x]*F[168,x,k[0]]
F[168,x,k[0]] = (F[169,x,k[0]]*k[0]-F[169,x,1])/(-1+k[0])
F[169,x,k[0]] = F[117,x,k[0]]+F[170,x]
F[170,x] = 1/F[12,x]*F[171,x]
F[171,x] = F[139,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[109,x]*F[159,x]
F[174,x] = F[175,x]
F[175,x] = F[12,x]*F[176,x]
F[176,x] = F[169,x,1]
F[177,x] = F[178,x]*F[5,x]
F[178,x] = F[179,x]
F[179,x] = F[12,x]*F[129,x]*F[180,x]*F[65,x]
F[180,x] = F[181,x,1]
F[181,x,k[0]] = (F[182,x,k[0]]*k[0]-F[182,x,1])/(-1+k[0])
F[182,x,k[0]] = (F[158,x,k[0]]*k[0]-F[158,x,1])/(-1+k[0])
F[183,x] = F[184,x]
F[184,x] = F[12,x]*F[185,x]
F[185,x] = F[186,x,1]
F[187,x,k[0]] = F[12,x]*F[186,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]
F[188,x,k[0]] = F[12,x]*F[189,x,k[0]]
F[190,x,k[0]] = F[189,x,k[0]]*F[50,x,k[0]]
F[190,x,k[0]] = F[155,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]
F[192,x,k[0]] = F[186,x,k[0]]*F[50,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[12,x]*F[195,x,k[0]]*F[66,x,k[0]]
F[196,x,k[0]] = F[12,x]*F[195,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]
F[198,x,k[0]] = F[197,x,k[0]]+F[212,x,k[0]]
F[199,x,k[0]] = F[198,x,k[0]]+F[209,x,k[0]]
F[199,x,k[0]] = F[191,x,k[0]]+F[200,x]
F[200,x] = F[201,x]+F[204,x]
F[201,x] = F[202,x]+F[90,x]
F[202,x] = F[203,x]
F[203,x] = F[5,x]*F[65,x]
F[204,x] = F[205,x]
F[205,x] = F[12,x]*F[206,x]
F[206,x] = F[207,x]+F[80,x]
F[207,x] = F[208,x]
F[208,x] = F[12,x]*F[185,x]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[12,x]*F[211,x,k[0]]
F[211,x,k[0]] = (F[79,x,k[0]]*k[0]-F[79,x,1])/(-1+k[0])
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[5,x]*F[62,x,k[0]]*F[65,x]
F[214,x] = F[215,x]
F[215,x] = F[12,x]*F[216,x]
F[216,x] = F[217,x]+F[223,x]
F[217,x] = F[218,x]+F[220,x]
F[218,x] = F[214,x]+F[219,x]
F[219,x] = F[108,x]+F[55,x]
F[220,x] = F[221,x]
F[221,x] = F[129,x]*F[222,x]*F[6,x]
F[222,x] = F[182,x,1]
F[223,x] = F[224,x]
F[224,x] = F[225,x,1]
F[225,x,k[0]] = -k[0]*(F[134,x,1]-F[134,x,k[0]])/(-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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{47}\! \left(x , y\right) = -\frac{-y F_{48}\! \left(x , y\right)+F_{48}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = y x
F_{51}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{214}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{6}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{59}\! \left(x , y\right) = F_{56}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right) F_{62}\! \left(x , y\right) F_{65}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{72}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{55}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{y \left(F_{76}\! \left(x , 1\right)-F_{76}\! \left(x , y\right)\right)}{-1+y}
F_{77}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{52}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{183}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{40}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{177}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = -\frac{y \left(F_{97}\! \left(x , 1\right)-F_{97}\! \left(x , y\right)\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x , 1\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = -\frac{y \left(F_{103}\! \left(x , 1\right)-F_{103}\! \left(x , y\right)\right)}{-1+y}
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_{12}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{50}\! \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_{151}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{12}\! \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_{138}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{129}\! \left(x \right) F_{6}\! \left(x \right)
F_{128}\! \left(x , y\right) = -\frac{F_{103}\! \left(x , 1\right)-F_{103}\! \left(x , y\right)}{-1+y}
F_{129}\! \left(x \right) = F_{1}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = -\frac{F_{134}\! \left(x , 1\right)-F_{134}\! \left(x , y\right)}{-1+y}
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{129}\! \left(x \right) F_{137}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{137}\! \left(x , y\right) = -\frac{y \left(F_{103}\! \left(x , 1\right)-F_{103}\! \left(x , y\right)\right)}{-1+y}
F_{138}\! \left(x \right) = -F_{147}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{82}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{143}\! \left(x \right) = F_{139}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{110}\! \left(x \right) F_{129}\! \left(x \right) F_{6}\! \left(x \right)
F_{146}\! \left(x \right) = F_{134}\! \left(x , 1\right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{82}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{153}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{172}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{159}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{109}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{5}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{12}\! \left(x \right) F_{162}\! \left(x \right) F_{9}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{164}\! \left(x \right)
F_{163}\! \left(x \right) = F_{129}\! \left(x \right) F_{5}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right) F_{160}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = -\frac{-y F_{169}\! \left(x , y\right)+F_{169}\! \left(x , 1\right)}{-1+y}
F_{169}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = \frac{F_{171}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{171}\! \left(x \right) = F_{139}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{109}\! \left(x \right) F_{159}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{12}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{169}\! \left(x , 1\right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{5}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right) F_{180}\! \left(x \right) F_{65}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x , 1\right)
F_{181}\! \left(x , y\right) = -\frac{-y F_{182}\! \left(x , y\right)+F_{182}\! \left(x , 1\right)}{-1+y}
F_{182}\! \left(x , y\right) = -\frac{-y F_{158}\! \left(x , y\right)+F_{158}\! \left(x , 1\right)}{-1+y}
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{12}\! \left(x \right) F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x , 1\right)
F_{187}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{186}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{189}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{195}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{195}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{204}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{90}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{5}\! \left(x \right) F_{65}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{12}\! \left(x \right) F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{80}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{12}\! \left(x \right) F_{185}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = -\frac{-y F_{79}\! \left(x , y\right)+F_{79}\! \left(x , 1\right)}{-1+y}
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{62}\! \left(x , y\right) F_{65}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{12}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{223}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{220}\! \left(x \right)
F_{218}\! \left(x \right) = F_{214}\! \left(x \right)+F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{108}\! \left(x \right)+F_{55}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{129}\! \left(x \right) F_{222}\! \left(x \right) F_{6}\! \left(x \right)
F_{222}\! \left(x \right) = F_{182}\! \left(x , 1\right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x , 1\right)
F_{225}\! \left(x , y\right) = -\frac{y \left(F_{134}\! \left(x , 1\right)-F_{134}\! \left(x , y\right)\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_12(x)*F_4(x))
Eq(F_4(x), F_40(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_12(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_12(x)*F_14(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_10(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_12(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), 2*F_20(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_12(x)*F_26(x))
Eq(F_39(x), F_12(x)*F_13(x))
Eq(F_40(x), F_41(x) + F_52(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_44(x) + F_45(x))
Eq(F_44(x), F_12(x)*F_43(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_47(x, k_0), (-k_0*F_48(x, k_0) + F_48(x, 1))/(1 - k_0))
Eq(F_48(x, k_0), F_1(x) + F_49(x, k_0) + F_51(x, k_0))
Eq(F_49(x, k_0), F_48(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), k_0*x)
Eq(F_51(x, k_0), F_12(x)*F_47(x, k_0))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_214(x) + F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_52(x) + F_6(x))
Eq(F_57(x), F_58(x, 1))
Eq(F_59(x, k_0), F_56(x) + F_58(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_67(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_5(x)*F_62(x, k_0)*F_65(x)*F_66(x, k_0))
Eq(F_62(x, k_0), F_1(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_50(x, k_0)*F_62(x, k_0))
Eq(F_65(x), F_1(x) + F_14(x))
Eq(F_66(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_193(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_72(x, k_0))
Eq(F_71(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_72(x, k_0), F_50(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), F_55(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), -F_76(x, 1) + (-k_0*F_76(x, k_0) + F_76(x, 1))/(1 - k_0))
Eq(F_77(x, k_0), F_76(x, k_0) + F_82(x))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_191(x, k_0) + F_80(x))
Eq(F_80(x), F_81(x)/F_12(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x) - F_85(x))
Eq(F_83(x), F_84(x)/F_12(x))
Eq(F_84(x), F_52(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_183(x) + F_88(x))
Eq(F_88(x), F_89(x)/F_12(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_40(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_177(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), -F_97(x, 1) + (-k_0*F_97(x, k_0) + F_97(x, 1))/(1 - k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_50(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_113(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_5(x))
Eq(F_102(x, k_0), F_101(x, k_0)*F_50(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_63(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_12(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_111(x, k_0))
Eq(F_107(x, k_0), F_108(x)*F_63(x, k_0))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_1(x) + F_42(x))
Eq(F_110(x), F_103(x, 1))
Eq(F_111(x, k_0), F_112(x, k_0)*F_62(x, k_0))
Eq(F_112(x, k_0), -F_103(x, 1) + (-k_0*F_103(x, k_0) + F_103(x, 1))/(1 - 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_12(x))
Eq(F_116(x, k_0), F_115(x, k_0)*F_50(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_151(x, k_0))
Eq(F_119(x, k_0), F_118(x, k_0)*F_12(x))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_121(x, k_0), F_120(x, k_0) + F_138(x))
Eq(F_121(x, k_0), F_122(x, k_0) + F_59(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_12(x)*F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_132(x, k_0))
Eq(F_125(x, k_0), F_121(x, k_0) + F_126(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0)*F_129(x)*F_6(x))
Eq(F_128(x, k_0), -F_103(x, k_0) + (k_0*F_103(x, k_0) - F_103(x, 1))/(k_0 - 1))
Eq(F_129(x), F_1(x) + F_130(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_12(x)*F_129(x))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), -F_134(x, k_0) + (k_0*F_134(x, k_0) - F_134(x, 1))/(k_0 - 1))
Eq(F_134(x, k_0), F_135(x, k_0) + F_97(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_129(x)*F_137(x, k_0)*F_6(x))
Eq(F_137(x, k_0), -F_103(x, 1) + (k_0*F_103(x, k_0) - F_103(x, 1))/(k_0 - 1))
Eq(F_138(x), F_139(x) - F_147(x))
Eq(F_139(x), F_140(x) + F_82(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_146(x))
Eq(F_143(x), F_139(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_110(x)*F_129(x)*F_6(x))
Eq(F_146(x), F_134(x, 1))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), -F_56(x) + F_82(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_12(x)*F_147(x))
Eq(F_151(x, k_0), F_152(x, k_0)*F_9(x))
Eq(F_153(x, k_0), F_152(x, k_0) + F_155(x, k_0))
Eq(F_154(x, k_0), F_12(x)*F_153(x, k_0))
Eq(F_154(x, k_0), F_58(x, k_0))
Eq(F_156(x, k_0), F_155(x, k_0) + F_172(x))
Eq(F_156(x, k_0), F_157(x, k_0) + F_166(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0)*F_159(x))
Eq(F_158(x, k_0), F_103(x, k_0) + F_109(x))
Eq(F_159(x), F_160(x) + F_5(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_12(x)*F_162(x)*F_9(x))
Eq(F_162(x), F_163(x) + F_164(x))
Eq(F_163(x), F_129(x)*F_5(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_12(x)*F_129(x)*F_160(x))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_167(x, k_0), F_12(x)*F_168(x, k_0))
Eq(F_168(x, k_0), (-k_0*F_169(x, k_0) + F_169(x, 1))/(1 - k_0))
Eq(F_169(x, k_0), F_117(x, k_0) + F_170(x))
Eq(F_170(x), F_171(x)/F_12(x))
Eq(F_171(x), F_139(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_109(x)*F_159(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_12(x)*F_176(x))
Eq(F_176(x), F_169(x, 1))
Eq(F_177(x), F_178(x)*F_5(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_12(x)*F_129(x)*F_180(x)*F_65(x))
Eq(F_180(x), F_181(x, 1))
Eq(F_181(x, k_0), (-k_0*F_182(x, k_0) + F_182(x, 1))/(1 - k_0))
Eq(F_182(x, k_0), (-k_0*F_158(x, k_0) + F_158(x, 1))/(1 - k_0))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_12(x)*F_185(x))
Eq(F_185(x), F_186(x, 1))
Eq(F_187(x, k_0), F_12(x)*F_186(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0))
Eq(F_188(x, k_0), F_12(x)*F_189(x, k_0))
Eq(F_190(x, k_0), F_189(x, k_0)*F_50(x, k_0))
Eq(F_190(x, k_0), F_155(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0))
Eq(F_192(x, k_0), F_186(x, k_0)*F_50(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_12(x)*F_195(x, k_0)*F_66(x, k_0))
Eq(F_196(x, k_0), F_12(x)*F_195(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0))
Eq(F_198(x, k_0), F_197(x, k_0) + F_212(x, k_0))
Eq(F_199(x, k_0), F_198(x, k_0) + F_209(x, k_0))
Eq(F_199(x, k_0), F_191(x, k_0) + F_200(x))
Eq(F_200(x), F_201(x) + F_204(x))
Eq(F_201(x), F_202(x) + F_90(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_5(x)*F_65(x))
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_12(x)*F_206(x))
Eq(F_206(x), F_207(x) + F_80(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_12(x)*F_185(x))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_12(x)*F_211(x, k_0))
Eq(F_211(x, k_0), (-k_0*F_79(x, k_0) + F_79(x, 1))/(1 - k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_5(x)*F_62(x, k_0)*F_65(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_12(x)*F_216(x))
Eq(F_216(x), F_217(x) + F_223(x))
Eq(F_217(x), F_218(x) + F_220(x))
Eq(F_218(x), F_214(x) + F_219(x))
Eq(F_219(x), F_108(x) + F_55(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_129(x)*F_222(x)*F_6(x))
Eq(F_222(x), F_182(x, 1))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_225(x, 1))
Eq(F_225(x, k_0), -F_134(x, 1) + (-k_0*F_134(x, k_0) + F_134(x, 1))/(1 - k_0))
Pack JSON:
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Specification JSON:
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