1032_2301_125034
Counting sequence:
1, 1, 2, 6, 22, 86, 339, 1327, 5150, 19854, 76207, 291779, 1115824, 4265768, 16311631, 62408147, 238953334, 915710678, 3512353576, 13484647856, 51817954180, 199302558244, 767232933822, 2956049094966, 11398657769708, 43988678547980, 169887272986273, 656600806194661, 2539515844733796, 9828746938209132, 38065568786413783, 147517363220479915, 572032590569193638, 2219503498227297638, 8616668223964686324, 33470549573238727596, 130082268367374971332, 505821598625885167876, 1967855596726121709722, 7659467618390172506914, 29826800934795476277188, 116201312263238480476516, 452903287026819046237742, 1765973099190564814331254, 6888762458183982317122160, 26882610263438038482199264, 104946891311649846095957030, 409855409527853384357955022, 1601216123953765776698518460, 6257817079905895496743292668, 24464988859841405630775390368, 95678030636685491494425695920, 374300533626986323198063887080, 1464757748881493693649533492392, 5733826909158786386577316812764, 22451904707976730366427697800140, 87940351637974042070207490578072, 344545268113741627626364999935448, 1350281380277557676235904100505317, 5293209661182967445982655514716873, 20755241269985071963262857383643340, 81404328743159346762760862956158580, 319356301596499925503279666534662311, 1253167461677515054969630295501816347, 4918648683156963216460450746034028294, 19310037024617537975461030970974613638, 75826085631094290923052183724772952476, 297817419600931105903915514733999019252, 1169971448726859255466012359608398249604, 4597185115455809311859172891463555753348, 18067505927854219981254637958601569692226, 71021836539650726585393063969029276096042, 279235819740083254353410377232946100058324, 1098080084424061308017116341547507345962868, 4318955612274211541310407005591523696258546, 16990397651381667292078598273119185580379082, 66850816646440384310633933418775014144089344, 263079257752022105934515857437344547271583888, 1035479758387251934518036235646453837022369666, 4076337937012456828231309622256341555074741882, 16049843509807372488488385508354439040973656404, 63203629208359459982936855809453613632375827348, 248932961172952266356312557300995167717522328976, 980597070990555988758439025791886430930112777472, 3863360535752769511907972935242557058445500783224, 15223168332234318420767998048503094654803550223928, 59994130331818470523862669493133901671606267249956, 236469510098552630665579579390186723333021252894132, 932186967767488520394277427833782957984423874665064, 3675286767554615814046947267551650445583207175333928, 14492344113774260955107079739256582762571915105246506, 57153673847772356705027565860120483065984215788425362, 225427403849681667117809990045063147972862017226807624, 889252865090800531833869527225618925836055383637265048, 3508317051404196219950954521776215621072179548644132886, 13842878617909455114825411885349723279175893192240630302, 54626961726971071413986968863916952919789975629782270044, 215595558431558067723981351191829998520668716484788433628, 850988699345872282950187886100877049315859304051440316776, 3359372110562576845922563105872173365413824029878419445912, 13263004170949752202457670768179675120201353599630473119464
Generating function in Maple syntax:
-1/2*(3*(1-4*x)^(1/2)*x^2+2*x^3-4*(1-4*x)^(1/2)*x-9*x^2+(1-4*x)^(1/2)+6*x-1)*(3*x-1)^2*(x-1)/x^6/(2*x-1)
Generating function in latex syntax:
-\frac{\left(3 \sqrt{1-4 x}\, x^{2}+2 x^{3}-4 \sqrt{1-4 x}\, x -9 x^{2}+\sqrt{1-4 x}+6 x -1\right) \left(3 x -1\right)^{2} \left(x -1\right)}{2 x^{6} \left(2 x -1\right)}
Generating function in sympy syntax:
(x - 1)*(3*x - 1)**2*(-x**3 - 3*x**2*sqrt(1 - 4*x)/2 + 9*x**2/2 + 2*x*sqrt(1 - 4*x) - 3*x - sqrt(1 - 4*x)/2 + 1/2)/(x**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x^6*(2*x-1)^2*F(x)^2+(x-1)*(x^2-4*x+1)*(3*x-1)^2*(2*x-1)^2*F(x)+(x-1)^2*(3*x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
x^{6} \left(2 x -1\right)^{2} F \! \left(x \right)^{2}+\left(x -1\right) \left(x^{2}-4 x +1\right) \left(3 x -1\right)^{2} \left(2 x -1\right)^{2} F \! \left(x \right)+\left(x -1\right)^{2} \left(3 x -1\right)^{4} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -12*(3+2*n)/(10+n)*a(n)+2*(94+25*n)/(10+n)*a(n+1)-7*(29+5*n)/(10+n)*a(n+2)+(79+10*n)/(10+n)*a(n+3), n >= 4
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(n +4\right) = -\frac{12 \left(3+2 n \right) a \! \left(n \right)}{10+n}+\frac{2 \left(94+25 n \right) a \! \left(n +1\right)}{10+n}-\frac{7 \left(29+5 n \right) a \! \left(n +2\right)}{10+n}+\frac{\left(79+10 n \right) a \! \left(n +3\right)}{10+n}, \quad n \geq 4
Specification 1
Strategy pack name: all_the_strategies_2_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24000/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[6,x]+F[87,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]+F[8,x]+F[91,x]
F[8,x] = F[9,x]
F[9,x] = -F[4,x]-F[68,x]+F[10,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = F[2,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[18,x,k[0]]+F[24,x,k[0]]+F[26,x]
F[18,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[19,x,k[0]] = F[1,x]+F[20,x,k[0]]+F[22,x,k[0]]
F[20,x,k[0]] = F[19,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[17,x,k[0]]*F[4,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[26,x] = F[27,x]
F[27,x] = 1/F[4,x]*F[28,x]
F[28,x] = -F[44,x]-F[67,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[62,x]
F[32,x] = 1/F[4,x]*F[33,x]
F[33,x] = -F[1,x]-F[61,x]+F[34,x]
F[34,x] = F[35,x]+F[48,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[36,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[1,x]+F[40,x]
F[43,x] = F[44,x]+F[45,x]+F[47,x]
F[44,x] = 0
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[37,x]+F[43,x]
F[47,x] = F[39,x]*F[4,x]
F[48,x] = F[49,x]
F[49,x] = -F[58,x]+F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[50,x]
F[53,x] = F[54,x]
F[54,x] = 1/F[4,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = -F[44,x]-F[57,x]+F[11,x]
F[57,x] = F[0,x]*F[4,x]
F[58,x] = F[44,x]+F[59,x]+F[60,x]
F[59,x] = F[4,x]*F[58,x]
F[60,x] = F[22,x,1]
F[61,x] = F[34,x]*F[4,x]
F[62,x] = F[63,x]
F[63,x] = F[44,x]+F[64,x]+F[65,x]
F[64,x] = F[4,x]*F[62,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[14,x]+F[63,x]
F[67,x] = F[4,x]*F[5,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]^2*F[70,x]
F[70,x] = F[5,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[5,x]+F[72,x]+F[74,x]+F[89,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = 1/F[37,x]/F[4,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]*F[88,x]
F[78,x] = -F[81,x]+F[79,x]
F[79,x] = 1/F[4,x]*F[80,x]
F[80,x] = -F[2,x]+F[81,x]
F[81,x] = F[44,x]+F[82,x]+F[87,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[40,x]+F[84,x]
F[84,x] = F[44,x]+F[82,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[37,x]+F[84,x]
F[87,x] = F[4,x]*F[70,x]
F[88,x] = F[42,x]+F[86,x]
F[89,x] = F[90,x]
F[90,x] = F[32,x]*F[4,x]*F[88,x]
F[91,x] = F[4,x]*F[7,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{87}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right)+F_{8}\! \left(x \right)+F_{91}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = -F_{4}\! \left(x \right)-F_{68}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{44}\! \left(x \right)-F_{67}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{62}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{33}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{61}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{48}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = 0
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \left(x \right)
F_{47}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{44}\! \left(x \right)-F_{57}\! \left(x \right)+F_{11}\! \left(x \right)
F_{57}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{61}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{44}\! \left(x \right)+F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right)+F_{63}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4} \left(x \right)^{2} F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{5}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{5}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)+F_{89}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{37}\! \left(x \right) F_{4}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right) F_{88}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{80}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{44}\! \left(x \right)+F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{40}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{44}\! \left(x \right)+F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{37}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{88}\! \left(x \right) = F_{42}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_6(x) + F_87(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x) + F_8(x) + F_91(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x) - F_4(x) - F_68(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_18(x, k_0) + F_24(x, k_0) + F_26(x))
Eq(F_18(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_19(x, k_0), F_1(x) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_20(x, k_0), F_19(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_17(x, k_0)*F_4(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)/F_4(x))
Eq(F_28(x), F_29(x) - F_44(x) - F_67(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_62(x))
Eq(F_32(x), F_33(x)/F_4(x))
Eq(F_33(x), -F_1(x) + F_34(x) - F_61(x))
Eq(F_34(x), F_35(x) + F_48(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_36(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_40(x))
Eq(F_43(x), F_44(x) + F_45(x) + F_47(x))
Eq(F_44(x), 0)
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_37(x) + F_43(x))
Eq(F_47(x), F_39(x)*F_4(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x) - F_58(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_50(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x)/F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x) - F_44(x) - F_57(x))
Eq(F_57(x), F_0(x)*F_4(x))
Eq(F_58(x), F_44(x) + F_59(x) + F_60(x))
Eq(F_59(x), F_4(x)*F_58(x))
Eq(F_60(x), F_22(x, 1))
Eq(F_61(x), F_34(x)*F_4(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_44(x) + F_64(x) + F_65(x))
Eq(F_64(x), F_4(x)*F_62(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_14(x) + F_63(x))
Eq(F_67(x), F_4(x)*F_5(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)**2*F_70(x))
Eq(F_70(x), F_5(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_5(x) + F_72(x) + F_74(x) + F_89(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x)/(F_37(x)*F_4(x)))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x)*F_88(x))
Eq(F_78(x), F_79(x) - F_81(x))
Eq(F_79(x), F_80(x)/F_4(x))
Eq(F_80(x), -F_2(x) + F_81(x))
Eq(F_81(x), F_44(x) + F_82(x) + F_87(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_40(x) + F_84(x))
Eq(F_84(x), F_44(x) + F_82(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_37(x) + F_84(x))
Eq(F_87(x), F_4(x)*F_70(x))
Eq(F_88(x), F_42(x) + F_86(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_32(x)*F_4(x)*F_88(x))
Eq(F_91(x), F_4(x)*F_7(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "ignore_parent": false, "strategy_class": "AllPlacementsFactory"}]], "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.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "all_the_strategies_2_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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 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]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [0, 3]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], 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[0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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 2
Strategy pack name: insertion_point_row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24001/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = -F[5,x]+F[3,x]
F[3,x] = 1/F[11,x]*F[4,x]
F[4,x] = -F[293,x]-F[6,x]+F[5,x]
F[5,x] = F[20,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[11,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]
F[11,x] = x
F[12,x] = F[1,x]+F[9,x]
F[13,x] = F[14,x]+F[15,x]+F[6,x]
F[14,x] = F[11,x]*F[8,x]
F[15,x] = F[11,x]*F[16,x]
F[16,x] = F[13,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[11,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[17,x]+F[5,x]
F[23,x] = F[24,x,1]
F[24,x,k[0]] = F[25,x,k[0]]+F[39,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[36,x,k[0]]+F[6,x]
F[26,x,k[0]] = F[27,x,k[0]]*F[30,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[9,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[31,x,k[0]]+F[6,x]
F[29,x,k[0]] = F[27,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0]] = F[11,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[28,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[30,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[36,x,k[0]] = F[11,x]*F[37,x,k[0]]
F[37,x,k[0]] = F[24,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[25,x,k[0]]+F[33,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[11,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = F[12,x]*F[25,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[46,x,k[0]]
F[44,x,k[0]] = F[32,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[2,x]+F[25,x,k[0]]
F[46,x,k[0]] = F[292,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[167,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[33,x,k[0]]*F[50,x]
F[50,x] = F[17,x]+F[51,x]
F[51,x] = F[52,x]+F[54,x]+F[6,x]
F[52,x] = F[11,x]*F[53,x]
F[53,x] = F[2,x]+F[51,x]
F[54,x] = F[11,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[17,x]
F[60,x] = F[51,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[101,x]+F[64,x]
F[64,x] = F[6,x]+F[65,x]+F[99,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[17,x]+F[64,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[59,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[72,x]
F[73,x,k[0]] = F[11,x]*F[17,x]*F[33,x,k[0]]*F[72,x]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[11,x]*F[17,x]*F[33,x,k[0]]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[17,x]*F[9,x]
F[77,x] = -F[98,x]+F[78,x]
F[78,x] = -F[97,x]+F[79,x]
F[79,x] = 1/F[11,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[12,x]*F[2,x]
F[85,x] = F[50,x]+F[86,x]
F[86,x] = F[13,x]+F[87,x]
F[87,x] = -F[5,x]+F[88,x]
F[88,x] = -F[50,x]+F[89,x]
F[89,x] = -F[23,x]+F[90,x]
F[90,x] = -F[84,x]+F[91,x]
F[91,x] = 1/F[11,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = -F[2,x]+F[94,x]
F[94,x] = -F[0,x]+F[95,x]
F[95,x] = 1/F[11,x]*F[96,x]
F[96,x] = F[2,x]
F[97,x] = F[2,x]+F[81,x]
F[98,x] = F[12,x]*F[17,x]
F[99,x] = F[100,x]*F[11,x]
F[100,x] = F[2,x]+F[64,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[17,x]*F[9,x]
F[103,x] = -F[108,x]+F[104,x]
F[104,x] = -F[102,x]+F[105,x]
F[105,x] = -F[166,x]+F[106,x]
F[106,x] = 1/F[11,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[11,x]*F[110,x]
F[110,x] = F[111,x]+F[164,x]
F[111,x] = -F[118,x]+F[112,x]
F[112,x] = 1/F[11,x]*F[113,x]
F[113,x] = F[114,x]
F[114,x] = -F[2,x]+F[115,x]
F[115,x] = -F[0,x]+F[116,x]
F[116,x] = 1/F[11,x]*F[117,x]
F[117,x] = F[2,x]
F[118,x] = F[119,x]+F[149,x]
F[119,x] = F[120,x]+F[2,x]
F[120,x] = F[121,x]
F[121,x] = F[11,x]*F[122,x]
F[122,x] = F[119,x]+F[123,x]
F[123,x] = F[124,x]+F[98,x]
F[124,x] = F[125,x,1]
F[125,x,k[0]] = F[126,x,k[0]]+F[5,x]
F[126,x,k[0]] = F[127,x,k[0]]+F[138,x,k[0]]+F[6,x]
F[127,x,k[0]] = F[11,x]*F[128,x,k[0]]
F[128,x,k[0]] = F[126,x,k[0]]+F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[30,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[129,x,k[0]]+F[2,x]
F[133,x,k[0]] = F[125,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[17,x]
F[135,x,k[0]] = F[1,x]+F[136,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]
F[137,x,k[0]] = F[135,x,k[0]]*F[30,x,k[0]]
F[138,x,k[0]] = F[11,x]*F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]+F[142,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[136,x,k[0]]*F[17,x]*F[19,x]
F[142,x,k[0]] = F[126,x,k[0]]+F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[148,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[136,x,k[0]]*F[17,x]*F[19,x]*F[9,x]
F[148,x,k[0]] = -k[0]*(F[142,x,1]-F[142,x,k[0]])/(-1+k[0])
F[149,x] = F[114,x]+F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[11,x]*F[152,x]
F[152,x] = F[149,x]+F[153,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[155,x]
F[155,x] = F[17,x]^2*F[12,x]
F[156,x] = F[157,x,1]
F[157,x,k[0]] = F[143,x,k[0]]+F[158,x]
F[158,x] = F[159,x]
F[159,x] = F[11,x]*F[160,x]
F[160,x] = F[161,x]+F[163,x]
F[161,x] = F[162,x]
F[162,x] = F[17,x]*F[19,x]*F[9,x]
F[163,x] = F[124,x]+F[156,x]
F[164,x] = F[12,x]*F[165,x]
F[165,x] = F[108,x]+F[9,x]
F[166,x] = F[100,x]+F[17,x]
F[167,x,k[0]] = F[168,x,k[0]]+F[251,x,k[0]]
F[168,x,k[0]] = (-F[169,x,1]*k[0]+F[169,x,k[0]])/(-1+k[0])
F[169,x,k[0]] = F[170,x,k[0]]+F[171,x,k[0]]+F[6,x]
F[170,x,k[0]] = F[28,x,k[0]]*F[30,x,k[0]]
F[171,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[176,x,k[0]]
F[173,x,k[0]] = F[169,x,k[0]]+F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]
F[176,x,k[0]] = F[169,x,k[0]]+F[177,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]*F[30,x,k[0]]
F[180,x,k[0]] = F[179,x,k[0]]+F[182,x]
F[181,x,k[0]] = F[180,x,k[0]]*F[30,x,k[0]]
F[181,x,k[0]] = F[39,x,k[0]]
F[182,x] = F[183,x]
F[183,x] = F[184,x]+F[93,x]
F[184,x] = F[185,x]+F[250,x]
F[185,x] = -F[249,x]+F[186,x]
F[186,x] = -F[250,x]+F[187,x]
F[187,x] = -F[249,x]+F[188,x]
F[188,x] = 1/F[11,x]*F[189,x]
F[189,x] = F[190,x]
F[190,x] = F[191,x]
F[191,x] = F[11,x]*F[192,x]
F[192,x] = F[193,x]+F[234,x]
F[193,x] = F[17,x]+F[194,x]
F[194,x] = F[195,x]+F[2,x]
F[195,x] = F[196,x,1]
F[196,x,k[0]] = F[197,x,k[0]]
F[197,x,k[0]] = F[11,x]*F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[202,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[201,x,k[0]]
F[200,x,k[0]] = F[196,x,k[0]]+F[33,x,k[0]]
F[201,x,k[0]] = F[33,x,k[0]]*F[35,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[233,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]+F[205,x,k[0]]
F[204,x,k[0]] = F[2,x]*F[33,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[11,x]*F[207,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[216,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]+F[214,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[213,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[11,x]*F[212,x,k[0]]
F[212,x,k[0]] = F[210,x,k[0]]+F[33,x,k[0]]
F[213,x,k[0]] = -k[0]*(F[196,x,1]-F[196,x,k[0]])/(-1+k[0])
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[33,x,k[0]]*F[64,x]
F[216,x,k[0]] = F[217,x,k[0]]+F[221,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[220,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[17,x]*F[2,x]*F[33,x,k[0]]
F[220,x,k[0]] = -k[0]*(F[205,x,1]-F[205,x,k[0]])/(-1+k[0])
F[221,x,k[0]] = F[222,x,k[0]]
F[222,x,k[0]] = F[223,x]*F[33,x,k[0]]
F[223,x] = -F[114,x]+F[224,x]
F[224,x] = -F[230,x]+F[225,x]
F[225,x] = -F[228,x]+F[226,x]
F[226,x] = 1/F[11,x]*F[227,x]
F[227,x] = F[114,x]
F[228,x] = F[100,x]+F[229,x]
F[229,x] = F[17,x]+F[195,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[17,x]*F[2,x]
F[232,x] = F[205,x,1]
F[233,x,k[0]] = F[196,x,k[0]]*F[35,x,k[0]]
F[234,x] = F[102,x]+F[235,x]
F[235,x] = F[190,x]+F[236,x]
F[236,x] = F[237,x]+F[248,x]+F[6,x]
F[237,x] = F[238,x,1]
F[205,x,k[0]] = F[238,x,k[0]]+F[239,x,k[0]]+F[6,x]
F[239,x,k[0]] = F[240,x,k[0]]*F[30,x,k[0]]
F[240,x,k[0]] = F[205,x,k[0]]+F[241,x]
F[241,x] = F[242,x]
F[242,x] = F[11,x]*F[243,x]
F[243,x] = F[244,x]+F[245,x]
F[244,x] = F[193,x]+F[64,x]
F[245,x] = F[223,x]+F[246,x]
F[246,x] = F[231,x]+F[247,x]
F[247,x] = F[232,x]+F[241,x]
F[248,x] = F[11,x]*F[235,x]
F[249,x] = F[190,x]+F[9,x]
F[250,x] = F[249,x]*F[9,x]
F[251,x,k[0]] = F[252,x,k[0]]+F[261,x,k[0]]+F[6,x]
F[252,x,k[0]] = F[253,x,k[0]]
F[253,x,k[0]] = F[11,x]*F[254,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[258,x,k[0]]
F[255,x,k[0]] = F[256,x]*F[33,x,k[0]]
F[256,x] = F[257,x]+F[87,x]
F[257,x] = F[2,x]*F[9,x]
F[258,x,k[0]] = F[259,x]*F[28,x,k[0]]
F[259,x] = F[260,x]+F[84,x]
F[260,x] = F[51,x]+F[87,x]
F[261,x,k[0]] = F[11,x]*F[262,x,k[0]]
F[262,x,k[0]] = F[263,x,k[0]]+F[286,x,k[0]]
F[263,x,k[0]] = F[264,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]+F[273,x,k[0]]
F[265,x,k[0]] = 2*F[6,x]+F[266,x,k[0]]+F[268,x,k[0]]
F[266,x,k[0]] = F[267,x,k[0]]*F[30,x,k[0]]
F[267,x,k[0]] = F[13,x]+F[265,x,k[0]]
F[268,x,k[0]] = F[11,x]*F[269,x,k[0]]
F[269,x,k[0]] = F[265,x,k[0]]+F[270,x,k[0]]
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[272,x,k[0]]*F[30,x,k[0]]
F[272,x,k[0]] = F[17,x]+F[270,x,k[0]]
F[273,x,k[0]] = F[17,x]*F[274,x,k[0]]
F[274,x,k[0]] = 2*F[6,x]+F[275,x,k[0]]+F[281,x,k[0]]
F[275,x,k[0]] = F[276,x,k[0]]*F[30,x,k[0]]
F[276,x,k[0]] = F[274,x,k[0]]+F[277,x]
F[277,x] = F[278,x]+F[279,x]+F[6,x]
F[278,x] = F[11,x]*F[9,x]
F[279,x] = F[11,x]*F[280,x]
F[280,x] = F[11,x]+F[277,x]
F[281,x,k[0]] = F[11,x]*F[282,x,k[0]]
F[282,x,k[0]] = F[274,x,k[0]]+F[283,x,k[0]]
F[283,x,k[0]] = F[284,x,k[0]]
F[284,x,k[0]] = F[285,x,k[0]]*F[30,x,k[0]]
F[285,x,k[0]] = F[11,x]+F[283,x,k[0]]
F[286,x,k[0]] = F[251,x,k[0]]+F[287,x,k[0]]
F[287,x,k[0]] = F[288,x,k[0]]
F[288,x,k[0]] = F[11,x]*F[289,x,k[0]]*F[63,x]
F[289,x,k[0]] = F[290,x,k[0]]+F[291,x,k[0]]
F[290,x,k[0]] = F[33,x,k[0]]*F[9,x]
F[291,x,k[0]] = F[12,x]*F[28,x,k[0]]
F[292,x,k[0]] = (-F[176,x,1]*k[0]+F[176,x,k[0]])/(-1+k[0])
F[293,x] = F[11,x]*F[294,x]
F[294,x] = F[295,x]+F[297,x]
F[295,x] = F[296,x]
F[296,x] = F[17,x]*F[19,x]
F[297,x] = F[158,x]+F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = \frac{F_{4}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{4}\! \left(x \right) = -F_{293}\! \left(x \right)-F_{6}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{11}\! \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_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)+F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
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_{17}\! \left(x \right)+F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{54}\! \left(x \right)+F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{60}\! \left(x \right) = F_{51}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{101}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{6}\! \left(x \right)+F_{65}\! \left(x \right)+F_{99}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{17}\! \left(x \right)+F_{64}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{59}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{72}\! \left(x \right)
F_{73}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{33}\! \left(x , y\right) F_{72}\! \left(x \right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{33}\! \left(x , y\right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{17}\! \left(x \right) F_{9}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{85}\! \left(x \right) = F_{50}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{2}\! \left(x \right)
F_{97}\! \left(x \right) = F_{2}\! \left(x \right)+F_{81}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{11}\! \left(x \right)
F_{100}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{17}\! \left(x \right) F_{9}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{166}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{11}\! \left(x \right) F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{164}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{118}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = \frac{F_{113}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{117}\! \left(x \right) = F_{2}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{149}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{2}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{11}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{98}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x , 1\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{30}\! \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) = F_{140}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{17}\! \left(x \right) F_{19}\! \left(x \right) F_{9}\! \left(x \right)
F_{148}\! \left(x , y\right) = -\frac{y \left(F_{142}\! \left(x , 1\right)-F_{142}\! \left(x , y\right)\right)}{-1+y}
F_{149}\! \left(x \right) = F_{114}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x , 1\right)
F_{157}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{11}\! \left(x \right) F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{163}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right) F_{9}\! \left(x \right)
F_{163}\! \left(x \right) = F_{124}\! \left(x \right)+F_{156}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{108}\! \left(x \right)+F_{9}\! \left(x \right)
F_{166}\! \left(x \right) = F_{100}\! \left(x \right)+F_{17}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{251}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = -\frac{F_{169}\! \left(x , 1\right) y -F_{169}\! \left(x , y\right)}{-1+y}
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{30}\! \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) = F_{173}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{182}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{93}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{250}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{249}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{250}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = -F_{249}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = \frac{F_{189}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{11}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{234}\! \left(x \right)
F_{193}\! \left(x \right) = F_{17}\! \left(x \right)+F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{2}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x , 1\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = -\frac{y \left(F_{196}\! \left(x , 1\right)-F_{196}\! \left(x , y\right)\right)}{-1+y}
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = -\frac{y \left(F_{205}\! \left(x , 1\right)-F_{205}\! \left(x , y\right)\right)}{-1+y}
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{223}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{230}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{228}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{227}\! \left(x \right) = F_{114}\! \left(x \right)
F_{228}\! \left(x \right) = F_{100}\! \left(x \right)+F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{17}\! \left(x \right)+F_{195}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right)
F_{232}\! \left(x \right) = F_{205}\! \left(x , 1\right)
F_{233}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{234}\! \left(x \right) = F_{102}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{190}\! \left(x \right)+F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{248}\! \left(x \right)+F_{6}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x , 1\right)
F_{205}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{239}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{11}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{245}\! \left(x \right)
F_{244}\! \left(x \right) = F_{193}\! \left(x \right)+F_{64}\! \left(x \right)
F_{245}\! \left(x \right) = F_{223}\! \left(x \right)+F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{231}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{232}\! \left(x \right)+F_{241}\! \left(x \right)
F_{248}\! \left(x \right) = F_{11}\! \left(x \right) F_{235}\! \left(x \right)
F_{249}\! \left(x \right) = F_{190}\! \left(x \right)+F_{9}\! \left(x \right)
F_{250}\! \left(x \right) = F_{249}\! \left(x \right) F_{9}\! \left(x \right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{261}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{254}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{87}\! \left(x \right)
F_{257}\! \left(x \right) = F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{84}\! \left(x \right)
F_{260}\! \left(x \right) = F_{51}\! \left(x \right)+F_{87}\! \left(x \right)
F_{261}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{263}\! \left(x , y\right)+F_{286}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{266}\! \left(x , y\right)+F_{268}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{267}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{265}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{269}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{272}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{270}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{274}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{275}\! \left(x , y\right)+F_{281}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{279}\! \left(x \right)+F_{6}\! \left(x \right)
F_{278}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{279}\! \left(x \right) = F_{11}\! \left(x \right) F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{11}\! \left(x \right)+F_{277}\! \left(x \right)
F_{281}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{282}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{284}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{285}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{283}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{288}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{289}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{289}\! \left(x , y\right) = F_{290}\! \left(x , y\right)+F_{291}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{291}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = -\frac{F_{176}\! \left(x , 1\right) y -F_{176}\! \left(x , y\right)}{-1+y}
F_{293}\! \left(x \right) = F_{11}\! \left(x \right) F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)+F_{297}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{297}\! \left(x \right) = F_{158}\! \left(x \right)+F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x) - F_5(x))
Eq(F_3(x), F_4(x)/F_11(x))
Eq(F_4(x), -F_293(x) + F_5(x) - F_6(x))
Eq(F_5(x), F_20(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_11(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_1(x) + F_9(x))
Eq(F_13(x), F_14(x) + F_15(x) + F_6(x))
Eq(F_14(x), F_11(x)*F_8(x))
Eq(F_15(x), F_11(x)*F_16(x))
Eq(F_16(x), F_13(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
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_17(x) + F_5(x))
Eq(F_23(x), F_24(x, 1))
Eq(F_24(x, k_0), F_25(x, k_0) + F_39(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_36(x, k_0) + F_6(x))
Eq(F_26(x, k_0), F_27(x, k_0)*F_30(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_9(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_31(x, k_0) + F_6(x))
Eq(F_29(x, k_0), F_27(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0), F_11(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_28(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_30(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_36(x, k_0), F_11(x)*F_37(x, k_0))
Eq(F_37(x, k_0), F_24(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_25(x, k_0) + F_33(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_11(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), F_12(x)*F_25(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_46(x, k_0))
Eq(F_44(x, k_0), F_32(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_2(x) + F_25(x, k_0))
Eq(F_46(x, k_0), F_292(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_167(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_33(x, k_0)*F_50(x))
Eq(F_50(x), F_17(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_54(x) + F_6(x))
Eq(F_52(x), F_11(x)*F_53(x))
Eq(F_53(x), F_2(x) + F_51(x))
Eq(F_54(x), F_11(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_17(x))
Eq(F_60(x), F_51(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_101(x) + F_64(x))
Eq(F_64(x), F_6(x) + F_65(x) + F_99(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_17(x) + F_64(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_59(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_72(x))
Eq(F_73(x, k_0), F_11(x)*F_17(x)*F_33(x, k_0)*F_72(x))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_11(x)*F_17(x)*F_33(x, k_0)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_17(x)*F_9(x))
Eq(F_77(x), F_78(x) - F_98(x))
Eq(F_78(x), F_79(x) - F_97(x))
Eq(F_79(x), F_80(x)/F_11(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_12(x)*F_2(x))
Eq(F_85(x), F_50(x) + F_86(x))
Eq(F_86(x), F_13(x) + F_87(x))
Eq(F_87(x), -F_5(x) + F_88(x))
Eq(F_88(x), -F_50(x) + F_89(x))
Eq(F_89(x), -F_23(x) + F_90(x))
Eq(F_90(x), -F_84(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_11(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), -F_2(x) + F_94(x))
Eq(F_94(x), -F_0(x) + F_95(x))
Eq(F_95(x), F_96(x)/F_11(x))
Eq(F_96(x), F_2(x))
Eq(F_97(x), F_2(x) + F_81(x))
Eq(F_98(x), F_12(x)*F_17(x))
Eq(F_99(x), F_100(x)*F_11(x))
Eq(F_100(x), F_2(x) + F_64(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_17(x)*F_9(x))
Eq(F_103(x), F_104(x) - F_108(x))
Eq(F_104(x), -F_102(x) + F_105(x))
Eq(F_105(x), F_106(x) - F_166(x))
Eq(F_106(x), F_107(x)/F_11(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_11(x)*F_110(x))
Eq(F_110(x), F_111(x) + F_164(x))
Eq(F_111(x), F_112(x) - F_118(x))
Eq(F_112(x), F_113(x)/F_11(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x) - F_2(x))
Eq(F_115(x), -F_0(x) + F_116(x))
Eq(F_116(x), F_117(x)/F_11(x))
Eq(F_117(x), F_2(x))
Eq(F_118(x), F_119(x) + F_149(x))
Eq(F_119(x), F_120(x) + F_2(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_11(x)*F_122(x))
Eq(F_122(x), F_119(x) + F_123(x))
Eq(F_123(x), F_124(x) + F_98(x))
Eq(F_124(x), F_125(x, 1))
Eq(F_125(x, k_0), F_126(x, k_0) + F_5(x))
Eq(F_126(x, k_0), F_127(x, k_0) + F_138(x, k_0) + F_6(x))
Eq(F_127(x, k_0), F_11(x)*F_128(x, k_0))
Eq(F_128(x, k_0), F_126(x, k_0) + F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_30(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_129(x, k_0) + F_2(x))
Eq(F_133(x, k_0), F_125(x, k_0) + F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_17(x))
Eq(F_135(x, k_0), F_1(x) + F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0))
Eq(F_137(x, k_0), F_135(x, k_0)*F_30(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) + F_142(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_136(x, k_0)*F_17(x)*F_19(x))
Eq(F_142(x, k_0), F_126(x, k_0) + F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_148(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_136(x, k_0)*F_17(x)*F_19(x)*F_9(x))
Eq(F_148(x, k_0), -F_142(x, 1) + (k_0*F_142(x, k_0) - F_142(x, 1))/(k_0 - 1))
Eq(F_149(x), F_114(x) + F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_11(x)*F_152(x))
Eq(F_152(x), F_149(x) + F_153(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_12(x)*F_17(x)**2)
Eq(F_156(x), F_157(x, 1))
Eq(F_157(x, k_0), F_143(x, k_0) + F_158(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_11(x)*F_160(x))
Eq(F_160(x), F_161(x) + F_163(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_17(x)*F_19(x)*F_9(x))
Eq(F_163(x), F_124(x) + F_156(x))
Eq(F_164(x), F_12(x)*F_165(x))
Eq(F_165(x), F_108(x) + F_9(x))
Eq(F_166(x), F_100(x) + F_17(x))
Eq(F_167(x, k_0), F_168(x, k_0) + F_251(x, k_0))
Eq(F_168(x, k_0), -F_169(x, 1) - F_169(x, k_0) + (-k_0*F_169(x, k_0) + F_169(x, 1))/(1 - k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_171(x, k_0) + F_6(x))
Eq(F_170(x, k_0), F_28(x, k_0)*F_30(x, k_0))
Eq(F_171(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_176(x, k_0))
Eq(F_173(x, k_0), F_169(x, k_0) + F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_30(x, k_0)*F_33(x, k_0))
Eq(F_176(x, k_0), F_169(x, k_0) + F_177(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0)*F_30(x, k_0))
Eq(F_180(x, k_0), F_179(x, k_0) + F_182(x))
Eq(F_181(x, k_0), F_180(x, k_0)*F_30(x, k_0))
Eq(F_181(x, k_0), F_39(x, k_0))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x) + F_93(x))
Eq(F_184(x), F_185(x) + F_250(x))
Eq(F_185(x), F_186(x) - F_249(x))
Eq(F_186(x), F_187(x) - F_250(x))
Eq(F_187(x), F_188(x) - F_249(x))
Eq(F_188(x), F_189(x)/F_11(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_11(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_234(x))
Eq(F_193(x), F_17(x) + F_194(x))
Eq(F_194(x), F_195(x) + F_2(x))
Eq(F_195(x), F_196(x, 1))
Eq(F_196(x, k_0), F_197(x, k_0))
Eq(F_197(x, k_0), F_11(x)*F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_202(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_201(x, k_0))
Eq(F_200(x, k_0), F_196(x, k_0) + F_33(x, k_0))
Eq(F_201(x, k_0), F_33(x, k_0)*F_35(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_233(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_205(x, k_0))
Eq(F_204(x, k_0), F_2(x)*F_33(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_11(x)*F_207(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_216(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_214(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_213(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_11(x)*F_212(x, k_0))
Eq(F_212(x, k_0), F_210(x, k_0) + F_33(x, k_0))
Eq(F_213(x, k_0), -F_196(x, 1) + (k_0*F_196(x, k_0) - F_196(x, 1))/(k_0 - 1))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_33(x, k_0)*F_64(x))
Eq(F_216(x, k_0), F_217(x, k_0) + F_221(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_220(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_17(x)*F_2(x)*F_33(x, k_0))
Eq(F_220(x, k_0), -F_205(x, 1) + (k_0*F_205(x, k_0) - F_205(x, 1))/(k_0 - 1))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x)*F_33(x, k_0))
Eq(F_223(x), -F_114(x) + F_224(x))
Eq(F_224(x), F_225(x) - F_230(x))
Eq(F_225(x), F_226(x) - F_228(x))
Eq(F_226(x), F_227(x)/F_11(x))
Eq(F_227(x), F_114(x))
Eq(F_228(x), F_100(x) + F_229(x))
Eq(F_229(x), F_17(x) + F_195(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_17(x)*F_2(x))
Eq(F_232(x), F_205(x, 1))
Eq(F_233(x, k_0), F_196(x, k_0)*F_35(x, k_0))
Eq(F_234(x), F_102(x) + F_235(x))
Eq(F_235(x), F_190(x) + F_236(x))
Eq(F_236(x), F_237(x) + F_248(x) + F_6(x))
Eq(F_237(x), F_238(x, 1))
Eq(F_205(x, k_0), F_238(x, k_0) + F_239(x, k_0) + F_6(x))
Eq(F_239(x, k_0), F_240(x, k_0)*F_30(x, k_0))
Eq(F_240(x, k_0), F_205(x, k_0) + F_241(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_11(x)*F_243(x))
Eq(F_243(x), F_244(x) + F_245(x))
Eq(F_244(x), F_193(x) + F_64(x))
Eq(F_245(x), F_223(x) + F_246(x))
Eq(F_246(x), F_231(x) + F_247(x))
Eq(F_247(x), F_232(x) + F_241(x))
Eq(F_248(x), F_11(x)*F_235(x))
Eq(F_249(x), F_190(x) + F_9(x))
Eq(F_250(x), F_249(x)*F_9(x))
Eq(F_251(x, k_0), F_252(x, k_0) + F_261(x, k_0) + F_6(x))
Eq(F_252(x, k_0), F_253(x, k_0))
Eq(F_253(x, k_0), F_11(x)*F_254(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_258(x, k_0))
Eq(F_255(x, k_0), F_256(x)*F_33(x, k_0))
Eq(F_256(x), F_257(x) + F_87(x))
Eq(F_257(x), F_2(x)*F_9(x))
Eq(F_258(x, k_0), F_259(x)*F_28(x, k_0))
Eq(F_259(x), F_260(x) + F_84(x))
Eq(F_260(x), F_51(x) + F_87(x))
Eq(F_261(x, k_0), F_11(x)*F_262(x, k_0))
Eq(F_262(x, k_0), F_263(x, k_0) + F_286(x, k_0))
Eq(F_263(x, k_0), F_264(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0) + F_273(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0) + F_268(x, k_0) + 2*F_6(x))
Eq(F_266(x, k_0), F_267(x, k_0)*F_30(x, k_0))
Eq(F_267(x, k_0), F_13(x) + F_265(x, k_0))
Eq(F_268(x, k_0), F_11(x)*F_269(x, k_0))
Eq(F_269(x, k_0), F_265(x, k_0) + F_270(x, k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_272(x, k_0)*F_30(x, k_0))
Eq(F_272(x, k_0), F_17(x) + F_270(x, k_0))
Eq(F_273(x, k_0), F_17(x)*F_274(x, k_0))
Eq(F_274(x, k_0), F_275(x, k_0) + F_281(x, k_0) + 2*F_6(x))
Eq(F_275(x, k_0), F_276(x, k_0)*F_30(x, k_0))
Eq(F_276(x, k_0), F_274(x, k_0) + F_277(x))
Eq(F_277(x), F_278(x) + F_279(x) + F_6(x))
Eq(F_278(x), F_11(x)*F_9(x))
Eq(F_279(x), F_11(x)*F_280(x))
Eq(F_280(x), F_11(x) + F_277(x))
Eq(F_281(x, k_0), F_11(x)*F_282(x, k_0))
Eq(F_282(x, k_0), F_274(x, k_0) + F_283(x, k_0))
Eq(F_283(x, k_0), F_284(x, k_0))
Eq(F_284(x, k_0), F_285(x, k_0)*F_30(x, k_0))
Eq(F_285(x, k_0), F_11(x) + F_283(x, k_0))
Eq(F_286(x, k_0), F_251(x, k_0) + F_287(x, k_0))
Eq(F_287(x, k_0), F_288(x, k_0))
Eq(F_288(x, k_0), F_11(x)*F_289(x, k_0)*F_63(x))
Eq(F_289(x, k_0), F_290(x, k_0) + F_291(x, k_0))
Eq(F_290(x, k_0), F_33(x, k_0)*F_9(x))
Eq(F_291(x, k_0), F_12(x)*F_28(x, k_0))
Eq(F_292(x, k_0), -F_176(x, 1) - F_176(x, k_0) + (-k_0*F_176(x, k_0) + F_176(x, 1))/(1 - k_0))
Eq(F_293(x), F_11(x)*F_294(x))
Eq(F_294(x), F_295(x) + F_297(x))
Eq(F_295(x), F_296(x))
Eq(F_296(x), F_17(x)*F_19(x))
Eq(F_297(x), F_158(x) + F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_row_and_col_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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], 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"strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [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": [{"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24002/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[100,x]+F[4,x]
F[4,x] = -F[1,x]-F[92,x]+F[5,x]
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[13,x]*F[7,x]
F[7,x] = F[5,x]+F[8,x]
F[8,x] = F[13,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]+F[16,x]+F[99,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[10,x]*F[13,x]*F[9,x]
F[16,x] = F[17,x]
F[17,x] = F[10,x]*F[13,x]*F[18,x]
F[18,x] = 1/F[13,x]*F[19,x]
F[19,x] = -F[1,x]-F[46,x]-F[80,x]-F[90,x]+F[20,x]
F[20,x] = F[21,x]+F[85,x]
F[21,x] = 1/F[13,x]*F[22,x]
F[22,x] = -F[1,x]-F[84,x]+F[23,x]
F[23,x] = F[1,x]+F[24,x]+F[35,x]
F[24,x] = F[13,x]*F[25,x]
F[25,x] = F[10,x]+F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[29,x]
F[29,x] = F[1,x]+F[27,x]
F[30,x] = F[31,x]+F[32,x]+F[34,x]
F[31,x] = 0
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[11,x]+F[30,x]
F[34,x] = F[13,x]*F[26,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[1,x]+F[37,x]+F[38,x]+F[39,x]
F[37,x] = F[13,x]*F[36,x]
F[38,x] = F[13,x]*F[20,x]
F[39,x] = F[13,x]*F[40,x]
F[40,x] = 1/F[13,x]*F[41,x]
F[41,x] = -F[1,x]-F[82,x]-F[83,x]+F[42,x]
F[42,x] = 1/F[13,x]*F[43,x]
F[43,x] = -F[1,x]-F[44,x]+F[3,x]
F[44,x] = F[13,x]*F[45,x]
F[45,x] = F[1,x]+F[4,x]+F[46,x]+F[80,x]
F[46,x] = F[13,x]*F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = F[49,x,k[0]]+F[74,x,k[0]]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]+F[52,x,k[0]]+F[73,x,k[0]]
F[50,x,k[0]] = F[49,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = k[0]*x
F[52,x,k[0]] = F[13,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[69,x]
F[55,x,k[0]] = F[13,x]*F[54,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[55,x,k[0]]+F[68,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[57,x,k[0]]+F[67,x,k[0]]
F[57,x,k[0]] = F[51,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[29,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[63,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[51,x,k[0]]*F[62,x,k[0]]
F[62,x,k[0]] = F[1,x]+F[60,x,k[0]]
F[63,x,k[0]] = F[31,x]+F[64,x,k[0]]+F[66,x,k[0]]
F[64,x,k[0]] = F[51,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[27,x]+F[63,x,k[0]]
F[66,x,k[0]] = F[13,x]*F[59,x,k[0]]
F[67,x,k[0]] = F[13,x]*F[49,x,k[0]]
F[68,x,k[0]] = F[51,x,k[0]]*F[56,x,k[0]]
F[69,x] = -F[70,x]+F[42,x]
F[70,x] = F[1,x]+F[71,x]+F[72,x]
F[71,x] = F[13,x]*F[45,x]
F[72,x] = F[13,x]*F[42,x]
F[73,x,k[0]] = F[13,x]*F[48,x,k[0]]
F[74,x,k[0]] = F[13,x]*F[75,x,k[0]]
F[75,x,k[0]] = (F[76,x,k[0]]*k[0]-F[76,x,1])/(-1+k[0])
F[76,x,k[0]] = F[54,x,k[0]]+F[77,x,k[0]]+F[78,x]
F[77,x,k[0]] = F[13,x]*F[75,x,k[0]]
F[78,x] = F[13,x]*F[79,x]
F[79,x] = 1/F[13,x]*F[69,x]
F[80,x] = F[13,x]*F[81,x]
F[81,x] = F[53,x,1]
F[82,x] = -F[1,x]-F[35,x]+F[70,x]
F[83,x] = F[13,x]*F[20,x]
F[84,x] = F[13,x]*F[23,x]
F[85,x] = F[13,x]*F[86,x]
F[86,x] = F[78,x]+F[87,x]+F[88,x]
F[87,x] = F[54,x,1]
F[88,x] = F[13,x]*F[89,x]
F[89,x] = F[75,x,1]
F[90,x] = F[13,x]*F[91,x]
F[91,x] = F[1,x]+F[19,x]+F[90,x]+F[92,x]
F[92,x] = F[13,x]*F[93,x]
F[93,x] = F[29,x]+F[94,x]
F[94,x] = F[11,x]+F[95,x]
F[95,x] = F[31,x]+F[96,x]+F[98,x]
F[96,x] = F[13,x]*F[97,x]
F[97,x] = F[27,x]+F[95,x]
F[98,x] = F[13,x]*F[94,x]
F[99,x] = F[10,x]*F[13,x]*F[93,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = F[1,x]+F[102,x]+F[103,x]+F[104,x]
F[102,x] = F[101,x]*F[13,x]
F[103,x] = F[13,x]*F[81,x]
F[104,x] = F[13,x]*F[47,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{92}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \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_{10}\! \left(x \right)+F_{14}\! \left(x \right)+F_{16}\! \left(x \right)+F_{99}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{19}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{46}\! \left(x \right)-F_{80}\! \left(x \right)-F_{90}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{85}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{84}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{41}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{82}\! \left(x \right)-F_{83}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{44}\! \left(x \right)+F_{3}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{46}\! \left(x \right)+F_{80}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = y x
F_{52}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{69}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{60}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{69}\! \left(x \right) = -F_{70}\! \left(x \right)+F_{42}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{42}\! \left(x \right)
F_{73}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}
F_{76}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{78}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{13}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{53}\! \left(x , 1\right)
F_{82}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{35}\! \left(x \right)+F_{70}\! \left(x \right)
F_{83}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{85}\! \left(x \right) = F_{13}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{78}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{54}\! \left(x , 1\right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{75}\! \left(x , 1\right)
F_{90}\! \left(x \right) = F_{13}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{29}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{31}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{13}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{27}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)+F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{103}\! \left(x \right) = F_{13}\! \left(x \right) F_{81}\! \left(x \right)
F_{104}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_100(x) + F_4(x))
Eq(F_4(x), -F_1(x) + F_5(x) - F_92(x))
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_13(x)*F_7(x))
Eq(F_7(x), F_5(x) + F_8(x))
Eq(F_8(x), F_13(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x) + F_16(x) + F_99(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_10(x)*F_13(x)*F_9(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_10(x)*F_13(x)*F_18(x))
Eq(F_18(x), F_19(x)/F_13(x))
Eq(F_19(x), -F_1(x) + F_20(x) - F_46(x) - F_80(x) - F_90(x))
Eq(F_20(x), F_21(x) + F_85(x))
Eq(F_21(x), F_22(x)/F_13(x))
Eq(F_22(x), -F_1(x) + F_23(x) - F_84(x))
Eq(F_23(x), F_1(x) + F_24(x) + F_35(x))
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_10(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_27(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_34(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_11(x) + F_30(x))
Eq(F_34(x), F_13(x)*F_26(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_1(x) + F_37(x) + F_38(x) + F_39(x))
Eq(F_37(x), F_13(x)*F_36(x))
Eq(F_38(x), F_13(x)*F_20(x))
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_13(x))
Eq(F_41(x), -F_1(x) + F_42(x) - F_82(x) - F_83(x))
Eq(F_42(x), F_43(x)/F_13(x))
Eq(F_43(x), -F_1(x) + F_3(x) - F_44(x))
Eq(F_44(x), F_13(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_4(x) + F_46(x) + F_80(x))
Eq(F_46(x), F_13(x)*F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), F_49(x, k_0) + F_74(x, k_0))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0) + F_52(x, k_0) + F_73(x, k_0))
Eq(F_50(x, k_0), F_49(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), k_0*x)
Eq(F_52(x, k_0), F_13(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_69(x))
Eq(F_55(x, k_0), F_13(x)*F_54(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_55(x, k_0) + F_68(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_57(x, k_0) + F_67(x, k_0))
Eq(F_57(x, k_0), F_51(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_29(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_63(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_51(x, k_0)*F_62(x, k_0))
Eq(F_62(x, k_0), F_1(x) + F_60(x, k_0))
Eq(F_63(x, k_0), F_31(x) + F_64(x, k_0) + F_66(x, k_0))
Eq(F_64(x, k_0), F_51(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_27(x) + F_63(x, k_0))
Eq(F_66(x, k_0), F_13(x)*F_59(x, k_0))
Eq(F_67(x, k_0), F_13(x)*F_49(x, k_0))
Eq(F_68(x, k_0), F_51(x, k_0)*F_56(x, k_0))
Eq(F_69(x), F_42(x) - F_70(x))
Eq(F_70(x), F_1(x) + F_71(x) + F_72(x))
Eq(F_71(x), F_13(x)*F_45(x))
Eq(F_72(x), F_13(x)*F_42(x))
Eq(F_73(x, k_0), F_13(x)*F_48(x, k_0))
Eq(F_74(x, k_0), F_13(x)*F_75(x, k_0))
Eq(F_75(x, k_0), (-k_0*F_76(x, k_0) + F_76(x, 1))/(1 - k_0))
Eq(F_76(x, k_0), F_54(x, k_0) + F_77(x, k_0) + F_78(x))
Eq(F_77(x, k_0), F_13(x)*F_75(x, k_0))
Eq(F_78(x), F_13(x)*F_79(x))
Eq(F_79(x), F_69(x)/F_13(x))
Eq(F_80(x), F_13(x)*F_81(x))
Eq(F_81(x), F_53(x, 1))
Eq(F_82(x), -F_1(x) - F_35(x) + F_70(x))
Eq(F_83(x), F_13(x)*F_20(x))
Eq(F_84(x), F_13(x)*F_23(x))
Eq(F_85(x), F_13(x)*F_86(x))
Eq(F_86(x), F_78(x) + F_87(x) + F_88(x))
Eq(F_87(x), F_54(x, 1))
Eq(F_88(x), F_13(x)*F_89(x))
Eq(F_89(x), F_75(x, 1))
Eq(F_90(x), F_13(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_19(x) + F_90(x) + F_92(x))
Eq(F_92(x), F_13(x)*F_93(x))
Eq(F_93(x), F_29(x) + F_94(x))
Eq(F_94(x), F_11(x) + F_95(x))
Eq(F_95(x), F_31(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_13(x)*F_97(x))
Eq(F_97(x), F_27(x) + F_95(x))
Eq(F_98(x), F_13(x)*F_94(x))
Eq(F_99(x), F_10(x)*F_13(x)*F_93(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_1(x) + F_102(x) + F_103(x) + F_104(x))
Eq(F_102(x), F_101(x)*F_13(x))
Eq(F_103(x), F_13(x)*F_81(x))
Eq(F_104(x), F_13(x)*F_47(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 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"pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [1, 2], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 3], [1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 3], [1, 3], [1, 2], [1, 3], [1, 3]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 3], [1, 3], 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{"patt": [1, 0, 3, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 5], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 1], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 4], [1, 1], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 5], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 5], [1, 4], [1, 4]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 2], [1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 4], [1, 4], [1, 5], [1, 4], [1, 4]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[2, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 1], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 4], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 4], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 1], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 3], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 3], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 4], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 3], [1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}]]}, "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", "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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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 4
Strategy pack name: insertion_point_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24003/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = -F[425,x]+F[6,x]
F[6,x] = 1/F[41,x]*F[7,x]
F[7,x] = -F[425,x]+F[8,x]
F[8,x] = 1/F[4,x]*F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[4,x]
F[13,x,k[0]] = F[14,x,k[0]]+F[22,x,k[0]]
F[14,x,k[0]] = F[15,x]*F[18,x,k[0]]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[33,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[25,x,k[0]]
F[24,x,k[0]] = F[18,x,k[0]]*F[21,x,k[0]]
F[25,x,k[0]] = F[11,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[18,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[28,x]+F[29,x,k[0]]+F[31,x,k[0]]
F[28,x] = 0
F[29,x,k[0]] = F[20,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = F[16,x]+F[27,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[4,x]
F[32,x,k[0]] = F[18,x,k[0]]+F[27,x,k[0]]
F[33,x,k[0]] = F[11,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[4,x]
F[36,x,k[0]] = F[37,x,k[0]]+F[53,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[44,x,k[0]]
F[38,x,k[0]] = F[11,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[41,x]^2*F[18,x,k[0]]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[1,x]+F[41,x]
F[44,x,k[0]] = F[45,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[11,x,k[0]]*F[16,x]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[18,x,k[0]]*F[41,x]*F[48,x]
F[48,x] = F[28,x]+F[49,x]+F[51,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[41,x]+F[48,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[16,x]+F[48,x]
F[53,x,k[0]] = F[54,x,k[0]]+F[86,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[59,x,k[0]]
F[55,x,k[0]] = F[18,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[38,x,k[0]]+F[57,x]
F[57,x] = F[2,x]+F[58,x]
F[58,x] = F[41,x]^2
F[59,x,k[0]] = F[60,x,k[0]]+F[82,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[62,x,k[0]]
F[61,x,k[0]] = F[2,x]*F[27,x,k[0]]
F[62,x,k[0]] = F[41,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[28,x]+F[64,x,k[0]]+F[78,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[68,x,k[0]]
F[67,x,k[0]] = F[18,x,k[0]]*F[50,x]
F[68,x,k[0]] = F[21,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[28,x]+F[64,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[4,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[28,x]+F[72,x,k[0]]+F[76,x,k[0]]
F[72,x,k[0]] = F[20,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = F[43,x]+F[72,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[4,x]*F[43,x]*F[73,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[4,x]*F[43,x]*F[71,x,k[0]]
F[78,x,k[0]] = F[4,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[28,x]+F[76,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[20,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[28,x]+F[74,x,k[0]]+F[80,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[84,x,k[0]]
F[83,x,k[0]] = F[11,x,k[0]]*F[27,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[18,x,k[0]]*F[41,x]*F[63,x,k[0]]
F[86,x,k[0]] = F[359,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[18,x,k[0]]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[0,x]*F[41,x]
F[91,x] = F[357,x]+F[92,x]
F[92,x] = F[28,x]+F[93,x]+F[95,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[2,x]+F[92,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[101,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[42,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[4,x]*F[41,x]
F[101,x] = F[102,x]+F[92,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[349,x]
F[105,x] = F[106,x]+F[28,x]+F[347,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[105,x]+F[41,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[100,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[16,x]*F[41,x]
F[115,x] = -F[238,x]+F[116,x]
F[116,x] = -F[346,x]+F[117,x]
F[117,x] = 1/F[4,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[15,x]*F[2,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[41,x]+F[92,x]
F[125,x] = F[126,x]+F[131,x]
F[126,x] = F[127,x]+F[129,x]+F[28,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[126,x]+F[16,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[126,x]+F[41,x]
F[131,x] = -F[338,x]+F[132,x]
F[132,x] = -F[143,x]+F[133,x]
F[133,x] = -F[89,x]+F[134,x]
F[134,x] = -F[141,x]+F[135,x]
F[135,x] = 1/F[4,x]*F[136,x]
F[136,x] = F[137,x]
F[137,x] = -F[2,x]+F[138,x]
F[138,x] = -F[0,x]+F[139,x]
F[139,x] = 1/F[4,x]*F[140,x]
F[140,x] = F[2,x]
F[141,x] = F[122,x]+F[142,x]
F[142,x] = F[41,x]*F[50,x]
F[143,x] = F[10,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]+F[301,x]
F[147,x] = F[148,x]+F[152,x]
F[148,x] = -F[2,x]+F[149,x]
F[149,x] = -F[0,x]+F[150,x]
F[150,x] = 1/F[4,x]*F[151,x]
F[151,x] = F[2,x]
F[152,x] = F[153,x]+F[286,x]
F[153,x] = F[154,x]
F[154,x] = F[155,x]*F[4,x]
F[155,x] = F[156,x]+F[249,x]
F[156,x] = F[157,x]+F[41,x]
F[157,x] = F[158,x]+F[2,x]
F[158,x] = F[159,x]
F[159,x] = F[160,x]*F[4,x]
F[160,x] = F[161,x]+F[167,x]
F[161,x] = F[162,x]+F[164,x]
F[162,x] = F[163,x]+F[41,x]
F[163,x] = F[41,x]*F[43,x]
F[164,x] = F[165,x]+F[166,x]
F[165,x] = F[2,x]*F[41,x]
F[166,x] = F[158,x]*F[43,x]
F[167,x] = F[168,x]+F[171,x]
F[168,x] = F[169,x]
F[169,x] = F[165,x]+F[170,x]
F[170,x] = F[41,x]^2*F[43,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[137,x]*F[41,x]
F[173,x] = F[174,x]*F[43,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[177,x]+F[179,x]
F[177,x] = F[178,x]
F[178,x] = F[16,x]*F[41,x]*F[43,x]
F[179,x] = F[180,x]+F[248,x]
F[180,x] = F[181,x,1]
F[181,x,k[0]] = F[10,x]+F[182,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]*F[4,x]
F[184,x,k[0]] = F[185,x,k[0]]+F[198,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]+F[191,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[41,x]*F[43,x]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[20,x,k[0]]
F[190,x,k[0]] = F[1,x]+F[188,x,k[0]]
F[191,x,k[0]] = F[182,x,k[0]]+F[192,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]*F[4,x]
F[194,x,k[0]] = F[195,x,k[0]]+F[197,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[16,x]*F[188,x,k[0]]*F[41,x]*F[43,x]
F[197,x,k[0]] = -k[0]*(F[191,x,1]-F[191,x,k[0]])/(-1+k[0])
F[198,x,k[0]] = F[199,x,k[0]]*F[41,x]
F[199,x,k[0]] = F[185,x,k[0]]+F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[209,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[204,x,k[0]]
F[202,x,k[0]] = F[188,x,k[0]]+F[203,x,k[0]]
F[203,x,k[0]] = F[188,x,k[0]]*F[190,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]+F[206,x,k[0]]
F[205,x,k[0]] = F[188,x,k[0]]*F[2,x]
F[206,x,k[0]] = F[190,x,k[0]]*F[207,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]
F[208,x,k[0]] = F[200,x,k[0]]*F[4,x]
F[209,x,k[0]] = F[207,x,k[0]]+F[210,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[20,x,k[0]]*F[212,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]+F[243,x,k[0]]
F[213,x,k[0]] = F[210,x,k[0]]+F[214,x]
F[214,x] = F[215,x]
F[215,x] = F[216,x]*F[4,x]
F[216,x] = F[217,x]+F[241,x]
F[217,x] = F[218,x]+F[223,x]
F[218,x] = F[16,x]+F[219,x]
F[219,x] = F[220,x]
F[220,x] = F[221,x]*F[4,x]
F[221,x] = F[217,x]+F[222,x]
F[222,x] = F[15,x]*F[218,x]
F[223,x] = -F[228,x]+F[224,x]
F[224,x] = -F[240,x]+F[225,x]
F[225,x] = -F[232,x]+F[226,x]
F[226,x] = 1/F[4,x]*F[227,x]
F[227,x] = F[228,x]
F[228,x] = -F[2,x]+F[229,x]
F[229,x] = -F[0,x]+F[230,x]
F[230,x] = 1/F[4,x]*F[231,x]
F[231,x] = F[2,x]
F[232,x] = F[233,x]+F[239,x]
F[233,x] = F[234,x]
F[234,x] = F[235,x]*F[4,x]
F[235,x] = F[236,x]+F[237,x]
F[236,x] = F[2,x]+F[233,x]
F[237,x] = F[180,x]+F[238,x]
F[238,x] = F[15,x]*F[41,x]
F[239,x] = F[210,x,1]
F[240,x] = F[2,x]+F[218,x]
F[241,x] = F[236,x]+F[242,x]
F[242,x] = F[214,x]+F[239,x]
F[243,x,k[0]] = F[244,x,k[0]]+F[246,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]
F[245,x,k[0]] = F[41,x]^2*F[190,x,k[0]]
F[246,x,k[0]] = F[192,x,k[0]]+F[247,x]
F[247,x] = F[175,x]
F[248,x] = F[246,x,1]
F[249,x] = F[250,x]+F[48,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[16,x]*F[2,x]
F[252,x] = F[253,x]+F[255,x]+F[28,x]
F[253,x] = F[254,x]*F[4,x]
F[254,x] = F[158,x]+F[252,x]
F[255,x] = F[256,x]*F[4,x]
F[256,x] = F[257,x]+F[264,x]
F[257,x] = F[258,x,1]
F[258,x,k[0]] = F[16,x]*F[259,x,k[0]]
F[259,x,k[0]] = F[188,x,k[0]]+F[260,x,k[0]]
F[260,x,k[0]] = F[261,x,k[0]]+F[263,x,k[0]]+F[28,x]
F[261,x,k[0]] = F[20,x,k[0]]*F[262,x,k[0]]
F[262,x,k[0]] = F[260,x,k[0]]+F[41,x]
F[263,x,k[0]] = F[259,x,k[0]]*F[4,x]
F[264,x] = F[265,x]+F[267,x]
F[265,x] = F[266,x,1]
F[266,x,k[0]] = F[188,x,k[0]]*F[236,x]
F[267,x] = F[252,x]+F[268,x]
F[268,x] = F[269,x,1]
F[269,x,k[0]] = F[270,x,k[0]]+F[279,x,k[0]]+F[28,x]
F[270,x,k[0]] = F[271,x,k[0]]*F[4,x]
F[271,x,k[0]] = F[269,x,k[0]]+F[272,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0]]
F[273,x,k[0]] = F[274,x,k[0]]*F[4,x]
F[274,x,k[0]] = F[275,x,k[0]]+F[277,x,k[0]]
F[275,x,k[0]] = F[276,x,k[0]]
F[276,x,k[0]] = F[16,x]*F[188,x,k[0]]*F[43,x]
F[277,x,k[0]] = -k[0]*(F[278,x,1]-F[278,x,k[0]])/(-1+k[0])
F[278,x,k[0]] = F[207,x,k[0]]+F[272,x,k[0]]
F[279,x,k[0]] = F[280,x,k[0]]*F[4,x]
F[280,x,k[0]] = F[281,x,k[0]]+F[283,x,k[0]]
F[281,x,k[0]] = F[282,x,k[0]]
F[282,x,k[0]] = F[16,x]*F[188,x,k[0]]*F[52,x]
F[283,x,k[0]] = -k[0]*(F[284,x,1]-F[284,x,k[0]])/(-1+k[0])
F[284,x,k[0]] = F[269,x,k[0]]+F[285,x,k[0]]
F[285,x,k[0]] = F[16,x]*F[207,x,k[0]]
F[286,x] = -F[153,x]+F[287,x]
F[287,x] = -F[300,x]+F[288,x]
F[288,x] = 1/F[4,x]*F[289,x]
F[289,x] = -F[28,x]-F[290,x]+F[148,x]
F[290,x] = F[291,x]*F[4,x]
F[291,x] = F[108,x]+F[292,x]
F[292,x] = F[293,x]+F[294,x]
F[293,x] = F[28,x]+F[290,x]+F[51,x]
F[294,x] = -F[299,x]+F[295,x]
F[295,x] = -F[298,x]+F[296,x]
F[296,x] = 1/F[4,x]*F[297,x]
F[297,x] = F[148,x]
F[298,x] = F[105,x]+F[156,x]
F[299,x] = F[250,x]+F[293,x]
F[300,x] = F[153,x]+F[16,x]
F[301,x] = F[302,x]+F[303,x]
F[302,x] = F[148,x]*F[41,x]
F[303,x] = F[304,x]+F[326,x]
F[304,x] = F[28,x]+F[305,x]+F[322,x]
F[305,x] = F[306,x]
F[306,x] = F[307,x]*F[4,x]
F[307,x] = F[142,x]+F[308,x]
F[308,x] = F[309,x]*F[43,x]
F[309,x] = F[310,x]
F[310,x] = F[311,x]*F[4,x]
F[311,x] = F[28,x]+F[312,x]+F[318,x]+F[321,x]
F[312,x] = F[313,x]*F[4,x]
F[313,x] = F[314,x]+F[315,x]+F[317,x]
F[314,x] = F[130,x]+F[15,x]
F[315,x] = F[316,x]
F[316,x] = F[313,x]*F[4,x]*F[43,x]
F[317,x] = F[313,x]*F[4,x]
F[318,x] = F[319,x]
F[319,x] = F[320,x]*F[4,x]*F[43,x]
F[320,x] = F[130,x]+F[310,x]
F[321,x] = F[311,x]*F[4,x]
F[322,x] = F[323,x]*F[4,x]
F[323,x] = F[324,x]+F[325,x]
F[324,x] = F[126,x]+F[304,x]
F[325,x] = F[304,x]+F[326,x]
F[326,x] = F[327,x,1]
F[328,x,k[0]] = F[327,x,k[0]]+F[331,x,k[0]]
F[329,x,k[0]] = F[328,x,k[0]]+F[332,x,k[0]]
F[330,x,k[0]] = F[329,x,k[0]]*F[4,x]
F[331,x,k[0]] = F[28,x]+F[330,x,k[0]]+F[64,x,k[0]]
F[332,x,k[0]] = F[27,x,k[0]]+F[331,x,k[0]]
F[333,x,k[0]] = F[332,x,k[0]]+F[337,x,k[0]]
F[334,x,k[0]] = F[333,x,k[0]]+F[336,x]
F[335,x,k[0]] = F[20,x,k[0]]*F[334,x,k[0]]
F[335,x,k[0]] = F[11,x,k[0]]
F[336,x] = F[2,x]+F[300,x]
F[337,x,k[0]] = F[18,x,k[0]]*F[2,x]
F[338,x] = F[339,x]
F[339,x] = F[340,x]*F[41,x]
F[340,x] = F[341,x]
F[341,x] = F[342,x]*F[4,x]
F[342,x] = F[28,x]+F[318,x]+F[321,x]+F[343,x]
F[343,x] = F[344,x]*F[4,x]
F[344,x] = F[128,x]+F[315,x]+F[345,x]
F[345,x] = F[344,x]*F[4,x]
F[346,x] = F[119,x]+F[2,x]
F[347,x] = F[348,x]*F[4,x]
F[348,x] = F[105,x]+F[2,x]
F[349,x] = F[350,x]+F[351,x]
F[350,x] = F[16,x]*F[41,x]
F[351,x] = -F[219,x]+F[352,x]
F[352,x] = -F[350,x]+F[353,x]
F[353,x] = -F[356,x]+F[354,x]
F[354,x] = 1/F[4,x]*F[355,x]
F[355,x] = F[219,x]
F[356,x] = F[348,x]+F[41,x]
F[357,x] = F[358,x]
F[358,x] = F[41,x]^3
F[359,x,k[0]] = F[360,x,k[0]]+F[369,x,k[0]]
F[360,x,k[0]] = (-F[361,x,1]*k[0]+F[361,x,k[0]])/(-1+k[0])
F[361,x,k[0]] = F[362,x,k[0]]+F[364,x,k[0]]
F[362,x,k[0]] = F[363,x,k[0]]
F[363,x,k[0]] = F[20,x,k[0]]*F[333,x,k[0]]
F[364,x,k[0]] = F[365,x,k[0]]
F[365,x,k[0]] = F[20,x,k[0]]*F[366,x,k[0]]
F[366,x,k[0]] = F[367,x,k[0]]+F[368,x,k[0]]
F[367,x,k[0]] = F[148,x]*F[18,x,k[0]]
F[368,x,k[0]] = F[327,x,k[0]]+F[331,x,k[0]]
F[369,x,k[0]] = F[370,x,k[0]]+F[410,x,k[0]]
F[370,x,k[0]] = F[28,x]+F[371,x,k[0]]+F[379,x,k[0]]
F[371,x,k[0]] = F[372,x,k[0]]
F[372,x,k[0]] = F[373,x,k[0]]*F[4,x]
F[373,x,k[0]] = F[374,x,k[0]]+F[376,x,k[0]]
F[374,x,k[0]] = F[18,x,k[0]]*F[375,x]
F[375,x] = F[131,x]+F[251,x]
F[376,x,k[0]] = F[27,x,k[0]]*F[377,x]
F[377,x] = F[122,x]+F[378,x]
F[378,x] = F[131,x]+F[92,x]
F[379,x,k[0]] = F[380,x,k[0]]*F[4,x]
F[380,x,k[0]] = F[381,x,k[0]]+F[404,x,k[0]]
F[381,x,k[0]] = F[382,x,k[0]]
F[382,x,k[0]] = F[383,x,k[0]]+F[391,x,k[0]]
F[383,x,k[0]] = 2*F[28,x]+F[384,x,k[0]]+F[386,x,k[0]]
F[384,x,k[0]] = F[20,x,k[0]]*F[385,x,k[0]]
F[385,x,k[0]] = F[126,x]+F[383,x,k[0]]
F[386,x,k[0]] = F[387,x,k[0]]*F[4,x]
F[387,x,k[0]] = F[383,x,k[0]]+F[388,x,k[0]]
F[388,x,k[0]] = F[389,x,k[0]]
F[389,x,k[0]] = F[20,x,k[0]]*F[390,x,k[0]]
F[390,x,k[0]] = F[388,x,k[0]]+F[41,x]
F[391,x,k[0]] = F[392,x,k[0]]*F[41,x]
F[392,x,k[0]] = 2*F[28,x]+F[393,x,k[0]]+F[399,x,k[0]]
F[393,x,k[0]] = F[20,x,k[0]]*F[394,x,k[0]]
F[394,x,k[0]] = F[392,x,k[0]]+F[395,x]
F[395,x] = F[28,x]+F[396,x]+F[397,x]
F[396,x] = F[16,x]*F[4,x]
F[397,x] = F[398,x]*F[4,x]
F[398,x] = F[395,x]+F[4,x]
F[399,x,k[0]] = F[4,x]*F[400,x,k[0]]
F[400,x,k[0]] = F[392,x,k[0]]+F[401,x,k[0]]
F[401,x,k[0]] = F[402,x,k[0]]
F[402,x,k[0]] = F[20,x,k[0]]*F[403,x,k[0]]
F[403,x,k[0]] = F[4,x]+F[401,x,k[0]]
F[404,x,k[0]] = F[370,x,k[0]]+F[405,x,k[0]]
F[405,x,k[0]] = F[406,x,k[0]]
F[406,x,k[0]] = F[104,x]*F[4,x]*F[407,x,k[0]]
F[407,x,k[0]] = F[408,x,k[0]]+F[409,x,k[0]]
F[408,x,k[0]] = F[16,x]*F[18,x,k[0]]
F[409,x,k[0]] = F[15,x]*F[27,x,k[0]]
F[410,x,k[0]] = F[411,x,k[0]]
F[411,x,k[0]] = (-F[412,x,1]*k[0]+F[412,x,k[0]])/(-1+k[0])
F[412,x,k[0]] = F[41,x]*F[413,x,k[0]]
F[413,x,k[0]] = F[28,x]+F[414,x,k[0]]+F[415,x,k[0]]
F[414,x,k[0]] = F[20,x,k[0]]*F[63,x,k[0]]
F[415,x,k[0]] = F[416,x,k[0]]
F[416,x,k[0]] = F[4,x]*F[417,x,k[0]]
F[417,x,k[0]] = F[418,x,k[0]]+F[420,x,k[0]]
F[418,x,k[0]] = F[28,x]+F[415,x,k[0]]+F[419,x,k[0]]
F[419,x,k[0]] = F[20,x,k[0]]*F[69,x,k[0]]
F[420,x,k[0]] = F[4,x]*F[421,x,k[0]]*F[43,x]
F[421,x,k[0]] = F[28,x]+F[422,x,k[0]]+F[423,x,k[0]]
F[422,x,k[0]] = F[20,x,k[0]]*F[71,x,k[0]]
F[423,x,k[0]] = F[424,x,k[0]]
F[424,x,k[0]] = F[4,x]*F[421,x,k[0]]*F[43,x]
F[425,x] = F[426,x]+F[427,x]
F[426,x] = F[163,x]
F[427,x] = F[10,x]+F[247,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = -F_{425}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = \frac{F_{7}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{7}\! \left(x \right) = -F_{425}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = \frac{F_{9}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41} \left(x \right)^{2} F_{18}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{41}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{28}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{48}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{41} \left(x \right)^{2}
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{50}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{72}\! \left(x , y\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) = F_{4}\! \left(x \right) F_{43}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{41}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{359}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right)
F_{91}\! \left(x \right) = F_{357}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{28}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{2}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{101}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{42}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{92}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{349}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{28}\! \left(x \right)+F_{347}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{105}\! \left(x \right)+F_{41}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{100}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{238}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = -F_{346}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{41}\! \left(x \right)+F_{92}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{131}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{129}\! \left(x \right)+F_{28}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{126}\! \left(x \right)+F_{16}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)+F_{41}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = -F_{141}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = \frac{F_{136}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{2}\! \left(x \right)
F_{141}\! \left(x \right) = F_{122}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{41}\! \left(x \right) F_{50}\! \left(x \right)
F_{143}\! \left(x \right) = F_{10}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{301}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{152}\! \left(x \right)
F_{148}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = \frac{F_{151}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{151}\! \left(x \right) = F_{2}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{286}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{4}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{249}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{41}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{2}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{167}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{164}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{41}\! \left(x \right)
F_{163}\! \left(x \right) = F_{41}\! \left(x \right) F_{43}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{166}\! \left(x \right)
F_{165}\! \left(x \right) = F_{2}\! \left(x \right) F_{41}\! \left(x \right)
F_{166}\! \left(x \right) = F_{158}\! \left(x \right) F_{43}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{171}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{165}\! \left(x \right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{41} \left(x \right)^{2} F_{43}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{137}\! \left(x \right) F_{41}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{43}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{179}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right) F_{43}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{248}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x , 1\right)
F_{181}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{41}\! \left(x \right) F_{43}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{188}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{188}\! \left(x , y\right) F_{41}\! \left(x \right) F_{43}\! \left(x \right)
F_{197}\! \left(x , y\right) = -\frac{y \left(F_{191}\! \left(x , 1\right)-F_{191}\! \left(x , y\right)\right)}{-1+y}
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{199}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{190}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right) F_{4}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{241}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{223}\! \left(x \right)
F_{218}\! \left(x \right) = F_{16}\! \left(x \right)+F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right) F_{4}\! \left(x \right)
F_{221}\! \left(x \right) = F_{217}\! \left(x \right)+F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{15}\! \left(x \right) F_{218}\! \left(x \right)
F_{223}\! \left(x \right) = -F_{228}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{240}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{232}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = \frac{F_{231}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{231}\! \left(x \right) = F_{2}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{239}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right) F_{4}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{237}\! \left(x \right)
F_{236}\! \left(x \right) = F_{2}\! \left(x \right)+F_{233}\! \left(x \right)
F_{237}\! \left(x \right) = F_{180}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{239}\! \left(x \right) = F_{210}\! \left(x , 1\right)
F_{240}\! \left(x \right) = F_{2}\! \left(x \right)+F_{218}\! \left(x \right)
F_{241}\! \left(x \right) = F_{236}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{214}\! \left(x \right)+F_{239}\! \left(x \right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{246}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{41} \left(x \right)^{2} F_{190}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{175}\! \left(x \right)
F_{248}\! \left(x \right) = F_{246}\! \left(x , 1\right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{48}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{255}\! \left(x \right)+F_{28}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right) F_{4}\! \left(x \right)
F_{254}\! \left(x \right) = F_{158}\! \left(x \right)+F_{252}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right) F_{4}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{264}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x , 1\right)
F_{258}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{261}\! \left(x , y\right)+F_{263}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{261}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{260}\! \left(x , y\right)+F_{41}\! \left(x \right)
F_{263}\! \left(x , y\right) = F_{259}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)+F_{267}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x , 1\right)
F_{266}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{236}\! \left(x \right)
F_{267}\! \left(x \right) = F_{252}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x , 1\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{279}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{271}\! \left(x , y\right) = F_{269}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)+F_{277}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{188}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{277}\! \left(x , y\right) = -\frac{y \left(F_{278}\! \left(x , 1\right)-F_{278}\! \left(x , y\right)\right)}{-1+y}
F_{278}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{280}\! \left(x , y\right) = F_{281}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{282}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{188}\! \left(x , y\right) F_{52}\! \left(x \right)
F_{283}\! \left(x , y\right) = -\frac{y \left(F_{284}\! \left(x , 1\right)-F_{284}\! \left(x , y\right)\right)}{-1+y}
F_{284}\! \left(x , y\right) = F_{269}\! \left(x , y\right)+F_{285}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{207}\! \left(x , y\right)
F_{286}\! \left(x \right) = -F_{153}\! \left(x \right)+F_{287}\! \left(x \right)
F_{287}\! \left(x \right) = -F_{300}\! \left(x \right)+F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = \frac{F_{289}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{289}\! \left(x \right) = -F_{28}\! \left(x \right)-F_{290}\! \left(x \right)+F_{148}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{4}\! \left(x \right)
F_{291}\! \left(x \right) = F_{108}\! \left(x \right)+F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x \right)+F_{294}\! \left(x \right)
F_{293}\! \left(x \right) = F_{28}\! \left(x \right)+F_{290}\! \left(x \right)+F_{51}\! \left(x \right)
F_{294}\! \left(x \right) = -F_{299}\! \left(x \right)+F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = -F_{298}\! \left(x \right)+F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = \frac{F_{297}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{297}\! \left(x \right) = F_{148}\! \left(x \right)
F_{298}\! \left(x \right) = F_{105}\! \left(x \right)+F_{156}\! \left(x \right)
F_{299}\! \left(x \right) = F_{250}\! \left(x \right)+F_{293}\! \left(x \right)
F_{300}\! \left(x \right) = F_{153}\! \left(x \right)+F_{16}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)+F_{303}\! \left(x \right)
F_{302}\! \left(x \right) = F_{148}\! \left(x \right) F_{41}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right)+F_{326}\! \left(x \right)
F_{304}\! \left(x \right) = F_{28}\! \left(x \right)+F_{305}\! \left(x \right)+F_{322}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right) F_{4}\! \left(x \right)
F_{307}\! \left(x \right) = F_{142}\! \left(x \right)+F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right) F_{43}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right) F_{4}\! \left(x \right)
F_{311}\! \left(x \right) = F_{28}\! \left(x \right)+F_{312}\! \left(x \right)+F_{318}\! \left(x \right)+F_{321}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right) F_{4}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)+F_{315}\! \left(x \right)+F_{317}\! \left(x \right)
F_{314}\! \left(x \right) = F_{130}\! \left(x \right)+F_{15}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{313}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{317}\! \left(x \right) = F_{313}\! \left(x \right) F_{4}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{320}\! \left(x \right) = F_{130}\! \left(x \right)+F_{310}\! \left(x \right)
F_{321}\! \left(x \right) = F_{311}\! \left(x \right) F_{4}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right) F_{4}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)+F_{325}\! \left(x \right)
F_{324}\! \left(x \right) = F_{126}\! \left(x \right)+F_{304}\! \left(x \right)
F_{325}\! \left(x \right) = F_{304}\! \left(x \right)+F_{326}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x , 1\right)
F_{328}\! \left(x , y\right) = F_{327}\! \left(x , y\right)+F_{331}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{328}\! \left(x , y\right)+F_{332}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{329}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{331}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{330}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{331}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{332}\! \left(x , y\right)+F_{337}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{333}\! \left(x , y\right)+F_{336}\! \left(x \right)
F_{335}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{334}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{336}\! \left(x \right) = F_{2}\! \left(x \right)+F_{300}\! \left(x \right)
F_{337}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{338}\! \left(x \right) = F_{339}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right) F_{41}\! \left(x \right)
F_{340}\! \left(x \right) = F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = F_{342}\! \left(x \right) F_{4}\! \left(x \right)
F_{342}\! \left(x \right) = F_{28}\! \left(x \right)+F_{318}\! \left(x \right)+F_{321}\! \left(x \right)+F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = F_{344}\! \left(x \right) F_{4}\! \left(x \right)
F_{344}\! \left(x \right) = F_{128}\! \left(x \right)+F_{315}\! \left(x \right)+F_{345}\! \left(x \right)
F_{345}\! \left(x \right) = F_{344}\! \left(x \right) F_{4}\! \left(x \right)
F_{346}\! \left(x \right) = F_{119}\! \left(x \right)+F_{2}\! \left(x \right)
F_{347}\! \left(x \right) = F_{348}\! \left(x \right) F_{4}\! \left(x \right)
F_{348}\! \left(x \right) = F_{105}\! \left(x \right)+F_{2}\! \left(x \right)
F_{349}\! \left(x \right) = F_{350}\! \left(x \right)+F_{351}\! \left(x \right)
F_{350}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{351}\! \left(x \right) = -F_{219}\! \left(x \right)+F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = -F_{350}\! \left(x \right)+F_{353}\! \left(x \right)
F_{353}\! \left(x \right) = -F_{356}\! \left(x \right)+F_{354}\! \left(x \right)
F_{354}\! \left(x \right) = \frac{F_{355}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{355}\! \left(x \right) = F_{219}\! \left(x \right)
F_{356}\! \left(x \right) = F_{348}\! \left(x \right)+F_{41}\! \left(x \right)
F_{357}\! \left(x \right) = F_{358}\! \left(x \right)
F_{358}\! \left(x \right) = F_{41} \left(x \right)^{3}
F_{359}\! \left(x , y\right) = F_{360}\! \left(x , y\right)+F_{369}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = -\frac{F_{361}\! \left(x , 1\right) y -F_{361}\! \left(x , y\right)}{-1+y}
F_{361}\! \left(x , y\right) = F_{362}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{363}\! \left(x , y\right)
F_{363}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{333}\! \left(x , y\right)
F_{364}\! \left(x , y\right) = F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{366}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = F_{367}\! \left(x , y\right)+F_{368}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{148}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{327}\! \left(x , y\right)+F_{331}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{370}\! \left(x , y\right)+F_{410}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{371}\! \left(x , y\right)+F_{379}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{372}\! \left(x , y\right)
F_{372}\! \left(x , y\right) = F_{373}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{373}\! \left(x , y\right) = F_{374}\! \left(x , y\right)+F_{376}\! \left(x , y\right)
F_{374}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{375}\! \left(x \right)
F_{375}\! \left(x \right) = F_{131}\! \left(x \right)+F_{251}\! \left(x \right)
F_{376}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{377}\! \left(x \right)
F_{377}\! \left(x \right) = F_{122}\! \left(x \right)+F_{378}\! \left(x \right)
F_{378}\! \left(x \right) = F_{131}\! \left(x \right)+F_{92}\! \left(x \right)
F_{379}\! \left(x , y\right) = F_{380}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{380}\! \left(x , y\right) = F_{381}\! \left(x , y\right)+F_{404}\! \left(x , y\right)
F_{381}\! \left(x , y\right) = F_{382}\! \left(x , y\right)
F_{382}\! \left(x , y\right) = F_{383}\! \left(x , y\right)+F_{391}\! \left(x , y\right)
F_{383}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{384}\! \left(x , y\right)+F_{386}\! \left(x , y\right)
F_{384}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{385}\! \left(x , y\right)
F_{385}\! \left(x , y\right) = F_{126}\! \left(x \right)+F_{383}\! \left(x , y\right)
F_{386}\! \left(x , y\right) = F_{387}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{387}\! \left(x , y\right) = F_{383}\! \left(x , y\right)+F_{388}\! \left(x , y\right)
F_{388}\! \left(x , y\right) = F_{389}\! \left(x , y\right)
F_{389}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{390}\! \left(x , y\right)
F_{390}\! \left(x , y\right) = F_{388}\! \left(x , y\right)+F_{41}\! \left(x \right)
F_{391}\! \left(x , y\right) = F_{392}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{392}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{393}\! \left(x , y\right)+F_{399}\! \left(x , y\right)
F_{393}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{394}\! \left(x , y\right)
F_{394}\! \left(x , y\right) = F_{392}\! \left(x , y\right)+F_{395}\! \left(x \right)
F_{395}\! \left(x \right) = F_{28}\! \left(x \right)+F_{396}\! \left(x \right)+F_{397}\! \left(x \right)
F_{396}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{397}\! \left(x \right) = F_{398}\! \left(x \right) F_{4}\! \left(x \right)
F_{398}\! \left(x \right) = F_{395}\! \left(x \right)+F_{4}\! \left(x \right)
F_{399}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{400}\! \left(x , y\right)
F_{400}\! \left(x , y\right) = F_{392}\! \left(x , y\right)+F_{401}\! \left(x , y\right)
F_{401}\! \left(x , y\right) = F_{402}\! \left(x , y\right)
F_{402}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{403}\! \left(x , y\right)
F_{403}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{401}\! \left(x , y\right)
F_{404}\! \left(x , y\right) = F_{370}\! \left(x , y\right)+F_{405}\! \left(x , y\right)
F_{405}\! \left(x , y\right) = F_{406}\! \left(x , y\right)
F_{406}\! \left(x , y\right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right) F_{407}\! \left(x , y\right)
F_{407}\! \left(x , y\right) = F_{408}\! \left(x , y\right)+F_{409}\! \left(x , y\right)
F_{408}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{409}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{410}\! \left(x , y\right) = F_{411}\! \left(x , y\right)
F_{411}\! \left(x , y\right) = -\frac{F_{412}\! \left(x , 1\right) y -F_{412}\! \left(x , y\right)}{-1+y}
F_{412}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{413}\! \left(x , y\right)
F_{413}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{414}\! \left(x , y\right)+F_{415}\! \left(x , y\right)
F_{414}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{415}\! \left(x , y\right) = F_{416}\! \left(x , y\right)
F_{416}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{417}\! \left(x , y\right)
F_{417}\! \left(x , y\right) = F_{418}\! \left(x , y\right)+F_{420}\! \left(x , y\right)
F_{418}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{415}\! \left(x , y\right)+F_{419}\! \left(x , y\right)
F_{419}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{420}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{421}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{421}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{422}\! \left(x , y\right)+F_{423}\! \left(x , y\right)
F_{422}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{423}\! \left(x , y\right) = F_{424}\! \left(x , y\right)
F_{424}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{421}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{425}\! \left(x \right) = F_{426}\! \left(x \right)+F_{427}\! \left(x \right)
F_{426}\! \left(x \right) = F_{163}\! \left(x \right)
F_{427}\! \left(x \right) = F_{10}\! \left(x \right)+F_{247}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), -F_425(x) + F_6(x))
Eq(F_6(x), F_7(x)/F_41(x))
Eq(F_7(x), -F_425(x) + F_8(x))
Eq(F_8(x), F_9(x)/F_4(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_4(x))
Eq(F_13(x, k_0), F_14(x, k_0) + F_22(x, k_0))
Eq(F_14(x, k_0), F_15(x)*F_18(x, k_0))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_33(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_25(x, k_0))
Eq(F_24(x, k_0), F_18(x, k_0)*F_21(x, k_0))
Eq(F_25(x, k_0), F_11(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_18(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x) + F_29(x, k_0) + F_31(x, k_0))
Eq(F_28(x), 0)
Eq(F_29(x, k_0), F_20(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), F_16(x) + F_27(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_4(x))
Eq(F_32(x, k_0), F_18(x, k_0) + F_27(x, k_0))
Eq(F_33(x, k_0), F_11(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_4(x))
Eq(F_36(x, k_0), F_37(x, k_0) + F_53(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_44(x, k_0))
Eq(F_38(x, k_0), F_11(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_18(x, k_0)*F_41(x)**2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_41(x))
Eq(F_44(x, k_0), F_45(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_11(x, k_0)*F_16(x))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_18(x, k_0)*F_41(x)*F_48(x))
Eq(F_48(x), F_28(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_41(x) + F_48(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_16(x) + F_48(x))
Eq(F_53(x, k_0), F_54(x, k_0) + F_86(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_59(x, k_0))
Eq(F_55(x, k_0), F_18(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_38(x, k_0) + F_57(x))
Eq(F_57(x), F_2(x) + F_58(x))
Eq(F_58(x), F_41(x)**2)
Eq(F_59(x, k_0), F_60(x, k_0) + F_82(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_62(x, k_0))
Eq(F_61(x, k_0), F_2(x)*F_27(x, k_0))
Eq(F_62(x, k_0), F_41(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_28(x) + F_64(x, k_0) + F_78(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_68(x, k_0))
Eq(F_67(x, k_0), F_18(x, k_0)*F_50(x))
Eq(F_68(x, k_0), F_21(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_28(x) + F_64(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_4(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_28(x) + F_72(x, k_0) + F_76(x, k_0))
Eq(F_72(x, k_0), F_20(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), F_43(x) + F_72(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_4(x)*F_43(x)*F_73(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_4(x)*F_43(x)*F_71(x, k_0))
Eq(F_78(x, k_0), F_4(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_28(x) + F_76(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_20(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_28(x) + F_74(x, k_0) + F_80(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_84(x, k_0))
Eq(F_83(x, k_0), F_11(x, k_0)*F_27(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_18(x, k_0)*F_41(x)*F_63(x, k_0))
Eq(F_86(x, k_0), F_359(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_18(x, k_0)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_0(x)*F_41(x))
Eq(F_91(x), F_357(x) + F_92(x))
Eq(F_92(x), F_28(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_2(x) + F_92(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_101(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_42(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_4(x)*F_41(x))
Eq(F_101(x), F_102(x) + F_92(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_349(x))
Eq(F_105(x), F_106(x) + F_28(x) + F_347(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_105(x) + F_41(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_100(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_16(x)*F_41(x))
Eq(F_115(x), F_116(x) - F_238(x))
Eq(F_116(x), F_117(x) - F_346(x))
Eq(F_117(x), F_118(x)/F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_15(x)*F_2(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_41(x) + F_92(x))
Eq(F_125(x), F_126(x) + F_131(x))
Eq(F_126(x), F_127(x) + F_129(x) + F_28(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_126(x) + F_16(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_126(x) + F_41(x))
Eq(F_131(x), F_132(x) - F_338(x))
Eq(F_132(x), F_133(x) - F_143(x))
Eq(F_133(x), F_134(x) - F_89(x))
Eq(F_134(x), F_135(x) - F_141(x))
Eq(F_135(x), F_136(x)/F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x) - F_2(x))
Eq(F_138(x), -F_0(x) + F_139(x))
Eq(F_139(x), F_140(x)/F_4(x))
Eq(F_140(x), F_2(x))
Eq(F_141(x), F_122(x) + F_142(x))
Eq(F_142(x), F_41(x)*F_50(x))
Eq(F_143(x), F_10(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x) + F_301(x))
Eq(F_147(x), F_148(x) + F_152(x))
Eq(F_148(x), F_149(x) - F_2(x))
Eq(F_149(x), -F_0(x) + F_150(x))
Eq(F_150(x), F_151(x)/F_4(x))
Eq(F_151(x), F_2(x))
Eq(F_152(x), F_153(x) + F_286(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x)*F_4(x))
Eq(F_155(x), F_156(x) + F_249(x))
Eq(F_156(x), F_157(x) + F_41(x))
Eq(F_157(x), F_158(x) + F_2(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x)*F_4(x))
Eq(F_160(x), F_161(x) + F_167(x))
Eq(F_161(x), F_162(x) + F_164(x))
Eq(F_162(x), F_163(x) + F_41(x))
Eq(F_163(x), F_41(x)*F_43(x))
Eq(F_164(x), F_165(x) + F_166(x))
Eq(F_165(x), F_2(x)*F_41(x))
Eq(F_166(x), F_158(x)*F_43(x))
Eq(F_167(x), F_168(x) + F_171(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_165(x) + F_170(x))
Eq(F_170(x), F_41(x)**2*F_43(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_137(x)*F_41(x))
Eq(F_173(x), F_174(x)*F_43(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_177(x) + F_179(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_16(x)*F_41(x)*F_43(x))
Eq(F_179(x), F_180(x) + F_248(x))
Eq(F_180(x), F_181(x, 1))
Eq(F_181(x, k_0), F_10(x) + F_182(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0)*F_4(x))
Eq(F_184(x, k_0), F_185(x, k_0) + F_198(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0) + F_191(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_41(x)*F_43(x))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_20(x, k_0))
Eq(F_190(x, k_0), F_1(x) + F_188(x, k_0))
Eq(F_191(x, k_0), F_182(x, k_0) + F_192(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0)*F_4(x))
Eq(F_194(x, k_0), F_195(x, k_0) + F_197(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_16(x)*F_188(x, k_0)*F_41(x)*F_43(x))
Eq(F_197(x, k_0), -F_191(x, 1) + (k_0*F_191(x, k_0) - F_191(x, 1))/(k_0 - 1))
Eq(F_198(x, k_0), F_199(x, k_0)*F_41(x))
Eq(F_199(x, k_0), F_185(x, k_0) + F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_209(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_204(x, k_0))
Eq(F_202(x, k_0), F_188(x, k_0) + F_203(x, k_0))
Eq(F_203(x, k_0), F_188(x, k_0)*F_190(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0) + F_206(x, k_0))
Eq(F_205(x, k_0), F_188(x, k_0)*F_2(x))
Eq(F_206(x, k_0), F_190(x, k_0)*F_207(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0))
Eq(F_208(x, k_0), F_200(x, k_0)*F_4(x))
Eq(F_209(x, k_0), F_207(x, k_0) + F_210(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_20(x, k_0)*F_212(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0) + F_243(x, k_0))
Eq(F_213(x, k_0), F_210(x, k_0) + F_214(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_216(x)*F_4(x))
Eq(F_216(x), F_217(x) + F_241(x))
Eq(F_217(x), F_218(x) + F_223(x))
Eq(F_218(x), F_16(x) + F_219(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_221(x)*F_4(x))
Eq(F_221(x), F_217(x) + F_222(x))
Eq(F_222(x), F_15(x)*F_218(x))
Eq(F_223(x), F_224(x) - F_228(x))
Eq(F_224(x), F_225(x) - F_240(x))
Eq(F_225(x), F_226(x) - F_232(x))
Eq(F_226(x), F_227(x)/F_4(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), -F_2(x) + F_229(x))
Eq(F_229(x), -F_0(x) + F_230(x))
Eq(F_230(x), F_231(x)/F_4(x))
Eq(F_231(x), F_2(x))
Eq(F_232(x), F_233(x) + F_239(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_235(x)*F_4(x))
Eq(F_235(x), F_236(x) + F_237(x))
Eq(F_236(x), F_2(x) + F_233(x))
Eq(F_237(x), F_180(x) + F_238(x))
Eq(F_238(x), F_15(x)*F_41(x))
Eq(F_239(x), F_210(x, 1))
Eq(F_240(x), F_2(x) + F_218(x))
Eq(F_241(x), F_236(x) + F_242(x))
Eq(F_242(x), F_214(x) + F_239(x))
Eq(F_243(x, k_0), F_244(x, k_0) + F_246(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0))
Eq(F_245(x, k_0), F_190(x, k_0)*F_41(x)**2)
Eq(F_246(x, k_0), F_192(x, k_0) + F_247(x))
Eq(F_247(x), F_175(x))
Eq(F_248(x), F_246(x, 1))
Eq(F_249(x), F_250(x) + F_48(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_16(x)*F_2(x))
Eq(F_252(x), F_253(x) + F_255(x) + F_28(x))
Eq(F_253(x), F_254(x)*F_4(x))
Eq(F_254(x), F_158(x) + F_252(x))
Eq(F_255(x), F_256(x)*F_4(x))
Eq(F_256(x), F_257(x) + F_264(x))
Eq(F_257(x), F_258(x, 1))
Eq(F_258(x, k_0), F_16(x)*F_259(x, k_0))
Eq(F_259(x, k_0), F_188(x, k_0) + F_260(x, k_0))
Eq(F_260(x, k_0), F_261(x, k_0) + F_263(x, k_0) + F_28(x))
Eq(F_261(x, k_0), F_20(x, k_0)*F_262(x, k_0))
Eq(F_262(x, k_0), F_260(x, k_0) + F_41(x))
Eq(F_263(x, k_0), F_259(x, k_0)*F_4(x))
Eq(F_264(x), F_265(x) + F_267(x))
Eq(F_265(x), F_266(x, 1))
Eq(F_266(x, k_0), F_188(x, k_0)*F_236(x))
Eq(F_267(x), F_252(x) + F_268(x))
Eq(F_268(x), F_269(x, 1))
Eq(F_269(x, k_0), F_270(x, k_0) + F_279(x, k_0) + F_28(x))
Eq(F_270(x, k_0), F_271(x, k_0)*F_4(x))
Eq(F_271(x, k_0), F_269(x, k_0) + F_272(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0))
Eq(F_273(x, k_0), F_274(x, k_0)*F_4(x))
Eq(F_274(x, k_0), F_275(x, k_0) + F_277(x, k_0))
Eq(F_275(x, k_0), F_276(x, k_0))
Eq(F_276(x, k_0), F_16(x)*F_188(x, k_0)*F_43(x))
Eq(F_277(x, k_0), -F_278(x, 1) + (k_0*F_278(x, k_0) - F_278(x, 1))/(k_0 - 1))
Eq(F_278(x, k_0), F_207(x, k_0) + F_272(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0)*F_4(x))
Eq(F_280(x, k_0), F_281(x, k_0) + F_283(x, k_0))
Eq(F_281(x, k_0), F_282(x, k_0))
Eq(F_282(x, k_0), F_16(x)*F_188(x, k_0)*F_52(x))
Eq(F_283(x, k_0), -F_284(x, 1) + (k_0*F_284(x, k_0) - F_284(x, 1))/(k_0 - 1))
Eq(F_284(x, k_0), F_269(x, k_0) + F_285(x, k_0))
Eq(F_285(x, k_0), F_16(x)*F_207(x, k_0))
Eq(F_286(x), -F_153(x) + F_287(x))
Eq(F_287(x), F_288(x) - F_300(x))
Eq(F_288(x), F_289(x)/F_4(x))
Eq(F_289(x), F_148(x) - F_28(x) - F_290(x))
Eq(F_290(x), F_291(x)*F_4(x))
Eq(F_291(x), F_108(x) + F_292(x))
Eq(F_292(x), F_293(x) + F_294(x))
Eq(F_293(x), F_28(x) + F_290(x) + F_51(x))
Eq(F_294(x), F_295(x) - F_299(x))
Eq(F_295(x), F_296(x) - F_298(x))
Eq(F_296(x), F_297(x)/F_4(x))
Eq(F_297(x), F_148(x))
Eq(F_298(x), F_105(x) + F_156(x))
Eq(F_299(x), F_250(x) + F_293(x))
Eq(F_300(x), F_153(x) + F_16(x))
Eq(F_301(x), F_302(x) + F_303(x))
Eq(F_302(x), F_148(x)*F_41(x))
Eq(F_303(x), F_304(x) + F_326(x))
Eq(F_304(x), F_28(x) + F_305(x) + F_322(x))
Eq(F_305(x), F_306(x))
Eq(F_306(x), F_307(x)*F_4(x))
Eq(F_307(x), F_142(x) + F_308(x))
Eq(F_308(x), F_309(x)*F_43(x))
Eq(F_309(x), F_310(x))
Eq(F_310(x), F_311(x)*F_4(x))
Eq(F_311(x), F_28(x) + F_312(x) + F_318(x) + F_321(x))
Eq(F_312(x), F_313(x)*F_4(x))
Eq(F_313(x), F_314(x) + F_315(x) + F_317(x))
Eq(F_314(x), F_130(x) + F_15(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_313(x)*F_4(x)*F_43(x))
Eq(F_317(x), F_313(x)*F_4(x))
Eq(F_318(x), F_319(x))
Eq(F_319(x), F_320(x)*F_4(x)*F_43(x))
Eq(F_320(x), F_130(x) + F_310(x))
Eq(F_321(x), F_311(x)*F_4(x))
Eq(F_322(x), F_323(x)*F_4(x))
Eq(F_323(x), F_324(x) + F_325(x))
Eq(F_324(x), F_126(x) + F_304(x))
Eq(F_325(x), F_304(x) + F_326(x))
Eq(F_326(x), F_327(x, 1))
Eq(F_328(x, k_0), F_327(x, k_0) + F_331(x, k_0))
Eq(F_329(x, k_0), F_328(x, k_0) + F_332(x, k_0))
Eq(F_330(x, k_0), F_329(x, k_0)*F_4(x))
Eq(F_331(x, k_0), F_28(x) + F_330(x, k_0) + F_64(x, k_0))
Eq(F_332(x, k_0), F_27(x, k_0) + F_331(x, k_0))
Eq(F_333(x, k_0), F_332(x, k_0) + F_337(x, k_0))
Eq(F_334(x, k_0), F_333(x, k_0) + F_336(x))
Eq(F_335(x, k_0), F_20(x, k_0)*F_334(x, k_0))
Eq(F_335(x, k_0), F_11(x, k_0))
Eq(F_336(x), F_2(x) + F_300(x))
Eq(F_337(x, k_0), F_18(x, k_0)*F_2(x))
Eq(F_338(x), F_339(x))
Eq(F_339(x), F_340(x)*F_41(x))
Eq(F_340(x), F_341(x))
Eq(F_341(x), F_342(x)*F_4(x))
Eq(F_342(x), F_28(x) + F_318(x) + F_321(x) + F_343(x))
Eq(F_343(x), F_344(x)*F_4(x))
Eq(F_344(x), F_128(x) + F_315(x) + F_345(x))
Eq(F_345(x), F_344(x)*F_4(x))
Eq(F_346(x), F_119(x) + F_2(x))
Eq(F_347(x), F_348(x)*F_4(x))
Eq(F_348(x), F_105(x) + F_2(x))
Eq(F_349(x), F_350(x) + F_351(x))
Eq(F_350(x), F_16(x)*F_41(x))
Eq(F_351(x), -F_219(x) + F_352(x))
Eq(F_352(x), -F_350(x) + F_353(x))
Eq(F_353(x), F_354(x) - F_356(x))
Eq(F_354(x), F_355(x)/F_4(x))
Eq(F_355(x), F_219(x))
Eq(F_356(x), F_348(x) + F_41(x))
Eq(F_357(x), F_358(x))
Eq(F_358(x), F_41(x)**3)
Eq(F_359(x, k_0), F_360(x, k_0) + F_369(x, k_0))
Eq(F_360(x, k_0), -F_361(x, 1) - F_361(x, k_0) + (-k_0*F_361(x, k_0) + F_361(x, 1))/(1 - k_0))
Eq(F_361(x, k_0), F_362(x, k_0) + F_364(x, k_0))
Eq(F_362(x, k_0), F_363(x, k_0))
Eq(F_363(x, k_0), F_20(x, k_0)*F_333(x, k_0))
Eq(F_364(x, k_0), F_365(x, k_0))
Eq(F_365(x, k_0), F_20(x, k_0)*F_366(x, k_0))
Eq(F_366(x, k_0), F_367(x, k_0) + F_368(x, k_0))
Eq(F_367(x, k_0), F_148(x)*F_18(x, k_0))
Eq(F_368(x, k_0), F_327(x, k_0) + F_331(x, k_0))
Eq(F_369(x, k_0), F_370(x, k_0) + F_410(x, k_0))
Eq(F_370(x, k_0), F_28(x) + F_371(x, k_0) + F_379(x, k_0))
Eq(F_371(x, k_0), F_372(x, k_0))
Eq(F_372(x, k_0), F_373(x, k_0)*F_4(x))
Eq(F_373(x, k_0), F_374(x, k_0) + F_376(x, k_0))
Eq(F_374(x, k_0), F_18(x, k_0)*F_375(x))
Eq(F_375(x), F_131(x) + F_251(x))
Eq(F_376(x, k_0), F_27(x, k_0)*F_377(x))
Eq(F_377(x), F_122(x) + F_378(x))
Eq(F_378(x), F_131(x) + F_92(x))
Eq(F_379(x, k_0), F_380(x, k_0)*F_4(x))
Eq(F_380(x, k_0), F_381(x, k_0) + F_404(x, k_0))
Eq(F_381(x, k_0), F_382(x, k_0))
Eq(F_382(x, k_0), F_383(x, k_0) + F_391(x, k_0))
Eq(F_383(x, k_0), 2*F_28(x) + F_384(x, k_0) + F_386(x, k_0))
Eq(F_384(x, k_0), F_20(x, k_0)*F_385(x, k_0))
Eq(F_385(x, k_0), F_126(x) + F_383(x, k_0))
Eq(F_386(x, k_0), F_387(x, k_0)*F_4(x))
Eq(F_387(x, k_0), F_383(x, k_0) + F_388(x, k_0))
Eq(F_388(x, k_0), F_389(x, k_0))
Eq(F_389(x, k_0), F_20(x, k_0)*F_390(x, k_0))
Eq(F_390(x, k_0), F_388(x, k_0) + F_41(x))
Eq(F_391(x, k_0), F_392(x, k_0)*F_41(x))
Eq(F_392(x, k_0), 2*F_28(x) + F_393(x, k_0) + F_399(x, k_0))
Eq(F_393(x, k_0), F_20(x, k_0)*F_394(x, k_0))
Eq(F_394(x, k_0), F_392(x, k_0) + F_395(x))
Eq(F_395(x), F_28(x) + F_396(x) + F_397(x))
Eq(F_396(x), F_16(x)*F_4(x))
Eq(F_397(x), F_398(x)*F_4(x))
Eq(F_398(x), F_395(x) + F_4(x))
Eq(F_399(x, k_0), F_4(x)*F_400(x, k_0))
Eq(F_400(x, k_0), F_392(x, k_0) + F_401(x, k_0))
Eq(F_401(x, k_0), F_402(x, k_0))
Eq(F_402(x, k_0), F_20(x, k_0)*F_403(x, k_0))
Eq(F_403(x, k_0), F_4(x) + F_401(x, k_0))
Eq(F_404(x, k_0), F_370(x, k_0) + F_405(x, k_0))
Eq(F_405(x, k_0), F_406(x, k_0))
Eq(F_406(x, k_0), F_104(x)*F_4(x)*F_407(x, k_0))
Eq(F_407(x, k_0), F_408(x, k_0) + F_409(x, k_0))
Eq(F_408(x, k_0), F_16(x)*F_18(x, k_0))
Eq(F_409(x, k_0), F_15(x)*F_27(x, k_0))
Eq(F_410(x, k_0), F_411(x, k_0))
Eq(F_411(x, k_0), -F_412(x, 1) - F_412(x, k_0) + (-k_0*F_412(x, k_0) + F_412(x, 1))/(1 - k_0))
Eq(F_412(x, k_0), F_41(x)*F_413(x, k_0))
Eq(F_413(x, k_0), F_28(x) + F_414(x, k_0) + F_415(x, k_0))
Eq(F_414(x, k_0), F_20(x, k_0)*F_63(x, k_0))
Eq(F_415(x, k_0), F_416(x, k_0))
Eq(F_416(x, k_0), F_4(x)*F_417(x, k_0))
Eq(F_417(x, k_0), F_418(x, k_0) + F_420(x, k_0))
Eq(F_418(x, k_0), F_28(x) + F_415(x, k_0) + F_419(x, k_0))
Eq(F_419(x, k_0), F_20(x, k_0)*F_69(x, k_0))
Eq(F_420(x, k_0), F_4(x)*F_421(x, k_0)*F_43(x))
Eq(F_421(x, k_0), F_28(x) + F_422(x, k_0) + F_423(x, k_0))
Eq(F_422(x, k_0), F_20(x, k_0)*F_71(x, k_0))
Eq(F_423(x, k_0), F_424(x, k_0))
Eq(F_424(x, k_0), F_4(x)*F_421(x, k_0)*F_43(x))
Eq(F_425(x), F_426(x) + F_427(x))
Eq(F_426(x), F_163(x))
Eq(F_427(x), F_10(x) + F_247(x))
Pack JSON:
{"expansion_strats": [[{"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"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 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{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[1, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": 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"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, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "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", "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, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 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", "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": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[2, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[1, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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 5
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24004/
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[31,x]*F[4,x]
F[4,x] = F[1,x]+F[165,x]+F[5,x]
F[5,x] = F[31,x]*F[6,x]
F[6,x] = F[163,x]+F[7,x]
F[7,x] = F[1,x]+F[162,x]+F[8,x]
F[8,x] = F[31,x]*F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[31,x]
F[12,x] = F[129,x]+F[13,x]+F[134,x]
F[13,x] = F[14,x,1]
F[14,x,k[0]] = F[15,x,k[0]]+F[7,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[42,x,k[0]]
F[17,x,k[0]] = F[122,x,k[0]]+F[18,x]
F[18,x] = 1/F[31,x]*F[19,x]
F[19,x] = -F[0,x]+F[20,x]
F[20,x] = -F[111,x]+F[21,x]
F[21,x] = F[0,x]+F[22,x]+F[79,x]
F[22,x] = F[23,x]*F[31,x]
F[23,x] = F[24,x]+F[4,x]
F[24,x] = F[25,x,1]
F[25,x,k[0]] = F[26,x]+F[27,x,k[0]]+F[76,x,k[0]]+F[77,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]*F[31,x]
F[28,x,k[0]] = F[26,x]+F[29,x,k[0]]+F[51,x,k[0]]+F[53,x,k[0]]+F[65,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x]*F[32,x,k[0]]
F[31,x] = x
F[32,x,k[0]] = -k[0]*(F[33,x,1]-F[33,x,k[0]])/(-1+k[0])
F[33,x,k[0]] = F[26,x]+F[34,x,k[0]]+F[36,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[31,x]*F[33,x,k[0]]
F[36,x,k[0]] = F[28,x,k[0]]*F[31,x]
F[37,x,k[0]] = F[38,x,k[0]]*F[42,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[43,x,k[0]]
F[39,x,k[0]] = F[1,x]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[39,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = k[0]*x
F[43,x,k[0]] = F[44,x]+F[47,x,k[0]]
F[44,x] = F[45,x]
F[45,x] = F[31,x]*F[46,x]
F[46,x] = F[1,x]+F[44,x]
F[47,x,k[0]] = F[26,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[31,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[40,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[42,x,k[0]]*F[43,x,k[0]]
F[51,x,k[0]] = F[31,x]*F[52,x,k[0]]
F[52,x,k[0]] = -k[0]*(F[28,x,1]-F[28,x,k[0]])/(-1+k[0])
F[53,x,k[0]] = F[31,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[26,x]+F[55,x,k[0]]+F[56,x,k[0]]+F[57,x,k[0]]+F[59,x,k[0]]
F[55,x,k[0]] = F[31,x]*F[54,x,k[0]]
F[56,x,k[0]] = F[27,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[31,x]*F[33,x,k[0]]
F[59,x,k[0]] = F[42,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[54,x,k[0]]+F[61,x]
F[61,x] = F[4,x]+F[62,x]
F[62,x] = 1/F[31,x]*F[63,x]
F[63,x] = -F[22,x]-F[26,x]+F[64,x]
F[64,x] = -F[0,x]+F[4,x]
F[65,x,k[0]] = F[42,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[38,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[43,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[69,x]+F[72,x,k[0]]
F[69,x] = F[70,x]
F[70,x] = F[31,x]*F[71,x]
F[71,x] = F[44,x]+F[69,x]
F[72,x,k[0]] = 2*F[26,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[31,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[47,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[42,x,k[0]]*F[68,x,k[0]]
F[76,x,k[0]] = F[58,x,k[0]]
F[77,x,k[0]] = F[42,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[25,x,k[0]]+F[4,x]
F[79,x] = F[31,x]*F[80,x]
F[80,x] = F[81,x]+F[96,x]
F[81,x] = F[82,x]+F[91,x]
F[82,x] = F[46,x]+F[83,x]
F[83,x] = F[84,x]+F[87,x]
F[84,x] = F[85,x]
F[85,x] = F[31,x]*F[86,x]
F[86,x] = F[1,x]+F[84,x]
F[87,x] = F[26,x]+F[88,x]+F[90,x]
F[88,x] = F[31,x]*F[89,x]
F[89,x] = F[44,x]+F[87,x]
F[90,x] = F[31,x]*F[83,x]
F[91,x] = F[44,x]+F[92,x]
F[92,x] = F[26,x]+F[93,x]+F[95,x]
F[93,x] = F[31,x]*F[94,x]
F[94,x] = F[84,x]+F[92,x]
F[95,x] = F[31,x]*F[91,x]
F[96,x] = F[109,x]+F[26,x]+F[97,x]
F[97,x] = F[31,x]*F[98,x]
F[98,x] = 1/F[31,x]*F[99,x]
F[99,x] = -F[4,x]+F[100,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[0,x]*F[86,x]
F[102,x] = F[103,x]+F[105,x]+F[26,x]
F[103,x] = F[104,x]
F[104,x] = F[24,x]*F[31,x]*F[86,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[31,x]
F[107,x] = 1/F[31,x]*F[108,x]
F[108,x] = F[62,x]
F[109,x] = F[110,x]
F[110,x] = F[31,x]*F[86,x]*F[96,x]
F[111,x] = F[112,x]+F[22,x]+F[26,x]
F[112,x] = F[113,x,1]
F[113,x,k[0]] = F[114,x,k[0]]*F[31,x]
F[114,x,k[0]] = F[115,x,k[0]]+F[118,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[42,x,k[0]]
F[117,x,k[0]] = F[1,x]+F[115,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[121,x,k[0]]+F[26,x]
F[119,x,k[0]] = F[120,x,k[0]]*F[42,x,k[0]]
F[120,x,k[0]] = F[118,x,k[0]]+F[84,x]
F[121,x,k[0]] = F[114,x,k[0]]*F[31,x]
F[123,x,k[0]] = F[122,x,k[0]]+F[20,x]
F[124,x,k[0]] = F[123,x,k[0]]*F[42,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[128,x,k[0]]+F[26,x]
F[126,x,k[0]] = F[127,x,k[0]]*F[42,x,k[0]]
F[127,x,k[0]] = F[0,x]+F[125,x,k[0]]
F[128,x,k[0]] = F[15,x,k[0]]*F[31,x]
F[129,x] = F[130,x]*F[31,x]
F[130,x] = F[131,x,1]
F[131,x,k[0]] = (F[132,x,k[0]]*k[0]-F[132,x,1])/(-1+k[0])
F[132,x,k[0]] = F[133,x,k[0]]+F[134,x]+F[14,x,k[0]]
F[133,x,k[0]] = F[131,x,k[0]]*F[31,x]
F[134,x] = F[135,x]*F[31,x]
F[135,x] = F[136,x]+F[158,x]+F[160,x]
F[136,x] = F[137,x,1]
F[137,x,k[0]] = F[1,x]+F[138,x,k[0]]+F[145,x,k[0]]+F[159,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[42,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]+F[46,x]
F[140,x,k[0]] = F[141,x,k[0]]+F[40,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[144,x,k[0]]+F[26,x]
F[142,x,k[0]] = F[143,x,k[0]]*F[42,x,k[0]]
F[143,x,k[0]] = F[141,x,k[0]]+F[44,x]
F[144,x,k[0]] = F[140,x,k[0]]*F[31,x]
F[145,x,k[0]] = F[146,x,k[0]]*F[31,x]
F[146,x,k[0]] = F[147,x,k[0]]+F[153,x,k[0]]
F[147,x,k[0]] = F[1,x]+F[148,x,k[0]]+F[149,x,k[0]]+F[152,x,k[0]]
F[148,x,k[0]] = F[147,x,k[0]]*F[42,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[31,x]
F[150,x,k[0]] = F[137,x,k[0]]+F[151,x,k[0]]
F[151,x,k[0]] = F[10,x]
F[152,x,k[0]] = F[146,x,k[0]]*F[31,x]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[31,x]
F[155,x,k[0]] = (F[156,x,k[0]]*k[0]-F[156,x,1])/(-1+k[0])
F[156,x,k[0]] = F[137,x,k[0]]+F[157,x,k[0]]+F[158,x]
F[157,x,k[0]] = F[155,x,k[0]]*F[31,x]
F[158,x] = F[12,x]*F[31,x]
F[159,x,k[0]] = F[150,x,k[0]]*F[31,x]
F[160,x] = F[161,x]*F[31,x]
F[161,x] = F[155,x,1]
F[162,x] = F[31,x]*F[6,x]
F[163,x] = F[164,x]
F[164,x] = F[135,x]*F[31,x]
F[165,x] = F[31,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{165}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{163}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{162}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{31}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{12}\! \left(x \right) = F_{129}\! \left(x \right)+F_{13}\! \left(x \right)+F_{134}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{31}\! \left(x \right)}
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right)+F_{22}\! \left(x \right)+F_{79}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{31}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{31}\! \left(x \right) = x
F_{32}\! \left(x , y\right) = -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = y x
F_{43}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{31}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = -\frac{y \left(F_{28}\! \left(x , 1\right)-F_{28}\! \left(x , y\right)\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{55}\! \left(x , y\right)+F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{31}\! \left(x \right)}
F_{63}\! \left(x \right) = -F_{22}\! \left(x \right)-F_{26}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{31}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{44}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{31}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{96}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{82}\! \left(x \right) = F_{46}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{31}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{1}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{26}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{31}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{44}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{31}\! \left(x \right) F_{83}\! \left(x \right)
F_{91}\! \left(x \right) = F_{44}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{31}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{31}\! \left(x \right) F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{109}\! \left(x \right)+F_{26}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{31}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{31}\! \left(x \right)}
F_{99}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right) F_{86}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{105}\! \left(x \right)+F_{26}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{86}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{31}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{31}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{62}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{31}\! \left(x \right) F_{86}\! \left(x \right) F_{96}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x , 1\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{115}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{121}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{84}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{20}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{125}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{31}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x , 1\right)
F_{131}\! \left(x , y\right) = -\frac{-y F_{132}\! \left(x , y\right)+F_{132}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{134}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{31}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{158}\! \left(x \right)+F_{160}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x , 1\right)
F_{137}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{138}\! \left(x , y\right)+F_{145}\! \left(x , y\right)+F_{159}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{44}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{149}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{10}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{155}\! \left(x , y\right) = -\frac{-y F_{156}\! \left(x , y\right)+F_{156}\! \left(x , 1\right)}{-1+y}
F_{156}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{158}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{158}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{31}\! \left(x \right)
F_{161}\! \left(x \right) = F_{155}\! \left(x , 1\right)
F_{162}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{135}\! \left(x \right) F_{31}\! \left(x \right)
F_{165}\! \left(x \right) = F_{31}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_31(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_165(x) + F_5(x))
Eq(F_5(x), F_31(x)*F_6(x))
Eq(F_6(x), F_163(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_162(x) + F_8(x))
Eq(F_8(x), F_31(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_31(x))
Eq(F_12(x), F_129(x) + F_13(x) + F_134(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), F_15(x, k_0) + F_7(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_42(x, k_0))
Eq(F_17(x, k_0), F_122(x, k_0) + F_18(x))
Eq(F_18(x), F_19(x)/F_31(x))
Eq(F_19(x), -F_0(x) + F_20(x))
Eq(F_20(x), -F_111(x) + F_21(x))
Eq(F_21(x), F_0(x) + F_22(x) + F_79(x))
Eq(F_22(x), F_23(x)*F_31(x))
Eq(F_23(x), F_24(x) + F_4(x))
Eq(F_24(x), F_25(x, 1))
Eq(F_25(x, k_0), F_26(x) + F_27(x, k_0) + F_76(x, k_0) + F_77(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0)*F_31(x))
Eq(F_28(x, k_0), F_26(x) + F_29(x, k_0) + F_51(x, k_0) + F_53(x, k_0) + F_65(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x)*F_32(x, k_0))
Eq(F_31(x), x)
Eq(F_32(x, k_0), -F_33(x, 1) + (k_0*F_33(x, k_0) - F_33(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_26(x) + F_34(x, k_0) + F_36(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_31(x)*F_33(x, k_0))
Eq(F_36(x, k_0), F_28(x, k_0)*F_31(x))
Eq(F_37(x, k_0), F_38(x, k_0)*F_42(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_43(x, k_0))
Eq(F_39(x, k_0), F_1(x) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_39(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), k_0*x)
Eq(F_43(x, k_0), F_44(x) + F_47(x, k_0))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_31(x)*F_46(x))
Eq(F_46(x), F_1(x) + F_44(x))
Eq(F_47(x, k_0), F_26(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_31(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_40(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_42(x, k_0)*F_43(x, k_0))
Eq(F_51(x, k_0), F_31(x)*F_52(x, k_0))
Eq(F_52(x, k_0), -F_28(x, 1) + (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_53(x, k_0), F_31(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_26(x) + F_55(x, k_0) + F_56(x, k_0) + F_57(x, k_0) + F_59(x, k_0))
Eq(F_55(x, k_0), F_31(x)*F_54(x, k_0))
Eq(F_56(x, k_0), F_27(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_31(x)*F_33(x, k_0))
Eq(F_59(x, k_0), F_42(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_54(x, k_0) + F_61(x))
Eq(F_61(x), F_4(x) + F_62(x))
Eq(F_62(x), F_63(x)/F_31(x))
Eq(F_63(x), -F_22(x) - F_26(x) + F_64(x))
Eq(F_64(x), -F_0(x) + F_4(x))
Eq(F_65(x, k_0), F_42(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_38(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_43(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x) + F_72(x, k_0))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_31(x)*F_71(x))
Eq(F_71(x), F_44(x) + F_69(x))
Eq(F_72(x, k_0), 2*F_26(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_31(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_47(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_42(x, k_0)*F_68(x, k_0))
Eq(F_76(x, k_0), F_58(x, k_0))
Eq(F_77(x, k_0), F_42(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_25(x, k_0) + F_4(x))
Eq(F_79(x), F_31(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_96(x))
Eq(F_81(x), F_82(x) + F_91(x))
Eq(F_82(x), F_46(x) + F_83(x))
Eq(F_83(x), F_84(x) + F_87(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_31(x)*F_86(x))
Eq(F_86(x), F_1(x) + F_84(x))
Eq(F_87(x), F_26(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_31(x)*F_89(x))
Eq(F_89(x), F_44(x) + F_87(x))
Eq(F_90(x), F_31(x)*F_83(x))
Eq(F_91(x), F_44(x) + F_92(x))
Eq(F_92(x), F_26(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_31(x)*F_94(x))
Eq(F_94(x), F_84(x) + F_92(x))
Eq(F_95(x), F_31(x)*F_91(x))
Eq(F_96(x), F_109(x) + F_26(x) + F_97(x))
Eq(F_97(x), F_31(x)*F_98(x))
Eq(F_98(x), F_99(x)/F_31(x))
Eq(F_99(x), F_100(x) - F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_0(x)*F_86(x))
Eq(F_102(x), F_103(x) + F_105(x) + F_26(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_24(x)*F_31(x)*F_86(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_31(x))
Eq(F_107(x), F_108(x)/F_31(x))
Eq(F_108(x), F_62(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_31(x)*F_86(x)*F_96(x))
Eq(F_111(x), F_112(x) + F_22(x) + F_26(x))
Eq(F_112(x), F_113(x, 1))
Eq(F_113(x, k_0), F_114(x, k_0)*F_31(x))
Eq(F_114(x, k_0), F_115(x, k_0) + F_118(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0)*F_42(x, k_0))
Eq(F_117(x, k_0), F_1(x) + F_115(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_121(x, k_0) + F_26(x))
Eq(F_119(x, k_0), F_120(x, k_0)*F_42(x, k_0))
Eq(F_120(x, k_0), F_118(x, k_0) + F_84(x))
Eq(F_121(x, k_0), F_114(x, k_0)*F_31(x))
Eq(F_123(x, k_0), F_122(x, k_0) + F_20(x))
Eq(F_124(x, k_0), F_123(x, k_0)*F_42(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_128(x, k_0) + F_26(x))
Eq(F_126(x, k_0), F_127(x, k_0)*F_42(x, k_0))
Eq(F_127(x, k_0), F_0(x) + F_125(x, k_0))
Eq(F_128(x, k_0), F_15(x, k_0)*F_31(x))
Eq(F_129(x), F_130(x)*F_31(x))
Eq(F_130(x), F_131(x, 1))
Eq(F_131(x, k_0), (-k_0*F_132(x, k_0) + F_132(x, 1))/(1 - k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_134(x) + F_14(x, k_0))
Eq(F_133(x, k_0), F_131(x, k_0)*F_31(x))
Eq(F_134(x), F_135(x)*F_31(x))
Eq(F_135(x), F_136(x) + F_158(x) + F_160(x))
Eq(F_136(x), F_137(x, 1))
Eq(F_137(x, k_0), F_1(x) + F_138(x, k_0) + F_145(x, k_0) + F_159(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_42(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0) + F_46(x))
Eq(F_140(x, k_0), F_141(x, k_0) + F_40(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_144(x, k_0) + F_26(x))
Eq(F_142(x, k_0), F_143(x, k_0)*F_42(x, k_0))
Eq(F_143(x, k_0), F_141(x, k_0) + F_44(x))
Eq(F_144(x, k_0), F_140(x, k_0)*F_31(x))
Eq(F_145(x, k_0), F_146(x, k_0)*F_31(x))
Eq(F_146(x, k_0), F_147(x, k_0) + F_153(x, k_0))
Eq(F_147(x, k_0), F_1(x) + F_148(x, k_0) + F_149(x, k_0) + F_152(x, k_0))
Eq(F_148(x, k_0), F_147(x, k_0)*F_42(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_31(x))
Eq(F_150(x, k_0), F_137(x, k_0) + F_151(x, k_0))
Eq(F_151(x, k_0), F_10(x))
Eq(F_152(x, k_0), F_146(x, k_0)*F_31(x))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_31(x))
Eq(F_155(x, k_0), (-k_0*F_156(x, k_0) + F_156(x, 1))/(1 - k_0))
Eq(F_156(x, k_0), F_137(x, k_0) + F_157(x, k_0) + F_158(x))
Eq(F_157(x, k_0), F_155(x, k_0)*F_31(x))
Eq(F_158(x), F_12(x)*F_31(x))
Eq(F_159(x, k_0), F_150(x, k_0)*F_31(x))
Eq(F_160(x), F_161(x)*F_31(x))
Eq(F_161(x), F_155(x, 1))
Eq(F_162(x), F_31(x)*F_6(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_135(x)*F_31(x))
Eq(F_165(x), F_31(x)*F_9(x))
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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 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