1032_2301_123504
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: point_and_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23997/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[107,x]+F[62,x]+F[8,x]
F[8,x] = F[0,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[13,x]+F[60,x]+F[61,x]
F[13,x] = F[1,x]+F[14,x]+F[59,x]
F[14,x] = F[11,x]*F[15,x]
F[15,x] = F[13,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[11,x]*F[18,x]
F[18,x] = F[19,x]+F[38,x]+F[56,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[28,x,k[0]]+F[42,x,k[0]]
F[21,x,k[0]] = F[11,x]*F[22,x,k[0]]
F[22,x,k[0]] = F[20,x,k[0]]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x]
F[24,x] = -F[4,x]+F[25,x]
F[25,x] = 1/F[11,x]*F[26,x]
F[26,x] = -F[1,x]-F[27,x]+F[4,x]
F[27,x] = F[11,x]*F[15,x]
F[28,x,k[0]] = F[11,x]*F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[35,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[32,x,k[0]]+F[33,x,k[0]]
F[31,x,k[0]] = F[11,x]*F[29,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[22,x,k[0]]
F[33,x,k[0]] = F[30,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = k[0]*x
F[35,x,k[0]] = F[11,x]*F[36,x,k[0]]
F[36,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[37,x,k[0]] = F[20,x,k[0]]+F[38,x]+F[41,x,k[0]]
F[38,x] = F[11,x]*F[39,x]
F[39,x] = 1/F[11,x]*F[40,x]
F[40,x] = F[24,x]
F[41,x,k[0]] = F[11,x]*F[36,x,k[0]]
F[42,x,k[0]] = F[34,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[34,x,k[0]]*F[44,x,k[0]]
F[47,x,k[0]] = F[48,x]+F[51,x,k[0]]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]
F[50,x] = F[1,x]+F[48,x]
F[51,x,k[0]] = F[52,x]+F[53,x,k[0]]+F[55,x,k[0]]
F[52,x] = 0
F[53,x,k[0]] = F[11,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[45,x,k[0]]+F[51,x,k[0]]
F[55,x,k[0]] = F[34,x,k[0]]*F[47,x,k[0]]
F[56,x] = F[11,x]*F[57,x]
F[57,x] = F[58,x,1]
F[58,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[59,x] = F[11,x]*F[25,x]
F[60,x] = F[11,x]*F[18,x]
F[61,x] = F[11,x]*F[39,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[64,x,1]
F[64,x,k[0]] = F[105,x,k[0]]+F[107,x]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[8,x]
F[66,x,k[0]] = F[103,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[34,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x]+F[95,x,k[0]]
F[70,x] = F[0,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = F[74,x]+F[77,x]+F[85,x]
F[74,x] = F[1,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[11,x]*F[74,x]
F[77,x] = F[78,x]
F[78,x] = F[11,x]*F[74,x]*F[79,x]
F[79,x] = F[74,x]+F[80,x]
F[80,x] = F[48,x]+F[81,x]
F[81,x] = F[52,x]+F[82,x]+F[84,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[75,x]+F[81,x]
F[84,x] = F[11,x]*F[80,x]
F[85,x] = -F[86,x]-F[90,x]+F[12,x]
F[86,x] = F[1,x]+F[87,x]+F[89,x]
F[87,x] = F[11,x]*F[88,x]
F[88,x] = F[30,x,1]
F[89,x] = F[11,x]*F[79,x]
F[90,x] = F[91,x]
F[91,x] = F[11,x]*F[92,x]
F[92,x] = F[61,x]+F[88,x]+F[93,x]+F[94,x]
F[93,x] = F[11,x]*F[57,x]
F[94,x] = F[11,x]*F[92,x]
F[95,x,k[0]] = F[34,x,k[0]]*F[96,x]
F[96,x] = F[70,x]+F[97,x]
F[98,x,k[0]] = F[34,x,k[0]]*F[97,x]
F[99,x,k[0]] = F[71,x]+F[98,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[101,x,k[0]]*F[34,x,k[0]]
F[102,x,k[0]] = F[66,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[11,x]
F[64,x,k[0]] = F[104,x,k[0]]+F[7,x]
F[105,x,k[0]] = F[106,x,k[0]]*F[11,x]
F[106,x,k[0]] = (F[64,x,k[0]]*k[0]-F[64,x,1])/(-1+k[0])
F[107,x] = F[108,x]*F[11,x]
F[108,x] = F[109,x]+F[118,x]+F[119,x]
F[109,x] = F[110,x,1]
F[110,x,k[0]] = F[111,x,k[0]]+F[114,x,k[0]]
F[111,x,k[0]] = F[1,x]+F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[34,x,k[0]]
F[113,x,k[0]] = F[11,x]*F[110,x,k[0]]
F[114,x,k[0]] = F[11,x]*F[115,x,k[0]]
F[115,x,k[0]] = F[110,x,k[0]]+F[116,x,k[0]]+F[118,x]
F[116,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[117,x,k[0]] = (F[115,x,k[0]]*k[0]-F[115,x,1])/(-1+k[0])
F[118,x] = F[11,x]*F[63,x]
F[119,x] = F[11,x]*F[120,x]
F[120,x] = F[117,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{107}\! \left(x \right)+F_{62}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \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_{13}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)+F_{59}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{56}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{26}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = y x
F_{35}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{38}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{24}\! \left(x \right)
F_{41}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{52}\! \left(x \right) = 0
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x , 1\right)
F_{64}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x \right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{70}\! \left(x \right) = F_{0}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{74}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{48}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{52}\! \left(x \right)+F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{86}\! \left(x \right)-F_{90}\! \left(x \right)+F_{12}\! \left(x \right)
F_{86}\! \left(x \right) = F_{1}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{61}\! \left(x \right)+F_{88}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \left(x \right)
F_{95}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{70}\! \left(x \right)+F_{97}\! \left(x \right)
F_{98}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{97}\! \left(x \right)
F_{99}\! \left(x , y\right) = F_{71}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{106}\! \left(x , y\right) = -\frac{-y F_{64}\! \left(x , y\right)+F_{64}\! \left(x , 1\right)}{-1+y}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{11}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x , 1\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{110}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{118}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = -\frac{-y F_{115}\! \left(x , y\right)+F_{115}\! \left(x , 1\right)}{-1+y}
F_{118}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{119}\! \left(x \right) = F_{11}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_107(x) + F_62(x) + F_8(x))
Eq(F_8(x), F_0(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_13(x) + F_60(x) + F_61(x))
Eq(F_13(x), F_1(x) + F_14(x) + F_59(x))
Eq(F_14(x), F_11(x)*F_15(x))
Eq(F_15(x), F_13(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_11(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_38(x) + F_56(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_28(x, k_0) + F_42(x, k_0))
Eq(F_21(x, k_0), F_11(x)*F_22(x, k_0))
Eq(F_22(x, k_0), F_20(x, k_0) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x))
Eq(F_24(x), F_25(x) - F_4(x))
Eq(F_25(x), F_26(x)/F_11(x))
Eq(F_26(x), -F_1(x) - F_27(x) + F_4(x))
Eq(F_27(x), F_11(x)*F_15(x))
Eq(F_28(x, k_0), F_11(x)*F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_35(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0) + F_32(x, k_0) + F_33(x, k_0))
Eq(F_31(x, k_0), F_11(x)*F_29(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_22(x, k_0))
Eq(F_33(x, k_0), F_30(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), k_0*x)
Eq(F_35(x, k_0), F_11(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_20(x, k_0) + F_38(x) + F_41(x, k_0))
Eq(F_38(x), F_11(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_11(x))
Eq(F_40(x), F_24(x))
Eq(F_41(x, k_0), F_11(x)*F_36(x, k_0))
Eq(F_42(x, k_0), F_34(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_34(x, k_0)*F_44(x, k_0))
Eq(F_47(x, k_0), F_48(x) + F_51(x, k_0))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_50(x))
Eq(F_50(x), F_1(x) + F_48(x))
Eq(F_51(x, k_0), F_52(x) + F_53(x, k_0) + F_55(x, k_0))
Eq(F_52(x), 0)
Eq(F_53(x, k_0), F_11(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_45(x, k_0) + F_51(x, k_0))
Eq(F_55(x, k_0), F_34(x, k_0)*F_47(x, k_0))
Eq(F_56(x), F_11(x)*F_57(x))
Eq(F_57(x), F_58(x, 1))
Eq(F_58(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_59(x), F_11(x)*F_25(x))
Eq(F_60(x), F_11(x)*F_18(x))
Eq(F_61(x), F_11(x)*F_39(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_64(x, 1))
Eq(F_64(x, k_0), F_105(x, k_0) + F_107(x) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_8(x))
Eq(F_66(x, k_0), F_103(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_34(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x) + F_95(x, k_0))
Eq(F_70(x), F_0(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_77(x) + F_85(x))
Eq(F_74(x), F_1(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_11(x)*F_74(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_11(x)*F_74(x)*F_79(x))
Eq(F_79(x), F_74(x) + F_80(x))
Eq(F_80(x), F_48(x) + F_81(x))
Eq(F_81(x), F_52(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_75(x) + F_81(x))
Eq(F_84(x), F_11(x)*F_80(x))
Eq(F_85(x), F_12(x) - F_86(x) - F_90(x))
Eq(F_86(x), F_1(x) + F_87(x) + F_89(x))
Eq(F_87(x), F_11(x)*F_88(x))
Eq(F_88(x), F_30(x, 1))
Eq(F_89(x), F_11(x)*F_79(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_11(x)*F_92(x))
Eq(F_92(x), F_61(x) + F_88(x) + F_93(x) + F_94(x))
Eq(F_93(x), F_11(x)*F_57(x))
Eq(F_94(x), F_11(x)*F_92(x))
Eq(F_95(x, k_0), F_34(x, k_0)*F_96(x))
Eq(F_96(x), F_70(x) + F_97(x))
Eq(F_98(x, k_0), F_34(x, k_0)*F_97(x))
Eq(F_99(x, k_0), F_71(x) + F_98(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_101(x, k_0)*F_34(x, k_0))
Eq(F_102(x, k_0), F_66(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_11(x))
Eq(F_64(x, k_0), F_104(x, k_0) + F_7(x))
Eq(F_105(x, k_0), F_106(x, k_0)*F_11(x))
Eq(F_106(x, k_0), (-k_0*F_64(x, k_0) + F_64(x, 1))/(1 - k_0))
Eq(F_107(x), F_108(x)*F_11(x))
Eq(F_108(x), F_109(x) + F_118(x) + F_119(x))
Eq(F_109(x), F_110(x, 1))
Eq(F_110(x, k_0), F_111(x, k_0) + F_114(x, k_0))
Eq(F_111(x, k_0), F_1(x) + F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_34(x, k_0))
Eq(F_113(x, k_0), F_11(x)*F_110(x, k_0))
Eq(F_114(x, k_0), F_11(x)*F_115(x, k_0))
Eq(F_115(x, k_0), F_110(x, k_0) + F_116(x, k_0) + F_118(x))
Eq(F_116(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_117(x, k_0), (-k_0*F_115(x, k_0) + F_115(x, 1))/(1 - k_0))
Eq(F_118(x), F_11(x)*F_63(x))
Eq(F_119(x), F_11(x)*F_120(x))
Eq(F_120(x), F_117(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_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, 3, 5, 0, 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, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 2], [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, 2], [1, 2], [1, 3], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [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, 3], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": 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"pos": [[0, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 2], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"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": [[1, 0], [1, 0], [1, 0], 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"pos": [[1, 1], [1, 0], [1, 2], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 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], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 2, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: insertion_row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23998/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[136,x]+F[9,x]
F[9,x] = F[10,x]+F[132,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[15,x]
F[14,x] = x
F[15,x] = F[1,x]+F[12,x]
F[16,x] = F[17,x]+F[18,x]+F[26,x]
F[17,x] = 0
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[17,x]+F[18,x]+F[24,x]
F[24,x] = F[14,x]*F[25,x]
F[25,x] = F[12,x]+F[23,x]
F[26,x] = -F[17,x]-F[31,x]+F[27,x]
F[27,x] = -F[2,x]+F[28,x]
F[28,x] = -F[0,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[2,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = F[33,x]+F[35,x]
F[33,x] = F[20,x]+F[34,x]
F[34,x] = F[17,x]+F[24,x]+F[31,x]
F[35,x] = F[34,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[123,x]+F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[12,x]*F[22,x]
F[42,x] = F[43,x]+F[92,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[43,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[15,x]*F[20,x]
F[49,x] = F[50,x]+F[91,x]
F[50,x] = F[17,x]+F[51,x]+F[53,x]
F[51,x] = F[14,x]*F[52,x]
F[52,x] = F[2,x]+F[50,x]
F[53,x] = F[14,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[20,x]*F[22,x]
F[57,x] = F[50,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[14,x]*F[60,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[20,x]*F[22,x]
F[63,x] = F[49,x]+F[64,x]
F[64,x] = F[58,x]+F[65,x]
F[65,x] = F[66,x,1]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[14,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[75,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[12,x]*F[20,x]*F[22,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]*F[74,x,k[0]]
F[73,x,k[0]] = k[0]*x
F[74,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[75,x,k[0]] = -k[0]*(F[76,x,1]-F[76,x,k[0]])/(-1+k[0])
F[76,x,k[0]] = F[66,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[17,x]+F[78,x,k[0]]+F[87,x,k[0]]
F[78,x,k[0]] = F[14,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[77,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[73,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[84,x,k[0]]
F[83,x,k[0]] = F[2,x]+F[80,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[20,x]*F[74,x,k[0]]
F[86,x,k[0]] = F[50,x]+F[77,x,k[0]]
F[87,x,k[0]] = F[14,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[76,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[20,x]*F[22,x]*F[71,x,k[0]]
F[91,x] = F[77,x,1]
F[92,x] = F[34,x]+F[93,x]
F[93,x] = F[121,x]+F[17,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[104,x]+F[97,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[20,x]*F[99,x]
F[99,x] = F[100,x]+F[12,x]
F[100,x] = F[12,x]*F[15,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[12,x]*F[34,x]
F[103,x] = F[15,x]*F[93,x]
F[104,x] = F[105,x]+F[93,x]
F[105,x] = F[106,x,1]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[14,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[111,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[12,x]*F[40,x]*F[71,x,k[0]]
F[111,x,k[0]] = -k[0]*(F[112,x,1]-F[112,x,k[0]])/(-1+k[0])
F[112,x,k[0]] = F[106,x,k[0]]+F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[73,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[117,x,k[0]]
F[116,x,k[0]] = F[113,x,k[0]]+F[27,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[120,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[20,x]^2*F[74,x,k[0]]
F[120,x,k[0]] = F[58,x]+F[66,x,k[0]]
F[121,x] = F[122,x]
F[122,x] = F[12,x]*F[14,x]*F[25,x]
F[123,x] = F[124,x]+F[131,x]
F[124,x] = F[125,x]+F[27,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[14,x]
F[127,x] = F[124,x]+F[128,x]
F[128,x] = F[129,x]+F[64,x]
F[129,x] = F[130,x]
F[130,x] = F[20,x]^2*F[15,x]
F[131,x] = F[105,x]+F[36,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[12,x]*F[2,x]
F[135,x] = F[12,x]^2*F[15,x]
F[136,x] = F[137,x]+F[218,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[2,x]*F[20,x]
F[139,x] = F[140,x]+F[44,x]
F[140,x] = F[141,x]+F[143,x]+F[17,x]
F[141,x] = F[14,x]*F[142,x]
F[142,x] = F[140,x]+F[16,x]
F[143,x] = F[14,x]*F[144,x]
F[144,x] = F[145,x]+F[159,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[14,x]*F[20,x]
F[147,x] = F[138,x]+F[148,x]
F[148,x] = F[14,x]*F[149,x]
F[149,x] = F[150,x]
F[150,x] = F[14,x]*F[151,x]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[2,x]*F[22,x]
F[153,x] = F[0,x]*F[154,x]
F[154,x] = F[12,x]+F[155,x]
F[155,x] = F[156,x]+F[158,x]+F[17,x]
F[156,x] = F[14,x]*F[157,x]
F[157,x] = F[155,x]+F[20,x]
F[158,x] = F[14,x]*F[154,x]
F[159,x] = F[160,x]+F[165,x]
F[160,x] = F[161,x]*F[20,x]
F[161,x] = F[162,x]+F[163,x]+F[17,x]
F[162,x] = F[12,x]*F[14,x]
F[163,x] = F[14,x]*F[164,x]
F[164,x] = F[14,x]+F[161,x]
F[165,x] = F[140,x]+F[166,x]
F[166,x] = F[167,x]+F[17,x]+F[170,x]
F[167,x] = F[168,x]
F[168,x] = F[14,x]*F[169,x]
F[169,x] = F[160,x]+F[166,x]
F[170,x] = F[14,x]*F[171,x]
F[171,x] = F[166,x]+F[172,x]
F[172,x] = -F[161,x]+F[173,x]
F[173,x] = -F[217,x]+F[174,x]
F[174,x] = -F[10,x]+F[175,x]
F[175,x] = 1/F[14,x]*F[176,x]
F[176,x] = F[177,x]
F[177,x] = -F[214,x]+F[178,x]
F[178,x] = -F[197,x]+F[179,x]
F[179,x] = 1/F[14,x]*F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[14,x]*F[182,x]
F[182,x] = F[10,x]+F[183,x]
F[183,x] = F[138,x]+F[184,x]
F[184,x] = F[185,x]+F[188,x]
F[185,x] = F[163,x]+F[17,x]+F[186,x]
F[186,x] = F[14,x]*F[187,x]
F[187,x] = F[12,x]+F[185,x]
F[188,x] = F[189,x]
F[189,x] = F[14,x]*F[190,x]*F[22,x]
F[190,x] = -F[193,x]+F[191,x]
F[191,x] = 1/F[14,x]*F[192,x]
F[192,x] = F[140,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = F[12,x]*F[2,x]*F[20,x]
F[196,x] = F[140,x]*F[15,x]
F[197,x] = F[198,x]+F[213,x]
F[198,x] = -F[206,x]+F[199,x]
F[199,x] = -F[203,x]+F[200,x]
F[200,x] = 1/F[14,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = -F[2,x]+F[203,x]
F[203,x] = -F[0,x]+F[204,x]
F[204,x] = 1/F[14,x]*F[205,x]
F[205,x] = F[2,x]
F[206,x] = F[207,x]+F[50,x]
F[207,x] = F[17,x]+F[208,x]+F[210,x]
F[208,x] = F[14,x]*F[209,x]
F[209,x] = F[207,x]+F[6,x]
F[210,x] = F[14,x]*F[211,x]
F[211,x] = F[212,x]+F[61,x]
F[212,x] = F[65,x]+F[91,x]
F[213,x] = F[178,x]*F[20,x]
F[214,x] = F[215,x]
F[215,x] = F[14,x]*F[216,x]
F[216,x] = F[1,x]+F[14,x]
F[217,x] = F[14,x]*F[2,x]
F[218,x] = F[219,x]
F[219,x] = -F[226,x]+F[220,x]
F[220,x] = -F[223,x]+F[221,x]
F[221,x] = 1/F[14,x]*F[222,x]
F[222,x] = F[44,x]
F[223,x] = F[224,x]+F[225,x]
F[224,x] = F[0,x]*F[12,x]
F[225,x] = F[15,x]^2*F[12,x]
F[226,x] = F[227,x]+F[44,x]
F[227,x] = F[12,x]*F[228,x]
F[228,x] = F[20,x]+F[229,x]
F[229,x] = F[17,x]+F[230,x]+F[232,x]
F[230,x] = F[14,x]*F[231,x]
F[231,x] = F[12,x]+F[229,x]
F[232,x] = F[14,x]*F[228,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{136}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{132}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{26}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{17}\! \left(x \right)-F_{31}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{123}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{92}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{91}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{57}\! \left(x \right) = F_{50}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x , 1\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = y x
F_{74}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{y \left(F_{76}\! \left(x , 1\right)-F_{76}\! \left(x , y\right)\right)}{-1+y}
F_{76}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{92}\! \left(x \right) = F_{34}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{121}\! \left(x \right)+F_{17}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{104}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{20}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{103}\! \left(x \right) = F_{15}\! \left(x \right) F_{93}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = -\frac{y \left(F_{112}\! \left(x , 1\right)-F_{112}\! \left(x , y\right)\right)}{-1+y}
F_{112}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{27}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{20} \left(x \right)^{2} F_{74}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{131}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{27}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{14}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{64}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{131}\! \left(x \right) = F_{105}\! \left(x \right)+F_{36}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{218}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{44}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{17}\! \left(x \right)
F_{141}\! \left(x \right) = F_{14}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{140}\! \left(x \right)+F_{16}\! \left(x \right)
F_{143}\! \left(x \right) = F_{14}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{159}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{147}\! \left(x \right) = F_{138}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{14}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{14}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{2}\! \left(x \right) F_{22}\! \left(x \right)
F_{153}\! \left(x \right) = F_{0}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{158}\! \left(x \right)+F_{17}\! \left(x \right)
F_{156}\! \left(x \right) = F_{14}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{155}\! \left(x \right)+F_{20}\! \left(x \right)
F_{158}\! \left(x \right) = F_{14}\! \left(x \right) F_{154}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{165}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{20}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)+F_{17}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{163}\! \left(x \right) = F_{14}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{14}\! \left(x \right)+F_{161}\! \left(x \right)
F_{165}\! \left(x \right) = F_{140}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{17}\! \left(x \right)+F_{170}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{14}\! \left(x \right) F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{160}\! \left(x \right)+F_{166}\! \left(x \right)
F_{170}\! \left(x \right) = F_{14}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{166}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = -F_{161}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{217}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = \frac{F_{176}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = -F_{214}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{197}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{14}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{10}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{138}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{188}\! \left(x \right)
F_{185}\! \left(x \right) = F_{163}\! \left(x \right)+F_{17}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{14}\! \left(x \right) F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right)+F_{185}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{14}\! \left(x \right) F_{190}\! \left(x \right) F_{22}\! \left(x \right)
F_{190}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = \frac{F_{192}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{192}\! \left(x \right) = F_{140}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{196}\! \left(x \right) = F_{140}\! \left(x \right) F_{15}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{213}\! \left(x \right)
F_{198}\! \left(x \right) = -F_{206}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = -F_{203}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = \frac{F_{205}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{205}\! \left(x \right) = F_{2}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{50}\! \left(x \right)
F_{207}\! \left(x \right) = F_{17}\! \left(x \right)+F_{208}\! \left(x \right)+F_{210}\! \left(x \right)
F_{208}\! \left(x \right) = F_{14}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{207}\! \left(x \right)+F_{6}\! \left(x \right)
F_{210}\! \left(x \right) = F_{14}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{61}\! \left(x \right)
F_{212}\! \left(x \right) = F_{65}\! \left(x \right)+F_{91}\! \left(x \right)
F_{213}\! \left(x \right) = F_{178}\! \left(x \right) F_{20}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{14}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{217}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = -F_{226}\! \left(x \right)+F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = -F_{223}\! \left(x \right)+F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = \frac{F_{222}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{222}\! \left(x \right) = F_{44}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)+F_{225}\! \left(x \right)
F_{224}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{225}\! \left(x \right) = F_{15} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{44}\! \left(x \right)
F_{227}\! \left(x \right) = F_{12}\! \left(x \right) F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{20}\! \left(x \right)+F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{17}\! \left(x \right)+F_{230}\! \left(x \right)+F_{232}\! \left(x \right)
F_{230}\! \left(x \right) = F_{14}\! \left(x \right) F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{12}\! \left(x \right)+F_{229}\! \left(x \right)
F_{232}\! \left(x \right) = F_{14}\! \left(x \right) F_{228}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_136(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_132(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_1(x) + F_12(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_26(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_17(x) + F_18(x) + F_24(x))
Eq(F_24(x), F_14(x)*F_25(x))
Eq(F_25(x), F_12(x) + F_23(x))
Eq(F_26(x), -F_17(x) + F_27(x) - F_31(x))
Eq(F_27(x), -F_2(x) + F_28(x))
Eq(F_28(x), -F_0(x) + F_29(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_2(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_35(x))
Eq(F_33(x), F_20(x) + F_34(x))
Eq(F_34(x), F_17(x) + F_24(x) + F_31(x))
Eq(F_35(x), F_34(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_123(x) + F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_12(x)*F_22(x))
Eq(F_42(x), F_43(x) + F_92(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_43(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_15(x)*F_20(x))
Eq(F_49(x), F_50(x) + F_91(x))
Eq(F_50(x), F_17(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_14(x)*F_52(x))
Eq(F_52(x), F_2(x) + F_50(x))
Eq(F_53(x), F_14(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_20(x)*F_22(x))
Eq(F_57(x), F_50(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_14(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_20(x)*F_22(x))
Eq(F_63(x), F_49(x) + F_64(x))
Eq(F_64(x), F_58(x) + F_65(x))
Eq(F_65(x), F_66(x, 1))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_14(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_75(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_12(x)*F_20(x)*F_22(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0)*F_74(x, k_0))
Eq(F_73(x, k_0), k_0*x)
Eq(F_74(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_75(x, k_0), -F_76(x, 1) + (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_76(x, k_0), F_66(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_17(x) + F_78(x, k_0) + F_87(x, k_0))
Eq(F_78(x, k_0), F_14(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_77(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_73(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_84(x, k_0))
Eq(F_83(x, k_0), F_2(x) + F_80(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_20(x)*F_74(x, k_0))
Eq(F_86(x, k_0), F_50(x) + F_77(x, k_0))
Eq(F_87(x, k_0), F_14(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_76(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_20(x)*F_22(x)*F_71(x, k_0))
Eq(F_91(x), F_77(x, 1))
Eq(F_92(x), F_34(x) + F_93(x))
Eq(F_93(x), F_121(x) + F_17(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_104(x) + F_97(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_20(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_12(x))
Eq(F_100(x), F_12(x)*F_15(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_12(x)*F_34(x))
Eq(F_103(x), F_15(x)*F_93(x))
Eq(F_104(x), F_105(x) + F_93(x))
Eq(F_105(x), F_106(x, 1))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_14(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_111(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_12(x)*F_40(x)*F_71(x, k_0))
Eq(F_111(x, k_0), -F_112(x, 1) + (k_0*F_112(x, k_0) - F_112(x, 1))/(k_0 - 1))
Eq(F_112(x, k_0), F_106(x, k_0) + F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_73(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_117(x, k_0))
Eq(F_116(x, k_0), F_113(x, k_0) + F_27(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_120(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_20(x)**2*F_74(x, k_0))
Eq(F_120(x, k_0), F_58(x) + F_66(x, k_0))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_12(x)*F_14(x)*F_25(x))
Eq(F_123(x), F_124(x) + F_131(x))
Eq(F_124(x), F_125(x) + F_27(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_14(x))
Eq(F_127(x), F_124(x) + F_128(x))
Eq(F_128(x), F_129(x) + F_64(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_15(x)*F_20(x)**2)
Eq(F_131(x), F_105(x) + F_36(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_12(x)*F_2(x))
Eq(F_135(x), F_12(x)**2*F_15(x))
Eq(F_136(x), F_137(x) + F_218(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_2(x)*F_20(x))
Eq(F_139(x), F_140(x) + F_44(x))
Eq(F_140(x), F_141(x) + F_143(x) + F_17(x))
Eq(F_141(x), F_14(x)*F_142(x))
Eq(F_142(x), F_140(x) + F_16(x))
Eq(F_143(x), F_14(x)*F_144(x))
Eq(F_144(x), F_145(x) + F_159(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_14(x)*F_20(x))
Eq(F_147(x), F_138(x) + F_148(x))
Eq(F_148(x), F_14(x)*F_149(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_14(x)*F_151(x))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_2(x)*F_22(x))
Eq(F_153(x), F_0(x)*F_154(x))
Eq(F_154(x), F_12(x) + F_155(x))
Eq(F_155(x), F_156(x) + F_158(x) + F_17(x))
Eq(F_156(x), F_14(x)*F_157(x))
Eq(F_157(x), F_155(x) + F_20(x))
Eq(F_158(x), F_14(x)*F_154(x))
Eq(F_159(x), F_160(x) + F_165(x))
Eq(F_160(x), F_161(x)*F_20(x))
Eq(F_161(x), F_162(x) + F_163(x) + F_17(x))
Eq(F_162(x), F_12(x)*F_14(x))
Eq(F_163(x), F_14(x)*F_164(x))
Eq(F_164(x), F_14(x) + F_161(x))
Eq(F_165(x), F_140(x) + F_166(x))
Eq(F_166(x), F_167(x) + F_17(x) + F_170(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_14(x)*F_169(x))
Eq(F_169(x), F_160(x) + F_166(x))
Eq(F_170(x), F_14(x)*F_171(x))
Eq(F_171(x), F_166(x) + F_172(x))
Eq(F_172(x), -F_161(x) + F_173(x))
Eq(F_173(x), F_174(x) - F_217(x))
Eq(F_174(x), -F_10(x) + F_175(x))
Eq(F_175(x), F_176(x)/F_14(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x) - F_214(x))
Eq(F_178(x), F_179(x) - F_197(x))
Eq(F_179(x), F_180(x)/F_14(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_14(x)*F_182(x))
Eq(F_182(x), F_10(x) + F_183(x))
Eq(F_183(x), F_138(x) + F_184(x))
Eq(F_184(x), F_185(x) + F_188(x))
Eq(F_185(x), F_163(x) + F_17(x) + F_186(x))
Eq(F_186(x), F_14(x)*F_187(x))
Eq(F_187(x), F_12(x) + F_185(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_14(x)*F_190(x)*F_22(x))
Eq(F_190(x), F_191(x) - F_193(x))
Eq(F_191(x), F_192(x)/F_14(x))
Eq(F_192(x), F_140(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), F_12(x)*F_2(x)*F_20(x))
Eq(F_196(x), F_140(x)*F_15(x))
Eq(F_197(x), F_198(x) + F_213(x))
Eq(F_198(x), F_199(x) - F_206(x))
Eq(F_199(x), F_200(x) - F_203(x))
Eq(F_200(x), F_201(x)/F_14(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), -F_2(x) + F_203(x))
Eq(F_203(x), -F_0(x) + F_204(x))
Eq(F_204(x), F_205(x)/F_14(x))
Eq(F_205(x), F_2(x))
Eq(F_206(x), F_207(x) + F_50(x))
Eq(F_207(x), F_17(x) + F_208(x) + F_210(x))
Eq(F_208(x), F_14(x)*F_209(x))
Eq(F_209(x), F_207(x) + F_6(x))
Eq(F_210(x), F_14(x)*F_211(x))
Eq(F_211(x), F_212(x) + F_61(x))
Eq(F_212(x), F_65(x) + F_91(x))
Eq(F_213(x), F_178(x)*F_20(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_14(x)*F_216(x))
Eq(F_216(x), F_1(x) + F_14(x))
Eq(F_217(x), F_14(x)*F_2(x))
Eq(F_218(x), F_219(x))
Eq(F_219(x), F_220(x) - F_226(x))
Eq(F_220(x), F_221(x) - F_223(x))
Eq(F_221(x), F_222(x)/F_14(x))
Eq(F_222(x), F_44(x))
Eq(F_223(x), F_224(x) + F_225(x))
Eq(F_224(x), F_0(x)*F_12(x))
Eq(F_225(x), F_12(x)*F_15(x)**2)
Eq(F_226(x), F_227(x) + F_44(x))
Eq(F_227(x), F_12(x)*F_228(x))
Eq(F_228(x), F_20(x) + F_229(x))
Eq(F_229(x), F_17(x) + F_230(x) + F_232(x))
Eq(F_230(x), F_14(x)*F_231(x))
Eq(F_231(x), F_12(x) + F_229(x))
Eq(F_232(x), F_14(x)*F_228(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.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_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, 3, 5, 0, 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], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [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, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[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": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 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, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "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, 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, 3, 5, 0, 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], [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], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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[[4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [3, 0], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [3, 0], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 1], [3, 1], [3, 0], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 1], [1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [3, 1], [3, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 1], [3, 1], [3, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 1], [1, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 1], [3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 2]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[1, 1]]}], "strategy_class": "ObstructionInferralStrategy"}}, "rule_class": 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"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 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]]}]]}], "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]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [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": 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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": 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 3
Strategy pack name: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23999/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[71,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[13,x]+F[6,x]
F[6,x] = F[0,x]+F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = 1/F[12,x]*F[9,x]
F[9,x] = -F[0,x]+F[10,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = -F[1,x]+F[0,x]
F[12,x] = x
F[13,x] = F[12,x]*F[14,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = 1/F[12,x]*F[16,x]
F[16,x] = -F[0,x]+F[10,x]
F[17,x] = F[12,x]*F[18,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]+F[69,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[68,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[67,x,k[0]]
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[53,x,k[0]]
F[23,x,k[0]] = F[12,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[32,x,k[0]]+F[52,x,k[0]]
F[25,x,k[0]] = F[12,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[12,x]*F[28,x,k[0]]
F[28,x,k[0]] = 1/(-1+k[0])*(F[29,x,k[0]]*k[0]-F[29,x,1])
F[29,x,k[0]] = F[30,x,k[0]]+F[8,x]
F[30,x,k[0]] = F[19,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = k[0]*x
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x]+F[51,x,k[0]]
F[34,x] = 1/F[12,x]*F[35,x]
F[35,x] = -F[1,x]-F[36,x]+F[10,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[1,x]+F[38,x]+F[40,x]+F[42,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[33,x,1]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[26,x,1]
F[42,x] = -F[1,x]-F[46,x]+F[43,x]
F[43,x] = F[1,x]+F[44,x]+F[45,x]
F[44,x] = F[12,x]*F[37,x]
F[45,x] = F[12,x]*F[34,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[1,x]+F[48,x]+F[49,x]+F[50,x]
F[48,x] = F[12,x]*F[41,x]
F[49,x] = F[12,x]*F[39,x]
F[50,x] = F[12,x]*F[47,x]
F[51,x,k[0]] = F[20,x,k[0]]*F[31,x,k[0]]
F[52,x,k[0]] = F[24,x,k[0]]*F[31,x,k[0]]
F[53,x,k[0]] = F[31,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[58,x,k[0]]
F[55,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[31,x,k[0]]*F[55,x,k[0]]
F[58,x,k[0]] = F[59,x]+F[62,x,k[0]]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[1,x]+F[59,x]
F[62,x,k[0]] = F[63,x]+F[64,x,k[0]]+F[66,x,k[0]]
F[63,x] = 0
F[64,x,k[0]] = F[12,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[56,x,k[0]]+F[62,x,k[0]]
F[66,x,k[0]] = F[31,x,k[0]]*F[58,x,k[0]]
F[67,x,k[0]] = F[12,x]*F[20,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[19,x,k[0]]
F[69,x,k[0]] = F[12,x]*F[70,x,k[0]]
F[70,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[6,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = 1/F[12,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = -F[0,x]+F[3,x]
F[79,x] = -F[82,x]+F[80,x]
F[80,x] = 1/F[12,x]*F[81,x]
F[81,x] = -F[0,x]-F[127,x]+F[82,x]
F[82,x] = F[83,x]+F[94,x]
F[83,x] = F[1,x]+F[42,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[1,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[86,x]
F[89,x] = F[59,x]+F[90,x]
F[90,x] = F[63,x]+F[91,x]+F[93,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[87,x]+F[90,x]
F[93,x] = F[12,x]*F[89,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[1,x]+F[107,x]+F[84,x]+F[96,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[85,x]+F[98,x]
F[98,x] = F[89,x]+F[99,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[100,x]+F[59,x]
F[103,x] = 2*F[63,x]+F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[103,x]+F[90,x]
F[106,x] = F[12,x]*F[99,x]
F[107,x] = -F[1,x]-F[109,x]-F[123,x]+F[108,x]
F[108,x] = 1/F[12,x]*F[42,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[116,x]
F[111,x] = F[112,x]+F[86,x]
F[112,x] = F[113,x]+F[87,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[113,x]+F[87,x]
F[116,x] = F[117,x]+F[89,x]
F[117,x] = F[118,x]+F[90,x]
F[118,x] = 2*F[63,x]+F[119,x]+F[121,x]
F[119,x] = F[12,x]*F[120,x]
F[120,x] = F[113,x]+F[118,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[118,x]+F[90,x]
F[123,x] = -F[1,x]-F[124,x]-F[96,x]+F[47,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x,1]
F[126,x,k[0]] = (F[24,x,k[0]]*k[0]-F[24,x,1])/(-1+k[0])
F[127,x] = F[12,x]*F[83,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{13}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{0}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = \frac{F_{9}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{9}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = -F_{1}\! \left(x \right)+F_{0}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = y x
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{35}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{36}\! \left(x \right)+F_{10}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{42}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{46}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)+F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{63}\! \left(x \right) = 0
F_{64}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{6}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{3}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{81}\! \left(x \right) = -F_{0}\! \left(x \right)-F_{127}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{1}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{59}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{63}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{87}\! \left(x \right)+F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{84}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{85}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{89}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)+F_{59}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{63}\! \left(x \right)+F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{90}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{109}\! \left(x \right)-F_{123}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{116}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{86}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{87}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{87}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{89}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{90}\! \left(x \right)
F_{118}\! \left(x \right) = 2 F_{63}\! \left(x \right)+F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{113}\! \left(x \right)+F_{118}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)+F_{90}\! \left(x \right)
F_{123}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{124}\! \left(x \right)-F_{96}\! \left(x \right)+F_{47}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x , 1\right)
F_{126}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_71(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_13(x) + F_6(x))
Eq(F_6(x), F_0(x) + F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x)/F_12(x))
Eq(F_9(x), -F_0(x) + F_10(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_0(x) - F_1(x))
Eq(F_12(x), x)
Eq(F_13(x), F_12(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x)/F_12(x))
Eq(F_16(x), -F_0(x) + F_10(x))
Eq(F_17(x), F_12(x)*F_18(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0) + F_69(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_68(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_67(x, k_0))
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0) + F_53(x, k_0))
Eq(F_23(x, k_0), F_12(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_32(x, k_0) + F_52(x, k_0))
Eq(F_25(x, k_0), F_12(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_12(x)*F_28(x, k_0))
Eq(F_28(x, k_0), (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_30(x, k_0) + F_8(x))
Eq(F_30(x, k_0), F_19(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x) + F_51(x, k_0))
Eq(F_34(x), F_35(x)/F_12(x))
Eq(F_35(x), -F_1(x) + F_10(x) - F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_1(x) + F_38(x) + F_40(x) + F_42(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_33(x, 1))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_26(x, 1))
Eq(F_42(x), -F_1(x) + F_43(x) - F_46(x))
Eq(F_43(x), F_1(x) + F_44(x) + F_45(x))
Eq(F_44(x), F_12(x)*F_37(x))
Eq(F_45(x), F_12(x)*F_34(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_48(x) + F_49(x) + F_50(x))
Eq(F_48(x), F_12(x)*F_41(x))
Eq(F_49(x), F_12(x)*F_39(x))
Eq(F_50(x), F_12(x)*F_47(x))
Eq(F_51(x, k_0), F_20(x, k_0)*F_31(x, k_0))
Eq(F_52(x, k_0), F_24(x, k_0)*F_31(x, k_0))
Eq(F_53(x, k_0), F_31(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_58(x, k_0))
Eq(F_55(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_31(x, k_0)*F_55(x, k_0))
Eq(F_58(x, k_0), F_59(x) + F_62(x, k_0))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_1(x) + F_59(x))
Eq(F_62(x, k_0), F_63(x) + F_64(x, k_0) + F_66(x, k_0))
Eq(F_63(x), 0)
Eq(F_64(x, k_0), F_12(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_56(x, k_0) + F_62(x, k_0))
Eq(F_66(x, k_0), F_31(x, k_0)*F_58(x, k_0))
Eq(F_67(x, k_0), F_12(x)*F_20(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_19(x, k_0))
Eq(F_69(x, k_0), F_12(x)*F_70(x, k_0))
Eq(F_70(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_6(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_77(x)/F_12(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), -F_0(x) + F_3(x))
Eq(F_79(x), F_80(x) - F_82(x))
Eq(F_80(x), F_81(x)/F_12(x))
Eq(F_81(x), -F_0(x) - F_127(x) + F_82(x))
Eq(F_82(x), F_83(x) + F_94(x))
Eq(F_83(x), F_1(x) + F_42(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_1(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_86(x))
Eq(F_89(x), F_59(x) + F_90(x))
Eq(F_90(x), F_63(x) + F_91(x) + F_93(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_87(x) + F_90(x))
Eq(F_93(x), F_12(x)*F_89(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_1(x) + F_107(x) + F_84(x) + F_96(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_85(x) + F_98(x))
Eq(F_98(x), F_89(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_100(x) + F_59(x))
Eq(F_103(x), F_104(x) + F_106(x) + 2*F_63(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_103(x) + F_90(x))
Eq(F_106(x), F_12(x)*F_99(x))
Eq(F_107(x), -F_1(x) + F_108(x) - F_109(x) - F_123(x))
Eq(F_108(x), F_42(x)/F_12(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_116(x))
Eq(F_111(x), F_112(x) + F_86(x))
Eq(F_112(x), F_113(x) + F_87(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_113(x) + F_87(x))
Eq(F_116(x), F_117(x) + F_89(x))
Eq(F_117(x), F_118(x) + F_90(x))
Eq(F_118(x), F_119(x) + F_121(x) + 2*F_63(x))
Eq(F_119(x), F_12(x)*F_120(x))
Eq(F_120(x), F_113(x) + F_118(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_118(x) + F_90(x))
Eq(F_123(x), -F_1(x) - F_124(x) + F_47(x) - F_96(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x, 1))
Eq(F_126(x, k_0), (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Eq(F_127(x), F_12(x)*F_83(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, 3, 5, 0, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [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, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "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": [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, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "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": "ReverseRule"}, {"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], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [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, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[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": [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, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 2], [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, 2], [1, 2], [1, 3], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [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, 3], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 5, 0, 4], "pos": [[1, 2], [1, 2], [1, 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