0123_1230
Counting sequence:
1, 1, 2, 6, 22, 89, 376, 1611, 6901, 29375, 123996, 518971, 2155145, 8888348, 36442184, 148669894, 603984658, 2445184835, 9870338447, 39746337616, 159728191141, 640811439917, 2567220813272, 10272592695691, 41064215020977, 164014588869574, 654627778362521, 2611244306191009, 10410752330836178, 41488934932279847, 165282459721996836, 658248561748273483, 2620851691625578237, 10432826819825090991, 41522516290362880512, 165234364708277435479, 657450776083197978601, 2615663280732777158770, 10405534993176160076087, 41392162782555792965451, 164645224264563040441906, 654881673626341268435477, 2604737000636637316464005, 10359918021358557165849838, 41204408562921519129218269, 163881168001293611438898809, 651801107159979950099489168, 2592412743240857909525660011, 10310939633138102048129914081, 41010886123944941692371108710, 163120451126517767285225917601, 648824683489248133234989708121, 2580816711545979849228267523282, 10265942176919663894780847699401, 40836939286109386513901840302517, 162450487584056336131412925614614, 646253571023102478661883527947421, 2570984969624483862239418637943261, 10228482911282737475780685466525226, 40694751400111958272549708420550425, 161912875114463845863645780370860721, 644229251040228539963181413910644696, 2563396429864811088377233030909085600, 10200173384445229043980372293524835718, 40589705464719788405325885334912936354, 161525427793604720318052528631194468419, 642809977817262290148466216626316573703, 2558238644947887569570615381083694674840, 10181604878566777232577993074993218073317, 40523611324938751596272951824973033950661, 161293446281910468292824752324634815211116, 642010191663709897206063155476230057804487, 2555545817981787395080265402245626778175665, 10172832262741280295230939615168798264013278, 40496403970925084777070132463566301942008929, 161215685156473473701130209671627582653403849, 641821507302992465519023868478600049858363378, 2555272691139710245935419852580767590897190885, 10173634334642007583312880899244263167075742147, 40507061540733244655718215285830015629413996976, 161287592168254531483126397973870796607266536061, 642224150929391373710961167005066877320512501377, 2557334948896332123816533907143792228147468981910, 10183656616447965798432704722029180077570917767733, 40554110187311640187938075996872951613480520661249, 161503093751047790567342864279607009594550974055154, 643193276057749869538692151373905191576886067545673, 2561631561215738511996442440414100457531846130631625, 10202490396991333047810808167260493822348083137231682, 40635903671649209015853921996963276742559925932348321, 161855583800632480782039626101301347045566837894984881, 644702459142667772719277656944262719452222950071673722, 2568057135730866982932526969027757172809676093742013485, 10229716352708032883847375408876485813562501364666817233, 40750777288036931239224949258112569431315347250819236864, 162338466314647503673592609600423776892300679847011772459, 646725610379535216823893553100530765951057586723103102913, 2576508637065612609540302087589517935213394227840318635750, 10264928137913892604935964853908794276586676290509390589457, 40897130527552763448749602898825168479823831281624733378281, 162945444409728355006053576975749144669559414717231227823826
Generating function in Maple syntax:
1/8*((-13*x^4+50*x^3-48*x^2+17*x-2)*(1-4*x)^(1/2)-20*x^5+77*x^4-122*x^3+78*x^2-21*x+2)/(x^2-3*x+1)/(x-1/4)/x^3
Generating function in latex syntax:
\frac{\left(-13 x^{4}+50 x^{3}-48 x^{2}+17 x -2\right) \sqrt{1-4 x}-20 x^{5}+77 x^{4}-122 x^{3}+78 x^{2}-21 x +2}{8 \left(x^{2}-3 x +1\right) \left(x -\frac{1}{4}\right) x^{3}}
Generating function in sympy syntax:
(-5*x**5/2 + 77*x**4/8 - 61*x**3/4 + 39*x**2/4 - 21*x/8 + sqrt(1 - 4*x)*(-13*x**4 + 50*x**3 - 48*x**2 + 17*x - 2)/8 + 1/4)/(x**3*(x - 1/4)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
x^3*(4*x-1)*(x^2-3*x+1)^2*F(x)^2+(4*x-1)*(x^2-3*x+1)*(5*x^4-18*x^3+26*x^2-13*x+2)*F(x)+25*x^6-144*x^5+304*x^4-275*x^3+120*x^2-25*x+2 = 0
Implicit equation for the generating function in latex syntax:
x^{3} \left(4 x -1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)^{2}+\left(4 x -1\right) \left(x^{2}-3 x +1\right) \left(5 x^{4}-18 x^{3}+26 x^{2}-13 x +2\right) F \! \left(x \right)+25 x^{6}-144 x^{5}+304 x^{4}-275 x^{3}+120 x^{2}-25 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 89
a(6) = 376
a(n+7) = 13*(3+2*n)/(10+n)*a(n)-1/2*(5292+1055*n)/(10+n)*a(3+n)-3/2*(320+123*n)/(10+n)*a(n+1)+1/2*(3512+933*n)/(10+n)*a(n+2)+1/2*(3862+615*n)/(10+n)*a(n+4)-1/2*(1454+193*n)/(10+n)*a(n+5)+1/2*(272+31*n)/(10+n)*a(n+6), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 89
a \! \left(6\right) = 376
a \! \left(n +7\right) = \frac{13 \left(3+2 n \right) a \! \left(n \right)}{10+n}-\frac{\left(5292+1055 n \right) a \! \left(3+n \right)}{2 \left(10+n \right)}-\frac{3 \left(320+123 n \right) a \! \left(n +1\right)}{2 \left(10+n \right)}+\frac{\left(3512+933 n \right) a \! \left(n +2\right)}{20+2 n}+\frac{\left(3862+615 n \right) a \! \left(n +4\right)}{20+2 n}-\frac{\left(1454+193 n \right) a \! \left(n +5\right)}{2 \left(10+n \right)}+\frac{\left(272+31 n \right) a \! \left(n +6\right)}{20+2 n}, \quad n \geq 7
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/32/
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[16,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[5,x]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[8,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[14,x] = x
F[15,x,k[0]] = k[0]*x
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[107,x]+F[19,x]+F[5,x]+F[76,x]
F[19,x] = F[14,x]*F[20,x]
F[20,x] = F[21,x]+F[40,x]
F[21,x] = 1/F[14,x]*F[22,x]
F[22,x] = -F[24,x]-F[5,x]+F[23,x]
F[23,x] = 1/F[14,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[39,x]
F[26,x] = 0
F[27,x] = F[14,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[26,x]+F[30,x,k[0]]+F[32,x,k[0]]+F[33,x,k[0]]
F[30,x,k[0]] = F[14,x]*F[31,x,k[0]]
F[31,x,k[0]] = 1/(-1+k[0])*(F[29,x,k[0]]*k[0]-F[29,x,1])
F[32,x,k[0]] = F[15,x,k[0]]*F[29,x,k[0]]
F[33,x,k[0]] = F[14,x]*F[34,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[35,x,k[0]]+F[38,x,k[0]]
F[35,x,k[0]] = F[14,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[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[38,x,k[0]] = F[15,x,k[0]]*F[34,x,k[0]]
F[39,x] = F[14,x]*F[7,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]+F[48,x]
F[42,x] = F[43,x,1]
F[44,x,k[0]] = F[14,x]*F[43,x,k[0]]
F[45,x,k[0]] = F[29,x,k[0]]+F[44,x,k[0]]
F[45,x,k[0]] = F[29,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[14,x]*F[47,x,k[0]]
F[47,x,k[0]] = 1/(-1+k[0])*(F[45,x,k[0]]*k[0]-F[45,x,1])
F[48,x] = F[14,x]*F[49,x]*F[73,x]
F[49,x] = F[50,x,1]
F[51,x,k[0]] = F[50,x,k[0]]+F[70,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[67,x,k[0]]+F[69,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[53,x,k[0]]+F[60,x,k[0]]+F[61,x,k[0]]
F[53,x,k[0]] = F[14,x]*F[54,x,k[0]]
F[54,x,k[0]] = 1/(-1+k[0])*(F[55,x,k[0]]*k[0]-F[55,x,1])
F[55,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]
F[56,x,k[0]] = F[29,x,k[0]]+F[8,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = (F[59,x,k[0]]-F[59,x,1])/(-1+k[0])
F[59,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[60,x,k[0]] = F[15,x,k[0]]*F[52,x,k[0]]
F[61,x,k[0]] = F[14,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[61,x,k[0]]+F[63,x,k[0]]+F[66,x,k[0]]
F[63,x,k[0]] = F[14,x]*F[64,x,k[0]]
F[64,x,k[0]] = 1/(-1+k[0])*(F[65,x,k[0]]*k[0]-F[65,x,1])
F[65,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[66,x,k[0]] = F[15,x,k[0]]*F[62,x,k[0]]
F[67,x,k[0]] = F[14,x]*F[68,x,k[0]]
F[68,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[69,x,k[0]] = F[14,x]*F[70,x,k[0]]
F[70,x,k[0]] = F[34,x,k[0]]+F[69,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[14,x]*F[72,x,k[0]]
F[72,x,k[0]] = 1/(-1+k[0])*(F[70,x,k[0]]*k[0]-F[70,x,1])
F[73,x] = F[1,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[14,x]*F[73,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = F[18,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[80,x]
F[80,x] = F[81,x,1]
F[81,x,k[0]] = (F[82,x,k[0]]*k[0]-F[82,x,1])/(-1+k[0])
F[83,x,k[0]] = F[15,x,k[0]]*F[82,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[85,x,k[0]] = F[101,x]+F[84,x,k[0]]
F[85,x,k[0]] = F[100,x,k[0]]+F[73,x]+F[86,x,k[0]]+F[98,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[14,x]*F[88,x,k[0]]
F[88,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[89,x,k[0]] = F[90,x,k[0]]+F[92,x,k[0]]
F[91,x,k[0]] = F[14,x]*F[90,x,k[0]]
F[11,x,k[0]] = F[8,x,k[0]]+F[91,x,k[0]]
F[92,x,k[0]] = F[73,x]*F[93,x,k[0]]
F[94,x,k[0]] = F[8,x,k[0]]+F[93,x,k[0]]
F[94,x,k[0]] = F[73,x]+F[95,x,k[0]]+F[97,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[14,x]*F[89,x,k[0]]
F[97,x,k[0]] = F[15,x,k[0]]*F[94,x,k[0]]
F[98,x,k[0]] = F[14,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[85,x,k[0]]*k[0]-F[85,x,1])
F[100,x,k[0]] = F[15,x,k[0]]*F[85,x,k[0]]
F[101,x] = F[102,x]+F[105,x]+F[73,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[14,x]
F[104,x] = F[89,x,1]
F[105,x] = F[106,x]*F[14,x]
F[106,x] = F[85,x,1]
F[107,x] = F[106,x]*F[14,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_{16}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{107}\! \left(x \right)+F_{19}\! \left(x \right)+F_{5}\! \left(x \right)+F_{76}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{40}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{24}\! \left(x \right)-F_{5}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \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) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = -\frac{-y F_{45}\! \left(x , y\right)+F_{45}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{49}\! \left(x \right) F_{73}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{51}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = -\frac{-y F_{55}\! \left(x , y\right)+F_{55}\! \left(x , 1\right)}{-1+y}
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = -\frac{-F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{60}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = -\frac{-y F_{65}\! \left(x , y\right)+F_{65}\! \left(x , 1\right)}{-1+y}
F_{65}\! \left(x , y\right) = -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}
F_{66}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{62}\! \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) = -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}
F_{69}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}
F_{73}\! \left(x \right) = F_{1}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{18}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x , 1\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{82}\! \left(x , y\right)+F_{82}\! \left(x , 1\right)}{-1+y}
F_{83}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{101}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{73}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \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) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{73}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{73}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{105}\! \left(x \right)+F_{73}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{89}\! \left(x , 1\right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{14}\! \left(x \right)
F_{106}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{107}\! \left(x \right) = F_{106}\! \left(x \right) F_{14}\! \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_16(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_5(x) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_15(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_8(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x))
Eq(F_13(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_14(x), x)
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_107(x) + F_19(x) + F_5(x) + F_76(x))
Eq(F_19(x), F_14(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_40(x))
Eq(F_21(x), F_22(x)/F_14(x))
Eq(F_22(x), F_23(x) - F_24(x) - F_5(x))
Eq(F_23(x), F_24(x)/F_14(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_39(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_14(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_26(x) + F_30(x, k_0) + F_32(x, k_0) + F_33(x, k_0))
Eq(F_30(x, k_0), F_14(x)*F_31(x, k_0))
Eq(F_31(x, k_0), (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_32(x, k_0), F_15(x, k_0)*F_29(x, k_0))
Eq(F_33(x, k_0), F_14(x)*F_34(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_33(x, k_0) + F_35(x, k_0) + F_38(x, k_0))
Eq(F_35(x, k_0), F_14(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), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_38(x, k_0), F_15(x, k_0)*F_34(x, k_0))
Eq(F_39(x), F_14(x)*F_7(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x) + F_48(x))
Eq(F_42(x), F_43(x, 1))
Eq(F_44(x, k_0), F_14(x)*F_43(x, k_0))
Eq(F_45(x, k_0), F_29(x, k_0) + F_44(x, k_0))
Eq(F_45(x, k_0), F_29(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_14(x)*F_47(x, k_0))
Eq(F_47(x, k_0), (k_0*F_45(x, k_0) - F_45(x, 1))/(k_0 - 1))
Eq(F_48(x), F_14(x)*F_49(x)*F_73(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_51(x, k_0), F_50(x, k_0) + F_70(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_67(x, k_0) + F_69(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_33(x, k_0) + F_53(x, k_0) + F_60(x, k_0) + F_61(x, k_0))
Eq(F_53(x, k_0), F_14(x)*F_54(x, k_0))
Eq(F_54(x, k_0), (k_0*F_55(x, k_0) - F_55(x, 1))/(k_0 - 1))
Eq(F_55(x, k_0), F_56(x, k_0) + F_57(x, k_0))
Eq(F_56(x, k_0), F_29(x, k_0) + F_8(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), -F_59(x, k_0) + (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_59(x, k_0), -F_9(x, 1) + (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_60(x, k_0), F_15(x, k_0)*F_52(x, k_0))
Eq(F_61(x, k_0), F_14(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_1(x) + F_33(x, k_0) + F_61(x, k_0) + F_63(x, k_0) + F_66(x, k_0))
Eq(F_63(x, k_0), F_14(x)*F_64(x, k_0))
Eq(F_64(x, k_0), (k_0*F_65(x, k_0) - F_65(x, 1))/(k_0 - 1))
Eq(F_65(x, k_0), (-k_0*F_37(x, k_0) + F_37(x, 1))/(1 - k_0))
Eq(F_66(x, k_0), F_15(x, k_0)*F_62(x, k_0))
Eq(F_67(x, k_0), F_14(x)*F_68(x, k_0))
Eq(F_68(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_69(x, k_0), F_14(x)*F_70(x, k_0))
Eq(F_70(x, k_0), F_34(x, k_0) + F_69(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_14(x)*F_72(x, k_0))
Eq(F_72(x, k_0), (k_0*F_70(x, k_0) - F_70(x, 1))/(k_0 - 1))
Eq(F_73(x), F_1(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_14(x)*F_73(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_18(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_80(x))
Eq(F_80(x), F_81(x, 1))
Eq(F_81(x, k_0), (-k_0*F_82(x, k_0) + F_82(x, 1))/(1 - k_0))
Eq(F_83(x, k_0), F_15(x, k_0)*F_82(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_85(x, k_0), F_101(x) + F_84(x, k_0))
Eq(F_85(x, k_0), F_100(x, k_0) + F_73(x) + F_86(x, k_0) + F_98(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_14(x)*F_88(x, k_0))
Eq(F_88(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_89(x, k_0), F_90(x, k_0) + F_92(x, k_0))
Eq(F_91(x, k_0), F_14(x)*F_90(x, k_0))
Eq(F_11(x, k_0), F_8(x, k_0) + F_91(x, k_0))
Eq(F_92(x, k_0), F_73(x)*F_93(x, k_0))
Eq(F_94(x, k_0), F_8(x, k_0) + F_93(x, k_0))
Eq(F_94(x, k_0), F_73(x) + F_95(x, k_0) + F_97(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_14(x)*F_89(x, k_0))
Eq(F_97(x, k_0), F_15(x, k_0)*F_94(x, k_0))
Eq(F_98(x, k_0), F_14(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_85(x, k_0) - F_85(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_15(x, k_0)*F_85(x, k_0))
Eq(F_101(x), F_102(x) + F_105(x) + F_73(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_14(x))
Eq(F_104(x), F_89(x, 1))
Eq(F_105(x), F_106(x)*F_14(x))
Eq(F_106(x), F_85(x, 1))
Eq(F_107(x), F_106(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[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": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [1, 2]], [[2, 1]]], 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[0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 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1, 2, 3], "pos": [[0, 0], [0, 1], [1, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[2, 1]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "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"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 2, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/33/
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[22,x]*F[4,x]
F[4,x] = F[23,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[5,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[22,x]
F[10,x] = 1/F[22,x]*F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x,1]
F[14,x,k[0]] = F[13,x,k[0]]+F[5,x]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[14,x,k[0]]*k[0]-F[14,x,1])/(-1+k[0])
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[122,x]+F[26,x]
F[26,x] = F[27,x]+F[37,x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = (F[29,x,k[0]]*k[0]-F[29,x,1])/(-1+k[0])
F[29,x,k[0]] = F[1,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[18,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0],1]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[33,x,k[0],k[1]] = F[1,x]+F[34,x,k[0],k[1]]+F[36,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[18,x,k[0]]*F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = (F[32,x,k[0],1]*k[0]-F[32,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[18,x,k[1]]*F[33,x,k[0],k[1]]
F[37,x] = -F[63,x]+F[38,x]
F[38,x] = 1/F[22,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[22,x]*F[42,x]
F[42,x] = F[43,x]+F[61,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[45,x,k[0]]+F[54,x,k[0]]
F[45,x,k[0]] = F[46,x]+F[49,x,k[0]]
F[46,x] = F[47,x]
F[47,x] = F[22,x]*F[48,x]
F[48,x] = F[1,x]+F[46,x]
F[49,x,k[0]] = F[50,x]+F[51,x,k[0]]+F[53,x,k[0]]
F[50,x] = 0
F[51,x,k[0]] = F[22,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[16,x,k[0]]+F[49,x,k[0]]
F[53,x,k[0]] = F[18,x,k[0]]*F[45,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[22,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[59,x,k[0]]
F[57,x,k[0]] = F[15,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = (F[44,x,k[0]]*k[0]-F[44,x,1])/(-1+k[0])
F[59,x,k[0]] = F[45,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[61,x] = F[46,x]*F[62,x]
F[62,x] = F[21,x,1]
F[63,x] = F[120,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[66,x]
F[66,x] = F[67,x]+F[73,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = 1/(-1+k[0])*(F[69,x,k[0]]*k[0]-F[69,x,1])
F[69,x,k[0]] = F[15,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[72,x,k[0]]
F[72,x,k[0]] = 1/(-1+k[0])*(F[69,x,k[0]]*k[0]-F[69,x,1])
F[73,x] = 1/F[46,x]*F[74,x]
F[74,x] = -F[116,x]+F[75,x]
F[75,x] = -F[107,x]+F[76,x]
F[76,x] = 1/F[22,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = -F[106,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[22,x]*F[81,x]
F[81,x] = 1/F[46,x]*F[82,x]
F[82,x] = -F[105,x]+F[83,x]
F[83,x] = F[84,x,1]
F[84,x,k[0]] = F[102,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[88,x,k[0]]
F[86,x,k[0]] = F[69,x,k[0]]*F[87,x]
F[87,x] = F[6,x]
F[88,x,k[0]] = F[46,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]+F[95,x,k[0]]
F[90,x,k[0]] = F[46,x]+F[91,x,k[0]]
F[91,x,k[0]] = F[50,x]+F[92,x,k[0]]+F[93,x,k[0]]
F[92,x,k[0]] = F[18,x,k[0]]*F[90,x,k[0]]
F[93,x,k[0]] = F[22,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[16,x,k[0]]+F[91,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[22,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[100,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[15,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[90,x,k[0]]
F[101,x,k[0]] = 1/(-1+k[0])*(F[68,x,k[0]]*k[0]-F[68,x,1])
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[22,x]
F[104,x,k[0]] = 1/(-1+k[0])*(F[84,x,k[0]]*k[0]-F[84,x,1])
F[105,x] = F[10,x]*F[87,x]
F[106,x] = F[46,x]^2
F[107,x] = F[108,x]*F[48,x]
F[108,x] = F[109,x]+F[79,x]
F[109,x] = F[110,x]*F[46,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[46,x]*F[48,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[22,x]*F[48,x]
F[114,x] = F[115,x]+F[73,x]
F[115,x] = F[110,x]*F[48,x]
F[116,x] = -F[119,x]+F[117,x]
F[117,x] = 1/F[22,x]*F[118,x]
F[118,x] = F[79,x]
F[119,x] = F[89,x,1]
F[120,x] = F[121,x]
F[121,x] = F[110,x]*F[46,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[22,x]
F[124,x] = F[125,x]+F[245,x]
F[125,x] = F[126,x]+F[137,x]
F[126,x] = F[127,x]+F[25,x]
F[127,x] = F[128,x]*F[46,x]
F[128,x] = 1/F[22,x]*F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[46,x]*F[48,x]
F[132,x] = F[133,x]+F[78,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[22,x]
F[135,x] = F[119,x]+F[136,x]
F[136,x] = F[46,x]*F[67,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[22,x]
F[139,x] = 1/F[22,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[239,x]+F[142,x]
F[142,x] = F[143,x]+F[220,x]
F[143,x] = F[144,x]+F[150,x]
F[144,x] = 1/F[22,x]/F[48,x]*F[145,x]
F[145,x] = F[146,x]
F[146,x] = -F[149,x]+F[147,x]
F[147,x] = 1/F[22,x]*F[148,x]
F[148,x] = F[40,x]
F[149,x] = F[48,x]*F[87,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]+F[164,x]
F[152,x] = 1/F[22,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = -F[43,x]+F[155,x]
F[155,x] = 1/F[22,x]*F[156,x]
F[156,x] = F[157,x]
F[157,x] = -F[161,x]+F[158,x]
F[158,x] = -F[159,x]+F[26,x]
F[159,x] = F[160,x]+F[48,x]
F[160,x] = F[40,x]+F[87,x]
F[161,x] = F[162,x,1]
F[162,x,k[0]] = (F[163,x,k[0]]-F[163,x,1])/(-1+k[0])
F[163,x,k[0]] = F[30,x,k[0]]
F[164,x] = F[165,x]*F[48,x]
F[165,x] = F[157,x]+F[166,x]
F[166,x] = -F[217,x]+F[167,x]
F[167,x] = F[168,x]+F[179,x]
F[168,x] = F[169,x]*F[46,x]
F[169,x] = F[170,x]
F[170,x] = F[171,x]*F[22,x]
F[171,x] = 1/F[87,x]*F[172,x]
F[172,x] = -F[178,x]+F[173,x]
F[173,x] = F[174,x]+F[177,x]
F[174,x] = F[175,x]*F[87,x]
F[175,x] = 1/F[22,x]*F[176,x]
F[176,x] = F[110,x]
F[177,x] = F[155,x]*F[46,x]
F[178,x] = F[105,x]+F[177,x]
F[179,x] = -F[216,x]+F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]*F[22,x]*F[48,x]
F[182,x] = -F[212,x]+F[183,x]
F[183,x] = 1/F[22,x]/F[48,x]*F[184,x]
F[184,x] = F[185,x]
F[185,x] = F[186,x]+F[188,x]
F[186,x] = F[187,x]
F[187,x] = F[48,x]^3*F[46,x]
F[188,x] = F[189,x]
F[189,x] = F[190,x]*F[22,x]*F[48,x]
F[190,x] = F[191,x]+F[195,x]
F[191,x] = F[192,x]*F[48,x]
F[192,x] = F[112,x]+F[193,x]
F[193,x] = F[194,x]
F[194,x] = F[22,x]*F[48,x]*F[67,x]
F[195,x] = F[196,x]+F[198,x]
F[196,x] = -F[197,x]+F[175,x]
F[197,x] = F[110,x]+F[7,x]
F[198,x] = -F[127,x]+F[199,x]
F[199,x] = F[200,x]
F[200,x] = F[201,x]*F[22,x]
F[201,x] = 1/F[22,x]*F[202,x]
F[202,x] = F[203,x]
F[203,x] = -F[209,x]+F[204,x]
F[204,x] = 1/F[22,x]*F[205,x]
F[205,x] = F[206,x]
F[206,x] = -F[110,x]+F[207,x]
F[207,x] = 1/F[22,x]*F[208,x]
F[208,x] = F[79,x]
F[209,x] = -F[125,x]+F[210,x]
F[210,x] = 1/F[22,x]*F[211,x]
F[211,x] = F[122,x]
F[212,x] = F[213,x,1]
F[213,x,k[0]] = (F[214,x,k[0]]*k[0]-F[214,x,1])/(-1+k[0])
F[215,x,k[0]] = F[18,x,k[0]]*F[214,x,k[0]]
F[215,x,k[0]] = F[13,x,k[0]]
F[216,x] = F[169,x]*F[48,x]
F[217,x] = F[218,x]*F[46,x]
F[218,x] = F[219,x]
F[219,x] = F[182,x]*F[22,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[46,x]
F[222,x] = F[223,x]+F[237,x]
F[223,x] = 1/F[22,x]*F[224,x]
F[224,x] = F[225,x]
F[225,x] = -F[235,x]+F[226,x]
F[226,x] = 1/F[46,x]*F[227,x]
F[227,x] = -F[231,x]+F[228,x]
F[228,x] = 1/F[22,x]*F[229,x]
F[229,x] = F[230,x]
F[230,x] = -F[106,x]+F[157,x]
F[231,x] = F[232,x]+F[234,x]
F[232,x] = F[233,x]
F[233,x] = F[152,x]*F[22,x]
F[234,x] = F[157,x]*F[48,x]
F[235,x] = F[236,x]*F[48,x]
F[236,x] = F[169,x]+F[8,x]
F[237,x] = F[238,x]*F[48,x]
F[238,x] = F[218,x]+F[236,x]
F[239,x] = 1/F[22,x]*F[240,x]
F[240,x] = F[241,x]
F[241,x] = F[242,x]+F[244,x]
F[242,x] = F[243,x,1]
F[243,x,k[0]] = -k[0]*(F[163,x,1]-F[163,x,k[0]])/(-1+k[0])
F[244,x] = F[230,x]+F[40,x]
F[245,x] = F[246,x]+F[256,x]
F[246,x] = F[247,x]
F[247,x] = 1/F[22,x]*F[248,x]
F[248,x] = F[249,x]
F[249,x] = -F[130,x]+F[250,x]
F[250,x] = -F[253,x]+F[251,x]
F[251,x] = 1/F[22,x]/F[48,x]*F[252,x]
F[252,x] = F[132,x]
F[253,x] = F[225,x]+F[254,x]
F[254,x] = F[255,x]
F[255,x] = F[238,x]*F[46,x]
F[256,x] = F[257,x]*F[46,x]
F[257,x] = F[247,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{22}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{122}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\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_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y , 1\right)
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , y z \right)
F_{33}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = F_{18}\! \left(x , y\right) F_{35}\! \left(x , y , z\right)
F_{35}\! \left(x , y , z\right) = \frac{y F_{32}\! \left(x , y , 1\right)-z F_{32}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{36}\! \left(x , y , z\right) = F_{18}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)
F_{37}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{61}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{50}\! \left(x \right) = 0
F_{51}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{61}\! \left(x \right) = F_{46}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{63}\! \left(x \right) = F_{120}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = -\frac{-y F_{69}\! \left(x , y\right)+F_{69}\! \left(x , 1\right)}{-1+y}
F_{69}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = -\frac{-y F_{69}\! \left(x , y\right)+F_{69}\! \left(x , 1\right)}{-1+y}
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{46}\! \left(x \right)}
F_{74}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{22}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{46}\! \left(x \right)}
F_{82}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{84}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{6}\! \left(x \right)
F_{88}\! \left(x , y\right) = F_{46}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = -\frac{-y F_{68}\! \left(x , y\right)+F_{68}\! \left(x , 1\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{104}\! \left(x , y\right) = -\frac{-y F_{84}\! \left(x , y\right)+F_{84}\! \left(x , 1\right)}{-1+y}
F_{105}\! \left(x \right) = F_{10}\! \left(x \right) F_{87}\! \left(x \right)
F_{106}\! \left(x \right) = F_{46} \left(x \right)^{2}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{48}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{79}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{46}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{46}\! \left(x \right) F_{48}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{73}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right) F_{48}\! \left(x \right)
F_{116}\! \left(x \right) = -F_{119}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{79}\! \left(x \right)
F_{119}\! \left(x \right) = F_{89}\! \left(x , 1\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{110}\! \left(x \right) F_{46}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{22}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{245}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{137}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{25}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{46}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{46}\! \left(x \right) F_{48}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{78}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{22}\! \left(x \right)
F_{135}\! \left(x \right) = F_{119}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{46}\! \left(x \right) F_{67}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{22}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{239}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{220}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{150}\! \left(x \right)
F_{144}\! \left(x \right) = \frac{F_{145}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = \frac{F_{148}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{148}\! \left(x \right) = F_{40}\! \left(x \right)
F_{149}\! \left(x \right) = F_{48}\! \left(x \right) F_{87}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{164}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = \frac{F_{156}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = -F_{161}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{159}\! \left(x \right)+F_{26}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{48}\! \left(x \right)
F_{160}\! \left(x \right) = F_{40}\! \left(x \right)+F_{87}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x , 1\right)
F_{162}\! \left(x , y\right) = -\frac{F_{163}\! \left(x , 1\right)-F_{163}\! \left(x , y\right)}{-1+y}
F_{163}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{48}\! \left(x \right)
F_{165}\! \left(x \right) = F_{157}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = -F_{217}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{179}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{46}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{22}\! \left(x \right)
F_{171}\! \left(x \right) = \frac{F_{172}\! \left(x \right)}{F_{87}\! \left(x \right)}
F_{172}\! \left(x \right) = -F_{178}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{177}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{87}\! \left(x \right)
F_{175}\! \left(x \right) = \frac{F_{176}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{176}\! \left(x \right) = F_{110}\! \left(x \right)
F_{177}\! \left(x \right) = F_{155}\! \left(x \right) F_{46}\! \left(x \right)
F_{178}\! \left(x \right) = F_{105}\! \left(x \right)+F_{177}\! \left(x \right)
F_{179}\! \left(x \right) = -F_{216}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)
F_{182}\! \left(x \right) = -F_{212}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = \frac{F_{184}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{188}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{48} \left(x \right)^{3} F_{46}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{195}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{48}\! \left(x \right)
F_{192}\! \left(x \right) = F_{112}\! \left(x \right)+F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{22}\! \left(x \right) F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{198}\! \left(x \right)
F_{196}\! \left(x \right) = -F_{197}\! \left(x \right)+F_{175}\! \left(x \right)
F_{197}\! \left(x \right) = F_{110}\! \left(x \right)+F_{7}\! \left(x \right)
F_{198}\! \left(x \right) = -F_{127}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{22}\! \left(x \right)
F_{201}\! \left(x \right) = \frac{F_{202}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = -F_{209}\! \left(x \right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = \frac{F_{205}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = \frac{F_{208}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{208}\! \left(x \right) = F_{79}\! \left(x \right)
F_{209}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = \frac{F_{211}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{211}\! \left(x \right) = F_{122}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x , 1\right)
F_{213}\! \left(x , y\right) = -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}
F_{215}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{214}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{216}\! \left(x \right) = F_{169}\! \left(x \right) F_{48}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{46}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{182}\! \left(x \right) F_{22}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{46}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{237}\! \left(x \right)
F_{223}\! \left(x \right) = \frac{F_{224}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{235}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{46}\! \left(x \right)}
F_{227}\! \left(x \right) = -F_{231}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = \frac{F_{229}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{157}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)+F_{234}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{152}\! \left(x \right) F_{22}\! \left(x \right)
F_{234}\! \left(x \right) = F_{157}\! \left(x \right) F_{48}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right) F_{48}\! \left(x \right)
F_{236}\! \left(x \right) = F_{169}\! \left(x \right)+F_{8}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right) F_{48}\! \left(x \right)
F_{238}\! \left(x \right) = F_{218}\! \left(x \right)+F_{236}\! \left(x \right)
F_{239}\! \left(x \right) = \frac{F_{240}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x , 1\right)
F_{243}\! \left(x , y\right) = -\frac{y \left(F_{163}\! \left(x , 1\right)-F_{163}\! \left(x , y\right)\right)}{-1+y}
F_{244}\! \left(x \right) = F_{230}\! \left(x \right)+F_{40}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)+F_{256}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = \frac{F_{248}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = -F_{253}\! \left(x \right)+F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = \frac{F_{252}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}
F_{252}\! \left(x \right) = F_{132}\! \left(x \right)
F_{253}\! \left(x \right) = F_{225}\! \left(x \right)+F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{238}\! \left(x \right) F_{46}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right) F_{46}\! \left(x \right)
F_{257}\! \left(x \right) = F_{247}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_22(x)*F_4(x))
Eq(F_4(x), F_23(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_5(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_22(x))
Eq(F_10(x), F_11(x)/F_22(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_14(x, k_0), F_13(x, k_0) + F_5(x))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_15(x, k_0)*F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_122(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_37(x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), (-k_0*F_29(x, k_0) + F_29(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_1(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_18(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0, 1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_33(x, k_0, k_1), F_1(x) + F_34(x, k_0, k_1) + F_36(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_18(x, k_0)*F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_18(x, k_1)*F_33(x, k_0, k_1))
Eq(F_37(x), F_38(x) - F_63(x))
Eq(F_38(x), F_39(x)/F_22(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_22(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_61(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_45(x, k_0) + F_54(x, k_0))
Eq(F_45(x, k_0), F_46(x) + F_49(x, k_0))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_22(x)*F_48(x))
Eq(F_48(x), F_1(x) + F_46(x))
Eq(F_49(x, k_0), F_50(x) + F_51(x, k_0) + F_53(x, k_0))
Eq(F_50(x), 0)
Eq(F_51(x, k_0), F_22(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_16(x, k_0) + F_49(x, k_0))
Eq(F_53(x, k_0), F_18(x, k_0)*F_45(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_22(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_59(x, k_0))
Eq(F_57(x, k_0), F_15(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), (-k_0*F_44(x, k_0) + F_44(x, 1))/(1 - k_0))
Eq(F_59(x, k_0), F_45(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), (k_0*F_21(x, k_0) - F_21(x, 1))/(k_0 - 1))
Eq(F_61(x), F_46(x)*F_62(x))
Eq(F_62(x), F_21(x, 1))
Eq(F_63(x), F_120(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_73(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), (-k_0*F_69(x, k_0) + F_69(x, 1))/(1 - k_0))
Eq(F_69(x, k_0), F_15(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_15(x, k_0)*F_22(x)*F_72(x, k_0))
Eq(F_72(x, k_0), (k_0*F_69(x, k_0) - F_69(x, 1))/(k_0 - 1))
Eq(F_73(x), F_74(x)/F_46(x))
Eq(F_74(x), -F_116(x) + F_75(x))
Eq(F_75(x), -F_107(x) + F_76(x))
Eq(F_76(x), F_77(x)/F_22(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), -F_106(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_22(x)*F_81(x))
Eq(F_81(x), F_82(x)/F_46(x))
Eq(F_82(x), -F_105(x) + F_83(x))
Eq(F_83(x), F_84(x, 1))
Eq(F_84(x, k_0), F_102(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_88(x, k_0))
Eq(F_86(x, k_0), F_69(x, k_0)*F_87(x))
Eq(F_87(x), F_6(x))
Eq(F_88(x, k_0), F_46(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0) + F_95(x, k_0))
Eq(F_90(x, k_0), F_46(x) + F_91(x, k_0))
Eq(F_91(x, k_0), F_50(x) + F_92(x, k_0) + F_93(x, k_0))
Eq(F_92(x, k_0), F_18(x, k_0)*F_90(x, k_0))
Eq(F_93(x, k_0), F_22(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_16(x, k_0) + F_91(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_22(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_100(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_15(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_90(x, k_0))
Eq(F_101(x, k_0), (k_0*F_68(x, k_0) - F_68(x, 1))/(k_0 - 1))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_22(x))
Eq(F_104(x, k_0), (k_0*F_84(x, k_0) - F_84(x, 1))/(k_0 - 1))
Eq(F_105(x), F_10(x)*F_87(x))
Eq(F_106(x), F_46(x)**2)
Eq(F_107(x), F_108(x)*F_48(x))
Eq(F_108(x), F_109(x) + F_79(x))
Eq(F_109(x), F_110(x)*F_46(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_46(x)*F_48(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_22(x)*F_48(x))
Eq(F_114(x), F_115(x) + F_73(x))
Eq(F_115(x), F_110(x)*F_48(x))
Eq(F_116(x), F_117(x) - F_119(x))
Eq(F_117(x), F_118(x)/F_22(x))
Eq(F_118(x), F_79(x))
Eq(F_119(x), F_89(x, 1))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_110(x)*F_46(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_22(x))
Eq(F_124(x), F_125(x) + F_245(x))
Eq(F_125(x), F_126(x) + F_137(x))
Eq(F_126(x), F_127(x) + F_25(x))
Eq(F_127(x), F_128(x)*F_46(x))
Eq(F_128(x), F_129(x)/F_22(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_46(x)*F_48(x))
Eq(F_132(x), F_133(x) + F_78(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_22(x))
Eq(F_135(x), F_119(x) + F_136(x))
Eq(F_136(x), F_46(x)*F_67(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_22(x))
Eq(F_139(x), F_140(x)/F_22(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x) - F_239(x))
Eq(F_142(x), F_143(x) + F_220(x))
Eq(F_143(x), F_144(x) + F_150(x))
Eq(F_144(x), F_145(x)/(F_22(x)*F_48(x)))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x) - F_149(x))
Eq(F_147(x), F_148(x)/F_22(x))
Eq(F_148(x), F_40(x))
Eq(F_149(x), F_48(x)*F_87(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x) + F_164(x))
Eq(F_152(x), F_153(x)/F_22(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x) - F_43(x))
Eq(F_155(x), F_156(x)/F_22(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x) - F_161(x))
Eq(F_158(x), -F_159(x) + F_26(x))
Eq(F_159(x), F_160(x) + F_48(x))
Eq(F_160(x), F_40(x) + F_87(x))
Eq(F_161(x), F_162(x, 1))
Eq(F_162(x, k_0), -F_163(x, k_0) + (-k_0*F_163(x, k_0) + F_163(x, 1))/(1 - k_0))
Eq(F_163(x, k_0), F_30(x, k_0))
Eq(F_164(x), F_165(x)*F_48(x))
Eq(F_165(x), F_157(x) + F_166(x))
Eq(F_166(x), F_167(x) - F_217(x))
Eq(F_167(x), F_168(x) + F_179(x))
Eq(F_168(x), F_169(x)*F_46(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_171(x)*F_22(x))
Eq(F_171(x), F_172(x)/F_87(x))
Eq(F_172(x), F_173(x) - F_178(x))
Eq(F_173(x), F_174(x) + F_177(x))
Eq(F_174(x), F_175(x)*F_87(x))
Eq(F_175(x), F_176(x)/F_22(x))
Eq(F_176(x), F_110(x))
Eq(F_177(x), F_155(x)*F_46(x))
Eq(F_178(x), F_105(x) + F_177(x))
Eq(F_179(x), F_180(x) - F_216(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x)*F_22(x)*F_48(x))
Eq(F_182(x), F_183(x) - F_212(x))
Eq(F_183(x), F_184(x)/(F_22(x)*F_48(x)))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x) + F_188(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_46(x)*F_48(x)**3)
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)*F_22(x)*F_48(x))
Eq(F_190(x), F_191(x) + F_195(x))
Eq(F_191(x), F_192(x)*F_48(x))
Eq(F_192(x), F_112(x) + F_193(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_22(x)*F_48(x)*F_67(x))
Eq(F_195(x), F_196(x) + F_198(x))
Eq(F_196(x), F_175(x) - F_197(x))
Eq(F_197(x), F_110(x) + F_7(x))
Eq(F_198(x), -F_127(x) + F_199(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_201(x)*F_22(x))
Eq(F_201(x), F_202(x)/F_22(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x) - F_209(x))
Eq(F_204(x), F_205(x)/F_22(x))
Eq(F_205(x), F_206(x))
Eq(F_206(x), -F_110(x) + F_207(x))
Eq(F_207(x), F_208(x)/F_22(x))
Eq(F_208(x), F_79(x))
Eq(F_209(x), -F_125(x) + F_210(x))
Eq(F_210(x), F_211(x)/F_22(x))
Eq(F_211(x), F_122(x))
Eq(F_212(x), F_213(x, 1))
Eq(F_213(x, k_0), (-k_0*F_214(x, k_0) + F_214(x, 1))/(1 - k_0))
Eq(F_215(x, k_0), F_18(x, k_0)*F_214(x, k_0))
Eq(F_215(x, k_0), F_13(x, k_0))
Eq(F_216(x), F_169(x)*F_48(x))
Eq(F_217(x), F_218(x)*F_46(x))
Eq(F_218(x), F_219(x))
Eq(F_219(x), F_182(x)*F_22(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_46(x))
Eq(F_222(x), F_223(x) + F_237(x))
Eq(F_223(x), F_224(x)/F_22(x))
Eq(F_224(x), F_225(x))
Eq(F_225(x), F_226(x) - F_235(x))
Eq(F_226(x), F_227(x)/F_46(x))
Eq(F_227(x), F_228(x) - F_231(x))
Eq(F_228(x), F_229(x)/F_22(x))
Eq(F_229(x), F_230(x))
Eq(F_230(x), -F_106(x) + F_157(x))
Eq(F_231(x), F_232(x) + F_234(x))
Eq(F_232(x), F_233(x))
Eq(F_233(x), F_152(x)*F_22(x))
Eq(F_234(x), F_157(x)*F_48(x))
Eq(F_235(x), F_236(x)*F_48(x))
Eq(F_236(x), F_169(x) + F_8(x))
Eq(F_237(x), F_238(x)*F_48(x))
Eq(F_238(x), F_218(x) + F_236(x))
Eq(F_239(x), F_240(x)/F_22(x))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_242(x) + F_244(x))
Eq(F_242(x), F_243(x, 1))
Eq(F_243(x, k_0), -F_163(x, 1) + (-k_0*F_163(x, k_0) + F_163(x, 1))/(1 - k_0))
Eq(F_244(x), F_230(x) + F_40(x))
Eq(F_245(x), F_246(x) + F_256(x))
Eq(F_246(x), F_247(x))
Eq(F_247(x), F_248(x)/F_22(x))
Eq(F_248(x), F_249(x))
Eq(F_249(x), -F_130(x) + F_250(x))
Eq(F_250(x), F_251(x) - F_253(x))
Eq(F_251(x), F_252(x)/(F_22(x)*F_48(x)))
Eq(F_252(x), F_132(x))
Eq(F_253(x), F_225(x) + F_254(x))
Eq(F_254(x), F_255(x))
Eq(F_255(x), F_238(x)*F_46(x))
Eq(F_256(x), F_257(x)*F_46(x))
Eq(F_257(x), F_247(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [1, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 3], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 3], [2, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [2, 3], [2, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 2], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 2], [0, 3], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], 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"tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 0, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 3
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/34/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[229,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[216,x,k[0]]+F[218,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[21,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[143,x,k[0]]+F[89,x,k[0]]+F[9,x,k[0]]+F[91,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[14,x,k[0]]
F[11,x,k[0],k[1]] = 1/(-1+k[1])*(F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[47,x,k[1]]
F[13,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0],k[1]] = F[14,x,k[1]]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,k[1]]+F[31,x,k[0],k[1]]
F[17,x,k[0]] = F[18,x]+F[22,x,k[0]]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = x
F[22,x,k[0]] = F[23,x,k[0]]+F[26,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[14,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[1,x]+F[23,x,k[0]]
F[26,x,k[0]] = F[27,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[27,x] = 0
F[28,x,k[0]] = F[14,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[19,x]+F[26,x,k[0]]
F[30,x,k[0]] = F[21,x]*F[22,x,k[0]]
F[31,x,k[0],k[1]] = F[32,x,k[0]]+F[36,x,k[0],k[1]]
F[32,x,k[0]] = F[23,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[14,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[19,x]+F[33,x,k[0]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[37,x,k[0],k[1]] = F[27,x]+F[38,x,k[0],k[1]]+F[40,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[14,x,k[0]]*F[39,x,k[0],k[1]]
F[39,x,k[0],k[1]] = F[23,x,k[1]]+F[37,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[14,x,k[1]]*F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[23,x,k[0]]+F[37,x,k[0],k[1]]
F[42,x,k[0],k[1]] = 2*F[27,x]+F[43,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[14,x,k[0]]*F[44,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[26,x,k[1]]+F[42,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[14,x,k[1]]*F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[33,x,k[0]]+F[42,x,k[0],k[1]]
F[47,x,k[0]] = F[21,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[1,x]+F[49,x,k[0]]+F[69,x,k[0]]+F[72,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0],1]
F[50,x,k[0],k[1]] = F[14,x,k[0]]*F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[52,x,k[0],1,k[1]]
F[52,x,k[0],k[1],k[2]] = F[53,x,k[0]*k[1],k[1],k[2]]
F[53,x,k[0],k[1],k[2]] = F[1,x]+F[54,x,k[0],k[1],k[2]]+F[55,x,k[0],k[1],k[2]]+F[57,x,k[0],k[1],k[2]]
F[54,x,k[0],k[1],k[2]] = F[14,x,k[0]]*F[53,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = F[14,x,k[1]]*F[56,x,k[0],k[1],k[2]]
F[56,x,k[0],k[1],k[2]] = (-F[52,x,1,k[1],k[2]]*k[1]+F[52,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[57,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[58,x,k[0],k[1],k[2]]
F[58,x,k[0],k[1],k[2]] = F[59,x,k[1],k[2]]+F[60,x,k[0],k[1],k[2]]
F[59,x,k[0],k[1]] = F[25,x,k[1]]+F[41,x,k[0],k[1]]
F[60,x,k[0],k[1],k[2]] = F[41,x,k[0],k[2]]+F[61,x,k[0],k[1],k[2]]
F[61,x,k[0],k[1],k[2]] = F[62,x,k[0],k[1]]+F[65,x,k[0],k[1],k[2]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]
F[63,x,k[0],k[1]] = F[14,x,k[1]]*F[64,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[23,x,k[0]]+F[62,x,k[0],k[1]]
F[65,x,k[0],k[1],k[2]] = 2*F[27,x]+F[66,x,k[0],k[1],k[2]]+F[68,x,k[0],k[1],k[2]]
F[66,x,k[0],k[1],k[2]] = F[14,x,k[1]]*F[67,x,k[0],k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = F[37,x,k[0],k[2]]+F[65,x,k[0],k[1],k[2]]
F[68,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[61,x,k[0],k[1],k[2]]
F[69,x,k[0]] = F[70,x,k[0],1]
F[70,x,k[0],k[1]] = F[14,x,k[1]]*F[71,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[56,x,k[0],k[1],1]
F[72,x,k[0]] = F[21,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x]+F[80,x,k[0]]
F[74,x] = F[18,x]+F[75,x]
F[75,x] = F[19,x]+F[76,x]
F[76,x] = F[27,x]+F[77,x]+F[79,x]
F[77,x] = F[21,x]*F[78,x]
F[78,x] = F[19,x]+F[76,x]
F[79,x] = F[21,x]*F[75,x]
F[80,x,k[0]] = F[22,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[21,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[23,x,k[0]]+F[82,x,k[0]]
F[85,x,k[0]] = 2*F[27,x]+F[86,x,k[0]]+F[88,x,k[0]]
F[86,x,k[0]] = F[21,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[26,x,k[0]]+F[85,x,k[0]]
F[88,x,k[0]] = F[21,x]*F[81,x,k[0]]
F[89,x,k[0]] = F[21,x]*F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[91,x,k[0]] = F[14,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[1,x]+F[140,x,k[0]]+F[142,x,k[0]]+F[91,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[21,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[105,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[17,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[75,x]+F[97,x,k[0]]
F[97,x,k[0]] = F[101,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[14,x,k[0]]
F[100,x,k[0]] = F[19,x]+F[98,x,k[0]]
F[101,x,k[0]] = 2*F[27,x]+F[102,x,k[0]]+F[104,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[14,x,k[0]]
F[103,x,k[0]] = F[101,x,k[0]]+F[76,x]
F[104,x,k[0]] = F[21,x]*F[97,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[122,x,k[0]]
F[106,x,k[0]] = F[107,x]+F[111,x,k[0]]
F[107,x] = F[108,x]+F[19,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[21,x]
F[110,x] = F[108,x]+F[19,x]
F[111,x,k[0]] = F[112,x,k[0]]+F[117,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[115,x,k[0]]+F[27,x]
F[113,x,k[0]] = F[114,x,k[0]]*F[21,x]
F[114,x,k[0]] = F[112,x,k[0]]+F[23,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[14,x,k[0]]
F[116,x,k[0]] = F[112,x,k[0]]+F[19,x]
F[117,x,k[0]] = 2*F[27,x]+F[118,x,k[0]]+F[120,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[21,x]
F[119,x,k[0]] = F[117,x,k[0]]+F[26,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[14,x,k[0]]
F[121,x,k[0]] = F[108,x]+F[117,x,k[0]]
F[122,x,k[0]] = F[123,x]+F[129,x,k[0]]
F[123,x] = F[124,x]+F[76,x]
F[124,x] = 2*F[27,x]+F[125,x]+F[127,x]
F[125,x] = F[126,x]*F[21,x]
F[126,x] = F[124,x]+F[76,x]
F[127,x] = F[128,x]*F[21,x]
F[128,x] = F[108,x]+F[124,x]
F[129,x,k[0]] = F[130,x,k[0]]+F[135,x,k[0]]
F[130,x,k[0]] = 2*F[27,x]+F[131,x,k[0]]+F[133,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[21,x]
F[132,x,k[0]] = F[130,x,k[0]]+F[98,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[14,x,k[0]]
F[134,x,k[0]] = F[130,x,k[0]]+F[76,x]
F[135,x,k[0]] = 3*F[27,x]+F[136,x,k[0]]+F[138,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[21,x]
F[137,x,k[0]] = F[101,x,k[0]]+F[135,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[14,x,k[0]]
F[139,x,k[0]] = F[124,x]+F[135,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[21,x]
F[141,x,k[0]] = 1/(-1+k[0])*(F[92,x,k[0]]*k[0]-F[92,x,1])
F[142,x,k[0]] = F[21,x]*F[95,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]*F[21,x]
F[144,x,k[0]] = F[1,x]+F[145,x,k[0]]+F[146,x,k[0]]+F[182,x,k[0]]+F[49,x,k[0]]
F[145,x,k[0]] = F[144,x,k[0]]*F[21,x]
F[146,x,k[0]] = F[147,x,1,k[0]]
F[147,x,k[0],k[1]] = F[148,x,k[0],k[1]]*F[21,x]
F[148,x,k[0],k[1]] = (F[149,x,k[0],k[1]]*k[1]-F[149,x,k[0],1])/(-1+k[1])
F[149,x,k[0],k[1]] = F[1,x]+F[147,x,k[0],k[1]]+F[150,x,k[0],k[1]]+F[151,x,k[0],k[1]]+F[49,x,k[1]]
F[150,x,k[0],k[1]] = F[14,x,k[0]]*F[149,x,k[0],k[1]]
F[151,x,k[0],k[1]] = F[152,x,k[0],k[1]]*F[21,x]
F[152,x,k[0],k[1]] = F[153,x,k[0],k[1]]+F[73,x,k[1]]
F[153,x,k[0],k[1]] = F[154,x,k[0]]+F[161,x,k[0],k[1]]
F[154,x,k[0]] = F[155,x,k[0]]+F[22,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[26,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[159,x,k[0]]+F[27,x]+F[88,x,k[0]]
F[157,x,k[0]] = F[14,x,k[0]]*F[158,x,k[0]]
F[158,x,k[0]] = F[156,x,k[0]]+F[76,x]
F[159,x,k[0]] = F[160,x,k[0]]*F[21,x]
F[160,x,k[0]] = F[156,x,k[0]]+F[26,x,k[0]]
F[161,x,k[0],k[1]] = F[162,x,k[0],k[1]]+F[167,x,k[0],k[1]]
F[162,x,k[0],k[1]] = F[163,x,k[0],k[1]]+F[62,x,k[0],k[1]]
F[163,x,k[0],k[1]] = 2*F[27,x]+F[164,x,k[0],k[1]]+F[166,x,k[0],k[1]]
F[164,x,k[0],k[1]] = F[14,x,k[1]]*F[165,x,k[0],k[1]]
F[165,x,k[0],k[1]] = F[163,x,k[0],k[1]]+F[26,x,k[0]]
F[166,x,k[0],k[1]] = F[162,x,k[0],k[1]]*F[21,x]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[168,x,k[0],k[1]] = F[169,x,k[0],k[1]]
F[169,x,k[0],k[1]] = F[170,x,k[0],k[1]]*F[21,x]
F[170,x,k[0],k[1]] = F[168,x,k[0],k[1]]+F[62,x,k[0],k[1]]
F[171,x,k[0],k[1]] = 3*F[27,x]+F[172,x,k[0],k[1]]+F[174,x,k[0],k[1]]
F[172,x,k[0],k[1]] = F[173,x,k[0],k[1]]*F[21,x]
F[173,x,k[0],k[1]] = F[163,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[175,x,k[0],k[1]]*F[21,x]
F[175,x,k[0],k[1]] = F[176,x,k[0],k[1]]+F[179,x,k[0],k[1]]
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[178,x,k[0],k[1]]*F[21,x]
F[178,x,k[0],k[1]] = F[176,x,k[0],k[1]]+F[62,x,k[0],k[1]]
F[179,x,k[0],k[1]] = 3*F[27,x]+F[174,x,k[0],k[1]]+F[180,x,k[0],k[1]]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]*F[21,x]
F[181,x,k[0],k[1]] = F[163,x,k[0],k[1]]+F[179,x,k[0],k[1]]
F[182,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[183,x,k[0]] = F[184,x,k[0]]+F[73,x,k[0]]
F[184,x,k[0]] = F[185,x]+F[200,x,k[0]]
F[185,x] = F[186,x]+F[75,x]
F[186,x] = F[187,x]+F[76,x]
F[187,x] = F[188,x]+F[190,x]+F[192,x]+F[27,x]
F[188,x] = F[189,x]*F[21,x]
F[189,x] = F[187,x]+F[76,x]
F[190,x] = F[191,x]*F[21,x]
F[191,x] = F[187,x]+F[76,x]
F[192,x] = F[193,x]*F[21,x]
F[193,x] = F[194,x]+F[197,x]
F[194,x] = F[195,x]
F[195,x] = F[196,x]*F[21,x]
F[196,x] = F[19,x]+F[194,x]
F[197,x] = 2*F[27,x]+F[192,x]+F[198,x]
F[198,x] = F[199,x]*F[21,x]
F[199,x] = F[197,x]+F[76,x]
F[200,x,k[0]] = F[201,x,k[0]]+F[97,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[205,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]*F[21,x]
F[204,x,k[0]] = F[202,x,k[0]]+F[98,x,k[0]]
F[205,x,k[0]] = 3*F[27,x]+F[206,x,k[0]]+F[208,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]*F[21,x]
F[207,x,k[0]] = F[101,x,k[0]]+F[205,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]*F[21,x]
F[209,x,k[0]] = F[210,x,k[0]]+F[213,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[21,x]*F[212,x,k[0]]
F[212,x,k[0]] = F[210,x,k[0]]+F[98,x,k[0]]
F[213,x,k[0]] = 3*F[27,x]+F[208,x,k[0]]+F[214,x,k[0]]
F[214,x,k[0]] = F[21,x]*F[215,x,k[0]]
F[215,x,k[0]] = F[101,x,k[0]]+F[213,x,k[0]]
F[216,x,k[0]] = F[217,x,1,k[0]]
F[217,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[14,x,k[1]]
F[218,x,k[0]] = F[21,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[1,x]+F[220,x,k[0]]+F[222,x,k[0]]+F[226,x,k[0]]+F[227,x,k[0]]
F[220,x,k[0]] = F[21,x]*F[221,x,k[0]]
F[221,x,k[0]] = 1/(-1+k[0])*(F[219,x,k[0]]*k[0]-F[219,x,1])
F[222,x,k[0]] = F[14,x,k[0]]*F[223,x,k[0]]
F[223,x,k[0]] = F[1,x]+F[142,x,k[0]]+F[222,x,k[0]]+F[224,x,k[0]]
F[224,x,k[0]] = F[21,x]*F[225,x,k[0]]
F[225,x,k[0]] = 1/(-1+k[0])*(F[223,x,k[0]]*k[0]-F[223,x,1])
F[226,x,k[0]] = F[183,x,k[0]]*F[21,x]
F[227,x,k[0]] = F[21,x]*F[228,x,k[0]]
F[228,x,k[0]] = F[148,x,1,k[0]]
F[229,x] = F[21,x]*F[230,x]
F[230,x] = F[1,x]+F[231,x]+F[232,x]+F[369,x]
F[231,x] = F[21,x]*F[230,x]
F[232,x] = F[21,x]*F[233,x]
F[233,x] = F[234,x,1]
F[234,x,k[0]] = F[1,x]+F[231,x]+F[235,x,k[0]]+F[363,x,k[0]]+F[366,x,k[0]]
F[235,x,k[0]] = F[236,x,k[0],1]
F[236,x,k[0],k[1]] = F[14,x,k[0]]*F[237,x,k[0],k[1]]
F[237,x,k[0],k[1]] = F[1,x]+F[238,x,k[0]]+F[284,x,k[0],k[1]]+F[286,x,k[0],k[1]]+F[353,x,k[0],k[1]]
F[238,x,k[0]] = F[14,x,k[0]]*F[239,x,k[0]]
F[239,x,k[0]] = F[1,x]+F[238,x,k[0]]+F[240,x,k[0]]+F[259,x,k[0]]
F[240,x,k[0]] = F[21,x]*F[241,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[74,x]
F[242,x,k[0]] = F[22,x,k[0]]+F[243,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]+F[26,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]+F[247,x,k[0]]+F[249,x,k[0]]+F[27,x]
F[245,x,k[0]] = F[14,x,k[0]]*F[246,x,k[0]]
F[246,x,k[0]] = F[244,x,k[0]]+F[76,x]
F[247,x,k[0]] = F[21,x]*F[248,x,k[0]]
F[248,x,k[0]] = F[244,x,k[0]]+F[26,x,k[0]]
F[249,x,k[0]] = F[21,x]*F[250,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]+F[26,x,k[0]]
F[251,x,k[0]] = F[249,x,k[0]]+F[252,x,k[0]]+F[257,x,k[0]]+F[27,x]
F[252,x,k[0]] = F[14,x,k[0]]*F[253,x,k[0]]
F[253,x,k[0]] = F[194,x]+F[254,x,k[0]]
F[254,x,k[0]] = 2*F[27,x]+F[252,x,k[0]]+F[255,x,k[0]]
F[255,x,k[0]] = F[21,x]*F[256,x,k[0]]
F[256,x,k[0]] = F[254,x,k[0]]+F[26,x,k[0]]
F[257,x,k[0]] = F[21,x]*F[258,x,k[0]]
F[258,x,k[0]] = F[251,x,k[0]]+F[26,x,k[0]]
F[259,x,k[0]] = F[21,x]*F[260,x,k[0]]
F[260,x,k[0]] = F[1,x]+F[261,x,k[0]]+F[262,x,k[0]]+F[263,x,k[0]]+F[264,x,k[0]]
F[261,x,k[0]] = F[14,x,k[0]]*F[260,x,k[0]]
F[262,x,k[0]] = F[21,x]*F[260,x,k[0]]
F[263,x,k[0]] = F[147,x,k[0],1]
F[264,x,k[0]] = F[21,x]*F[265,x,k[0]]
F[265,x,k[0]] = F[266,x]+F[268,x,k[0]]
F[266,x] = F[267,x]+F[74,x]
F[267,x] = F[193,x]+F[75,x]
F[268,x,k[0]] = F[154,x,k[0]]+F[269,x,k[0]]
F[269,x,k[0]] = F[155,x,k[0]]+F[270,x,k[0]]
F[270,x,k[0]] = F[254,x,k[0]]+F[271,x,k[0]]
F[271,x,k[0]] = 2*F[27,x]+F[272,x,k[0]]+F[274,x,k[0]]+F[276,x,k[0]]
F[272,x,k[0]] = F[14,x,k[0]]*F[273,x,k[0]]
F[273,x,k[0]] = F[197,x]+F[271,x,k[0]]
F[274,x,k[0]] = F[21,x]*F[275,x,k[0]]
F[275,x,k[0]] = F[156,x,k[0]]+F[271,x,k[0]]
F[276,x,k[0]] = F[21,x]*F[277,x,k[0]]
F[277,x,k[0]] = F[278,x,k[0]]+F[281,x,k[0]]
F[278,x,k[0]] = F[279,x,k[0]]
F[279,x,k[0]] = F[21,x]*F[280,x,k[0]]
F[280,x,k[0]] = F[278,x,k[0]]+F[82,x,k[0]]
F[281,x,k[0]] = 3*F[27,x]+F[276,x,k[0]]+F[282,x,k[0]]
F[282,x,k[0]] = F[21,x]*F[283,x,k[0]]
F[283,x,k[0]] = F[281,x,k[0]]+F[85,x,k[0]]
F[284,x,k[0],k[1]] = F[14,x,k[1]]*F[285,x,k[0],k[1]]
F[285,x,k[0],k[1]] = (F[239,x,k[0]]*k[0]-F[239,x,k[1]]*k[1])/(-k[1]+k[0])
F[286,x,k[0],k[1]] = F[21,x]*F[287,x,k[0],k[1]]
F[287,x,k[0],k[1]] = (F[288,x,k[0]]*k[0]-F[288,x,k[1]]*k[1])/(-k[1]+k[0])
F[288,x,k[0]] = F[289,x,k[0],1]
F[289,x,k[0],k[1]] = F[1,x]+F[290,x,k[0],k[1]]+F[291,x,k[0],k[1]]+F[293,x,k[0],k[1]]+F[312,x,k[0],k[1]]
F[290,x,k[0],k[1]] = F[14,x,k[0]]*F[289,x,k[0],k[1]]
F[291,x,k[0],k[1]] = F[21,x]*F[292,x,k[0],k[1]]
F[292,x,k[0],k[1]] = (F[289,x,k[0],k[1]]*k[0]-F[289,x,1,k[1]])/(-1+k[0])
F[293,x,k[0],k[1]] = F[14,x,k[1]]*F[294,x,k[0],k[1]]
F[294,x,k[0],k[1]] = (F[295,x,k[0],k[1]]*k[0]-F[295,x,1,k[1]])/(-1+k[0])
F[295,x,k[0],k[1]] = F[1,x]+F[296,x,k[0],k[1]]+F[297,x,k[0],k[1]]+F[298,x,k[0],k[1]]
F[296,x,k[0],k[1]] = F[14,x,k[0]]*F[295,x,k[0],k[1]]
F[297,x,k[0],k[1]] = F[14,x,k[1]]*F[295,x,k[0],k[1]]
F[298,x,k[0],k[1]] = F[21,x]*F[299,x,k[0],k[1]]
F[299,x,k[0],k[1]] = 1/(-1+k[1])*(F[300,x,k[0],k[1]]*k[1]-F[300,x,k[0],1])
F[300,x,k[0],k[1]] = F[1,x]+F[301,x,k[0],k[1]]+F[302,x,k[0],k[1]]+F[311,x,k[0],k[1]]
F[301,x,k[0],k[1]] = F[14,x,k[0]]*F[300,x,k[0],k[1]]
F[302,x,k[0],k[1]] = F[14,x,k[1]]*F[303,x,k[0],k[1]]
F[303,x,k[0],k[1]] = F[17,x,k[1]]+F[304,x,k[0],k[1]]
F[304,x,k[0],k[1]] = F[22,x,k[0]]+F[305,x,k[0],k[1]]
F[305,x,k[0],k[1]] = F[306,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[306,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[27,x]+F[307,x,k[0],k[1]]+F[309,x,k[0],k[1]]
F[307,x,k[0],k[1]] = F[14,x,k[0]]*F[308,x,k[0],k[1]]
F[308,x,k[0],k[1]] = F[26,x,k[1]]+F[306,x,k[0],k[1]]
F[309,x,k[0],k[1]] = F[14,x,k[1]]*F[310,x,k[0],k[1]]
F[310,x,k[0],k[1]] = F[26,x,k[0]]+F[306,x,k[0],k[1]]
F[311,x,k[0],k[1]] = F[149,x,k[0],k[1]]*F[21,x]
F[312,x,k[0],k[1]] = F[21,x]*F[313,x,k[0],k[1]]
F[313,x,k[0],k[1]] = 1/(-1+k[1])*(F[314,x,k[0],k[1]]*k[1]-F[314,x,k[0],1])
F[314,x,k[0],k[1]] = F[1,x]+F[315,x,k[0],k[1]]+F[317,x,k[0],k[1]]+F[319,x,k[0],k[1]]+F[351,x,k[0],k[1]]
F[315,x,k[0],k[1]] = F[14,x,k[0]]*F[316,x,k[0],k[1]]
F[316,x,k[0],k[1]] = 1/(-1+k[1])*(F[300,x,k[0],k[1]]*k[1]-F[300,x,k[0],1])
F[317,x,k[0],k[1]] = F[21,x]*F[318,x,k[0],k[1]]
F[318,x,k[0],k[1]] = 1/(-1+k[1])*(F[314,x,k[0],k[1]]*k[1]-F[314,x,k[0],1])
F[319,x,k[0],k[1]] = F[14,x,k[1]]*F[320,x,k[0],k[1]]
F[320,x,k[0],k[1]] = F[1,x]+F[319,x,k[0],k[1]]+F[321,x,k[0],k[1]]+F[344,x,k[0],k[1]]+F[346,x,k[0],k[1]]
F[321,x,k[0],k[1]] = F[14,x,k[0]]*F[322,x,k[0],k[1]]
F[322,x,k[0],k[1]] = F[323,x,k[0],k[1]]+F[95,x,k[1]]
F[323,x,k[0],k[1]] = F[304,x,k[0],k[1]]+F[324,x,k[0],k[1]]
F[324,x,k[0],k[1]] = F[155,x,k[0]]+F[325,x,k[0],k[1]]
F[325,x,k[0],k[1]] = F[326,x,k[0],k[1]]+F[331,x,k[0],k[1]]
F[326,x,k[0],k[1]] = 2*F[27,x]+F[327,x,k[0],k[1]]+F[329,x,k[0],k[1]]
F[327,x,k[0],k[1]] = F[14,x,k[0]]*F[328,x,k[0],k[1]]
F[328,x,k[0],k[1]] = F[326,x,k[0],k[1]]+F[98,x,k[1]]
F[329,x,k[0],k[1]] = F[14,x,k[1]]*F[330,x,k[0],k[1]]
F[330,x,k[0],k[1]] = F[26,x,k[0]]+F[326,x,k[0],k[1]]
F[331,x,k[0],k[1]] = 2*F[27,x]+F[332,x,k[0],k[1]]+F[334,x,k[0],k[1]]+F[336,x,k[0],k[1]]
F[332,x,k[0],k[1]] = F[14,x,k[0]]*F[333,x,k[0],k[1]]
F[333,x,k[0],k[1]] = F[101,x,k[1]]+F[331,x,k[0],k[1]]
F[334,x,k[0],k[1]] = F[14,x,k[1]]*F[335,x,k[0],k[1]]
F[335,x,k[0],k[1]] = F[156,x,k[0]]+F[331,x,k[0],k[1]]
F[336,x,k[0],k[1]] = F[21,x]*F[337,x,k[0],k[1]]
F[337,x,k[0],k[1]] = F[338,x,k[0],k[1]]+F[341,x,k[0],k[1]]
F[338,x,k[0],k[1]] = F[339,x,k[0],k[1]]
F[339,x,k[0],k[1]] = F[14,x,k[1]]*F[340,x,k[0],k[1]]
F[340,x,k[0],k[1]] = F[338,x,k[0],k[1]]+F[82,x,k[0]]
F[341,x,k[0],k[1]] = 3*F[27,x]+F[336,x,k[0],k[1]]+F[342,x,k[0],k[1]]
F[342,x,k[0],k[1]] = F[14,x,k[1]]*F[343,x,k[0],k[1]]
F[343,x,k[0],k[1]] = F[341,x,k[0],k[1]]+F[85,x,k[0]]
F[344,x,k[0],k[1]] = F[21,x]*F[345,x,k[0],k[1]]
F[345,x,k[0],k[1]] = 1/(-1+k[1])*(F[320,x,k[0],k[1]]*k[1]-F[320,x,k[0],1])
F[346,x,k[0],k[1]] = F[21,x]*F[347,x,k[0],k[1]]
F[347,x,k[0],k[1]] = F[348,x,k[0],k[1]]+F[95,x,k[1]]
F[348,x,k[0],k[1]] = F[349,x,k[0],k[1]]+F[350,x,k[0],k[1]]
F[349,x,k[0],k[1]] = F[162,x,k[0],k[1]]+F[22,x,k[0]]
F[350,x,k[0],k[1]] = F[337,x,k[0],k[1]]+F[81,x,k[0]]
F[351,x,k[0],k[1]] = F[21,x]*F[352,x,k[0],k[1]]
F[352,x,k[0],k[1]] = (F[149,x,k[0],k[1]]*k[0]-F[149,x,1,k[1]])/(-1+k[0])
F[353,x,k[0],k[1]] = F[21,x]*F[354,x,k[0],k[1]]
F[354,x,k[0],k[1]] = (F[355,x,k[0]]*k[0]-F[355,x,k[1]]*k[1])/(-k[1]+k[0])
F[355,x,k[0]] = F[1,x]+F[356,x,k[0]]+F[357,x,k[0]]+F[359,x,k[0]]+F[361,x,k[0]]
F[356,x,k[0]] = F[14,x,k[0]]*F[355,x,k[0]]
F[357,x,k[0]] = F[21,x]*F[358,x,k[0]]
F[358,x,k[0]] = F[354,x,k[0],1]
F[359,x,k[0]] = F[21,x]*F[360,x,k[0]]
F[360,x,k[0]] = F[352,x,k[0],1]
F[361,x,k[0]] = F[21,x]*F[362,x,k[0]]
F[362,x,k[0]] = F[320,x,k[0],1]
F[363,x,k[0]] = F[21,x]*F[364,x,k[0]]
F[364,x,k[0]] = F[365,x,k[0],1]
F[365,x,k[0],k[1]] = (F[237,x,k[0],k[1]]*k[0]-F[237,x,1,k[1]])/(-1+k[0])
F[366,x,k[0]] = F[21,x]*F[367,x,k[0]]
F[367,x,k[0]] = F[368,x,k[0],1]
F[368,x,k[0],k[1]] = (F[314,x,k[0],k[1]]*k[0]-F[314,x,1,k[1]])/(-1+k[0])
F[369,x] = F[370,x,1]
F[370,x,k[0]] = F[21,x]*F[371,x,k[0]]
F[371,x,k[0]] = F[1,x]+F[372,x,k[0]]+F[374,x,k[0]]+F[375,x,k[0]]+F[376,x,k[0]]
F[372,x,k[0]] = F[14,x,k[0]]*F[373,x,k[0]]
F[373,x,k[0]] = F[299,x,k[0],1]
F[374,x,k[0]] = F[317,x,k[0],1]
F[375,x,k[0]] = F[319,x,k[0],1]
F[376,x,k[0]] = F[351,x,k[0],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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{229}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{216}\! \left(x , y_{0}\right)+F_{218}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{143}\! \left(x , y_{0}\right)+F_{89}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{47}\! \left(x , y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x \right)+F_{22}\! \left(x , y_{0}\right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{19}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{19}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = 2 F_{27}\! \left(x \right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{50}\! \left(x , y_{0}, 1\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{52}\! \left(x , y_{0}, 1, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{52}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{52}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{59}\! \left(x , y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{41}\! \left(x , y_{0}, y_{2}\right)+F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{0}, y_{1}\right)+F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{64}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 2 F_{27}\! \left(x \right)+F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}\right) F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{2}\right)+F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}, 1\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{71}\! \left(x , y_{0}, y_{1}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0}, y_{1}, 1\right)
F_{72}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{73}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{74}\! \left(x \right)+F_{80}\! \left(x , y_{0}\right)
F_{74}\! \left(x \right) = F_{18}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{27}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right)
F_{80}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{82}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{86}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{81}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{8}\! \left(x , y_{0}\right)+F_{8}\! \left(x , 1\right)}{-1+y_{0}}
F_{91}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{140}\! \left(x , y_{0}\right)+F_{142}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{75}\! \left(x \right)+F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{19}\! \left(x \right)+F_{98}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{102}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)
F_{104}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{97}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)+F_{122}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x \right)+F_{111}\! \left(x , y_{0}\right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{19}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{21}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{19}\! \left(x \right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{117}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{113}\! \left(x , y_{0}\right)+F_{115}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)
F_{113}\! \left(x , y_{0}\right) = F_{114}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{114}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{116}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{19}\! \left(x \right)
F_{117}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{118}\! \left(x , y_{0}\right)+F_{120}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{119}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{119}\! \left(x , y_{0}\right) = F_{117}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}\right) = F_{108}\! \left(x \right)+F_{117}\! \left(x , y_{0}\right)
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x \right)+F_{129}\! \left(x , y_{0}\right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{76}\! \left(x \right)
F_{124}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{21}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)+F_{76}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{21}\! \left(x \right)
F_{128}\! \left(x \right) = F_{108}\! \left(x \right)+F_{124}\! \left(x \right)
F_{129}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{131}\! \left(x , y_{0}\right)+F_{133}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{132}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{132}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{133}\! \left(x , y_{0}\right) = F_{134}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{134}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)
F_{135}\! \left(x , y_{0}\right) = 3 F_{27}\! \left(x \right)+F_{136}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}\right)
F_{136}\! \left(x , y_{0}\right) = F_{137}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{137}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}\right)
F_{138}\! \left(x , y_{0}\right) = F_{139}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{139}\! \left(x , y_{0}\right) = F_{124}\! \left(x \right)+F_{135}\! \left(x , y_{0}\right)
F_{140}\! \left(x , y_{0}\right) = F_{141}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{141}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{92}\! \left(x , y_{0}\right)+F_{92}\! \left(x , 1\right)}{-1+y_{0}}
F_{142}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{95}\! \left(x , y_{0}\right)
F_{143}\! \left(x , y_{0}\right) = F_{144}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{144}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{145}\! \left(x , y_{0}\right)+F_{146}\! \left(x , y_{0}\right)+F_{182}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}\right) = F_{144}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{146}\! \left(x , y_{0}\right) = F_{147}\! \left(x , 1, y_{0}\right)
F_{147}\! \left(x , y_{0}, y_{1}\right) = F_{148}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{148}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{149}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{149}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{147}\! \left(x , y_{0}, y_{1}\right)+F_{150}\! \left(x , y_{0}, y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{149}\! \left(x , y_{0}, y_{1}\right)
F_{151}\! \left(x , y_{0}, y_{1}\right) = F_{152}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{152}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{73}\! \left(x , y_{1}\right)
F_{153}\! \left(x , y_{0}, y_{1}\right) = F_{154}\! \left(x , y_{0}\right)+F_{161}\! \left(x , y_{0}, y_{1}\right)
F_{154}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{155}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{156}\! \left(x , y_{0}\right) = F_{157}\! \left(x , y_{0}\right)+F_{159}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)+F_{88}\! \left(x , y_{0}\right)
F_{157}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{158}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{160}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{167}\! \left(x , y_{0}, y_{1}\right)
F_{162}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = 2 F_{27}\! \left(x \right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{166}\! \left(x , y_{0}, y_{1}\right)
F_{164}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{165}\! \left(x , y_{0}, y_{1}\right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{169}\! \left(x , y_{0}, y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{171}\! \left(x , y_{0}, y_{1}\right) = 3 F_{27}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, y_{1}\right)
F_{172}\! \left(x , y_{0}, y_{1}\right) = F_{173}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{0}, y_{1}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{178}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{179}\! \left(x , y_{0}, y_{1}\right) = 3 F_{27}\! \left(x \right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{180}\! \left(x , y_{0}, y_{1}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}\right) = F_{183}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{183}\! \left(x , y_{0}\right) = F_{184}\! \left(x , y_{0}\right)+F_{73}\! \left(x , y_{0}\right)
F_{184}\! \left(x , y_{0}\right) = F_{185}\! \left(x \right)+F_{200}\! \left(x , y_{0}\right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{75}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{76}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{192}\! \left(x \right)+F_{27}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{21}\! \left(x \right)
F_{189}\! \left(x \right) = F_{187}\! \left(x \right)+F_{76}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{21}\! \left(x \right)
F_{191}\! \left(x \right) = F_{187}\! \left(x \right)+F_{76}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{21}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{197}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{21}\! \left(x \right)
F_{196}\! \left(x \right) = F_{19}\! \left(x \right)+F_{194}\! \left(x \right)
F_{197}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{192}\! \left(x \right)+F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{21}\! \left(x \right)
F_{199}\! \left(x \right) = F_{197}\! \left(x \right)+F_{76}\! \left(x \right)
F_{200}\! \left(x , y_{0}\right) = F_{201}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)
F_{201}\! \left(x , y_{0}\right) = F_{202}\! \left(x , y_{0}\right)+F_{205}\! \left(x , y_{0}\right)
F_{202}\! \left(x , y_{0}\right) = F_{203}\! \left(x , y_{0}\right)
F_{203}\! \left(x , y_{0}\right) = F_{204}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{204}\! \left(x , y_{0}\right) = F_{202}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{205}\! \left(x , y_{0}\right) = 3 F_{27}\! \left(x \right)+F_{206}\! \left(x , y_{0}\right)+F_{208}\! \left(x , y_{0}\right)
F_{206}\! \left(x , y_{0}\right) = F_{207}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{207}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{205}\! \left(x , y_{0}\right)
F_{208}\! \left(x , y_{0}\right) = F_{209}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{209}\! \left(x , y_{0}\right) = F_{210}\! \left(x , y_{0}\right)+F_{213}\! \left(x , y_{0}\right)
F_{210}\! \left(x , y_{0}\right) = F_{211}\! \left(x , y_{0}\right)
F_{211}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{212}\! \left(x , y_{0}\right)
F_{212}\! \left(x , y_{0}\right) = F_{210}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{213}\! \left(x , y_{0}\right) = 3 F_{27}\! \left(x \right)+F_{208}\! \left(x , y_{0}\right)+F_{214}\! \left(x , y_{0}\right)
F_{214}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{215}\! \left(x , y_{0}\right)
F_{215}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{213}\! \left(x , y_{0}\right)
F_{216}\! \left(x , y_{0}\right) = F_{217}\! \left(x , 1, y_{0}\right)
F_{217}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{1}\right)
F_{218}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{219}\! \left(x , y_{0}\right)
F_{219}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{220}\! \left(x , y_{0}\right)+F_{222}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}\right)+F_{227}\! \left(x , y_{0}\right)
F_{220}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{221}\! \left(x , y_{0}\right)
F_{221}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{219}\! \left(x , y_{0}\right)+F_{219}\! \left(x , 1\right)}{-1+y_{0}}
F_{222}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{223}\! \left(x , y_{0}\right)
F_{223}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{142}\! \left(x , y_{0}\right)+F_{222}\! \left(x , y_{0}\right)+F_{224}\! \left(x , y_{0}\right)
F_{224}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{225}\! \left(x , y_{0}\right)
F_{225}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{223}\! \left(x , y_{0}\right)+F_{223}\! \left(x , 1\right)}{-1+y_{0}}
F_{226}\! \left(x , y_{0}\right) = F_{183}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)
F_{227}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{228}\! \left(x , y_{0}\right)
F_{228}\! \left(x , y_{0}\right) = F_{148}\! \left(x , 1, y_{0}\right)
F_{229}\! \left(x \right) = F_{21}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{1}\! \left(x \right)+F_{231}\! \left(x \right)+F_{232}\! \left(x \right)+F_{369}\! \left(x \right)
F_{231}\! \left(x \right) = F_{21}\! \left(x \right) F_{230}\! \left(x \right)
F_{232}\! \left(x \right) = F_{21}\! \left(x \right) F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x , 1\right)
F_{234}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{231}\! \left(x \right)+F_{235}\! \left(x , y_{0}\right)+F_{363}\! \left(x , y_{0}\right)+F_{366}\! \left(x , y_{0}\right)
F_{235}\! \left(x , y_{0}\right) = F_{236}\! \left(x , y_{0}, 1\right)
F_{236}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{237}\! \left(x , y_{0}, y_{1}\right)
F_{237}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{238}\! \left(x , y_{0}\right)+F_{284}\! \left(x , y_{0}, y_{1}\right)+F_{286}\! \left(x , y_{0}, y_{1}\right)+F_{353}\! \left(x , y_{0}, y_{1}\right)
F_{238}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{239}\! \left(x , y_{0}\right)
F_{239}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{238}\! \left(x , y_{0}\right)+F_{240}\! \left(x , y_{0}\right)+F_{259}\! \left(x , y_{0}\right)
F_{240}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{241}\! \left(x , y_{0}\right)
F_{241}\! \left(x , y_{0}\right) = F_{242}\! \left(x , y_{0}\right)+F_{74}\! \left(x \right)
F_{242}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right)+F_{243}\! \left(x , y_{0}\right)
F_{243}\! \left(x , y_{0}\right) = F_{244}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{244}\! \left(x , y_{0}\right) = F_{245}\! \left(x , y_{0}\right)+F_{247}\! \left(x , y_{0}\right)+F_{249}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)
F_{245}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{246}\! \left(x , y_{0}\right)
F_{246}\! \left(x , y_{0}\right) = F_{244}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)
F_{247}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{248}\! \left(x , y_{0}\right)
F_{248}\! \left(x , y_{0}\right) = F_{244}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{249}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{250}\! \left(x , y_{0}\right)
F_{250}\! \left(x , y_{0}\right) = F_{251}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{251}\! \left(x , y_{0}\right) = F_{249}\! \left(x , y_{0}\right)+F_{252}\! \left(x , y_{0}\right)+F_{257}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)
F_{252}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{253}\! \left(x , y_{0}\right)
F_{253}\! \left(x , y_{0}\right) = F_{194}\! \left(x \right)+F_{254}\! \left(x , y_{0}\right)
F_{254}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{252}\! \left(x , y_{0}\right)+F_{255}\! \left(x , y_{0}\right)
F_{255}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{256}\! \left(x , y_{0}\right)
F_{256}\! \left(x , y_{0}\right) = F_{254}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{257}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{258}\! \left(x , y_{0}\right)
F_{258}\! \left(x , y_{0}\right) = F_{251}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{259}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{260}\! \left(x , y_{0}\right)
F_{260}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{261}\! \left(x , y_{0}\right)+F_{262}\! \left(x , y_{0}\right)+F_{263}\! \left(x , y_{0}\right)+F_{264}\! \left(x , y_{0}\right)
F_{261}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{260}\! \left(x , y_{0}\right)
F_{262}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{260}\! \left(x , y_{0}\right)
F_{263}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}, 1\right)
F_{264}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{265}\! \left(x , y_{0}\right)
F_{265}\! \left(x , y_{0}\right) = F_{266}\! \left(x \right)+F_{268}\! \left(x , y_{0}\right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{74}\! \left(x \right)
F_{267}\! \left(x \right) = F_{193}\! \left(x \right)+F_{75}\! \left(x \right)
F_{268}\! \left(x , y_{0}\right) = F_{154}\! \left(x , y_{0}\right)+F_{269}\! \left(x , y_{0}\right)
F_{269}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)+F_{270}\! \left(x , y_{0}\right)
F_{270}\! \left(x , y_{0}\right) = F_{254}\! \left(x , y_{0}\right)+F_{271}\! \left(x , y_{0}\right)
F_{271}\! \left(x , y_{0}\right) = 2 F_{27}\! \left(x \right)+F_{272}\! \left(x , y_{0}\right)+F_{274}\! \left(x , y_{0}\right)+F_{276}\! \left(x , y_{0}\right)
F_{272}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{273}\! \left(x , y_{0}\right)
F_{273}\! \left(x , y_{0}\right) = F_{197}\! \left(x \right)+F_{271}\! \left(x , y_{0}\right)
F_{274}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{275}\! \left(x , y_{0}\right)
F_{275}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right)+F_{271}\! \left(x , y_{0}\right)
F_{276}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{277}\! \left(x , y_{0}\right)
F_{277}\! \left(x , y_{0}\right) = F_{278}\! \left(x , y_{0}\right)+F_{281}\! \left(x , y_{0}\right)
F_{278}\! \left(x , y_{0}\right) = F_{279}\! \left(x , y_{0}\right)
F_{279}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{280}\! \left(x , y_{0}\right)
F_{280}\! \left(x , y_{0}\right) = F_{278}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{281}\! \left(x , y_{0}\right) = 3 F_{27}\! \left(x \right)+F_{276}\! \left(x , y_{0}\right)+F_{282}\! \left(x , y_{0}\right)
F_{282}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{283}\! \left(x , y_{0}\right)
F_{283}\! \left(x , y_{0}\right) = F_{281}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)
F_{284}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{285}\! \left(x , y_{0}, y_{1}\right)
F_{285}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{239}\! \left(x , y_{0}\right)-y_{1} F_{239}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{286}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{287}\! \left(x , y_{0}, y_{1}\right)
F_{287}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{288}\! \left(x , y_{0}\right)-y_{1} F_{288}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{288}\! \left(x , y_{0}\right) = F_{289}\! \left(x , y_{0}, 1\right)
F_{289}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{290}\! \left(x , y_{0}, y_{1}\right)+F_{291}\! \left(x , y_{0}, y_{1}\right)+F_{293}\! \left(x , y_{0}, y_{1}\right)+F_{312}\! \left(x , y_{0}, y_{1}\right)
F_{290}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{289}\! \left(x , y_{0}, y_{1}\right)
F_{291}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{292}\! \left(x , y_{0}, y_{1}\right)
F_{292}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{289}\! \left(x , y_{0}, y_{1}\right)+F_{289}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{293}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{294}\! \left(x , y_{0}, y_{1}\right)
F_{294}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{295}\! \left(x , y_{0}, y_{1}\right)+F_{295}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{295}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{296}\! \left(x , y_{0}, y_{1}\right)+F_{297}\! \left(x , y_{0}, y_{1}\right)+F_{298}\! \left(x , y_{0}, y_{1}\right)
F_{296}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{295}\! \left(x , y_{0}, y_{1}\right)
F_{297}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{295}\! \left(x , y_{0}, y_{1}\right)
F_{298}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{299}\! \left(x , y_{0}, y_{1}\right)
F_{299}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{300}\! \left(x , y_{0}, y_{1}\right)+F_{300}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{300}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{301}\! \left(x , y_{0}, y_{1}\right)+F_{302}\! \left(x , y_{0}, y_{1}\right)+F_{311}\! \left(x , y_{0}, y_{1}\right)
F_{301}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{300}\! \left(x , y_{0}, y_{1}\right)
F_{302}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{303}\! \left(x , y_{0}, y_{1}\right)
F_{303}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{1}\right)+F_{304}\! \left(x , y_{0}, y_{1}\right)
F_{304}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right)+F_{305}\! \left(x , y_{0}, y_{1}\right)
F_{305}\! \left(x , y_{0}, y_{1}\right) = F_{306}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{306}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)+F_{307}\! \left(x , y_{0}, y_{1}\right)+F_{309}\! \left(x , y_{0}, y_{1}\right)
F_{307}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{308}\! \left(x , y_{0}, y_{1}\right)
F_{308}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}\right)+F_{306}\! \left(x , y_{0}, y_{1}\right)
F_{309}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{310}\! \left(x , y_{0}, y_{1}\right)
F_{310}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}\right)+F_{306}\! \left(x , y_{0}, y_{1}\right)
F_{311}\! \left(x , y_{0}, y_{1}\right) = F_{149}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)
F_{312}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{313}\! \left(x , y_{0}, y_{1}\right)
F_{313}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{314}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{315}\! \left(x , y_{0}, y_{1}\right)+F_{317}\! \left(x , y_{0}, y_{1}\right)+F_{319}\! \left(x , y_{0}, y_{1}\right)+F_{351}\! \left(x , y_{0}, y_{1}\right)
F_{315}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{316}\! \left(x , y_{0}, y_{1}\right)
F_{316}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{300}\! \left(x , y_{0}, y_{1}\right)+F_{300}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{317}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{318}\! \left(x , y_{0}, y_{1}\right)
F_{318}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{319}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{320}\! \left(x , y_{0}, y_{1}\right)
F_{320}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{319}\! \left(x , y_{0}, y_{1}\right)+F_{321}\! \left(x , y_{0}, y_{1}\right)+F_{344}\! \left(x , y_{0}, y_{1}\right)+F_{346}\! \left(x , y_{0}, y_{1}\right)
F_{321}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{322}\! \left(x , y_{0}, y_{1}\right)
F_{322}\! \left(x , y_{0}, y_{1}\right) = F_{323}\! \left(x , y_{0}, y_{1}\right)+F_{95}\! \left(x , y_{1}\right)
F_{323}\! \left(x , y_{0}, y_{1}\right) = F_{304}\! \left(x , y_{0}, y_{1}\right)+F_{324}\! \left(x , y_{0}, y_{1}\right)
F_{324}\! \left(x , y_{0}, y_{1}\right) = F_{155}\! \left(x , y_{0}\right)+F_{325}\! \left(x , y_{0}, y_{1}\right)
F_{325}\! \left(x , y_{0}, y_{1}\right) = F_{326}\! \left(x , y_{0}, y_{1}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)
F_{326}\! \left(x , y_{0}, y_{1}\right) = 2 F_{27}\! \left(x \right)+F_{327}\! \left(x , y_{0}, y_{1}\right)+F_{329}\! \left(x , y_{0}, y_{1}\right)
F_{327}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{328}\! \left(x , y_{0}, y_{1}\right)
F_{328}\! \left(x , y_{0}, y_{1}\right) = F_{326}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)
F_{329}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{330}\! \left(x , y_{0}, y_{1}\right)
F_{330}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}\right)+F_{326}\! \left(x , y_{0}, y_{1}\right)
F_{331}\! \left(x , y_{0}, y_{1}\right) = 2 F_{27}\! \left(x \right)+F_{332}\! \left(x , y_{0}, y_{1}\right)+F_{334}\! \left(x , y_{0}, y_{1}\right)+F_{336}\! \left(x , y_{0}, y_{1}\right)
F_{332}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{333}\! \left(x , y_{0}, y_{1}\right)
F_{333}\! \left(x , y_{0}, y_{1}\right) = F_{101}\! \left(x , y_{1}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)
F_{334}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{335}\! \left(x , y_{0}, y_{1}\right)
F_{335}\! \left(x , y_{0}, y_{1}\right) = F_{156}\! \left(x , y_{0}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)
F_{336}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{337}\! \left(x , y_{0}, y_{1}\right)
F_{337}\! \left(x , y_{0}, y_{1}\right) = F_{338}\! \left(x , y_{0}, y_{1}\right)+F_{341}\! \left(x , y_{0}, y_{1}\right)
F_{338}\! \left(x , y_{0}, y_{1}\right) = F_{339}\! \left(x , y_{0}, y_{1}\right)
F_{339}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{340}\! \left(x , y_{0}, y_{1}\right)
F_{340}\! \left(x , y_{0}, y_{1}\right) = F_{338}\! \left(x , y_{0}, y_{1}\right)+F_{82}\! \left(x , y_{0}\right)
F_{341}\! \left(x , y_{0}, y_{1}\right) = 3 F_{27}\! \left(x \right)+F_{336}\! \left(x , y_{0}, y_{1}\right)+F_{342}\! \left(x , y_{0}, y_{1}\right)
F_{342}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{343}\! \left(x , y_{0}, y_{1}\right)
F_{343}\! \left(x , y_{0}, y_{1}\right) = F_{341}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{0}\right)
F_{344}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{345}\! \left(x , y_{0}, y_{1}\right)
F_{345}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{320}\! \left(x , y_{0}, y_{1}\right)+F_{320}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{346}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{347}\! \left(x , y_{0}, y_{1}\right)
F_{347}\! \left(x , y_{0}, y_{1}\right) = F_{348}\! \left(x , y_{0}, y_{1}\right)+F_{95}\! \left(x , y_{1}\right)
F_{348}\! \left(x , y_{0}, y_{1}\right) = F_{349}\! \left(x , y_{0}, y_{1}\right)+F_{350}\! \left(x , y_{0}, y_{1}\right)
F_{349}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}\right)
F_{350}\! \left(x , y_{0}, y_{1}\right) = F_{337}\! \left(x , y_{0}, y_{1}\right)+F_{81}\! \left(x , y_{0}\right)
F_{351}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{352}\! \left(x , y_{0}, y_{1}\right)
F_{352}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{149}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{353}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{354}\! \left(x , y_{0}, y_{1}\right)
F_{354}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{355}\! \left(x , y_{0}\right)-y_{1} F_{355}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{355}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{356}\! \left(x , y_{0}\right)+F_{357}\! \left(x , y_{0}\right)+F_{359}\! \left(x , y_{0}\right)+F_{361}\! \left(x , y_{0}\right)
F_{356}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{355}\! \left(x , y_{0}\right)
F_{357}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{358}\! \left(x , y_{0}\right)
F_{358}\! \left(x , y_{0}\right) = F_{354}\! \left(x , y_{0}, 1\right)
F_{359}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{360}\! \left(x , y_{0}\right)
F_{360}\! \left(x , y_{0}\right) = F_{352}\! \left(x , y_{0}, 1\right)
F_{361}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{362}\! \left(x , y_{0}\right)
F_{362}\! \left(x , y_{0}\right) = F_{320}\! \left(x , y_{0}, 1\right)
F_{363}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{364}\! \left(x , y_{0}\right)
F_{364}\! \left(x , y_{0}\right) = F_{365}\! \left(x , y_{0}, 1\right)
F_{365}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{237}\! \left(x , y_{0}, y_{1}\right)+F_{237}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{366}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{367}\! \left(x , y_{0}\right)
F_{367}\! \left(x , y_{0}\right) = F_{368}\! \left(x , y_{0}, 1\right)
F_{368}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{369}\! \left(x \right) = F_{370}\! \left(x , 1\right)
F_{370}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{371}\! \left(x , y_{0}\right)
F_{371}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{372}\! \left(x , y_{0}\right)+F_{374}\! \left(x , y_{0}\right)+F_{375}\! \left(x , y_{0}\right)+F_{376}\! \left(x , y_{0}\right)
F_{372}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{373}\! \left(x , y_{0}\right)
F_{373}\! \left(x , y_{0}\right) = F_{299}\! \left(x , y_{0}, 1\right)
F_{374}\! \left(x , y_{0}\right) = F_{317}\! \left(x , y_{0}, 1\right)
F_{375}\! \left(x , y_{0}\right) = F_{319}\! \left(x , y_{0}, 1\right)
F_{376}\! \left(x , y_{0}\right) = F_{351}\! \left(x , y_{0}, 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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_229(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_216(x, k_0) + F_218(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_21(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_143(x, k_0) + F_89(x, k_0) + F_9(x, k_0) + F_91(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1)*F_14(x, k_0))
Eq(F_11(x, k_0, k_1), (k_1*F_12(x, k_0, k_1) - F_12(x, k_0, 1))/(k_1 - 1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_47(x, k_1))
Eq(F_13(x, k_0, k_1), F_12(x, k_0, k_1)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0, k_1), F_14(x, k_1)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, k_1) + F_31(x, k_0, k_1))
Eq(F_17(x, k_0), F_18(x) + F_22(x, k_0))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x, k_0), F_23(x, k_0) + F_26(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_14(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_1(x) + F_23(x, k_0))
Eq(F_26(x, k_0), F_27(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_27(x), 0)
Eq(F_28(x, k_0), F_14(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_19(x) + F_26(x, k_0))
Eq(F_30(x, k_0), F_21(x)*F_22(x, k_0))
Eq(F_31(x, k_0, k_1), F_32(x, k_0) + F_36(x, k_0, k_1))
Eq(F_32(x, k_0), F_23(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_14(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_19(x) + F_33(x, k_0))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_27(x) + F_38(x, k_0, k_1) + F_40(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_14(x, k_0)*F_39(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), F_23(x, k_1) + F_37(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_14(x, k_1)*F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_23(x, k_0) + F_37(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), 2*F_27(x) + F_43(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_14(x, k_0)*F_44(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_26(x, k_1) + F_42(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_14(x, k_1)*F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_33(x, k_0) + F_42(x, k_0, k_1))
Eq(F_47(x, k_0), F_21(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_1(x) + F_49(x, k_0) + F_69(x, k_0) + F_72(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0, 1))
Eq(F_50(x, k_0, k_1), F_14(x, k_0)*F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, 1, k_1))
Eq(F_52(x, k_0, k_1, k_2), F_53(x, k_0*k_1, k_1, k_2))
Eq(F_53(x, k_0, k_1, k_2), F_1(x) + F_54(x, k_0, k_1, k_2) + F_55(x, k_0, k_1, k_2) + F_57(x, k_0, k_1, k_2))
Eq(F_54(x, k_0, k_1, k_2), F_14(x, k_0)*F_53(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_14(x, k_1)*F_56(x, k_0, k_1, k_2))
Eq(F_56(x, k_0, k_1, k_2), (-k_0*F_52(x, k_0/k_1, k_1, k_2) + k_1*F_52(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_57(x, k_0, k_1, k_2), F_14(x, k_2)*F_58(x, k_0, k_1, k_2))
Eq(F_58(x, k_0, k_1, k_2), F_59(x, k_1, k_2) + F_60(x, k_0, k_1, k_2))
Eq(F_59(x, k_0, k_1), F_25(x, k_1) + F_41(x, k_0, k_1))
Eq(F_60(x, k_0, k_1, k_2), F_41(x, k_0, k_2) + F_61(x, k_0, k_1, k_2))
Eq(F_61(x, k_0, k_1, k_2), F_62(x, k_0, k_1) + F_65(x, k_0, k_1, k_2))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1))
Eq(F_63(x, k_0, k_1), F_14(x, k_1)*F_64(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_23(x, k_0) + F_62(x, k_0, k_1))
Eq(F_65(x, k_0, k_1, k_2), 2*F_27(x) + F_66(x, k_0, k_1, k_2) + F_68(x, k_0, k_1, k_2))
Eq(F_66(x, k_0, k_1, k_2), F_14(x, k_1)*F_67(x, k_0, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), F_37(x, k_0, k_2) + F_65(x, k_0, k_1, k_2))
Eq(F_68(x, k_0, k_1, k_2), F_14(x, k_2)*F_61(x, k_0, k_1, k_2))
Eq(F_69(x, k_0), F_70(x, k_0, 1))
Eq(F_70(x, k_0, k_1), F_14(x, k_1)*F_71(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_56(x, k_0, k_1, 1))
Eq(F_72(x, k_0), F_21(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x) + F_80(x, k_0))
Eq(F_74(x), F_18(x) + F_75(x))
Eq(F_75(x), F_19(x) + F_76(x))
Eq(F_76(x), F_27(x) + F_77(x) + F_79(x))
Eq(F_77(x), F_21(x)*F_78(x))
Eq(F_78(x), F_19(x) + F_76(x))
Eq(F_79(x), F_21(x)*F_75(x))
Eq(F_80(x, k_0), F_22(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_21(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_23(x, k_0) + F_82(x, k_0))
Eq(F_85(x, k_0), 2*F_27(x) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_86(x, k_0), F_21(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_26(x, k_0) + F_85(x, k_0))
Eq(F_88(x, k_0), F_21(x)*F_81(x, k_0))
Eq(F_89(x, k_0), F_21(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_14(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_1(x) + F_140(x, k_0) + F_142(x, k_0) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_21(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_105(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_17(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_75(x) + F_97(x, k_0))
Eq(F_97(x, k_0), F_101(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_14(x, k_0))
Eq(F_100(x, k_0), F_19(x) + F_98(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_104(x, k_0) + 2*F_27(x))
Eq(F_102(x, k_0), F_103(x, k_0)*F_14(x, k_0))
Eq(F_103(x, k_0), F_101(x, k_0) + F_76(x))
Eq(F_104(x, k_0), F_21(x)*F_97(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_122(x, k_0))
Eq(F_106(x, k_0), F_107(x) + F_111(x, k_0))
Eq(F_107(x), F_108(x) + F_19(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_21(x))
Eq(F_110(x), F_108(x) + F_19(x))
Eq(F_111(x, k_0), F_112(x, k_0) + F_117(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0) + F_27(x))
Eq(F_113(x, k_0), F_114(x, k_0)*F_21(x))
Eq(F_114(x, k_0), F_112(x, k_0) + F_23(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_14(x, k_0))
Eq(F_116(x, k_0), F_112(x, k_0) + F_19(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_120(x, k_0) + 2*F_27(x))
Eq(F_118(x, k_0), F_119(x, k_0)*F_21(x))
Eq(F_119(x, k_0), F_117(x, k_0) + F_26(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_14(x, k_0))
Eq(F_121(x, k_0), F_108(x) + F_117(x, k_0))
Eq(F_122(x, k_0), F_123(x) + F_129(x, k_0))
Eq(F_123(x), F_124(x) + F_76(x))
Eq(F_124(x), F_125(x) + F_127(x) + 2*F_27(x))
Eq(F_125(x), F_126(x)*F_21(x))
Eq(F_126(x), F_124(x) + F_76(x))
Eq(F_127(x), F_128(x)*F_21(x))
Eq(F_128(x), F_108(x) + F_124(x))
Eq(F_129(x, k_0), F_130(x, k_0) + F_135(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_133(x, k_0) + 2*F_27(x))
Eq(F_131(x, k_0), F_132(x, k_0)*F_21(x))
Eq(F_132(x, k_0), F_130(x, k_0) + F_98(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_14(x, k_0))
Eq(F_134(x, k_0), F_130(x, k_0) + F_76(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_138(x, k_0) + 3*F_27(x))
Eq(F_136(x, k_0), F_137(x, k_0)*F_21(x))
Eq(F_137(x, k_0), F_101(x, k_0) + F_135(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_14(x, k_0))
Eq(F_139(x, k_0), F_124(x) + F_135(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_21(x))
Eq(F_141(x, k_0), (k_0*F_92(x, k_0) - F_92(x, 1))/(k_0 - 1))
Eq(F_142(x, k_0), F_21(x)*F_95(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0)*F_21(x))
Eq(F_144(x, k_0), F_1(x) + F_145(x, k_0) + F_146(x, k_0) + F_182(x, k_0) + F_49(x, k_0))
Eq(F_145(x, k_0), F_144(x, k_0)*F_21(x))
Eq(F_146(x, k_0), F_147(x, 1, k_0))
Eq(F_147(x, k_0, k_1), F_148(x, k_0, k_1)*F_21(x))
Eq(F_148(x, k_0, k_1), (-k_1*F_149(x, k_0, k_1) + F_149(x, k_0, 1))/(1 - k_1))
Eq(F_149(x, k_0, k_1), F_1(x) + F_147(x, k_0, k_1) + F_150(x, k_0, k_1) + F_151(x, k_0, k_1) + F_49(x, k_1))
Eq(F_150(x, k_0, k_1), F_14(x, k_0)*F_149(x, k_0, k_1))
Eq(F_151(x, k_0, k_1), F_152(x, k_0, k_1)*F_21(x))
Eq(F_152(x, k_0, k_1), F_153(x, k_0, k_1) + F_73(x, k_1))
Eq(F_153(x, k_0, k_1), F_154(x, k_0) + F_161(x, k_0, k_1))
Eq(F_154(x, k_0), F_155(x, k_0) + F_22(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_26(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_159(x, k_0) + F_27(x) + F_88(x, k_0))
Eq(F_157(x, k_0), F_14(x, k_0)*F_158(x, k_0))
Eq(F_158(x, k_0), F_156(x, k_0) + F_76(x))
Eq(F_159(x, k_0), F_160(x, k_0)*F_21(x))
Eq(F_160(x, k_0), F_156(x, k_0) + F_26(x, k_0))
Eq(F_161(x, k_0, k_1), F_162(x, k_0, k_1) + F_167(x, k_0, k_1))
Eq(F_162(x, k_0, k_1), F_163(x, k_0, k_1) + F_62(x, k_0, k_1))
Eq(F_163(x, k_0, k_1), F_164(x, k_0, k_1) + F_166(x, k_0, k_1) + 2*F_27(x))
Eq(F_164(x, k_0, k_1), F_14(x, k_1)*F_165(x, k_0, k_1))
Eq(F_165(x, k_0, k_1), F_163(x, k_0, k_1) + F_26(x, k_0))
Eq(F_166(x, k_0, k_1), F_162(x, k_0, k_1)*F_21(x))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_168(x, k_0, k_1), F_169(x, k_0, k_1))
Eq(F_169(x, k_0, k_1), F_170(x, k_0, k_1)*F_21(x))
Eq(F_170(x, k_0, k_1), F_168(x, k_0, k_1) + F_62(x, k_0, k_1))
Eq(F_171(x, k_0, k_1), F_172(x, k_0, k_1) + F_174(x, k_0, k_1) + 3*F_27(x))
Eq(F_172(x, k_0, k_1), F_173(x, k_0, k_1)*F_21(x))
Eq(F_173(x, k_0, k_1), F_163(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_175(x, k_0, k_1)*F_21(x))
Eq(F_175(x, k_0, k_1), F_176(x, k_0, k_1) + F_179(x, k_0, k_1))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1))
Eq(F_177(x, k_0, k_1), F_178(x, k_0, k_1)*F_21(x))
Eq(F_178(x, k_0, k_1), F_176(x, k_0, k_1) + F_62(x, k_0, k_1))
Eq(F_179(x, k_0, k_1), F_174(x, k_0, k_1) + F_180(x, k_0, k_1) + 3*F_27(x))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1)*F_21(x))
Eq(F_181(x, k_0, k_1), F_163(x, k_0, k_1) + F_179(x, k_0, k_1))
Eq(F_182(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_183(x, k_0), F_184(x, k_0) + F_73(x, k_0))
Eq(F_184(x, k_0), F_185(x) + F_200(x, k_0))
Eq(F_185(x), F_186(x) + F_75(x))
Eq(F_186(x), F_187(x) + F_76(x))
Eq(F_187(x), F_188(x) + F_190(x) + F_192(x) + F_27(x))
Eq(F_188(x), F_189(x)*F_21(x))
Eq(F_189(x), F_187(x) + F_76(x))
Eq(F_190(x), F_191(x)*F_21(x))
Eq(F_191(x), F_187(x) + F_76(x))
Eq(F_192(x), F_193(x)*F_21(x))
Eq(F_193(x), F_194(x) + F_197(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_196(x)*F_21(x))
Eq(F_196(x), F_19(x) + F_194(x))
Eq(F_197(x), F_192(x) + F_198(x) + 2*F_27(x))
Eq(F_198(x), F_199(x)*F_21(x))
Eq(F_199(x), F_197(x) + F_76(x))
Eq(F_200(x, k_0), F_201(x, k_0) + F_97(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_205(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0)*F_21(x))
Eq(F_204(x, k_0), F_202(x, k_0) + F_98(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_208(x, k_0) + 3*F_27(x))
Eq(F_206(x, k_0), F_207(x, k_0)*F_21(x))
Eq(F_207(x, k_0), F_101(x, k_0) + F_205(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0)*F_21(x))
Eq(F_209(x, k_0), F_210(x, k_0) + F_213(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_21(x)*F_212(x, k_0))
Eq(F_212(x, k_0), F_210(x, k_0) + F_98(x, k_0))
Eq(F_213(x, k_0), F_208(x, k_0) + F_214(x, k_0) + 3*F_27(x))
Eq(F_214(x, k_0), F_21(x)*F_215(x, k_0))
Eq(F_215(x, k_0), F_101(x, k_0) + F_213(x, k_0))
Eq(F_216(x, k_0), F_217(x, 1, k_0))
Eq(F_217(x, k_0, k_1), F_12(x, k_0, k_1)*F_14(x, k_1))
Eq(F_218(x, k_0), F_21(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_1(x) + F_220(x, k_0) + F_222(x, k_0) + F_226(x, k_0) + F_227(x, k_0))
Eq(F_220(x, k_0), F_21(x)*F_221(x, k_0))
Eq(F_221(x, k_0), (k_0*F_219(x, k_0) - F_219(x, 1))/(k_0 - 1))
Eq(F_222(x, k_0), F_14(x, k_0)*F_223(x, k_0))
Eq(F_223(x, k_0), F_1(x) + F_142(x, k_0) + F_222(x, k_0) + F_224(x, k_0))
Eq(F_224(x, k_0), F_21(x)*F_225(x, k_0))
Eq(F_225(x, k_0), (k_0*F_223(x, k_0) - F_223(x, 1))/(k_0 - 1))
Eq(F_226(x, k_0), F_183(x, k_0)*F_21(x))
Eq(F_227(x, k_0), F_21(x)*F_228(x, k_0))
Eq(F_228(x, k_0), F_148(x, 1, k_0))
Eq(F_229(x), F_21(x)*F_230(x))
Eq(F_230(x), F_1(x) + F_231(x) + F_232(x) + F_369(x))
Eq(F_231(x), F_21(x)*F_230(x))
Eq(F_232(x), F_21(x)*F_233(x))
Eq(F_233(x), F_234(x, 1))
Eq(F_234(x, k_0), F_1(x) + F_231(x) + F_235(x, k_0) + F_363(x, k_0) + F_366(x, k_0))
Eq(F_235(x, k_0), F_236(x, k_0, 1))
Eq(F_236(x, k_0, k_1), F_14(x, k_0)*F_237(x, k_0, k_1))
Eq(F_237(x, k_0, k_1), F_1(x) + F_238(x, k_0) + F_284(x, k_0, k_1) + F_286(x, k_0, k_1) + F_353(x, k_0, k_1))
Eq(F_238(x, k_0), F_14(x, k_0)*F_239(x, k_0))
Eq(F_239(x, k_0), F_1(x) + F_238(x, k_0) + F_240(x, k_0) + F_259(x, k_0))
Eq(F_240(x, k_0), F_21(x)*F_241(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_74(x))
Eq(F_242(x, k_0), F_22(x, k_0) + F_243(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0) + F_26(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0) + F_247(x, k_0) + F_249(x, k_0) + F_27(x))
Eq(F_245(x, k_0), F_14(x, k_0)*F_246(x, k_0))
Eq(F_246(x, k_0), F_244(x, k_0) + F_76(x))
Eq(F_247(x, k_0), F_21(x)*F_248(x, k_0))
Eq(F_248(x, k_0), F_244(x, k_0) + F_26(x, k_0))
Eq(F_249(x, k_0), F_21(x)*F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0) + F_26(x, k_0))
Eq(F_251(x, k_0), F_249(x, k_0) + F_252(x, k_0) + F_257(x, k_0) + F_27(x))
Eq(F_252(x, k_0), F_14(x, k_0)*F_253(x, k_0))
Eq(F_253(x, k_0), F_194(x) + F_254(x, k_0))
Eq(F_254(x, k_0), F_252(x, k_0) + F_255(x, k_0) + 2*F_27(x))
Eq(F_255(x, k_0), F_21(x)*F_256(x, k_0))
Eq(F_256(x, k_0), F_254(x, k_0) + F_26(x, k_0))
Eq(F_257(x, k_0), F_21(x)*F_258(x, k_0))
Eq(F_258(x, k_0), F_251(x, k_0) + F_26(x, k_0))
Eq(F_259(x, k_0), F_21(x)*F_260(x, k_0))
Eq(F_260(x, k_0), F_1(x) + F_261(x, k_0) + F_262(x, k_0) + F_263(x, k_0) + F_264(x, k_0))
Eq(F_261(x, k_0), F_14(x, k_0)*F_260(x, k_0))
Eq(F_262(x, k_0), F_21(x)*F_260(x, k_0))
Eq(F_263(x, k_0), F_147(x, k_0, 1))
Eq(F_264(x, k_0), F_21(x)*F_265(x, k_0))
Eq(F_265(x, k_0), F_266(x) + F_268(x, k_0))
Eq(F_266(x), F_267(x) + F_74(x))
Eq(F_267(x), F_193(x) + F_75(x))
Eq(F_268(x, k_0), F_154(x, k_0) + F_269(x, k_0))
Eq(F_269(x, k_0), F_155(x, k_0) + F_270(x, k_0))
Eq(F_270(x, k_0), F_254(x, k_0) + F_271(x, k_0))
Eq(F_271(x, k_0), 2*F_27(x) + F_272(x, k_0) + F_274(x, k_0) + F_276(x, k_0))
Eq(F_272(x, k_0), F_14(x, k_0)*F_273(x, k_0))
Eq(F_273(x, k_0), F_197(x) + F_271(x, k_0))
Eq(F_274(x, k_0), F_21(x)*F_275(x, k_0))
Eq(F_275(x, k_0), F_156(x, k_0) + F_271(x, k_0))
Eq(F_276(x, k_0), F_21(x)*F_277(x, k_0))
Eq(F_277(x, k_0), F_278(x, k_0) + F_281(x, k_0))
Eq(F_278(x, k_0), F_279(x, k_0))
Eq(F_279(x, k_0), F_21(x)*F_280(x, k_0))
Eq(F_280(x, k_0), F_278(x, k_0) + F_82(x, k_0))
Eq(F_281(x, k_0), 3*F_27(x) + F_276(x, k_0) + F_282(x, k_0))
Eq(F_282(x, k_0), F_21(x)*F_283(x, k_0))
Eq(F_283(x, k_0), F_281(x, k_0) + F_85(x, k_0))
Eq(F_284(x, k_0, k_1), F_14(x, k_1)*F_285(x, k_0, k_1))
Eq(F_285(x, k_0, k_1), (-k_0*F_239(x, k_0) + k_1*F_239(x, k_1))/(-k_0 + k_1))
Eq(F_286(x, k_0, k_1), F_21(x)*F_287(x, k_0, k_1))
Eq(F_287(x, k_0, k_1), (-k_0*F_288(x, k_0) + k_1*F_288(x, k_1))/(-k_0 + k_1))
Eq(F_288(x, k_0), F_289(x, k_0, 1))
Eq(F_289(x, k_0, k_1), F_1(x) + F_290(x, k_0, k_1) + F_291(x, k_0, k_1) + F_293(x, k_0, k_1) + F_312(x, k_0, k_1))
Eq(F_290(x, k_0, k_1), F_14(x, k_0)*F_289(x, k_0, k_1))
Eq(F_291(x, k_0, k_1), F_21(x)*F_292(x, k_0, k_1))
Eq(F_292(x, k_0, k_1), (-k_0*F_289(x, k_0, k_1) + F_289(x, 1, k_1))/(1 - k_0))
Eq(F_293(x, k_0, k_1), F_14(x, k_1)*F_294(x, k_0, k_1))
Eq(F_294(x, k_0, k_1), (-k_0*F_295(x, k_0, k_1) + F_295(x, 1, k_1))/(1 - k_0))
Eq(F_295(x, k_0, k_1), F_1(x) + F_296(x, k_0, k_1) + F_297(x, k_0, k_1) + F_298(x, k_0, k_1))
Eq(F_296(x, k_0, k_1), F_14(x, k_0)*F_295(x, k_0, k_1))
Eq(F_297(x, k_0, k_1), F_14(x, k_1)*F_295(x, k_0, k_1))
Eq(F_298(x, k_0, k_1), F_21(x)*F_299(x, k_0, k_1))
Eq(F_299(x, k_0, k_1), (-k_1*F_300(x, k_0, k_1) + F_300(x, k_0, 1))/(1 - k_1))
Eq(F_300(x, k_0, k_1), F_1(x) + F_301(x, k_0, k_1) + F_302(x, k_0, k_1) + F_311(x, k_0, k_1))
Eq(F_301(x, k_0, k_1), F_14(x, k_0)*F_300(x, k_0, k_1))
Eq(F_302(x, k_0, k_1), F_14(x, k_1)*F_303(x, k_0, k_1))
Eq(F_303(x, k_0, k_1), F_17(x, k_1) + F_304(x, k_0, k_1))
Eq(F_304(x, k_0, k_1), F_22(x, k_0) + F_305(x, k_0, k_1))
Eq(F_305(x, k_0, k_1), F_306(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_306(x, k_0, k_1), F_166(x, k_0, k_1) + F_27(x) + F_307(x, k_0, k_1) + F_309(x, k_0, k_1))
Eq(F_307(x, k_0, k_1), F_14(x, k_0)*F_308(x, k_0, k_1))
Eq(F_308(x, k_0, k_1), F_26(x, k_1) + F_306(x, k_0, k_1))
Eq(F_309(x, k_0, k_1), F_14(x, k_1)*F_310(x, k_0, k_1))
Eq(F_310(x, k_0, k_1), F_26(x, k_0) + F_306(x, k_0, k_1))
Eq(F_311(x, k_0, k_1), F_149(x, k_0, k_1)*F_21(x))
Eq(F_312(x, k_0, k_1), F_21(x)*F_313(x, k_0, k_1))
Eq(F_313(x, k_0, k_1), (-k_1*F_314(x, k_0, k_1) + F_314(x, k_0, 1))/(1 - k_1))
Eq(F_314(x, k_0, k_1), F_1(x) + F_315(x, k_0, k_1) + F_317(x, k_0, k_1) + F_319(x, k_0, k_1) + F_351(x, k_0, k_1))
Eq(F_315(x, k_0, k_1), F_14(x, k_0)*F_316(x, k_0, k_1))
Eq(F_316(x, k_0, k_1), (k_1*F_300(x, k_0, k_1) - F_300(x, k_0, 1))/(k_1 - 1))
Eq(F_317(x, k_0, k_1), F_21(x)*F_318(x, k_0, k_1))
Eq(F_318(x, k_0, k_1), (k_1*F_314(x, k_0, k_1) - F_314(x, k_0, 1))/(k_1 - 1))
Eq(F_319(x, k_0, k_1), F_14(x, k_1)*F_320(x, k_0, k_1))
Eq(F_320(x, k_0, k_1), F_1(x) + F_319(x, k_0, k_1) + F_321(x, k_0, k_1) + F_344(x, k_0, k_1) + F_346(x, k_0, k_1))
Eq(F_321(x, k_0, k_1), F_14(x, k_0)*F_322(x, k_0, k_1))
Eq(F_322(x, k_0, k_1), F_323(x, k_0, k_1) + F_95(x, k_1))
Eq(F_323(x, k_0, k_1), F_304(x, k_0, k_1) + F_324(x, k_0, k_1))
Eq(F_324(x, k_0, k_1), F_155(x, k_0) + F_325(x, k_0, k_1))
Eq(F_325(x, k_0, k_1), F_326(x, k_0, k_1) + F_331(x, k_0, k_1))
Eq(F_326(x, k_0, k_1), 2*F_27(x) + F_327(x, k_0, k_1) + F_329(x, k_0, k_1))
Eq(F_327(x, k_0, k_1), F_14(x, k_0)*F_328(x, k_0, k_1))
Eq(F_328(x, k_0, k_1), F_326(x, k_0, k_1) + F_98(x, k_1))
Eq(F_329(x, k_0, k_1), F_14(x, k_1)*F_330(x, k_0, k_1))
Eq(F_330(x, k_0, k_1), F_26(x, k_0) + F_326(x, k_0, k_1))
Eq(F_331(x, k_0, k_1), 2*F_27(x) + F_332(x, k_0, k_1) + F_334(x, k_0, k_1) + F_336(x, k_0, k_1))
Eq(F_332(x, k_0, k_1), F_14(x, k_0)*F_333(x, k_0, k_1))
Eq(F_333(x, k_0, k_1), F_101(x, k_1) + F_331(x, k_0, k_1))
Eq(F_334(x, k_0, k_1), F_14(x, k_1)*F_335(x, k_0, k_1))
Eq(F_335(x, k_0, k_1), F_156(x, k_0) + F_331(x, k_0, k_1))
Eq(F_336(x, k_0, k_1), F_21(x)*F_337(x, k_0, k_1))
Eq(F_337(x, k_0, k_1), F_338(x, k_0, k_1) + F_341(x, k_0, k_1))
Eq(F_338(x, k_0, k_1), F_339(x, k_0, k_1))
Eq(F_339(x, k_0, k_1), F_14(x, k_1)*F_340(x, k_0, k_1))
Eq(F_340(x, k_0, k_1), F_338(x, k_0, k_1) + F_82(x, k_0))
Eq(F_341(x, k_0, k_1), 3*F_27(x) + F_336(x, k_0, k_1) + F_342(x, k_0, k_1))
Eq(F_342(x, k_0, k_1), F_14(x, k_1)*F_343(x, k_0, k_1))
Eq(F_343(x, k_0, k_1), F_341(x, k_0, k_1) + F_85(x, k_0))
Eq(F_344(x, k_0, k_1), F_21(x)*F_345(x, k_0, k_1))
Eq(F_345(x, k_0, k_1), (k_1*F_320(x, k_0, k_1) - F_320(x, k_0, 1))/(k_1 - 1))
Eq(F_346(x, k_0, k_1), F_21(x)*F_347(x, k_0, k_1))
Eq(F_347(x, k_0, k_1), F_348(x, k_0, k_1) + F_95(x, k_1))
Eq(F_348(x, k_0, k_1), F_349(x, k_0, k_1) + F_350(x, k_0, k_1))
Eq(F_349(x, k_0, k_1), F_162(x, k_0, k_1) + F_22(x, k_0))
Eq(F_350(x, k_0, k_1), F_337(x, k_0, k_1) + F_81(x, k_0))
Eq(F_351(x, k_0, k_1), F_21(x)*F_352(x, k_0, k_1))
Eq(F_352(x, k_0, k_1), (-k_0*F_149(x, k_0, k_1) + F_149(x, 1, k_1))/(1 - k_0))
Eq(F_353(x, k_0, k_1), F_21(x)*F_354(x, k_0, k_1))
Eq(F_354(x, k_0, k_1), (-k_0*F_355(x, k_0) + k_1*F_355(x, k_1))/(-k_0 + k_1))
Eq(F_355(x, k_0), F_1(x) + F_356(x, k_0) + F_357(x, k_0) + F_359(x, k_0) + F_361(x, k_0))
Eq(F_356(x, k_0), F_14(x, k_0)*F_355(x, k_0))
Eq(F_357(x, k_0), F_21(x)*F_358(x, k_0))
Eq(F_358(x, k_0), F_354(x, k_0, 1))
Eq(F_359(x, k_0), F_21(x)*F_360(x, k_0))
Eq(F_360(x, k_0), F_352(x, k_0, 1))
Eq(F_361(x, k_0), F_21(x)*F_362(x, k_0))
Eq(F_362(x, k_0), F_320(x, k_0, 1))
Eq(F_363(x, k_0), F_21(x)*F_364(x, k_0))
Eq(F_364(x, k_0), F_365(x, k_0, 1))
Eq(F_365(x, k_0, k_1), (-k_0*F_237(x, k_0, k_1) + F_237(x, 1, k_1))/(1 - k_0))
Eq(F_366(x, k_0), F_21(x)*F_367(x, k_0))
Eq(F_367(x, k_0), F_368(x, k_0, 1))
Eq(F_368(x, k_0, k_1), (-k_0*F_314(x, k_0, k_1) + F_314(x, 1, k_1))/(1 - k_0))
Eq(F_369(x), F_370(x, 1))
Eq(F_370(x, k_0), F_21(x)*F_371(x, k_0))
Eq(F_371(x, k_0), F_1(x) + F_372(x, k_0) + F_374(x, k_0) + F_375(x, k_0) + F_376(x, k_0))
Eq(F_372(x, k_0), F_14(x, k_0)*F_373(x, k_0))
Eq(F_373(x, k_0), F_299(x, k_0, 1))
Eq(F_374(x, k_0), F_317(x, k_0, 1))
Eq(F_375(x, k_0), F_319(x, k_0, 1))
Eq(F_376(x, k_0), F_351(x, k_0, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": 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[0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], 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"pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1], [3, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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"pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1], [3, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/35/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[92,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[8,x,k[0]]+F[84,x,k[0]]+F[90,x,k[0]]
F[8,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[73,x,k[0]]+F[75,x,k[0]]+F[83,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[5,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[37,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[24,x,k[0]]
F[13,x,k[0]] = F[14,x]+F[17,x,k[0]]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[5,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[17,x,k[0]]*F[5,x]
F[24,x,k[0]] = F[25,x]+F[31,x,k[0]]
F[25,x] = F[15,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[5,x]
F[29,x] = F[15,x]+F[26,x]
F[30,x] = F[25,x]*F[5,x]
F[31,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[20,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[15,x]+F[32,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[31,x,k[0]]*F[5,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[49,x,k[0]]
F[38,x,k[0]] = F[25,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]+F[45,x,k[0]]
F[40,x,k[0]] = F[27,x]+F[41,x,k[0]]+F[43,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]*F[5,x]
F[42,x,k[0]] = F[18,x,k[0]]+F[40,x,k[0]]
F[43,x,k[0]] = F[20,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[15,x]+F[40,x,k[0]]
F[45,x,k[0]] = 2*F[27,x]+F[46,x,k[0]]+F[48,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[5,x]
F[47,x,k[0]] = F[22,x,k[0]]+F[45,x,k[0]]
F[48,x,k[0]] = F[39,x,k[0]]*F[5,x]
F[49,x,k[0]] = F[50,x]+F[63,x,k[0]]
F[50,x] = F[26,x]+F[51,x]
F[51,x] = F[27,x]+F[52,x]+F[54,x]+F[62,x]
F[52,x] = F[5,x]*F[53,x]
F[53,x] = F[26,x]+F[51,x]
F[54,x] = F[5,x]*F[55,x]
F[55,x] = F[56,x]+F[59,x]
F[56,x] = F[57,x]
F[57,x] = F[5,x]*F[58,x]
F[58,x] = F[15,x]+F[56,x]
F[59,x] = 2*F[27,x]+F[54,x]+F[60,x]
F[60,x] = F[5,x]*F[61,x]
F[61,x] = F[26,x]+F[59,x]
F[62,x] = F[5,x]*F[50,x]
F[63,x,k[0]] = F[64,x,k[0]]+F[69,x,k[0]]
F[64,x,k[0]] = 2*F[27,x]+F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[5,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[32,x,k[0]]+F[64,x,k[0]]
F[67,x,k[0]] = F[20,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[26,x]+F[64,x,k[0]]
F[69,x,k[0]] = 3*F[27,x]+F[70,x,k[0]]+F[72,x,k[0]]
F[70,x,k[0]] = F[5,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[35,x,k[0]]+F[69,x,k[0]]
F[72,x,k[0]] = F[5,x]*F[63,x,k[0]]
F[73,x,k[0]] = F[5,x]*F[74,x,k[0]]
F[74,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[75,x,k[0]] = F[20,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[75,x,k[0]]+F[77,x,k[0]]+F[81,x,k[0]]
F[77,x,k[0]] = F[5,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[21,x,k[0]]+F[34,x,k[0]]
F[80,x,k[0]] = F[44,x,k[0]]+F[68,x,k[0]]
F[81,x,k[0]] = F[5,x]*F[82,x,k[0]]
F[82,x,k[0]] = 1/(-1+k[0])*(F[76,x,k[0]]*k[0]-F[76,x,1])
F[83,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[84,x,k[0]] = F[20,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[1,x]+F[84,x,k[0]]+F[86,x,k[0]]+F[88,x,k[0]]
F[86,x,k[0]] = F[5,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[13,x,k[0]]+F[38,x,k[0]]
F[88,x,k[0]] = F[5,x]*F[89,x,k[0]]
F[89,x,k[0]] = (F[85,x,k[0]]*k[0]-F[85,x,1])/(-1+k[0])
F[90,x,k[0]] = F[5,x]*F[91,x,k[0]]
F[91,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[92,x] = F[5,x]*F[93,x]
F[93,x] = F[94,x,1]
F[94,x,k[0]] = F[1,x]+F[306,x,k[0]]+F[308,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[5,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[134,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[1,x]+F[129,x,k[0]]+F[130,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[5,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[100,x,k[0]]*k[0]-F[100,x,1])
F[100,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[118,x,k[0]]+F[128,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[5,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[21,x,k[0]]+F[44,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[44,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[26,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[109,x,k[0]]+F[117,x,k[0]]+F[27,x]
F[107,x,k[0]] = F[108,x,k[0]]*F[5,x]
F[108,x,k[0]] = F[106,x,k[0]]+F[40,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[5,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[114,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[5,x]
F[113,x,k[0]] = F[111,x,k[0]]+F[18,x,k[0]]
F[114,x,k[0]] = 2*F[27,x]+F[109,x,k[0]]+F[115,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[5,x]
F[116,x,k[0]] = F[114,x,k[0]]+F[40,x,k[0]]
F[117,x,k[0]] = F[105,x,k[0]]*F[20,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[5,x]
F[119,x,k[0]] = F[100,x,k[0]]+F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]*F[5,x]
F[122,x,k[0]] = 1/(-1+k[0])*(F[123,x,k[0]]*k[0]-F[123,x,1])
F[124,x,k[0]] = 1/(-1+k[0])*(F[123,x,k[0]]*k[0]-F[123,x,1])
F[125,x,k[0]] = F[124,x,k[0]]*F[20,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]
F[9,x,k[0]] = F[126,x,k[0]]+F[127,x]
F[127,x] = F[100,x,1]
F[128,x,k[0]] = F[100,x,k[0]]*F[20,x,k[0]]
F[129,x,k[0]] = F[5,x]*F[96,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[20,x,k[0]]
F[131,x,k[0]] = F[1,x]+F[130,x,k[0]]+F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[119,x,k[0]]*F[5,x]
F[133,x,k[0]] = F[102,x,k[0]]*F[5,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[5,x]
F[136,x,k[0]] = F[137,x,k[0]]+F[305,x,k[0]]
F[138,x,k[0]] = F[137,x,k[0]]+F[299,x,k[0]]
F[139,x,k[0]] = F[138,x,k[0]]*F[5,x]
F[140,x,k[0]] = F[139,x,k[0]]+F[238,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[236,x,k[0]]
F[141,x,k[0]] = F[142,x]+F[143,x,k[0]]+F[144,x,k[0]]+F[235,x,k[0]]
F[142,x] = F[14,x]^2
F[143,x,k[0]] = F[141,x,k[0]]*F[5,x]
F[145,x,k[0]] = F[142,x]+F[144,x,k[0]]+F[227,x,k[0]]+F[228,x,k[0]]
F[146,x,k[0]] = F[145,x,k[0]]+F[225,x]
F[146,x,k[0]] = F[147,x,k[0]]+F[217,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]+F[180,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]+F[177,x]
F[149,x,k[0]] = F[1,x]+F[150,x]+F[152,x,k[0]]+F[174,x,k[0]]
F[150,x] = F[151,x]*F[5,x]
F[151,x] = F[14,x]+F[25,x]
F[152,x,k[0]] = F[153,x,k[0]]*F[5,x]
F[153,x,k[0]] = F[1,x]+F[154,x,k[0]]+F[155,x,k[0]]+F[172,x,k[0]]+F[75,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]*F[5,x]
F[155,x,k[0]] = F[156,x,k[0]]*F[5,x]
F[156,x,k[0]] = F[157,x,k[0]]+F[78,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]+F[164,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[160,x,k[0]]
F[159,x,k[0]] = F[111,x,k[0]]+F[15,x]
F[160,x,k[0]] = F[161,x,k[0]]+F[56,x]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[5,x]
F[163,x,k[0]] = F[161,x,k[0]]+F[32,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[166,x,k[0]]
F[165,x,k[0]] = F[114,x,k[0]]+F[26,x]
F[166,x,k[0]] = F[167,x,k[0]]+F[59,x]
F[167,x,k[0]] = 3*F[27,x]+F[168,x,k[0]]+F[170,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[5,x]
F[169,x,k[0]] = F[167,x,k[0]]+F[64,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]*F[5,x]
F[171,x,k[0]] = F[161,x,k[0]]+F[167,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]*F[5,x]
F[173,x,k[0]] = 1/(-1+k[0])*(F[153,x,k[0]]*k[0]-F[153,x,1])
F[174,x,k[0]] = F[175,x,k[0]]*F[20,x,k[0]]
F[175,x,k[0]] = F[103,x,k[0]]+F[176,x,k[0]]
F[176,x,k[0]] = F[159,x,k[0]]+F[165,x,k[0]]
F[177,x] = F[178,x]
F[178,x] = F[179,x,1]
F[179,x,k[0]] = F[123,x,k[0]]*F[5,x]
F[180,x,k[0]] = F[181,x,k[0]]*F[5,x]
F[181,x,k[0]] = F[182,x,k[0]]+F[211,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[194,x,k[0]]
F[183,x,k[0]] = F[14,x]+F[184,x,k[0]]+F[191,x,k[0]]+F[193,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[14,x]*F[186,x,k[0]]*F[5,x]
F[186,x,k[0]] = 1/(-1+k[0])*(F[187,x,k[0]]*k[0]-F[187,x,1])
F[187,x,k[0]] = F[14,x]+F[188,x,k[0]]+F[190,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[14,x]*F[187,x,k[0]]*F[5,x]
F[190,x,k[0]] = F[187,x,k[0]]*F[20,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]*F[5,x]
F[192,x,k[0]] = 1/(-1+k[0])*(F[183,x,k[0]]*k[0]-F[183,x,1])
F[193,x,k[0]] = F[183,x,k[0]]*F[20,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]*F[5,x]
F[195,x,k[0]] = F[183,x,k[0]]+F[196,x,k[0]]+F[197,x,k[0]]+F[209,x,k[0]]
F[196,x,k[0]] = F[195,x,k[0]]*F[5,x]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[14,x]*F[199,x,k[0]]*F[5,x]
F[199,x,k[0]] = 1/(-1+k[0])*(F[200,x,k[0]]*k[0]-F[200,x,1])
F[200,x,k[0]] = F[187,x,k[0]]+F[201,x,k[0]]+F[202,x,k[0]]
F[201,x,k[0]] = F[200,x,k[0]]*F[5,x]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[187,x,k[0]]*F[204,x]*F[5,x]
F[204,x] = F[151,x]+F[205,x]
F[205,x] = F[206,x]*F[5,x]
F[206,x] = F[151,x]+F[205,x]+F[207,x]
F[207,x] = F[208,x]
F[208,x] = F[151,x]*F[204,x]*F[5,x]
F[209,x,k[0]] = F[210,x,k[0]]*F[5,x]
F[210,x,k[0]] = 1/(-1+k[0])*(F[195,x,k[0]]*k[0]-F[195,x,1])
F[211,x] = F[212,x]
F[212,x] = F[213,x]*F[5,x]
F[213,x] = F[214,x,1]
F[214,x,k[0]] = F[122,x,k[0]]+F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[5,x]
F[216,x,k[0]] = 1/(-1+k[0])*(F[214,x,k[0]]*k[0]-F[214,x,1])
F[217,x,k[0]] = F[14,x]*F[218,x,k[0]]*F[5,x]
F[218,x,k[0]] = F[219,x,k[0]]+F[220,x]
F[219,x,k[0]] = F[187,x,k[0]]+F[201,x,k[0]]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[5,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[123,x,1]
F[224,x] = F[213,x]*F[5,x]
F[225,x] = F[226,x]
F[226,x] = F[14,x]*F[222,x]*F[5,x]
F[227,x,k[0]] = F[145,x,k[0]]*F[5,x]
F[228,x,k[0]] = F[20,x,k[0]]*F[229,x,k[0]]
F[229,x,k[0]] = F[142,x]+F[228,x,k[0]]+F[230,x,k[0]]
F[230,x,k[0]] = F[231,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]*F[5,x]
F[232,x,k[0]] = F[233,x,k[0]]+F[234,x,k[0]]
F[233,x,k[0]] = 1/(-1+k[0])*(F[229,x,k[0]]*k[0]-F[229,x,1])
F[234,x,k[0]] = F[14,x]^2*F[187,x,k[0]]*F[5,x]
F[235,x,k[0]] = F[141,x,k[0]]*F[20,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]
F[237,x,k[0]] = F[14,x]*F[214,x,k[0]]*F[5,x]
F[140,x,k[0]] = F[238,x,k[0]]+F[239,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]*F[5,x]
F[240,x,k[0]] = F[241,x,k[0]]+F[252,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[250,x,k[0]]
F[242,x,k[0]] = F[14,x]+F[243,x,k[0]]+F[244,x,k[0]]+F[247,x,k[0]]+F[249,x,k[0]]
F[243,x,k[0]] = F[242,x,k[0]]*F[5,x]
F[244,x,k[0]] = F[245,x,k[0]]
F[245,x,k[0]] = F[14,x]*F[246,x,k[0]]*F[5,x]
F[246,x,k[0]] = 1/(-1+k[0])*(F[219,x,k[0]]*k[0]-F[219,x,1])
F[247,x,k[0]] = F[248,x,k[0]]*F[5,x]
F[248,x,k[0]] = 1/(-1+k[0])*(F[182,x,k[0]]*k[0]-F[182,x,1])
F[249,x,k[0]] = F[20,x,k[0]]*F[242,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]
F[251,x,k[0]] = F[216,x,k[0]]*F[5,x]
F[252,x,k[0]] = F[14,x]*F[253,x,k[0]]*F[5,x]
F[253,x,k[0]] = F[254,x]+F[265,x,k[0]]+F[275,x,k[0]]+F[277,x,k[0]]+F[281,x,k[0]]
F[254,x] = F[14,x]*F[255,x]
F[255,x] = F[1,x]+F[256,x]
F[256,x] = F[257,x]*F[5,x]
F[257,x] = F[1,x]+F[258,x]+F[259,x]
F[258,x] = F[257,x]*F[5,x]
F[259,x] = F[260,x]*F[5,x]
F[260,x] = F[261,x,1]
F[261,x,k[0]] = (F[262,x,k[0]]*k[0]-F[262,x,1])/(-1+k[0])
F[262,x,k[0]] = F[1,x]+F[263,x,k[0]]+F[264,x,k[0]]
F[263,x,k[0]] = F[20,x,k[0]]*F[262,x,k[0]]
F[264,x,k[0]] = F[261,x,k[0]]*F[5,x]
F[265,x,k[0]] = F[266,x,k[0]]*F[5,x]
F[266,x,k[0]] = 1/(-1+k[0])*(F[267,x,k[0]]*k[0]-F[267,x,1])
F[267,x,k[0]] = F[268,x,k[0]]+F[274,x,k[0]]
F[268,x,k[0]] = 1/(-1+k[0])*(F[269,x,k[0]]*k[0]-F[269,x,1])
F[270,x,k[0]] = F[269,x,k[0]]*F[5,x]
F[271,x,k[0]] = F[255,x]+F[270,x,k[0]]+F[273,x,k[0]]
F[271,x,k[0]] = F[103,x,k[0]]+F[272,x,k[0]]
F[272,x,k[0]] = F[179,x,k[0]]
F[273,x,k[0]] = F[20,x,k[0]]*F[271,x,k[0]]
F[274,x,k[0]] = F[266,x,k[0]]*F[5,x]
F[275,x,k[0]] = F[276,x,k[0]]
F[276,x,k[0]] = F[14,x]*F[253,x,k[0]]*F[5,x]
F[277,x,k[0]] = F[14,x]*F[278,x,k[0]]*F[5,x]
F[278,x,k[0]] = F[102,x,k[0]]+F[279,x,k[0]]
F[279,x,k[0]] = F[280,x,k[0]]
F[280,x,k[0]] = F[122,x,k[0]]*F[5,x]
F[281,x,k[0]] = F[20,x,k[0]]*F[282,x,k[0]]
F[282,x,k[0]] = F[283,x,k[0]]+F[291,x,k[0]]
F[283,x,k[0]] = F[284,x,k[0]]+F[289,x,k[0]]
F[284,x,k[0]] = F[14,x]+F[285,x,k[0]]+F[286,x,k[0]]+F[288,x,k[0]]
F[285,x,k[0]] = F[284,x,k[0]]*F[5,x]
F[286,x,k[0]] = F[287,x,k[0]]
F[287,x,k[0]] = F[14,x]*F[219,x,k[0]]*F[5,x]
F[288,x,k[0]] = F[20,x,k[0]]*F[284,x,k[0]]
F[289,x,k[0]] = F[290,x,k[0]]
F[290,x,k[0]] = F[123,x,k[0]]*F[14,x]*F[5,x]
F[291,x,k[0]] = F[292,x,k[0]]
F[292,x,k[0]] = F[103,x,k[0]]*F[293,x,k[0]]*F[5,x]
F[293,x,k[0]] = F[14,x]+F[294,x]+F[295,x,k[0]]+F[297,x,k[0]]+F[298,x,k[0]]
F[294,x] = F[206,x]*F[5,x]
F[295,x,k[0]] = F[296,x,k[0]]
F[296,x,k[0]] = F[14,x]*F[293,x,k[0]]*F[5,x]
F[297,x,k[0]] = F[14,x]*F[175,x,k[0]]*F[5,x]
F[298,x,k[0]] = F[20,x,k[0]]*F[293,x,k[0]]
F[299,x,k[0]] = F[14,x]*F[300,x,k[0]]*F[5,x]
F[301,x,k[0]] = F[300,x,k[0]]*F[5,x]
F[302,x,k[0]] = F[278,x,k[0]]+F[301,x,k[0]]
F[302,x,k[0]] = F[284,x,k[0]]+F[303,x,k[0]]
F[303,x,k[0]] = F[304,x,k[0]]
F[304,x,k[0]] = F[214,x,k[0]]*F[5,x]
F[305,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]*F[300,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]*F[5,x]
F[307,x,k[0]] = 1/(-1+k[0])*(F[94,x,k[0]]*k[0]-F[94,x,1])
F[308,x,k[0]] = F[20,x,k[0]]*F[94,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{92}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{8}\! \left(x , y\right)+F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{27}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)+F_{62}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{5}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{5}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{5}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{26}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{75}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{75}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}
F_{83}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}
F_{90}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{92}\! \left(x \right) = F_{5}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{94}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{306}\! \left(x , y\right)+F_{308}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{100}\! \left(x , y\right)+F_{100}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{27}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{5}\! \left(x \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_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{122}\! \left(x , y\right) = -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}
F_{124}\! \left(x , y\right) = -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{128}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{235}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{14} \left(x \right)^{2}
F_{143}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{142}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{225}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{177}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{5}\! \left(x \right)
F_{151}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{154}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{59}\! \left(x \right)
F_{167}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{168}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{173}\! \left(x , y\right) = -\frac{-y F_{153}\! \left(x , y\right)+F_{153}\! \left(x , 1\right)}{-1+y}
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x , 1\right)
F_{179}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{211}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{184}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{186}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{186}\! \left(x , y\right) = -\frac{-y F_{187}\! \left(x , y\right)+F_{187}\! \left(x , 1\right)}{-1+y}
F_{187}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{188}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{187}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{192}\! \left(x , y\right) = -\frac{-y F_{183}\! \left(x , y\right)+F_{183}\! \left(x , 1\right)}{-1+y}
F_{193}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{196}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{199}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{199}\! \left(x , y\right) = -\frac{-y F_{200}\! \left(x , y\right)+F_{200}\! \left(x , 1\right)}{-1+y}
F_{200}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{204}\! \left(x \right) F_{5}\! \left(x \right)
F_{204}\! \left(x \right) = F_{151}\! \left(x \right)+F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right) F_{5}\! \left(x \right)
F_{206}\! \left(x \right) = F_{151}\! \left(x \right)+F_{205}\! \left(x \right)+F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{151}\! \left(x \right) F_{204}\! \left(x \right) F_{5}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{210}\! \left(x , y\right) = -\frac{-y F_{195}\! \left(x , y\right)+F_{195}\! \left(x , 1\right)}{-1+y}
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right) F_{5}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x , 1\right)
F_{214}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{216}\! \left(x , y\right) = -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}
F_{217}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{218}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{220}\! \left(x \right)
F_{219}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{5}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{224}\! \left(x \right) = F_{213}\! \left(x \right) F_{5}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = F_{14}\! \left(x \right) F_{222}\! \left(x \right) F_{5}\! \left(x \right)
F_{227}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{228}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{142}\! \left(x \right)+F_{228}\! \left(x , y\right)+F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{231}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = -\frac{-y F_{229}\! \left(x , y\right)+F_{229}\! \left(x , 1\right)}{-1+y}
F_{234}\! \left(x , y\right) = F_{14} \left(x \right)^{2} F_{187}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{235}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{214}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{243}\! \left(x , y\right)+F_{244}\! \left(x , y\right)+F_{247}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{242}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{246}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{246}\! \left(x , y\right) = -\frac{-y F_{219}\! \left(x , y\right)+F_{219}\! \left(x , 1\right)}{-1+y}
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{248}\! \left(x , y\right) = -\frac{-y F_{182}\! \left(x , y\right)+F_{182}\! \left(x , 1\right)}{-1+y}
F_{249}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{242}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{253}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x \right)+F_{265}\! \left(x , y\right)+F_{275}\! \left(x , y\right)+F_{277}\! \left(x , y\right)+F_{281}\! \left(x , y\right)
F_{254}\! \left(x \right) = F_{14}\! \left(x \right) F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{1}\! \left(x \right)+F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right) F_{5}\! \left(x \right)
F_{257}\! \left(x \right) = F_{1}\! \left(x \right)+F_{258}\! \left(x \right)+F_{259}\! \left(x \right)
F_{258}\! \left(x \right) = F_{257}\! \left(x \right) F_{5}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right) F_{5}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x , 1\right)
F_{261}\! \left(x , y\right) = -\frac{-y F_{262}\! \left(x , y\right)+F_{262}\! \left(x , 1\right)}{-1+y}
F_{262}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{263}\! \left(x , y\right)+F_{264}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{262}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{261}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{266}\! \left(x , y\right) = -\frac{-y F_{267}\! \left(x , y\right)+F_{267}\! \left(x , 1\right)}{-1+y}
F_{267}\! \left(x , y\right) = F_{268}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = -\frac{-y F_{269}\! \left(x , y\right)+F_{269}\! \left(x , 1\right)}{-1+y}
F_{270}\! \left(x , y\right) = F_{269}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{271}\! \left(x , y\right) = F_{255}\! \left(x \right)+F_{270}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{271}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{266}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{253}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{277}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{278}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{278}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{281}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{282}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{283}\! \left(x , y\right)+F_{291}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{285}\! \left(x , y\right)+F_{286}\! \left(x , y\right)+F_{288}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{284}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{219}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{288}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{284}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{290}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{291}\! \left(x , y\right) = F_{292}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{293}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{293}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{294}\! \left(x \right)+F_{295}\! \left(x , y\right)+F_{297}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{294}\! \left(x \right) = F_{206}\! \left(x \right) F_{5}\! \left(x \right)
F_{295}\! \left(x , y\right) = F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{293}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{297}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{175}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{298}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{293}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{300}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{301}\! \left(x , y\right) = F_{300}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{302}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{301}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{214}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{305}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{300}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{307}\! \left(x , y\right) = -\frac{-y F_{94}\! \left(x , y\right)+F_{94}\! \left(x , 1\right)}{-1+y}
F_{308}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{94}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_92(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_8(x, k_0) + F_84(x, k_0) + F_90(x, k_0))
Eq(F_8(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_73(x, k_0) + F_75(x, k_0) + F_83(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_5(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_37(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_24(x, k_0))
Eq(F_13(x, k_0), F_14(x) + F_17(x, k_0))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_5(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_17(x, k_0)*F_5(x))
Eq(F_24(x, k_0), F_25(x) + F_31(x, k_0))
Eq(F_25(x), F_15(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_5(x))
Eq(F_29(x), F_15(x) + F_26(x))
Eq(F_30(x), F_25(x)*F_5(x))
Eq(F_31(x, k_0), F_32(x, k_0) + F_35(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_20(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_15(x) + F_32(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_31(x, k_0)*F_5(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_49(x, k_0))
Eq(F_38(x, k_0), F_25(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0) + F_45(x, k_0))
Eq(F_40(x, k_0), F_27(x) + F_41(x, k_0) + F_43(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0)*F_5(x))
Eq(F_42(x, k_0), F_18(x, k_0) + F_40(x, k_0))
Eq(F_43(x, k_0), F_20(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_15(x) + F_40(x, k_0))
Eq(F_45(x, k_0), 2*F_27(x) + F_46(x, k_0) + F_48(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_5(x))
Eq(F_47(x, k_0), F_22(x, k_0) + F_45(x, k_0))
Eq(F_48(x, k_0), F_39(x, k_0)*F_5(x))
Eq(F_49(x, k_0), F_50(x) + F_63(x, k_0))
Eq(F_50(x), F_26(x) + F_51(x))
Eq(F_51(x), F_27(x) + F_52(x) + F_54(x) + F_62(x))
Eq(F_52(x), F_5(x)*F_53(x))
Eq(F_53(x), F_26(x) + F_51(x))
Eq(F_54(x), F_5(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_59(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_5(x)*F_58(x))
Eq(F_58(x), F_15(x) + F_56(x))
Eq(F_59(x), 2*F_27(x) + F_54(x) + F_60(x))
Eq(F_60(x), F_5(x)*F_61(x))
Eq(F_61(x), F_26(x) + F_59(x))
Eq(F_62(x), F_5(x)*F_50(x))
Eq(F_63(x, k_0), F_64(x, k_0) + F_69(x, k_0))
Eq(F_64(x, k_0), 2*F_27(x) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_5(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_32(x, k_0) + F_64(x, k_0))
Eq(F_67(x, k_0), F_20(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_26(x) + F_64(x, k_0))
Eq(F_69(x, k_0), 3*F_27(x) + F_70(x, k_0) + F_72(x, k_0))
Eq(F_70(x, k_0), F_5(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_35(x, k_0) + F_69(x, k_0))
Eq(F_72(x, k_0), F_5(x)*F_63(x, k_0))
Eq(F_73(x, k_0), F_5(x)*F_74(x, k_0))
Eq(F_74(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_75(x, k_0), F_20(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_75(x, k_0) + F_77(x, k_0) + F_81(x, k_0))
Eq(F_77(x, k_0), F_5(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_21(x, k_0) + F_34(x, k_0))
Eq(F_80(x, k_0), F_44(x, k_0) + F_68(x, k_0))
Eq(F_81(x, k_0), F_5(x)*F_82(x, k_0))
Eq(F_82(x, k_0), (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_83(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_84(x, k_0), F_20(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_1(x) + F_84(x, k_0) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_86(x, k_0), F_5(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_13(x, k_0) + F_38(x, k_0))
Eq(F_88(x, k_0), F_5(x)*F_89(x, k_0))
Eq(F_89(x, k_0), (-k_0*F_85(x, k_0) + F_85(x, 1))/(1 - k_0))
Eq(F_90(x, k_0), F_5(x)*F_91(x, k_0))
Eq(F_91(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_92(x), F_5(x)*F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_94(x, k_0), F_1(x) + F_306(x, k_0) + F_308(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_5(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_134(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_1(x) + F_129(x, k_0) + F_130(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_5(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_100(x, k_0) - F_100(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_1(x) + F_101(x, k_0) + F_118(x, k_0) + F_128(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_5(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_21(x, k_0) + F_44(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_44(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_26(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_109(x, k_0) + F_117(x, k_0) + F_27(x))
Eq(F_107(x, k_0), F_108(x, k_0)*F_5(x))
Eq(F_108(x, k_0), F_106(x, k_0) + F_40(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_5(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_114(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_5(x))
Eq(F_113(x, k_0), F_111(x, k_0) + F_18(x, k_0))
Eq(F_114(x, k_0), F_109(x, k_0) + F_115(x, k_0) + 2*F_27(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_5(x))
Eq(F_116(x, k_0), F_114(x, k_0) + F_40(x, k_0))
Eq(F_117(x, k_0), F_105(x, k_0)*F_20(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_5(x))
Eq(F_119(x, k_0), F_100(x, k_0) + F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0)*F_5(x))
Eq(F_122(x, k_0), (k_0*F_123(x, k_0) - F_123(x, 1))/(k_0 - 1))
Eq(F_124(x, k_0), (-k_0*F_123(x, k_0) + F_123(x, 1))/(1 - k_0))
Eq(F_125(x, k_0), F_124(x, k_0)*F_20(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0))
Eq(F_9(x, k_0), F_126(x, k_0) + F_127(x))
Eq(F_127(x), F_100(x, 1))
Eq(F_128(x, k_0), F_100(x, k_0)*F_20(x, k_0))
Eq(F_129(x, k_0), F_5(x)*F_96(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_20(x, k_0))
Eq(F_131(x, k_0), F_1(x) + F_130(x, k_0) + F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_119(x, k_0)*F_5(x))
Eq(F_133(x, k_0), F_102(x, k_0)*F_5(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_5(x))
Eq(F_136(x, k_0), F_137(x, k_0) + F_305(x, k_0))
Eq(F_138(x, k_0), F_137(x, k_0) + F_299(x, k_0))
Eq(F_139(x, k_0), F_138(x, k_0)*F_5(x))
Eq(F_140(x, k_0), F_139(x, k_0) + F_238(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_236(x, k_0))
Eq(F_141(x, k_0), F_142(x) + F_143(x, k_0) + F_144(x, k_0) + F_235(x, k_0))
Eq(F_142(x), F_14(x)**2)
Eq(F_143(x, k_0), F_141(x, k_0)*F_5(x))
Eq(F_145(x, k_0), F_142(x) + F_144(x, k_0) + F_227(x, k_0) + F_228(x, k_0))
Eq(F_146(x, k_0), F_145(x, k_0) + F_225(x))
Eq(F_146(x, k_0), F_147(x, k_0) + F_217(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + F_180(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0) + F_177(x))
Eq(F_149(x, k_0), F_1(x) + F_150(x) + F_152(x, k_0) + F_174(x, k_0))
Eq(F_150(x), F_151(x)*F_5(x))
Eq(F_151(x), F_14(x) + F_25(x))
Eq(F_152(x, k_0), F_153(x, k_0)*F_5(x))
Eq(F_153(x, k_0), F_1(x) + F_154(x, k_0) + F_155(x, k_0) + F_172(x, k_0) + F_75(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0)*F_5(x))
Eq(F_155(x, k_0), F_156(x, k_0)*F_5(x))
Eq(F_156(x, k_0), F_157(x, k_0) + F_78(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0) + F_164(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_160(x, k_0))
Eq(F_159(x, k_0), F_111(x, k_0) + F_15(x))
Eq(F_160(x, k_0), F_161(x, k_0) + F_56(x))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_5(x))
Eq(F_163(x, k_0), F_161(x, k_0) + F_32(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_166(x, k_0))
Eq(F_165(x, k_0), F_114(x, k_0) + F_26(x))
Eq(F_166(x, k_0), F_167(x, k_0) + F_59(x))
Eq(F_167(x, k_0), F_168(x, k_0) + F_170(x, k_0) + 3*F_27(x))
Eq(F_168(x, k_0), F_169(x, k_0)*F_5(x))
Eq(F_169(x, k_0), F_167(x, k_0) + F_64(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0)*F_5(x))
Eq(F_171(x, k_0), F_161(x, k_0) + F_167(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0)*F_5(x))
Eq(F_173(x, k_0), (k_0*F_153(x, k_0) - F_153(x, 1))/(k_0 - 1))
Eq(F_174(x, k_0), F_175(x, k_0)*F_20(x, k_0))
Eq(F_175(x, k_0), F_103(x, k_0) + F_176(x, k_0))
Eq(F_176(x, k_0), F_159(x, k_0) + F_165(x, k_0))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_179(x, 1))
Eq(F_179(x, k_0), F_123(x, k_0)*F_5(x))
Eq(F_180(x, k_0), F_181(x, k_0)*F_5(x))
Eq(F_181(x, k_0), F_182(x, k_0) + F_211(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_194(x, k_0))
Eq(F_183(x, k_0), F_14(x) + F_184(x, k_0) + F_191(x, k_0) + F_193(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_14(x)*F_186(x, k_0)*F_5(x))
Eq(F_186(x, k_0), (k_0*F_187(x, k_0) - F_187(x, 1))/(k_0 - 1))
Eq(F_187(x, k_0), F_14(x) + F_188(x, k_0) + F_190(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_14(x)*F_187(x, k_0)*F_5(x))
Eq(F_190(x, k_0), F_187(x, k_0)*F_20(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0)*F_5(x))
Eq(F_192(x, k_0), (k_0*F_183(x, k_0) - F_183(x, 1))/(k_0 - 1))
Eq(F_193(x, k_0), F_183(x, k_0)*F_20(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0)*F_5(x))
Eq(F_195(x, k_0), F_183(x, k_0) + F_196(x, k_0) + F_197(x, k_0) + F_209(x, k_0))
Eq(F_196(x, k_0), F_195(x, k_0)*F_5(x))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_14(x)*F_199(x, k_0)*F_5(x))
Eq(F_199(x, k_0), (k_0*F_200(x, k_0) - F_200(x, 1))/(k_0 - 1))
Eq(F_200(x, k_0), F_187(x, k_0) + F_201(x, k_0) + F_202(x, k_0))
Eq(F_201(x, k_0), F_200(x, k_0)*F_5(x))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_187(x, k_0)*F_204(x)*F_5(x))
Eq(F_204(x), F_151(x) + F_205(x))
Eq(F_205(x), F_206(x)*F_5(x))
Eq(F_206(x), F_151(x) + F_205(x) + F_207(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_151(x)*F_204(x)*F_5(x))
Eq(F_209(x, k_0), F_210(x, k_0)*F_5(x))
Eq(F_210(x, k_0), (k_0*F_195(x, k_0) - F_195(x, 1))/(k_0 - 1))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_213(x)*F_5(x))
Eq(F_213(x), F_214(x, 1))
Eq(F_214(x, k_0), F_122(x, k_0) + F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_5(x))
Eq(F_216(x, k_0), (k_0*F_214(x, k_0) - F_214(x, 1))/(k_0 - 1))
Eq(F_217(x, k_0), F_14(x)*F_218(x, k_0)*F_5(x))
Eq(F_218(x, k_0), F_219(x, k_0) + F_220(x))
Eq(F_219(x, k_0), F_187(x, k_0) + F_201(x, k_0))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_5(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_123(x, 1))
Eq(F_224(x), F_213(x)*F_5(x))
Eq(F_225(x), F_226(x))
Eq(F_226(x), F_14(x)*F_222(x)*F_5(x))
Eq(F_227(x, k_0), F_145(x, k_0)*F_5(x))
Eq(F_228(x, k_0), F_20(x, k_0)*F_229(x, k_0))
Eq(F_229(x, k_0), F_142(x) + F_228(x, k_0) + F_230(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0)*F_5(x))
Eq(F_232(x, k_0), F_233(x, k_0) + F_234(x, k_0))
Eq(F_233(x, k_0), (k_0*F_229(x, k_0) - F_229(x, 1))/(k_0 - 1))
Eq(F_234(x, k_0), F_14(x)**2*F_187(x, k_0)*F_5(x))
Eq(F_235(x, k_0), F_141(x, k_0)*F_20(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0))
Eq(F_237(x, k_0), F_14(x)*F_214(x, k_0)*F_5(x))
Eq(F_140(x, k_0), F_238(x, k_0) + F_239(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0)*F_5(x))
Eq(F_240(x, k_0), F_241(x, k_0) + F_252(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_250(x, k_0))
Eq(F_242(x, k_0), F_14(x) + F_243(x, k_0) + F_244(x, k_0) + F_247(x, k_0) + F_249(x, k_0))
Eq(F_243(x, k_0), F_242(x, k_0)*F_5(x))
Eq(F_244(x, k_0), F_245(x, k_0))
Eq(F_245(x, k_0), F_14(x)*F_246(x, k_0)*F_5(x))
Eq(F_246(x, k_0), (k_0*F_219(x, k_0) - F_219(x, 1))/(k_0 - 1))
Eq(F_247(x, k_0), F_248(x, k_0)*F_5(x))
Eq(F_248(x, k_0), (k_0*F_182(x, k_0) - F_182(x, 1))/(k_0 - 1))
Eq(F_249(x, k_0), F_20(x, k_0)*F_242(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0))
Eq(F_251(x, k_0), F_216(x, k_0)*F_5(x))
Eq(F_252(x, k_0), F_14(x)*F_253(x, k_0)*F_5(x))
Eq(F_253(x, k_0), F_254(x) + F_265(x, k_0) + F_275(x, k_0) + F_277(x, k_0) + F_281(x, k_0))
Eq(F_254(x), F_14(x)*F_255(x))
Eq(F_255(x), F_1(x) + F_256(x))
Eq(F_256(x), F_257(x)*F_5(x))
Eq(F_257(x), F_1(x) + F_258(x) + F_259(x))
Eq(F_258(x), F_257(x)*F_5(x))
Eq(F_259(x), F_260(x)*F_5(x))
Eq(F_260(x), F_261(x, 1))
Eq(F_261(x, k_0), (-k_0*F_262(x, k_0) + F_262(x, 1))/(1 - k_0))
Eq(F_262(x, k_0), F_1(x) + F_263(x, k_0) + F_264(x, k_0))
Eq(F_263(x, k_0), F_20(x, k_0)*F_262(x, k_0))
Eq(F_264(x, k_0), F_261(x, k_0)*F_5(x))
Eq(F_265(x, k_0), F_266(x, k_0)*F_5(x))
Eq(F_266(x, k_0), (k_0*F_267(x, k_0) - F_267(x, 1))/(k_0 - 1))
Eq(F_267(x, k_0), F_268(x, k_0) + F_274(x, k_0))
Eq(F_268(x, k_0), (k_0*F_269(x, k_0) - F_269(x, 1))/(k_0 - 1))
Eq(F_270(x, k_0), F_269(x, k_0)*F_5(x))
Eq(F_271(x, k_0), F_255(x) + F_270(x, k_0) + F_273(x, k_0))
Eq(F_271(x, k_0), F_103(x, k_0) + F_272(x, k_0))
Eq(F_272(x, k_0), F_179(x, k_0))
Eq(F_273(x, k_0), F_20(x, k_0)*F_271(x, k_0))
Eq(F_274(x, k_0), F_266(x, k_0)*F_5(x))
Eq(F_275(x, k_0), F_276(x, k_0))
Eq(F_276(x, k_0), F_14(x)*F_253(x, k_0)*F_5(x))
Eq(F_277(x, k_0), F_14(x)*F_278(x, k_0)*F_5(x))
Eq(F_278(x, k_0), F_102(x, k_0) + F_279(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0))
Eq(F_280(x, k_0), F_122(x, k_0)*F_5(x))
Eq(F_281(x, k_0), F_20(x, k_0)*F_282(x, k_0))
Eq(F_282(x, k_0), F_283(x, k_0) + F_291(x, k_0))
Eq(F_283(x, k_0), F_284(x, k_0) + F_289(x, k_0))
Eq(F_284(x, k_0), F_14(x) + F_285(x, k_0) + F_286(x, k_0) + F_288(x, k_0))
Eq(F_285(x, k_0), F_284(x, k_0)*F_5(x))
Eq(F_286(x, k_0), F_287(x, k_0))
Eq(F_287(x, k_0), F_14(x)*F_219(x, k_0)*F_5(x))
Eq(F_288(x, k_0), F_20(x, k_0)*F_284(x, k_0))
Eq(F_289(x, k_0), F_290(x, k_0))
Eq(F_290(x, k_0), F_123(x, k_0)*F_14(x)*F_5(x))
Eq(F_291(x, k_0), F_292(x, k_0))
Eq(F_292(x, k_0), F_103(x, k_0)*F_293(x, k_0)*F_5(x))
Eq(F_293(x, k_0), F_14(x) + F_294(x) + F_295(x, k_0) + F_297(x, k_0) + F_298(x, k_0))
Eq(F_294(x), F_206(x)*F_5(x))
Eq(F_295(x, k_0), F_296(x, k_0))
Eq(F_296(x, k_0), F_14(x)*F_293(x, k_0)*F_5(x))
Eq(F_297(x, k_0), F_14(x)*F_175(x, k_0)*F_5(x))
Eq(F_298(x, k_0), F_20(x, k_0)*F_293(x, k_0))
Eq(F_299(x, k_0), F_14(x)*F_300(x, k_0)*F_5(x))
Eq(F_301(x, k_0), F_300(x, k_0)*F_5(x))
Eq(F_302(x, k_0), F_278(x, k_0) + F_301(x, k_0))
Eq(F_302(x, k_0), F_284(x, k_0) + F_303(x, k_0))
Eq(F_303(x, k_0), F_304(x, k_0))
Eq(F_304(x, k_0), F_214(x, k_0)*F_5(x))
Eq(F_305(x, k_0), F_20(x, k_0)*F_21(x, k_0)*F_300(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0)*F_5(x))
Eq(F_307(x, k_0), (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_308(x, k_0), F_20(x, k_0)*F_94(x, k_0))
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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 3], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 2]]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 5]]}, {"patt": [0, 1], "pos": [[0, 5], [0, 5]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [0, 2], [0, 4], [0, 5], [2, 0], [2, 2]], [[1, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": 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"pos": [[1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}], "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, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 2]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/36/
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[5,x]
F[3,x] = F[1,x]+F[119,x]+F[4,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[117,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0],1]
F[10,x,k[0],k[1]] = F[1,x]+F[100,x,k[1],k[0]]+F[11,x,k[0],k[1]]+F[74,x,k[0],k[1]]+F[76,x,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[5,x]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]+F[38,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[1]]+F[19,x,k[0],k[1]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0],k[1]] = F[16,x,k[0]]+F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[1],k[0]]
F[21,x,k[0],k[1]] = F[18,x,k[0]]*F[19,x,k[1],k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[1]]+F[32,x,k[0],k[1]]
F[23,x,k[0]] = F[24,x]+F[27,x,k[0]]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[5,x]
F[26,x] = F[1,x]+F[24,x]
F[27,x,k[0]] = F[28,x]+F[29,x,k[0]]+F[31,x,k[0]]
F[28,x] = 0
F[29,x,k[0]] = F[30,x,k[0]]*F[5,x]
F[30,x,k[0]] = F[16,x,k[0]]+F[27,x,k[0]]
F[31,x,k[0]] = F[18,x,k[0]]*F[23,x,k[0]]
F[32,x,k[0],k[1]] = F[33,x,k[0]]+F[36,x,k[0],k[1]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[18,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[24,x]+F[33,x,k[0]]
F[36,x,k[0],k[1]] = F[37,x,k[1],k[0]]
F[37,x,k[0],k[1]] = F[18,x,k[0]]*F[32,x,k[1],k[0]]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[39,x,k[0],k[1]] = F[23,x,k[1]]+F[40,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[27,x,k[0]]+F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = 2*F[28,x]+F[42,x,k[0],k[1]]+F[44,x,k[1],k[0]]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]*F[5,x]
F[43,x,k[0],k[1]] = F[20,x,k[0],k[1]]+F[41,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[18,x,k[0]]*F[40,x,k[1],k[0]]
F[45,x,k[0],k[1]] = F[46,x,k[1]]+F[64,x,k[0],k[1]]
F[46,x,k[0]] = F[47,x]+F[52,x,k[0]]
F[47,x] = F[28,x]+F[48,x]+F[50,x]
F[48,x] = F[49,x]*F[5,x]
F[49,x] = F[24,x]+F[47,x]
F[50,x] = F[5,x]*F[51,x]
F[51,x] = F[24,x]+F[47,x]
F[52,x,k[0]] = F[28,x]+F[53,x,k[0]]+F[55,x,k[0]]+F[63,x,k[0]]
F[53,x,k[0]] = F[5,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[27,x,k[0]]+F[52,x,k[0]]
F[55,x,k[0]] = F[5,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[5,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[16,x,k[0]]+F[57,x,k[0]]
F[60,x,k[0]] = 2*F[28,x]+F[55,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[5,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[27,x,k[0]]+F[60,x,k[0]]
F[63,x,k[0]] = F[18,x,k[0]]*F[46,x,k[0]]
F[64,x,k[0],k[1]] = F[65,x,k[0]]+F[70,x,k[0],k[1]]
F[65,x,k[0]] = 2*F[28,x]+F[66,x,k[0]]+F[68,x,k[0]]
F[66,x,k[0]] = F[5,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[33,x,k[0]]+F[65,x,k[0]]
F[68,x,k[0]] = F[18,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[47,x]+F[65,x,k[0]]
F[70,x,k[0],k[1]] = 3*F[28,x]+F[71,x,k[0],k[1]]+F[73,x,k[1],k[0]]
F[71,x,k[0],k[1]] = F[5,x]*F[72,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[36,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[18,x,k[0]]*F[64,x,k[1],k[0]]
F[74,x,k[0],k[1]] = F[5,x]*F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = 1/(-1+k[0])*(F[10,x,k[0],k[1]]*k[0]-F[10,x,1,k[1]])
F[76,x,k[0]] = F[18,x,k[0]]*F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,1,k[0]]
F[78,x,k[0],k[1]] = F[1,x]+F[79,x,k[0],k[1]]+F[93,x,k[0],k[1]]+F[99,x,k[1],k[0]]
F[79,x,k[0],k[1]] = F[80,x,k[0],1,k[1]]
F[80,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[81,x,k[0],k[1],k[2]]
F[81,x,k[0],k[1],k[2]] = F[14,x,k[1],k[2]]+F[82,x,k[0],k[1],k[2]]
F[82,x,k[0],k[1],k[2]] = F[83,x,k[0],k[2]]+F[88,x,k[0],k[1],k[2]]
F[83,x,k[0],k[1]] = F[16,x,k[0]]+F[84,x,k[0],k[1]]
F[84,x,k[0],k[1]] = F[28,x]+F[85,x,k[0],k[1]]+F[87,x,k[1],k[0]]
F[85,x,k[0],k[1]] = F[18,x,k[0]]*F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = F[16,x,k[1]]+F[84,x,k[0],k[1]]
F[87,x,k[0],k[1]] = F[18,x,k[0]]*F[83,x,k[1],k[0]]
F[88,x,k[0],k[1],k[2]] = F[84,x,k[0],k[1]]+F[89,x,k[0],k[1],k[2]]
F[89,x,k[0],k[1],k[2]] = 2*F[28,x]+F[90,x,k[0],k[1],k[2]]+F[92,x,k[2],k[0],k[1]]
F[90,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[91,x,k[0],k[1],k[2]]
F[91,x,k[0],k[1],k[2]] = F[20,x,k[1],k[2]]+F[89,x,k[0],k[1],k[2]]
F[92,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[88,x,k[1],k[2],k[0]]
F[93,x,k[0],k[1]] = F[94,x,1,k[0],k[1]]
F[94,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[95,x,k[1],k[0],k[2]]
F[95,x,k[0],k[1],k[2]] = (F[96,x,k[0],k[1],1]*k[1]-F[96,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[96,x,k[0],k[1],k[2]] = F[97,x,k[0],k[1],k[1]*k[2]]
F[97,x,k[0],k[1],k[2]] = F[1,x]+F[80,x,k[0],k[1],k[2]]+F[94,x,k[1],k[0],k[2]]+F[98,x,k[2],k[0],k[1]]
F[98,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[97,x,k[1],k[2],k[0]]
F[99,x,k[0],k[1]] = F[18,x,k[0]]*F[78,x,k[1],k[0]]
F[100,x,k[0],k[1]] = F[10,x,k[1],k[0]]*F[18,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[18,x,k[0]]
F[102,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[103,x,k[0]]+F[115,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[5,x]
F[104,x,k[0]] = F[105,x,k[0]]+F[109,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[26,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[16,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[106,x,k[0]]*F[5,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[51,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[27,x,k[0]]
F[111,x,k[0]] = 2*F[28,x]+F[112,x,k[0]]+F[114,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[5,x]
F[113,x,k[0]] = F[107,x,k[0]]+F[111,x,k[0]]
F[114,x,k[0]] = F[110,x,k[0]]*F[5,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[5,x]
F[116,x,k[0]] = (F[102,x,k[0]]*k[0]-F[102,x,1])/(-1+k[0])
F[117,x,k[0]] = F[118,x,k[0]]*F[5,x]
F[118,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[119,x] = F[120,x]*F[5,x]
F[120,x] = F[121,x,1]
F[121,x,k[0]] = F[1,x]+F[122,x,k[0]]+F[191,x,k[0]]+F[193,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]*F[5,x]
F[123,x,k[0]] = F[124,x,1,k[0]]
F[124,x,k[0],k[1]] = F[1,x]+F[125,x,k[0],k[1]]+F[127,x,k[0],k[1]]+F[180,x,k[0],k[1]]+F[182,x,k[0],k[1]]
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[5,x]
F[126,x,k[0],k[1]] = 1/(-1+k[1])*(F[10,x,k[0],k[1]]*k[1]-F[10,x,k[0],1])
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[18,x,k[0]]
F[128,x,k[0],k[1]] = F[1,x]+F[127,x,k[0],k[1]]+F[129,x,k[0],k[1]]+F[145,x,k[0],k[1]]+F[147,x,k[0],k[1]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]*F[5,x]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[137,x,k[0],k[1]]
F[131,x,k[0],k[1]] = F[132,x,k[1]]+F[133,x,k[0],k[1]]
F[132,x,k[0]] = F[15,x,k[0]]+F[35,x,k[0]]
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]+F[19,x,k[0],k[1]]
F[134,x,k[0],k[1]] = F[107,x,k[0]]+F[135,x,k[0],k[1]]
F[135,x,k[0],k[1]] = F[136,x,k[1],k[0]]
F[136,x,k[0],k[1]] = F[134,x,k[1],k[0]]*F[18,x,k[0]]
F[137,x,k[0],k[1]] = F[138,x,k[1]]+F[139,x,k[0],k[1]]
F[138,x,k[0]] = F[23,x,k[0]]+F[69,x,k[0]]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]+F[40,x,k[0],k[1]]
F[140,x,k[0],k[1]] = F[111,x,k[0]]+F[141,x,k[0],k[1]]
F[141,x,k[0],k[1]] = 3*F[28,x]+F[142,x,k[0],k[1]]+F[144,x,k[1],k[0]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]*F[5,x]
F[143,x,k[0],k[1]] = F[135,x,k[0],k[1]]+F[141,x,k[0],k[1]]
F[144,x,k[0],k[1]] = F[140,x,k[1],k[0]]*F[18,x,k[0]]
F[145,x,k[0],k[1]] = F[146,x,k[0],k[1]]*F[5,x]
F[146,x,k[0],k[1]] = (F[128,x,k[0],k[1]]*k[0]-F[128,x,1,k[1]])/(-1+k[0])
F[147,x,k[0],k[1]] = F[148,x,k[0],k[1]]*F[18,x,k[1]]
F[148,x,k[0],k[1]] = F[149,x,k[0],k[1]]+F[157,x,k[0],k[1]]
F[149,x,k[0],k[1]] = F[150,x,k[1]]+F[151,x,k[0],k[1]]
F[150,x,k[0]] = F[15,x,k[0]]+F[23,x,k[0]]
F[151,x,k[0],k[1]] = F[152,x,k[0],k[1]]+F[83,x,k[0],k[1]]
F[152,x,k[0],k[1]] = F[107,x,k[0]]+F[153,x,k[0],k[1]]
F[153,x,k[0],k[1]] = 2*F[28,x]+F[154,x,k[0],k[1]]+F[156,x,k[1],k[0]]
F[154,x,k[0],k[1]] = F[155,x,k[0],k[1]]*F[5,x]
F[155,x,k[0],k[1]] = F[153,x,k[0],k[1]]+F[84,x,k[0],k[1]]
F[156,x,k[0],k[1]] = F[152,x,k[1],k[0]]*F[18,x,k[0]]
F[157,x,k[0],k[1]] = F[158,x,k[1]]+F[159,x,k[0],k[1]]
F[158,x,k[0]] = F[23,x,k[0]]+F[46,x,k[0]]
F[159,x,k[0],k[1]] = F[160,x,k[0],k[1]]+F[170,x,k[0],k[1]]
F[160,x,k[0],k[1]] = F[161,x,k[0],k[1]]+F[27,x,k[0]]
F[161,x,k[0],k[1]] = F[162,x,k[0],k[1]]+F[164,x,k[0],k[1]]+F[169,x,k[1],k[0]]+F[28,x]
F[162,x,k[0],k[1]] = F[163,x,k[0],k[1]]*F[5,x]
F[163,x,k[0],k[1]] = F[161,x,k[0],k[1]]+F[84,x,k[0],k[1]]
F[164,x,k[0],k[1]] = F[165,x,k[0],k[1]]*F[18,x,k[0]]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[57,x,k[1]]
F[166,x,k[0],k[1]] = 2*F[28,x]+F[164,x,k[0],k[1]]+F[167,x,k[0],k[1]]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]*F[5,x]
F[168,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[84,x,k[0],k[1]]
F[169,x,k[0],k[1]] = F[160,x,k[1],k[0]]*F[18,x,k[0]]
F[170,x,k[0],k[1]] = F[111,x,k[0]]+F[171,x,k[0],k[1]]
F[171,x,k[0],k[1]] = 2*F[28,x]+F[172,x,k[0],k[1]]+F[174,x,k[0],k[1]]+F[179,x,k[1],k[0]]
F[172,x,k[0],k[1]] = F[173,x,k[0],k[1]]*F[5,x]
F[173,x,k[0],k[1]] = F[153,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[175,x,k[0],k[1]]*F[5,x]
F[175,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[176,x,k[0],k[1]]
F[176,x,k[0],k[1]] = 3*F[28,x]+F[174,x,k[0],k[1]]+F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[178,x,k[0],k[1]]*F[5,x]
F[178,x,k[0],k[1]] = F[153,x,k[0],k[1]]+F[176,x,k[0],k[1]]
F[179,x,k[0],k[1]] = F[170,x,k[1],k[0]]*F[18,x,k[0]]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]*F[5,x]
F[181,x,k[0],k[1]] = (F[124,x,k[0],k[1]]*k[0]-F[124,x,1,k[1]])/(-1+k[0])
F[182,x,k[0],k[1]] = F[18,x,k[1]]*F[183,x,k[0],k[1]]
F[183,x,k[0],k[1]] = (F[184,x,k[0],k[1]]*k[0]-F[184,x,1,k[1]])/(-1+k[0])
F[184,x,k[0],k[1]] = F[1,x]+F[185,x,k[0],k[1]]+F[186,x,k[0],k[1]]+F[190,x,k[0],k[1]]
F[185,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[5,x]
F[186,x,k[0],k[1]] = F[18,x,k[0]]*F[187,x,k[0],k[1]]
F[187,x,k[0],k[1]] = F[188,x,k[0],k[1]]+F[189,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[15,x,k[1]]+F[83,x,k[0],k[1]]
F[189,x,k[0],k[1]] = F[160,x,k[0],k[1]]+F[23,x,k[1]]
F[190,x,k[0],k[1]] = F[18,x,k[1]]*F[184,x,k[0],k[1]]
F[191,x,k[0]] = F[192,x,k[0]]*F[5,x]
F[192,x,k[0]] = 1/(-1+k[0])*(F[121,x,k[0]]*k[0]-F[121,x,1])
F[193,x,k[0]] = F[121,x,k[0]]*F[18,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{119}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y_{0}\right)+F_{117}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}, 1\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y_{1}, y_{0}\right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)+F_{76}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = y_{0} x
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}, y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{1}, y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right)+F_{27}\! \left(x , y_{0}\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x , y_{0}\right) = F_{28}\! \left(x \right)+F_{29}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{30}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{1}, y_{0}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{1}, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = 2 F_{28}\! \left(x \right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{1}, y_{0}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{43}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{40}\! \left(x , y_{1}, y_{0}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{1}\right)+F_{64}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)
F_{47}\! \left(x \right) = F_{28}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{5}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{5}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{52}\! \left(x , y_{0}\right) = F_{28}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{57}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = 2 F_{28}\! \left(x \right)+F_{55}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{62}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{65}\! \left(x , y_{0}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}\right) = 2 F_{28}\! \left(x \right)+F_{66}\! \left(x , y_{0}\right)+F_{68}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{47}\! \left(x \right)+F_{65}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = 3 F_{28}\! \left(x \right)+F_{71}\! \left(x , y_{0}, y_{1}\right)+F_{73}\! \left(x , y_{1}, y_{0}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = F_{5}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{1}, y_{0}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{5}\! \left(x \right) F_{75}\! \left(x , y_{0}, y_{1}\right)
F_{75}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{10}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{76}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , 1, y_{0}\right)
F_{78}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{79}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{1}, y_{0}\right)
F_{79}\! \left(x , y_{0}, y_{1}\right) = F_{80}\! \left(x , y_{0}, 1, y_{1}\right)
F_{80}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}, y_{2}\right)+F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{83}\! \left(x , y_{0}, y_{2}\right)+F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{83}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x \right)+F_{85}\! \left(x , y_{0}, y_{1}\right)+F_{87}\! \left(x , y_{1}, y_{0}\right)
F_{85}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)
F_{86}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{87}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{1}, y_{0}\right)
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{84}\! \left(x , y_{0}, y_{1}\right)+F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 2 F_{28}\! \left(x \right)+F_{90}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{92}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{90}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{1}, y_{2}\right)+F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{93}\! \left(x , y_{0}, y_{1}\right) = F_{94}\! \left(x , 1, y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{95}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{96}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{96}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{96}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{97}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{80}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{94}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{98}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{98}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{97}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{99}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{1}, y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y_{0}\right)+F_{103}\! \left(x , y_{0}\right)+F_{115}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{109}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)+F_{26}\! \left(x \right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{109}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)+F_{51}\! \left(x \right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{111}\! \left(x , y_{0}\right) = 2 F_{28}\! \left(x \right)+F_{112}\! \left(x , y_{0}\right)+F_{114}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{113}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{113}\! \left(x , y_{0}\right) = F_{107}\! \left(x , y_{0}\right)+F_{111}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{116}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{102}\! \left(x , y_{0}\right)+F_{102}\! \left(x , 1\right)}{-1+y_{0}}
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{118}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{5}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x , 1\right)
F_{121}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{122}\! \left(x , y_{0}\right)+F_{191}\! \left(x , y_{0}\right)+F_{193}\! \left(x , y_{0}\right)
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{123}\! \left(x , y_{0}\right) = F_{124}\! \left(x , 1, y_{0}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{125}\! \left(x , y_{0}, y_{1}\right)+F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{180}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , y_{0}, y_{1}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{126}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{10}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{127}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)
F_{128}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{129}\! \left(x , y_{0}, y_{1}\right)+F_{145}\! \left(x , y_{0}, y_{1}\right)+F_{147}\! \left(x , y_{0}, y_{1}\right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{1}\right)+F_{133}\! \left(x , y_{0}, y_{1}\right)
F_{132}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}, y_{1}\right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = F_{136}\! \left(x , y_{1}, y_{0}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = F_{138}\! \left(x , y_{1}\right)+F_{139}\! \left(x , y_{0}, y_{1}\right)
F_{138}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{140}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}\right)+F_{141}\! \left(x , y_{0}, y_{1}\right)
F_{141}\! \left(x , y_{0}, y_{1}\right) = 3 F_{28}\! \left(x \right)+F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{144}\! \left(x , y_{1}, y_{0}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{143}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{143}\! \left(x , y_{0}, y_{1}\right) = F_{135}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \left(x , y_{0}, y_{1}\right)
F_{144}\! \left(x , y_{0}, y_{1}\right) = F_{140}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{146}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{146}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{128}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{147}\! \left(x , y_{0}, y_{1}\right) = F_{148}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{1}\right)
F_{148}\! \left(x , y_{0}, y_{1}\right) = F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{157}\! \left(x , y_{0}, y_{1}\right)
F_{149}\! \left(x , y_{0}, y_{1}\right) = F_{150}\! \left(x , y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)
F_{150}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}, y_{1}\right) = F_{152}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)
F_{152}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}\right)+F_{153}\! \left(x , y_{0}, y_{1}\right)
F_{153}\! \left(x , y_{0}, y_{1}\right) = 2 F_{28}\! \left(x \right)+F_{154}\! \left(x , y_{0}, y_{1}\right)+F_{156}\! \left(x , y_{1}, y_{0}\right)
F_{154}\! \left(x , y_{0}, y_{1}\right) = F_{155}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = F_{152}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{157}\! \left(x , y_{0}, y_{1}\right) = F_{158}\! \left(x , y_{1}\right)+F_{159}\! \left(x , y_{0}, y_{1}\right)
F_{158}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{159}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{170}\! \left(x , y_{0}, y_{1}\right)
F_{160}\! \left(x , y_{0}, y_{1}\right) = F_{161}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{1}, y_{0}\right)+F_{28}\! \left(x \right)
F_{162}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = F_{161}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{164}\! \left(x , y_{0}, y_{1}\right) = F_{165}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{1}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = 2 F_{28}\! \left(x \right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{167}\! \left(x , y_{0}, y_{1}\right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{171}\! \left(x , y_{0}, y_{1}\right) = 2 F_{28}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{1}, y_{0}\right)
F_{172}\! \left(x , y_{0}, y_{1}\right) = F_{173}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{176}\! \left(x , y_{0}, y_{1}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = 3 F_{28}\! \left(x \right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{178}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{176}\! \left(x , y_{0}, y_{1}\right)
F_{179}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{124}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{182}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{1}\right) F_{183}\! \left(x , y_{0}, y_{1}\right)
F_{183}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{184}\! \left(x , y_{0}, y_{1}\right)+F_{184}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{184}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{186}\! \left(x , y_{0}, y_{1}\right)+F_{190}\! \left(x , y_{0}, y_{1}\right)
F_{185}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{186}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{187}\! \left(x , y_{0}, y_{1}\right)
F_{187}\! \left(x , y_{0}, y_{1}\right) = F_{188}\! \left(x , y_{0}, y_{1}\right)+F_{189}\! \left(x , y_{0}, y_{1}\right)
F_{188}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)
F_{189}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{1}\right)
F_{190}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{1}\right) F_{184}\! \left(x , y_{0}, y_{1}\right)
F_{191}\! \left(x , y_{0}\right) = F_{192}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)
F_{192}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{121}\! \left(x , y_{0}\right)+F_{121}\! \left(x , 1\right)}{-1+y_{0}}
F_{193}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_5(x))
Eq(F_3(x), F_1(x) + F_119(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_101(x, k_0) + F_117(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0, 1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_100(x, k_1, k_0) + F_11(x, k_0, k_1) + F_74(x, k_0, k_1) + F_76(x, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0, k_1)*F_5(x))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_1) + F_19(x, k_0, k_1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0, k_1), F_16(x, k_0) + F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_1, k_0))
Eq(F_21(x, k_0, k_1), F_18(x, k_0)*F_19(x, k_1, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_1) + F_32(x, k_0, k_1))
Eq(F_23(x, k_0), F_24(x) + F_27(x, k_0))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_5(x))
Eq(F_26(x), F_1(x) + F_24(x))
Eq(F_27(x, k_0), F_28(x) + F_29(x, k_0) + F_31(x, k_0))
Eq(F_28(x), 0)
Eq(F_29(x, k_0), F_30(x, k_0)*F_5(x))
Eq(F_30(x, k_0), F_16(x, k_0) + F_27(x, k_0))
Eq(F_31(x, k_0), F_18(x, k_0)*F_23(x, k_0))
Eq(F_32(x, k_0, k_1), F_33(x, k_0) + F_36(x, k_0, k_1))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_18(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_24(x) + F_33(x, k_0))
Eq(F_36(x, k_0, k_1), F_37(x, k_1, k_0))
Eq(F_37(x, k_0, k_1), F_18(x, k_0)*F_32(x, k_1, k_0))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), F_23(x, k_1) + F_40(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_27(x, k_0) + F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), 2*F_28(x) + F_42(x, k_0, k_1) + F_44(x, k_1, k_0))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1)*F_5(x))
Eq(F_43(x, k_0, k_1), F_20(x, k_0, k_1) + F_41(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_18(x, k_0)*F_40(x, k_1, k_0))
Eq(F_45(x, k_0, k_1), F_46(x, k_1) + F_64(x, k_0, k_1))
Eq(F_46(x, k_0), F_47(x) + F_52(x, k_0))
Eq(F_47(x), F_28(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_49(x)*F_5(x))
Eq(F_49(x), F_24(x) + F_47(x))
Eq(F_50(x), F_5(x)*F_51(x))
Eq(F_51(x), F_24(x) + F_47(x))
Eq(F_52(x, k_0), F_28(x) + F_53(x, k_0) + F_55(x, k_0) + F_63(x, k_0))
Eq(F_53(x, k_0), F_5(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_27(x, k_0) + F_52(x, k_0))
Eq(F_55(x, k_0), F_5(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_5(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_16(x, k_0) + F_57(x, k_0))
Eq(F_60(x, k_0), 2*F_28(x) + F_55(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_5(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_27(x, k_0) + F_60(x, k_0))
Eq(F_63(x, k_0), F_18(x, k_0)*F_46(x, k_0))
Eq(F_64(x, k_0, k_1), F_65(x, k_0) + F_70(x, k_0, k_1))
Eq(F_65(x, k_0), 2*F_28(x) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_66(x, k_0), F_5(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_33(x, k_0) + F_65(x, k_0))
Eq(F_68(x, k_0), F_18(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_47(x) + F_65(x, k_0))
Eq(F_70(x, k_0, k_1), 3*F_28(x) + F_71(x, k_0, k_1) + F_73(x, k_1, k_0))
Eq(F_71(x, k_0, k_1), F_5(x)*F_72(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_36(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_18(x, k_0)*F_64(x, k_1, k_0))
Eq(F_74(x, k_0, k_1), F_5(x)*F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), (k_0*F_10(x, k_0, k_1) - F_10(x, 1, k_1))/(k_0 - 1))
Eq(F_76(x, k_0), F_18(x, k_0)*F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, 1, k_0))
Eq(F_78(x, k_0, k_1), F_1(x) + F_79(x, k_0, k_1) + F_93(x, k_0, k_1) + F_99(x, k_1, k_0))
Eq(F_79(x, k_0, k_1), F_80(x, k_0, 1, k_1))
Eq(F_80(x, k_0, k_1, k_2), F_18(x, k_0)*F_81(x, k_0, k_1, k_2))
Eq(F_81(x, k_0, k_1, k_2), F_14(x, k_1, k_2) + F_82(x, k_0, k_1, k_2))
Eq(F_82(x, k_0, k_1, k_2), F_83(x, k_0, k_2) + F_88(x, k_0, k_1, k_2))
Eq(F_83(x, k_0, k_1), F_16(x, k_0) + F_84(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), F_28(x) + F_85(x, k_0, k_1) + F_87(x, k_1, k_0))
Eq(F_85(x, k_0, k_1), F_18(x, k_0)*F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), F_16(x, k_1) + F_84(x, k_0, k_1))
Eq(F_87(x, k_0, k_1), F_18(x, k_0)*F_83(x, k_1, k_0))
Eq(F_88(x, k_0, k_1, k_2), F_84(x, k_0, k_1) + F_89(x, k_0, k_1, k_2))
Eq(F_89(x, k_0, k_1, k_2), 2*F_28(x) + F_90(x, k_0, k_1, k_2) + F_92(x, k_2, k_0, k_1))
Eq(F_90(x, k_0, k_1, k_2), F_18(x, k_0)*F_91(x, k_0, k_1, k_2))
Eq(F_91(x, k_0, k_1, k_2), F_20(x, k_1, k_2) + F_89(x, k_0, k_1, k_2))
Eq(F_92(x, k_0, k_1, k_2), F_18(x, k_0)*F_88(x, k_1, k_2, k_0))
Eq(F_93(x, k_0, k_1), F_94(x, 1, k_0, k_1))
Eq(F_94(x, k_0, k_1, k_2), F_18(x, k_0)*F_95(x, k_1, k_0, k_2))
Eq(F_95(x, k_0, k_1, k_2), (-k_1*F_96(x, k_0, k_1, 1) + k_2*F_96(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_96(x, k_0, k_1, k_2), F_97(x, k_0, k_1, k_1*k_2))
Eq(F_97(x, k_0, k_1, k_2), F_1(x) + F_80(x, k_0, k_1, k_2) + F_94(x, k_1, k_0, k_2) + F_98(x, k_2, k_0, k_1))
Eq(F_98(x, k_0, k_1, k_2), F_18(x, k_0)*F_97(x, k_1, k_2, k_0))
Eq(F_99(x, k_0, k_1), F_18(x, k_0)*F_78(x, k_1, k_0))
Eq(F_100(x, k_0, k_1), F_10(x, k_1, k_0)*F_18(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_18(x, k_0))
Eq(F_102(x, k_0), F_1(x) + F_101(x, k_0) + F_103(x, k_0) + F_115(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_5(x))
Eq(F_104(x, k_0), F_105(x, k_0) + F_109(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_26(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_16(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_106(x, k_0)*F_5(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_51(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_27(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_114(x, k_0) + 2*F_28(x))
Eq(F_112(x, k_0), F_113(x, k_0)*F_5(x))
Eq(F_113(x, k_0), F_107(x, k_0) + F_111(x, k_0))
Eq(F_114(x, k_0), F_110(x, k_0)*F_5(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_5(x))
Eq(F_116(x, k_0), (-k_0*F_102(x, k_0) + F_102(x, 1))/(1 - k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_5(x))
Eq(F_118(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_119(x), F_120(x)*F_5(x))
Eq(F_120(x), F_121(x, 1))
Eq(F_121(x, k_0), F_1(x) + F_122(x, k_0) + F_191(x, k_0) + F_193(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_5(x))
Eq(F_123(x, k_0), F_124(x, 1, k_0))
Eq(F_124(x, k_0, k_1), F_1(x) + F_125(x, k_0, k_1) + F_127(x, k_0, k_1) + F_180(x, k_0, k_1) + F_182(x, k_0, k_1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1)*F_5(x))
Eq(F_126(x, k_0, k_1), (k_1*F_10(x, k_0, k_1) - F_10(x, k_0, 1))/(k_1 - 1))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1)*F_18(x, k_0))
Eq(F_128(x, k_0, k_1), F_1(x) + F_127(x, k_0, k_1) + F_129(x, k_0, k_1) + F_145(x, k_0, k_1) + F_147(x, k_0, k_1))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1)*F_5(x))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1) + F_137(x, k_0, k_1))
Eq(F_131(x, k_0, k_1), F_132(x, k_1) + F_133(x, k_0, k_1))
Eq(F_132(x, k_0), F_15(x, k_0) + F_35(x, k_0))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1) + F_19(x, k_0, k_1))
Eq(F_134(x, k_0, k_1), F_107(x, k_0) + F_135(x, k_0, k_1))
Eq(F_135(x, k_0, k_1), F_136(x, k_1, k_0))
Eq(F_136(x, k_0, k_1), F_134(x, k_1, k_0)*F_18(x, k_0))
Eq(F_137(x, k_0, k_1), F_138(x, k_1) + F_139(x, k_0, k_1))
Eq(F_138(x, k_0), F_23(x, k_0) + F_69(x, k_0))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1) + F_40(x, k_0, k_1))
Eq(F_140(x, k_0, k_1), F_111(x, k_0) + F_141(x, k_0, k_1))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1) + F_144(x, k_1, k_0) + 3*F_28(x))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1)*F_5(x))
Eq(F_143(x, k_0, k_1), F_135(x, k_0, k_1) + F_141(x, k_0, k_1))
Eq(F_144(x, k_0, k_1), F_140(x, k_1, k_0)*F_18(x, k_0))
Eq(F_145(x, k_0, k_1), F_146(x, k_0, k_1)*F_5(x))
Eq(F_146(x, k_0, k_1), (-k_0*F_128(x, k_0, k_1) + F_128(x, 1, k_1))/(1 - k_0))
Eq(F_147(x, k_0, k_1), F_148(x, k_0, k_1)*F_18(x, k_1))
Eq(F_148(x, k_0, k_1), F_149(x, k_0, k_1) + F_157(x, k_0, k_1))
Eq(F_149(x, k_0, k_1), F_150(x, k_1) + F_151(x, k_0, k_1))
Eq(F_150(x, k_0), F_15(x, k_0) + F_23(x, k_0))
Eq(F_151(x, k_0, k_1), F_152(x, k_0, k_1) + F_83(x, k_0, k_1))
Eq(F_152(x, k_0, k_1), F_107(x, k_0) + F_153(x, k_0, k_1))
Eq(F_153(x, k_0, k_1), F_154(x, k_0, k_1) + F_156(x, k_1, k_0) + 2*F_28(x))
Eq(F_154(x, k_0, k_1), F_155(x, k_0, k_1)*F_5(x))
Eq(F_155(x, k_0, k_1), F_153(x, k_0, k_1) + F_84(x, k_0, k_1))
Eq(F_156(x, k_0, k_1), F_152(x, k_1, k_0)*F_18(x, k_0))
Eq(F_157(x, k_0, k_1), F_158(x, k_1) + F_159(x, k_0, k_1))
Eq(F_158(x, k_0), F_23(x, k_0) + F_46(x, k_0))
Eq(F_159(x, k_0, k_1), F_160(x, k_0, k_1) + F_170(x, k_0, k_1))
Eq(F_160(x, k_0, k_1), F_161(x, k_0, k_1) + F_27(x, k_0))
Eq(F_161(x, k_0, k_1), F_162(x, k_0, k_1) + F_164(x, k_0, k_1) + F_169(x, k_1, k_0) + F_28(x))
Eq(F_162(x, k_0, k_1), F_163(x, k_0, k_1)*F_5(x))
Eq(F_163(x, k_0, k_1), F_161(x, k_0, k_1) + F_84(x, k_0, k_1))
Eq(F_164(x, k_0, k_1), F_165(x, k_0, k_1)*F_18(x, k_0))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1) + F_57(x, k_1))
Eq(F_166(x, k_0, k_1), F_164(x, k_0, k_1) + F_167(x, k_0, k_1) + 2*F_28(x))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1)*F_5(x))
Eq(F_168(x, k_0, k_1), F_166(x, k_0, k_1) + F_84(x, k_0, k_1))
Eq(F_169(x, k_0, k_1), F_160(x, k_1, k_0)*F_18(x, k_0))
Eq(F_170(x, k_0, k_1), F_111(x, k_0) + F_171(x, k_0, k_1))
Eq(F_171(x, k_0, k_1), F_172(x, k_0, k_1) + F_174(x, k_0, k_1) + F_179(x, k_1, k_0) + 2*F_28(x))
Eq(F_172(x, k_0, k_1), F_173(x, k_0, k_1)*F_5(x))
Eq(F_173(x, k_0, k_1), F_153(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_175(x, k_0, k_1)*F_5(x))
Eq(F_175(x, k_0, k_1), F_166(x, k_0, k_1) + F_176(x, k_0, k_1))
Eq(F_176(x, k_0, k_1), F_174(x, k_0, k_1) + F_177(x, k_0, k_1) + 3*F_28(x))
Eq(F_177(x, k_0, k_1), F_178(x, k_0, k_1)*F_5(x))
Eq(F_178(x, k_0, k_1), F_153(x, k_0, k_1) + F_176(x, k_0, k_1))
Eq(F_179(x, k_0, k_1), F_170(x, k_1, k_0)*F_18(x, k_0))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1)*F_5(x))
Eq(F_181(x, k_0, k_1), (-k_0*F_124(x, k_0, k_1) + F_124(x, 1, k_1))/(1 - k_0))
Eq(F_182(x, k_0, k_1), F_18(x, k_1)*F_183(x, k_0, k_1))
Eq(F_183(x, k_0, k_1), (-k_0*F_184(x, k_0, k_1) + F_184(x, 1, k_1))/(1 - k_0))
Eq(F_184(x, k_0, k_1), F_1(x) + F_185(x, k_0, k_1) + F_186(x, k_0, k_1) + F_190(x, k_0, k_1))
Eq(F_185(x, k_0, k_1), F_10(x, k_0, k_1)*F_5(x))
Eq(F_186(x, k_0, k_1), F_18(x, k_0)*F_187(x, k_0, k_1))
Eq(F_187(x, k_0, k_1), F_188(x, k_0, k_1) + F_189(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_15(x, k_1) + F_83(x, k_0, k_1))
Eq(F_189(x, k_0, k_1), F_160(x, k_0, k_1) + F_23(x, k_1))
Eq(F_190(x, k_0, k_1), F_18(x, k_1)*F_184(x, k_0, k_1))
Eq(F_191(x, k_0), F_192(x, k_0)*F_5(x))
Eq(F_192(x, k_0), (k_0*F_121(x, k_0) - F_121(x, 1))/(k_0 - 1))
Eq(F_193(x, k_0), F_121(x, k_0)*F_18(x, k_0))
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": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], 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