02314_02341_02431_03124_03214_03241_30124_30214_30241

Counting sequence:
1, 1, 2, 6, 24, 111, 548, 2792, 14490, 76153, 403989, 2158895, 11605559, 62695038, 340095695, 1851452224, 10110273505, 55358848378, 303842999465, 1671231351504, 9209882169820, 50841809859533, 281104718307670, 1556451688470070, 8629218231057789, 47899384242055856, 266177210332382105, 1480671239102005897, 8244446831008083702, 45946362649392346708, 256272494303433246547, 1430510720770469621847, 7990936839263933274130, 44668652343211351599479, 249855759882181240679910, 1398432548012874308490037, 7831499410813658185463914, 43881990871059517198633948, 246010446304688350529963796, 1379861038648784417800551147, 7743215214259252947374334432, 43471221154360153028812877521, 244156295205883711507811034860, 1371864618287444206392569761393, 7711237137649886523444661320327, 43360979412841041406706139989729, 243909965361850508567931544561976, 1372489681690391580676141185705541, 7725591719721883940230065558194530, 43500268640933991073165749833125394, 245010320666269279154419171453950772, 1380397329780663157091734607283022985, 7779406322233943665191871736783599864, 43853776194460832062949275419405083849, 247275765953313317856978313484607342563, 1394653058865393456435351033534064664670, 7867869290246668978018370625643983799409, 44396717775776031326251285467364867274922, 250578611298268794508852790868988835096933, 1414598968659852842867176028069218414489959, 7987591340283391016891833684401457131549538, 45111638568544910858734641917785525469329992, 254829012447357201214064679998985424940866702, 1439772963137277153005355865576075730572861456, 8136198205637306372646501942989965049412709952, 45986355491130543971977250675069020671778815210, 259964556608032461921118580725046067214143612958, 1469855949833728780625903803694696261045756346630, 8312062474535189409963270249901924084318640395782, 47012593038447082712591890961316943045641220448474, 265943312038583024619382106072587739143986453093733, 1504636374623238247707968516024520055524716086717444, 8514122368121328635219668020833685936104401163289485, 48185056013827096482665414473174763330221712798363696, 272739077358874595820426886828730947313333354272311905, 1543985852808864805776797334481732350009037899449262609, 8741756594928662519048822790237667950710824523448216934, 49500786150969659559429479595410035137111040330399767695, 280338070538247971801085670595263901217827167610620173879, 1587842113370456386786194230004858087000787977579859324661, 8994696414538023584064325763876490050009173531375488407917, 50958708355373301890410362811231405342534895741161741608435, 288736585684858547222259550818600154282932404329507632052047, 1636196890239754279691183119929278515570838688212196229156424, 9272963025826047284058693230195234139399194005469114435941219, 52559306773325601654633079327027438882964566744587432543103683, 297939316342659161582654881201476799585785976930579149604056085, 1689087240034307721803427140986659792872565093324016518545627279, 9576822594351106564406441346769875392850756498311916804851567472, 54304391787490099732600475354454381840049191548554346955135967499, 307958148117455775498990014851778369701857174022728087053481328458, 1746589285446338876487887241193823135348208438830386072867461206540, 9906753832482162256106169286096887965288963747072437888896989295010, 56196932055434605840925540432181998011106410945182102601003222960688, 318811288752147928939446411537070138630021648101571129975065366921741, 1808813711538570459816548952627562407874172674899111399862444968968006, 10263424696445956629414881049913311533134647339066722917423096273160391, 58240934024065000496531921638768674013140151019483299982339977849851384, 330522645734646603112410237372313465597783200977736087467482635984031425, 1875902554225427822505131774446977318266046483038063707938999859833100373, 10647675837199271288765807730284639371058240001265359161215899912741622134

Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24576/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]+F[199,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[23,x,k[0]]
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[20,x] = x
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[195,x,k[0]]+F[197,x,k[0]]+F[26,x]+F[85,x,k[0]]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[20,x]*F[29,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[82,x,k[0]]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[36,x]*F[39,x]
F[39,x] = F[1,x]+F[20,x]
F[40,x] = F[41,x]+F[52,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[43,x]
F[43,x] = F[39,x]+F[44,x]
F[44,x] = F[41,x]+F[45,x]
F[45,x] = F[46,x]+F[47,x]+F[51,x]
F[46,x] = 0
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[20,x]
F[50,x] = F[45,x]
F[51,x] = F[20,x]*F[41,x]
F[52,x] = F[46,x]+F[53,x]+F[80,x]
F[53,x] = F[20,x]*F[54,x]
F[54,x] = F[55,x]+F[65,x]
F[55,x] = F[56,x]+F[62,x]
F[56,x] = F[57,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[36,x]+F[59,x]
F[59,x] = F[20,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[20,x]*F[56,x]
F[62,x] = F[46,x]+F[61,x]+F[63,x]
F[63,x] = F[20,x]*F[64,x]
F[64,x] = F[59,x]
F[65,x] = F[52,x]+F[66,x]
F[66,x] = F[46,x]+F[67,x]+F[71,x]+F[72,x]
F[67,x] = F[20,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[62,x]
F[70,x] = F[66,x]
F[71,x] = F[20,x]*F[52,x]
F[72,x] = F[20,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[45,x]+F[75,x]
F[75,x] = 2*F[46,x]+F[71,x]+F[76,x]
F[76,x] = F[20,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[60,x]
F[79,x] = F[75,x]
F[80,x] = F[20,x]*F[81,x]
F[81,x] = F[40,x]+F[74,x]
F[82,x,k[0]] = F[1,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[82,x,k[0]]
F[85,x,k[0]] = F[20,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[177,x,k[0]]+F[87,x]
F[87,x] = 1/F[20,x]*F[88,x]
F[88,x] = -F[26,x]-F[89,x]+F[7,x]
F[89,x] = F[90,x]
F[90,x] = F[20,x]*F[91,x]
F[91,x] = F[173,x]+F[175,x]+F[92,x]+F[94,x]
F[92,x] = F[39,x]*F[93,x]
F[93,x] = F[13,x,1]
F[94,x] = F[20,x]*F[95,x]
F[95,x] = F[123,x]+F[96,x]
F[96,x] = F[39,x]*F[97,x]
F[97,x] = 1/F[20,x]*F[98,x]
F[98,x] = -F[93,x]-F[99,x]+F[7,x]
F[99,x] = F[100,x]*F[20,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[25,x,1]
F[102,x] = 2*F[46,x]+F[103,x]+F[121,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[20,x]
F[105,x] = F[106,x,1]
F[106,x,k[0]] = 2*F[46,x]+F[107,x,k[0]]+F[110,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[20,x]
F[109,x,k[0]] = 1/(-1+k[0])*(F[106,x,k[0]]*k[0]-F[106,x,1])
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[114,x]*F[20,x]*F[39,x]
F[113,x,k[0]] = F[112,x,k[0]]*F[20,x]
F[113,x,k[0]] = F[17,x,k[0]]
F[114,x] = F[1,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[20,x]
F[117,x] = F[118,x]+F[39,x]
F[118,x] = F[115,x]+F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[115,x]*F[20,x]
F[121,x] = F[122,x]
F[122,x] = F[114,x]*F[20,x]*F[39,x]*F[7,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x,1]
F[125,x,k[0]] = F[126,x]+F[167,x,k[0]]+F[170,x,k[0]]+F[46,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[20,x]
F[128,x] = F[129,x]+F[141,x]+F[165,x]
F[129,x] = F[130,x]+F[138,x]+F[140,x]+F[46,x]
F[130,x] = F[131,x]*F[20,x]
F[131,x] = F[132,x,1]
F[132,x,k[0]] = (F[133,x,k[0]]*k[0]-F[133,x,1])/(-1+k[0])
F[133,x,k[0]] = 2*F[46,x]+F[134,x,k[0]]+F[137,x,k[0]]
F[134,x,k[0]] = F[135,x]
F[135,x] = -F[136,x]-2*F[46,x]+F[129,x]
F[136,x] = F[20,x]*F[26,x]
F[137,x,k[0]] = F[20,x]*F[27,x,k[0]]
F[138,x] = F[139,x]
F[139,x] = F[20,x]^2*F[32,x]*F[36,x]*F[39,x]
F[140,x] = F[20,x]*F[32,x]
F[141,x] = F[142,x]*F[20,x]
F[142,x] = -F[164,x]+F[143,x]
F[143,x] = 1/F[20,x]*F[144,x]
F[144,x] = F[145,x]
F[145,x] = -F[146,x]-F[147,x]-F[158,x]+F[100,x]
F[146,x] = F[129,x]+F[26,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[20,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[6,x]+F[91,x]
F[151,x] = 3*F[46,x]+F[152,x]+F[157,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[20,x]*F[39,x]
F[154,x] = 1/F[20,x]*F[155,x]
F[155,x] = F[156,x]
F[156,x] = -F[6,x]-2*F[46,x]+F[128,x]
F[157,x] = F[20,x]*F[91,x]
F[158,x] = F[159,x]
F[159,x] = F[160,x]*F[20,x]
F[160,x] = F[161,x]+F[163,x]
F[161,x] = F[100,x]+F[162,x]
F[162,x] = F[128,x]
F[163,x] = F[100,x]*F[20,x]
F[164,x] = F[86,x,1]
F[165,x] = F[166,x]
F[166,x] = F[151,x]*F[20,x]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[20,x]
F[169,x,k[0]] = 1/(-1+k[0])*(F[125,x,k[0]]*k[0]-F[125,x,1])
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[112,x,k[0]]*F[172,x]*F[20,x]
F[172,x] = F[20,x]+F[39,x]
F[173,x] = F[174,x]
F[174,x] = F[160,x]*F[20,x]
F[175,x] = F[176,x]
F[176,x] = F[149,x]*F[20,x]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = -k[0]*(F[179,x,1]-F[179,x,k[0]])/(-1+k[0])
F[179,x,k[0]] = F[180,x,k[0]]
F[181,x,k[0]] = F[180,x,k[0]]+F[191,x]
F[181,x,k[0]] = F[182,x,k[0]]+F[186,x,k[0]]+F[190,x,k[0]]
F[183,x,k[0]] = F[182,x,k[0]]*F[20,x]
F[13,x,k[0]] = F[1,x]+F[183,x,k[0]]+F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[20,x]
F[188,x,k[0]] = F[189,x,k[0]]+F[91,x]
F[189,x,k[0]] = F[22,x,k[0]]*F[7,x]
F[190,x,k[0]] = F[20,x]*F[86,x,k[0]]
F[191,x] = F[192,x]+F[194,x]+F[4,x]
F[192,x] = F[193,x]
F[193,x] = F[20,x]*F[91,x]
F[194,x] = F[20,x]*F[87,x]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[188,x,k[0]]*F[20,x]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]
F[200,x,k[0]] = F[20,x]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[204,x,k[0]]
F[203,x,k[0]] = F[114,x]*F[20,x]*F[202,x,k[0]]*F[39,x]
F[203,x,k[0]] = F[106,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]
F[205,x,k[0]] = F[20,x]*F[206,x]*F[208,x]*F[217,x,k[0]]
F[206,x] = 1/F[20,x]*F[207,x]
F[207,x] = F[128,x]
F[208,x] = F[209,x]+F[39,x]
F[209,x] = F[210,x]+F[213,x]
F[210,x] = F[211,x]
F[211,x] = F[20,x]*F[212,x]
F[212,x] = F[1,x]+F[210,x]
F[213,x] = F[214,x]+F[216,x]+F[46,x]
F[214,x] = F[20,x]*F[215,x]
F[215,x] = F[20,x]+F[213,x]
F[216,x] = F[20,x]*F[210,x]
F[217,x,k[0]] = F[1,x]+F[218,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[22,x,k[0]]*F[220,x,k[0]]
F[220,x,k[0]] = F[21,x,k[0]]+F[221,x,k[0]]
F[221,x,k[0]] = F[218,x,k[0]]+F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[218,x,k[0]]*F[22,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_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{36}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)+F_{80}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{65}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{46}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{20}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{45}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{20}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{60}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{40}\! \left(x \right)+F_{74}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{88}\! \left(x \right) = -F_{26}\! \left(x \right)-F_{89}\! \left(x \right)+F_{7}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{173}\! \left(x \right)+F_{175}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{39}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{123}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{39}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{98}\! \left(x \right) = -F_{93}\! \left(x \right)-F_{99}\! \left(x \right)+F_{7}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{102}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{103}\! \left(x \right)+F_{121}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{20}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{106}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{107}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{109}\! \left(x , y\right) = -\frac{-F_{106}\! \left(x , y\right) y +F_{106}\! \left(x , 1\right)}{-1+y}
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{20}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{39}\! \left(x \right)
F_{118}\! \left(x \right) = F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{115}\! \left(x \right) F_{20}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right) F_{7}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x , 1\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x \right)+F_{167}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{20}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{141}\! \left(x \right)+F_{165}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)+F_{46}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{20}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x , 1\right)
F_{132}\! \left(x , y\right) = -\frac{-y F_{133}\! \left(x , y\right)+F_{133}\! \left(x , 1\right)}{-1+y}
F_{133}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{136}\! \left(x \right)-2 F_{46}\! \left(x \right)+F_{129}\! \left(x \right)
F_{136}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{39}\! \left(x \right)
F_{140}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{20}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{164}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{146}\! \left(x \right)-F_{147}\! \left(x \right)-F_{158}\! \left(x \right)+F_{100}\! \left(x \right)
F_{146}\! \left(x \right) = F_{129}\! \left(x \right)+F_{26}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{6}\! \left(x \right)+F_{91}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{46}\! \left(x \right)+F_{152}\! \left(x \right)+F_{157}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{155}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{6}\! \left(x \right)-2 F_{46}\! \left(x \right)+F_{128}\! \left(x \right)
F_{157}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{20}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{163}\! \left(x \right)
F_{161}\! \left(x \right) = F_{100}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{128}\! \left(x \right)
F_{163}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right)
F_{164}\! \left(x \right) = F_{86}\! \left(x , 1\right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{151}\! \left(x \right) F_{20}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{169}\! \left(x , y\right) = -\frac{-y F_{125}\! \left(x , y\right)+F_{125}\! \left(x , 1\right)}{-1+y}
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{172}\! \left(x \right) F_{20}\! \left(x \right)
F_{172}\! \left(x \right) = F_{20}\! \left(x \right)+F_{39}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{160}\! \left(x \right) F_{20}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = -\frac{y \left(F_{179}\! \left(x , 1\right)-F_{179}\! \left(x , y\right)\right)}{-1+y}
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{191}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{186}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{183}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{194}\! \left(x \right)+F_{4}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{194}\! \left(x \right) = F_{20}\! \left(x \right) F_{87}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{202}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{206}\! \left(x \right) F_{208}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{206}\! \left(x \right) = \frac{F_{207}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{207}\! \left(x \right) = F_{128}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{39}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{213}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{20}\! \left(x \right) F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{1}\! \left(x \right)+F_{210}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{216}\! \left(x \right)+F_{46}\! \left(x \right)
F_{214}\! \left(x \right) = F_{20}\! \left(x \right) F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{20}\! \left(x \right)+F_{213}\! \left(x \right)
F_{216}\! \left(x \right) = F_{20}\! \left(x \right) F_{210}\! \left(x \right)
F_{217}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{22}\! \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))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0) + F_199(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_23(x, k_0))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x))
Eq(F_19(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_195(x, k_0) + F_197(x, k_0) + F_26(x) + F_85(x, k_0))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_20(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_82(x, k_0))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_36(x)*F_39(x))
Eq(F_39(x), F_1(x) + F_20(x))
Eq(F_40(x), F_41(x) + F_52(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_43(x))
Eq(F_43(x), F_39(x) + F_44(x))
Eq(F_44(x), F_41(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_47(x) + F_51(x))
Eq(F_46(x), 0)
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_20(x))
Eq(F_50(x), F_45(x))
Eq(F_51(x), F_20(x)*F_41(x))
Eq(F_52(x), F_46(x) + F_53(x) + F_80(x))
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_65(x))
Eq(F_55(x), F_56(x) + F_62(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_36(x) + F_59(x))
Eq(F_59(x), F_20(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_20(x)*F_56(x))
Eq(F_62(x), F_46(x) + F_61(x) + F_63(x))
Eq(F_63(x), F_20(x)*F_64(x))
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_52(x) + F_66(x))
Eq(F_66(x), F_46(x) + F_67(x) + F_71(x) + F_72(x))
Eq(F_67(x), F_20(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_62(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_20(x)*F_52(x))
Eq(F_72(x), F_20(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_45(x) + F_75(x))
Eq(F_75(x), 2*F_46(x) + F_71(x) + F_76(x))
Eq(F_76(x), F_20(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_60(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_20(x)*F_81(x))
Eq(F_81(x), F_40(x) + F_74(x))
Eq(F_82(x, k_0), F_1(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_82(x, k_0))
Eq(F_85(x, k_0), F_20(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_177(x, k_0) + F_87(x))
Eq(F_87(x), F_88(x)/F_20(x))
Eq(F_88(x), -F_26(x) + F_7(x) - F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_20(x)*F_91(x))
Eq(F_91(x), F_173(x) + F_175(x) + F_92(x) + F_94(x))
Eq(F_92(x), F_39(x)*F_93(x))
Eq(F_93(x), F_13(x, 1))
Eq(F_94(x), F_20(x)*F_95(x))
Eq(F_95(x), F_123(x) + F_96(x))
Eq(F_96(x), F_39(x)*F_97(x))
Eq(F_97(x), F_98(x)/F_20(x))
Eq(F_98(x), F_7(x) - F_93(x) - F_99(x))
Eq(F_99(x), F_100(x)*F_20(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_25(x, 1))
Eq(F_102(x), F_103(x) + F_121(x) + 2*F_46(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_20(x))
Eq(F_105(x), F_106(x, 1))
Eq(F_106(x, k_0), F_107(x, k_0) + F_110(x, k_0) + 2*F_46(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_20(x))
Eq(F_109(x, k_0), (k_0*F_106(x, k_0) - F_106(x, 1))/(k_0 - 1))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_114(x)*F_20(x)*F_39(x))
Eq(F_113(x, k_0), F_112(x, k_0)*F_20(x))
Eq(F_113(x, k_0), F_17(x, k_0))
Eq(F_114(x), F_1(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_20(x))
Eq(F_117(x), F_118(x) + F_39(x))
Eq(F_118(x), F_115(x) + F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_115(x)*F_20(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_114(x)*F_20(x)*F_39(x)*F_7(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x, 1))
Eq(F_125(x, k_0), F_126(x) + F_167(x, k_0) + F_170(x, k_0) + F_46(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_20(x))
Eq(F_128(x), F_129(x) + F_141(x) + F_165(x))
Eq(F_129(x), F_130(x) + F_138(x) + F_140(x) + F_46(x))
Eq(F_130(x), F_131(x)*F_20(x))
Eq(F_131(x), F_132(x, 1))
Eq(F_132(x, k_0), (-k_0*F_133(x, k_0) + F_133(x, 1))/(1 - k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_137(x, k_0) + 2*F_46(x))
Eq(F_134(x, k_0), F_135(x))
Eq(F_135(x), F_129(x) - F_136(x) - 2*F_46(x))
Eq(F_136(x), F_20(x)*F_26(x))
Eq(F_137(x, k_0), F_20(x)*F_27(x, k_0))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_20(x)**2*F_32(x)*F_36(x)*F_39(x))
Eq(F_140(x), F_20(x)*F_32(x))
Eq(F_141(x), F_142(x)*F_20(x))
Eq(F_142(x), F_143(x) - F_164(x))
Eq(F_143(x), F_144(x)/F_20(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_100(x) - F_146(x) - F_147(x) - F_158(x))
Eq(F_146(x), F_129(x) + F_26(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_20(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_6(x) + F_91(x))
Eq(F_151(x), F_152(x) + F_157(x) + 3*F_46(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_20(x)*F_39(x))
Eq(F_154(x), F_155(x)/F_20(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_128(x) - 2*F_46(x) - F_6(x))
Eq(F_157(x), F_20(x)*F_91(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x)*F_20(x))
Eq(F_160(x), F_161(x) + F_163(x))
Eq(F_161(x), F_100(x) + F_162(x))
Eq(F_162(x), F_128(x))
Eq(F_163(x), F_100(x)*F_20(x))
Eq(F_164(x), F_86(x, 1))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_151(x)*F_20(x))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_20(x))
Eq(F_169(x, k_0), (k_0*F_125(x, k_0) - F_125(x, 1))/(k_0 - 1))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_112(x, k_0)*F_172(x)*F_20(x))
Eq(F_172(x), F_20(x) + F_39(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_160(x)*F_20(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_149(x)*F_20(x))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), -F_179(x, 1) + (k_0*F_179(x, k_0) - F_179(x, 1))/(k_0 - 1))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_181(x, k_0), F_180(x, k_0) + F_191(x))
Eq(F_181(x, k_0), F_182(x, k_0) + F_186(x, k_0) + F_190(x, k_0))
Eq(F_183(x, k_0), F_182(x, k_0)*F_20(x))
Eq(F_13(x, k_0), F_1(x) + F_183(x, k_0) + F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_13(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_20(x))
Eq(F_188(x, k_0), F_189(x, k_0) + F_91(x))
Eq(F_189(x, k_0), F_22(x, k_0)*F_7(x))
Eq(F_190(x, k_0), F_20(x)*F_86(x, k_0))
Eq(F_191(x), F_192(x) + F_194(x) + F_4(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_20(x)*F_91(x))
Eq(F_194(x), F_20(x)*F_87(x))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_188(x, k_0)*F_20(x))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0))
Eq(F_200(x, k_0), F_20(x)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_204(x, k_0))
Eq(F_203(x, k_0), F_114(x)*F_20(x)*F_202(x, k_0)*F_39(x))
Eq(F_203(x, k_0), F_106(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0))
Eq(F_205(x, k_0), F_20(x)*F_206(x)*F_208(x)*F_217(x, k_0))
Eq(F_206(x), F_207(x)/F_20(x))
Eq(F_207(x), F_128(x))
Eq(F_208(x), F_209(x) + F_39(x))
Eq(F_209(x), F_210(x) + F_213(x))
Eq(F_210(x), F_211(x))
Eq(F_211(x), F_20(x)*F_212(x))
Eq(F_212(x), F_1(x) + F_210(x))
Eq(F_213(x), F_214(x) + F_216(x) + F_46(x))
Eq(F_214(x), F_20(x)*F_215(x))
Eq(F_215(x), F_20(x) + F_213(x))
Eq(F_216(x), F_20(x)*F_210(x))
Eq(F_217(x, k_0), F_1(x) + F_218(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_22(x, k_0)*F_220(x, k_0))
Eq(F_220(x, k_0), F_21(x, k_0) + F_221(x, k_0))
Eq(F_221(x, k_0), F_218(x, k_0) + F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_218(x, k_0)*F_22(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", 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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}

Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24955/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]+F[199,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[23,x,k[0]]
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[20,x] = x
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[195,x,k[0]]+F[197,x,k[0]]+F[26,x]+F[85,x,k[0]]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[20,x]*F[29,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[82,x,k[0]]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[36,x]*F[39,x]
F[39,x] = F[1,x]+F[20,x]
F[40,x] = F[41,x]+F[52,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[43,x]
F[43,x] = F[39,x]+F[44,x]
F[44,x] = F[41,x]+F[45,x]
F[45,x] = F[46,x]+F[47,x]+F[51,x]
F[46,x] = 0
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[20,x]
F[50,x] = F[45,x]
F[51,x] = F[20,x]*F[41,x]
F[52,x] = F[46,x]+F[53,x]+F[80,x]
F[53,x] = F[20,x]*F[54,x]
F[54,x] = F[55,x]+F[65,x]
F[55,x] = F[56,x]+F[62,x]
F[56,x] = F[57,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[36,x]+F[59,x]
F[59,x] = F[20,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[20,x]*F[56,x]
F[62,x] = F[46,x]+F[61,x]+F[63,x]
F[63,x] = F[20,x]*F[64,x]
F[64,x] = F[59,x]
F[65,x] = F[52,x]+F[66,x]
F[66,x] = F[46,x]+F[67,x]+F[71,x]+F[72,x]
F[67,x] = F[20,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[62,x]
F[70,x] = F[66,x]
F[71,x] = F[20,x]*F[52,x]
F[72,x] = F[20,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[45,x]+F[75,x]
F[75,x] = 2*F[46,x]+F[71,x]+F[76,x]
F[76,x] = F[20,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[60,x]
F[79,x] = F[75,x]
F[80,x] = F[20,x]*F[81,x]
F[81,x] = F[40,x]+F[74,x]
F[82,x,k[0]] = F[1,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[82,x,k[0]]
F[85,x,k[0]] = F[20,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[177,x,k[0]]+F[87,x]
F[87,x] = 1/F[20,x]*F[88,x]
F[88,x] = -F[26,x]-F[89,x]+F[7,x]
F[89,x] = F[90,x]
F[90,x] = F[20,x]*F[91,x]
F[91,x] = F[173,x]+F[175,x]+F[92,x]+F[94,x]
F[92,x] = F[39,x]*F[93,x]
F[93,x] = F[13,x,1]
F[94,x] = F[20,x]*F[95,x]
F[95,x] = F[123,x]+F[96,x]
F[96,x] = F[39,x]*F[97,x]
F[97,x] = 1/F[20,x]*F[98,x]
F[98,x] = -F[93,x]-F[99,x]+F[7,x]
F[99,x] = F[100,x]*F[20,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[25,x,1]
F[102,x] = 2*F[46,x]+F[103,x]+F[121,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[20,x]
F[105,x] = F[106,x,1]
F[106,x,k[0]] = 2*F[46,x]+F[107,x,k[0]]+F[110,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[20,x]
F[109,x,k[0]] = 1/(-1+k[0])*(F[106,x,k[0]]*k[0]-F[106,x,1])
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[114,x]*F[20,x]*F[39,x]
F[113,x,k[0]] = F[112,x,k[0]]*F[20,x]
F[113,x,k[0]] = F[17,x,k[0]]
F[114,x] = F[1,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[20,x]
F[117,x] = F[118,x]+F[39,x]
F[118,x] = F[115,x]+F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[115,x]*F[20,x]
F[121,x] = F[122,x]
F[122,x] = F[114,x]*F[20,x]*F[39,x]*F[7,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x,1]
F[125,x,k[0]] = F[126,x]+F[167,x,k[0]]+F[170,x,k[0]]+F[46,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[20,x]
F[128,x] = F[129,x]+F[141,x]+F[165,x]
F[129,x] = F[130,x]+F[138,x]+F[140,x]+F[46,x]
F[130,x] = F[131,x]*F[20,x]
F[131,x] = F[132,x,1]
F[132,x,k[0]] = (F[133,x,k[0]]*k[0]-F[133,x,1])/(-1+k[0])
F[133,x,k[0]] = 2*F[46,x]+F[134,x,k[0]]+F[137,x,k[0]]
F[134,x,k[0]] = F[135,x]
F[135,x] = -F[136,x]-2*F[46,x]+F[129,x]
F[136,x] = F[20,x]*F[26,x]
F[137,x,k[0]] = F[20,x]*F[27,x,k[0]]
F[138,x] = F[139,x]
F[139,x] = F[20,x]^2*F[32,x]*F[36,x]*F[39,x]
F[140,x] = F[20,x]*F[32,x]
F[141,x] = F[142,x]*F[20,x]
F[142,x] = -F[164,x]+F[143,x]
F[143,x] = 1/F[20,x]*F[144,x]
F[144,x] = F[145,x]
F[145,x] = -F[146,x]-F[147,x]-F[158,x]+F[100,x]
F[146,x] = F[129,x]+F[26,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[20,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[6,x]+F[91,x]
F[151,x] = 3*F[46,x]+F[152,x]+F[157,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[20,x]*F[39,x]
F[154,x] = 1/F[20,x]*F[155,x]
F[155,x] = F[156,x]
F[156,x] = -F[6,x]-2*F[46,x]+F[128,x]
F[157,x] = F[20,x]*F[91,x]
F[158,x] = F[159,x]
F[159,x] = F[160,x]*F[20,x]
F[160,x] = F[161,x]+F[163,x]
F[161,x] = F[100,x]+F[162,x]
F[162,x] = F[128,x]
F[163,x] = F[100,x]*F[20,x]
F[164,x] = F[86,x,1]
F[165,x] = F[166,x]
F[166,x] = F[151,x]*F[20,x]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[20,x]
F[169,x,k[0]] = 1/(-1+k[0])*(F[125,x,k[0]]*k[0]-F[125,x,1])
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[112,x,k[0]]*F[172,x]*F[20,x]
F[172,x] = F[20,x]+F[39,x]
F[173,x] = F[174,x]
F[174,x] = F[160,x]*F[20,x]
F[175,x] = F[176,x]
F[176,x] = F[149,x]*F[20,x]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = -k[0]*(F[179,x,1]-F[179,x,k[0]])/(-1+k[0])
F[179,x,k[0]] = F[180,x,k[0]]
F[181,x,k[0]] = F[180,x,k[0]]+F[191,x]
F[181,x,k[0]] = F[182,x,k[0]]+F[186,x,k[0]]+F[190,x,k[0]]
F[183,x,k[0]] = F[182,x,k[0]]*F[20,x]
F[13,x,k[0]] = F[1,x]+F[183,x,k[0]]+F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[20,x]
F[188,x,k[0]] = F[189,x,k[0]]+F[91,x]
F[189,x,k[0]] = F[22,x,k[0]]*F[7,x]
F[190,x,k[0]] = F[20,x]*F[86,x,k[0]]
F[191,x] = F[192,x]+F[194,x]+F[4,x]
F[192,x] = F[193,x]
F[193,x] = F[20,x]*F[91,x]
F[194,x] = F[20,x]*F[87,x]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[188,x,k[0]]*F[20,x]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]
F[200,x,k[0]] = F[20,x]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[204,x,k[0]]
F[203,x,k[0]] = F[114,x]*F[20,x]*F[202,x,k[0]]*F[39,x]
F[203,x,k[0]] = F[106,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]
F[205,x,k[0]] = F[20,x]*F[206,x]*F[208,x]*F[217,x,k[0]]
F[206,x] = 1/F[20,x]*F[207,x]
F[207,x] = F[128,x]
F[208,x] = F[209,x]+F[39,x]
F[209,x] = F[210,x]+F[213,x]
F[210,x] = F[211,x]
F[211,x] = F[20,x]*F[212,x]
F[212,x] = F[1,x]+F[210,x]
F[213,x] = F[214,x]+F[216,x]+F[46,x]
F[214,x] = F[20,x]*F[215,x]
F[215,x] = F[20,x]+F[213,x]
F[216,x] = F[20,x]*F[210,x]
F[217,x,k[0]] = F[1,x]+F[218,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[22,x,k[0]]*F[220,x,k[0]]
F[220,x,k[0]] = F[21,x,k[0]]+F[221,x,k[0]]
F[221,x,k[0]] = F[218,x,k[0]]+F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[218,x,k[0]]*F[22,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_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{36}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{41}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)+F_{80}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{65}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{46}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{20}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{45}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{20}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{60}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{40}\! \left(x \right)+F_{74}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{88}\! \left(x \right) = -F_{26}\! \left(x \right)-F_{89}\! \left(x \right)+F_{7}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{173}\! \left(x \right)+F_{175}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{39}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{123}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{39}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{98}\! \left(x \right) = -F_{93}\! \left(x \right)-F_{99}\! \left(x \right)+F_{7}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{102}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{103}\! \left(x \right)+F_{121}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{20}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{106}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{107}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{109}\! \left(x , y\right) = -\frac{-F_{106}\! \left(x , y\right) y +F_{106}\! \left(x , 1\right)}{-1+y}
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{20}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{39}\! \left(x \right)
F_{118}\! \left(x \right) = F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{115}\! \left(x \right) F_{20}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right) F_{7}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x , 1\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x \right)+F_{167}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{20}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{141}\! \left(x \right)+F_{165}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)+F_{46}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{20}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x , 1\right)
F_{132}\! \left(x , y\right) = -\frac{-y F_{133}\! \left(x , y\right)+F_{133}\! \left(x , 1\right)}{-1+y}
F_{133}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{136}\! \left(x \right)-2 F_{46}\! \left(x \right)+F_{129}\! \left(x \right)
F_{136}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{39}\! \left(x \right)
F_{140}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{20}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{164}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{146}\! \left(x \right)-F_{147}\! \left(x \right)-F_{158}\! \left(x \right)+F_{100}\! \left(x \right)
F_{146}\! \left(x \right) = F_{129}\! \left(x \right)+F_{26}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{6}\! \left(x \right)+F_{91}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{46}\! \left(x \right)+F_{152}\! \left(x \right)+F_{157}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{155}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{6}\! \left(x \right)-2 F_{46}\! \left(x \right)+F_{128}\! \left(x \right)
F_{157}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{20}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{163}\! \left(x \right)
F_{161}\! \left(x \right) = F_{100}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{128}\! \left(x \right)
F_{163}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right)
F_{164}\! \left(x \right) = F_{86}\! \left(x , 1\right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{151}\! \left(x \right) F_{20}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{169}\! \left(x , y\right) = -\frac{-y F_{125}\! \left(x , y\right)+F_{125}\! \left(x , 1\right)}{-1+y}
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{172}\! \left(x \right) F_{20}\! \left(x \right)
F_{172}\! \left(x \right) = F_{20}\! \left(x \right)+F_{39}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{160}\! \left(x \right) F_{20}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = -\frac{y \left(F_{179}\! \left(x , 1\right)-F_{179}\! \left(x , y\right)\right)}{-1+y}
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{191}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{186}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{183}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{194}\! \left(x \right)+F_{4}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{20}\! \left(x \right) F_{91}\! \left(x \right)
F_{194}\! \left(x \right) = F_{20}\! \left(x \right) F_{87}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{202}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{206}\! \left(x \right) F_{208}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{206}\! \left(x \right) = \frac{F_{207}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{207}\! \left(x \right) = F_{128}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{39}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{213}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{20}\! \left(x \right) F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{1}\! \left(x \right)+F_{210}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{216}\! \left(x \right)+F_{46}\! \left(x \right)
F_{214}\! \left(x \right) = F_{20}\! \left(x \right) F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{20}\! \left(x \right)+F_{213}\! \left(x \right)
F_{216}\! \left(x \right) = F_{20}\! \left(x \right) F_{210}\! \left(x \right)
F_{217}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{22}\! \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))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0) + F_199(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_23(x, k_0))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x))
Eq(F_19(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_195(x, k_0) + F_197(x, k_0) + F_26(x) + F_85(x, k_0))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_20(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_82(x, k_0))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_36(x)*F_39(x))
Eq(F_39(x), F_1(x) + F_20(x))
Eq(F_40(x), F_41(x) + F_52(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_43(x))
Eq(F_43(x), F_39(x) + F_44(x))
Eq(F_44(x), F_41(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_47(x) + F_51(x))
Eq(F_46(x), 0)
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_20(x))
Eq(F_50(x), F_45(x))
Eq(F_51(x), F_20(x)*F_41(x))
Eq(F_52(x), F_46(x) + F_53(x) + F_80(x))
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_65(x))
Eq(F_55(x), F_56(x) + F_62(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_36(x) + F_59(x))
Eq(F_59(x), F_20(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_20(x)*F_56(x))
Eq(F_62(x), F_46(x) + F_61(x) + F_63(x))
Eq(F_63(x), F_20(x)*F_64(x))
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_52(x) + F_66(x))
Eq(F_66(x), F_46(x) + F_67(x) + F_71(x) + F_72(x))
Eq(F_67(x), F_20(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_62(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_20(x)*F_52(x))
Eq(F_72(x), F_20(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_45(x) + F_75(x))
Eq(F_75(x), 2*F_46(x) + F_71(x) + F_76(x))
Eq(F_76(x), F_20(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_60(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_20(x)*F_81(x))
Eq(F_81(x), F_40(x) + F_74(x))
Eq(F_82(x, k_0), F_1(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_82(x, k_0))
Eq(F_85(x, k_0), F_20(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_177(x, k_0) + F_87(x))
Eq(F_87(x), F_88(x)/F_20(x))
Eq(F_88(x), -F_26(x) + F_7(x) - F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_20(x)*F_91(x))
Eq(F_91(x), F_173(x) + F_175(x) + F_92(x) + F_94(x))
Eq(F_92(x), F_39(x)*F_93(x))
Eq(F_93(x), F_13(x, 1))
Eq(F_94(x), F_20(x)*F_95(x))
Eq(F_95(x), F_123(x) + F_96(x))
Eq(F_96(x), F_39(x)*F_97(x))
Eq(F_97(x), F_98(x)/F_20(x))
Eq(F_98(x), F_7(x) - F_93(x) - F_99(x))
Eq(F_99(x), F_100(x)*F_20(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_25(x, 1))
Eq(F_102(x), F_103(x) + F_121(x) + 2*F_46(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_20(x))
Eq(F_105(x), F_106(x, 1))
Eq(F_106(x, k_0), F_107(x, k_0) + F_110(x, k_0) + 2*F_46(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_20(x))
Eq(F_109(x, k_0), (k_0*F_106(x, k_0) - F_106(x, 1))/(k_0 - 1))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_114(x)*F_20(x)*F_39(x))
Eq(F_113(x, k_0), F_112(x, k_0)*F_20(x))
Eq(F_113(x, k_0), F_17(x, k_0))
Eq(F_114(x), F_1(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_20(x))
Eq(F_117(x), F_118(x) + F_39(x))
Eq(F_118(x), F_115(x) + F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_115(x)*F_20(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_114(x)*F_20(x)*F_39(x)*F_7(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x, 1))
Eq(F_125(x, k_0), F_126(x) + F_167(x, k_0) + F_170(x, k_0) + F_46(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_20(x))
Eq(F_128(x), F_129(x) + F_141(x) + F_165(x))
Eq(F_129(x), F_130(x) + F_138(x) + F_140(x) + F_46(x))
Eq(F_130(x), F_131(x)*F_20(x))
Eq(F_131(x), F_132(x, 1))
Eq(F_132(x, k_0), (-k_0*F_133(x, k_0) + F_133(x, 1))/(1 - k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_137(x, k_0) + 2*F_46(x))
Eq(F_134(x, k_0), F_135(x))
Eq(F_135(x), F_129(x) - F_136(x) - 2*F_46(x))
Eq(F_136(x), F_20(x)*F_26(x))
Eq(F_137(x, k_0), F_20(x)*F_27(x, k_0))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_20(x)**2*F_32(x)*F_36(x)*F_39(x))
Eq(F_140(x), F_20(x)*F_32(x))
Eq(F_141(x), F_142(x)*F_20(x))
Eq(F_142(x), F_143(x) - F_164(x))
Eq(F_143(x), F_144(x)/F_20(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_100(x) - F_146(x) - F_147(x) - F_158(x))
Eq(F_146(x), F_129(x) + F_26(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_20(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_6(x) + F_91(x))
Eq(F_151(x), F_152(x) + F_157(x) + 3*F_46(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_20(x)*F_39(x))
Eq(F_154(x), F_155(x)/F_20(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_128(x) - 2*F_46(x) - F_6(x))
Eq(F_157(x), F_20(x)*F_91(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x)*F_20(x))
Eq(F_160(x), F_161(x) + F_163(x))
Eq(F_161(x), F_100(x) + F_162(x))
Eq(F_162(x), F_128(x))
Eq(F_163(x), F_100(x)*F_20(x))
Eq(F_164(x), F_86(x, 1))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_151(x)*F_20(x))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_20(x))
Eq(F_169(x, k_0), (k_0*F_125(x, k_0) - F_125(x, 1))/(k_0 - 1))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_112(x, k_0)*F_172(x)*F_20(x))
Eq(F_172(x), F_20(x) + F_39(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_160(x)*F_20(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_149(x)*F_20(x))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), -F_179(x, 1) + (k_0*F_179(x, k_0) - F_179(x, 1))/(k_0 - 1))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_181(x, k_0), F_180(x, k_0) + F_191(x))
Eq(F_181(x, k_0), F_182(x, k_0) + F_186(x, k_0) + F_190(x, k_0))
Eq(F_183(x, k_0), F_182(x, k_0)*F_20(x))
Eq(F_13(x, k_0), F_1(x) + F_183(x, k_0) + F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_13(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_20(x))
Eq(F_188(x, k_0), F_189(x, k_0) + F_91(x))
Eq(F_189(x, k_0), F_22(x, k_0)*F_7(x))
Eq(F_190(x, k_0), F_20(x)*F_86(x, k_0))
Eq(F_191(x), F_192(x) + F_194(x) + F_4(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_20(x)*F_91(x))
Eq(F_194(x), F_20(x)*F_87(x))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_188(x, k_0)*F_20(x))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0))
Eq(F_200(x, k_0), F_20(x)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_204(x, k_0))
Eq(F_203(x, k_0), F_114(x)*F_20(x)*F_202(x, k_0)*F_39(x))
Eq(F_203(x, k_0), F_106(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0))
Eq(F_205(x, k_0), F_20(x)*F_206(x)*F_208(x)*F_217(x, k_0))
Eq(F_206(x), F_207(x)/F_20(x))
Eq(F_207(x), F_128(x))
Eq(F_208(x), F_209(x) + F_39(x))
Eq(F_209(x), F_210(x) + F_213(x))
Eq(F_210(x), F_211(x))
Eq(F_211(x), F_20(x)*F_212(x))
Eq(F_212(x), F_1(x) + F_210(x))
Eq(F_213(x), F_214(x) + F_216(x) + F_46(x))
Eq(F_214(x), F_20(x)*F_215(x))
Eq(F_215(x), F_20(x) + F_213(x))
Eq(F_216(x), F_20(x)*F_210(x))
Eq(F_217(x, k_0), F_1(x) + F_218(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_22(x, k_0)*F_220(x, k_0))
Eq(F_220(x, k_0), F_21(x, k_0) + F_221(x, k_0))
Eq(F_221(x, k_0), F_218(x, k_0) + F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_218(x, k_0)*F_22(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
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{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"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, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}

Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25143/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]+F[197,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[23,x,k[0]]
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[20,x] = x
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[193,x,k[0]]+F[195,x,k[0]]+F[26,x]+F[83,x,k[0]]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[20,x]*F[29,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[80,x,k[0]]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[43,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[37,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[1,x]+F[20,x]
F[48,x] = F[44,x]+F[49,x]
F[49,x] = F[50,x]+F[51,x]+F[55,x]
F[50,x] = 0
F[51,x] = F[20,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[20,x]
F[54,x] = F[49,x]
F[55,x] = F[20,x]*F[44,x]
F[56,x] = F[50,x]+F[57,x]+F[78,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[37,x]+F[60,x]
F[60,x] = F[42,x]+F[50,x]+F[61,x]
F[61,x] = F[20,x]*F[62,x]
F[62,x] = F[40,x]
F[63,x] = F[56,x]+F[64,x]
F[64,x] = F[50,x]+F[65,x]+F[69,x]+F[70,x]
F[65,x] = F[20,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[60,x]
F[68,x] = F[64,x]
F[69,x] = F[20,x]*F[56,x]
F[70,x] = F[20,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[49,x]+F[73,x]
F[73,x] = 2*F[50,x]+F[69,x]+F[74,x]
F[74,x] = F[20,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[41,x]
F[77,x] = F[73,x]
F[78,x] = F[20,x]*F[79,x]
F[79,x] = F[43,x]+F[72,x]
F[80,x,k[0]] = F[1,x]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[80,x,k[0]]
F[83,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[175,x,k[0]]+F[85,x]
F[85,x] = 1/F[20,x]*F[86,x]
F[86,x] = -F[26,x]-F[87,x]+F[7,x]
F[87,x] = F[88,x]
F[88,x] = F[20,x]*F[89,x]
F[89,x] = F[171,x]+F[173,x]+F[90,x]+F[92,x]
F[90,x] = F[47,x]*F[91,x]
F[91,x] = F[13,x,1]
F[92,x] = F[20,x]*F[93,x]
F[93,x] = F[121,x]+F[94,x]
F[94,x] = F[47,x]*F[95,x]
F[95,x] = 1/F[20,x]*F[96,x]
F[96,x] = -F[91,x]-F[97,x]+F[7,x]
F[97,x] = F[20,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[25,x,1]
F[100,x] = 2*F[50,x]+F[101,x]+F[119,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[20,x]
F[103,x] = F[104,x,1]
F[104,x,k[0]] = 2*F[50,x]+F[105,x,k[0]]+F[108,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[20,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[104,x,k[0]]*k[0]-F[104,x,1])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[112,x]*F[20,x]*F[47,x]
F[111,x,k[0]] = F[110,x,k[0]]*F[20,x]
F[111,x,k[0]] = F[17,x,k[0]]
F[112,x] = F[1,x]+F[113,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[20,x]
F[115,x] = F[116,x]+F[47,x]
F[116,x] = F[113,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[113,x]*F[20,x]
F[119,x] = F[120,x]
F[120,x] = F[112,x]*F[20,x]*F[47,x]*F[7,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x,1]
F[123,x,k[0]] = F[124,x]+F[165,x,k[0]]+F[168,x,k[0]]+F[50,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[20,x]
F[126,x] = F[127,x]+F[139,x]+F[163,x]
F[127,x] = F[128,x]+F[136,x]+F[138,x]+F[50,x]
F[128,x] = F[129,x]*F[20,x]
F[129,x] = F[130,x,1]
F[130,x,k[0]] = (F[131,x,k[0]]*k[0]-F[131,x,1])/(-1+k[0])
F[131,x,k[0]] = 2*F[50,x]+F[132,x,k[0]]+F[135,x,k[0]]
F[132,x,k[0]] = F[133,x]
F[133,x] = -F[134,x]-2*F[50,x]+F[127,x]
F[134,x] = F[20,x]*F[26,x]
F[135,x,k[0]] = F[20,x]*F[27,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = F[20,x]^2*F[32,x]*F[36,x]*F[47,x]
F[138,x] = F[20,x]*F[32,x]
F[139,x] = F[140,x]*F[20,x]
F[140,x] = -F[162,x]+F[141,x]
F[141,x] = 1/F[20,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[144,x]-F[145,x]-F[156,x]+F[98,x]
F[144,x] = F[127,x]+F[26,x]
F[145,x] = F[146,x]
F[146,x] = F[147,x]*F[20,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[6,x]+F[89,x]
F[149,x] = 3*F[50,x]+F[150,x]+F[155,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[20,x]*F[47,x]
F[152,x] = 1/F[20,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = -F[6,x]-2*F[50,x]+F[126,x]
F[155,x] = F[20,x]*F[89,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[20,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[160,x]+F[98,x]
F[160,x] = F[126,x]
F[161,x] = F[20,x]*F[98,x]
F[162,x] = F[84,x,1]
F[163,x] = F[164,x]
F[164,x] = F[149,x]*F[20,x]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[20,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[123,x,k[0]]*k[0]-F[123,x,1])
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[110,x,k[0]]*F[170,x]*F[20,x]
F[170,x] = F[20,x]+F[47,x]
F[171,x] = F[172,x]
F[172,x] = F[158,x]*F[20,x]
F[173,x] = F[174,x]
F[174,x] = F[147,x]*F[20,x]
F[175,x,k[0]] = F[176,x,k[0]]
F[176,x,k[0]] = -k[0]*(F[177,x,1]-F[177,x,k[0]])/(-1+k[0])
F[177,x,k[0]] = F[178,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]+F[189,x]
F[179,x,k[0]] = F[180,x,k[0]]+F[184,x,k[0]]+F[188,x,k[0]]
F[181,x,k[0]] = F[180,x,k[0]]*F[20,x]
F[13,x,k[0]] = F[1,x]+F[181,x,k[0]]+F[182,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]
F[183,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[20,x]
F[186,x,k[0]] = F[187,x,k[0]]+F[89,x]
F[187,x,k[0]] = F[22,x,k[0]]*F[7,x]
F[188,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[189,x] = F[190,x]+F[192,x]+F[4,x]
F[190,x] = F[191,x]
F[191,x] = F[20,x]*F[89,x]
F[192,x] = F[20,x]*F[85,x]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[186,x,k[0]]*F[20,x]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[20,x]
F[199,x,k[0]] = F[200,x,k[0]]+F[202,x,k[0]]
F[201,x,k[0]] = F[112,x]*F[20,x]*F[200,x,k[0]]*F[47,x]
F[201,x,k[0]] = F[104,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[20,x]*F[204,x]*F[206,x]*F[215,x,k[0]]
F[204,x] = 1/F[20,x]*F[205,x]
F[205,x] = F[126,x]
F[206,x] = F[207,x]+F[47,x]
F[207,x] = F[208,x]+F[211,x]
F[208,x] = F[209,x]
F[209,x] = F[20,x]*F[210,x]
F[210,x] = F[1,x]+F[208,x]
F[211,x] = F[212,x]+F[214,x]+F[50,x]
F[212,x] = F[20,x]*F[213,x]
F[213,x] = F[20,x]+F[211,x]
F[214,x] = F[20,x]*F[208,x]
F[215,x,k[0]] = F[1,x]+F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]*F[22,x,k[0]]
F[218,x,k[0]] = F[21,x,k[0]]+F[219,x,k[0]]
F[219,x,k[0]] = F[216,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]
F[221,x,k[0]] = F[216,x,k[0]]*F[22,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_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{43}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = 0
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)+F_{78}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{37}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{42}\! \left(x \right)+F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right)
F_{63}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{50}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{49}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{20}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{43}\! \left(x \right)+F_{72}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{86}\! \left(x \right) = -F_{26}\! \left(x \right)-F_{87}\! \left(x \right)+F_{7}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{171}\! \left(x \right)+F_{173}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{47}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{121}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{47}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{96}\! \left(x \right) = -F_{91}\! \left(x \right)-F_{97}\! \left(x \right)+F_{7}\! \left(x \right)
F_{97}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{100}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{101}\! \left(x \right)+F_{119}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{20}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{104}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{20}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{47}\! \left(x \right)
F_{116}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{113}\! \left(x \right) F_{20}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right) F_{7}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x \right)+F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{139}\! \left(x \right)+F_{163}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{136}\! \left(x \right)+F_{138}\! \left(x \right)+F_{50}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{20}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x , 1\right)
F_{130}\! \left(x , y\right) = -\frac{-y F_{131}\! \left(x , y\right)+F_{131}\! \left(x , 1\right)}{-1+y}
F_{131}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{132}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{134}\! \left(x \right)-2 F_{50}\! \left(x \right)+F_{127}\! \left(x \right)
F_{134}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{47}\! \left(x \right)
F_{138}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{20}\! \left(x \right)
F_{140}\! \left(x \right) = -F_{162}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{144}\! \left(x \right)-F_{145}\! \left(x \right)-F_{156}\! \left(x \right)+F_{98}\! \left(x \right)
F_{144}\! \left(x \right) = F_{127}\! \left(x \right)+F_{26}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{20}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{6}\! \left(x \right)+F_{89}\! \left(x \right)
F_{149}\! \left(x \right) = 3 F_{50}\! \left(x \right)+F_{150}\! \left(x \right)+F_{155}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{6}\! \left(x \right)-2 F_{50}\! \left(x \right)+F_{126}\! \left(x \right)
F_{155}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{20}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{98}\! \left(x \right)
F_{160}\! \left(x \right) = F_{126}\! \left(x \right)
F_{161}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{162}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{167}\! \left(x , y\right) = -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{170}\! \left(x \right) F_{20}\! \left(x \right)
F_{170}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{158}\! \left(x \right) F_{20}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{147}\! \left(x \right) F_{20}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = -\frac{y \left(F_{177}\! \left(x , 1\right)-F_{177}\! \left(x , y\right)\right)}{-1+y}
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{189}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{181}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{89}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{192}\! \left(x \right)+F_{4}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{192}\! \left(x \right) = F_{20}\! \left(x \right) F_{85}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{200}\! \left(x , y\right) F_{47}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{204}\! \left(x \right) F_{206}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{204}\! \left(x \right) = \frac{F_{205}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{205}\! \left(x \right) = F_{126}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{47}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{211}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{20}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{1}\! \left(x \right)+F_{208}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{214}\! \left(x \right)+F_{50}\! \left(x \right)
F_{212}\! \left(x \right) = F_{20}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{20}\! \left(x \right)+F_{211}\! \left(x \right)
F_{214}\! \left(x \right) = F_{20}\! \left(x \right) F_{208}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{22}\! \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))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0) + F_197(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_23(x, k_0))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x))
Eq(F_19(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_193(x, k_0) + F_195(x, k_0) + F_26(x) + F_83(x, k_0))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_20(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_80(x, k_0))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_43(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_37(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_1(x) + F_20(x))
Eq(F_48(x), F_44(x) + F_49(x))
Eq(F_49(x), F_50(x) + F_51(x) + F_55(x))
Eq(F_50(x), 0)
Eq(F_51(x), F_20(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_20(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_20(x)*F_44(x))
Eq(F_56(x), F_50(x) + F_57(x) + F_78(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_37(x) + F_60(x))
Eq(F_60(x), F_42(x) + F_50(x) + F_61(x))
Eq(F_61(x), F_20(x)*F_62(x))
Eq(F_62(x), F_40(x))
Eq(F_63(x), F_56(x) + F_64(x))
Eq(F_64(x), F_50(x) + F_65(x) + F_69(x) + F_70(x))
Eq(F_65(x), F_20(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_60(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), F_20(x)*F_56(x))
Eq(F_70(x), F_20(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_49(x) + F_73(x))
Eq(F_73(x), 2*F_50(x) + F_69(x) + F_74(x))
Eq(F_74(x), F_20(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_41(x))
Eq(F_77(x), F_73(x))
Eq(F_78(x), F_20(x)*F_79(x))
Eq(F_79(x), F_43(x) + F_72(x))
Eq(F_80(x, k_0), F_1(x) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_80(x, k_0))
Eq(F_83(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_175(x, k_0) + F_85(x))
Eq(F_85(x), F_86(x)/F_20(x))
Eq(F_86(x), -F_26(x) + F_7(x) - F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_20(x)*F_89(x))
Eq(F_89(x), F_171(x) + F_173(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_47(x)*F_91(x))
Eq(F_91(x), F_13(x, 1))
Eq(F_92(x), F_20(x)*F_93(x))
Eq(F_93(x), F_121(x) + F_94(x))
Eq(F_94(x), F_47(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_20(x))
Eq(F_96(x), F_7(x) - F_91(x) - F_97(x))
Eq(F_97(x), F_20(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_25(x, 1))
Eq(F_100(x), F_101(x) + F_119(x) + 2*F_50(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_20(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_104(x, k_0), F_105(x, k_0) + F_108(x, k_0) + 2*F_50(x))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_20(x))
Eq(F_107(x, k_0), (k_0*F_104(x, k_0) - F_104(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_112(x)*F_20(x)*F_47(x))
Eq(F_111(x, k_0), F_110(x, k_0)*F_20(x))
Eq(F_111(x, k_0), F_17(x, k_0))
Eq(F_112(x), F_1(x) + F_113(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_20(x))
Eq(F_115(x), F_116(x) + F_47(x))
Eq(F_116(x), F_113(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_113(x)*F_20(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_112(x)*F_20(x)*F_47(x)*F_7(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x, 1))
Eq(F_123(x, k_0), F_124(x) + F_165(x, k_0) + F_168(x, k_0) + F_50(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_20(x))
Eq(F_126(x), F_127(x) + F_139(x) + F_163(x))
Eq(F_127(x), F_128(x) + F_136(x) + F_138(x) + F_50(x))
Eq(F_128(x), F_129(x)*F_20(x))
Eq(F_129(x), F_130(x, 1))
Eq(F_130(x, k_0), (-k_0*F_131(x, k_0) + F_131(x, 1))/(1 - k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_135(x, k_0) + 2*F_50(x))
Eq(F_132(x, k_0), F_133(x))
Eq(F_133(x), F_127(x) - F_134(x) - 2*F_50(x))
Eq(F_134(x), F_20(x)*F_26(x))
Eq(F_135(x, k_0), F_20(x)*F_27(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_20(x)**2*F_32(x)*F_36(x)*F_47(x))
Eq(F_138(x), F_20(x)*F_32(x))
Eq(F_139(x), F_140(x)*F_20(x))
Eq(F_140(x), F_141(x) - F_162(x))
Eq(F_141(x), F_142(x)/F_20(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), -F_144(x) - F_145(x) - F_156(x) + F_98(x))
Eq(F_144(x), F_127(x) + F_26(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x)*F_20(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_6(x) + F_89(x))
Eq(F_149(x), F_150(x) + F_155(x) + 3*F_50(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_20(x)*F_47(x))
Eq(F_152(x), F_153(x)/F_20(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_126(x) - 2*F_50(x) - F_6(x))
Eq(F_155(x), F_20(x)*F_89(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_20(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_160(x) + F_98(x))
Eq(F_160(x), F_126(x))
Eq(F_161(x), F_20(x)*F_98(x))
Eq(F_162(x), F_84(x, 1))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_149(x)*F_20(x))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_20(x))
Eq(F_167(x, k_0), (k_0*F_123(x, k_0) - F_123(x, 1))/(k_0 - 1))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_110(x, k_0)*F_170(x)*F_20(x))
Eq(F_170(x), F_20(x) + F_47(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_158(x)*F_20(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_147(x)*F_20(x))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_176(x, k_0), -F_177(x, 1) + (k_0*F_177(x, k_0) - F_177(x, 1))/(k_0 - 1))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0) + F_189(x))
Eq(F_179(x, k_0), F_180(x, k_0) + F_184(x, k_0) + F_188(x, k_0))
Eq(F_181(x, k_0), F_180(x, k_0)*F_20(x))
Eq(F_13(x, k_0), F_1(x) + F_181(x, k_0) + F_182(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0))
Eq(F_183(x, k_0), F_13(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_20(x))
Eq(F_186(x, k_0), F_187(x, k_0) + F_89(x))
Eq(F_187(x, k_0), F_22(x, k_0)*F_7(x))
Eq(F_188(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_189(x), F_190(x) + F_192(x) + F_4(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_20(x)*F_89(x))
Eq(F_192(x), F_20(x)*F_85(x))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_186(x, k_0)*F_20(x))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_20(x))
Eq(F_199(x, k_0), F_200(x, k_0) + F_202(x, k_0))
Eq(F_201(x, k_0), F_112(x)*F_20(x)*F_200(x, k_0)*F_47(x))
Eq(F_201(x, k_0), F_104(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_20(x)*F_204(x)*F_206(x)*F_215(x, k_0))
Eq(F_204(x), F_205(x)/F_20(x))
Eq(F_205(x), F_126(x))
Eq(F_206(x), F_207(x) + F_47(x))
Eq(F_207(x), F_208(x) + F_211(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_20(x)*F_210(x))
Eq(F_210(x), F_1(x) + F_208(x))
Eq(F_211(x), F_212(x) + F_214(x) + F_50(x))
Eq(F_212(x), F_20(x)*F_213(x))
Eq(F_213(x), F_20(x) + F_211(x))
Eq(F_214(x), F_20(x)*F_208(x))
Eq(F_215(x, k_0), F_1(x) + F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0)*F_22(x, k_0))
Eq(F_218(x, k_0), F_21(x, k_0) + F_219(x, k_0))
Eq(F_219(x, k_0), F_216(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0))
Eq(F_221(x, k_0), F_216(x, k_0)*F_22(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [2, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 1], [2, 1], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [2, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 2], [0, 1], [2, 1], [2, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 2], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 2], [0, 1], [2, 2], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 1], [0, 1], [0, 1], [2, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 1], [0, 1], [2, 1], [2, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 1], [0, 1], [0, 1], [2, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 1], [0, 1], [2, 1], [2, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 1], [0, 1], [0, 2], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 1], [0, 1], [2, 2], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[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": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}

Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25465/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]+F[193,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[23,x,k[0]]
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[20,x] = x
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[189,x,k[0]]+F[191,x,k[0]]+F[26,x]+F[83,x,k[0]]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[20,x]*F[29,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[80,x,k[0]]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[43,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[37,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[1,x]+F[20,x]
F[48,x] = F[44,x]+F[49,x]
F[49,x] = F[50,x]+F[51,x]+F[55,x]
F[50,x] = 0
F[51,x] = F[20,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[20,x]
F[54,x] = F[49,x]
F[55,x] = F[20,x]*F[44,x]
F[56,x] = F[50,x]+F[57,x]+F[78,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[37,x]+F[60,x]
F[60,x] = F[42,x]+F[50,x]+F[61,x]
F[61,x] = F[20,x]*F[62,x]
F[62,x] = F[40,x]
F[63,x] = F[56,x]+F[64,x]
F[64,x] = F[50,x]+F[65,x]+F[69,x]+F[70,x]
F[65,x] = F[20,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[60,x]
F[68,x] = F[64,x]
F[69,x] = F[20,x]*F[56,x]
F[70,x] = F[20,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[49,x]+F[73,x]
F[73,x] = 2*F[50,x]+F[69,x]+F[74,x]
F[74,x] = F[20,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[41,x]
F[77,x] = F[73,x]
F[78,x] = F[20,x]*F[79,x]
F[79,x] = F[43,x]+F[72,x]
F[80,x,k[0]] = F[1,x]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[80,x,k[0]]
F[83,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[171,x,k[0]]+F[85,x]
F[85,x] = 1/F[20,x]*F[86,x]
F[86,x] = -F[26,x]-F[87,x]+F[7,x]
F[87,x] = F[88,x]
F[88,x] = F[20,x]*F[89,x]
F[89,x] = F[167,x]+F[169,x]+F[90,x]+F[92,x]
F[90,x] = F[47,x]*F[91,x]
F[91,x] = F[13,x,1]
F[92,x] = F[20,x]*F[93,x]
F[93,x] = F[121,x]+F[94,x]
F[94,x] = F[47,x]*F[95,x]
F[95,x] = 1/F[20,x]*F[96,x]
F[96,x] = -F[91,x]-F[97,x]+F[7,x]
F[97,x] = F[20,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[25,x,1]
F[100,x] = 2*F[50,x]+F[101,x]+F[119,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[20,x]
F[103,x] = F[104,x,1]
F[104,x,k[0]] = 2*F[50,x]+F[105,x,k[0]]+F[108,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[20,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[104,x,k[0]]*k[0]-F[104,x,1])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[112,x]*F[20,x]*F[47,x]
F[111,x,k[0]] = F[110,x,k[0]]*F[20,x]
F[111,x,k[0]] = F[17,x,k[0]]
F[112,x] = F[1,x]+F[113,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[20,x]
F[115,x] = F[116,x]+F[47,x]
F[116,x] = F[113,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[113,x]*F[20,x]
F[119,x] = F[120,x]
F[120,x] = F[112,x]*F[20,x]*F[47,x]*F[7,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x,1]
F[123,x,k[0]] = F[124,x]+F[161,x,k[0]]+F[164,x,k[0]]+F[50,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[20,x]
F[126,x] = F[127,x]+F[135,x]+F[159,x]
F[127,x] = F[128,x,1]
F[128,x,k[0]] = k[0]*F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[132,x,k[0]]+F[134,x]+F[50,x]
F[130,x,k[0]] = F[131,x,k[0]]*F[20,x]
F[131,x,k[0]] = 1/(-1+k[0])*(F[129,x,k[0]]*k[0]-F[129,x,1])
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[20,x]*F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[80,x,k[0]]
F[134,x] = F[20,x]*F[32,x]
F[135,x] = F[136,x]*F[20,x]
F[136,x] = -F[158,x]+F[137,x]
F[137,x] = 1/F[20,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[140,x]-F[141,x]-F[152,x]+F[98,x]
F[140,x] = F[127,x]+F[26,x]
F[141,x] = F[142,x]
F[142,x] = F[143,x]*F[20,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[6,x]+F[89,x]
F[145,x] = 3*F[50,x]+F[146,x]+F[151,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[20,x]*F[47,x]
F[148,x] = 1/F[20,x]*F[149,x]
F[149,x] = F[150,x]
F[150,x] = -F[6,x]-2*F[50,x]+F[126,x]
F[151,x] = F[20,x]*F[89,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[20,x]
F[154,x] = F[155,x]+F[157,x]
F[155,x] = F[156,x]+F[98,x]
F[156,x] = F[126,x]
F[157,x] = F[20,x]*F[98,x]
F[158,x] = F[84,x,1]
F[159,x] = F[160,x]
F[160,x] = F[145,x]*F[20,x]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[20,x]
F[163,x,k[0]] = 1/(-1+k[0])*(F[123,x,k[0]]*k[0]-F[123,x,1])
F[164,x,k[0]] = F[165,x,k[0]]
F[165,x,k[0]] = F[110,x,k[0]]*F[166,x]*F[20,x]
F[166,x] = F[20,x]+F[47,x]
F[167,x] = F[168,x]
F[168,x] = F[154,x]*F[20,x]
F[169,x] = F[170,x]
F[170,x] = F[143,x]*F[20,x]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = -k[0]*(F[173,x,1]-F[173,x,k[0]])/(-1+k[0])
F[173,x,k[0]] = F[174,x,k[0]]
F[175,x,k[0]] = F[174,x,k[0]]+F[185,x]
F[175,x,k[0]] = F[176,x,k[0]]+F[180,x,k[0]]+F[184,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[20,x]
F[13,x,k[0]] = F[1,x]+F[177,x,k[0]]+F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[20,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[89,x]
F[183,x,k[0]] = F[22,x,k[0]]*F[7,x]
F[184,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[185,x] = F[186,x]+F[188,x]+F[4,x]
F[186,x] = F[187,x]
F[187,x] = F[20,x]*F[89,x]
F[188,x] = F[20,x]*F[85,x]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[182,x,k[0]]*F[20,x]
F[191,x,k[0]] = F[192,x,k[0]]
F[192,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]*F[20,x]
F[195,x,k[0]] = F[196,x,k[0]]+F[198,x,k[0]]
F[197,x,k[0]] = F[112,x]*F[196,x,k[0]]*F[20,x]*F[47,x]
F[197,x,k[0]] = F[104,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]
F[199,x,k[0]] = F[20,x]*F[200,x]*F[202,x]*F[211,x,k[0]]
F[200,x] = 1/F[20,x]*F[201,x]
F[201,x] = F[126,x]
F[202,x] = F[203,x]+F[47,x]
F[203,x] = F[204,x]+F[207,x]
F[204,x] = F[205,x]
F[205,x] = F[20,x]*F[206,x]
F[206,x] = F[1,x]+F[204,x]
F[207,x] = F[208,x]+F[210,x]+F[50,x]
F[208,x] = F[20,x]*F[209,x]
F[209,x] = F[20,x]+F[207,x]
F[210,x] = F[20,x]*F[204,x]
F[211,x,k[0]] = F[1,x]+F[212,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]*F[22,x,k[0]]
F[214,x,k[0]] = F[21,x,k[0]]+F[215,x,k[0]]
F[215,x,k[0]] = F[212,x,k[0]]+F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]
F[217,x,k[0]] = F[212,x,k[0]]*F[22,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_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{43}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = 0
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)+F_{78}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{37}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{42}\! \left(x \right)+F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right)
F_{63}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{50}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{49}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{20}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{43}\! \left(x \right)+F_{72}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{86}\! \left(x \right) = -F_{26}\! \left(x \right)-F_{87}\! \left(x \right)+F_{7}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{167}\! \left(x \right)+F_{169}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{47}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{121}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{47}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{96}\! \left(x \right) = -F_{91}\! \left(x \right)-F_{97}\! \left(x \right)+F_{7}\! \left(x \right)
F_{97}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{100}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{101}\! \left(x \right)+F_{119}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{20}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{104}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{20}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{47}\! \left(x \right)
F_{116}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{113}\! \left(x \right) F_{20}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right) F_{7}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x \right)+F_{161}\! \left(x , y\right)+F_{164}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{135}\! \left(x \right)+F_{159}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x , 1\right)
F_{128}\! \left(x , y\right) = y F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{132}\! \left(x , y\right)+F_{134}\! \left(x \right)+F_{50}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{131}\! \left(x , y\right) = -\frac{-y F_{129}\! \left(x , y\right)+F_{129}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{20}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{140}\! \left(x \right)-F_{141}\! \left(x \right)-F_{152}\! \left(x \right)+F_{98}\! \left(x \right)
F_{140}\! \left(x \right) = F_{127}\! \left(x \right)+F_{26}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{20}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{6}\! \left(x \right)+F_{89}\! \left(x \right)
F_{145}\! \left(x \right) = 3 F_{50}\! \left(x \right)+F_{146}\! \left(x \right)+F_{151}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{148}\! \left(x \right) = \frac{F_{149}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = -F_{6}\! \left(x \right)-2 F_{50}\! \left(x \right)+F_{126}\! \left(x \right)
F_{151}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{20}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{157}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{98}\! \left(x \right)
F_{156}\! \left(x \right) = F_{126}\! \left(x \right)
F_{157}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{158}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{145}\! \left(x \right) F_{20}\! \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_{20}\! \left(x \right)
F_{163}\! \left(x , y\right) = -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{166}\! \left(x \right) F_{20}\! \left(x \right)
F_{166}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{154}\! \left(x \right) F_{20}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{143}\! \left(x \right) F_{20}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = -\frac{y \left(F_{173}\! \left(x , 1\right)-F_{173}\! \left(x , y\right)\right)}{-1+y}
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{185}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{89}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{188}\! \left(x \right)+F_{4}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{188}\! \left(x \right) = F_{20}\! \left(x \right) F_{85}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{112}\! \left(x \right) F_{196}\! \left(x , y\right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{200}\! \left(x \right) F_{202}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{126}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{47}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)+F_{207}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{20}\! \left(x \right) F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{1}\! \left(x \right)+F_{204}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{210}\! \left(x \right)+F_{50}\! \left(x \right)
F_{208}\! \left(x \right) = F_{20}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{20}\! \left(x \right)+F_{207}\! \left(x \right)
F_{210}\! \left(x \right) = F_{20}\! \left(x \right) F_{204}\! \left(x \right)
F_{211}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{214}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{212}\! \left(x , y\right) F_{22}\! \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))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0) + F_193(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_23(x, k_0))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x))
Eq(F_19(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_189(x, k_0) + F_191(x, k_0) + F_26(x) + F_83(x, k_0))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_20(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_80(x, k_0))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_43(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_37(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_1(x) + F_20(x))
Eq(F_48(x), F_44(x) + F_49(x))
Eq(F_49(x), F_50(x) + F_51(x) + F_55(x))
Eq(F_50(x), 0)
Eq(F_51(x), F_20(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_20(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_20(x)*F_44(x))
Eq(F_56(x), F_50(x) + F_57(x) + F_78(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_37(x) + F_60(x))
Eq(F_60(x), F_42(x) + F_50(x) + F_61(x))
Eq(F_61(x), F_20(x)*F_62(x))
Eq(F_62(x), F_40(x))
Eq(F_63(x), F_56(x) + F_64(x))
Eq(F_64(x), F_50(x) + F_65(x) + F_69(x) + F_70(x))
Eq(F_65(x), F_20(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_60(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), F_20(x)*F_56(x))
Eq(F_70(x), F_20(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_49(x) + F_73(x))
Eq(F_73(x), 2*F_50(x) + F_69(x) + F_74(x))
Eq(F_74(x), F_20(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_41(x))
Eq(F_77(x), F_73(x))
Eq(F_78(x), F_20(x)*F_79(x))
Eq(F_79(x), F_43(x) + F_72(x))
Eq(F_80(x, k_0), F_1(x) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_80(x, k_0))
Eq(F_83(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_171(x, k_0) + F_85(x))
Eq(F_85(x), F_86(x)/F_20(x))
Eq(F_86(x), -F_26(x) + F_7(x) - F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_20(x)*F_89(x))
Eq(F_89(x), F_167(x) + F_169(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_47(x)*F_91(x))
Eq(F_91(x), F_13(x, 1))
Eq(F_92(x), F_20(x)*F_93(x))
Eq(F_93(x), F_121(x) + F_94(x))
Eq(F_94(x), F_47(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_20(x))
Eq(F_96(x), F_7(x) - F_91(x) - F_97(x))
Eq(F_97(x), F_20(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_25(x, 1))
Eq(F_100(x), F_101(x) + F_119(x) + 2*F_50(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_20(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_104(x, k_0), F_105(x, k_0) + F_108(x, k_0) + 2*F_50(x))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_20(x))
Eq(F_107(x, k_0), (k_0*F_104(x, k_0) - F_104(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_112(x)*F_20(x)*F_47(x))
Eq(F_111(x, k_0), F_110(x, k_0)*F_20(x))
Eq(F_111(x, k_0), F_17(x, k_0))
Eq(F_112(x), F_1(x) + F_113(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_20(x))
Eq(F_115(x), F_116(x) + F_47(x))
Eq(F_116(x), F_113(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_113(x)*F_20(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_112(x)*F_20(x)*F_47(x)*F_7(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x, 1))
Eq(F_123(x, k_0), F_124(x) + F_161(x, k_0) + F_164(x, k_0) + F_50(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_20(x))
Eq(F_126(x), F_127(x) + F_135(x) + F_159(x))
Eq(F_127(x), F_128(x, 1))
Eq(F_128(x, k_0), k_0*F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_132(x, k_0) + F_134(x) + F_50(x))
Eq(F_130(x, k_0), F_131(x, k_0)*F_20(x))
Eq(F_131(x, k_0), (k_0*F_129(x, k_0) - F_129(x, 1))/(k_0 - 1))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_20(x)*F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_80(x, k_0))
Eq(F_134(x), F_20(x)*F_32(x))
Eq(F_135(x), F_136(x)*F_20(x))
Eq(F_136(x), F_137(x) - F_158(x))
Eq(F_137(x), F_138(x)/F_20(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), -F_140(x) - F_141(x) - F_152(x) + F_98(x))
Eq(F_140(x), F_127(x) + F_26(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_143(x)*F_20(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_6(x) + F_89(x))
Eq(F_145(x), F_146(x) + F_151(x) + 3*F_50(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_20(x)*F_47(x))
Eq(F_148(x), F_149(x)/F_20(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_126(x) - 2*F_50(x) - F_6(x))
Eq(F_151(x), F_20(x)*F_89(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_20(x))
Eq(F_154(x), F_155(x) + F_157(x))
Eq(F_155(x), F_156(x) + F_98(x))
Eq(F_156(x), F_126(x))
Eq(F_157(x), F_20(x)*F_98(x))
Eq(F_158(x), F_84(x, 1))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_145(x)*F_20(x))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_20(x))
Eq(F_163(x, k_0), (k_0*F_123(x, k_0) - F_123(x, 1))/(k_0 - 1))
Eq(F_164(x, k_0), F_165(x, k_0))
Eq(F_165(x, k_0), F_110(x, k_0)*F_166(x)*F_20(x))
Eq(F_166(x), F_20(x) + F_47(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_154(x)*F_20(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_143(x)*F_20(x))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), -F_173(x, 1) + (k_0*F_173(x, k_0) - F_173(x, 1))/(k_0 - 1))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_175(x, k_0), F_174(x, k_0) + F_185(x))
Eq(F_175(x, k_0), F_176(x, k_0) + F_180(x, k_0) + F_184(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_20(x))
Eq(F_13(x, k_0), F_1(x) + F_177(x, k_0) + F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_13(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_20(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_89(x))
Eq(F_183(x, k_0), F_22(x, k_0)*F_7(x))
Eq(F_184(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_185(x), F_186(x) + F_188(x) + F_4(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_20(x)*F_89(x))
Eq(F_188(x), F_20(x)*F_85(x))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_182(x, k_0)*F_20(x))
Eq(F_191(x, k_0), F_192(x, k_0))
Eq(F_192(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0)*F_20(x))
Eq(F_195(x, k_0), F_196(x, k_0) + F_198(x, k_0))
Eq(F_197(x, k_0), F_112(x)*F_196(x, k_0)*F_20(x)*F_47(x))
Eq(F_197(x, k_0), F_104(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0))
Eq(F_199(x, k_0), F_20(x)*F_200(x)*F_202(x)*F_211(x, k_0))
Eq(F_200(x), F_201(x)/F_20(x))
Eq(F_201(x), F_126(x))
Eq(F_202(x), F_203(x) + F_47(x))
Eq(F_203(x), F_204(x) + F_207(x))
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_20(x)*F_206(x))
Eq(F_206(x), F_1(x) + F_204(x))
Eq(F_207(x), F_208(x) + F_210(x) + F_50(x))
Eq(F_208(x), F_20(x)*F_209(x))
Eq(F_209(x), F_20(x) + F_207(x))
Eq(F_210(x), F_20(x)*F_204(x))
Eq(F_211(x, k_0), F_1(x) + F_212(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0)*F_22(x, k_0))
Eq(F_214(x, k_0), F_21(x, k_0) + F_215(x, k_0))
Eq(F_215(x, k_0), F_212(x, k_0) + F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0))
Eq(F_217(x, k_0), F_212(x, k_0)*F_22(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"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, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"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, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[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": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 5
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25493/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]+F[197,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[23,x,k[0]]
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[20,x] = x
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[193,x,k[0]]+F[195,x,k[0]]+F[26,x]+F[83,x,k[0]]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[20,x]*F[29,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[32,x]*F[80,x,k[0]]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[20,x]*F[35,x]
F[35,x] = F[36,x]+F[43,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[37,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[1,x]+F[20,x]
F[48,x] = F[44,x]+F[49,x]
F[49,x] = F[50,x]+F[51,x]+F[55,x]
F[50,x] = 0
F[51,x] = F[20,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[20,x]
F[54,x] = F[49,x]
F[55,x] = F[20,x]*F[44,x]
F[56,x] = F[50,x]+F[57,x]+F[78,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[37,x]+F[60,x]
F[60,x] = F[42,x]+F[50,x]+F[61,x]
F[61,x] = F[20,x]*F[62,x]
F[62,x] = F[40,x]
F[63,x] = F[56,x]+F[64,x]
F[64,x] = F[50,x]+F[65,x]+F[69,x]+F[70,x]
F[65,x] = F[20,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[60,x]
F[68,x] = F[64,x]
F[69,x] = F[20,x]*F[56,x]
F[70,x] = F[20,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[49,x]+F[73,x]
F[73,x] = 2*F[50,x]+F[69,x]+F[74,x]
F[74,x] = F[20,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[41,x]
F[77,x] = F[73,x]
F[78,x] = F[20,x]*F[79,x]
F[79,x] = F[43,x]+F[72,x]
F[80,x,k[0]] = F[1,x]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[80,x,k[0]]
F[83,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[175,x,k[0]]+F[85,x]
F[85,x] = 1/F[20,x]*F[86,x]
F[86,x] = -F[26,x]-F[87,x]+F[7,x]
F[87,x] = F[88,x]
F[88,x] = F[20,x]*F[89,x]
F[89,x] = F[171,x]+F[173,x]+F[90,x]+F[92,x]
F[90,x] = F[47,x]*F[91,x]
F[91,x] = F[13,x,1]
F[92,x] = F[20,x]*F[93,x]
F[93,x] = F[121,x]+F[94,x]
F[94,x] = F[47,x]*F[95,x]
F[95,x] = 1/F[20,x]*F[96,x]
F[96,x] = -F[91,x]-F[97,x]+F[7,x]
F[97,x] = F[20,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[25,x,1]
F[100,x] = 2*F[50,x]+F[101,x]+F[119,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[20,x]
F[103,x] = F[104,x,1]
F[104,x,k[0]] = 2*F[50,x]+F[105,x,k[0]]+F[108,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[20,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[104,x,k[0]]*k[0]-F[104,x,1])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[112,x]*F[20,x]*F[47,x]
F[111,x,k[0]] = F[110,x,k[0]]*F[20,x]
F[111,x,k[0]] = F[17,x,k[0]]
F[112,x] = F[1,x]+F[113,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[20,x]
F[115,x] = F[116,x]+F[47,x]
F[116,x] = F[113,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[113,x]*F[20,x]
F[119,x] = F[120,x]
F[120,x] = F[112,x]*F[20,x]*F[47,x]*F[7,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x,1]
F[123,x,k[0]] = F[124,x]+F[165,x,k[0]]+F[168,x,k[0]]+F[50,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[20,x]
F[126,x] = F[127,x]+F[139,x]+F[163,x]
F[127,x] = F[128,x]+F[136,x]+F[138,x]+F[50,x]
F[128,x] = F[129,x]*F[20,x]
F[129,x] = F[130,x,1]
F[130,x,k[0]] = (F[131,x,k[0]]*k[0]-F[131,x,1])/(-1+k[0])
F[131,x,k[0]] = 2*F[50,x]+F[132,x,k[0]]+F[135,x,k[0]]
F[132,x,k[0]] = F[133,x]
F[133,x] = -F[134,x]-2*F[50,x]+F[127,x]
F[134,x] = F[20,x]*F[26,x]
F[135,x,k[0]] = F[20,x]*F[27,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = F[20,x]^2*F[32,x]*F[36,x]*F[47,x]
F[138,x] = F[20,x]*F[32,x]
F[139,x] = F[140,x]*F[20,x]
F[140,x] = -F[162,x]+F[141,x]
F[141,x] = 1/F[20,x]*F[142,x]
F[142,x] = F[143,x]
F[143,x] = -F[144,x]-F[145,x]-F[156,x]+F[98,x]
F[144,x] = F[127,x]+F[26,x]
F[145,x] = F[146,x]
F[146,x] = F[147,x]*F[20,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[6,x]+F[89,x]
F[149,x] = 3*F[50,x]+F[150,x]+F[155,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[20,x]*F[47,x]
F[152,x] = 1/F[20,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = -F[6,x]-2*F[50,x]+F[126,x]
F[155,x] = F[20,x]*F[89,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[20,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[160,x]+F[98,x]
F[160,x] = F[126,x]
F[161,x] = F[20,x]*F[98,x]
F[162,x] = F[84,x,1]
F[163,x] = F[164,x]
F[164,x] = F[149,x]*F[20,x]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[20,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[123,x,k[0]]*k[0]-F[123,x,1])
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[110,x,k[0]]*F[170,x]*F[20,x]
F[170,x] = F[20,x]+F[47,x]
F[171,x] = F[172,x]
F[172,x] = F[158,x]*F[20,x]
F[173,x] = F[174,x]
F[174,x] = F[147,x]*F[20,x]
F[175,x,k[0]] = F[176,x,k[0]]
F[176,x,k[0]] = -k[0]*(F[177,x,1]-F[177,x,k[0]])/(-1+k[0])
F[177,x,k[0]] = F[178,x,k[0]]
F[179,x,k[0]] = F[178,x,k[0]]+F[189,x]
F[179,x,k[0]] = F[180,x,k[0]]+F[184,x,k[0]]+F[188,x,k[0]]
F[181,x,k[0]] = F[180,x,k[0]]*F[20,x]
F[13,x,k[0]] = F[1,x]+F[181,x,k[0]]+F[182,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]
F[183,x,k[0]] = F[13,x,k[0]]*F[21,x,k[0]]*F[22,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[20,x]
F[186,x,k[0]] = F[187,x,k[0]]+F[89,x]
F[187,x,k[0]] = F[22,x,k[0]]*F[7,x]
F[188,x,k[0]] = F[20,x]*F[84,x,k[0]]
F[189,x] = F[190,x]+F[192,x]+F[4,x]
F[190,x] = F[191,x]
F[191,x] = F[20,x]*F[89,x]
F[192,x] = F[20,x]*F[85,x]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[186,x,k[0]]*F[20,x]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[20,x]
F[199,x,k[0]] = F[200,x,k[0]]+F[202,x,k[0]]
F[201,x,k[0]] = F[112,x]*F[20,x]*F[200,x,k[0]]*F[47,x]
F[201,x,k[0]] = F[104,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]
F[203,x,k[0]] = F[20,x]*F[204,x]*F[206,x]*F[215,x,k[0]]
F[204,x] = 1/F[20,x]*F[205,x]
F[205,x] = F[126,x]
F[206,x] = F[207,x]+F[47,x]
F[207,x] = F[208,x]+F[211,x]
F[208,x] = F[209,x]
F[209,x] = F[20,x]*F[210,x]
F[210,x] = F[1,x]+F[208,x]
F[211,x] = F[212,x]+F[214,x]+F[50,x]
F[212,x] = F[20,x]*F[213,x]
F[213,x] = F[20,x]+F[211,x]
F[214,x] = F[20,x]*F[208,x]
F[215,x,k[0]] = F[1,x]+F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]*F[22,x,k[0]]
F[218,x,k[0]] = F[21,x,k[0]]+F[219,x,k[0]]
F[219,x,k[0]] = F[216,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]
F[221,x,k[0]] = F[216,x,k[0]]*F[22,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_{3}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{32}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{43}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = 0
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)+F_{78}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{37}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{42}\! \left(x \right)+F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right)
F_{63}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{50}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{49}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{20}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{43}\! \left(x \right)+F_{72}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{86}\! \left(x \right) = -F_{26}\! \left(x \right)-F_{87}\! \left(x \right)+F_{7}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{171}\! \left(x \right)+F_{173}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{47}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{121}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{47}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{96}\! \left(x \right) = -F_{91}\! \left(x \right)-F_{97}\! \left(x \right)+F_{7}\! \left(x \right)
F_{97}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{100}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{101}\! \left(x \right)+F_{119}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{20}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{104}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{20}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{47}\! \left(x \right)
F_{116}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{113}\! \left(x \right) F_{20}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right) F_{7}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x \right)+F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{139}\! \left(x \right)+F_{163}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{136}\! \left(x \right)+F_{138}\! \left(x \right)+F_{50}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{20}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x , 1\right)
F_{130}\! \left(x , y\right) = -\frac{-y F_{131}\! \left(x , y\right)+F_{131}\! \left(x , 1\right)}{-1+y}
F_{131}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{132}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{134}\! \left(x \right)-2 F_{50}\! \left(x \right)+F_{127}\! \left(x \right)
F_{134}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{47}\! \left(x \right)
F_{138}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{20}\! \left(x \right)
F_{140}\! \left(x \right) = -F_{162}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{144}\! \left(x \right)-F_{145}\! \left(x \right)-F_{156}\! \left(x \right)+F_{98}\! \left(x \right)
F_{144}\! \left(x \right) = F_{127}\! \left(x \right)+F_{26}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{20}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{6}\! \left(x \right)+F_{89}\! \left(x \right)
F_{149}\! \left(x \right) = 3 F_{50}\! \left(x \right)+F_{150}\! \left(x \right)+F_{155}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{6}\! \left(x \right)-2 F_{50}\! \left(x \right)+F_{126}\! \left(x \right)
F_{155}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{20}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{98}\! \left(x \right)
F_{160}\! \left(x \right) = F_{126}\! \left(x \right)
F_{161}\! \left(x \right) = F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{162}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{149}\! \left(x \right) F_{20}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{167}\! \left(x , y\right) = -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{170}\! \left(x \right) F_{20}\! \left(x \right)
F_{170}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{158}\! \left(x \right) F_{20}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{147}\! \left(x \right) F_{20}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = -\frac{y \left(F_{177}\! \left(x , 1\right)-F_{177}\! \left(x , y\right)\right)}{-1+y}
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{189}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{181}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{89}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{192}\! \left(x \right)+F_{4}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{192}\! \left(x \right) = F_{20}\! \left(x \right) F_{85}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{112}\! \left(x \right) F_{20}\! \left(x \right) F_{200}\! \left(x , y\right) F_{47}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{204}\! \left(x \right) F_{206}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{204}\! \left(x \right) = \frac{F_{205}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{205}\! \left(x \right) = F_{126}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{47}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{211}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{20}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{1}\! \left(x \right)+F_{208}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{214}\! \left(x \right)+F_{50}\! \left(x \right)
F_{212}\! \left(x \right) = F_{20}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{20}\! \left(x \right)+F_{211}\! \left(x \right)
F_{214}\! \left(x \right) = F_{20}\! \left(x \right) F_{208}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{22}\! \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))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0) + F_197(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_23(x, k_0))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x))
Eq(F_19(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_193(x, k_0) + F_195(x, k_0) + F_26(x) + F_83(x, k_0))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_20(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_32(x)*F_80(x, k_0))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_20(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_43(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_37(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_1(x) + F_20(x))
Eq(F_48(x), F_44(x) + F_49(x))
Eq(F_49(x), F_50(x) + F_51(x) + F_55(x))
Eq(F_50(x), 0)
Eq(F_51(x), F_20(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_20(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_20(x)*F_44(x))
Eq(F_56(x), F_50(x) + F_57(x) + F_78(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_37(x) + F_60(x))
Eq(F_60(x), F_42(x) + F_50(x) + F_61(x))
Eq(F_61(x), F_20(x)*F_62(x))
Eq(F_62(x), F_40(x))
Eq(F_63(x), F_56(x) + F_64(x))
Eq(F_64(x), F_50(x) + F_65(x) + F_69(x) + F_70(x))
Eq(F_65(x), F_20(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_60(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), F_20(x)*F_56(x))
Eq(F_70(x), F_20(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_49(x) + F_73(x))
Eq(F_73(x), 2*F_50(x) + F_69(x) + F_74(x))
Eq(F_74(x), F_20(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_41(x))
Eq(F_77(x), F_73(x))
Eq(F_78(x), F_20(x)*F_79(x))
Eq(F_79(x), F_43(x) + F_72(x))
Eq(F_80(x, k_0), F_1(x) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_80(x, k_0))
Eq(F_83(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_175(x, k_0) + F_85(x))
Eq(F_85(x), F_86(x)/F_20(x))
Eq(F_86(x), -F_26(x) + F_7(x) - F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_20(x)*F_89(x))
Eq(F_89(x), F_171(x) + F_173(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_47(x)*F_91(x))
Eq(F_91(x), F_13(x, 1))
Eq(F_92(x), F_20(x)*F_93(x))
Eq(F_93(x), F_121(x) + F_94(x))
Eq(F_94(x), F_47(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_20(x))
Eq(F_96(x), F_7(x) - F_91(x) - F_97(x))
Eq(F_97(x), F_20(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_25(x, 1))
Eq(F_100(x), F_101(x) + F_119(x) + 2*F_50(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_20(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_104(x, k_0), F_105(x, k_0) + F_108(x, k_0) + 2*F_50(x))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_20(x))
Eq(F_107(x, k_0), (k_0*F_104(x, k_0) - F_104(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_112(x)*F_20(x)*F_47(x))
Eq(F_111(x, k_0), F_110(x, k_0)*F_20(x))
Eq(F_111(x, k_0), F_17(x, k_0))
Eq(F_112(x), F_1(x) + F_113(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_20(x))
Eq(F_115(x), F_116(x) + F_47(x))
Eq(F_116(x), F_113(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_113(x)*F_20(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_112(x)*F_20(x)*F_47(x)*F_7(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x, 1))
Eq(F_123(x, k_0), F_124(x) + F_165(x, k_0) + F_168(x, k_0) + F_50(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_20(x))
Eq(F_126(x), F_127(x) + F_139(x) + F_163(x))
Eq(F_127(x), F_128(x) + F_136(x) + F_138(x) + F_50(x))
Eq(F_128(x), F_129(x)*F_20(x))
Eq(F_129(x), F_130(x, 1))
Eq(F_130(x, k_0), (-k_0*F_131(x, k_0) + F_131(x, 1))/(1 - k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_135(x, k_0) + 2*F_50(x))
Eq(F_132(x, k_0), F_133(x))
Eq(F_133(x), F_127(x) - F_134(x) - 2*F_50(x))
Eq(F_134(x), F_20(x)*F_26(x))
Eq(F_135(x, k_0), F_20(x)*F_27(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_20(x)**2*F_32(x)*F_36(x)*F_47(x))
Eq(F_138(x), F_20(x)*F_32(x))
Eq(F_139(x), F_140(x)*F_20(x))
Eq(F_140(x), F_141(x) - F_162(x))
Eq(F_141(x), F_142(x)/F_20(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), -F_144(x) - F_145(x) - F_156(x) + F_98(x))
Eq(F_144(x), F_127(x) + F_26(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x)*F_20(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_6(x) + F_89(x))
Eq(F_149(x), F_150(x) + F_155(x) + 3*F_50(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_20(x)*F_47(x))
Eq(F_152(x), F_153(x)/F_20(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_126(x) - 2*F_50(x) - F_6(x))
Eq(F_155(x), F_20(x)*F_89(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_20(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_160(x) + F_98(x))
Eq(F_160(x), F_126(x))
Eq(F_161(x), F_20(x)*F_98(x))
Eq(F_162(x), F_84(x, 1))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_149(x)*F_20(x))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_20(x))
Eq(F_167(x, k_0), (k_0*F_123(x, k_0) - F_123(x, 1))/(k_0 - 1))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_110(x, k_0)*F_170(x)*F_20(x))
Eq(F_170(x), F_20(x) + F_47(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_158(x)*F_20(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_147(x)*F_20(x))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_176(x, k_0), -F_177(x, 1) + (k_0*F_177(x, k_0) - F_177(x, 1))/(k_0 - 1))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_179(x, k_0), F_178(x, k_0) + F_189(x))
Eq(F_179(x, k_0), F_180(x, k_0) + F_184(x, k_0) + F_188(x, k_0))
Eq(F_181(x, k_0), F_180(x, k_0)*F_20(x))
Eq(F_13(x, k_0), F_1(x) + F_181(x, k_0) + F_182(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0))
Eq(F_183(x, k_0), F_13(x, k_0)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_20(x))
Eq(F_186(x, k_0), F_187(x, k_0) + F_89(x))
Eq(F_187(x, k_0), F_22(x, k_0)*F_7(x))
Eq(F_188(x, k_0), F_20(x)*F_84(x, k_0))
Eq(F_189(x), F_190(x) + F_192(x) + F_4(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_20(x)*F_89(x))
Eq(F_192(x), F_20(x)*F_85(x))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_186(x, k_0)*F_20(x))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_21(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_20(x))
Eq(F_199(x, k_0), F_200(x, k_0) + F_202(x, k_0))
Eq(F_201(x, k_0), F_112(x)*F_20(x)*F_200(x, k_0)*F_47(x))
Eq(F_201(x, k_0), F_104(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0))
Eq(F_203(x, k_0), F_20(x)*F_204(x)*F_206(x)*F_215(x, k_0))
Eq(F_204(x), F_205(x)/F_20(x))
Eq(F_205(x), F_126(x))
Eq(F_206(x), F_207(x) + F_47(x))
Eq(F_207(x), F_208(x) + F_211(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_20(x)*F_210(x))
Eq(F_210(x), F_1(x) + F_208(x))
Eq(F_211(x), F_212(x) + F_214(x) + F_50(x))
Eq(F_212(x), F_20(x)*F_213(x))
Eq(F_213(x), F_20(x) + F_211(x))
Eq(F_214(x), F_20(x)*F_208(x))
Eq(F_215(x, k_0), F_1(x) + F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0)*F_22(x, k_0))
Eq(F_218(x, k_0), F_21(x, k_0) + F_219(x, k_0))
Eq(F_219(x, k_0), F_216(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0))
Eq(F_221(x, k_0), F_216(x, k_0)*F_22(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", 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