0123_0231
Counting sequence:
1, 1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910, 5900843531665, 29464355189120, 147522603762870, 740471407808372, 3725334547101464, 18782663124890072, 94889671255981134, 480277198610107582, 2435135955040907671, 12367005533005155312, 62903123907986269322, 320410141070011568932, 1634293872608010087381, 8346616080180775069696, 42679208684027480231382, 218483984130530550767072, 1119680382073012936719354, 5744015596247651175636152, 29495915660258107925967820, 151604521940977209923648720, 779914804987975878040481284, 4015586460746926630035392312, 20691924792873408736997259546, 106705618985310241433574110370, 550672748581976234737822488805, 2843846266975183589976948893440, 14696437495127338652763097055630, 75997521331493118265138165727740, 393239267985656673266643544950060, 2035981303766618996324690564085880, 10547271431411660816565301769357944, 54669667570338188518808267351070296, 283520056202789661399301981916660948, 1471105230548700577048290842673214928, 7636921100093650990019809240950826336, 39664310661082487431240978976246424072, 206101610729453324356777460391138149024, 1071410551972957191221289069972769221632, 5572076153071230412747757960941049129686, 28990693811032669921432888203232778124782, 150894971235609071749188839490748563182223, 785705774737959074164746512777232093551008, 4092689864780031335242595161737002490748954, 21326342345646664574048652153377838299209460, 111167473347764442879095716834540721579139060, 579679973373640928437277027891094108076647668, 3023734475237525784805324692624677201715582614, 15777550602061498589689340707341831078507697642, 82351601790504172460038126146758994628215747135, 429969048634260130718427149947042653863113678720, 2245594353262735304080348963684001050792064457970, 11731426959660910139593483683675467734954302114500, 61304504737390252069652917880595931554013258413780, 320444395200776815427742510184915121132511795341480, 1675438828876902239755032385151102496629355504337460, 8762278650190533722504929489823010649382512442407204, 45836899276073400458046332065511972915585343884825082, 239839273384971247643377892987119773633823316601587536, 1255248123257802278953854705379914735373122750763711996, 6571136505741766714658507037121858809780951934446754152, 34407295304852326235871710481719758321683976937395123374, 180201050424352882566595997324147082167511896537328115712, 943970724221470412577121935459402826765855504027022028596, 4945975093864926604623279634889002731656873821685404997552, 25920021849660584162802805894647809591058079622134825581524, 135864739731028290887972014271711712162163566848982376494288, 712301913215824060129105630235225755286314480928406867477824, 3735127854249706092898259351265589546974958671268446467746952, 19589753480870052386962970538008290044198934934742051629395740, 102762057985640523801033065466751518214841982722445151126975920, 539156922625341398039481088401567893745640656709104227105096314, 2829270373347614169637862854202320385042387180848601759635604362, 14849401467158298860096485562071208639669968558025915233767711661, 77950173574012803155197942595373205119391631456232657505924165120, 409258138212987556194464964531771603852682827154419855427292169870, 2149058161193294160068205742279850765675432256929074434239552375260, 11286731004093410526432901900786465705955740458650480468385659847100, 59286517113485666457597092584578132232802365982942868696417433448120, 311465607241696658266229088679059227440017198951922800730509725317320, 1636550212811501424105372991199914742456604920287685142205387141743560
Implicit equation for the generating function in Maple syntax:
x*(x^2-2*x+2)*F(x)^4+(2*x^2-4*x-1)*F(x)^3+(2*x+3)*F(x)^2-3*F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}-2 x +2\right) F \! \left(x \right)^{4}+\left(2 x^{2}-4 x -1\right) F \! \left(x \right)^{3}+\left(2 x +3\right) F \! \left(x \right)^{2}-3 F \! \left(x \right)+1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 89
a(6) = 380
a(7) = 1678
a(n+8) = -2/9*(4*n+5)*(2*n+3)*(4*n+3)/(n+9)/(n+7)/(n+6)*a(n)+1/27*(14276*n^3+105300*n^2+252862*n+196515)/(n+9)/(n+7)/(n+6)*a(n+1)-1/54*(88628*n^3+756114*n^2+2152783*n+2046777)/(n+9)/(n+7)/(n+6)*a(n+2)+1/108*(271825*n^3+2607174*n^2+8461187*n+9320358)/(n+9)/(n+7)/(n+6)*a(n+3)-1/108*(200183*n^3+2331978*n^2+9033313*n+11721078)/(n+9)/(n+7)/(n+6)*a(n+4)+1/27*(20005*n^3+283212*n^2+1323137*n+2050536)/(n+9)/(n+7)/(n+6)*a(n+5)-2/27*(2258*n^3+37968*n^2+210241*n+384615)/(n+9)/(n+7)/(n+6)*a(n+6)+1/9*(181*n^2+2436*n+7931)/(n+7)/(n+9)*a(n+7), n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 89
a \! \left(6\right) = 380
a \! \left(7\right) = 1678
a \! \left(n +8\right) = -\frac{2 \left(4 n +5\right) \left(2 n +3\right) \left(4 n +3\right) a \! \left(n \right)}{9 \left(n +9\right) \left(n +7\right) \left(n +6\right)}+\frac{\left(14276 n^{3}+105300 n^{2}+252862 n +196515\right) a \! \left(n +1\right)}{27 \left(n +9\right) \left(n +7\right) \left(n +6\right)}-\frac{\left(88628 n^{3}+756114 n^{2}+2152783 n +2046777\right) a \! \left(n +2\right)}{54 \left(n +9\right) \left(n +7\right) \left(n +6\right)}+\frac{\left(271825 n^{3}+2607174 n^{2}+8461187 n +9320358\right) a \! \left(n +3\right)}{108 \left(n +9\right) \left(n +7\right) \left(n +6\right)}-\frac{\left(200183 n^{3}+2331978 n^{2}+9033313 n +11721078\right) a \! \left(n +4\right)}{108 \left(n +9\right) \left(n +7\right) \left(n +6\right)}+\frac{\left(20005 n^{3}+283212 n^{2}+1323137 n +2050536\right) a \! \left(n +5\right)}{27 \left(n +9\right) \left(n +7\right) \left(n +6\right)}-\frac{2 \left(2258 n^{3}+37968 n^{2}+210241 n +384615\right) a \! \left(n +6\right)}{27 \left(n +9\right) \left(n +7\right) \left(n +6\right)}+\frac{\left(181 n^{2}+2436 n +7931\right) a \! \left(n +7\right)}{9 \left(n +7\right) \left(n +9\right)}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/27/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[24,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]*F[9,x]
F[7,x] = F[1,x]+F[10,x]+F[8,x]
F[8,x] = F[7,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]*F[9,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = (F[13,x,k[0]]*k[0]-F[13,x,1])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]+F[5,x]
F[14,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[18,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[9,x]
F[21,x,k[0]] = F[22,x,k[0]]+F[23,x,k[0]]
F[22,x,k[0]] = -k[0]*(F[14,x,1]-F[14,x,k[0]])/(-1+k[0])
F[23,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[9,x]
F[26,x] = F[220,x]+F[27,x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = F[29,x,k[0]]+F[4,x]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[17,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[215,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[195,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[28,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[35,x,k[0]]*k[0]-F[35,x,1])
F[35,x,k[0]] = F[36,x,k[0]]+F[38,x,k[0]]
F[36,x,k[0]] = F[18,x,k[0]]*F[37,x]
F[37,x] = F[6,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]*F[9,x]
F[40,x,k[0]] = F[189,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x]*F[52,x,k[0]]*F[9,x]
F[43,x] = F[44,x]+F[5,x]
F[44,x] = F[45,x,1]
F[45,x,k[0]] = F[15,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[9,x]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[15,x,k[0]]*F[43,x]
F[50,x,k[0]] = F[18,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = -k[0]*(F[45,x,1]-F[45,x,k[0]])/(-1+k[0])
F[52,x,k[0]] = F[185,x,k[0]]+F[53,x,k[0]]
F[54,x,k[0]] = F[161,x,k[0]]+F[53,x,k[0]]
F[55,x,k[0]] = F[18,x,k[0]]^2*F[17,x,k[0]]*F[54,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[18,x,k[0]]^2*F[17,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[61,x,k[0]]
F[58,x,k[0]] = F[18,x,k[0]]*F[59,x,k[0]]
F[60,x,k[0]] = F[17,x,k[0]]*F[59,x,k[0]]
F[60,x,k[0]] = F[45,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[59,x,k[0]]*F[63,x,k[0]]*F[9,x]
F[64,x,k[0]] = F[160,x]*F[63,x,k[0]]*F[9,x]
F[64,x,k[0]] = F[65,x,k[0]]
F[66,x,k[0]] = F[159,x,k[0]]+F[65,x,k[0]]
F[67,x,k[0]] = F[66,x,k[0]]+F[72,x,k[0]]
F[68,x,k[0]] = F[17,x,k[0]]*F[67,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[130,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[17,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[79,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[75,x,k[0]]
F[74,x,k[0]] = F[0,x]+F[70,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[9,x]
F[77,x,k[0]] = 1/(-1+k[0])*(F[78,x,k[0]]*k[0]-F[78,x,1])
F[78,x,k[0]] = F[66,x,k[0]]+F[73,x,k[0]]
F[79,x,k[0]] = F[149,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[130,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[17,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x]+F[97,x,k[0]]
F[84,x] = F[0,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[87,x]*F[9,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[73,x,1]
F[89,x] = F[90,x]+F[94,x]
F[90,x] = F[44,x]*F[91,x]
F[91,x] = F[1,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[9,x]*F[91,x]
F[94,x] = F[95,x,1]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[45,x,k[0]]*F[63,x,k[0]]*F[9,x]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[17,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[101,x,k[0]]
F[100,x,k[0]] = F[18,x,k[0]]*F[84,x]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[18,x,k[0]]*F[9,x]
F[104,x,k[0]] = F[103,x,k[0]]*F[129,x,k[0]]*F[9,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]+F[128,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]*F[9,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]+F[121,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]+F[112,x,k[0]]
F[111,x,k[0]] = F[110,x,k[0]]*F[17,x,k[0]]
F[111,x,k[0]] = F[70,x,k[0]]
F[112,x,k[0]] = F[0,x]*F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[18,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[15,x,k[0]]
F[115,x,k[0]] = F[116,x]+F[117,x,k[0]]+F[120,x,k[0]]
F[116,x] = 0
F[117,x,k[0]] = F[118,x,k[0]]*F[17,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[15,x,k[0]]
F[119,x,k[0]] = F[117,x,k[0]]
F[120,x,k[0]] = F[114,x,k[0]]*F[17,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]+F[124,x,k[0]]
F[122,x,k[0]] = F[109,x,k[0]]+F[123,x,k[0]]
F[123,x,k[0]] = F[113,x,k[0]]*F[2,x]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[9,x]
F[127,x,k[0]] = F[126,x,k[0]]*F[17,x,k[0]]
F[127,x,k[0]] = F[29,x,k[0]]
F[128,x,k[0]] = F[121,x,k[0]]*F[84,x]
F[129,x,k[0]] = F[113,x,k[0]]+F[121,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]+F[132,x,k[0]]
F[131,x,k[0]] = F[15,x,k[0]]*F[92,x]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[9,x]
F[134,x,k[0]] = F[135,x,k[0]]+F[139,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[92,x]
F[136,x,k[0]] = F[137,x,k[0]]+F[97,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[17,x,k[0]]*F[54,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[91,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]*F[17,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[146,x,k[0]]
F[144,x,k[0]] = F[145,x]*F[18,x,k[0]]
F[145,x] = F[22,x,1]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x]*F[63,x,k[0]]*F[9,x]
F[148,x] = F[145,x]
F[149,x,k[0]] = F[150,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]*F[17,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]+F[157,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]*F[18,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[45,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[9,x]
F[156,x,k[0]] = -k[0]*(F[153,x,1]-F[153,x,k[0]])/(-1+k[0])
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[153,x,k[0]]*F[63,x,k[0]]*F[9,x]
F[159,x,k[0]] = F[160,x]*F[18,x,k[0]]
F[160,x] = F[14,x,1]
F[161,x,k[0]] = F[162,x,k[0]]+F[172,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[18,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[9,x]
F[165,x,k[0]] = F[166,x,k[0]]+F[170,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[84,x]
F[167,x,k[0]] = F[168,x,k[0]]+F[18,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[53,x,k[0]]*F[9,x]
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[103,x,k[0]]*F[167,x,k[0]]*F[9,x]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]*F[18,x,k[0]]*F[9,x]
F[175,x,k[0]] = F[174,x,k[0]]*F[9,x]
F[175,x,k[0]] = F[176,x,k[0]]
F[177,x,k[0]] = F[163,x,k[0]]+F[176,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]*F[9,x]
F[179,x,k[0]] = F[180,x,k[0]]+F[183,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]*F[84,x]
F[182,x,k[0]] = F[18,x,k[0]]*F[181,x,k[0]]*F[9,x]
F[182,x,k[0]] = F[168,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[103,x,k[0]]*F[181,x,k[0]]*F[9,x]
F[186,x,k[0]] = F[185,x,k[0]]+F[188,x,k[0]]
F[187,x,k[0]] = F[186,x,k[0]]*F[9,x]
F[187,x,k[0]] = F[38,x,k[0]]
F[188,x,k[0]] = F[37,x]*F[52,x,k[0]]
F[190,x,k[0]] = F[189,x,k[0]]+F[193,x,k[0]]
F[191,x,k[0]] = F[17,x,k[0]]*F[190,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]
F[181,x,k[0]] = F[192,x,k[0]]+F[43,x]
F[193,x,k[0]] = F[194,x,k[0]]+F[41,x,k[0]]
F[194,x,k[0]] = F[18,x,k[0]]*F[43,x]
F[196,x,k[0]] = F[195,x,k[0]]+F[205,x,k[0]]
F[197,x,k[0]] = F[196,x,k[0]]*F[9,x]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[17,x,k[0]]*F[199,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[202,x,k[0]]
F[200,x,k[0]] = F[18,x,k[0]]*F[201,x,k[0]]
F[201,x,k[0]] = F[37,x]+F[46,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[95,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]
F[204,x,k[0]] = F[5,x]*F[63,x,k[0]]*F[9,x]
F[205,x,k[0]] = F[15,x,k[0]]*F[206,x,k[0]]
F[207,x,k[0]] = F[18,x,k[0]]*F[206,x,k[0]]*F[9,x]
F[207,x,k[0]] = F[208,x,k[0]]
F[208,x,k[0]] = F[201,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[17,x,k[0]]*F[211,x,k[0]]
F[211,x,k[0]] = F[200,x,k[0]]+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[52,x,k[0]]*F[9,x]
F[214,x,k[0]] = F[45,x,k[0]]+F[5,x]
F[215,x,k[0]] = F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]*F[9,x]
F[218,x,k[0]] = F[17,x,k[0]]*F[217,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = -k[0]*(F[29,x,1]-F[29,x,k[0]])/(-1+k[0])
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[9,x]
F[222,x] = F[190,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{24}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = -\frac{y \left(F_{14}\! \left(x , 1\right)-F_{14}\! \left(x , y\right)\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{220}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{35}\! \left(x , y\right)+F_{35}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{6}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{52}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{45}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{50}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{y \left(F_{45}\! \left(x , 1\right)-F_{45}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{18}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{18}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{160}\! \left(x \right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{70}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{77}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{78}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{130}\! \left(x , y\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_{17}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{84}\! \left(x \right) = F_{0}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right) F_{9}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{73}\! \left(x , 1\right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{94}\! \left(x \right)
F_{90}\! \left(x \right) = F_{44}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{9}\! \left(x \right) F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x , 1\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{101}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{84}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{129}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{116}\! \left(x \right) = 0
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{84}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{92}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{92}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{91}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{145}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x \right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{148}\! \left(x \right) = F_{145}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{156}\! \left(x , y\right) = -\frac{y \left(F_{153}\! \left(x , 1\right)-F_{153}\! \left(x , y\right)\right)}{-1+y}
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{160}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{84}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{167}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{174}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right) F_{84}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{181}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{181}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{37}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{190}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{43}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{196}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{37}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{206}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{206}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{200}\! \left(x , y\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_{52}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{218}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{217}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = -\frac{y \left(F_{29}\! \left(x , 1\right)-F_{29}\! \left(x , y\right)\right)}{-1+y}
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{9}\! \left(x \right)
F_{222}\! \left(x \right) = F_{190}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_9(x))
Eq(F_4(x), F_24(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x)*F_9(x))
Eq(F_7(x), F_1(x) + F_10(x) + F_8(x))
Eq(F_8(x), F_7(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x)*F_9(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_5(x))
Eq(F_14(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_18(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_9(x))
Eq(F_21(x, k_0), F_22(x, k_0) + F_23(x, k_0))
Eq(F_22(x, k_0), -F_14(x, 1) + (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_9(x))
Eq(F_26(x), F_220(x) + F_27(x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), F_29(x, k_0) + F_4(x))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_17(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_215(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_195(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_28(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_38(x, k_0))
Eq(F_36(x, k_0), F_18(x, k_0)*F_37(x))
Eq(F_37(x), F_6(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0)*F_9(x))
Eq(F_40(x, k_0), F_189(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x)*F_52(x, k_0)*F_9(x))
Eq(F_43(x), F_44(x) + F_5(x))
Eq(F_44(x), F_45(x, 1))
Eq(F_45(x, k_0), F_15(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_9(x))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_15(x, k_0)*F_43(x))
Eq(F_50(x, k_0), F_18(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), -F_45(x, 1) + (k_0*F_45(x, k_0) - F_45(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_185(x, k_0) + F_53(x, k_0))
Eq(F_54(x, k_0), F_161(x, k_0) + F_53(x, k_0))
Eq(F_55(x, k_0), F_17(x, k_0)*F_18(x, k_0)**2*F_54(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_17(x, k_0)*F_18(x, k_0)**2*F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_61(x, k_0))
Eq(F_58(x, k_0), F_18(x, k_0)*F_59(x, k_0))
Eq(F_60(x, k_0), F_17(x, k_0)*F_59(x, k_0))
Eq(F_60(x, k_0), F_45(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_59(x, k_0)*F_63(x, k_0)*F_9(x))
Eq(F_64(x, k_0), F_160(x)*F_63(x, k_0)*F_9(x))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_66(x, k_0), F_159(x, k_0) + F_65(x, k_0))
Eq(F_67(x, k_0), F_66(x, k_0) + F_72(x, k_0))
Eq(F_68(x, k_0), F_17(x, k_0)*F_67(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_130(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_17(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_79(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_75(x, k_0))
Eq(F_74(x, k_0), F_0(x) + F_70(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_9(x))
Eq(F_77(x, k_0), (k_0*F_78(x, k_0) - F_78(x, 1))/(k_0 - 1))
Eq(F_78(x, k_0), F_66(x, k_0) + F_73(x, k_0))
Eq(F_79(x, k_0), F_149(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_130(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_17(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x) + F_97(x, k_0))
Eq(F_84(x), F_0(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_87(x)*F_9(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_73(x, 1))
Eq(F_89(x), F_90(x) + F_94(x))
Eq(F_90(x), F_44(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_9(x)*F_91(x))
Eq(F_94(x), F_95(x, 1))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_45(x, k_0)*F_63(x, k_0)*F_9(x))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_17(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_101(x, k_0))
Eq(F_100(x, k_0), F_18(x, k_0)*F_84(x))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_18(x, k_0)*F_9(x))
Eq(F_104(x, k_0), F_103(x, k_0)*F_129(x, k_0)*F_9(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0) + F_128(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0)*F_9(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0) + F_121(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0) + F_112(x, k_0))
Eq(F_111(x, k_0), F_110(x, k_0)*F_17(x, k_0))
Eq(F_111(x, k_0), F_70(x, k_0))
Eq(F_112(x, k_0), F_0(x)*F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_18(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_15(x, k_0))
Eq(F_115(x, k_0), F_116(x) + F_117(x, k_0) + F_120(x, k_0))
Eq(F_116(x), 0)
Eq(F_117(x, k_0), F_118(x, k_0)*F_17(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_15(x, k_0))
Eq(F_119(x, k_0), F_117(x, k_0))
Eq(F_120(x, k_0), F_114(x, k_0)*F_17(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0) + F_124(x, k_0))
Eq(F_122(x, k_0), F_109(x, k_0) + F_123(x, k_0))
Eq(F_123(x, k_0), F_113(x, k_0)*F_2(x))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_9(x))
Eq(F_127(x, k_0), F_126(x, k_0)*F_17(x, k_0))
Eq(F_127(x, k_0), F_29(x, k_0))
Eq(F_128(x, k_0), F_121(x, k_0)*F_84(x))
Eq(F_129(x, k_0), F_113(x, k_0) + F_121(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_132(x, k_0))
Eq(F_131(x, k_0), F_15(x, k_0)*F_92(x))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_9(x))
Eq(F_134(x, k_0), F_135(x, k_0) + F_139(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_92(x))
Eq(F_136(x, k_0), F_137(x, k_0) + F_97(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_17(x, k_0)*F_54(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_91(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0)*F_17(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_146(x, k_0))
Eq(F_144(x, k_0), F_145(x)*F_18(x, k_0))
Eq(F_145(x), F_22(x, 1))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x)*F_63(x, k_0)*F_9(x))
Eq(F_148(x), F_145(x))
Eq(F_149(x, k_0), F_150(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_17(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0) + F_157(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_18(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_45(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_9(x))
Eq(F_156(x, k_0), -F_153(x, 1) + (k_0*F_153(x, k_0) - F_153(x, 1))/(k_0 - 1))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_153(x, k_0)*F_63(x, k_0)*F_9(x))
Eq(F_159(x, k_0), F_160(x)*F_18(x, k_0))
Eq(F_160(x), F_14(x, 1))
Eq(F_161(x, k_0), F_162(x, k_0) + F_172(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_18(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_9(x))
Eq(F_165(x, k_0), F_166(x, k_0) + F_170(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_84(x))
Eq(F_167(x, k_0), F_168(x, k_0) + F_18(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_53(x, k_0)*F_9(x))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_103(x, k_0)*F_167(x, k_0)*F_9(x))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0)*F_18(x, k_0)*F_9(x))
Eq(F_175(x, k_0), F_174(x, k_0)*F_9(x))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_177(x, k_0), F_163(x, k_0) + F_176(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0)*F_9(x))
Eq(F_179(x, k_0), F_180(x, k_0) + F_183(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0)*F_84(x))
Eq(F_182(x, k_0), F_18(x, k_0)*F_181(x, k_0)*F_9(x))
Eq(F_182(x, k_0), F_168(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_103(x, k_0)*F_181(x, k_0)*F_9(x))
Eq(F_186(x, k_0), F_185(x, k_0) + F_188(x, k_0))
Eq(F_187(x, k_0), F_186(x, k_0)*F_9(x))
Eq(F_187(x, k_0), F_38(x, k_0))
Eq(F_188(x, k_0), F_37(x)*F_52(x, k_0))
Eq(F_190(x, k_0), F_189(x, k_0) + F_193(x, k_0))
Eq(F_191(x, k_0), F_17(x, k_0)*F_190(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0))
Eq(F_181(x, k_0), F_192(x, k_0) + F_43(x))
Eq(F_193(x, k_0), F_194(x, k_0) + F_41(x, k_0))
Eq(F_194(x, k_0), F_18(x, k_0)*F_43(x))
Eq(F_196(x, k_0), F_195(x, k_0) + F_205(x, k_0))
Eq(F_197(x, k_0), F_196(x, k_0)*F_9(x))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_17(x, k_0)*F_199(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_202(x, k_0))
Eq(F_200(x, k_0), F_18(x, k_0)*F_201(x, k_0))
Eq(F_201(x, k_0), F_37(x) + F_46(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_95(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0))
Eq(F_204(x, k_0), F_5(x)*F_63(x, k_0)*F_9(x))
Eq(F_205(x, k_0), F_15(x, k_0)*F_206(x, k_0))
Eq(F_207(x, k_0), F_18(x, k_0)*F_206(x, k_0)*F_9(x))
Eq(F_207(x, k_0), F_208(x, k_0))
Eq(F_208(x, k_0), F_201(x, k_0) + F_209(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_17(x, k_0)*F_211(x, k_0))
Eq(F_211(x, k_0), F_200(x, k_0) + 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_52(x, k_0)*F_9(x))
Eq(F_214(x, k_0), F_45(x, k_0) + F_5(x))
Eq(F_215(x, k_0), F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0)*F_9(x))
Eq(F_218(x, k_0), F_17(x, k_0)*F_217(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), -F_29(x, 1) + (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_9(x))
Eq(F_222(x), F_190(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[2, 3], [4, 3]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[4, 3], [4, 3]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [4, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [4, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [4, 3], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [4, 3], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 3], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/28/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[11,x]
F[18,x] = F[14,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x,1]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[24,x]+F[25,x,k[0]]+F[41,x,k[0]]
F[24,x] = 0
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = -k[0]*(F[27,x,1]-F[27,x,k[0]])/(-1+k[0])
F[27,x,k[0]] = F[23,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[31,x,k[0]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[30,x,k[0]]*F[32,x,k[0]]
F[35,x,k[0]] = F[28,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[30,x,k[0]]*F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = F[33,x,k[0]]
F[40,x,k[0]] = F[36,x,k[0]]
F[41,x,k[0]] = F[30,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[141,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[2,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[140,x,k[0]]+F[24,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[68,x,k[0]]
F[47,x,k[0]] = F[33,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[24,x]+F[49,x,k[0]]+F[66,x,k[0]]
F[49,x,k[0]] = F[4,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[55,x,k[0]]
F[51,x,k[0]] = F[33,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[30,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[11,x]+F[52,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[61,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[4,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[60,x,k[0]]
F[59,x,k[0]] = F[33,x,k[0]]
F[60,x,k[0]] = F[56,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[65,x,k[0]]
F[64,x,k[0]] = F[52,x,k[0]]
F[65,x,k[0]] = F[61,x,k[0]]
F[66,x,k[0]] = F[30,x,k[0]]*F[67,x,k[0]]
F[67,x,k[0]] = F[48,x,k[0]]+F[7,x]
F[68,x,k[0]] = F[44,x,k[0]]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,1,k[0]]
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[138,x,k[1],k[0]]+F[24,x]+F[73,x,k[0],k[1]]+F[96,x,k[0],k[1]]
F[73,x,k[0],k[1]] = -k[0]*(F[74,x,1,k[1]]-F[74,x,k[0],k[1]])/(-1+k[0])
F[74,x,k[0],k[1]] = F[4,x]*F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = F[72,x,k[0],k[1]]+F[76,x,k[0],k[1]]
F[76,x,k[0],k[1]] = F[24,x]+F[77,x,k[0],k[1]]+F[94,x,k[1],k[0]]
F[77,x,k[0],k[1]] = F[30,x,k[0]]*F[78,x,k[0],k[1]]
F[78,x,k[0],k[1]] = F[79,x,k[0],k[1]]+F[83,x,k[0],k[1]]
F[79,x,k[0],k[1]] = F[33,x,k[1]]+F[80,x,k[0],k[1]]
F[80,x,k[0],k[1]] = F[81,x,k[1],k[0]]
F[81,x,k[0],k[1]] = F[30,x,k[0]]*F[82,x,k[1],k[0]]
F[82,x,k[0],k[1]] = F[33,x,k[0]]+F[80,x,k[0],k[1]]
F[83,x,k[0],k[1]] = F[84,x,k[0],k[1]]+F[89,x,k[0],k[1]]
F[84,x,k[0],k[1]] = F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[30,x,k[0]]*F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = F[87,x,k[0],k[1]]+F[88,x,k[0],k[1]]
F[87,x,k[0],k[1]] = F[33,x,k[1]]
F[88,x,k[0],k[1]] = F[84,x,k[0],k[1]]
F[89,x,k[0],k[1]] = F[90,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[30,x,k[0]]*F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[92,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[92,x,k[0],k[1]] = F[80,x,k[0],k[1]]
F[93,x,k[0],k[1]] = F[89,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[30,x,k[0]]*F[95,x,k[1],k[0]]
F[95,x,k[0],k[1]] = F[28,x,k[0]]+F[76,x,k[0],k[1]]
F[96,x,k[0],k[1]] = k[1]*(F[97,x,k[0],1]-F[97,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[97,x,k[0],k[1]] = F[98,x,k[0],k[0]*k[1]]
F[99,x,k[0],k[1]] = F[98,x,k[0]*k[1],k[1]]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]*F[30,x,k[1]]
F[100,x,k[0],k[1]] = F[101,x,k[0],k[1]]+F[44,x,k[1]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[0],k[1]]*F[30,x,k[1]]
F[103,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[104,x,k[0],k[1]]
F[104,x,k[0],k[1]] = F[105,x,k[0]*k[1],k[1]]
F[106,x,k[0],k[1]] = F[105,x,k[0],k[0]*k[1]]
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]+F[109,x,k[0],k[1]]
F[107,x,k[0],k[1]] = F[108,x,k[0],k[1]]
F[108,x,k[0],k[1]] = F[11,x]*F[32,x,k[0]]*F[33,x,k[1]]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[0]*k[1]]
F[111,x,k[0],k[1]] = F[110,x,k[0]*k[1],k[1]]
F[111,x,k[0],k[1]] = F[112,x,k[1]]+F[122,x,k[0],k[1]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[4,x]
F[114,x,k[0]] = F[115,x,k[0]]+F[118,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[56,x,k[0]]
F[116,x,k[0]] = F[117,x,1,k[0]]
F[100,x,k[0],k[1]] = F[117,x,k[0]*k[1],k[1]]
F[118,x,k[0]] = F[119,x,k[0]]+F[121,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[11,x]^2*F[33,x,k[0]]
F[121,x,k[0]] = F[109,x,1,k[0]]
F[122,x,k[0],k[1]] = F[123,x,k[0]*k[1],k[1]]
F[123,x,k[0],k[1]] = F[124,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[125,x,k[0],k[1]]*F[4,x]
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]+F[134,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[127,x,k[0],k[1]]+F[132,x,k[0],k[1]]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]
F[128,x,k[0],k[1]] = F[129,x,k[0],k[1]]*F[30,x,k[0]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]+F[131,x,k[0],k[1]]
F[130,x,k[0],k[1]] = F[56,x,k[1]]
F[131,x,k[0],k[1]] = F[127,x,k[0],k[1]]
F[132,x,k[0],k[1]] = -k[0]*(F[133,x,1,k[1]]-F[133,x,k[0],k[1]])/(-1+k[0])
F[101,x,k[0],k[1]] = F[133,x,k[0]*k[1],k[1]]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]+F[137,x,k[0],k[1]]
F[135,x,k[0],k[1]] = F[136,x,k[0],k[1]]
F[136,x,k[0],k[1]] = F[11,x]^2*F[33,x,k[0]]*F[33,x,k[1]]
F[137,x,k[0],k[1]] = -k[0]*(F[123,x,1,k[1]]-F[123,x,k[0],k[1]])/(-1+k[0])
F[138,x,k[0],k[1]] = F[139,x,k[1],k[0]]*F[30,x,k[0]]
F[139,x,k[0],k[1]] = F[23,x,k[0]]+F[72,x,k[0],k[1]]
F[140,x,k[0]] = F[30,x,k[0]]*F[43,x,k[0]]
F[141,x,k[0]] = F[142,x,1,k[0]]
F[142,x,k[0],k[1]] = F[143,x,k[0]*k[1],k[1]]
F[143,x,k[0],k[1]] = F[133,x,k[0],k[1]]+F[23,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{y \left(F_{27}\! \left(x , 1\right)-F_{27}\! \left(x , y\right)\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{24}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , 1, y\right)
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right)
F_{72}\! \left(x , y , z\right) = F_{138}\! \left(x , z , y\right)+F_{24}\! \left(x \right)+F_{73}\! \left(x , y , z\right)+F_{96}\! \left(x , y , z\right)
F_{73}\! \left(x , y , z\right) = -\frac{y \left(F_{74}\! \left(x , 1, z\right)-F_{74}\! \left(x , y , z\right)\right)}{-1+y}
F_{74}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{75}\! \left(x , y , z\right)
F_{75}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right)+F_{76}\! \left(x , y , z\right)
F_{76}\! \left(x , y , z\right) = F_{24}\! \left(x \right)+F_{77}\! \left(x , y , z\right)+F_{94}\! \left(x , z , y\right)
F_{77}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right) F_{78}\! \left(x , y , z\right)
F_{78}\! \left(x , y , z\right) = F_{79}\! \left(x , y , z\right)+F_{83}\! \left(x , y , z\right)
F_{79}\! \left(x , y , z\right) = F_{33}\! \left(x , z\right)+F_{80}\! \left(x , y , z\right)
F_{80}\! \left(x , y , z\right) = F_{81}\! \left(x , z , y\right)
F_{81}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right) F_{82}\! \left(x , z , y\right)
F_{82}\! \left(x , y , z\right) = F_{33}\! \left(x , y\right)+F_{80}\! \left(x , y , z\right)
F_{83}\! \left(x , y , z\right) = F_{84}\! \left(x , y , z\right)+F_{89}\! \left(x , y , z\right)
F_{84}\! \left(x , y , z\right) = F_{85}\! \left(x , y , z\right)
F_{85}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right) F_{86}\! \left(x , y , z\right)
F_{86}\! \left(x , y , z\right) = F_{87}\! \left(x , y , z\right)+F_{88}\! \left(x , y , z\right)
F_{87}\! \left(x , y , z\right) = F_{33}\! \left(x , z\right)
F_{88}\! \left(x , y , z\right) = F_{84}\! \left(x , y , z\right)
F_{89}\! \left(x , y , z\right) = F_{90}\! \left(x , y , z\right)
F_{90}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right) F_{91}\! \left(x , y , z\right)
F_{91}\! \left(x , y , z\right) = F_{92}\! \left(x , y , z\right)+F_{93}\! \left(x , y , z\right)
F_{92}\! \left(x , y , z\right) = F_{80}\! \left(x , y , z\right)
F_{93}\! \left(x , y , z\right) = F_{89}\! \left(x , y , z\right)
F_{94}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right) F_{95}\! \left(x , z , y\right)
F_{95}\! \left(x , y , z\right) = F_{28}\! \left(x , y\right)+F_{76}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = \frac{z \left(F_{97}\! \left(x , y , 1\right)-F_{97}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{97}\! \left(x , y , z\right) = F_{98}\! \left(x , y , y z \right)
F_{99}\! \left(x , y , z\right) = F_{98}\! \left(x , y z , z\right)
F_{99}\! \left(x , y , z\right) = F_{100}\! \left(x , y , z\right) F_{30}\! \left(x , z\right)
F_{100}\! \left(x , y , z\right) = F_{101}\! \left(x , y , z\right)+F_{44}\! \left(x , z\right)
F_{101}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)
F_{102}\! \left(x , y , z\right) = F_{103}\! \left(x , y , z\right) F_{30}\! \left(x , z\right)
F_{103}\! \left(x , y , z\right) = F_{100}\! \left(x , y , z\right)+F_{104}\! \left(x , y , z\right)
F_{104}\! \left(x , y , z\right) = F_{105}\! \left(x , y z , z\right)
F_{106}\! \left(x , y , z\right) = F_{105}\! \left(x , y , y z \right)
F_{106}\! \left(x , y , z\right) = F_{107}\! \left(x , y , z\right)+F_{109}\! \left(x , y , z\right)
F_{107}\! \left(x , y , z\right) = F_{108}\! \left(x , y , z\right)
F_{108}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{32}\! \left(x , y\right) F_{33}\! \left(x , z\right)
F_{109}\! \left(x , y , z\right) = F_{110}\! \left(x , y , y z \right)
F_{111}\! \left(x , y , z\right) = F_{110}\! \left(x , y z , z\right)
F_{111}\! \left(x , y , z\right) = F_{112}\! \left(x , z\right)+F_{122}\! \left(x , y , z\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , 1, y\right)
F_{100}\! \left(x , y , z\right) = F_{117}\! \left(x , y z , z\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{11} \left(x \right)^{2} F_{33}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{109}\! \left(x , 1, y\right)
F_{122}\! \left(x , y , z\right) = F_{123}\! \left(x , y z , z\right)
F_{123}\! \left(x , y , z\right) = F_{124}\! \left(x , y , z\right)
F_{124}\! \left(x , y , z\right) = F_{125}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{125}\! \left(x , y , z\right) = F_{126}\! \left(x , y , z\right)+F_{134}\! \left(x , y , z\right)
F_{126}\! \left(x , y , z\right) = F_{127}\! \left(x , y , z\right)+F_{132}\! \left(x , y , z\right)
F_{127}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right)
F_{128}\! \left(x , y , z\right) = F_{129}\! \left(x , y , z\right) F_{30}\! \left(x , y\right)
F_{129}\! \left(x , y , z\right) = F_{130}\! \left(x , y , z\right)+F_{131}\! \left(x , y , z\right)
F_{130}\! \left(x , y , z\right) = F_{56}\! \left(x , z\right)
F_{131}\! \left(x , y , z\right) = F_{127}\! \left(x , y , z\right)
F_{132}\! \left(x , y , z\right) = -\frac{y \left(F_{133}\! \left(x , 1, z\right)-F_{133}\! \left(x , y , z\right)\right)}{-1+y}
F_{101}\! \left(x , y , z\right) = F_{133}\! \left(x , y z , z\right)
F_{134}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right)+F_{137}\! \left(x , y , z\right)
F_{135}\! \left(x , y , z\right) = F_{136}\! \left(x , y , z\right)
F_{136}\! \left(x , y , z\right) = F_{11} \left(x \right)^{2} F_{33}\! \left(x , y\right) F_{33}\! \left(x , z\right)
F_{137}\! \left(x , y , z\right) = -\frac{y \left(F_{123}\! \left(x , 1, z\right)-F_{123}\! \left(x , y , z\right)\right)}{-1+y}
F_{138}\! \left(x , y , z\right) = F_{139}\! \left(x , z , y\right) F_{30}\! \left(x , y\right)
F_{139}\! \left(x , y , z\right) = F_{23}\! \left(x , y\right)+F_{72}\! \left(x , y , z\right)
F_{140}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , 1, y\right)
F_{142}\! \left(x , y , z\right) = F_{143}\! \left(x , y z , z\right)
F_{143}\! \left(x , y , z\right) = F_{133}\! \left(x , y , z\right)+F_{23}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_11(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x, 1))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x) + F_25(x, k_0) + F_41(x, k_0))
Eq(F_24(x), 0)
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), -F_27(x, 1) + (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_27(x, k_0), F_23(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_31(x, k_0))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0), F_32(x, k_0) + F_35(x, k_0))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_30(x, k_0)*F_32(x, k_0))
Eq(F_35(x, k_0), F_28(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_30(x, k_0)*F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), F_33(x, k_0))
Eq(F_40(x, k_0), F_36(x, k_0))
Eq(F_41(x, k_0), F_30(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_141(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_2(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_140(x, k_0) + F_24(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_68(x, k_0))
Eq(F_47(x, k_0), F_33(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_24(x) + F_49(x, k_0) + F_66(x, k_0))
Eq(F_49(x, k_0), F_4(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_55(x, k_0))
Eq(F_51(x, k_0), F_33(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_30(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_11(x) + F_52(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_61(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_4(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_60(x, k_0))
Eq(F_59(x, k_0), F_33(x, k_0))
Eq(F_60(x, k_0), F_56(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_65(x, k_0))
Eq(F_64(x, k_0), F_52(x, k_0))
Eq(F_65(x, k_0), F_61(x, k_0))
Eq(F_66(x, k_0), F_30(x, k_0)*F_67(x, k_0))
Eq(F_67(x, k_0), F_48(x, k_0) + F_7(x))
Eq(F_68(x, k_0), F_44(x, k_0) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, 1, k_0))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_138(x, k_1, k_0) + F_24(x) + F_73(x, k_0, k_1) + F_96(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), -F_74(x, 1, k_1) + (k_0*F_74(x, k_0, k_1) - F_74(x, 1, k_1))/(k_0 - 1))
Eq(F_74(x, k_0, k_1), F_4(x)*F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), F_72(x, k_0, k_1) + F_76(x, k_0, k_1))
Eq(F_76(x, k_0, k_1), F_24(x) + F_77(x, k_0, k_1) + F_94(x, k_1, k_0))
Eq(F_77(x, k_0, k_1), F_30(x, k_0)*F_78(x, k_0, k_1))
Eq(F_78(x, k_0, k_1), F_79(x, k_0, k_1) + F_83(x, k_0, k_1))
Eq(F_79(x, k_0, k_1), F_33(x, k_1) + F_80(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), F_81(x, k_1, k_0))
Eq(F_81(x, k_0, k_1), F_30(x, k_0)*F_82(x, k_1, k_0))
Eq(F_82(x, k_0, k_1), F_33(x, k_0) + F_80(x, k_0, k_1))
Eq(F_83(x, k_0, k_1), F_84(x, k_0, k_1) + F_89(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_30(x, k_0)*F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), F_87(x, k_0, k_1) + F_88(x, k_0, k_1))
Eq(F_87(x, k_0, k_1), F_33(x, k_1))
Eq(F_88(x, k_0, k_1), F_84(x, k_0, k_1))
Eq(F_89(x, k_0, k_1), F_90(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_30(x, k_0)*F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_92(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_92(x, k_0, k_1), F_80(x, k_0, k_1))
Eq(F_93(x, k_0, k_1), F_89(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_30(x, k_0)*F_95(x, k_1, k_0))
Eq(F_95(x, k_0, k_1), F_28(x, k_0) + F_76(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), -F_97(x, k_0, 1) + (-k_0*F_97(x, k_0, 1) + k_1*F_97(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_97(x, k_0, k_1), F_98(x, k_0, k_0*k_1))
Eq(F_99(x, k_0, k_1), F_98(x, k_0*k_1, k_1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1)*F_30(x, k_1))
Eq(F_100(x, k_0, k_1), F_101(x, k_0, k_1) + F_44(x, k_1))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_0, k_1)*F_30(x, k_1))
Eq(F_103(x, k_0, k_1), F_100(x, k_0, k_1) + F_104(x, k_0, k_1))
Eq(F_104(x, k_0, k_1), F_105(x, k_0*k_1, k_1))
Eq(F_106(x, k_0, k_1), F_105(x, k_0, k_0*k_1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1) + F_109(x, k_0, k_1))
Eq(F_107(x, k_0, k_1), F_108(x, k_0, k_1))
Eq(F_108(x, k_0, k_1), F_11(x)*F_32(x, k_0)*F_33(x, k_1))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_0*k_1))
Eq(F_111(x, k_0, k_1), F_110(x, k_0*k_1, k_1))
Eq(F_111(x, k_0, k_1), F_112(x, k_1) + F_122(x, k_0, k_1))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_4(x))
Eq(F_114(x, k_0), F_115(x, k_0) + F_118(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_56(x, k_0))
Eq(F_116(x, k_0), F_117(x, 1, k_0))
Eq(F_100(x, k_0, k_1), F_117(x, k_0*k_1, k_1))
Eq(F_118(x, k_0), F_119(x, k_0) + F_121(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_11(x)**2*F_33(x, k_0))
Eq(F_121(x, k_0), F_109(x, 1, k_0))
Eq(F_122(x, k_0, k_1), F_123(x, k_0*k_1, k_1))
Eq(F_123(x, k_0, k_1), F_124(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_125(x, k_0, k_1)*F_4(x))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1) + F_134(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_127(x, k_0, k_1) + F_132(x, k_0, k_1))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1))
Eq(F_128(x, k_0, k_1), F_129(x, k_0, k_1)*F_30(x, k_0))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1) + F_131(x, k_0, k_1))
Eq(F_130(x, k_0, k_1), F_56(x, k_1))
Eq(F_131(x, k_0, k_1), F_127(x, k_0, k_1))
Eq(F_132(x, k_0, k_1), -F_133(x, 1, k_1) + (k_0*F_133(x, k_0, k_1) - F_133(x, 1, k_1))/(k_0 - 1))
Eq(F_101(x, k_0, k_1), F_133(x, k_0*k_1, k_1))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1) + F_137(x, k_0, k_1))
Eq(F_135(x, k_0, k_1), F_136(x, k_0, k_1))
Eq(F_136(x, k_0, k_1), F_11(x)**2*F_33(x, k_0)*F_33(x, k_1))
Eq(F_137(x, k_0, k_1), -F_123(x, 1, k_1) + (k_0*F_123(x, k_0, k_1) - F_123(x, 1, k_1))/(k_0 - 1))
Eq(F_138(x, k_0, k_1), F_139(x, k_1, k_0)*F_30(x, k_0))
Eq(F_139(x, k_0, k_1), F_23(x, k_0) + F_72(x, k_0, k_1))
Eq(F_140(x, k_0), F_30(x, k_0)*F_43(x, k_0))
Eq(F_141(x, k_0), F_142(x, 1, k_0))
Eq(F_142(x, k_0, k_1), F_143(x, k_0*k_1, k_1))
Eq(F_143(x, k_0, k_1), F_133(x, k_0, k_1) + F_23(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": 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"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 3
Strategy pack name: row_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/29/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[9,x,k[0],1]
F[9,x,k[0],k[1]] = F[10,x,1,k[0],k[1]]
F[10,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1],k[2]]*F[24,x,k[1]]
F[11,x,k[0],k[1],k[2]] = F[1,x]+F[10,x,k[0],k[1],k[2]]+F[12,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0],k[1],k[2]]*F[7,x]
F[13,x,k[0],k[1],k[2]] = F[14,x,k[0]*k[1],k[1]*k[2]]
F[15,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[15,x,k[0],k[1]] = F[16,x,1,k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[1]*k[2]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1],k[2]]+F[28,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[7,x]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[24,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[11,x,1,k[0],k[1]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0],k[1],k[2]] = F[24,x,k[1]]*F[26,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[1]*k[2]]
F[27,x,k[0],k[1],k[2]] = (-F[11,x,1,k[1],k[2]]*k[1]+F[11,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[28,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = (F[30,x,k[0],k[2]]*k[0]-F[30,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[31,x,k[0],1,k[1]]
F[31,x,k[0],k[1],k[2]] = (F[32,x,k[0]*k[1]]*k[0]-F[32,x,k[1]*k[2]]*k[2])/(k[0]-k[2])
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[41,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[7,x]
F[34,x,k[0]] = F[35,x,1,k[0]]
F[35,x,k[0],k[1]] = F[1,x]+F[36,x,k[0],k[1]]+F[38,x,k[0],k[1]]+F[39,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[1]]*F[7,x]
F[37,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[38,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[24,x,k[0]]
F[39,x,k[0],k[1]] = F[40,x,k[0],1,k[1]]
F[40,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[31,x,k[0],k[1],k[2]]
F[41,x,k[0]] = F[24,x,k[0]]*F[32,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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{9}\! \left(x , y_{0}, 1\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , 1, y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , 1, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{22}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{22}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{23}\! \left(x , y_{0}, 1\right)-y_{1} F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , 1, y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{11}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{11}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{30}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{30}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, 1, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{32}\! \left(x , y_{0} y_{1}\right) y_{0}-y_{2} F_{32}\! \left(x , y_{1} y_{2}\right)}{y_{0}-y_{2}}
F_{32}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , 1, y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{35}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{40}\! \left(x , y_{0}, 1, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_9(x, k_0, 1))
Eq(F_9(x, k_0, k_1), F_10(x, 1, k_0, k_1))
Eq(F_10(x, k_0, k_1, k_2), F_11(x, k_0, k_1, k_2)*F_24(x, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_1(x) + F_10(x, k_0, k_1, k_2) + F_12(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0, k_1, k_2)*F_7(x))
Eq(F_13(x, k_0, k_1, k_2), F_14(x, k_0*k_1, k_1*k_2))
Eq(F_15(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_15(x, k_0, k_1), F_16(x, 1, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_1*k_2))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_25(x, k_0, k_1, k_2) + F_28(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_7(x))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_24(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_11(x, 1, k_0, k_1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0, k_1, k_2), F_24(x, k_1)*F_26(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_1*k_2))
Eq(F_27(x, k_0, k_1, k_2), (-k_0*F_11(x, k_0/k_1, k_1, k_2) + k_1*F_11(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_28(x, k_0, k_1, k_2), F_24(x, k_2)*F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), (-k_0*F_30(x, k_0, k_2) + k_1*F_30(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, 1, k_1))
Eq(F_31(x, k_0, k_1, k_2), (-k_0*k_1*F_32(x, k_0*k_1) + k_1*k_2*F_32(x, k_1*k_2))/(-k_0*k_1 + k_1*k_2))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_41(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_7(x))
Eq(F_34(x, k_0), F_35(x, 1, k_0))
Eq(F_35(x, k_0, k_1), F_1(x) + F_36(x, k_0, k_1) + F_38(x, k_0, k_1) + F_39(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_1)*F_7(x))
Eq(F_37(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_38(x, k_0, k_1), F_22(x, k_0, k_1)*F_24(x, k_0))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, 1, k_1))
Eq(F_40(x, k_0, k_1, k_2), F_24(x, k_2)*F_31(x, k_0, k_1, k_2))
Eq(F_41(x, k_0), F_24(x, k_0)*F_32(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"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, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"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]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 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]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], 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{"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]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"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], [1, 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], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"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], [1, 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], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/30/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[21,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]*F[9,x]
F[7,x] = F[1,x]+F[10,x]+F[8,x]
F[8,x] = F[7,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]*F[9,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = (F[13,x,k[0]]*k[0]-F[13,x,1])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]+F[5,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[9,x]
F[20,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[9,x]
F[23,x] = F[24,x]+F[269,x]
F[24,x] = F[25,x,1]
F[25,x,k[0]] = F[26,x,k[0]]+F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[16,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[255,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[214,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[25,x,k[0]]+F[31,x,k[0]]
F[31,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[9,x]
F[35,x,k[0]] = F[16,x,k[0]]*F[34,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[37,x,k[0]] = F[212,x]+F[36,x,k[0]]
F[38,x,k[0]] = F[206,x,k[0]]+F[37,x,k[0]]
F[38,x,k[0]] = F[141,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]+F[44,x,k[0]]
F[40,x,k[0]] = F[0,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[1,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[16,x,k[0]]*F[41,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[41,x,k[0]]*F[46,x,k[0]]*F[9,x]
F[46,x,k[0]] = F[123,x,k[0]]+F[47,x]
F[47,x] = F[118,x]+F[48,x]
F[48,x] = F[49,x,1]
F[49,x,k[0]] = F[50,x,k[0]]+F[66,x,k[0]]
F[50,x,k[0]] = F[0,x]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[61,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[16,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[41,x,k[0]]+F[55,x,k[0]]
F[55,x,k[0]] = F[52,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[16,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[60,x,k[0]]
F[59,x,k[0]] = F[42,x,k[0]]
F[60,x,k[0]] = F[56,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[16,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[96,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[2,x]+F[61,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[9,x]
F[68,x,k[0]] = 1/(-1+k[0])*(F[69,x,k[0]]*k[0]-F[69,x,1])
F[69,x,k[0]] = F[49,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[75,x,k[0]]
F[71,x,k[0]] = F[41,x,k[0]]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]*F[9,x]
F[74,x] = F[17,x,1]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[9,x]
F[78,x,k[0]] = F[77,x,k[0]]+F[95,x,k[0]]
F[79,x,k[0]] = F[16,x,k[0]]*F[78,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]+F[86,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[84,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[16,x,k[0]]*F[39,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[80,x,k[0]]*F[9,x]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[16,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[41,x,k[0]]*F[90,x]
F[90,x] = F[18,x,1]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[9,x]*F[90,x]*F[93,x,k[0]]
F[94,x,k[0]] = F[72,x]*F[9,x]*F[93,x,k[0]]
F[94,x,k[0]] = F[75,x,k[0]]
F[95,x,k[0]] = F[41,x,k[0]]*F[74,x]
F[96,x,k[0]] = F[114,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[41,x,k[0]]*F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[16,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]
F[101,x,k[0]] = F[102,x]*F[41,x,k[0]]
F[102,x] = F[6,x]
F[104,x,k[0]] = F[103,x,k[0]]+F[113,x,k[0]]
F[105,x,k[0]] = F[104,x,k[0]]*F[16,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[16,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[110,x,k[0]]
F[109,x,k[0]] = F[106,x,k[0]]+F[5,x]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[9,x]
F[112,x,k[0]] = 1/(-1+k[0])*(F[108,x,k[0]]*k[0]-F[108,x,1])
F[113,x,k[0]] = F[41,x,k[0]]*F[5,x]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[16,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[108,x,k[0]]*F[9,x]*F[93,x,k[0]]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[9,x]
F[120,x] = F[121,x,1]
F[121,x,k[0]] = F[116,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = F[108,x,k[0]]*F[41,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[16,x,k[0]]
F[126,x,k[0]] = F[125,x,k[0]]*F[135,x,k[0]]*F[9,x]
F[126,x,k[0]] = F[127,x,k[0]]
F[128,x,k[0]] = F[127,x,k[0]]+F[134,x,k[0]]
F[129,x,k[0]] = F[128,x,k[0]]*F[9,x]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[9,x]
F[133,x,k[0]] = F[132,x,k[0]]*F[16,x,k[0]]
F[133,x,k[0]] = F[26,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[138,x]
F[136,x,k[0]] = F[130,x,k[0]]+F[135,x,k[0]]
F[137,x,k[0]] = F[136,x,k[0]]*F[16,x,k[0]]
F[137,x,k[0]] = F[51,x,k[0]]
F[138,x] = F[0,x]+F[139,x]
F[139,x] = F[140,x]
F[140,x] = F[47,x]*F[9,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[9,x]
F[144,x,k[0]] = F[143,x,k[0]]*F[41,x,k[0]]*F[9,x]
F[144,x,k[0]] = F[145,x,k[0]]
F[146,x,k[0]] = F[145,x,k[0]]+F[205,x,k[0]]
F[147,x,k[0]] = F[146,x,k[0]]*F[16,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[16,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[155,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]*F[41,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]+F[153,x,k[0]]
F[152,x,k[0]] = F[41,x,k[0]]*F[5,x]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[5,x]*F[9,x]*F[93,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[157,x,k[0]]
F[156,x,k[0]] = F[103,x,k[0]]*F[41,x,k[0]]
F[158,x,k[0]] = F[157,x,k[0]]+F[196,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]*F[9,x]*F[93,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]*F[41,x,k[0]]
F[162,x,k[0]] = F[158,x,k[0]]+F[161,x,k[0]]
F[163,x,k[0]] = F[16,x,k[0]]*F[162,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[165,x,k[0]] = F[164,x,k[0]]+F[189,x,k[0]]
F[166,x,k[0]] = F[165,x,k[0]]+F[168,x,k[0]]
F[167,x,k[0]] = F[166,x,k[0]]*F[9,x]
F[167,x,k[0]] = F[65,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]+F[171,x,k[0]]
F[169,x,k[0]] = F[0,x]*F[170,x,k[0]]
F[170,x,k[0]] = F[1,x]+F[52,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[16,x,k[0]]*F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[181,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]+F[176,x,k[0]]
F[175,x,k[0]] = F[41,x,k[0]]*F[49,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[41,x,k[0]]^2*F[16,x,k[0]]*F[178,x,k[0]]
F[179,x,k[0]] = F[16,x,k[0]]*F[178,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]
F[180,x,k[0]] = F[121,x,k[0]]*F[16,x,k[0]]
F[181,x,k[0]] = F[151,x,k[0]]*F[182,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]+F[42,x,k[0]]
F[183,x,k[0]] = F[184,x]+F[185,x,k[0]]+F[188,x,k[0]]
F[184,x] = 0
F[185,x,k[0]] = F[16,x,k[0]]*F[186,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]+F[42,x,k[0]]
F[187,x,k[0]] = F[185,x,k[0]]
F[188,x,k[0]] = F[16,x,k[0]]*F[182,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]*F[9,x]
F[191,x,k[0]] = F[192,x,k[0]]+F[193,x,k[0]]
F[192,x,k[0]] = F[170,x,k[0]]*F[47,x]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[125,x,k[0]]*F[16,x,k[0]]*F[195,x,k[0]]
F[195,x,k[0]] = F[182,x,k[0]]+F[41,x,k[0]]
F[197,x,k[0]] = F[196,x,k[0]]+F[204,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[9,x]*F[93,x,k[0]]
F[200,x,k[0]] = F[199,x,k[0]]*F[41,x,k[0]]
F[201,x,k[0]] = F[197,x,k[0]]+F[200,x,k[0]]
F[202,x,k[0]] = F[201,x,k[0]]+F[203,x,k[0]]
F[202,x,k[0]] = F[162,x,k[0]]+F[173,x,k[0]]
F[203,x,k[0]] = F[155,x,k[0]]+F[174,x,k[0]]
F[204,x,k[0]] = F[153,x,k[0]]*F[182,x,k[0]]
F[205,x,k[0]] = F[39,x,k[0]]*F[41,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]*F[9,x]
F[208,x,k[0]] = F[209,x,k[0]]+F[210,x,k[0]]
F[209,x,k[0]] = F[138,x]*F[37,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]
F[211,x,k[0]] = F[125,x,k[0]]*F[37,x,k[0]]*F[9,x]
F[212,x] = F[213,x]+F[5,x]
F[213,x] = F[106,x,1]
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[9,x]
F[216,x,k[0]] = 1/(-1+k[0])*(F[217,x,k[0]]*k[0]-F[217,x,1])
F[217,x,k[0]] = F[218,x,k[0]]+F[29,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]*F[9,x]
F[221,x,k[0]] = F[16,x,k[0]]*F[220,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]
F[222,x,k[0]] = F[16,x,k[0]]*F[223,x,k[0]]
F[224,x,k[0]] = F[223,x,k[0]]*F[9,x]
F[224,x,k[0]] = F[225,x,k[0]]
F[226,x,k[0]] = F[225,x,k[0]]+F[228,x,k[0]]
F[227,x,k[0]] = F[16,x,k[0]]*F[226,x,k[0]]
F[227,x,k[0]] = F[80,x,k[0]]
F[229,x,k[0]] = F[228,x,k[0]]*F[9,x]
F[229,x,k[0]] = F[230,x,k[0]]
F[230,x,k[0]] = F[231,x,k[0]]+F[72,x]
F[231,x,k[0]] = F[232,x,k[0]]
F[232,x,k[0]] = F[16,x,k[0]]*F[233,x,k[0]]
F[233,x,k[0]] = F[234,x,k[0]]+F[71,x,k[0]]
F[234,x,k[0]] = F[235,x,k[0]]
F[235,x,k[0]] = F[236,x,k[0]]*F[72,x]*F[9,x]
F[236,x,k[0]] = F[237,x,k[0]]+F[244,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]+F[242,x,k[0]]
F[238,x,k[0]] = F[230,x,k[0]]+F[239,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[41,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]
F[241,x,k[0]] = F[237,x,k[0]]*F[9,x]
F[242,x,k[0]] = F[243,x,k[0]]
F[243,x,k[0]] = F[16,x,k[0]]*F[236,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]*F[9,x]
F[247,x,k[0]] = F[246,x,k[0]]*F[9,x]
F[247,x,k[0]] = F[248,x,k[0]]
F[34,x,k[0]] = F[248,x,k[0]]+F[249,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[251,x,k[0]]
F[250,x,k[0]] = F[239,x,k[0]]+F[32,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]+F[253,x,k[0]]
F[252,x,k[0]] = F[213,x]*F[41,x,k[0]]
F[253,x,k[0]] = F[254,x,k[0]]
F[254,x,k[0]] = F[213,x]*F[236,x,k[0]]*F[9,x]
F[255,x,k[0]] = F[256,x,k[0]]
F[256,x,k[0]] = F[16,x,k[0]]*F[257,x,k[0]]
F[258,x,k[0]] = F[257,x,k[0]]*F[9,x]
F[258,x,k[0]] = F[259,x,k[0]]
F[178,x,k[0]] = F[259,x,k[0]]+F[260,x,k[0]]
F[260,x,k[0]] = F[108,x,k[0]]+F[261,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]
F[262,x,k[0]] = F[16,x,k[0]]*F[263,x,k[0]]
F[264,x,k[0]] = F[16,x,k[0]]*F[263,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]
F[265,x,k[0]] = F[266,x,k[0]]+F[267,x,k[0]]
F[266,x,k[0]] = F[106,x,k[0]]*F[41,x,k[0]]
F[267,x,k[0]] = F[268,x,k[0]]
F[268,x,k[0]] = F[106,x,k[0]]*F[236,x,k[0]]*F[9,x]
F[269,x] = F[270,x]
F[270,x] = F[271,x]*F[9,x]
F[271,x] = F[34,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{5}\! \left(x \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_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{9}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{269}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{214}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-y F_{32}\! \left(x , y\right)+F_{32}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{212}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{46}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{118}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{68}\! \left(x , y\right) = -\frac{-y F_{69}\! \left(x , y\right)+F_{69}\! \left(x , 1\right)}{-1+y}
F_{69}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{9}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{80}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{90}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{72}\! \left(x \right) F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{74}\! \left(x \right)
F_{96}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{102}\! \left(x \right) = F_{6}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{16}\! \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_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{5}\! \left(x \right)
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_{9}\! \left(x \right)
F_{112}\! \left(x , y\right) = -\frac{-y F_{108}\! \left(x , y\right)+F_{108}\! \left(x , 1\right)}{-1+y}
F_{113}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{9}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x , 1\right)
F_{121}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{135}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{138}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{138}\! \left(x \right) = F_{0}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{47}\! \left(x \right) F_{9}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{41}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{162}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{41}\! \left(x , y\right)^{2} F_{16}\! \left(x , y\right) F_{178}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{178}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x \right)+F_{185}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{184}\! \left(x \right) = 0
F_{185}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{182}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{47}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{204}\! \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_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{182}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{138}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{5}\! \left(x \right)
F_{213}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{216}\! \left(x , y\right) = -\frac{-y F_{217}\! \left(x , y\right)+F_{217}\! \left(x , 1\right)}{-1+y}
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{220}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{223}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{223}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{226}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{228}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{231}\! \left(x , y\right)+F_{72}\! \left(x \right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{236}\! \left(x , y\right) F_{72}\! \left(x \right) F_{9}\! \left(x \right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{242}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{237}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{242}\! \left(x , y\right) = F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{236}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{247}\! \left(x , y\right) = F_{246}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{248}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{213}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{213}\! \left(x \right) F_{236}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{257}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{257}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{263}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{263}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{265}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{267}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{236}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right) F_{9}\! \left(x \right)
F_{271}\! \left(x \right) = F_{34}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_9(x))
Eq(F_4(x), F_21(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x)*F_9(x))
Eq(F_7(x), F_1(x) + F_10(x) + F_8(x))
Eq(F_8(x), F_7(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x)*F_9(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_5(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_17(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_13(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_9(x))
Eq(F_20(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_9(x))
Eq(F_23(x), F_24(x) + F_269(x))
Eq(F_24(x), F_25(x, 1))
Eq(F_25(x, k_0), F_26(x, k_0) + F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_16(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_255(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_214(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_25(x, k_0) + F_31(x, k_0))
Eq(F_31(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_9(x))
Eq(F_35(x, k_0), F_16(x, k_0)*F_34(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_37(x, k_0), F_212(x) + F_36(x, k_0))
Eq(F_38(x, k_0), F_206(x, k_0) + F_37(x, k_0))
Eq(F_38(x, k_0), F_141(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0) + F_44(x, k_0))
Eq(F_40(x, k_0), F_0(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_1(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_16(x, k_0)*F_41(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_41(x, k_0)*F_46(x, k_0)*F_9(x))
Eq(F_46(x, k_0), F_123(x, k_0) + F_47(x))
Eq(F_47(x), F_118(x) + F_48(x))
Eq(F_48(x), F_49(x, 1))
Eq(F_49(x, k_0), F_50(x, k_0) + F_66(x, k_0))
Eq(F_50(x, k_0), F_0(x) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_61(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_16(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_41(x, k_0) + F_55(x, k_0))
Eq(F_55(x, k_0), F_52(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_16(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_60(x, k_0))
Eq(F_59(x, k_0), F_42(x, k_0))
Eq(F_60(x, k_0), F_56(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_96(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_2(x) + F_61(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_9(x))
Eq(F_68(x, k_0), (k_0*F_69(x, k_0) - F_69(x, 1))/(k_0 - 1))
Eq(F_69(x, k_0), F_49(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_75(x, k_0))
Eq(F_71(x, k_0), F_41(x, k_0)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x)*F_9(x))
Eq(F_74(x), F_17(x, 1))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_9(x))
Eq(F_78(x, k_0), F_77(x, k_0) + F_95(x, k_0))
Eq(F_79(x, k_0), F_16(x, k_0)*F_78(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0) + F_86(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_84(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_16(x, k_0)*F_39(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_80(x, k_0)*F_9(x))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_16(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_41(x, k_0)*F_90(x))
Eq(F_90(x), F_18(x, 1))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_9(x)*F_90(x)*F_93(x, k_0))
Eq(F_94(x, k_0), F_72(x)*F_9(x)*F_93(x, k_0))
Eq(F_94(x, k_0), F_75(x, k_0))
Eq(F_95(x, k_0), F_41(x, k_0)*F_74(x))
Eq(F_96(x, k_0), F_114(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_41(x, k_0)*F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_16(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0))
Eq(F_101(x, k_0), F_102(x)*F_41(x, k_0))
Eq(F_102(x), F_6(x))
Eq(F_104(x, k_0), F_103(x, k_0) + F_113(x, k_0))
Eq(F_105(x, k_0), F_104(x, k_0)*F_16(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_16(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_110(x, k_0))
Eq(F_109(x, k_0), F_106(x, k_0) + F_5(x))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_9(x))
Eq(F_112(x, k_0), (k_0*F_108(x, k_0) - F_108(x, 1))/(k_0 - 1))
Eq(F_113(x, k_0), F_41(x, k_0)*F_5(x))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_16(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_108(x, k_0)*F_9(x)*F_93(x, k_0))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_9(x))
Eq(F_120(x), F_121(x, 1))
Eq(F_121(x, k_0), F_116(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_108(x, k_0)*F_41(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_16(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0)*F_135(x, k_0)*F_9(x))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_128(x, k_0), F_127(x, k_0) + F_134(x, k_0))
Eq(F_129(x, k_0), F_128(x, k_0)*F_9(x))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_9(x))
Eq(F_133(x, k_0), F_132(x, k_0)*F_16(x, k_0))
Eq(F_133(x, k_0), F_26(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_138(x))
Eq(F_136(x, k_0), F_130(x, k_0) + F_135(x, k_0))
Eq(F_137(x, k_0), F_136(x, k_0)*F_16(x, k_0))
Eq(F_137(x, k_0), F_51(x, k_0))
Eq(F_138(x), F_0(x) + F_139(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_47(x)*F_9(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_9(x))
Eq(F_144(x, k_0), F_143(x, k_0)*F_41(x, k_0)*F_9(x))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_146(x, k_0), F_145(x, k_0) + F_205(x, k_0))
Eq(F_147(x, k_0), F_146(x, k_0)*F_16(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_16(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_155(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_41(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0) + F_153(x, k_0))
Eq(F_152(x, k_0), F_41(x, k_0)*F_5(x))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_5(x)*F_9(x)*F_93(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_157(x, k_0))
Eq(F_156(x, k_0), F_103(x, k_0)*F_41(x, k_0))
Eq(F_158(x, k_0), F_157(x, k_0) + F_196(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0)*F_9(x)*F_93(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0)*F_41(x, k_0))
Eq(F_162(x, k_0), F_158(x, k_0) + F_161(x, k_0))
Eq(F_163(x, k_0), F_16(x, k_0)*F_162(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_165(x, k_0), F_164(x, k_0) + F_189(x, k_0))
Eq(F_166(x, k_0), F_165(x, k_0) + F_168(x, k_0))
Eq(F_167(x, k_0), F_166(x, k_0)*F_9(x))
Eq(F_167(x, k_0), F_65(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0) + F_171(x, k_0))
Eq(F_169(x, k_0), F_0(x)*F_170(x, k_0))
Eq(F_170(x, k_0), F_1(x) + F_52(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_16(x, k_0)*F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_181(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0) + F_176(x, k_0))
Eq(F_175(x, k_0), F_41(x, k_0)*F_49(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_16(x, k_0)*F_178(x, k_0)*F_41(x, k_0)**2)
Eq(F_179(x, k_0), F_16(x, k_0)*F_178(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_180(x, k_0), F_121(x, k_0)*F_16(x, k_0))
Eq(F_181(x, k_0), F_151(x, k_0)*F_182(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0) + F_42(x, k_0))
Eq(F_183(x, k_0), F_184(x) + F_185(x, k_0) + F_188(x, k_0))
Eq(F_184(x), 0)
Eq(F_185(x, k_0), F_16(x, k_0)*F_186(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0) + F_42(x, k_0))
Eq(F_187(x, k_0), F_185(x, k_0))
Eq(F_188(x, k_0), F_16(x, k_0)*F_182(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0)*F_9(x))
Eq(F_191(x, k_0), F_192(x, k_0) + F_193(x, k_0))
Eq(F_192(x, k_0), F_170(x, k_0)*F_47(x))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_125(x, k_0)*F_16(x, k_0)*F_195(x, k_0))
Eq(F_195(x, k_0), F_182(x, k_0) + F_41(x, k_0))
Eq(F_197(x, k_0), F_196(x, k_0) + F_204(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_9(x)*F_93(x, k_0))
Eq(F_200(x, k_0), F_199(x, k_0)*F_41(x, k_0))
Eq(F_201(x, k_0), F_197(x, k_0) + F_200(x, k_0))
Eq(F_202(x, k_0), F_201(x, k_0) + F_203(x, k_0))
Eq(F_202(x, k_0), F_162(x, k_0) + F_173(x, k_0))
Eq(F_203(x, k_0), F_155(x, k_0) + F_174(x, k_0))
Eq(F_204(x, k_0), F_153(x, k_0)*F_182(x, k_0))
Eq(F_205(x, k_0), F_39(x, k_0)*F_41(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0)*F_9(x))
Eq(F_208(x, k_0), F_209(x, k_0) + F_210(x, k_0))
Eq(F_209(x, k_0), F_138(x)*F_37(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0))
Eq(F_211(x, k_0), F_125(x, k_0)*F_37(x, k_0)*F_9(x))
Eq(F_212(x), F_213(x) + F_5(x))
Eq(F_213(x), F_106(x, 1))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_9(x))
Eq(F_216(x, k_0), (k_0*F_217(x, k_0) - F_217(x, 1))/(k_0 - 1))
Eq(F_217(x, k_0), F_218(x, k_0) + F_29(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0)*F_9(x))
Eq(F_221(x, k_0), F_16(x, k_0)*F_220(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_222(x, k_0), F_16(x, k_0)*F_223(x, k_0))
Eq(F_224(x, k_0), F_223(x, k_0)*F_9(x))
Eq(F_224(x, k_0), F_225(x, k_0))
Eq(F_226(x, k_0), F_225(x, k_0) + F_228(x, k_0))
Eq(F_227(x, k_0), F_16(x, k_0)*F_226(x, k_0))
Eq(F_227(x, k_0), F_80(x, k_0))
Eq(F_229(x, k_0), F_228(x, k_0)*F_9(x))
Eq(F_229(x, k_0), F_230(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0) + F_72(x))
Eq(F_231(x, k_0), F_232(x, k_0))
Eq(F_232(x, k_0), F_16(x, k_0)*F_233(x, k_0))
Eq(F_233(x, k_0), F_234(x, k_0) + F_71(x, k_0))
Eq(F_234(x, k_0), F_235(x, k_0))
Eq(F_235(x, k_0), F_236(x, k_0)*F_72(x)*F_9(x))
Eq(F_236(x, k_0), F_237(x, k_0) + F_244(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0) + F_242(x, k_0))
Eq(F_238(x, k_0), F_230(x, k_0) + F_239(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_41(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0))
Eq(F_241(x, k_0), F_237(x, k_0)*F_9(x))
Eq(F_242(x, k_0), F_243(x, k_0))
Eq(F_243(x, k_0), F_16(x, k_0)*F_236(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0)*F_9(x))
Eq(F_247(x, k_0), F_246(x, k_0)*F_9(x))
Eq(F_247(x, k_0), F_248(x, k_0))
Eq(F_34(x, k_0), F_248(x, k_0) + F_249(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_251(x, k_0))
Eq(F_250(x, k_0), F_239(x, k_0) + F_32(x, k_0))
Eq(F_251(x, k_0), F_252(x, k_0) + F_253(x, k_0))
Eq(F_252(x, k_0), F_213(x)*F_41(x, k_0))
Eq(F_253(x, k_0), F_254(x, k_0))
Eq(F_254(x, k_0), F_213(x)*F_236(x, k_0)*F_9(x))
Eq(F_255(x, k_0), F_256(x, k_0))
Eq(F_256(x, k_0), F_16(x, k_0)*F_257(x, k_0))
Eq(F_258(x, k_0), F_257(x, k_0)*F_9(x))
Eq(F_258(x, k_0), F_259(x, k_0))
Eq(F_178(x, k_0), F_259(x, k_0) + F_260(x, k_0))
Eq(F_260(x, k_0), F_108(x, k_0) + F_261(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0))
Eq(F_262(x, k_0), F_16(x, k_0)*F_263(x, k_0))
Eq(F_264(x, k_0), F_16(x, k_0)*F_263(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0) + F_267(x, k_0))
Eq(F_266(x, k_0), F_106(x, k_0)*F_41(x, k_0))
Eq(F_267(x, k_0), F_268(x, k_0))
Eq(F_268(x, k_0), F_106(x, k_0)*F_236(x, k_0)*F_9(x))
Eq(F_269(x), F_270(x))
Eq(F_270(x), F_271(x)*F_9(x))
Eq(F_271(x), F_34(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [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, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": 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"class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 0, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 5
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/31/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[9,x,k[0],1]
F[9,x,k[0],k[1]] = F[10,x,1,k[0],k[1]]
F[10,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1],k[2]]*F[24,x,k[1]]
F[11,x,k[0],k[1],k[2]] = F[1,x]+F[10,x,k[0],k[1],k[2]]+F[12,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0],k[1],k[2]]*F[7,x]
F[13,x,k[0],k[1],k[2]] = F[14,x,k[0]*k[1],k[1]*k[2]]
F[15,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[15,x,k[0],k[1]] = F[16,x,1,k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[1]*k[2]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1],k[2]]+F[28,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[7,x]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[24,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[11,x,1,k[0],k[1]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0],k[1],k[2]] = F[24,x,k[1]]*F[26,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[1]*k[2]]
F[27,x,k[0],k[1],k[2]] = (-F[11,x,1,k[1],k[2]]*k[1]+F[11,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[28,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = (F[30,x,k[0],k[2]]*k[0]-F[30,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[31,x,k[0],1,k[1]]
F[31,x,k[0],k[1],k[2]] = (F[32,x,k[0]*k[1]]*k[0]-F[32,x,k[1]*k[2]]*k[2])/(k[0]-k[2])
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[41,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[7,x]
F[34,x,k[0]] = F[35,x,1,k[0]]
F[35,x,k[0],k[1]] = F[1,x]+F[36,x,k[0],k[1]]+F[38,x,k[0],k[1]]+F[39,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[1]]*F[7,x]
F[37,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[38,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[24,x,k[0]]
F[39,x,k[0],k[1]] = F[40,x,k[0],1,k[1]]
F[40,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[31,x,k[0],k[1],k[2]]
F[41,x,k[0]] = F[24,x,k[0]]*F[32,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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{9}\! \left(x , y_{0}, 1\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , 1, y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , 1, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{22}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{22}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{23}\! \left(x , y_{0}, 1\right)-y_{1} F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , 1, y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{11}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{11}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{30}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{30}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, 1, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{32}\! \left(x , y_{0} y_{1}\right) y_{0}-y_{2} F_{32}\! \left(x , y_{1} y_{2}\right)}{y_{0}-y_{2}}
F_{32}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , 1, y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{35}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{40}\! \left(x , y_{0}, 1, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_9(x, k_0, 1))
Eq(F_9(x, k_0, k_1), F_10(x, 1, k_0, k_1))
Eq(F_10(x, k_0, k_1, k_2), F_11(x, k_0, k_1, k_2)*F_24(x, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_1(x) + F_10(x, k_0, k_1, k_2) + F_12(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0, k_1, k_2)*F_7(x))
Eq(F_13(x, k_0, k_1, k_2), F_14(x, k_0*k_1, k_1*k_2))
Eq(F_15(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_15(x, k_0, k_1), F_16(x, 1, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_1*k_2))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_25(x, k_0, k_1, k_2) + F_28(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_7(x))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_24(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_11(x, 1, k_0, k_1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0, k_1, k_2), F_24(x, k_1)*F_26(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_1*k_2))
Eq(F_27(x, k_0, k_1, k_2), (-k_0*F_11(x, k_0/k_1, k_1, k_2) + k_1*F_11(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_28(x, k_0, k_1, k_2), F_24(x, k_2)*F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), (-k_0*F_30(x, k_0, k_2) + k_1*F_30(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, 1, k_1))
Eq(F_31(x, k_0, k_1, k_2), (-k_0*k_1*F_32(x, k_0*k_1) + k_1*k_2*F_32(x, k_1*k_2))/(-k_0*k_1 + k_1*k_2))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_41(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_7(x))
Eq(F_34(x, k_0), F_35(x, 1, k_0))
Eq(F_35(x, k_0, k_1), F_1(x) + F_36(x, k_0, k_1) + F_38(x, k_0, k_1) + F_39(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_1)*F_7(x))
Eq(F_37(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_38(x, k_0, k_1), F_22(x, k_0, k_1)*F_24(x, k_0))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, 1, k_1))
Eq(F_40(x, k_0, k_1, k_2), F_24(x, k_2)*F_31(x, k_0, k_1, k_2))
Eq(F_41(x, k_0), F_24(x, k_0)*F_32(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"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, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"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]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 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]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"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, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"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]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 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]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"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], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"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], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": 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