01324_01342_01432_03124_03142_10324_10342_10432
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2920, 15453, 82664, 445237, 2409175, 13078298, 71162538, 387887162, 2117038246, 11566153470, 63239606144, 345984777032, 1893815568592, 10370249416230, 56803999567971, 311229834124815, 1705594732544476, 9348600528047480, 51248418517507351, 280974492174318146, 1540626229027880701, 8448208046652005140, 46330077844508759732, 254090116515395665849, 1393589399563202529949, 7643651572370100549061, 41925970379164689894062, 229974249359543289814637, 1261499731380892582582594, 6919987426448016484891284, 37960525687617296551926227, 208241216388605914165689771, 1142372386398733002802405141, 6266922902595265279653125936, 34380002463075891090361993930, 188608692436847005656031762844, 1034716079132056597636754471778, 5676542650234343497647996143840, 31142208835102006016045182600267, 170850936204890778182558005492778, 937319056352241291652715627051582, 5142323515836983030267167430321424, 28211941674707696466109157288693842, 154777557634397441067063816944136747, 849149690252796618712109855800412860, 4658666510086236020226220200059920243, 25558770415530429233241516401195332605, 140222963520765415516045877203007184408, 769305919283405566076150802013496122964, 4220653167850968179858498896479478091157, 23155855854201883651853359348995580462870, 127040595619553101494750747663359599547873, 696986966195800600219069862120512364652742, 3823905853131169197519817464242571433728971, 20979255778100809679237844043451688582603866, 115099457363825050263108380853597814049216764, 631475855538619349415835345730602163947146939, 3464499218196106855380105706794080277826860821, 19007473834653031295132942822068375447830675082, 104281801780908772721118053586910032258551088501, 572127497007050873639809341855361197327081078082, 3138898452130812198191427230077686146155438194607, 17221137896529187289762465792120310900734921645827, 94481448147018206505711901556152462871542509757035, 518359835446172616382237976390362424163143542332813, 2843912557401560128631452307424056985212544096814751, 15602752427955629113920190672495266093829598074115150, 85602464848985593499631100478278797945647325081251814, 469646822283105254763800151738474788892823283572977151, 2576656732462313273814736267150517514449225450560078649, 14136496612717398893067587293251517404123239356629278263, 77558083420060943905565824673410383627124683316207826744, 425512560870642463624362453326231620347319900194193647908, 2334520746334390563619816909806201387113401061796819844163, 12808053222321506289788789744904996267286297436944329253768, 70269771062287733530715969292953818436967767147511851606700, 385526272868787670338119339482618423001576098982394907010437, 2115141586256440833056462635050011481465480501006130767977814, 11604459821633563576057027420004559283958904556521328684640885, 63666420428307078245371132140972858122208736994557421487456031, 349297882610592708976583315766434476284494851245522928088412494, 1916379374336505454007144934499427129226600236500275147593376906, 10513977326580754146895921773307979330536409892552382643294463607, 57683631803923025057293430249747078633291619098475567776699546021, 316474094959822436014537437134024782413270757941791499112322225107, 1736295926972922144268526632266989626260958025726540303408408829882, 9525972749556825652323335201229502863191462575825132410253837775242, 52263071628962014151767581935179177839041483836390938379746985178360, 286734884753835160621056925395465688096015630383291429326409330083733, 1573135537479392872233072722908591171091306301348028110427680966358541, 8630813973636374954795581939048454674169800392045926087592365666170015, 47351896198560316071220217283121321292062425546933890100027448129798294, 259790339915161245264758778180989994511421135194189935587215375617736856, 1425307680032521149587554064514125859002695231492425806989097359992378494
Generating function in Maple syntax:
((-10*x^6+36*x^5-75*x^4+72*x^3-11*x^2-13*x+2)*(5*x^2-6*x+1)^(1/2)-20*x^7+64*x^6-69*x^5-115*x^4+481*x^3-544*x^2+237*x-28)/(10*x^7-92*x^6+340*x^5-742*x^4+980*x^3-712*x^2+244*x-26)
Generating function in latex syntax:
\frac{\left(-10 x^{6}+36 x^{5}-75 x^{4}+72 x^{3}-11 x^{2}-13 x +2\right) \sqrt{5 x^{2}-6 x +1}-20 x^{7}+64 x^{6}-69 x^{5}-115 x^{4}+481 x^{3}-544 x^{2}+237 x -28}{10 x^{7}-92 x^{6}+340 x^{5}-742 x^{4}+980 x^{3}-712 x^{2}+244 x -26}
Generating function in sympy syntax:
(-20*x**7 + 64*x**6 - 69*x**5 - 115*x**4 + 481*x**3 - 544*x**2 + 237*x + sqrt(5*x**2 - 6*x + 1)*(-10*x**6 + 36*x**5 - 75*x**4 + 72*x**3 - 11*x**2 - 13*x + 2) - 28)/(10*x**7 - 92*x**6 + 340*x**5 - 742*x**4 + 980*x**3 - 712*x**2 + 244*x - 26)
Implicit equation for the generating function in Maple syntax:
(5*x^7-46*x^6+170*x^5-371*x^4+490*x^3-356*x^2+122*x-13)*F(x)^2+(20*x^7-64*x^6+69*x^5+115*x^4-481*x^3+544*x^2-237*x+28)*F(x)-5*x^7+36*x^6-76*x^5+79*x^4+63*x^3-186*x^2+113*x-15 = 0
Implicit equation for the generating function in latex syntax:
\left(5 x^{7}-46 x^{6}+170 x^{5}-371 x^{4}+490 x^{3}-356 x^{2}+122 x -13\right) F \! \left(x \right)^{2}+\left(20 x^{7}-64 x^{6}+69 x^{5}+115 x^{4}-481 x^{3}+544 x^{2}-237 x +28\right) F \! \left(x \right)-5 x^{7}+36 x^{6}-76 x^{5}+79 x^{4}+63 x^{3}-186 x^{2}+113 x -15 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2920
a(8) = 15453
a(9) = 82664
a(10) = 445237
a(11) = 2409175
a(12) = 13078298
a(13) = 71162538
a(14) = 387887162
a(n+15) = -125/13*n/(n+15)*a(n)+125/13*(14*n+9)/(n+15)*a(n+1)-135/26*(167*n+238)/(n+15)*a(n+2)+1/26*(91226*n+205731)/(n+15)*a(n+3)-1/26*(798085+257436*n)/(n+15)*a(n+4)+1/26*(528408*n+2083711)/(n+15)*a(n+5)-1/26*(3805825+798409*n)/(n+15)*a(n+6)+1/26*(875671*n+4851500)/(n+15)*a(n+7)-1/26*(4123511+665831*n)/(n+15)*a(n+8)+1/13*(156979*n+1015156)/(n+15)*a(n+9)-1/26*(231164+58205*n)/(n+15)*a(n+10)-1/26*(361381+24192*n)/(n+15)*a(n+11)+1/26*(18325*n+233723)/(n+15)*a(n+12)-1/26*(62710+4763*n)/(n+15)*a(n+13)+1/26*(569*n+7963)/(n+15)*a(n+14), n >= 15
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2920
a(8) = 15453
a(9) = 82664
a(10) = 445237
a(11) = 2409175
a(12) = 13078298
a(13) = 71162538
a(14) = 387887162
a{\left(n + 15 \right)} = - \frac{125 n a{\left(n \right)}}{13 \left(n + 15\right)} + \frac{125 \left(14 n + 9\right) a{\left(n + 1 \right)}}{13 \left(n + 15\right)} - \frac{135 \left(167 n + 238\right) a{\left(n + 2 \right)}}{26 \left(n + 15\right)} + \frac{\left(569 n + 7963\right) a{\left(n + 14 \right)}}{26 \left(n + 15\right)} - \frac{\left(4763 n + 62710\right) a{\left(n + 13 \right)}}{26 \left(n + 15\right)} + \frac{\left(18325 n + 233723\right) a{\left(n + 12 \right)}}{26 \left(n + 15\right)} - \frac{\left(24192 n + 361381\right) a{\left(n + 11 \right)}}{26 \left(n + 15\right)} - \frac{\left(58205 n + 231164\right) a{\left(n + 10 \right)}}{26 \left(n + 15\right)} + \frac{\left(91226 n + 205731\right) a{\left(n + 3 \right)}}{26 \left(n + 15\right)} + \frac{\left(156979 n + 1015156\right) a{\left(n + 9 \right)}}{13 \left(n + 15\right)} - \frac{\left(257436 n + 798085\right) a{\left(n + 4 \right)}}{26 \left(n + 15\right)} + \frac{\left(528408 n + 2083711\right) a{\left(n + 5 \right)}}{26 \left(n + 15\right)} - \frac{\left(665831 n + 4123511\right) a{\left(n + 8 \right)}}{26 \left(n + 15\right)} - \frac{\left(798409 n + 3805825\right) a{\left(n + 6 \right)}}{26 \left(n + 15\right)} + \frac{\left(875671 n + 4851500\right) a{\left(n + 7 \right)}}{26 \left(n + 15\right)}, \quad n \geq 15
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24628/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[56,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x]+F[60,x]
F[12,x] = F[13,x]*F[45,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = -F[54,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[24,x]+F[7,x]
F[24,x] = F[25,x]+F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[27,x]
F[27,x] = F[18,x]*F[28,x]
F[28,x] = 1/F[18,x]*F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[18,x]*F[32,x]
F[32,x] = F[33,x]+F[47,x]
F[33,x] = F[34,x]
F[34,x] = F[18,x]*F[35,x]*F[36,x]
F[35,x] = F[0,x]+F[26,x]
F[36,x] = 1/F[0,x]*F[37,x]
F[37,x] = -F[40,x]+F[38,x]
F[38,x] = 1/F[18,x]*F[39,x]
F[39,x] = F[5,x]
F[40,x] = -F[46,x]+F[41,x]
F[41,x] = 1/F[18,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[2,x]+F[44,x]
F[44,x] = -F[45,x]+F[4,x]
F[45,x] = -1+F[45,x]^2*(x^2-2*x)+(2+x)*F[45,x]
F[46,x] = F[2,x]*F[36,x]
F[47,x] = F[48,x]
F[48,x] = F[18,x]*F[49,x]
F[49,x] = F[50,x]+F[52,x]
F[50,x] = F[36,x]*F[51,x]
F[51,x] = F[30,x]+F[5,x]
F[52,x] = F[45,x]*F[53,x]
F[53,x] = -F[24,x]+F[28,x]
F[54,x] = F[55,x]
F[55,x] = -F[25,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[32,x]
F[60,x] = F[61,x]
F[61,x] = F[18,x]*F[62,x]*F[65,x]
F[62,x] = F[58,x]+F[63,x]
F[63,x] = 1/F[18,x]*F[64,x]
F[64,x] = F[54,x]
F[65,x] = F[45,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[18,x]*F[69,x]
F[69,x] = 1/F[18,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = 1/F[173,x]/F[87,x]/F[98,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[252,x]+F[74,x]
F[74,x] = 1/F[18,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[205,x]+F[77,x]
F[77,x] = F[182,x]*F[78,x]
F[78,x] = -F[203,x]+F[79,x]
F[79,x] = -F[200,x]+F[80,x]
F[80,x] = 1/F[18,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[18,x]*F[83,x]
F[83,x] = F[174,x]+F[84,x]
F[84,x] = F[171,x]+F[85,x]
F[85,x] = F[86,x]*F[98,x]
F[86,x] = F[116,x]+F[87,x]
F[87,x] = F[1,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[18,x]*F[90,x]
F[90,x] = F[91,x]+F[99,x]
F[91,x] = F[1,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[18,x]*F[94,x]
F[94,x] = F[91,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = F[1,x]+F[96,x]
F[99,x] = F[100,x]+F[88,x]
F[100,x] = F[101,x]+F[102,x]+F[106,x]
F[101,x] = 0
F[102,x] = F[103,x]*F[18,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[92,x]
F[105,x] = F[100,x]
F[106,x] = F[107,x]*F[18,x]
F[107,x] = F[108,x]+F[99,x]
F[108,x] = F[109,x]
F[109,x] = F[101,x]+F[110,x]+F[114,x]
F[110,x] = F[111,x]*F[18,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[96,x]
F[113,x] = F[109,x]
F[114,x] = F[115,x]*F[18,x]
F[115,x] = F[109,x]+F[88,x]
F[116,x] = F[117,x]+F[128,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[18,x]
F[119,x] = F[120,x]+F[98,x]
F[120,x] = F[121,x]+F[124,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[18,x]
F[123,x] = F[1,x]+F[121,x]
F[124,x] = F[101,x]+F[125,x]+F[127,x]
F[125,x] = F[126,x]*F[18,x]
F[126,x] = F[124,x]+F[96,x]
F[127,x] = F[120,x]*F[18,x]
F[128,x] = F[101,x]+F[129,x]+F[145,x]
F[129,x] = F[130,x]*F[18,x]
F[130,x] = F[131,x]+F[135,x]
F[131,x] = F[132,x]+F[18,x]
F[132,x] = F[101,x]+F[133,x]+F[134,x]
F[133,x] = F[131,x]*F[18,x]
F[134,x] = F[18,x]*F[96,x]
F[135,x] = F[136,x]+F[140,x]
F[136,x] = F[101,x]+F[137,x]+F[139,x]
F[137,x] = F[138,x]*F[18,x]
F[138,x] = F[136,x]+F[18,x]
F[139,x] = F[121,x]*F[18,x]
F[140,x] = F[101,x]+F[141,x]+F[143,x]+F[144,x]
F[141,x] = F[142,x]*F[18,x]
F[142,x] = F[132,x]+F[140,x]
F[143,x] = F[135,x]*F[18,x]
F[144,x] = F[124,x]*F[18,x]
F[145,x] = F[146,x]*F[18,x]
F[146,x] = F[147,x]+F[155,x]
F[147,x] = F[117,x]+F[148,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[18,x]
F[150,x] = F[147,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[18,x]
F[154,x] = F[117,x]+F[152,x]
F[155,x] = F[128,x]+F[156,x]
F[156,x] = 2*F[101,x]+F[157,x]+F[161,x]
F[157,x] = F[158,x]*F[18,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[148,x]
F[160,x] = F[156,x]
F[161,x] = F[162,x]*F[18,x]
F[162,x] = F[155,x]+F[163,x]
F[163,x] = F[164,x]
F[164,x] = 2*F[101,x]+F[165,x]+F[169,x]
F[165,x] = F[166,x]*F[18,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[152,x]
F[168,x] = F[164,x]
F[169,x] = F[170,x]*F[18,x]
F[170,x] = F[128,x]+F[164,x]
F[171,x] = F[172,x]
F[172,x] = F[131,x]*F[173,x]*F[87,x]
F[173,x] = F[1,x]+F[117,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[18,x]
F[176,x] = F[177,x]+F[198,x]
F[177,x] = F[178,x]*F[98,x]
F[178,x] = F[179,x]+F[186,x]
F[179,x] = 1/F[18,x]*F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = (x*F[182,x]+x-2*F[182,x])*(x*F[182,x]+x-1)
F[183,x] = F[184,x]
F[184,x] = F[18,x]*F[185,x]*F[86,x]
F[185,x] = F[182,x]+F[67,x]
F[186,x] = F[187,x]
F[187,x] = F[18,x]*F[188,x]*F[87,x]
F[188,x] = F[189,x]+F[197,x]
F[189,x] = F[190,x]*F[36,x]
F[190,x] = F[191,x]+F[194,x]
F[191,x] = F[192,x]+F[193,x]
F[192,x] = F[1,x]+F[18,x]
F[193,x] = F[132,x]+F[96,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = F[121,x]+F[136,x]
F[196,x] = F[124,x]+F[140,x]
F[197,x] = F[119,x]*F[71,x]
F[198,x] = F[199,x]
F[199,x] = F[131,x]*F[173,x]*F[36,x]*F[87,x]
F[200,x] = 1/F[18,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[174,x]*F[18,x]
F[203,x] = F[204,x]
F[204,x] = F[173,x]*F[87,x]*F[96,x]
F[205,x] = F[206,x]
F[206,x] = F[173,x]*F[207,x]*F[87,x]*F[98,x]
F[207,x] = F[208,x]
F[208,x] = F[18,x]*F[209,x]
F[209,x] = F[210,x]+F[232,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[18,x]*F[45,x]
F[212,x] = F[213,x]
F[213,x] = F[18,x]*F[214,x]
F[214,x] = F[215,x]+F[228,x]
F[215,x] = F[138,x]*F[216,x]
F[216,x] = F[217,x]+F[221,x]
F[217,x] = F[218,x]+F[45,x]
F[218,x] = F[219,x]
F[219,x] = F[18,x]*F[220,x]
F[220,x] = F[216,x]+F[218,x]
F[221,x] = F[222,x]
F[222,x] = F[18,x]*F[217,x]*F[223,x]
F[223,x] = F[224,x]+F[227,x]
F[224,x] = F[225,x]+F[45,x]
F[225,x] = F[226,x]
F[226,x] = F[18,x]*F[220,x]
F[227,x] = F[226,x]
F[228,x] = F[123,x]*F[229,x]
F[229,x] = F[210,x]+F[230,x]
F[230,x] = F[231,x]
F[231,x] = F[18,x]*F[210,x]*F[223,x]
F[232,x] = F[233,x]+F[234,x]
F[233,x] = F[18,x]+F[207,x]
F[234,x] = F[235,x]
F[235,x] = F[18,x]*F[236,x]
F[236,x] = F[234,x]+F[237,x]
F[237,x] = F[232,x]+F[238,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = F[241,x]+F[242,x]
F[241,x] = F[223,x]*F[232,x]
F[242,x] = F[217,x]*F[243,x]
F[243,x] = F[244,x]+F[251,x]
F[244,x] = F[233,x]+F[245,x]
F[245,x] = F[246,x]
F[246,x] = F[18,x]*F[247,x]
F[247,x] = F[248,x]+F[250,x]
F[248,x] = F[229,x]+F[249,x]
F[249,x] = F[212,x]
F[250,x] = F[236,x]
F[251,x] = F[246,x]
F[252,x] = F[253,x]*F[36,x]
F[253,x] = -F[256,x]+F[254,x]
F[254,x] = 1/F[18,x]*F[255,x]
F[255,x] = F[82,x]
F[256,x] = 1/F[18,x]*F[257,x]
F[257,x] = F[202,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{56}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{60}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{37}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = x^{2} F_{45} \left(x \right)^{2}-2 x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+2 F_{45}\! \left(x \right)-1
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{30}\! \left(x \right)+F_{5}\! \left(x \right)
F_{52}\! \left(x \right) = F_{45}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{32}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{18}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{54}\! \left(x \right)
F_{65}\! \left(x \right) = F_{45}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{252}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{205}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{182}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{203}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{200}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{18}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{174}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{171}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right) F_{98}\! \left(x \right)
F_{86}\! \left(x \right) = F_{116}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{18}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{99}\! \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_{18}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{88}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{101}\! \left(x \right) = 0
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{18}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{92}\! \left(x \right)
F_{105}\! \left(x \right) = F_{100}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{18}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{99}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{101}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{18}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{96}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{18}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right)+F_{88}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{128}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{18}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{98}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{18}\! \left(x \right)
F_{123}\! \left(x \right) = F_{1}\! \left(x \right)+F_{121}\! \left(x \right)
F_{124}\! \left(x \right) = F_{101}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{18}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)+F_{96}\! \left(x \right)
F_{127}\! \left(x \right) = F_{120}\! \left(x \right) F_{18}\! \left(x \right)
F_{128}\! \left(x \right) = F_{101}\! \left(x \right)+F_{129}\! \left(x \right)+F_{145}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{18}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{18}\! \left(x \right)
F_{132}\! \left(x \right) = F_{101}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{131}\! \left(x \right) F_{18}\! \left(x \right)
F_{134}\! \left(x \right) = F_{18}\! \left(x \right) F_{96}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{140}\! \left(x \right)
F_{136}\! \left(x \right) = F_{101}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{18}\! \left(x \right)
F_{138}\! \left(x \right) = F_{136}\! \left(x \right)+F_{18}\! \left(x \right)
F_{139}\! \left(x \right) = F_{121}\! \left(x \right) F_{18}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right)+F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{18}\! \left(x \right)
F_{142}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{143}\! \left(x \right) = F_{135}\! \left(x \right) F_{18}\! \left(x \right)
F_{144}\! \left(x \right) = F_{124}\! \left(x \right) F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{18}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{155}\! \left(x \right)
F_{147}\! \left(x \right) = F_{117}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{18}\! \left(x \right)
F_{150}\! \left(x \right) = F_{147}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{18}\! \left(x \right)
F_{154}\! \left(x \right) = F_{117}\! \left(x \right)+F_{152}\! \left(x \right)
F_{155}\! \left(x \right) = F_{128}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = 2 F_{101}\! \left(x \right)+F_{157}\! \left(x \right)+F_{161}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{18}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{148}\! \left(x \right)
F_{160}\! \left(x \right) = F_{156}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{18}\! \left(x \right)
F_{162}\! \left(x \right) = F_{155}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{101}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{18}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{152}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{18}\! \left(x \right)
F_{170}\! \left(x \right) = F_{128}\! \left(x \right)+F_{164}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{87}\! \left(x \right)
F_{173}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{18}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{198}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{98}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{186}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = x^{2} F_{182} \left(x \right)^{2}+2 x^{2} F_{182}\! \left(x \right)-2 x F_{182} \left(x \right)^{2}+x^{2}-3 x F_{182}\! \left(x \right)-x +2 F_{182}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{18}\! \left(x \right) F_{185}\! \left(x \right) F_{86}\! \left(x \right)
F_{185}\! \left(x \right) = F_{182}\! \left(x \right)+F_{67}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{18}\! \left(x \right) F_{188}\! \left(x \right) F_{87}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{197}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{36}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{194}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{193}\! \left(x \right)
F_{192}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{193}\! \left(x \right) = F_{132}\! \left(x \right)+F_{96}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = F_{121}\! \left(x \right)+F_{136}\! \left(x \right)
F_{196}\! \left(x \right) = F_{124}\! \left(x \right)+F_{140}\! \left(x \right)
F_{197}\! \left(x \right) = F_{119}\! \left(x \right) F_{71}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{36}\! \left(x \right) F_{87}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{174}\! \left(x \right) F_{18}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{96}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{173}\! \left(x \right) F_{207}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{18}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{232}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{18}\! \left(x \right) F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{228}\! \left(x \right)
F_{215}\! \left(x \right) = F_{138}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{221}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{45}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{18}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{216}\! \left(x \right)+F_{218}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{18}\! \left(x \right) F_{217}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)+F_{227}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)+F_{45}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = F_{18}\! \left(x \right) F_{220}\! \left(x \right)
F_{227}\! \left(x \right) = F_{226}\! \left(x \right)
F_{228}\! \left(x \right) = F_{123}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{210}\! \left(x \right)+F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{18}\! \left(x \right) F_{210}\! \left(x \right) F_{223}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{233}\! \left(x \right) = F_{18}\! \left(x \right)+F_{207}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{18}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{234}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{232}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{242}\! \left(x \right)
F_{241}\! \left(x \right) = F_{223}\! \left(x \right) F_{232}\! \left(x \right)
F_{242}\! \left(x \right) = F_{217}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{251}\! \left(x \right)
F_{244}\! \left(x \right) = F_{233}\! \left(x \right)+F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{18}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{250}\! \left(x \right)
F_{248}\! \left(x \right) = F_{229}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{212}\! \left(x \right)
F_{250}\! \left(x \right) = F_{236}\! \left(x \right)
F_{251}\! \left(x \right) = F_{246}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right) F_{36}\! \left(x \right)
F_{253}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = \frac{F_{255}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{255}\! \left(x \right) = F_{82}\! \left(x \right)
F_{256}\! \left(x \right) = \frac{F_{257}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{257}\! \left(x \right) = F_{202}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_56(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_60(x))
Eq(F_12(x), F_13(x)*F_45(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), F_22(x) - F_54(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_24(x) + F_7(x))
Eq(F_24(x), F_25(x) + F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_18(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_18(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_18(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_47(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_18(x)*F_35(x)*F_36(x))
Eq(F_35(x), F_0(x) + F_26(x))
Eq(F_36(x), F_37(x)/F_0(x))
Eq(F_37(x), F_38(x) - F_40(x))
Eq(F_38(x), F_39(x)/F_18(x))
Eq(F_39(x), F_5(x))
Eq(F_40(x), F_41(x) - F_46(x))
Eq(F_41(x), F_42(x)/F_18(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_2(x) + F_44(x))
Eq(F_44(x), F_4(x) - F_45(x))
Eq(F_45(x), x*(x - 2)*F_45(x)**2 + (x + 2)*F_45(x) - 1)
Eq(F_46(x), F_2(x)*F_36(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_18(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_52(x))
Eq(F_50(x), F_36(x)*F_51(x))
Eq(F_51(x), F_30(x) + F_5(x))
Eq(F_52(x), F_45(x)*F_53(x))
Eq(F_53(x), -F_24(x) + F_28(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), -F_25(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_32(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_18(x)*F_62(x)*F_65(x))
Eq(F_62(x), F_58(x) + F_63(x))
Eq(F_63(x), F_64(x)/F_18(x))
Eq(F_64(x), F_54(x))
Eq(F_65(x), F_45(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_18(x)*F_69(x))
Eq(F_69(x), F_70(x)/F_18(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)/(F_173(x)*F_87(x)*F_98(x)))
Eq(F_72(x), F_73(x))
Eq(F_73(x), -F_252(x) + F_74(x))
Eq(F_74(x), F_75(x)/F_18(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_205(x) + F_77(x))
Eq(F_77(x), F_182(x)*F_78(x))
Eq(F_78(x), -F_203(x) + F_79(x))
Eq(F_79(x), -F_200(x) + F_80(x))
Eq(F_80(x), F_81(x)/F_18(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_18(x)*F_83(x))
Eq(F_83(x), F_174(x) + F_84(x))
Eq(F_84(x), F_171(x) + F_85(x))
Eq(F_85(x), F_86(x)*F_98(x))
Eq(F_86(x), F_116(x) + F_87(x))
Eq(F_87(x), F_1(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_18(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_99(x))
Eq(F_91(x), F_1(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_18(x)*F_94(x))
Eq(F_94(x), F_91(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), F_1(x) + F_96(x))
Eq(F_99(x), F_100(x) + F_88(x))
Eq(F_100(x), F_101(x) + F_102(x) + F_106(x))
Eq(F_101(x), 0)
Eq(F_102(x), F_103(x)*F_18(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_92(x))
Eq(F_105(x), F_100(x))
Eq(F_106(x), F_107(x)*F_18(x))
Eq(F_107(x), F_108(x) + F_99(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_101(x) + F_110(x) + F_114(x))
Eq(F_110(x), F_111(x)*F_18(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_96(x))
Eq(F_113(x), F_109(x))
Eq(F_114(x), F_115(x)*F_18(x))
Eq(F_115(x), F_109(x) + F_88(x))
Eq(F_116(x), F_117(x) + F_128(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_18(x))
Eq(F_119(x), F_120(x) + F_98(x))
Eq(F_120(x), F_121(x) + F_124(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_18(x))
Eq(F_123(x), F_1(x) + F_121(x))
Eq(F_124(x), F_101(x) + F_125(x) + F_127(x))
Eq(F_125(x), F_126(x)*F_18(x))
Eq(F_126(x), F_124(x) + F_96(x))
Eq(F_127(x), F_120(x)*F_18(x))
Eq(F_128(x), F_101(x) + F_129(x) + F_145(x))
Eq(F_129(x), F_130(x)*F_18(x))
Eq(F_130(x), F_131(x) + F_135(x))
Eq(F_131(x), F_132(x) + F_18(x))
Eq(F_132(x), F_101(x) + F_133(x) + F_134(x))
Eq(F_133(x), F_131(x)*F_18(x))
Eq(F_134(x), F_18(x)*F_96(x))
Eq(F_135(x), F_136(x) + F_140(x))
Eq(F_136(x), F_101(x) + F_137(x) + F_139(x))
Eq(F_137(x), F_138(x)*F_18(x))
Eq(F_138(x), F_136(x) + F_18(x))
Eq(F_139(x), F_121(x)*F_18(x))
Eq(F_140(x), F_101(x) + F_141(x) + F_143(x) + F_144(x))
Eq(F_141(x), F_142(x)*F_18(x))
Eq(F_142(x), F_132(x) + F_140(x))
Eq(F_143(x), F_135(x)*F_18(x))
Eq(F_144(x), F_124(x)*F_18(x))
Eq(F_145(x), F_146(x)*F_18(x))
Eq(F_146(x), F_147(x) + F_155(x))
Eq(F_147(x), F_117(x) + F_148(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_18(x))
Eq(F_150(x), F_147(x) + F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_18(x))
Eq(F_154(x), F_117(x) + F_152(x))
Eq(F_155(x), F_128(x) + F_156(x))
Eq(F_156(x), 2*F_101(x) + F_157(x) + F_161(x))
Eq(F_157(x), F_158(x)*F_18(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_148(x))
Eq(F_160(x), F_156(x))
Eq(F_161(x), F_162(x)*F_18(x))
Eq(F_162(x), F_155(x) + F_163(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), 2*F_101(x) + F_165(x) + F_169(x))
Eq(F_165(x), F_166(x)*F_18(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_152(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_170(x)*F_18(x))
Eq(F_170(x), F_128(x) + F_164(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_131(x)*F_173(x)*F_87(x))
Eq(F_173(x), F_1(x) + F_117(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_18(x))
Eq(F_176(x), F_177(x) + F_198(x))
Eq(F_177(x), F_178(x)*F_98(x))
Eq(F_178(x), F_179(x) + F_186(x))
Eq(F_179(x), F_180(x)/F_18(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), x*(x - 2)*(F_182(x) + 1)**2 + (x + 1)*(F_182(x) + 1) + F_182(x) - 1)
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_18(x)*F_185(x)*F_86(x))
Eq(F_185(x), F_182(x) + F_67(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_18(x)*F_188(x)*F_87(x))
Eq(F_188(x), F_189(x) + F_197(x))
Eq(F_189(x), F_190(x)*F_36(x))
Eq(F_190(x), F_191(x) + F_194(x))
Eq(F_191(x), F_192(x) + F_193(x))
Eq(F_192(x), F_1(x) + F_18(x))
Eq(F_193(x), F_132(x) + F_96(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), F_121(x) + F_136(x))
Eq(F_196(x), F_124(x) + F_140(x))
Eq(F_197(x), F_119(x)*F_71(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_131(x)*F_173(x)*F_36(x)*F_87(x))
Eq(F_200(x), F_201(x)/F_18(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_174(x)*F_18(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_173(x)*F_87(x)*F_96(x))
Eq(F_205(x), F_206(x))
Eq(F_206(x), F_173(x)*F_207(x)*F_87(x)*F_98(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_18(x)*F_209(x))
Eq(F_209(x), F_210(x) + F_232(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_18(x)*F_45(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_18(x)*F_214(x))
Eq(F_214(x), F_215(x) + F_228(x))
Eq(F_215(x), F_138(x)*F_216(x))
Eq(F_216(x), F_217(x) + F_221(x))
Eq(F_217(x), F_218(x) + F_45(x))
Eq(F_218(x), F_219(x))
Eq(F_219(x), F_18(x)*F_220(x))
Eq(F_220(x), F_216(x) + F_218(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_18(x)*F_217(x)*F_223(x))
Eq(F_223(x), F_224(x) + F_227(x))
Eq(F_224(x), F_225(x) + F_45(x))
Eq(F_225(x), F_226(x))
Eq(F_226(x), F_18(x)*F_220(x))
Eq(F_227(x), F_226(x))
Eq(F_228(x), F_123(x)*F_229(x))
Eq(F_229(x), F_210(x) + F_230(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_18(x)*F_210(x)*F_223(x))
Eq(F_232(x), F_233(x) + F_234(x))
Eq(F_233(x), F_18(x) + F_207(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_18(x)*F_236(x))
Eq(F_236(x), F_234(x) + F_237(x))
Eq(F_237(x), F_232(x) + F_238(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_241(x) + F_242(x))
Eq(F_241(x), F_223(x)*F_232(x))
Eq(F_242(x), F_217(x)*F_243(x))
Eq(F_243(x), F_244(x) + F_251(x))
Eq(F_244(x), F_233(x) + F_245(x))
Eq(F_245(x), F_246(x))
Eq(F_246(x), F_18(x)*F_247(x))
Eq(F_247(x), F_248(x) + F_250(x))
Eq(F_248(x), F_229(x) + F_249(x))
Eq(F_249(x), F_212(x))
Eq(F_250(x), F_236(x))
Eq(F_251(x), F_246(x))
Eq(F_252(x), F_253(x)*F_36(x))
Eq(F_253(x), F_254(x) - F_256(x))
Eq(F_254(x), F_255(x)/F_18(x))
Eq(F_255(x), F_82(x))
Eq(F_256(x), F_257(x)/F_18(x))
Eq(F_257(x), F_202(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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"pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24922/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[56,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x]+F[60,x]
F[12,x] = F[13,x]*F[45,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = -F[54,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[24,x]+F[7,x]
F[24,x] = F[25,x]+F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[27,x]
F[27,x] = F[18,x]*F[28,x]
F[28,x] = 1/F[18,x]*F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[18,x]*F[32,x]
F[32,x] = F[33,x]+F[47,x]
F[33,x] = F[34,x]
F[34,x] = F[18,x]*F[35,x]*F[36,x]
F[35,x] = F[0,x]+F[26,x]
F[36,x] = 1/F[0,x]*F[37,x]
F[37,x] = -F[40,x]+F[38,x]
F[38,x] = 1/F[18,x]*F[39,x]
F[39,x] = F[5,x]
F[40,x] = -F[46,x]+F[41,x]
F[41,x] = 1/F[18,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[2,x]+F[44,x]
F[44,x] = -F[45,x]+F[4,x]
F[45,x] = -1+(x^2-2*x)*F[45,x]^2+(2+x)*F[45,x]
F[46,x] = F[2,x]*F[36,x]
F[47,x] = F[48,x]
F[48,x] = F[18,x]*F[49,x]
F[49,x] = F[50,x]+F[52,x]
F[50,x] = F[36,x]*F[51,x]
F[51,x] = F[30,x]+F[5,x]
F[52,x] = F[45,x]*F[53,x]
F[53,x] = -F[24,x]+F[28,x]
F[54,x] = F[55,x]
F[55,x] = -F[25,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[32,x]
F[60,x] = F[61,x]
F[61,x] = F[18,x]*F[62,x]*F[65,x]
F[62,x] = F[58,x]+F[63,x]
F[63,x] = 1/F[18,x]*F[64,x]
F[64,x] = F[54,x]
F[65,x] = F[45,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[18,x]*F[69,x]
F[69,x] = 1/F[18,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = 1/F[173,x]/F[87,x]/F[98,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[252,x]+F[74,x]
F[74,x] = 1/F[18,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[205,x]+F[77,x]
F[77,x] = F[182,x]*F[78,x]
F[78,x] = -F[203,x]+F[79,x]
F[79,x] = -F[200,x]+F[80,x]
F[80,x] = 1/F[18,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[18,x]*F[83,x]
F[83,x] = F[174,x]+F[84,x]
F[84,x] = F[171,x]+F[85,x]
F[85,x] = F[86,x]*F[98,x]
F[86,x] = F[116,x]+F[87,x]
F[87,x] = F[1,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[18,x]*F[90,x]
F[90,x] = F[91,x]+F[99,x]
F[91,x] = F[1,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[18,x]*F[94,x]
F[94,x] = F[91,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = F[1,x]+F[96,x]
F[99,x] = F[100,x]+F[88,x]
F[100,x] = F[101,x]+F[102,x]+F[106,x]
F[101,x] = 0
F[102,x] = F[103,x]*F[18,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[92,x]
F[105,x] = F[100,x]
F[106,x] = F[107,x]*F[18,x]
F[107,x] = F[108,x]+F[99,x]
F[108,x] = F[109,x]
F[109,x] = F[101,x]+F[110,x]+F[114,x]
F[110,x] = F[111,x]*F[18,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[96,x]
F[113,x] = F[109,x]
F[114,x] = F[115,x]*F[18,x]
F[115,x] = F[109,x]+F[88,x]
F[116,x] = F[117,x]+F[128,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[18,x]
F[119,x] = F[120,x]+F[98,x]
F[120,x] = F[121,x]+F[124,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[18,x]
F[123,x] = F[1,x]+F[121,x]
F[124,x] = F[101,x]+F[125,x]+F[127,x]
F[125,x] = F[126,x]*F[18,x]
F[126,x] = F[124,x]+F[96,x]
F[127,x] = F[120,x]*F[18,x]
F[128,x] = F[101,x]+F[129,x]+F[145,x]
F[129,x] = F[130,x]*F[18,x]
F[130,x] = F[131,x]+F[135,x]
F[131,x] = F[132,x]+F[18,x]
F[132,x] = F[101,x]+F[133,x]+F[134,x]
F[133,x] = F[131,x]*F[18,x]
F[134,x] = F[18,x]*F[96,x]
F[135,x] = F[136,x]+F[140,x]
F[136,x] = F[101,x]+F[137,x]+F[139,x]
F[137,x] = F[138,x]*F[18,x]
F[138,x] = F[136,x]+F[18,x]
F[139,x] = F[121,x]*F[18,x]
F[140,x] = F[101,x]+F[141,x]+F[143,x]+F[144,x]
F[141,x] = F[142,x]*F[18,x]
F[142,x] = F[132,x]+F[140,x]
F[143,x] = F[135,x]*F[18,x]
F[144,x] = F[124,x]*F[18,x]
F[145,x] = F[146,x]*F[18,x]
F[146,x] = F[147,x]+F[155,x]
F[147,x] = F[117,x]+F[148,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[18,x]
F[150,x] = F[147,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[18,x]
F[154,x] = F[117,x]+F[152,x]
F[155,x] = F[128,x]+F[156,x]
F[156,x] = 2*F[101,x]+F[157,x]+F[161,x]
F[157,x] = F[158,x]*F[18,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[148,x]
F[160,x] = F[156,x]
F[161,x] = F[162,x]*F[18,x]
F[162,x] = F[155,x]+F[163,x]
F[163,x] = F[164,x]
F[164,x] = 2*F[101,x]+F[165,x]+F[169,x]
F[165,x] = F[166,x]*F[18,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[152,x]
F[168,x] = F[164,x]
F[169,x] = F[170,x]*F[18,x]
F[170,x] = F[128,x]+F[164,x]
F[171,x] = F[172,x]
F[172,x] = F[131,x]*F[173,x]*F[87,x]
F[173,x] = F[1,x]+F[117,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[18,x]
F[176,x] = F[177,x]+F[198,x]
F[177,x] = F[178,x]*F[98,x]
F[178,x] = F[179,x]+F[186,x]
F[179,x] = 1/F[18,x]*F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = (x*F[182,x]+x-1)*(x*F[182,x]+x-2*F[182,x])
F[183,x] = F[184,x]
F[184,x] = F[18,x]*F[185,x]*F[86,x]
F[185,x] = F[182,x]+F[67,x]
F[186,x] = F[187,x]
F[187,x] = F[18,x]*F[188,x]*F[87,x]
F[188,x] = F[189,x]+F[197,x]
F[189,x] = F[190,x]*F[36,x]
F[190,x] = F[191,x]+F[194,x]
F[191,x] = F[192,x]+F[193,x]
F[192,x] = F[1,x]+F[18,x]
F[193,x] = F[132,x]+F[96,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = F[121,x]+F[136,x]
F[196,x] = F[124,x]+F[140,x]
F[197,x] = F[119,x]*F[71,x]
F[198,x] = F[199,x]
F[199,x] = F[131,x]*F[173,x]*F[36,x]*F[87,x]
F[200,x] = 1/F[18,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[174,x]*F[18,x]
F[203,x] = F[204,x]
F[204,x] = F[173,x]*F[87,x]*F[96,x]
F[205,x] = F[206,x]
F[206,x] = F[173,x]*F[207,x]*F[87,x]*F[98,x]
F[207,x] = F[208,x]
F[208,x] = F[18,x]*F[209,x]
F[209,x] = F[210,x]+F[232,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[18,x]*F[45,x]
F[212,x] = F[213,x]
F[213,x] = F[18,x]*F[214,x]
F[214,x] = F[215,x]+F[228,x]
F[215,x] = F[138,x]*F[216,x]
F[216,x] = F[217,x]+F[221,x]
F[217,x] = F[218,x]+F[45,x]
F[218,x] = F[219,x]
F[219,x] = F[18,x]*F[220,x]
F[220,x] = F[216,x]+F[218,x]
F[221,x] = F[222,x]
F[222,x] = F[18,x]*F[217,x]*F[223,x]
F[223,x] = F[224,x]+F[227,x]
F[224,x] = F[225,x]+F[45,x]
F[225,x] = F[226,x]
F[226,x] = F[18,x]*F[220,x]
F[227,x] = F[226,x]
F[228,x] = F[123,x]*F[229,x]
F[229,x] = F[210,x]+F[230,x]
F[230,x] = F[231,x]
F[231,x] = F[18,x]*F[210,x]*F[223,x]
F[232,x] = F[233,x]+F[234,x]
F[233,x] = F[18,x]+F[207,x]
F[234,x] = F[235,x]
F[235,x] = F[18,x]*F[236,x]
F[236,x] = F[234,x]+F[237,x]
F[237,x] = F[232,x]+F[238,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = F[241,x]+F[242,x]
F[241,x] = F[223,x]*F[232,x]
F[242,x] = F[217,x]*F[243,x]
F[243,x] = F[244,x]+F[251,x]
F[244,x] = F[233,x]+F[245,x]
F[245,x] = F[246,x]
F[246,x] = F[18,x]*F[247,x]
F[247,x] = F[248,x]+F[250,x]
F[248,x] = F[229,x]+F[249,x]
F[249,x] = F[212,x]
F[250,x] = F[236,x]
F[251,x] = F[246,x]
F[252,x] = F[253,x]*F[36,x]
F[253,x] = -F[256,x]+F[254,x]
F[254,x] = 1/F[18,x]*F[255,x]
F[255,x] = F[82,x]
F[256,x] = 1/F[18,x]*F[257,x]
F[257,x] = F[202,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{56}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{60}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{37}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = x^{2} F_{45} \left(x \right)^{2}-2 x F_{45} \left(x \right)^{2}+F_{45}\! \left(x \right) x +2 F_{45}\! \left(x \right)-1
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{30}\! \left(x \right)+F_{5}\! \left(x \right)
F_{52}\! \left(x \right) = F_{45}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{32}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{18}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{54}\! \left(x \right)
F_{65}\! \left(x \right) = F_{45}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{252}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{205}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{182}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{203}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{200}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{18}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{174}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{171}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right) F_{98}\! \left(x \right)
F_{86}\! \left(x \right) = F_{116}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{18}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{99}\! \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_{18}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{88}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{101}\! \left(x \right) = 0
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{18}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{92}\! \left(x \right)
F_{105}\! \left(x \right) = F_{100}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{18}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{99}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{101}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{18}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{96}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{18}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right)+F_{88}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{128}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{18}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{98}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{18}\! \left(x \right)
F_{123}\! \left(x \right) = F_{1}\! \left(x \right)+F_{121}\! \left(x \right)
F_{124}\! \left(x \right) = F_{101}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{18}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)+F_{96}\! \left(x \right)
F_{127}\! \left(x \right) = F_{120}\! \left(x \right) F_{18}\! \left(x \right)
F_{128}\! \left(x \right) = F_{101}\! \left(x \right)+F_{129}\! \left(x \right)+F_{145}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{18}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{18}\! \left(x \right)
F_{132}\! \left(x \right) = F_{101}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{131}\! \left(x \right) F_{18}\! \left(x \right)
F_{134}\! \left(x \right) = F_{18}\! \left(x \right) F_{96}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{140}\! \left(x \right)
F_{136}\! \left(x \right) = F_{101}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{18}\! \left(x \right)
F_{138}\! \left(x \right) = F_{136}\! \left(x \right)+F_{18}\! \left(x \right)
F_{139}\! \left(x \right) = F_{121}\! \left(x \right) F_{18}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right)+F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{18}\! \left(x \right)
F_{142}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{143}\! \left(x \right) = F_{135}\! \left(x \right) F_{18}\! \left(x \right)
F_{144}\! \left(x \right) = F_{124}\! \left(x \right) F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{18}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{155}\! \left(x \right)
F_{147}\! \left(x \right) = F_{117}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{18}\! \left(x \right)
F_{150}\! \left(x \right) = F_{147}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{18}\! \left(x \right)
F_{154}\! \left(x \right) = F_{117}\! \left(x \right)+F_{152}\! \left(x \right)
F_{155}\! \left(x \right) = F_{128}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = 2 F_{101}\! \left(x \right)+F_{157}\! \left(x \right)+F_{161}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{18}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{148}\! \left(x \right)
F_{160}\! \left(x \right) = F_{156}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{18}\! \left(x \right)
F_{162}\! \left(x \right) = F_{155}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{101}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{18}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{152}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{18}\! \left(x \right)
F_{170}\! \left(x \right) = F_{128}\! \left(x \right)+F_{164}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{87}\! \left(x \right)
F_{173}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{18}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{198}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{98}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{186}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = x^{2} F_{182} \left(x \right)^{2}+2 x^{2} F_{182}\! \left(x \right)-2 x F_{182} \left(x \right)^{2}+x^{2}-3 x F_{182}\! \left(x \right)-x +2 F_{182}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{18}\! \left(x \right) F_{185}\! \left(x \right) F_{86}\! \left(x \right)
F_{185}\! \left(x \right) = F_{182}\! \left(x \right)+F_{67}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{18}\! \left(x \right) F_{188}\! \left(x \right) F_{87}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{197}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{36}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{194}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{193}\! \left(x \right)
F_{192}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{193}\! \left(x \right) = F_{132}\! \left(x \right)+F_{96}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = F_{121}\! \left(x \right)+F_{136}\! \left(x \right)
F_{196}\! \left(x \right) = F_{124}\! \left(x \right)+F_{140}\! \left(x \right)
F_{197}\! \left(x \right) = F_{119}\! \left(x \right) F_{71}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{36}\! \left(x \right) F_{87}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{174}\! \left(x \right) F_{18}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{96}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{173}\! \left(x \right) F_{207}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{18}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{232}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{18}\! \left(x \right) F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{228}\! \left(x \right)
F_{215}\! \left(x \right) = F_{138}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{221}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{45}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{18}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{216}\! \left(x \right)+F_{218}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{18}\! \left(x \right) F_{217}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)+F_{227}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)+F_{45}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = F_{18}\! \left(x \right) F_{220}\! \left(x \right)
F_{227}\! \left(x \right) = F_{226}\! \left(x \right)
F_{228}\! \left(x \right) = F_{123}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{210}\! \left(x \right)+F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{18}\! \left(x \right) F_{210}\! \left(x \right) F_{223}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{233}\! \left(x \right) = F_{18}\! \left(x \right)+F_{207}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{18}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{234}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{232}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{242}\! \left(x \right)
F_{241}\! \left(x \right) = F_{223}\! \left(x \right) F_{232}\! \left(x \right)
F_{242}\! \left(x \right) = F_{217}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{251}\! \left(x \right)
F_{244}\! \left(x \right) = F_{233}\! \left(x \right)+F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{18}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{250}\! \left(x \right)
F_{248}\! \left(x \right) = F_{229}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{212}\! \left(x \right)
F_{250}\! \left(x \right) = F_{236}\! \left(x \right)
F_{251}\! \left(x \right) = F_{246}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right) F_{36}\! \left(x \right)
F_{253}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = \frac{F_{255}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{255}\! \left(x \right) = F_{82}\! \left(x \right)
F_{256}\! \left(x \right) = \frac{F_{257}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{257}\! \left(x \right) = F_{202}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_56(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_60(x))
Eq(F_12(x), F_13(x)*F_45(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), F_22(x) - F_54(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_24(x) + F_7(x))
Eq(F_24(x), F_25(x) + F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_18(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_18(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_18(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_47(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_18(x)*F_35(x)*F_36(x))
Eq(F_35(x), F_0(x) + F_26(x))
Eq(F_36(x), F_37(x)/F_0(x))
Eq(F_37(x), F_38(x) - F_40(x))
Eq(F_38(x), F_39(x)/F_18(x))
Eq(F_39(x), F_5(x))
Eq(F_40(x), F_41(x) - F_46(x))
Eq(F_41(x), F_42(x)/F_18(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_2(x) + F_44(x))
Eq(F_44(x), F_4(x) - F_45(x))
Eq(F_45(x), x*(x - 2)*F_45(x)**2 + (x + 2)*F_45(x) - 1)
Eq(F_46(x), F_2(x)*F_36(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_18(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_52(x))
Eq(F_50(x), F_36(x)*F_51(x))
Eq(F_51(x), F_30(x) + F_5(x))
Eq(F_52(x), F_45(x)*F_53(x))
Eq(F_53(x), -F_24(x) + F_28(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), -F_25(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_32(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_18(x)*F_62(x)*F_65(x))
Eq(F_62(x), F_58(x) + F_63(x))
Eq(F_63(x), F_64(x)/F_18(x))
Eq(F_64(x), F_54(x))
Eq(F_65(x), F_45(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_18(x)*F_69(x))
Eq(F_69(x), F_70(x)/F_18(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)/(F_173(x)*F_87(x)*F_98(x)))
Eq(F_72(x), F_73(x))
Eq(F_73(x), -F_252(x) + F_74(x))
Eq(F_74(x), F_75(x)/F_18(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_205(x) + F_77(x))
Eq(F_77(x), F_182(x)*F_78(x))
Eq(F_78(x), -F_203(x) + F_79(x))
Eq(F_79(x), -F_200(x) + F_80(x))
Eq(F_80(x), F_81(x)/F_18(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_18(x)*F_83(x))
Eq(F_83(x), F_174(x) + F_84(x))
Eq(F_84(x), F_171(x) + F_85(x))
Eq(F_85(x), F_86(x)*F_98(x))
Eq(F_86(x), F_116(x) + F_87(x))
Eq(F_87(x), F_1(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_18(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_99(x))
Eq(F_91(x), F_1(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_18(x)*F_94(x))
Eq(F_94(x), F_91(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), F_1(x) + F_96(x))
Eq(F_99(x), F_100(x) + F_88(x))
Eq(F_100(x), F_101(x) + F_102(x) + F_106(x))
Eq(F_101(x), 0)
Eq(F_102(x), F_103(x)*F_18(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_92(x))
Eq(F_105(x), F_100(x))
Eq(F_106(x), F_107(x)*F_18(x))
Eq(F_107(x), F_108(x) + F_99(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_101(x) + F_110(x) + F_114(x))
Eq(F_110(x), F_111(x)*F_18(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_96(x))
Eq(F_113(x), F_109(x))
Eq(F_114(x), F_115(x)*F_18(x))
Eq(F_115(x), F_109(x) + F_88(x))
Eq(F_116(x), F_117(x) + F_128(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_18(x))
Eq(F_119(x), F_120(x) + F_98(x))
Eq(F_120(x), F_121(x) + F_124(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_18(x))
Eq(F_123(x), F_1(x) + F_121(x))
Eq(F_124(x), F_101(x) + F_125(x) + F_127(x))
Eq(F_125(x), F_126(x)*F_18(x))
Eq(F_126(x), F_124(x) + F_96(x))
Eq(F_127(x), F_120(x)*F_18(x))
Eq(F_128(x), F_101(x) + F_129(x) + F_145(x))
Eq(F_129(x), F_130(x)*F_18(x))
Eq(F_130(x), F_131(x) + F_135(x))
Eq(F_131(x), F_132(x) + F_18(x))
Eq(F_132(x), F_101(x) + F_133(x) + F_134(x))
Eq(F_133(x), F_131(x)*F_18(x))
Eq(F_134(x), F_18(x)*F_96(x))
Eq(F_135(x), F_136(x) + F_140(x))
Eq(F_136(x), F_101(x) + F_137(x) + F_139(x))
Eq(F_137(x), F_138(x)*F_18(x))
Eq(F_138(x), F_136(x) + F_18(x))
Eq(F_139(x), F_121(x)*F_18(x))
Eq(F_140(x), F_101(x) + F_141(x) + F_143(x) + F_144(x))
Eq(F_141(x), F_142(x)*F_18(x))
Eq(F_142(x), F_132(x) + F_140(x))
Eq(F_143(x), F_135(x)*F_18(x))
Eq(F_144(x), F_124(x)*F_18(x))
Eq(F_145(x), F_146(x)*F_18(x))
Eq(F_146(x), F_147(x) + F_155(x))
Eq(F_147(x), F_117(x) + F_148(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_18(x))
Eq(F_150(x), F_147(x) + F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_18(x))
Eq(F_154(x), F_117(x) + F_152(x))
Eq(F_155(x), F_128(x) + F_156(x))
Eq(F_156(x), 2*F_101(x) + F_157(x) + F_161(x))
Eq(F_157(x), F_158(x)*F_18(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_148(x))
Eq(F_160(x), F_156(x))
Eq(F_161(x), F_162(x)*F_18(x))
Eq(F_162(x), F_155(x) + F_163(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), 2*F_101(x) + F_165(x) + F_169(x))
Eq(F_165(x), F_166(x)*F_18(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_152(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_170(x)*F_18(x))
Eq(F_170(x), F_128(x) + F_164(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_131(x)*F_173(x)*F_87(x))
Eq(F_173(x), F_1(x) + F_117(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_18(x))
Eq(F_176(x), F_177(x) + F_198(x))
Eq(F_177(x), F_178(x)*F_98(x))
Eq(F_178(x), F_179(x) + F_186(x))
Eq(F_179(x), F_180(x)/F_18(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), x*(x - 2)*(F_182(x) + 1)**2 + (x + 1)*(F_182(x) + 1) + F_182(x) - 1)
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_18(x)*F_185(x)*F_86(x))
Eq(F_185(x), F_182(x) + F_67(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_18(x)*F_188(x)*F_87(x))
Eq(F_188(x), F_189(x) + F_197(x))
Eq(F_189(x), F_190(x)*F_36(x))
Eq(F_190(x), F_191(x) + F_194(x))
Eq(F_191(x), F_192(x) + F_193(x))
Eq(F_192(x), F_1(x) + F_18(x))
Eq(F_193(x), F_132(x) + F_96(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), F_121(x) + F_136(x))
Eq(F_196(x), F_124(x) + F_140(x))
Eq(F_197(x), F_119(x)*F_71(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_131(x)*F_173(x)*F_36(x)*F_87(x))
Eq(F_200(x), F_201(x)/F_18(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_174(x)*F_18(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_173(x)*F_87(x)*F_96(x))
Eq(F_205(x), F_206(x))
Eq(F_206(x), F_173(x)*F_207(x)*F_87(x)*F_98(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_18(x)*F_209(x))
Eq(F_209(x), F_210(x) + F_232(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_18(x)*F_45(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_18(x)*F_214(x))
Eq(F_214(x), F_215(x) + F_228(x))
Eq(F_215(x), F_138(x)*F_216(x))
Eq(F_216(x), F_217(x) + F_221(x))
Eq(F_217(x), F_218(x) + F_45(x))
Eq(F_218(x), F_219(x))
Eq(F_219(x), F_18(x)*F_220(x))
Eq(F_220(x), F_216(x) + F_218(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_18(x)*F_217(x)*F_223(x))
Eq(F_223(x), F_224(x) + F_227(x))
Eq(F_224(x), F_225(x) + F_45(x))
Eq(F_225(x), F_226(x))
Eq(F_226(x), F_18(x)*F_220(x))
Eq(F_227(x), F_226(x))
Eq(F_228(x), F_123(x)*F_229(x))
Eq(F_229(x), F_210(x) + F_230(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_18(x)*F_210(x)*F_223(x))
Eq(F_232(x), F_233(x) + F_234(x))
Eq(F_233(x), F_18(x) + F_207(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_18(x)*F_236(x))
Eq(F_236(x), F_234(x) + F_237(x))
Eq(F_237(x), F_232(x) + F_238(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_241(x) + F_242(x))
Eq(F_241(x), F_223(x)*F_232(x))
Eq(F_242(x), F_217(x)*F_243(x))
Eq(F_243(x), F_244(x) + F_251(x))
Eq(F_244(x), F_233(x) + F_245(x))
Eq(F_245(x), F_246(x))
Eq(F_246(x), F_18(x)*F_247(x))
Eq(F_247(x), F_248(x) + F_250(x))
Eq(F_248(x), F_229(x) + F_249(x))
Eq(F_249(x), F_212(x))
Eq(F_250(x), F_236(x))
Eq(F_251(x), F_246(x))
Eq(F_252(x), F_253(x)*F_36(x))
Eq(F_253(x), F_254(x) - F_256(x))
Eq(F_254(x), F_255(x)/F_18(x))
Eq(F_255(x), F_82(x))
Eq(F_256(x), F_257(x)/F_18(x))
Eq(F_257(x), F_202(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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{"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 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{"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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"strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 3]]}, 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"pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25208/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[64,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x]+F[68,x]
F[12,x] = F[13,x]*F[36,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = -F[62,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[24,x]+F[7,x]
F[24,x] = F[25,x]+F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[27,x]
F[27,x] = F[18,x]*F[28,x]
F[28,x] = 1/F[18,x]*F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[18,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]*F[34,x]
F[34,x] = F[35,x]+F[37,x]
F[35,x] = F[28,x]*F[36,x]
F[36,x] = -1+(x^2-2*x)*F[36,x]^2+(2+x)*F[36,x]
F[37,x] = F[38,x]
F[38,x] = F[18,x]*F[24,x]*F[39,x]
F[39,x] = 1/F[18,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[18,x]*F[43,x]*F[55,x]
F[43,x] = F[36,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[18,x]*F[46,x]
F[46,x] = F[44,x]+F[47,x]
F[47,x] = F[43,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[18,x]*F[43,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[36,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[18,x]*F[46,x]
F[54,x] = F[53,x]
F[55,x] = F[36,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]*F[61,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[18,x]*F[58,x]
F[61,x] = F[36,x]+F[41,x]
F[62,x] = F[63,x]
F[63,x] = -F[25,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = 1/F[18,x]*F[67,x]
F[67,x] = F[32,x]
F[68,x] = F[69,x]
F[69,x] = F[18,x]*F[70,x]*F[82,x]
F[70,x] = 1/F[18,x]/F[36,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = 1/F[18,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[75,x]+F[64,x]
F[75,x] = F[26,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[18,x]*F[78,x]
F[78,x] = 1/F[18,x]/F[55,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[37,x]
F[82,x] = F[36,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[18,x]*F[85,x]
F[85,x] = 1/F[18,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = 1/F[103,x]/F[114,x]/F[186,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[256,x]+F[90,x]
F[90,x] = 1/F[18,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[221,x]+F[93,x]
F[93,x] = F[195,x]*F[94,x]
F[94,x] = -F[219,x]+F[95,x]
F[95,x] = -F[216,x]+F[96,x]
F[96,x] = 1/F[18,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[18,x]*F[99,x]
F[99,x] = F[100,x]+F[187,x]
F[100,x] = F[101,x]+F[184,x]
F[101,x] = F[102,x]*F[114,x]
F[102,x] = F[103,x]+F[132,x]
F[103,x] = F[1,x]+F[104,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[18,x]
F[106,x] = F[107,x]+F[115,x]
F[107,x] = F[1,x]+F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[18,x]
F[110,x] = F[107,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[18,x]
F[114,x] = F[1,x]+F[112,x]
F[115,x] = F[104,x]+F[116,x]
F[116,x] = F[117,x]+F[118,x]+F[122,x]
F[117,x] = 0
F[118,x] = F[119,x]*F[18,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[108,x]
F[121,x] = F[116,x]
F[122,x] = F[123,x]*F[18,x]
F[123,x] = F[115,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[117,x]+F[126,x]+F[130,x]
F[126,x] = F[127,x]*F[18,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[112,x]
F[129,x] = F[125,x]
F[130,x] = F[131,x]*F[18,x]
F[131,x] = F[104,x]+F[125,x]
F[132,x] = F[133,x]+F[141,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[18,x]
F[135,x] = F[114,x]+F[136,x]
F[136,x] = F[137,x]+F[59,x]
F[137,x] = F[117,x]+F[138,x]+F[140,x]
F[138,x] = F[139,x]*F[18,x]
F[139,x] = F[112,x]+F[137,x]
F[140,x] = F[136,x]*F[18,x]
F[141,x] = F[117,x]+F[142,x]+F[158,x]
F[142,x] = F[143,x]*F[18,x]
F[143,x] = F[144,x]+F[148,x]
F[144,x] = F[145,x]+F[18,x]
F[145,x] = F[117,x]+F[146,x]+F[147,x]
F[146,x] = F[144,x]*F[18,x]
F[147,x] = F[112,x]*F[18,x]
F[148,x] = F[149,x]+F[153,x]
F[149,x] = F[117,x]+F[150,x]+F[152,x]
F[150,x] = F[151,x]*F[18,x]
F[151,x] = F[149,x]+F[18,x]
F[152,x] = F[18,x]*F[59,x]
F[153,x] = F[117,x]+F[154,x]+F[156,x]+F[157,x]
F[154,x] = F[155,x]*F[18,x]
F[155,x] = F[145,x]+F[153,x]
F[156,x] = F[148,x]*F[18,x]
F[157,x] = F[137,x]*F[18,x]
F[158,x] = F[159,x]*F[18,x]
F[159,x] = F[160,x]+F[168,x]
F[160,x] = F[133,x]+F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[18,x]
F[163,x] = F[160,x]+F[164,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[18,x]
F[167,x] = F[133,x]+F[165,x]
F[168,x] = F[141,x]+F[169,x]
F[169,x] = 2*F[117,x]+F[170,x]+F[174,x]
F[170,x] = F[171,x]*F[18,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[161,x]
F[173,x] = F[169,x]
F[174,x] = F[175,x]*F[18,x]
F[175,x] = F[168,x]+F[176,x]
F[176,x] = F[177,x]
F[177,x] = 2*F[117,x]+F[178,x]+F[182,x]
F[178,x] = F[179,x]*F[18,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[165,x]
F[181,x] = F[177,x]
F[182,x] = F[18,x]*F[183,x]
F[183,x] = F[141,x]+F[177,x]
F[184,x] = F[185,x]
F[185,x] = F[103,x]*F[144,x]*F[186,x]
F[186,x] = F[1,x]+F[133,x]
F[187,x] = F[188,x]
F[188,x] = F[18,x]*F[189,x]
F[189,x] = F[190,x]+F[214,x]
F[190,x] = F[114,x]*F[191,x]
F[191,x] = F[192,x]+F[199,x]
F[192,x] = 1/F[18,x]*F[193,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = (x*F[195,x]+x-2*F[195,x])*(x*F[195,x]+x-1)
F[196,x] = F[197,x]
F[197,x] = F[102,x]*F[18,x]*F[198,x]
F[198,x] = F[195,x]+F[83,x]
F[199,x] = F[200,x]
F[200,x] = F[103,x]*F[18,x]*F[201,x]
F[201,x] = F[202,x]+F[213,x]
F[202,x] = F[203,x]*F[210,x]
F[203,x] = F[204,x]+F[207,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[1,x]+F[18,x]
F[206,x] = F[112,x]+F[145,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[149,x]+F[59,x]
F[209,x] = F[137,x]+F[153,x]
F[210,x] = F[211,x]+F[36,x]
F[211,x] = F[212,x]
F[212,x] = F[18,x]*F[39,x]
F[213,x] = F[135,x]*F[87,x]
F[214,x] = F[215,x]
F[215,x] = F[103,x]*F[144,x]*F[186,x]*F[210,x]
F[216,x] = 1/F[18,x]*F[217,x]
F[217,x] = F[218,x]
F[218,x] = F[18,x]*F[187,x]
F[219,x] = F[220,x]
F[220,x] = F[103,x]*F[112,x]*F[186,x]
F[221,x] = F[222,x]
F[222,x] = F[103,x]*F[114,x]*F[186,x]*F[223,x]
F[223,x] = F[224,x]
F[224,x] = F[18,x]*F[225,x]
F[225,x] = F[226,x]+F[236,x]
F[226,x] = F[227,x]+F[228,x]
F[227,x] = F[18,x]*F[36,x]
F[228,x] = F[229,x]
F[229,x] = F[18,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[151,x]*F[47,x]
F[232,x] = F[233,x]*F[58,x]
F[233,x] = F[226,x]+F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[18,x]*F[226,x]*F[50,x]
F[236,x] = F[237,x]+F[238,x]
F[237,x] = F[18,x]+F[223,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = F[238,x]+F[241,x]
F[241,x] = F[236,x]+F[242,x]
F[242,x] = F[243,x]
F[243,x] = F[18,x]*F[244,x]
F[244,x] = F[245,x]+F[246,x]
F[245,x] = F[236,x]*F[50,x]
F[246,x] = F[247,x]*F[43,x]
F[247,x] = F[248,x]+F[255,x]
F[248,x] = F[237,x]+F[249,x]
F[249,x] = F[250,x]
F[250,x] = F[18,x]*F[251,x]
F[251,x] = F[252,x]+F[254,x]
F[252,x] = F[233,x]+F[253,x]
F[253,x] = F[228,x]
F[254,x] = F[240,x]
F[255,x] = F[250,x]
F[256,x] = F[210,x]*F[257,x]
F[257,x] = -F[260,x]+F[258,x]
F[258,x] = 1/F[18,x]*F[259,x]
F[259,x] = F[98,x]
F[260,x] = 1/F[18,x]*F[261,x]
F[261,x] = F[218,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{64}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = x^{2} F_{36} \left(x \right)^{2}-2 x F_{36} \left(x \right)^{2}+F_{36}\! \left(x \right) x +2 F_{36}\! \left(x \right)-1
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{18}\! \left(x \right) F_{24}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{55}\! \left(x \right)
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{36}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right) F_{46}\! \left(x \right)
F_{54}\! \left(x \right) = F_{53}\! \left(x \right)
F_{55}\! \left(x \right) = F_{36}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{32}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{70}\! \left(x \right) F_{82}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right) F_{36}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{64}\! \left(x \right)
F_{75}\! \left(x \right) = F_{26}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{18}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{18}\! \left(x \right) F_{55}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{37}\! \left(x \right)
F_{82}\! \left(x \right) = F_{36}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{221}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{195}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{219}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{216}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{18}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{187}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{184}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{114}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{132}\! \left(x \right)
F_{103}\! \left(x \right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{18}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{115}\! \left(x \right)
F_{107}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{18}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{18}\! \left(x \right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)
F_{115}\! \left(x \right) = F_{104}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = 0
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{18}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{108}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{18}\! \left(x \right)
F_{123}\! \left(x \right) = F_{115}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{117}\! \left(x \right)+F_{126}\! \left(x \right)+F_{130}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{18}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{112}\! \left(x \right)
F_{129}\! \left(x \right) = F_{125}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{18}\! \left(x \right)
F_{131}\! \left(x \right) = F_{104}\! \left(x \right)+F_{125}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{141}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{18}\! \left(x \right)
F_{135}\! \left(x \right) = F_{114}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{59}\! \left(x \right)
F_{137}\! \left(x \right) = F_{117}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{18}\! \left(x \right)
F_{139}\! \left(x \right) = F_{112}\! \left(x \right)+F_{137}\! \left(x \right)
F_{140}\! \left(x \right) = F_{136}\! \left(x \right) F_{18}\! \left(x \right)
F_{141}\! \left(x \right) = F_{117}\! \left(x \right)+F_{142}\! \left(x \right)+F_{158}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{18}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{148}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{117}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right) F_{18}\! \left(x \right)
F_{147}\! \left(x \right) = F_{112}\! \left(x \right) F_{18}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{149}\! \left(x \right) = F_{117}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{18}\! \left(x \right)
F_{151}\! \left(x \right) = F_{149}\! \left(x \right)+F_{18}\! \left(x \right)
F_{152}\! \left(x \right) = F_{18}\! \left(x \right) F_{59}\! \left(x \right)
F_{153}\! \left(x \right) = F_{117}\! \left(x \right)+F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{18}\! \left(x \right)
F_{155}\! \left(x \right) = F_{145}\! \left(x \right)+F_{153}\! \left(x \right)
F_{156}\! \left(x \right) = F_{148}\! \left(x \right) F_{18}\! \left(x \right)
F_{157}\! \left(x \right) = F_{137}\! \left(x \right) F_{18}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{18}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{168}\! \left(x \right)
F_{160}\! \left(x \right) = F_{133}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{18}\! \left(x \right)
F_{163}\! \left(x \right) = F_{160}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{18}\! \left(x \right)
F_{167}\! \left(x \right) = F_{133}\! \left(x \right)+F_{165}\! \left(x \right)
F_{168}\! \left(x \right) = F_{141}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = 2 F_{117}\! \left(x \right)+F_{170}\! \left(x \right)+F_{174}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{18}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{161}\! \left(x \right)
F_{173}\! \left(x \right) = F_{169}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{18}\! \left(x \right)
F_{175}\! \left(x \right) = F_{168}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = 2 F_{117}\! \left(x \right)+F_{178}\! \left(x \right)+F_{182}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{18}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{165}\! \left(x \right)
F_{181}\! \left(x \right) = F_{177}\! \left(x \right)
F_{182}\! \left(x \right) = F_{18}\! \left(x \right) F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{141}\! \left(x \right)+F_{177}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{18}\! \left(x \right) F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{214}\! \left(x \right)
F_{190}\! \left(x \right) = F_{114}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{199}\! \left(x \right)
F_{192}\! \left(x \right) = \frac{F_{193}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = x^{2} F_{195} \left(x \right)^{2}+2 x^{2} F_{195}\! \left(x \right)-2 x F_{195} \left(x \right)^{2}+x^{2}-3 x F_{195}\! \left(x \right)-x +2 F_{195}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{102}\! \left(x \right) F_{18}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{195}\! \left(x \right)+F_{83}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{103}\! \left(x \right) F_{18}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{213}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{210}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)+F_{207}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{206}\! \left(x \right) = F_{112}\! \left(x \right)+F_{145}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{149}\! \left(x \right)+F_{59}\! \left(x \right)
F_{209}\! \left(x \right) = F_{137}\! \left(x \right)+F_{153}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{36}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{18}\! \left(x \right) F_{39}\! \left(x \right)
F_{213}\! \left(x \right) = F_{135}\! \left(x \right) F_{87}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right) F_{210}\! \left(x \right)
F_{216}\! \left(x \right) = \frac{F_{217}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{18}\! \left(x \right) F_{187}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{103}\! \left(x \right) F_{112}\! \left(x \right) F_{186}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{18}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)+F_{236}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{228}\! \left(x \right)
F_{227}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{18}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{151}\! \left(x \right) F_{47}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{58}\! \left(x \right)
F_{233}\! \left(x \right) = F_{226}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{18}\! \left(x \right) F_{226}\! \left(x \right) F_{50}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{238}\! \left(x \right)
F_{237}\! \left(x \right) = F_{18}\! \left(x \right)+F_{223}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{238}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{236}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{18}\! \left(x \right) F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)+F_{246}\! \left(x \right)
F_{245}\! \left(x \right) = F_{236}\! \left(x \right) F_{50}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{43}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{255}\! \left(x \right)
F_{248}\! \left(x \right) = F_{237}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{18}\! \left(x \right) F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{254}\! \left(x \right)
F_{252}\! \left(x \right) = F_{233}\! \left(x \right)+F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{228}\! \left(x \right)
F_{254}\! \left(x \right) = F_{240}\! \left(x \right)
F_{255}\! \left(x \right) = F_{250}\! \left(x \right)
F_{256}\! \left(x \right) = F_{210}\! \left(x \right) F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = -F_{260}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = \frac{F_{259}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{259}\! \left(x \right) = F_{98}\! \left(x \right)
F_{260}\! \left(x \right) = \frac{F_{261}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{261}\! \left(x \right) = F_{218}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_64(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_68(x))
Eq(F_12(x), F_13(x)*F_36(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), F_22(x) - F_62(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_24(x) + F_7(x))
Eq(F_24(x), F_25(x) + F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_18(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_18(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_18(x)*F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_37(x))
Eq(F_35(x), F_28(x)*F_36(x))
Eq(F_36(x), x*(x - 2)*F_36(x)**2 + (x + 2)*F_36(x) - 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_18(x)*F_24(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_18(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_18(x)*F_43(x)*F_55(x))
Eq(F_43(x), F_36(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_18(x)*F_46(x))
Eq(F_46(x), F_44(x) + F_47(x))
Eq(F_47(x), F_43(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_18(x)*F_43(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_36(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_18(x)*F_46(x))
Eq(F_54(x), F_53(x))
Eq(F_55(x), F_36(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x)*F_61(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_18(x)*F_58(x))
Eq(F_61(x), F_36(x) + F_41(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), -F_25(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_67(x)/F_18(x))
Eq(F_67(x), F_32(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_18(x)*F_70(x)*F_82(x))
Eq(F_70(x), F_71(x)/(F_18(x)*F_36(x)))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x)/F_18(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_64(x) - F_75(x))
Eq(F_75(x), F_26(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_18(x)*F_78(x))
Eq(F_78(x), F_79(x)/(F_18(x)*F_55(x)))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_37(x))
Eq(F_82(x), F_36(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_18(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_18(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x)/(F_103(x)*F_114(x)*F_186(x)))
Eq(F_88(x), F_89(x))
Eq(F_89(x), -F_256(x) + F_90(x))
Eq(F_90(x), F_91(x)/F_18(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_221(x) + F_93(x))
Eq(F_93(x), F_195(x)*F_94(x))
Eq(F_94(x), -F_219(x) + F_95(x))
Eq(F_95(x), -F_216(x) + F_96(x))
Eq(F_96(x), F_97(x)/F_18(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_18(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_187(x))
Eq(F_100(x), F_101(x) + F_184(x))
Eq(F_101(x), F_102(x)*F_114(x))
Eq(F_102(x), F_103(x) + F_132(x))
Eq(F_103(x), F_1(x) + F_104(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_18(x))
Eq(F_106(x), F_107(x) + F_115(x))
Eq(F_107(x), F_1(x) + F_108(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_18(x))
Eq(F_110(x), F_107(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_18(x))
Eq(F_114(x), F_1(x) + F_112(x))
Eq(F_115(x), F_104(x) + F_116(x))
Eq(F_116(x), F_117(x) + F_118(x) + F_122(x))
Eq(F_117(x), 0)
Eq(F_118(x), F_119(x)*F_18(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_108(x))
Eq(F_121(x), F_116(x))
Eq(F_122(x), F_123(x)*F_18(x))
Eq(F_123(x), F_115(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_117(x) + F_126(x) + F_130(x))
Eq(F_126(x), F_127(x)*F_18(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_112(x))
Eq(F_129(x), F_125(x))
Eq(F_130(x), F_131(x)*F_18(x))
Eq(F_131(x), F_104(x) + F_125(x))
Eq(F_132(x), F_133(x) + F_141(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_18(x))
Eq(F_135(x), F_114(x) + F_136(x))
Eq(F_136(x), F_137(x) + F_59(x))
Eq(F_137(x), F_117(x) + F_138(x) + F_140(x))
Eq(F_138(x), F_139(x)*F_18(x))
Eq(F_139(x), F_112(x) + F_137(x))
Eq(F_140(x), F_136(x)*F_18(x))
Eq(F_141(x), F_117(x) + F_142(x) + F_158(x))
Eq(F_142(x), F_143(x)*F_18(x))
Eq(F_143(x), F_144(x) + F_148(x))
Eq(F_144(x), F_145(x) + F_18(x))
Eq(F_145(x), F_117(x) + F_146(x) + F_147(x))
Eq(F_146(x), F_144(x)*F_18(x))
Eq(F_147(x), F_112(x)*F_18(x))
Eq(F_148(x), F_149(x) + F_153(x))
Eq(F_149(x), F_117(x) + F_150(x) + F_152(x))
Eq(F_150(x), F_151(x)*F_18(x))
Eq(F_151(x), F_149(x) + F_18(x))
Eq(F_152(x), F_18(x)*F_59(x))
Eq(F_153(x), F_117(x) + F_154(x) + F_156(x) + F_157(x))
Eq(F_154(x), F_155(x)*F_18(x))
Eq(F_155(x), F_145(x) + F_153(x))
Eq(F_156(x), F_148(x)*F_18(x))
Eq(F_157(x), F_137(x)*F_18(x))
Eq(F_158(x), F_159(x)*F_18(x))
Eq(F_159(x), F_160(x) + F_168(x))
Eq(F_160(x), F_133(x) + F_161(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_18(x))
Eq(F_163(x), F_160(x) + F_164(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_18(x))
Eq(F_167(x), F_133(x) + F_165(x))
Eq(F_168(x), F_141(x) + F_169(x))
Eq(F_169(x), 2*F_117(x) + F_170(x) + F_174(x))
Eq(F_170(x), F_171(x)*F_18(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_161(x))
Eq(F_173(x), F_169(x))
Eq(F_174(x), F_175(x)*F_18(x))
Eq(F_175(x), F_168(x) + F_176(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), 2*F_117(x) + F_178(x) + F_182(x))
Eq(F_178(x), F_179(x)*F_18(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_165(x))
Eq(F_181(x), F_177(x))
Eq(F_182(x), F_18(x)*F_183(x))
Eq(F_183(x), F_141(x) + F_177(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_103(x)*F_144(x)*F_186(x))
Eq(F_186(x), F_1(x) + F_133(x))
Eq(F_187(x), F_188(x))
Eq(F_188(x), F_18(x)*F_189(x))
Eq(F_189(x), F_190(x) + F_214(x))
Eq(F_190(x), F_114(x)*F_191(x))
Eq(F_191(x), F_192(x) + F_199(x))
Eq(F_192(x), F_193(x)/F_18(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), x*(x - 2)*(F_195(x) + 1)**2 + (x + 1)*(F_195(x) + 1) + F_195(x) - 1)
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_102(x)*F_18(x)*F_198(x))
Eq(F_198(x), F_195(x) + F_83(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_103(x)*F_18(x)*F_201(x))
Eq(F_201(x), F_202(x) + F_213(x))
Eq(F_202(x), F_203(x)*F_210(x))
Eq(F_203(x), F_204(x) + F_207(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_1(x) + F_18(x))
Eq(F_206(x), F_112(x) + F_145(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_149(x) + F_59(x))
Eq(F_209(x), F_137(x) + F_153(x))
Eq(F_210(x), F_211(x) + F_36(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_18(x)*F_39(x))
Eq(F_213(x), F_135(x)*F_87(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_103(x)*F_144(x)*F_186(x)*F_210(x))
Eq(F_216(x), F_217(x)/F_18(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_18(x)*F_187(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_103(x)*F_112(x)*F_186(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_103(x)*F_114(x)*F_186(x)*F_223(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_18(x)*F_225(x))
Eq(F_225(x), F_226(x) + F_236(x))
Eq(F_226(x), F_227(x) + F_228(x))
Eq(F_227(x), F_18(x)*F_36(x))
Eq(F_228(x), F_229(x))
Eq(F_229(x), F_18(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_151(x)*F_47(x))
Eq(F_232(x), F_233(x)*F_58(x))
Eq(F_233(x), F_226(x) + F_234(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_18(x)*F_226(x)*F_50(x))
Eq(F_236(x), F_237(x) + F_238(x))
Eq(F_237(x), F_18(x) + F_223(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_238(x) + F_241(x))
Eq(F_241(x), F_236(x) + F_242(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_18(x)*F_244(x))
Eq(F_244(x), F_245(x) + F_246(x))
Eq(F_245(x), F_236(x)*F_50(x))
Eq(F_246(x), F_247(x)*F_43(x))
Eq(F_247(x), F_248(x) + F_255(x))
Eq(F_248(x), F_237(x) + F_249(x))
Eq(F_249(x), F_250(x))
Eq(F_250(x), F_18(x)*F_251(x))
Eq(F_251(x), F_252(x) + F_254(x))
Eq(F_252(x), F_233(x) + F_253(x))
Eq(F_253(x), F_228(x))
Eq(F_254(x), F_240(x))
Eq(F_255(x), F_250(x))
Eq(F_256(x), F_210(x)*F_257(x))
Eq(F_257(x), F_258(x) - F_260(x))
Eq(F_258(x), F_259(x)/F_18(x))
Eq(F_259(x), F_98(x))
Eq(F_260(x), F_261(x)/F_18(x))
Eq(F_261(x), F_218(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 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"comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25263/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = 1/F[20,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[20,x]
F[11,x] = F[12,x]+F[21,x]
F[12,x] = F[13,x]+F[15,x]
F[13,x] = F[0,x]*F[14,x]
F[14,x] = -1+(x^2-2*x)*F[14,x]^2+(2+x)*F[14,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[20,x]*F[7,x]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[19,x,k[0]] = x^2*F[19,x,k[0]]^2*k[0]^2-2*x*F[19,x,k[0]]^2*k[0]+x*F[19,x,k[0]]*k[0]+2*F[19,x,k[0]]-1
F[20,x] = x
F[21,x] = F[22,x]+F[34,x]
F[22,x] = F[23,x]
F[23,x] = F[20,x]*F[24,x]*F[7,x]
F[24,x] = F[25,x,1]
F[26,x,k[0]] = F[25,x,k[0]]*F[31,x,k[0]]*F[32,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[28,x,k[0]] = F[19,x,k[0]]+F[27,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]*F[31,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = (x*(1+F[30,x,k[0]])*k[0]-2*F[30,x,k[0]])*(-1+x*(1+F[30,x,k[0]])*k[0])
F[31,x,k[0]] = k[0]*x
F[33,x,k[0]] = F[31,x,k[0]]*F[32,x,k[0]]
F[33,x,k[0]] = F[30,x,k[0]]
F[34,x] = F[35,x]
F[35,x] = F[20,x]*F[36,x]
F[36,x] = F[37,x,1]
F[37,x,k[0]] = (F[38,x,k[0]]*k[0]-F[38,x,1])/(-1+k[0])
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[20,x]*F[40,x]*F[49,x,k[0]]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[42,x]+F[9,x]
F[42,x] = F[43,x]
F[43,x] = F[20,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[14,x]*F[7,x]
F[48,x] = F[38,x,1]
F[50,x,k[0]] = F[20,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[20,x]*F[25,x,k[0]]*F[52,x]
F[52,x] = F[32,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_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{15}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x^{2} F_{14} \left(x \right)^{2}-2 x F_{14} \left(x \right)^{2}+F_{14}\! \left(x \right) x +2 F_{14}\! \left(x \right)-1
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y\right) = -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = x^{2} F_{19}\! \left(x , y\right)^{2} y^{2}-2 y x F_{19}\! \left(x , y\right)^{2}+x F_{19}\! \left(x , y\right) y +2 F_{19}\! \left(x , y\right)-1
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{31}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = x^{2} F_{30}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{30}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{30}\! \left(x , y\right)^{2} y -3 x F_{30}\! \left(x , y\right) y -y x +2 F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = y x
F_{33}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x , 1\right)
F_{37}\! \left(x , y\right) = -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{40}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{20}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{25}\! \left(x , y\right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{32}\! \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_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_20(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_20(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_20(x))
Eq(F_11(x), F_12(x) + F_21(x))
Eq(F_12(x), F_13(x) + F_15(x))
Eq(F_13(x), F_0(x)*F_14(x))
Eq(F_14(x), x*(x - 2)*F_14(x)**2 + (x + 2)*F_14(x) - 1)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_20(x)*F_7(x))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), k_0*x*(k_0*x - 2)*F_19(x, k_0)**2 + (k_0*x + 2)*F_19(x, k_0) - 1)
Eq(F_20(x), x)
Eq(F_21(x), F_22(x) + F_34(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_20(x)*F_24(x)*F_7(x))
Eq(F_24(x), F_25(x, 1))
Eq(F_26(x, k_0), F_25(x, k_0)*F_31(x, k_0)*F_32(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_28(x, k_0), F_19(x, k_0) + F_27(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0)*F_31(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), k_0*x*(k_0*x - 2)*(F_30(x, k_0) + 1)**2 + (k_0*x + 1)*(F_30(x, k_0) + 1) + F_30(x, k_0) - 1)
Eq(F_31(x, k_0), k_0*x)
Eq(F_33(x, k_0), F_31(x, k_0)*F_32(x, k_0))
Eq(F_33(x, k_0), F_30(x, k_0))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_20(x)*F_36(x))
Eq(F_36(x), F_37(x, 1))
Eq(F_37(x, k_0), (-k_0*F_38(x, k_0) + F_38(x, 1))/(1 - k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_20(x)*F_40(x)*F_49(x, k_0))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_9(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_20(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_14(x)*F_7(x))
Eq(F_48(x), F_38(x, 1))
Eq(F_50(x, k_0), F_20(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_20(x)*F_25(x, k_0)*F_52(x))
Eq(F_52(x), F_32(x, 1))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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[0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25439/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[64,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x]+F[68,x]
F[12,x] = F[13,x]*F[36,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = -F[62,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[24,x]+F[7,x]
F[24,x] = F[25,x]+F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[27,x]
F[27,x] = F[18,x]*F[28,x]
F[28,x] = 1/F[18,x]*F[29,x]
F[29,x] = F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[18,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]*F[34,x]
F[34,x] = F[35,x]+F[37,x]
F[35,x] = F[28,x]*F[36,x]
F[36,x] = -1+(x^2-2*x)*F[36,x]^2+(2+x)*F[36,x]
F[37,x] = F[38,x]
F[38,x] = F[18,x]*F[24,x]*F[39,x]
F[39,x] = 1/F[18,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[18,x]*F[43,x]*F[55,x]
F[43,x] = F[36,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[18,x]*F[46,x]
F[46,x] = F[44,x]+F[47,x]
F[47,x] = F[43,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[18,x]*F[43,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[36,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[18,x]*F[46,x]
F[54,x] = F[53,x]
F[55,x] = F[36,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]*F[61,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[18,x]*F[58,x]
F[61,x] = F[36,x]+F[41,x]
F[62,x] = F[63,x]
F[63,x] = -F[25,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = 1/F[18,x]*F[67,x]
F[67,x] = F[32,x]
F[68,x] = F[69,x]
F[69,x] = F[18,x]*F[70,x]*F[82,x]
F[70,x] = 1/F[18,x]/F[36,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = 1/F[18,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[75,x]+F[64,x]
F[75,x] = F[26,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[18,x]*F[78,x]
F[78,x] = 1/F[18,x]/F[55,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[37,x]
F[82,x] = F[36,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[18,x]*F[85,x]
F[85,x] = 1/F[18,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = 1/F[103,x]/F[114,x]/F[186,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[256,x]+F[90,x]
F[90,x] = 1/F[18,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[221,x]+F[93,x]
F[93,x] = F[195,x]*F[94,x]
F[94,x] = -F[219,x]+F[95,x]
F[95,x] = -F[216,x]+F[96,x]
F[96,x] = 1/F[18,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[18,x]*F[99,x]
F[99,x] = F[100,x]+F[187,x]
F[100,x] = F[101,x]+F[184,x]
F[101,x] = F[102,x]*F[114,x]
F[102,x] = F[103,x]+F[132,x]
F[103,x] = F[1,x]+F[104,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[18,x]
F[106,x] = F[107,x]+F[115,x]
F[107,x] = F[1,x]+F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[18,x]
F[110,x] = F[107,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[18,x]
F[114,x] = F[1,x]+F[112,x]
F[115,x] = F[104,x]+F[116,x]
F[116,x] = F[117,x]+F[118,x]+F[122,x]
F[117,x] = 0
F[118,x] = F[119,x]*F[18,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[108,x]
F[121,x] = F[116,x]
F[122,x] = F[123,x]*F[18,x]
F[123,x] = F[115,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[117,x]+F[126,x]+F[130,x]
F[126,x] = F[127,x]*F[18,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[112,x]
F[129,x] = F[125,x]
F[130,x] = F[131,x]*F[18,x]
F[131,x] = F[104,x]+F[125,x]
F[132,x] = F[133,x]+F[141,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[18,x]
F[135,x] = F[114,x]+F[136,x]
F[136,x] = F[137,x]+F[59,x]
F[137,x] = F[117,x]+F[138,x]+F[140,x]
F[138,x] = F[139,x]*F[18,x]
F[139,x] = F[112,x]+F[137,x]
F[140,x] = F[136,x]*F[18,x]
F[141,x] = F[117,x]+F[142,x]+F[158,x]
F[142,x] = F[143,x]*F[18,x]
F[143,x] = F[144,x]+F[148,x]
F[144,x] = F[145,x]+F[18,x]
F[145,x] = F[117,x]+F[146,x]+F[147,x]
F[146,x] = F[144,x]*F[18,x]
F[147,x] = F[112,x]*F[18,x]
F[148,x] = F[149,x]+F[153,x]
F[149,x] = F[117,x]+F[150,x]+F[152,x]
F[150,x] = F[151,x]*F[18,x]
F[151,x] = F[149,x]+F[18,x]
F[152,x] = F[18,x]*F[59,x]
F[153,x] = F[117,x]+F[154,x]+F[156,x]+F[157,x]
F[154,x] = F[155,x]*F[18,x]
F[155,x] = F[145,x]+F[153,x]
F[156,x] = F[148,x]*F[18,x]
F[157,x] = F[137,x]*F[18,x]
F[158,x] = F[159,x]*F[18,x]
F[159,x] = F[160,x]+F[168,x]
F[160,x] = F[133,x]+F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[18,x]
F[163,x] = F[160,x]+F[164,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[18,x]
F[167,x] = F[133,x]+F[165,x]
F[168,x] = F[141,x]+F[169,x]
F[169,x] = 2*F[117,x]+F[170,x]+F[174,x]
F[170,x] = F[171,x]*F[18,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[161,x]
F[173,x] = F[169,x]
F[174,x] = F[175,x]*F[18,x]
F[175,x] = F[168,x]+F[176,x]
F[176,x] = F[177,x]
F[177,x] = 2*F[117,x]+F[178,x]+F[182,x]
F[178,x] = F[179,x]*F[18,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[165,x]
F[181,x] = F[177,x]
F[182,x] = F[18,x]*F[183,x]
F[183,x] = F[141,x]+F[177,x]
F[184,x] = F[185,x]
F[185,x] = F[103,x]*F[144,x]*F[186,x]
F[186,x] = F[1,x]+F[133,x]
F[187,x] = F[188,x]
F[188,x] = F[18,x]*F[189,x]
F[189,x] = F[190,x]+F[214,x]
F[190,x] = F[114,x]*F[191,x]
F[191,x] = F[192,x]+F[199,x]
F[192,x] = 1/F[18,x]*F[193,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = (x*F[195,x]+x-1)*(x*F[195,x]+x-2*F[195,x])
F[196,x] = F[197,x]
F[197,x] = F[102,x]*F[18,x]*F[198,x]
F[198,x] = F[195,x]+F[83,x]
F[199,x] = F[200,x]
F[200,x] = F[103,x]*F[18,x]*F[201,x]
F[201,x] = F[202,x]+F[213,x]
F[202,x] = F[203,x]*F[210,x]
F[203,x] = F[204,x]+F[207,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[1,x]+F[18,x]
F[206,x] = F[112,x]+F[145,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[149,x]+F[59,x]
F[209,x] = F[137,x]+F[153,x]
F[210,x] = F[211,x]+F[36,x]
F[211,x] = F[212,x]
F[212,x] = F[18,x]*F[39,x]
F[213,x] = F[135,x]*F[87,x]
F[214,x] = F[215,x]
F[215,x] = F[103,x]*F[144,x]*F[186,x]*F[210,x]
F[216,x] = 1/F[18,x]*F[217,x]
F[217,x] = F[218,x]
F[218,x] = F[18,x]*F[187,x]
F[219,x] = F[220,x]
F[220,x] = F[103,x]*F[112,x]*F[186,x]
F[221,x] = F[222,x]
F[222,x] = F[103,x]*F[114,x]*F[186,x]*F[223,x]
F[223,x] = F[224,x]
F[224,x] = F[18,x]*F[225,x]
F[225,x] = F[226,x]+F[236,x]
F[226,x] = F[227,x]+F[228,x]
F[227,x] = F[18,x]*F[36,x]
F[228,x] = F[229,x]
F[229,x] = F[18,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[151,x]*F[47,x]
F[232,x] = F[233,x]*F[58,x]
F[233,x] = F[226,x]+F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[18,x]*F[226,x]*F[50,x]
F[236,x] = F[237,x]+F[238,x]
F[237,x] = F[18,x]+F[223,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = F[238,x]+F[241,x]
F[241,x] = F[236,x]+F[242,x]
F[242,x] = F[243,x]
F[243,x] = F[18,x]*F[244,x]
F[244,x] = F[245,x]+F[246,x]
F[245,x] = F[236,x]*F[50,x]
F[246,x] = F[247,x]*F[43,x]
F[247,x] = F[248,x]+F[255,x]
F[248,x] = F[237,x]+F[249,x]
F[249,x] = F[250,x]
F[250,x] = F[18,x]*F[251,x]
F[251,x] = F[252,x]+F[254,x]
F[252,x] = F[233,x]+F[253,x]
F[253,x] = F[228,x]
F[254,x] = F[240,x]
F[255,x] = F[250,x]
F[256,x] = F[210,x]*F[257,x]
F[257,x] = -F[260,x]+F[258,x]
F[258,x] = 1/F[18,x]*F[259,x]
F[259,x] = F[98,x]
F[260,x] = 1/F[18,x]*F[261,x]
F[261,x] = F[218,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{64}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = x^{2} F_{36} \left(x \right)^{2}-2 x F_{36} \left(x \right)^{2}+F_{36}\! \left(x \right) x +2 F_{36}\! \left(x \right)-1
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{18}\! \left(x \right) F_{24}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{55}\! \left(x \right)
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{36}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right) F_{46}\! \left(x \right)
F_{54}\! \left(x \right) = F_{53}\! \left(x \right)
F_{55}\! \left(x \right) = F_{36}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{32}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{70}\! \left(x \right) F_{82}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right) F_{36}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{64}\! \left(x \right)
F_{75}\! \left(x \right) = F_{26}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{18}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{18}\! \left(x \right) F_{55}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{37}\! \left(x \right)
F_{82}\! \left(x \right) = F_{36}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{256}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{221}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{195}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{219}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{216}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{18}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{187}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{184}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{114}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{132}\! \left(x \right)
F_{103}\! \left(x \right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{18}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{115}\! \left(x \right)
F_{107}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{18}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{18}\! \left(x \right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)
F_{115}\! \left(x \right) = F_{104}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = 0
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{18}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{108}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{18}\! \left(x \right)
F_{123}\! \left(x \right) = F_{115}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{117}\! \left(x \right)+F_{126}\! \left(x \right)+F_{130}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{18}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{112}\! \left(x \right)
F_{129}\! \left(x \right) = F_{125}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{18}\! \left(x \right)
F_{131}\! \left(x \right) = F_{104}\! \left(x \right)+F_{125}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{141}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{18}\! \left(x \right)
F_{135}\! \left(x \right) = F_{114}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{59}\! \left(x \right)
F_{137}\! \left(x \right) = F_{117}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{18}\! \left(x \right)
F_{139}\! \left(x \right) = F_{112}\! \left(x \right)+F_{137}\! \left(x \right)
F_{140}\! \left(x \right) = F_{136}\! \left(x \right) F_{18}\! \left(x \right)
F_{141}\! \left(x \right) = F_{117}\! \left(x \right)+F_{142}\! \left(x \right)+F_{158}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{18}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{148}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{117}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right) F_{18}\! \left(x \right)
F_{147}\! \left(x \right) = F_{112}\! \left(x \right) F_{18}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{149}\! \left(x \right) = F_{117}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{18}\! \left(x \right)
F_{151}\! \left(x \right) = F_{149}\! \left(x \right)+F_{18}\! \left(x \right)
F_{152}\! \left(x \right) = F_{18}\! \left(x \right) F_{59}\! \left(x \right)
F_{153}\! \left(x \right) = F_{117}\! \left(x \right)+F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{18}\! \left(x \right)
F_{155}\! \left(x \right) = F_{145}\! \left(x \right)+F_{153}\! \left(x \right)
F_{156}\! \left(x \right) = F_{148}\! \left(x \right) F_{18}\! \left(x \right)
F_{157}\! \left(x \right) = F_{137}\! \left(x \right) F_{18}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{18}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{168}\! \left(x \right)
F_{160}\! \left(x \right) = F_{133}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{18}\! \left(x \right)
F_{163}\! \left(x \right) = F_{160}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{18}\! \left(x \right)
F_{167}\! \left(x \right) = F_{133}\! \left(x \right)+F_{165}\! \left(x \right)
F_{168}\! \left(x \right) = F_{141}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = 2 F_{117}\! \left(x \right)+F_{170}\! \left(x \right)+F_{174}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{18}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{161}\! \left(x \right)
F_{173}\! \left(x \right) = F_{169}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{18}\! \left(x \right)
F_{175}\! \left(x \right) = F_{168}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = 2 F_{117}\! \left(x \right)+F_{178}\! \left(x \right)+F_{182}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{18}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{165}\! \left(x \right)
F_{181}\! \left(x \right) = F_{177}\! \left(x \right)
F_{182}\! \left(x \right) = F_{18}\! \left(x \right) F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{141}\! \left(x \right)+F_{177}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{18}\! \left(x \right) F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{214}\! \left(x \right)
F_{190}\! \left(x \right) = F_{114}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{199}\! \left(x \right)
F_{192}\! \left(x \right) = \frac{F_{193}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = x^{2} F_{195} \left(x \right)^{2}+2 x^{2} F_{195}\! \left(x \right)-2 x F_{195} \left(x \right)^{2}+x^{2}-3 x F_{195}\! \left(x \right)-x +2 F_{195}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{102}\! \left(x \right) F_{18}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{195}\! \left(x \right)+F_{83}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{103}\! \left(x \right) F_{18}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{213}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{210}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)+F_{207}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{206}\! \left(x \right) = F_{112}\! \left(x \right)+F_{145}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{149}\! \left(x \right)+F_{59}\! \left(x \right)
F_{209}\! \left(x \right) = F_{137}\! \left(x \right)+F_{153}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{36}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{18}\! \left(x \right) F_{39}\! \left(x \right)
F_{213}\! \left(x \right) = F_{135}\! \left(x \right) F_{87}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right) F_{210}\! \left(x \right)
F_{216}\! \left(x \right) = \frac{F_{217}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{18}\! \left(x \right) F_{187}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{103}\! \left(x \right) F_{112}\! \left(x \right) F_{186}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{18}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)+F_{236}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{228}\! \left(x \right)
F_{227}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{18}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{151}\! \left(x \right) F_{47}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{58}\! \left(x \right)
F_{233}\! \left(x \right) = F_{226}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{18}\! \left(x \right) F_{226}\! \left(x \right) F_{50}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{238}\! \left(x \right)
F_{237}\! \left(x \right) = F_{18}\! \left(x \right)+F_{223}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{238}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{236}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{18}\! \left(x \right) F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)+F_{246}\! \left(x \right)
F_{245}\! \left(x \right) = F_{236}\! \left(x \right) F_{50}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{43}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{255}\! \left(x \right)
F_{248}\! \left(x \right) = F_{237}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{18}\! \left(x \right) F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{254}\! \left(x \right)
F_{252}\! \left(x \right) = F_{233}\! \left(x \right)+F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{228}\! \left(x \right)
F_{254}\! \left(x \right) = F_{240}\! \left(x \right)
F_{255}\! \left(x \right) = F_{250}\! \left(x \right)
F_{256}\! \left(x \right) = F_{210}\! \left(x \right) F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = -F_{260}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = \frac{F_{259}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{259}\! \left(x \right) = F_{98}\! \left(x \right)
F_{260}\! \left(x \right) = \frac{F_{261}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{261}\! \left(x \right) = F_{218}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_64(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_68(x))
Eq(F_12(x), F_13(x)*F_36(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), F_22(x) - F_62(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_24(x) + F_7(x))
Eq(F_24(x), F_25(x) + F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_18(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_18(x))
Eq(F_29(x), F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_18(x)*F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_37(x))
Eq(F_35(x), F_28(x)*F_36(x))
Eq(F_36(x), x*(x - 2)*F_36(x)**2 + (x + 2)*F_36(x) - 1)
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_18(x)*F_24(x)*F_39(x))
Eq(F_39(x), F_40(x)/F_18(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_18(x)*F_43(x)*F_55(x))
Eq(F_43(x), F_36(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_18(x)*F_46(x))
Eq(F_46(x), F_44(x) + F_47(x))
Eq(F_47(x), F_43(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_18(x)*F_43(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_36(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_18(x)*F_46(x))
Eq(F_54(x), F_53(x))
Eq(F_55(x), F_36(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x)*F_61(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_18(x)*F_58(x))
Eq(F_61(x), F_36(x) + F_41(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), -F_25(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_67(x)/F_18(x))
Eq(F_67(x), F_32(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_18(x)*F_70(x)*F_82(x))
Eq(F_70(x), F_71(x)/(F_18(x)*F_36(x)))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x)/F_18(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_64(x) - F_75(x))
Eq(F_75(x), F_26(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_18(x)*F_78(x))
Eq(F_78(x), F_79(x)/(F_18(x)*F_55(x)))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_37(x))
Eq(F_82(x), F_36(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_18(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_18(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x)/(F_103(x)*F_114(x)*F_186(x)))
Eq(F_88(x), F_89(x))
Eq(F_89(x), -F_256(x) + F_90(x))
Eq(F_90(x), F_91(x)/F_18(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_221(x) + F_93(x))
Eq(F_93(x), F_195(x)*F_94(x))
Eq(F_94(x), -F_219(x) + F_95(x))
Eq(F_95(x), -F_216(x) + F_96(x))
Eq(F_96(x), F_97(x)/F_18(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_18(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_187(x))
Eq(F_100(x), F_101(x) + F_184(x))
Eq(F_101(x), F_102(x)*F_114(x))
Eq(F_102(x), F_103(x) + F_132(x))
Eq(F_103(x), F_1(x) + F_104(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_18(x))
Eq(F_106(x), F_107(x) + F_115(x))
Eq(F_107(x), F_1(x) + F_108(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_18(x))
Eq(F_110(x), F_107(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_18(x))
Eq(F_114(x), F_1(x) + F_112(x))
Eq(F_115(x), F_104(x) + F_116(x))
Eq(F_116(x), F_117(x) + F_118(x) + F_122(x))
Eq(F_117(x), 0)
Eq(F_118(x), F_119(x)*F_18(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_108(x))
Eq(F_121(x), F_116(x))
Eq(F_122(x), F_123(x)*F_18(x))
Eq(F_123(x), F_115(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_117(x) + F_126(x) + F_130(x))
Eq(F_126(x), F_127(x)*F_18(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_112(x))
Eq(F_129(x), F_125(x))
Eq(F_130(x), F_131(x)*F_18(x))
Eq(F_131(x), F_104(x) + F_125(x))
Eq(F_132(x), F_133(x) + F_141(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_18(x))
Eq(F_135(x), F_114(x) + F_136(x))
Eq(F_136(x), F_137(x) + F_59(x))
Eq(F_137(x), F_117(x) + F_138(x) + F_140(x))
Eq(F_138(x), F_139(x)*F_18(x))
Eq(F_139(x), F_112(x) + F_137(x))
Eq(F_140(x), F_136(x)*F_18(x))
Eq(F_141(x), F_117(x) + F_142(x) + F_158(x))
Eq(F_142(x), F_143(x)*F_18(x))
Eq(F_143(x), F_144(x) + F_148(x))
Eq(F_144(x), F_145(x) + F_18(x))
Eq(F_145(x), F_117(x) + F_146(x) + F_147(x))
Eq(F_146(x), F_144(x)*F_18(x))
Eq(F_147(x), F_112(x)*F_18(x))
Eq(F_148(x), F_149(x) + F_153(x))
Eq(F_149(x), F_117(x) + F_150(x) + F_152(x))
Eq(F_150(x), F_151(x)*F_18(x))
Eq(F_151(x), F_149(x) + F_18(x))
Eq(F_152(x), F_18(x)*F_59(x))
Eq(F_153(x), F_117(x) + F_154(x) + F_156(x) + F_157(x))
Eq(F_154(x), F_155(x)*F_18(x))
Eq(F_155(x), F_145(x) + F_153(x))
Eq(F_156(x), F_148(x)*F_18(x))
Eq(F_157(x), F_137(x)*F_18(x))
Eq(F_158(x), F_159(x)*F_18(x))
Eq(F_159(x), F_160(x) + F_168(x))
Eq(F_160(x), F_133(x) + F_161(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_18(x))
Eq(F_163(x), F_160(x) + F_164(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_18(x))
Eq(F_167(x), F_133(x) + F_165(x))
Eq(F_168(x), F_141(x) + F_169(x))
Eq(F_169(x), 2*F_117(x) + F_170(x) + F_174(x))
Eq(F_170(x), F_171(x)*F_18(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_161(x))
Eq(F_173(x), F_169(x))
Eq(F_174(x), F_175(x)*F_18(x))
Eq(F_175(x), F_168(x) + F_176(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), 2*F_117(x) + F_178(x) + F_182(x))
Eq(F_178(x), F_179(x)*F_18(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_165(x))
Eq(F_181(x), F_177(x))
Eq(F_182(x), F_18(x)*F_183(x))
Eq(F_183(x), F_141(x) + F_177(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_103(x)*F_144(x)*F_186(x))
Eq(F_186(x), F_1(x) + F_133(x))
Eq(F_187(x), F_188(x))
Eq(F_188(x), F_18(x)*F_189(x))
Eq(F_189(x), F_190(x) + F_214(x))
Eq(F_190(x), F_114(x)*F_191(x))
Eq(F_191(x), F_192(x) + F_199(x))
Eq(F_192(x), F_193(x)/F_18(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), x*(x - 2)*(F_195(x) + 1)**2 + (x + 1)*(F_195(x) + 1) + F_195(x) - 1)
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_102(x)*F_18(x)*F_198(x))
Eq(F_198(x), F_195(x) + F_83(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_103(x)*F_18(x)*F_201(x))
Eq(F_201(x), F_202(x) + F_213(x))
Eq(F_202(x), F_203(x)*F_210(x))
Eq(F_203(x), F_204(x) + F_207(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_1(x) + F_18(x))
Eq(F_206(x), F_112(x) + F_145(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_149(x) + F_59(x))
Eq(F_209(x), F_137(x) + F_153(x))
Eq(F_210(x), F_211(x) + F_36(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_18(x)*F_39(x))
Eq(F_213(x), F_135(x)*F_87(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_103(x)*F_144(x)*F_186(x)*F_210(x))
Eq(F_216(x), F_217(x)/F_18(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_18(x)*F_187(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_103(x)*F_112(x)*F_186(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_103(x)*F_114(x)*F_186(x)*F_223(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_18(x)*F_225(x))
Eq(F_225(x), F_226(x) + F_236(x))
Eq(F_226(x), F_227(x) + F_228(x))
Eq(F_227(x), F_18(x)*F_36(x))
Eq(F_228(x), F_229(x))
Eq(F_229(x), F_18(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_151(x)*F_47(x))
Eq(F_232(x), F_233(x)*F_58(x))
Eq(F_233(x), F_226(x) + F_234(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_18(x)*F_226(x)*F_50(x))
Eq(F_236(x), F_237(x) + F_238(x))
Eq(F_237(x), F_18(x) + F_223(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_238(x) + F_241(x))
Eq(F_241(x), F_236(x) + F_242(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_18(x)*F_244(x))
Eq(F_244(x), F_245(x) + F_246(x))
Eq(F_245(x), F_236(x)*F_50(x))
Eq(F_246(x), F_247(x)*F_43(x))
Eq(F_247(x), F_248(x) + F_255(x))
Eq(F_248(x), F_237(x) + F_249(x))
Eq(F_249(x), F_250(x))
Eq(F_250(x), F_18(x)*F_251(x))
Eq(F_251(x), F_252(x) + F_254(x))
Eq(F_252(x), F_233(x) + F_253(x))
Eq(F_253(x), F_228(x))
Eq(F_254(x), F_240(x))
Eq(F_255(x), F_250(x))
Eq(F_256(x), F_210(x)*F_257(x))
Eq(F_257(x), F_258(x) - F_260(x))
Eq(F_258(x), F_259(x)/F_18(x))
Eq(F_259(x), F_98(x))
Eq(F_260(x), F_261(x)/F_18(x))
Eq(F_261(x), F_218(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 1], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [2, 1], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": 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