0132_2301
Counting sequence:
1, 1, 2, 6, 22, 86, 337, 1295, 4854, 17760, 63594, 223488, 772841, 2635733, 8882042, 29622114, 97901974, 321016826, 1045294921, 3382803539, 10887874254, 34873641228, 111215129370, 353295398148, 1118381630705, 3529144183433, 11104719198770, 34851434248542, 109121784244342, 340934806542302, 1063118478620257, 3309139515711095, 10283396319967974, 31908356550079320, 98871477001767210, 305973242319212616, 945767074458153497, 2920193276017035293, 9007418532635812394, 27757594666666440186, 85464258849946496182, 262926464170669091330, 808266629456504527513, 2482944292036221877115, 7622383453080231352638, 23385351836300627110980, 71703870541275291559578, 219736276734716957890764, 673030963283762794321505, 2060416286669711780429969, 6304825309205749837039970, 19284122620355274546363702, 58958334811569231105783382, 180184750518058002298234982, 550461148332002932843552753, 1681042993353961990906798943, 5131940470634319525365517270, 15661799353673695745349393360, 47782086187338928210675464042, 145732926936637875785041112208, 444349535715755974345846371785, 1354475696227692508955522499557, 4127639890890911024113736825306, 12575372028666373361889327339282, 38302967933845526750981840687446, 116638088369411384507090815758602, 355098100977057848254938019334761, 1080835734897549445987189217650211, 3289104211583442351844056708332718, 10007029789323880771807999701936636, 30440041004731752308798145418536858, 92576437639085773671118792244193684, 281496796765113766915583548187178065, 855788898403574236268527191419666969, 2601251573882240843497269840548486546, 7905380632621211523301919678431939470, 24020942158494700266835262908916500918, 72977018406658664401216672436119953902, 221673068237705285174062898659028196865, 673243727936313761676011824385007014855, 2044400672289183363986378902385923626438, 6207199498589030177181195572868419075784, 18843561391878972633165496262417495384874, 57196493399324369726639353747831699992024, 173586694247398816014893939506680389531129, 526751150824527657895047321040134186101549, 1598225114566286996137186308381244502253194, 4848586188574786779519654698548184778777258, 14707479982409901726415304963884694828575606, 44607574359777057117883702378670924824828178, 135278046266215285943787028685090609723956921, 410199893657097205705855556229980763236105291, 1243696369869459377014153186383960534369370398, 3770377633195327608062534642625652199053935156, 11428994335198487750445887543215183698944562714, 34640556234297835477345545771891795839638132572, 104982358718441261649049489904180455320954101441, 318129066756145754838455888815517929230490939169, 963932959401370448511278019988914155621518124738, 2920435586447410712308367529717257507606885606502, 8847215361245364935842603691145241075984923951766
Generating function in Maple syntax:
-(2*x-1)*(14*x^8-82*x^7+260*x^6-447*x^5+438*x^4-249*x^3+81*x^2-14*x+1)/(x-1)^2/(3*x-1)^2/(x^2-3*x+1)^3
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(14 x^{8}-82 x^{7}+260 x^{6}-447 x^{5}+438 x^{4}-249 x^{3}+81 x^{2}-14 x +1\right)}{\left(x -1\right)^{2} \left(3 x -1\right)^{2} \left(x^{2}-3 x +1\right)^{3}}
Generating function in sympy syntax:
(1 - 2*x)*(14*x**8 - 82*x**7 + 260*x**6 - 447*x**5 + 438*x**4 - 249*x**3 + 81*x**2 - 14*x + 1)/((x - 1)**2*(3*x - 1)**2*(x**2 - 3*x + 1)**3)
Implicit equation for the generating function in Maple syntax:
(x-1)^2*(3*x-1)^2*(x^2-3*x+1)^3*F(x)+(2*x-1)*(14*x^8-82*x^7+260*x^6-447*x^5+438*x^4-249*x^3+81*x^2-14*x+1) = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{2} \left(3 x -1\right)^{2} \left(x^{2}-3 x +1\right)^{3} F \! \left(x \right)+\left(2 x -1\right) \left(14 x^{8}-82 x^{7}+260 x^{6}-447 x^{5}+438 x^{4}-249 x^{3}+81 x^{2}-14 x +1\right) = 0
Explicit closed form in Maple syntax:
147/100*(((n^2+8/5*n+391/105)*5^(1/2)-47/21*n^2-76/21*n-293/35)*(3/2-1/2*5^(1/2))^(-n)+((-2/5*n-41/105)*5^(1/2)+2/21*n^2+22/21*n+43/35)*(3/2+1/2*5^(1/2))^(-n)+5/18*((n+3)*3^n+3*n-9)*(5^(1/2)-15/7))*(15/7+5^(1/2))
Explicit closed form in latex syntax:
\frac{147 \left(\left(\left(n^{2}+\frac{8}{5} n +\frac{391}{105}\right) \sqrt{5}-\frac{47 n^{2}}{21}-\frac{76 n}{21}-\frac{293}{35}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}+\left(\left(-\frac{2 n}{5}-\frac{41}{105}\right) \sqrt{5}+\frac{2 n^{2}}{21}+\frac{22 n}{21}+\frac{43}{35}\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}+\frac{5 \left(\left(n +3\right) 3^{n}+3 n -9\right) \left(\sqrt{5}-\frac{15}{7}\right)}{18}\right) \left(\frac{15}{7}+\sqrt{5}\right)}{100}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 86
a(6) = 337
a(7) = 1295
a(8) = 4854
a(9) = 17760
a(n+8) = -9*a(n)+87*a(n+1)-325*a(n+2)+594*a(n+3)-570*a(n+4)+306*a(n+5)-93*a(n+6)+15*a(n+7)-2*n+2, n >= 10
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 86
a \! \left(6\right) = 337
a \! \left(7\right) = 1295
a \! \left(8\right) = 4854
a \! \left(9\right) = 17760
a \! \left(n +8\right) = -9 a \! \left(n \right)+87 a \! \left(n +1\right)-325 a \! \left(n +2\right)+594 a \! \left(n +3\right)-570 a \! \left(n +4\right)+306 a \! \left(n +5\right)-93 a \! \left(n +6\right)+15 a \! \left(n +7\right)-2 n +2, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/87/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[76,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[45,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[15,x]
F[14,x] = x
F[15,x] = F[1,x]+F[12,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[10,x]+F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[14,x]*F[23,x]
F[23,x] = F[24,x]+F[40,x]
F[24,x] = F[15,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[14,x]*F[15,x]*F[27,x]
F[27,x] = F[24,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[14,x]*F[24,x]*F[30,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[31,x]
F[34,x] = F[12,x]+F[35,x]
F[35,x] = F[36,x]+F[37,x]+F[39,x]
F[36,x] = 0
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[32,x]+F[35,x]
F[39,x] = F[14,x]*F[34,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[23,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[14,x]*F[15,x]*F[42,x]
F[45,x] = F[46,x]
F[46,x] = F[14,x]*F[47,x]
F[47,x] = F[48,x]+F[63,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[14,x]*F[15,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[14,x]*F[53,x]*F[57,x]
F[53,x] = F[15,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[15,x]*F[56,x]
F[56,x] = F[51,x]+F[53,x]
F[57,x] = F[31,x]+F[58,x]
F[58,x] = F[12,x]+F[59,x]
F[59,x] = F[36,x]+F[60,x]+F[62,x]
F[60,x] = F[14,x]*F[61,x]
F[61,x] = F[32,x]+F[59,x]
F[62,x] = F[14,x]*F[58,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[14,x]*F[15,x]*F[65,x]
F[65,x] = F[66,x]+F[75,x]
F[66,x] = F[67,x]+F[73,x]
F[67,x] = F[15,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[15,x]*F[70,x]
F[70,x] = F[57,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[14,x]*F[57,x]*F[65,x]
F[73,x] = F[74,x]
F[74,x] = F[14,x]*F[15,x]*F[65,x]
F[75,x] = F[51,x]
F[76,x] = F[77,x]+F[83,x]
F[77,x] = F[78,x]
F[78,x] = F[14,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[12,x]+F[77,x]
F[81,x] = F[76,x]+F[82,x]
F[82,x] = F[12,x]*F[53,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[76,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[14,x]*F[43,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[14,x]*F[15,x]*F[91,x]
F[91,x] = F[92,x]+F[98,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[15,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[15,x]*F[92,x]
F[96,x] = F[97,x]
F[97,x] = F[14,x]*F[15,x]*F[91,x]
F[98,x] = F[28,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{76}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{40}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{23}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{63}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right) F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{15}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{36}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{32}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{75}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{57}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{57}\! \left(x \right) F_{65}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{75}\! \left(x \right) = F_{51}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{83}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right)+F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{76}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{15}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{92}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{91}\! \left(x \right)
F_{98}\! \left(x \right) = F_{28}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_76(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_45(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_1(x) + F_12(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_10(x) + F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_14(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_40(x))
Eq(F_24(x), F_15(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_14(x)*F_15(x)*F_27(x))
Eq(F_27(x), F_24(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_14(x)*F_24(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_31(x))
Eq(F_34(x), F_12(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_39(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_32(x) + F_35(x))
Eq(F_39(x), F_14(x)*F_34(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_23(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_14(x)*F_15(x)*F_42(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_14(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_63(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_14(x)*F_15(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_14(x)*F_53(x)*F_57(x))
Eq(F_53(x), F_15(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_15(x)*F_56(x))
Eq(F_56(x), F_51(x) + F_53(x))
Eq(F_57(x), F_31(x) + F_58(x))
Eq(F_58(x), F_12(x) + F_59(x))
Eq(F_59(x), F_36(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_14(x)*F_61(x))
Eq(F_61(x), F_32(x) + F_59(x))
Eq(F_62(x), F_14(x)*F_58(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_14(x)*F_15(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_75(x))
Eq(F_66(x), F_67(x) + F_73(x))
Eq(F_67(x), F_15(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_15(x)*F_70(x))
Eq(F_70(x), F_57(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_14(x)*F_57(x)*F_65(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_14(x)*F_15(x)*F_65(x))
Eq(F_75(x), F_51(x))
Eq(F_76(x), F_77(x) + F_83(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_14(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_12(x) + F_77(x))
Eq(F_81(x), F_76(x) + F_82(x))
Eq(F_82(x), F_12(x)*F_53(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_76(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_14(x)*F_43(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_14(x)*F_15(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_98(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_15(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_15(x)*F_92(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_14(x)*F_15(x)*F_91(x))
Eq(F_98(x), F_28(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": 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{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/88/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[14,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]+F[246,x]
F[15,x] = F[16,x]+F[236,x]
F[16,x] = F[11,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[19,x]
F[19,x] = F[20,x]+F[217,x]
F[20,x] = F[21,x]+F[41,x]
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[26,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[13,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[23,x]*F[26,x]
F[34,x] = F[22,x]*F[35,x]
F[35,x] = F[11,x]+F[36,x]
F[36,x] = F[37,x]+F[38,x]+F[40,x]
F[37,x] = 0
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[27,x]+F[36,x]
F[40,x] = F[13,x]*F[35,x]
F[41,x] = F[17,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[13,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[10,x]*F[17,x]
F[46,x] = F[207,x]+F[47,x]
F[47,x] = F[200,x]+F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[50,x]
F[50,x] = F[13,x]*F[51,x]
F[51,x] = F[11,x]+F[49,x]
F[52,x] = F[53,x]
F[53,x] = F[10,x]*F[11,x]*F[13,x]*F[54,x]
F[54,x] = F[23,x]+F[55,x]
F[55,x] = F[11,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[13,x]*F[58,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[55,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[10,x]*F[11,x]*F[23,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[11,x]*F[64,x]
F[64,x] = F[22,x]+F[55,x]
F[65,x] = F[66,x]
F[66,x] = F[10,x]*F[67,x]
F[67,x] = F[56,x]+F[68,x]
F[68,x] = F[11,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[71,x]
F[71,x] = F[72,x]+F[82,x]
F[72,x] = F[23,x]+F[73,x]
F[73,x] = F[11,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[13,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[10,x]*F[73,x]
F[78,x] = F[11,x]*F[79,x]
F[79,x] = F[77,x]+F[80,x]
F[80,x] = F[22,x]+F[81,x]
F[81,x] = F[10,x]*F[23,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[11,x]*F[23,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[37,x]+F[86,x]+F[88,x]
F[86,x] = F[13,x]*F[87,x]
F[87,x] = F[11,x]+F[85,x]
F[88,x] = F[13,x]*F[89,x]
F[89,x] = F[11,x]+F[85,x]
F[90,x] = F[91,x]
F[91,x] = F[13,x]*F[92,x]
F[92,x] = F[169,x]+F[93,x]
F[93,x] = F[104,x]+F[94,x]
F[94,x] = F[101,x]+F[37,x]+F[95,x]
F[95,x] = F[13,x]*F[96,x]
F[96,x] = F[37,x]+F[95,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[26,x]*F[99,x]
F[99,x] = F[100,x]+F[26,x]+F[97,x]
F[100,x] = F[13,x]*F[99,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[13,x]*F[26,x]
F[103,x] = F[100,x]+F[101,x]+F[37,x]
F[104,x] = F[105,x]+F[90,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[13,x]
F[107,x] = F[108,x]+F[140,x]
F[108,x] = F[109,x]+F[127,x]
F[109,x] = F[11,x]*F[110,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[27,x]^2
F[112,x] = F[113,x]+F[116,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[23,x]*F[27,x]
F[115,x] = F[26,x]*F[30,x]
F[116,x] = F[117,x]*F[27,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[13,x]
F[119,x] = F[120,x]+F[125,x]
F[120,x] = F[11,x]+F[121,x]
F[121,x] = F[122,x]+F[124,x]+F[37,x]
F[122,x] = F[123,x]*F[13,x]
F[123,x] = F[121,x]+F[27,x]
F[124,x] = F[120,x]*F[13,x]
F[125,x] = F[126,x]*F[23,x]
F[126,x] = F[120,x]+F[26,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[27,x]^2*F[85,x]
F[129,x] = F[130,x]+F[133,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[27,x]*F[90,x]
F[132,x] = F[105,x]*F[26,x]
F[133,x] = F[134,x]*F[27,x]
F[134,x] = F[135,x]
F[135,x] = F[13,x]*F[136,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[11,x]*F[26,x]*F[85,x]
F[138,x] = F[10,x]*F[139,x]
F[139,x] = F[134,x]+F[90,x]
F[140,x] = F[11,x]*F[141,x]
F[141,x] = F[108,x]+F[142,x]
F[142,x] = F[110,x]+F[143,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[27,x]^2*F[11,x]
F[145,x] = F[146,x]+F[151,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[27,x]*F[74,x]
F[148,x] = F[149,x]*F[26,x]
F[149,x] = F[150,x]
F[150,x] = F[13,x]*F[142,x]
F[151,x] = F[152,x]*F[27,x]
F[152,x] = F[153,x]
F[153,x] = F[13,x]*F[154,x]
F[154,x] = F[155,x]+F[156,x]
F[155,x] = F[27,x]*F[73,x]
F[156,x] = F[157,x]+F[168,x]
F[157,x] = F[158,x]+F[162,x]
F[158,x] = F[11,x]*F[159,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[22,x]*F[27,x]
F[161,x] = F[26,x]*F[27,x]
F[162,x] = F[163,x]+F[167,x]
F[163,x] = F[164,x]*F[27,x]
F[164,x] = F[165,x]+F[74,x]
F[165,x] = F[166,x]
F[166,x] = F[11,x]^2*F[23,x]
F[167,x] = F[152,x]*F[26,x]
F[168,x] = F[11,x]*F[27,x]*F[73,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[26,x]*F[85,x]
F[171,x] = F[172,x]+F[180,x]
F[172,x] = 2*F[37,x]+F[173,x]+F[178,x]
F[173,x] = F[13,x]*F[174,x]
F[174,x] = F[172,x]+F[175,x]
F[175,x] = F[176,x]
F[176,x] = F[13,x]*F[177,x]
F[177,x] = F[11,x]+F[175,x]
F[178,x] = F[13,x]*F[179,x]
F[179,x] = F[172,x]+F[85,x]
F[180,x] = F[181,x]
F[181,x] = F[13,x]*F[182,x]
F[182,x] = F[183,x]+F[184,x]
F[183,x] = F[36,x]*F[89,x]
F[184,x] = F[185,x]*F[199,x]
F[185,x] = F[186,x]+F[193,x]+F[37,x]
F[186,x] = F[13,x]*F[187,x]
F[187,x] = F[188,x]+F[192,x]+F[37,x]
F[188,x] = F[189,x]
F[189,x] = F[10,x]*F[13,x]*F[190,x]
F[190,x] = F[188,x]+F[191,x]+F[37,x]
F[191,x] = F[13,x]*F[99,x]
F[192,x] = F[13,x]*F[96,x]
F[193,x] = F[194,x]
F[194,x] = F[13,x]*F[195,x]
F[195,x] = F[196,x]+F[198,x]
F[196,x] = F[193,x]+F[197,x]+F[37,x]
F[197,x] = F[13,x]*F[190,x]
F[198,x] = F[103,x]*F[13,x]*F[26,x]
F[199,x] = F[10,x]+F[89,x]
F[200,x] = F[201,x]+F[203,x]
F[201,x] = F[202,x]
F[202,x] = F[11,x]*F[69,x]
F[203,x] = F[204,x]
F[204,x] = F[11,x]*F[13,x]*F[205,x]*F[54,x]
F[205,x] = F[206,x]+F[87,x]
F[206,x] = F[11,x]*F[199,x]
F[207,x] = F[208,x]
F[208,x] = F[11,x]*F[209,x]
F[209,x] = F[210,x]+F[69,x]
F[210,x] = F[211,x]
F[211,x] = F[13,x]*F[212,x]
F[212,x] = F[209,x]+F[213,x]
F[213,x] = F[11,x]*F[214,x]
F[214,x] = F[209,x]+F[215,x]
F[215,x] = F[216,x]
F[216,x] = F[10,x]*F[23,x]
F[217,x] = F[16,x]+F[218,x]
F[218,x] = F[11,x]*F[219,x]
F[219,x] = F[11,x]+F[220,x]
F[220,x] = F[221,x]
F[221,x] = F[13,x]*F[222,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[11,x]*F[25,x]
F[224,x] = F[10,x]*F[225,x]
F[225,x] = F[226,x]+F[230,x]
F[226,x] = F[11,x]+F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[13,x]*F[229,x]
F[229,x] = F[227,x]+F[27,x]
F[230,x] = F[220,x]+F[231,x]
F[231,x] = F[232,x]
F[232,x] = F[13,x]*F[233,x]
F[233,x] = F[234,x]+F[235,x]
F[234,x] = F[220,x]*F[26,x]
F[235,x] = F[219,x]*F[35,x]
F[236,x] = F[237,x]+F[310,x]
F[237,x] = F[238,x]
F[238,x] = F[13,x]*F[239,x]
F[239,x] = F[240,x]+F[241,x]
F[240,x] = F[10,x]*F[11,x]
F[241,x] = F[242,x]+F[246,x]
F[242,x] = F[243,x]+F[244,x]
F[243,x] = F[10,x]*F[11,x]
F[244,x] = F[237,x]+F[245,x]
F[245,x] = F[11,x]*F[85,x]
F[246,x] = F[237,x]+F[247,x]
F[247,x] = F[248,x]
F[248,x] = F[13,x]*F[249,x]
F[249,x] = F[250,x]+F[280,x]
F[250,x] = F[251,x]
F[251,x] = F[252,x]+F[256,x]
F[252,x] = F[253,x]+F[254,x]
F[253,x] = F[11,x]*F[23,x]
F[254,x] = F[255,x]+F[83,x]
F[255,x] = F[11,x]*F[220,x]
F[256,x] = F[257,x]+F[259,x]
F[257,x] = F[258,x]
F[258,x] = F[10,x]*F[11,x]*F[23,x]
F[259,x] = F[260,x]+F[276,x]
F[260,x] = F[11,x]*F[261,x]
F[261,x] = F[11,x]+F[262,x]
F[262,x] = F[263,x]
F[263,x] = F[13,x]*F[264,x]
F[264,x] = F[265,x]+F[273,x]
F[265,x] = F[219,x]+F[266,x]
F[266,x] = F[262,x]+F[267,x]
F[267,x] = F[268,x]
F[268,x] = F[13,x]*F[269,x]
F[269,x] = F[270,x]+F[272,x]
F[270,x] = F[271,x]
F[271,x] = F[10,x]*F[11,x]*F[23,x]
F[272,x] = F[10,x]*F[266,x]
F[273,x] = F[11,x]*F[274,x]
F[274,x] = F[265,x]+F[275,x]
F[275,x] = F[80,x]
F[276,x] = F[277,x]+F[278,x]
F[277,x] = F[11,x]*F[262,x]
F[278,x] = F[279,x]
F[279,x] = F[11,x]^2*F[220,x]
F[280,x] = F[281,x]+F[286,x]
F[281,x] = F[282,x]
F[282,x] = F[23,x]*F[283,x]
F[283,x] = F[284,x]+F[285,x]
F[284,x] = F[11,x]^2
F[285,x] = F[10,x]*F[85,x]
F[286,x] = F[287,x]+F[289,x]
F[287,x] = F[288,x]
F[288,x] = F[11,x]*F[254,x]
F[289,x] = F[290,x]+F[308,x]
F[290,x] = F[172,x]+F[291,x]
F[291,x] = F[292,x]
F[292,x] = F[13,x]*F[293,x]
F[293,x] = F[294,x]+F[306,x]
F[294,x] = F[10,x]*F[295,x]
F[295,x] = F[296,x]
F[296,x] = F[13,x]*F[297,x]
F[297,x] = F[298,x]+F[303,x]
F[298,x] = F[299,x]+F[300,x]
F[299,x] = F[22,x]*F[85,x]
F[300,x] = F[295,x]+F[301,x]
F[301,x] = F[302,x]
F[302,x] = F[11,x]*F[23,x]*F[85,x]
F[303,x] = F[289,x]+F[304,x]
F[304,x] = F[287,x]+F[305,x]
F[305,x] = F[295,x]+F[85,x]
F[306,x] = F[307,x]*F[89,x]
F[307,x] = F[74,x]+F[90,x]
F[308,x] = F[309,x]
F[309,x] = F[11,x]*F[276,x]
F[310,x] = F[311,x]
F[311,x] = F[13,x]*F[312,x]
F[312,x] = F[313,x]+F[314,x]
F[313,x] = F[17,x]+F[310,x]
F[314,x] = F[315,x]+F[45,x]
F[315,x] = F[203,x]+F[52,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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{246}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{236}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{217}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{41}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = 0
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{46}\! \left(x \right) = F_{207}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{200}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{13}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right)+F_{55}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{10}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{56}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{10}\! \left(x \right) F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{22}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{10}\! \left(x \right) F_{23}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{37}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{13}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{169}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{104}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{101}\! \left(x \right)+F_{37}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{37}\! \left(x \right)+F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{26}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{103}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)+F_{37}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{90}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{13}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{140}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{127}\! \left(x \right)
F_{109}\! \left(x \right) = F_{11}\! \left(x \right) F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{27} \left(x \right)^{2}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{115}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{27}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{13}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{125}\! \left(x \right)
F_{120}\! \left(x \right) = F_{11}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{124}\! \left(x \right)+F_{37}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{13}\! \left(x \right)
F_{123}\! \left(x \right) = F_{121}\! \left(x \right)+F_{27}\! \left(x \right)
F_{124}\! \left(x \right) = F_{120}\! \left(x \right) F_{13}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{23}\! \left(x \right)
F_{126}\! \left(x \right) = F_{120}\! \left(x \right)+F_{26}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{27} \left(x \right)^{2} F_{85}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{133}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{27}\! \left(x \right) F_{90}\! \left(x \right)
F_{132}\! \left(x \right) = F_{105}\! \left(x \right) F_{26}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{27}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{13}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right) F_{85}\! \left(x \right)
F_{138}\! \left(x \right) = F_{10}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{134}\! \left(x \right)+F_{90}\! \left(x \right)
F_{140}\! \left(x \right) = F_{11}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{108}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{110}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{27} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{151}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{27}\! \left(x \right) F_{74}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{26}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{13}\! \left(x \right) F_{142}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{27}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{13}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{156}\! \left(x \right)
F_{155}\! \left(x \right) = F_{27}\! \left(x \right) F_{73}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{168}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{162}\! \left(x \right)
F_{158}\! \left(x \right) = F_{11}\! \left(x \right) F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{22}\! \left(x \right) F_{27}\! \left(x \right)
F_{161}\! \left(x \right) = F_{26}\! \left(x \right) F_{27}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{167}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{27}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{74}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{23}\! \left(x \right)
F_{167}\! \left(x \right) = F_{152}\! \left(x \right) F_{26}\! \left(x \right)
F_{168}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right) F_{73}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{26}\! \left(x \right) F_{85}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{180}\! \left(x \right)
F_{172}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{173}\! \left(x \right)+F_{178}\! \left(x \right)
F_{173}\! \left(x \right) = F_{13}\! \left(x \right) F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{172}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{13}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{11}\! \left(x \right)+F_{175}\! \left(x \right)
F_{178}\! \left(x \right) = F_{13}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{172}\! \left(x \right)+F_{85}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{13}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{184}\! \left(x \right)
F_{183}\! \left(x \right) = F_{36}\! \left(x \right) F_{89}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{199}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{193}\! \left(x \right)+F_{37}\! \left(x \right)
F_{186}\! \left(x \right) = F_{13}\! \left(x \right) F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{192}\! \left(x \right)+F_{37}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{188}\! \left(x \right)+F_{191}\! \left(x \right)+F_{37}\! \left(x \right)
F_{191}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{192}\! \left(x \right) = F_{13}\! \left(x \right) F_{96}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{13}\! \left(x \right) F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{198}\! \left(x \right)
F_{196}\! \left(x \right) = F_{193}\! \left(x \right)+F_{197}\! \left(x \right)+F_{37}\! \left(x \right)
F_{197}\! \left(x \right) = F_{13}\! \left(x \right) F_{190}\! \left(x \right)
F_{198}\! \left(x \right) = F_{103}\! \left(x \right) F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{199}\! \left(x \right) = F_{10}\! \left(x \right)+F_{89}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{205}\! \left(x \right) F_{54}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{87}\! \left(x \right)
F_{206}\! \left(x \right) = F_{11}\! \left(x \right) F_{199}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{11}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{69}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{13}\! \left(x \right) F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{209}\! \left(x \right)+F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{11}\! \left(x \right) F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{209}\! \left(x \right)+F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{10}\! \left(x \right) F_{23}\! \left(x \right)
F_{217}\! \left(x \right) = F_{16}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{11}\! \left(x \right) F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{11}\! \left(x \right)+F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{13}\! \left(x \right) F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{224}\! \left(x \right) = F_{10}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)+F_{230}\! \left(x \right)
F_{226}\! \left(x \right) = F_{11}\! \left(x \right)+F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{13}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{227}\! \left(x \right)+F_{27}\! \left(x \right)
F_{230}\! \left(x \right) = F_{220}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{13}\! \left(x \right) F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{235}\! \left(x \right)
F_{234}\! \left(x \right) = F_{220}\! \left(x \right) F_{26}\! \left(x \right)
F_{235}\! \left(x \right) = F_{219}\! \left(x \right) F_{35}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{310}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{13}\! \left(x \right) F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{241}\! \left(x \right)
F_{240}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{246}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{244}\! \left(x \right)
F_{243}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{244}\! \left(x \right) = F_{237}\! \left(x \right)+F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{246}\! \left(x \right) = F_{237}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{13}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{280}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{256}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{254}\! \left(x \right)
F_{253}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)+F_{83}\! \left(x \right)
F_{255}\! \left(x \right) = F_{11}\! \left(x \right) F_{220}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{259}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{276}\! \left(x \right)
F_{260}\! \left(x \right) = F_{11}\! \left(x \right) F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{11}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = F_{13}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)+F_{273}\! \left(x \right)
F_{265}\! \left(x \right) = F_{219}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{262}\! \left(x \right)+F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{13}\! \left(x \right) F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)+F_{272}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{272}\! \left(x \right) = F_{10}\! \left(x \right) F_{266}\! \left(x \right)
F_{273}\! \left(x \right) = F_{11}\! \left(x \right) F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{265}\! \left(x \right)+F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{80}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{278}\! \left(x \right)
F_{277}\! \left(x \right) = F_{11}\! \left(x \right) F_{262}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{220}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{286}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = F_{23}\! \left(x \right) F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)+F_{285}\! \left(x \right)
F_{284}\! \left(x \right) = F_{11} \left(x \right)^{2}
F_{285}\! \left(x \right) = F_{10}\! \left(x \right) F_{85}\! \left(x \right)
F_{286}\! \left(x \right) = F_{287}\! \left(x \right)+F_{289}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{11}\! \left(x \right) F_{254}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)+F_{308}\! \left(x \right)
F_{290}\! \left(x \right) = F_{172}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = F_{13}\! \left(x \right) F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)+F_{306}\! \left(x \right)
F_{294}\! \left(x \right) = F_{10}\! \left(x \right) F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{13}\! \left(x \right) F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)+F_{303}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{300}\! \left(x \right)
F_{299}\! \left(x \right) = F_{22}\! \left(x \right) F_{85}\! \left(x \right)
F_{300}\! \left(x \right) = F_{295}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{85}\! \left(x \right)
F_{303}\! \left(x \right) = F_{289}\! \left(x \right)+F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{287}\! \left(x \right)+F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{295}\! \left(x \right)+F_{85}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right) F_{89}\! \left(x \right)
F_{307}\! \left(x \right) = F_{74}\! \left(x \right)+F_{90}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{11}\! \left(x \right) F_{276}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = F_{13}\! \left(x \right) F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)+F_{314}\! \left(x \right)
F_{313}\! \left(x \right) = F_{17}\! \left(x \right)+F_{310}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)+F_{45}\! \left(x \right)
F_{315}\! \left(x \right) = F_{203}\! \left(x \right)+F_{52}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_14(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_246(x))
Eq(F_15(x), F_16(x) + F_236(x))
Eq(F_16(x), F_11(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_217(x))
Eq(F_20(x), F_21(x) + F_41(x))
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_26(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_13(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_23(x)*F_26(x))
Eq(F_34(x), F_22(x)*F_35(x))
Eq(F_35(x), F_11(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_40(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_27(x) + F_36(x))
Eq(F_40(x), F_13(x)*F_35(x))
Eq(F_41(x), F_17(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_13(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_10(x)*F_17(x))
Eq(F_46(x), F_207(x) + F_47(x))
Eq(F_47(x), F_200(x) + F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_13(x)*F_51(x))
Eq(F_51(x), F_11(x) + F_49(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_10(x)*F_11(x)*F_13(x)*F_54(x))
Eq(F_54(x), F_23(x) + F_55(x))
Eq(F_55(x), F_11(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_13(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_55(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_10(x)*F_11(x)*F_23(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_11(x)*F_64(x))
Eq(F_64(x), F_22(x) + F_55(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_10(x)*F_67(x))
Eq(F_67(x), F_56(x) + F_68(x))
Eq(F_68(x), F_11(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_82(x))
Eq(F_72(x), F_23(x) + F_73(x))
Eq(F_73(x), F_11(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_13(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_10(x)*F_73(x))
Eq(F_78(x), F_11(x)*F_79(x))
Eq(F_79(x), F_77(x) + F_80(x))
Eq(F_80(x), F_22(x) + F_81(x))
Eq(F_81(x), F_10(x)*F_23(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_11(x)*F_23(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_37(x) + F_86(x) + F_88(x))
Eq(F_86(x), F_13(x)*F_87(x))
Eq(F_87(x), F_11(x) + F_85(x))
Eq(F_88(x), F_13(x)*F_89(x))
Eq(F_89(x), F_11(x) + F_85(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_13(x)*F_92(x))
Eq(F_92(x), F_169(x) + F_93(x))
Eq(F_93(x), F_104(x) + F_94(x))
Eq(F_94(x), F_101(x) + F_37(x) + F_95(x))
Eq(F_95(x), F_13(x)*F_96(x))
Eq(F_96(x), F_37(x) + F_95(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_26(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_26(x) + F_97(x))
Eq(F_100(x), F_13(x)*F_99(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_13(x)*F_26(x))
Eq(F_103(x), F_100(x) + F_101(x) + F_37(x))
Eq(F_104(x), F_105(x) + F_90(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_13(x))
Eq(F_107(x), F_108(x) + F_140(x))
Eq(F_108(x), F_109(x) + F_127(x))
Eq(F_109(x), F_11(x)*F_110(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_27(x)**2)
Eq(F_112(x), F_113(x) + F_116(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_23(x)*F_27(x))
Eq(F_115(x), F_26(x)*F_30(x))
Eq(F_116(x), F_117(x)*F_27(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_13(x))
Eq(F_119(x), F_120(x) + F_125(x))
Eq(F_120(x), F_11(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_124(x) + F_37(x))
Eq(F_122(x), F_123(x)*F_13(x))
Eq(F_123(x), F_121(x) + F_27(x))
Eq(F_124(x), F_120(x)*F_13(x))
Eq(F_125(x), F_126(x)*F_23(x))
Eq(F_126(x), F_120(x) + F_26(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_27(x)**2*F_85(x))
Eq(F_129(x), F_130(x) + F_133(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_27(x)*F_90(x))
Eq(F_132(x), F_105(x)*F_26(x))
Eq(F_133(x), F_134(x)*F_27(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_13(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_11(x)*F_26(x)*F_85(x))
Eq(F_138(x), F_10(x)*F_139(x))
Eq(F_139(x), F_134(x) + F_90(x))
Eq(F_140(x), F_11(x)*F_141(x))
Eq(F_141(x), F_108(x) + F_142(x))
Eq(F_142(x), F_110(x) + F_143(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_11(x)*F_27(x)**2)
Eq(F_145(x), F_146(x) + F_151(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_27(x)*F_74(x))
Eq(F_148(x), F_149(x)*F_26(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_13(x)*F_142(x))
Eq(F_151(x), F_152(x)*F_27(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_13(x)*F_154(x))
Eq(F_154(x), F_155(x) + F_156(x))
Eq(F_155(x), F_27(x)*F_73(x))
Eq(F_156(x), F_157(x) + F_168(x))
Eq(F_157(x), F_158(x) + F_162(x))
Eq(F_158(x), F_11(x)*F_159(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_22(x)*F_27(x))
Eq(F_161(x), F_26(x)*F_27(x))
Eq(F_162(x), F_163(x) + F_167(x))
Eq(F_163(x), F_164(x)*F_27(x))
Eq(F_164(x), F_165(x) + F_74(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_11(x)**2*F_23(x))
Eq(F_167(x), F_152(x)*F_26(x))
Eq(F_168(x), F_11(x)*F_27(x)*F_73(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_26(x)*F_85(x))
Eq(F_171(x), F_172(x) + F_180(x))
Eq(F_172(x), F_173(x) + F_178(x) + 2*F_37(x))
Eq(F_173(x), F_13(x)*F_174(x))
Eq(F_174(x), F_172(x) + F_175(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_13(x)*F_177(x))
Eq(F_177(x), F_11(x) + F_175(x))
Eq(F_178(x), F_13(x)*F_179(x))
Eq(F_179(x), F_172(x) + F_85(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_13(x)*F_182(x))
Eq(F_182(x), F_183(x) + F_184(x))
Eq(F_183(x), F_36(x)*F_89(x))
Eq(F_184(x), F_185(x)*F_199(x))
Eq(F_185(x), F_186(x) + F_193(x) + F_37(x))
Eq(F_186(x), F_13(x)*F_187(x))
Eq(F_187(x), F_188(x) + F_192(x) + F_37(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_10(x)*F_13(x)*F_190(x))
Eq(F_190(x), F_188(x) + F_191(x) + F_37(x))
Eq(F_191(x), F_13(x)*F_99(x))
Eq(F_192(x), F_13(x)*F_96(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_13(x)*F_195(x))
Eq(F_195(x), F_196(x) + F_198(x))
Eq(F_196(x), F_193(x) + F_197(x) + F_37(x))
Eq(F_197(x), F_13(x)*F_190(x))
Eq(F_198(x), F_103(x)*F_13(x)*F_26(x))
Eq(F_199(x), F_10(x) + F_89(x))
Eq(F_200(x), F_201(x) + F_203(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_11(x)*F_69(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_11(x)*F_13(x)*F_205(x)*F_54(x))
Eq(F_205(x), F_206(x) + F_87(x))
Eq(F_206(x), F_11(x)*F_199(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_11(x)*F_209(x))
Eq(F_209(x), F_210(x) + F_69(x))
Eq(F_210(x), F_211(x))
Eq(F_211(x), F_13(x)*F_212(x))
Eq(F_212(x), F_209(x) + F_213(x))
Eq(F_213(x), F_11(x)*F_214(x))
Eq(F_214(x), F_209(x) + F_215(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_10(x)*F_23(x))
Eq(F_217(x), F_16(x) + F_218(x))
Eq(F_218(x), F_11(x)*F_219(x))
Eq(F_219(x), F_11(x) + F_220(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_13(x)*F_222(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_11(x)*F_25(x))
Eq(F_224(x), F_10(x)*F_225(x))
Eq(F_225(x), F_226(x) + F_230(x))
Eq(F_226(x), F_11(x) + F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_13(x)*F_229(x))
Eq(F_229(x), F_227(x) + F_27(x))
Eq(F_230(x), F_220(x) + F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_13(x)*F_233(x))
Eq(F_233(x), F_234(x) + F_235(x))
Eq(F_234(x), F_220(x)*F_26(x))
Eq(F_235(x), F_219(x)*F_35(x))
Eq(F_236(x), F_237(x) + F_310(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_13(x)*F_239(x))
Eq(F_239(x), F_240(x) + F_241(x))
Eq(F_240(x), F_10(x)*F_11(x))
Eq(F_241(x), F_242(x) + F_246(x))
Eq(F_242(x), F_243(x) + F_244(x))
Eq(F_243(x), F_10(x)*F_11(x))
Eq(F_244(x), F_237(x) + F_245(x))
Eq(F_245(x), F_11(x)*F_85(x))
Eq(F_246(x), F_237(x) + F_247(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_13(x)*F_249(x))
Eq(F_249(x), F_250(x) + F_280(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_252(x) + F_256(x))
Eq(F_252(x), F_253(x) + F_254(x))
Eq(F_253(x), F_11(x)*F_23(x))
Eq(F_254(x), F_255(x) + F_83(x))
Eq(F_255(x), F_11(x)*F_220(x))
Eq(F_256(x), F_257(x) + F_259(x))
Eq(F_257(x), F_258(x))
Eq(F_258(x), F_10(x)*F_11(x)*F_23(x))
Eq(F_259(x), F_260(x) + F_276(x))
Eq(F_260(x), F_11(x)*F_261(x))
Eq(F_261(x), F_11(x) + F_262(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_13(x)*F_264(x))
Eq(F_264(x), F_265(x) + F_273(x))
Eq(F_265(x), F_219(x) + F_266(x))
Eq(F_266(x), F_262(x) + F_267(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_13(x)*F_269(x))
Eq(F_269(x), F_270(x) + F_272(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_10(x)*F_11(x)*F_23(x))
Eq(F_272(x), F_10(x)*F_266(x))
Eq(F_273(x), F_11(x)*F_274(x))
Eq(F_274(x), F_265(x) + F_275(x))
Eq(F_275(x), F_80(x))
Eq(F_276(x), F_277(x) + F_278(x))
Eq(F_277(x), F_11(x)*F_262(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), F_11(x)**2*F_220(x))
Eq(F_280(x), F_281(x) + F_286(x))
Eq(F_281(x), F_282(x))
Eq(F_282(x), F_23(x)*F_283(x))
Eq(F_283(x), F_284(x) + F_285(x))
Eq(F_284(x), F_11(x)**2)
Eq(F_285(x), F_10(x)*F_85(x))
Eq(F_286(x), F_287(x) + F_289(x))
Eq(F_287(x), F_288(x))
Eq(F_288(x), F_11(x)*F_254(x))
Eq(F_289(x), F_290(x) + F_308(x))
Eq(F_290(x), F_172(x) + F_291(x))
Eq(F_291(x), F_292(x))
Eq(F_292(x), F_13(x)*F_293(x))
Eq(F_293(x), F_294(x) + F_306(x))
Eq(F_294(x), F_10(x)*F_295(x))
Eq(F_295(x), F_296(x))
Eq(F_296(x), F_13(x)*F_297(x))
Eq(F_297(x), F_298(x) + F_303(x))
Eq(F_298(x), F_299(x) + F_300(x))
Eq(F_299(x), F_22(x)*F_85(x))
Eq(F_300(x), F_295(x) + F_301(x))
Eq(F_301(x), F_302(x))
Eq(F_302(x), F_11(x)*F_23(x)*F_85(x))
Eq(F_303(x), F_289(x) + F_304(x))
Eq(F_304(x), F_287(x) + F_305(x))
Eq(F_305(x), F_295(x) + F_85(x))
Eq(F_306(x), F_307(x)*F_89(x))
Eq(F_307(x), F_74(x) + F_90(x))
Eq(F_308(x), F_309(x))
Eq(F_309(x), F_11(x)*F_276(x))
Eq(F_310(x), F_311(x))
Eq(F_311(x), F_13(x)*F_312(x))
Eq(F_312(x), F_313(x) + F_314(x))
Eq(F_313(x), F_17(x) + F_310(x))
Eq(F_314(x), F_315(x) + F_45(x))
Eq(F_315(x), F_203(x) + F_52(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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[0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[3, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_req_corrob
Tree: http://permpal.com/tree/89/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[3,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[122,x]
F[10,x] = F[11,x]+F[25,x]
F[11,x] = F[12,x]+F[13,x]+F[24,x]
F[12,x] = 0
F[13,x] = F[14,x]*F[15,x]
F[14,x] = x
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[16,x]
F[19,x] = F[17,x]+F[20,x]
F[20,x] = F[12,x]+F[21,x]+F[23,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[17,x]+F[20,x]
F[23,x] = F[14,x]*F[19,x]
F[24,x] = F[10,x]*F[14,x]
F[25,x] = F[26,x]
F[26,x] = F[14,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[11,x]*F[16,x]
F[29,x] = F[30,x]+F[99,x]
F[30,x] = F[31,x]+F[91,x]
F[31,x] = F[10,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[16,x]*F[17,x]*F[34,x]
F[34,x] = F[35,x]+F[40,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[16,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[34,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[16,x]*F[38,x]
F[43,x] = F[44,x]
F[44,x] = F[14,x]*F[16,x]*F[17,x]*F[45,x]
F[45,x] = F[46,x]+F[90,x]
F[46,x] = F[47,x]+F[59,x]
F[47,x] = F[1,x]+F[48,x]+F[58,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[50,x]
F[50,x] = F[47,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[14,x]*F[16,x]*F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[1,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[14,x]*F[47,x]
F[57,x] = F[16,x]*F[55,x]
F[58,x] = F[14,x]*F[47,x]
F[59,x] = F[14,x]*F[60,x]
F[60,x] = F[61,x]+F[68,x]
F[61,x] = F[62,x]+F[65,x]+F[66,x]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[14,x]*F[62,x]
F[65,x] = F[14,x]*F[61,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[61,x]*F[62,x]
F[68,x] = F[12,x]+F[69,x]+F[71,x]+F[89,x]
F[69,x] = F[70,x]
F[70,x] = F[14,x]*F[16,x]*F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[14,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[16,x]*F[50,x]
F[75,x] = F[16,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[14,x]*F[16,x]*F[79,x]
F[79,x] = F[77,x]+F[80,x]+F[81,x]
F[80,x] = F[16,x]*F[54,x]
F[81,x] = F[82,x]
F[82,x] = F[14,x]*F[54,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]+F[87,x]
F[84,x] = F[16,x]^2
F[85,x] = F[86,x]
F[86,x] = F[14,x]*F[16,x]*F[83,x]
F[87,x] = F[88,x]
F[88,x] = F[14,x]*F[16,x]*F[83,x]
F[89,x] = F[14,x]*F[68,x]
F[90,x] = F[17,x]*F[61,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]+F[93,x]+F[94,x]+F[98,x]
F[93,x] = F[14,x]*F[15,x]*F[55,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[16,x]*F[17,x]*F[96,x]
F[96,x] = F[76,x]+F[97,x]
F[97,x] = F[16,x]*F[55,x]
F[98,x] = F[14,x]*F[92,x]
F[99,x] = F[100,x]*F[19,x]
F[100,x] = F[101,x]+F[108,x]+F[12,x]
F[101,x] = F[102,x]*F[14,x]
F[102,x] = F[1,x]+F[103,x]+F[13,x]
F[103,x] = F[104,x]*F[14,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[53,x]
F[106,x] = F[107,x]+F[108,x]+F[12,x]+F[121,x]
F[107,x] = F[104,x]*F[14,x]
F[108,x] = F[109,x]*F[14,x]
F[109,x] = F[110,x]+F[12,x]+F[120,x]+F[13,x]
F[110,x] = F[111,x]*F[14,x]
F[111,x] = F[106,x]+F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[100,x]*F[114,x]*F[14,x]
F[114,x] = F[115,x]+F[62,x]
F[115,x] = F[116,x]+F[17,x]
F[116,x] = F[117,x]+F[119,x]+F[12,x]
F[117,x] = F[118,x]*F[14,x]
F[118,x] = F[116,x]+F[63,x]
F[119,x] = F[115,x]*F[14,x]
F[120,x] = F[109,x]*F[14,x]
F[121,x] = F[111,x]*F[14,x]
F[122,x] = F[123,x]+F[152,x]+F[3,x]
F[123,x] = F[124,x]*F[14,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[15,x]*F[17,x]
F[126,x] = F[127,x]+F[141,x]+F[151,x]
F[127,x] = F[12,x]+F[128,x]+F[129,x]
F[128,x] = F[127,x]*F[14,x]
F[129,x] = F[130,x]*F[14,x]
F[130,x] = F[1,x]+F[131,x]+F[132,x]+F[140,x]
F[131,x] = F[130,x]*F[14,x]
F[132,x] = F[133,x]*F[14,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[109,x]+F[47,x]
F[135,x] = F[136,x]
F[136,x] = F[12,x]+F[129,x]+F[137,x]+F[138,x]
F[137,x] = F[136,x]*F[14,x]
F[138,x] = F[139,x]
F[139,x] = F[136,x]*F[14,x]
F[140,x] = F[130,x]*F[14,x]
F[141,x] = F[14,x]*F[142,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[127,x]*F[15,x]
F[144,x] = F[12,x]+F[145,x]+F[146,x]+F[149,x]
F[145,x] = F[14,x]*F[144,x]
F[146,x] = F[147,x]
F[147,x] = F[14,x]*F[148,x]*F[16,x]
F[148,x] = F[76,x]+F[80,x]
F[149,x] = F[150,x]
F[150,x] = F[14,x]*F[144,x]*F[16,x]
F[151,x] = F[126,x]*F[14,x]
F[152,x] = F[122,x]*F[14,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{3}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{122}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{24}\! \left(x \right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{99}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{91}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{38}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{90}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{59}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)+F_{58}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{14}\! \left(x \right) F_{47}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{14}\! \left(x \right) F_{47}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right) F_{62}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)+F_{89}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{75}\! \left(x \right) = F_{16}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{16}\! \left(x \right) F_{54}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{16} \left(x \right)^{2}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{83}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right)
F_{90}\! \left(x \right) = F_{17}\! \left(x \right) F_{61}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{17}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{76}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{16}\! \left(x \right) F_{55}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{92}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{19}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)+F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)+F_{13}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{53}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)+F_{12}\! \left(x \right)+F_{121}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{14}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{12}\! \left(x \right)+F_{120}\! \left(x \right)+F_{13}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{100}\! \left(x \right) F_{114}\! \left(x \right) F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{62}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{17}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{119}\! \left(x \right)+F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right)
F_{118}\! \left(x \right) = F_{116}\! \left(x \right)+F_{63}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{120}\! \left(x \right) = F_{109}\! \left(x \right) F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{152}\! \left(x \right)+F_{3}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{14}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{141}\! \left(x \right)+F_{151}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right)+F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{127}\! \left(x \right) F_{14}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{14}\! \left(x \right)
F_{130}\! \left(x \right) = F_{1}\! \left(x \right)+F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{131}\! \left(x \right) = F_{130}\! \left(x \right) F_{14}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{14}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{109}\! \left(x \right)+F_{47}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right)+F_{129}\! \left(x \right)+F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{136}\! \left(x \right) F_{14}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{136}\! \left(x \right) F_{14}\! \left(x \right)
F_{140}\! \left(x \right) = F_{130}\! \left(x \right) F_{14}\! \left(x \right)
F_{141}\! \left(x \right) = F_{14}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{127}\! \left(x \right) F_{15}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right)+F_{145}\! \left(x \right)+F_{146}\! \left(x \right)+F_{149}\! \left(x \right)
F_{145}\! \left(x \right) = F_{14}\! \left(x \right) F_{144}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{14}\! \left(x \right) F_{148}\! \left(x \right) F_{16}\! \left(x \right)
F_{148}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{14}\! \left(x \right) F_{144}\! \left(x \right) F_{16}\! \left(x \right)
F_{151}\! \left(x \right) = F_{126}\! \left(x \right) F_{14}\! \left(x \right)
F_{152}\! \left(x \right) = F_{122}\! \left(x \right) F_{14}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_3(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_122(x))
Eq(F_10(x), F_11(x) + F_25(x))
Eq(F_11(x), F_12(x) + F_13(x) + F_24(x))
Eq(F_12(x), 0)
Eq(F_13(x), F_14(x)*F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_16(x))
Eq(F_19(x), F_17(x) + F_20(x))
Eq(F_20(x), F_12(x) + F_21(x) + F_23(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_17(x) + F_20(x))
Eq(F_23(x), F_14(x)*F_19(x))
Eq(F_24(x), F_10(x)*F_14(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_14(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_11(x)*F_16(x))
Eq(F_29(x), F_30(x) + F_99(x))
Eq(F_30(x), F_31(x) + F_91(x))
Eq(F_31(x), F_10(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_16(x)*F_17(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_40(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_16(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_14(x)*F_34(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_16(x)*F_38(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_14(x)*F_16(x)*F_17(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_90(x))
Eq(F_46(x), F_47(x) + F_59(x))
Eq(F_47(x), F_1(x) + F_48(x) + F_58(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_50(x))
Eq(F_50(x), F_47(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_14(x)*F_16(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_1(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_14(x)*F_47(x))
Eq(F_57(x), F_16(x)*F_55(x))
Eq(F_58(x), F_14(x)*F_47(x))
Eq(F_59(x), F_14(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_68(x))
Eq(F_61(x), F_62(x) + F_65(x) + F_66(x))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_14(x)*F_62(x))
Eq(F_65(x), F_14(x)*F_61(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_61(x)*F_62(x))
Eq(F_68(x), F_12(x) + F_69(x) + F_71(x) + F_89(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_14(x)*F_16(x)*F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_14(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_16(x)*F_50(x))
Eq(F_75(x), F_16(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_14(x)*F_16(x)*F_79(x))
Eq(F_79(x), F_77(x) + F_80(x) + F_81(x))
Eq(F_80(x), F_16(x)*F_54(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_14(x)*F_54(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x) + F_87(x))
Eq(F_84(x), F_16(x)**2)
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_14(x)*F_16(x)*F_83(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_14(x)*F_16(x)*F_83(x))
Eq(F_89(x), F_14(x)*F_68(x))
Eq(F_90(x), F_17(x)*F_61(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x) + F_93(x) + F_94(x) + F_98(x))
Eq(F_93(x), F_14(x)*F_15(x)*F_55(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_16(x)*F_17(x)*F_96(x))
Eq(F_96(x), F_76(x) + F_97(x))
Eq(F_97(x), F_16(x)*F_55(x))
Eq(F_98(x), F_14(x)*F_92(x))
Eq(F_99(x), F_100(x)*F_19(x))
Eq(F_100(x), F_101(x) + F_108(x) + F_12(x))
Eq(F_101(x), F_102(x)*F_14(x))
Eq(F_102(x), F_1(x) + F_103(x) + F_13(x))
Eq(F_103(x), F_104(x)*F_14(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_53(x))
Eq(F_106(x), F_107(x) + F_108(x) + F_12(x) + F_121(x))
Eq(F_107(x), F_104(x)*F_14(x))
Eq(F_108(x), F_109(x)*F_14(x))
Eq(F_109(x), F_110(x) + F_12(x) + F_120(x) + F_13(x))
Eq(F_110(x), F_111(x)*F_14(x))
Eq(F_111(x), F_106(x) + F_112(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_100(x)*F_114(x)*F_14(x))
Eq(F_114(x), F_115(x) + F_62(x))
Eq(F_115(x), F_116(x) + F_17(x))
Eq(F_116(x), F_117(x) + F_119(x) + F_12(x))
Eq(F_117(x), F_118(x)*F_14(x))
Eq(F_118(x), F_116(x) + F_63(x))
Eq(F_119(x), F_115(x)*F_14(x))
Eq(F_120(x), F_109(x)*F_14(x))
Eq(F_121(x), F_111(x)*F_14(x))
Eq(F_122(x), F_123(x) + F_152(x) + F_3(x))
Eq(F_123(x), F_124(x)*F_14(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_15(x)*F_17(x))
Eq(F_126(x), F_127(x) + F_141(x) + F_151(x))
Eq(F_127(x), F_12(x) + F_128(x) + F_129(x))
Eq(F_128(x), F_127(x)*F_14(x))
Eq(F_129(x), F_130(x)*F_14(x))
Eq(F_130(x), F_1(x) + F_131(x) + F_132(x) + F_140(x))
Eq(F_131(x), F_130(x)*F_14(x))
Eq(F_132(x), F_133(x)*F_14(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_109(x) + F_47(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_12(x) + F_129(x) + F_137(x) + F_138(x))
Eq(F_137(x), F_136(x)*F_14(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_136(x)*F_14(x))
Eq(F_140(x), F_130(x)*F_14(x))
Eq(F_141(x), F_14(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_127(x)*F_15(x))
Eq(F_144(x), F_12(x) + F_145(x) + F_146(x) + F_149(x))
Eq(F_145(x), F_14(x)*F_144(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_14(x)*F_148(x)*F_16(x))
Eq(F_148(x), F_76(x) + F_80(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_14(x)*F_144(x)*F_16(x))
Eq(F_151(x), F_126(x)*F_14(x))
Eq(F_152(x), F_122(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[2, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_col_placements_req_corrob
Tree: http://permpal.com/tree/90/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[3,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[15,x]
F[10,x] = F[11,x]*F[3,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[104,x]+F[16,x]
F[16,x] = F[17,x]+F[27,x]
F[17,x] = F[18,x]+F[19,x]+F[26,x]
F[18,x] = 0
F[19,x] = F[14,x]*F[20,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[12,x]+F[22,x]
F[22,x] = F[18,x]+F[23,x]+F[25,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[12,x]+F[22,x]
F[25,x] = F[14,x]*F[21,x]
F[26,x] = F[14,x]*F[16,x]
F[27,x] = F[28,x]
F[28,x] = F[14,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[11,x]*F[17,x]
F[31,x] = F[32,x]+F[77,x]
F[32,x] = F[33,x]+F[71,x]
F[33,x] = F[16,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[12,x]*F[14,x]*F[36,x]
F[36,x] = F[37,x]+F[42,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[11,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[36,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[11,x]*F[40,x]
F[45,x] = F[46,x]
F[46,x] = F[11,x]*F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[55,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[1,x]+F[48,x]
F[53,x] = F[54,x]
F[54,x] = F[11,x]^2*F[14,x]*F[48,x]
F[55,x] = F[14,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[11,x]*F[48,x]
F[58,x] = F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[11,x]*F[14,x]*F[61,x]
F[61,x] = F[59,x]+F[62,x]+F[63,x]
F[62,x] = F[11,x]*F[52,x]
F[63,x] = F[64,x]
F[64,x] = F[14,x]*F[52,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]+F[69,x]
F[66,x] = F[11,x]^2
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[14,x]*F[65,x]
F[69,x] = F[70,x]
F[70,x] = F[11,x]*F[14,x]*F[65,x]
F[71,x] = F[72,x]
F[72,x] = F[18,x]+F[73,x]+F[74,x]+F[76,x]
F[73,x] = F[14,x]*F[20,x]*F[48,x]
F[74,x] = F[75,x]
F[75,x] = F[11,x]*F[12,x]*F[14,x]*F[56,x]
F[76,x] = F[14,x]*F[72,x]
F[77,x] = F[21,x]*F[78,x]
F[78,x] = F[12,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[14,x]*F[81,x]
F[81,x] = F[103,x]+F[82,x]
F[82,x] = F[102,x]+F[18,x]+F[83,x]+F[86,x]
F[83,x] = F[14,x]*F[84,x]
F[84,x] = F[82,x]+F[85,x]
F[85,x] = F[50,x]
F[86,x] = F[14,x]*F[87,x]
F[87,x] = F[101,x]+F[18,x]+F[19,x]+F[88,x]
F[88,x] = F[14,x]*F[89,x]
F[89,x] = F[82,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[14,x]*F[78,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[1,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[93,x]
F[96,x] = F[12,x]+F[97,x]
F[97,x] = F[100,x]+F[18,x]+F[98,x]
F[98,x] = F[14,x]*F[99,x]
F[99,x] = F[94,x]+F[97,x]
F[100,x] = F[14,x]*F[96,x]
F[101,x] = F[14,x]*F[87,x]
F[102,x] = F[14,x]*F[89,x]
F[103,x] = F[12,x]*F[20,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]+F[131,x]+F[18,x]
F[106,x] = F[107,x]*F[14,x]
F[107,x] = F[103,x]+F[108,x]
F[108,x] = F[109,x]+F[120,x]+F[130,x]
F[109,x] = F[110,x]+F[111,x]+F[18,x]
F[110,x] = F[109,x]*F[14,x]
F[111,x] = F[112,x]*F[14,x]
F[112,x] = F[113,x]+F[117,x]
F[113,x] = F[11,x]+F[114,x]
F[114,x] = F[115,x]+F[116,x]+F[18,x]
F[115,x] = F[14,x]*F[24,x]
F[116,x] = F[14,x]*F[84,x]
F[117,x] = F[109,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[109,x]*F[14,x]*F[20,x]
F[120,x] = F[121,x]*F[14,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[109,x]*F[20,x]
F[123,x] = F[124,x]+F[125,x]+F[128,x]+F[18,x]
F[124,x] = F[123,x]*F[14,x]
F[125,x] = F[126,x]
F[126,x] = F[11,x]*F[127,x]*F[14,x]
F[127,x] = F[58,x]+F[62,x]
F[128,x] = F[129,x]
F[129,x] = F[11,x]*F[123,x]*F[14,x]
F[130,x] = F[108,x]*F[14,x]
F[131,x] = F[105,x]*F[14,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{3}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{104}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{77}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{71}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{36}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11} \left(x \right)^{2}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right)+F_{73}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{103}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{102}\! \left(x \right)+F_{18}\! \left(x \right)+F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{50}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{101}\! \left(x \right)+F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{14}\! \left(x \right) F_{78}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{1}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{18}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{102}\! \left(x \right) = F_{14}\! \left(x \right) F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{131}\! \left(x \right)+F_{18}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{120}\! \left(x \right)+F_{130}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)+F_{18}\! \left(x \right)
F_{110}\! \left(x \right) = F_{109}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{14}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{11}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)+F_{18}\! \left(x \right)
F_{115}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{116}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{117}\! \left(x \right) = F_{109}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{109}\! \left(x \right) F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{109}\! \left(x \right) F_{20}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)+F_{128}\! \left(x \right)+F_{18}\! \left(x \right)
F_{124}\! \left(x \right) = F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{11}\! \left(x \right) F_{127}\! \left(x \right) F_{14}\! \left(x \right)
F_{127}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{11}\! \left(x \right) F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{130}\! \left(x \right) = F_{108}\! \left(x \right) F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{105}\! \left(x \right) F_{14}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_3(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_15(x))
Eq(F_10(x), F_11(x)*F_3(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_104(x) + F_16(x))
Eq(F_16(x), F_17(x) + F_27(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_26(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_14(x)*F_20(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_12(x) + F_22(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_25(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_12(x) + F_22(x))
Eq(F_25(x), F_14(x)*F_21(x))
Eq(F_26(x), F_14(x)*F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_14(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_11(x)*F_17(x))
Eq(F_31(x), F_32(x) + F_77(x))
Eq(F_32(x), F_33(x) + F_71(x))
Eq(F_33(x), F_16(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_12(x)*F_14(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_42(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_11(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_36(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_11(x)*F_40(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_11(x)*F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_55(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_1(x) + F_48(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_11(x)**2*F_14(x)*F_48(x))
Eq(F_55(x), F_14(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_11(x)*F_48(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_11(x)*F_14(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_62(x) + F_63(x))
Eq(F_62(x), F_11(x)*F_52(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_14(x)*F_52(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x) + F_69(x))
Eq(F_66(x), F_11(x)**2)
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_14(x)*F_65(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_11(x)*F_14(x)*F_65(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_18(x) + F_73(x) + F_74(x) + F_76(x))
Eq(F_73(x), F_14(x)*F_20(x)*F_48(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_11(x)*F_12(x)*F_14(x)*F_56(x))
Eq(F_76(x), F_14(x)*F_72(x))
Eq(F_77(x), F_21(x)*F_78(x))
Eq(F_78(x), F_12(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_14(x)*F_81(x))
Eq(F_81(x), F_103(x) + F_82(x))
Eq(F_82(x), F_102(x) + F_18(x) + F_83(x) + F_86(x))
Eq(F_83(x), F_14(x)*F_84(x))
Eq(F_84(x), F_82(x) + F_85(x))
Eq(F_85(x), F_50(x))
Eq(F_86(x), F_14(x)*F_87(x))
Eq(F_87(x), F_101(x) + F_18(x) + F_19(x) + F_88(x))
Eq(F_88(x), F_14(x)*F_89(x))
Eq(F_89(x), F_82(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_14(x)*F_78(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_1(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_93(x))
Eq(F_96(x), F_12(x) + F_97(x))
Eq(F_97(x), F_100(x) + F_18(x) + F_98(x))
Eq(F_98(x), F_14(x)*F_99(x))
Eq(F_99(x), F_94(x) + F_97(x))
Eq(F_100(x), F_14(x)*F_96(x))
Eq(F_101(x), F_14(x)*F_87(x))
Eq(F_102(x), F_14(x)*F_89(x))
Eq(F_103(x), F_12(x)*F_20(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) + F_131(x) + F_18(x))
Eq(F_106(x), F_107(x)*F_14(x))
Eq(F_107(x), F_103(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_120(x) + F_130(x))
Eq(F_109(x), F_110(x) + F_111(x) + F_18(x))
Eq(F_110(x), F_109(x)*F_14(x))
Eq(F_111(x), F_112(x)*F_14(x))
Eq(F_112(x), F_113(x) + F_117(x))
Eq(F_113(x), F_11(x) + F_114(x))
Eq(F_114(x), F_115(x) + F_116(x) + F_18(x))
Eq(F_115(x), F_14(x)*F_24(x))
Eq(F_116(x), F_14(x)*F_84(x))
Eq(F_117(x), F_109(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_109(x)*F_14(x)*F_20(x))
Eq(F_120(x), F_121(x)*F_14(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_109(x)*F_20(x))
Eq(F_123(x), F_124(x) + F_125(x) + F_128(x) + F_18(x))
Eq(F_124(x), F_123(x)*F_14(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_11(x)*F_127(x)*F_14(x))
Eq(F_127(x), F_58(x) + F_62(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_11(x)*F_123(x)*F_14(x))
Eq(F_130(x), F_108(x)*F_14(x))
Eq(F_131(x), F_105(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_col_placements_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: insertion_row_and_col_placements
Tree: http://permpal.com/tree/91/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[15,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]*F[9,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[4,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[110,x]+F[17,x]+F[18,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[16,x]+F[7,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[23,x]
F[23,x] = F[13,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = 2*F[17,x]+F[26,x]+F[83,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[30,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[23,x]
F[30,x] = F[31,x]+F[33,x]
F[31,x] = F[32,x]
F[32,x] = F[13,x]^2*F[7,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[13,x]*F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[50,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[48,x]
F[39,x] = F[40,x]+F[46,x]
F[40,x] = F[13,x]+F[41,x]
F[41,x] = F[17,x]+F[42,x]+F[44,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[41,x]+F[7,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[4,x]*F[40,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[13,x]*F[7,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[36,x]+F[7,x]
F[50,x] = F[23,x]+F[51,x]
F[51,x] = F[17,x]+F[52,x]+F[58,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[13,x]*F[56,x]
F[56,x] = F[36,x]+F[7,x]
F[57,x] = F[12,x]*F[50,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[67,x]
F[61,x] = F[51,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[49,x]+F[7,x]
F[66,x] = F[23,x]+F[61,x]
F[67,x] = F[13,x]*F[68,x]
F[68,x] = F[69,x]+F[74,x]
F[69,x] = F[17,x]+F[70,x]+F[72,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[13,x]+F[69,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[13,x]+F[69,x]
F[74,x] = F[17,x]+F[75,x]+F[81,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[13,x]*F[43,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[23,x]+F[74,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[4,x]*F[68,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[106,x]+F[85,x]
F[85,x] = F[102,x]+F[86,x]
F[86,x] = F[17,x]+F[87,x]+F[97,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[7,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[13,x]+F[89,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[13,x]*F[95,x]
F[95,x] = F[6,x]+F[92,x]
F[96,x] = F[12,x]*F[89,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[101,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[13,x]*F[6,x]
F[101,x] = F[25,x]+F[86,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[12,x]*F[4,x]
F[104,x] = F[105,x]+F[23,x]
F[105,x] = F[13,x]*F[71,x]
F[106,x] = F[107,x]+F[25,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[12,x]*F[13,x]*F[4,x]
F[109,x] = F[41,x]+F[80,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[124,x]
F[112,x] = F[113,x]+F[2,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[92,x]
F[116,x] = F[117,x]+F[96,x]
F[117,x] = F[100,x]+F[118,x]
F[118,x] = F[119,x]+F[69,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[118,x]+F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[13,x]*F[93,x]
F[124,x] = F[125,x]+F[16,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[167,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[132,x]+F[17,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[129,x]+F[7,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[142,x]
F[134,x] = F[13,x]+F[135,x]
F[135,x] = F[136,x]+F[141,x]+F[17,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[135,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[1,x]+F[138,x]
F[141,x] = F[134,x]*F[4,x]
F[142,x] = F[129,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[146,x]+F[157,x]
F[146,x] = F[147,x]+F[155,x]
F[147,x] = F[148,x]+F[151,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[13,x]+F[148,x]
F[151,x] = 2*F[17,x]+F[152,x]+F[154,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[135,x]+F[151,x]
F[154,x] = F[147,x]*F[4,x]
F[155,x] = F[156,x]*F[7,x]
F[156,x] = F[134,x]+F[147,x]
F[157,x] = F[158,x]+F[160,x]
F[158,x] = F[13,x]*F[159,x]
F[159,x] = F[134,x]+F[147,x]
F[160,x] = F[161,x]+F[164,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[129,x]*F[140,x]
F[163,x] = F[134,x]*F[89,x]
F[164,x] = F[165,x]+F[166,x]
F[165,x] = F[129,x]*F[134,x]
F[166,x] = F[147,x]*F[89,x]
F[167,x] = F[168,x]+F[189,x]
F[168,x] = F[169,x]+F[23,x]
F[169,x] = F[17,x]+F[170,x]+F[175,x]
F[170,x] = F[171,x]
F[171,x] = F[172,x]*F[4,x]
F[172,x] = F[173,x]+F[78,x]
F[173,x] = F[168,x]+F[174,x]
F[174,x] = F[13,x]*F[80,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[118,x]+F[177,x]
F[177,x] = F[169,x]+F[178,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[12,x]*F[169,x]
F[182,x] = F[183,x]
F[183,x] = F[13,x]*F[131,x]*F[184,x]
F[184,x] = F[13,x]+F[185,x]
F[185,x] = F[17,x]+F[186,x]+F[188,x]
F[186,x] = F[187,x]*F[4,x]
F[187,x] = F[13,x]+F[185,x]
F[188,x] = F[184,x]*F[4,x]
F[189,x] = F[190,x]+F[191,x]
F[190,x] = F[185,x]*F[7,x]
F[191,x] = F[192,x]
F[192,x] = F[193,x]*F[4,x]
F[193,x] = F[194,x]+F[196,x]
F[194,x] = F[195,x]
F[195,x] = F[12,x]*F[129,x]*F[13,x]
F[196,x] = F[197,x]+F[200,x]
F[197,x] = F[169,x]+F[198,x]
F[198,x] = F[199,x]
F[199,x] = F[13,x]^2*F[129,x]
F[200,x] = F[191,x]+F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[129,x]*F[13,x]*F[185,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{15}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{110}\! \left(x \right)+F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{26}\! \left(x \right)+F_{83}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{50}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{48}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{36}\! \left(x \right)+F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{36}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{61}\! \left(x \right) = F_{51}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{49}\! \left(x \right)+F_{7}\! \left(x \right)
F_{66}\! \left(x \right) = F_{23}\! \left(x \right)+F_{61}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{69}\! \left(x \right) = F_{17}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{13}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{13}\! \left(x \right)+F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x \right)+F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{43}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{23}\! \left(x \right)+F_{74}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{106}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{102}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{17}\! \left(x \right)+F_{87}\! \left(x \right)+F_{97}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{7}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{13}\! \left(x \right)+F_{89}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{13}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{6}\! \left(x \right)+F_{92}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{101}\! \left(x \right) = F_{25}\! \left(x \right)+F_{86}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{23}\! \left(x \right)
F_{105}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{25}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{41}\! \left(x \right)+F_{80}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{124}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{92}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{96}\! \left(x \right)
F_{117}\! \left(x \right) = F_{100}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{69}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{16}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{167}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{17}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{129}\! \left(x \right)+F_{7}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{142}\! \left(x \right)
F_{134}\! \left(x \right) = F_{13}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{141}\! \left(x \right)+F_{17}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{135}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{1}\! \left(x \right)+F_{138}\! \left(x \right)
F_{141}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{129}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{157}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{155}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{151}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{13}\! \left(x \right)+F_{148}\! \left(x \right)
F_{151}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{152}\! \left(x \right)+F_{154}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{135}\! \left(x \right)+F_{151}\! \left(x \right)
F_{154}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{7}\! \left(x \right)
F_{156}\! \left(x \right) = F_{134}\! \left(x \right)+F_{147}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{160}\! \left(x \right)
F_{158}\! \left(x \right) = F_{13}\! \left(x \right) F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{134}\! \left(x \right)+F_{147}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{164}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{129}\! \left(x \right) F_{140}\! \left(x \right)
F_{163}\! \left(x \right) = F_{134}\! \left(x \right) F_{89}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{166}\! \left(x \right)
F_{165}\! \left(x \right) = F_{129}\! \left(x \right) F_{134}\! \left(x \right)
F_{166}\! \left(x \right) = F_{147}\! \left(x \right) F_{89}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{189}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{23}\! \left(x \right)
F_{169}\! \left(x \right) = F_{17}\! \left(x \right)+F_{170}\! \left(x \right)+F_{175}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{78}\! \left(x \right)
F_{173}\! \left(x \right) = F_{168}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{13}\! \left(x \right) F_{80}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{118}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{169}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{12}\! \left(x \right) F_{169}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{13}\! \left(x \right) F_{131}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{13}\! \left(x \right)+F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{17}\! \left(x \right)+F_{186}\! \left(x \right)+F_{188}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{4}\! \left(x \right)
F_{187}\! \left(x \right) = F_{13}\! \left(x \right)+F_{185}\! \left(x \right)
F_{188}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{191}\! \left(x \right)
F_{190}\! \left(x \right) = F_{185}\! \left(x \right) F_{7}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{196}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right) F_{13}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{200}\! \left(x \right)
F_{197}\! \left(x \right) = F_{169}\! \left(x \right)+F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{129}\! \left(x \right)
F_{200}\! \left(x \right) = F_{191}\! \left(x \right)+F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{129}\! \left(x \right) F_{13}\! \left(x \right) F_{185}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_15(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x)*F_9(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_110(x) + F_17(x) + F_18(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_16(x) + F_7(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_13(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), 2*F_17(x) + F_26(x) + F_83(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_30(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_23(x))
Eq(F_30(x), F_31(x) + F_33(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_13(x)**2*F_7(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_13(x)*F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_50(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_48(x))
Eq(F_39(x), F_40(x) + F_46(x))
Eq(F_40(x), F_13(x) + F_41(x))
Eq(F_41(x), F_17(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_41(x) + F_7(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_4(x)*F_40(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_13(x)*F_7(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_36(x) + F_7(x))
Eq(F_50(x), F_23(x) + F_51(x))
Eq(F_51(x), F_17(x) + F_52(x) + F_58(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_13(x)*F_56(x))
Eq(F_56(x), F_36(x) + F_7(x))
Eq(F_57(x), F_12(x)*F_50(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_67(x))
Eq(F_61(x), F_51(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_49(x) + F_7(x))
Eq(F_66(x), F_23(x) + F_61(x))
Eq(F_67(x), F_13(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_74(x))
Eq(F_69(x), F_17(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_13(x) + F_69(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_13(x) + F_69(x))
Eq(F_74(x), F_17(x) + F_75(x) + F_81(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_13(x)*F_43(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_23(x) + F_74(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_4(x)*F_68(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_106(x) + F_85(x))
Eq(F_85(x), F_102(x) + F_86(x))
Eq(F_86(x), F_17(x) + F_87(x) + F_97(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_7(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_13(x) + F_89(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_13(x)*F_95(x))
Eq(F_95(x), F_6(x) + F_92(x))
Eq(F_96(x), F_12(x)*F_89(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_101(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_13(x)*F_6(x))
Eq(F_101(x), F_25(x) + F_86(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_12(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_23(x))
Eq(F_105(x), F_13(x)*F_71(x))
Eq(F_106(x), F_107(x) + F_25(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_12(x)*F_13(x)*F_4(x))
Eq(F_109(x), F_41(x) + F_80(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_124(x))
Eq(F_112(x), F_113(x) + F_2(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_92(x))
Eq(F_116(x), F_117(x) + F_96(x))
Eq(F_117(x), F_100(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_69(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_118(x) + F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_13(x)*F_93(x))
Eq(F_124(x), F_125(x) + F_16(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_167(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_132(x) + F_17(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_129(x) + F_7(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_142(x))
Eq(F_134(x), F_13(x) + F_135(x))
Eq(F_135(x), F_136(x) + F_141(x) + F_17(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_135(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_1(x) + F_138(x))
Eq(F_141(x), F_134(x)*F_4(x))
Eq(F_142(x), F_129(x) + F_143(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_146(x) + F_157(x))
Eq(F_146(x), F_147(x) + F_155(x))
Eq(F_147(x), F_148(x) + F_151(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_13(x) + F_148(x))
Eq(F_151(x), F_152(x) + F_154(x) + 2*F_17(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_135(x) + F_151(x))
Eq(F_154(x), F_147(x)*F_4(x))
Eq(F_155(x), F_156(x)*F_7(x))
Eq(F_156(x), F_134(x) + F_147(x))
Eq(F_157(x), F_158(x) + F_160(x))
Eq(F_158(x), F_13(x)*F_159(x))
Eq(F_159(x), F_134(x) + F_147(x))
Eq(F_160(x), F_161(x) + F_164(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_129(x)*F_140(x))
Eq(F_163(x), F_134(x)*F_89(x))
Eq(F_164(x), F_165(x) + F_166(x))
Eq(F_165(x), F_129(x)*F_134(x))
Eq(F_166(x), F_147(x)*F_89(x))
Eq(F_167(x), F_168(x) + F_189(x))
Eq(F_168(x), F_169(x) + F_23(x))
Eq(F_169(x), F_17(x) + F_170(x) + F_175(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_172(x)*F_4(x))
Eq(F_172(x), F_173(x) + F_78(x))
Eq(F_173(x), F_168(x) + F_174(x))
Eq(F_174(x), F_13(x)*F_80(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_118(x) + F_177(x))
Eq(F_177(x), F_169(x) + F_178(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_12(x)*F_169(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_13(x)*F_131(x)*F_184(x))
Eq(F_184(x), F_13(x) + F_185(x))
Eq(F_185(x), F_17(x) + F_186(x) + F_188(x))
Eq(F_186(x), F_187(x)*F_4(x))
Eq(F_187(x), F_13(x) + F_185(x))
Eq(F_188(x), F_184(x)*F_4(x))
Eq(F_189(x), F_190(x) + F_191(x))
Eq(F_190(x), F_185(x)*F_7(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_193(x)*F_4(x))
Eq(F_193(x), F_194(x) + F_196(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_12(x)*F_129(x)*F_13(x))
Eq(F_196(x), F_197(x) + F_200(x))
Eq(F_197(x), F_169(x) + F_198(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_129(x)*F_13(x)**2)
Eq(F_200(x), F_191(x) + F_201(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_129(x)*F_13(x)*F_185(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_and_col_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 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{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], 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