0213_1230
Counting sequence:
1, 1, 2, 6, 22, 87, 352, 1428, 5768, 23156, 92416, 367007, 1451780, 5725959, 22535868, 88566290, 347742688, 1364637732, 5353992916, 21005649217, 82425637860, 323523434437, 1270281675368, 4989615315114, 19607400037358, 77084254889327, 303184014866196, 1193001145648675, 4696411154680870, 18495977971097900, 72873347059741324, 287232836781335425, 1132574680784778530, 4467456684406912938, 17628200938285714996, 69583026727474637292, 274751495708764361688, 1085206097676964301766, 4287597818311356028436, 16944939735282827390172, 66986143300880786222000, 264876806525837309645632, 1047640342576030761981908, 4144626334927772387476894, 16400581067121406521007028, 64912718408260499093537430, 256976437162805027938237728, 1017527586689471747874235532, 4029814814917043694874638556, 15962716356141373919704977032, 63242391504135468779462687356, 250603237760225624852125357026, 993205803748634857007747099712, 3936981794739924464011606014706, 15608339021180727969037560479972, 61889469067399462717764172993492, 245437761665681894008053299517272, 973483159341833890187029722354198, 3861676778176143686398205589883728, 15320815713527181614443708343408726, 60791731029360249535959287898391816, 241247060702878077307965669636251912, 957486756623245690829969661673248220, 3800626081346286781939702675085819874, 15087858602949741668833631362672306998, 59903016727715927114094075773028318595, 237857586545816163861662379157837514228, 944563595502024124507832377238369944912, 3751370791693214385561272791028267250386, 14900201473024016871939060682291133289357, 59188381268384435009151424804161628262040, 235137459062151435652776201833406727225967, 934215615771738053483961405002691765525718, 3712028631571205537149197110877160148505404, 14750726003119653107137972590890003634258088, 58620887218587649332725740689712954513351995, 232984675339822114943091444824275620254864568, 926056326145870000133008068930686399944157707, 3681134286542343718965586431998165056335663596, 14633873415504970018645930660350780802491857272, 58179434761640757566424978183708150779932356050, 231319100304681591467592454273806498322627549487, 919781214178933443249626462747281670281722116448, 3657529992963578976850705182098929760650803363649, 14545239567366364802980464679026831566401277041258, 57847261975093907446643471777015661528138785896250, 230076907361321481213565255134962577959520429829548, 915147121308919584536455686579157787793758000269457, 3640288958899398015501746901074738483430492909617876, 14481290393052162681228568372834470936113434182178927, 57610886630100401118182378347649863573952138619279480, 229206640198887065599285904672522325164043974781122822, 911957575498667368790240233327269638356405129380502138, 3628660696959563992517243649348057854015236364943020539, 14439158005035253557324261279423966672359965603622925568, 57459345143355598169511909815979090915840740222894801685, 228666370218538490800405450479050242439437589005645485458, 910052166748942694906291270216004525460530088444747067132, 3622031287235587666720274395465097876854652658365503869096, 14416491973865528868099323334167386459529261871773665267337, 57383635617306796715971641967305049488537065340949671084520
Generating function in Maple syntax:
1/8*((-4*x^4+17*x^3-26*x^2+13*x-2)*(1-4*x)^(1/2)+4*x^4+7*x^3-6*x^2+x)/(-1/4+x)/(x^2-3*x+1)^2
Generating function in latex syntax:
\frac{\left(-4 x^{4}+17 x^{3}-26 x^{2}+13 x -2\right) \sqrt{1-4 x}+4 x^{4}+7 x^{3}-6 x^{2}+x}{8 \left(-\frac{1}{4}+x \right) \left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(x**4/2 + 7*x**3/8 - 3*x**2/4 + x/8 + sqrt(1 - 4*x)*(-4*x**4 + 17*x**3 - 26*x**2 + 13*x - 2)/8)/((x - 1/4)*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(-1+4*x)*(x^2-3*x+1)^4*F(x)^2-x*(-1+4*x)*(x^2+2*x-1)*(x^2-3*x+1)^2*F(x)+4*x^8-33*x^7+128*x^6-246*x^5+279*x^4-184*x^3+68*x^2-13*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+4 x \right) \left(x^{2}-3 x +1\right)^{4} F \! \left(x \right)^{2}-x \left(-1+4 x \right) \left(x^{2}+2 x -1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+4 x^{8}-33 x^{7}+128 x^{6}-246 x^{5}+279 x^{4}-184 x^{3}+68 x^{2}-13 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 87
a(6) = 352
a(7) = 1428
a(8) = 5768
a(n+9) = 4*(1+2*n)/(n+9)*a(n)-3*(37+28*n)/(n+9)*a(n+1)+1/2*(1651+729*n)/(n+9)*a(n+2)-18*(154+47*n)/(n+9)*a(n+3)+2*(2432+567*n)/(n+9)*a(n+4)-4*(1176+223*n)/(n+9)*a(n+5)+32*(81+13*n)/(n+9)*a(n+6)-(810+113*n)/(n+9)*a(n+7)+3/2*(89+11*n)/(n+9)*a(n+8), n >= 9
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) = 87
a \! \left(6\right) = 352
a \! \left(7\right) = 1428
a \! \left(8\right) = 5768
a \! \left(n +9\right) = \frac{4 \left(1+2 n \right) a \! \left(n \right)}{n +9}-\frac{3 \left(37+28 n \right) a \! \left(n +1\right)}{n +9}+\frac{\left(1651+729 n \right) a \! \left(n +2\right)}{2 n +18}-\frac{18 \left(154+47 n \right) a \! \left(n +3\right)}{n +9}+\frac{2 \left(2432+567 n \right) a \! \left(n +4\right)}{n +9}-\frac{4 \left(1176+223 n \right) a \! \left(n +5\right)}{n +9}+\frac{32 \left(81+13 n \right) a \! \left(n +6\right)}{n +9}-\frac{\left(810+113 n \right) a \! \left(n +7\right)}{n +9}+\frac{3 \left(89+11 n \right) a \! \left(n +8\right)}{2 \left(n +9\right)}, \quad n \geq 9
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/109/
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[6,x]
F[4,x] = F[1,x]+F[5,x]+F[85,x]
F[5,x] = F[6,x]*F[7,x]
F[6,x] = x
F[7,x] = F[1,x]+F[69,x]+F[70,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]*F[6,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[38,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[17,x]+F[37,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[6,x]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[15,x,k[0]]+F[9,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[6,x]
F[15,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x] = F[18,x]*F[6,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[6,x]
F[21,x] = F[1,x]+F[22,x]+F[36,x]
F[22,x] = F[23,x]
F[23,x] = F[18,x]*F[24,x]*F[6,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]+F[6,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = F[28,x]
F[28,x] = F[24,x]*F[6,x]
F[29,x] = F[30,x]+F[31,x]+F[35,x]
F[30,x] = 0
F[31,x] = F[32,x]*F[6,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[6,x]
F[34,x] = F[29,x]
F[35,x] = F[27,x]*F[6,x]
F[36,x] = F[21,x]*F[6,x]
F[37,x,k[0]] = F[11,x,k[0]]*F[16,x,k[0]]
F[38,x,k[0]] = F[39,x]+F[41,x,k[0]]
F[39,x] = F[40,x]
F[40,x] = F[18,x]*F[26,x]
F[41,x,k[0]] = 3*F[30,x]+F[42,x,k[0]]+F[68,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[6,x]
F[43,x,k[0]] = F[44,x,k[0]]+F[67,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[54,x,k[0]]
F[45,x,k[0]] = F[30,x]+F[46,x,k[0]]+F[50,x,k[0]]+F[51,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[6,x]
F[47,x,k[0]] = F[15,x,k[0]]+F[30,x]+F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[44,x,k[0]]*F[6,x]
F[49,x,k[0]] = F[47,x,k[0]]*F[6,x]
F[50,x,k[0]] = F[44,x,k[0]]*F[6,x]
F[51,x,k[0]] = F[16,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[51,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[10,x,k[0]]*F[6,x]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[18,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[16,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[57,x,k[0]]+F[6,x]
F[60,x,k[0]] = 2*F[30,x]+F[61,x,k[0]]+F[65,x,k[0]]
F[61,x,k[0]] = F[6,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[57,x,k[0]]
F[64,x,k[0]] = F[60,x,k[0]]
F[65,x,k[0]] = F[16,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[29,x]+F[60,x,k[0]]
F[67,x,k[0]] = F[55,x,k[0]]
F[68,x,k[0]] = F[16,x,k[0]]*F[38,x,k[0]]
F[69,x] = F[6,x]*F[7,x]
F[70,x] = F[6,x]*F[71,x]
F[71,x] = F[7,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[6,x]*F[74,x]*F[77,x]
F[74,x] = F[7,x]+F[75,x]
F[75,x] = F[19,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[1,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[6,x]*F[77,x]
F[80,x] = F[78,x]+F[81,x]
F[81,x] = F[30,x]+F[82,x]+F[84,x]
F[82,x] = F[6,x]*F[83,x]
F[83,x] = F[78,x]+F[81,x]
F[84,x] = F[6,x]*F[80,x]
F[85,x] = F[6,x]*F[86,x]
F[86,x] = F[87,x,1]
F[87,x,k[0]] = F[1,x]+F[132,x,k[0]]+F[140,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[6,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[1,x]+F[130,x,k[0]]+F[90,x,k[0]]+F[93,x,k[0]]+F[94,x,k[0]]
F[90,x,k[0]] = F[6,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[10,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = (F[44,x,k[0]]-F[44,x,1])/(-1+k[0])
F[93,x,k[0]] = F[6,x]*F[89,x,k[0]]
F[94,x,k[0]] = F[6,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[89,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = 2*F[30,x]+F[122,x,k[0]]+F[124,x,k[0]]+F[93,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[18,x]*F[6,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[107,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[59,x,k[0]]
F[101,x,k[0]] = F[102,x]+F[105,x,k[0]]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[6,x]
F[104,x] = F[102,x]+F[6,x]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[101,x,k[0]]*F[16,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[66,x,k[0]]
F[108,x,k[0]] = F[109,x]+F[116,x,k[0]]
F[109,x] = 2*F[30,x]+F[110,x]+F[114,x]
F[110,x] = F[111,x]*F[6,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[102,x]
F[113,x] = F[109,x]
F[114,x] = F[115,x]*F[6,x]
F[115,x] = F[109,x]+F[29,x]
F[116,x,k[0]] = 3*F[30,x]+F[117,x,k[0]]+F[121,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[6,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = F[105,x,k[0]]
F[120,x,k[0]] = F[116,x,k[0]]
F[121,x,k[0]] = F[108,x,k[0]]*F[16,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[6,x]*F[96,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[16,x,k[0]]
F[126,x,k[0]] = 2*F[30,x]+F[125,x,k[0]]+F[127,x,k[0]]+F[14,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[18,x]*F[6,x]
F[129,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[16,x,k[0]]
F[131,x,k[0]] = F[126,x,k[0]]+F[13,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]*F[6,x]
F[133,x,k[0]] = F[1,x]+F[134,x,k[0]]+F[136,x,k[0]]+F[138,x]+F[139,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[6,x]
F[135,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[136,x,k[0]] = F[137,x,k[0]]*F[6,x]
F[137,x,k[0]] = 1/(-1+k[0])*(F[133,x,k[0]]*k[0]-F[133,x,1])
F[138,x] = F[6,x]*F[86,x]
F[139,x,k[0]] = F[133,x,k[0]]*F[16,x,k[0]]
F[140,x,k[0]] = F[16,x,k[0]]*F[87,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{85}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{17}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{6}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{6}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)+F_{36}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right) F_{24}\! \left(x \right) F_{6}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right) F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{6}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{6}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right) F_{6}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right) F_{6}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right) F_{26}\! \left(x \right)
F_{41}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{50}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{60}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{60}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{69}\! \left(x \right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{70}\! \left(x \right) = F_{6}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{7}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{6}\! \left(x \right) F_{74}\! \left(x \right) F_{77}\! \left(x \right)
F_{74}\! \left(x \right) = F_{7}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{6}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{30}\! \left(x \right)+F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{6}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{6}\! \left(x \right) F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{6}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x , 1\right)
F_{87}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{132}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = \frac{F_{44}\! \left(x , y\right)-F_{44}\! \left(x , 1\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{122}\! \left(x , y\right)+F_{124}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{6}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x \right)+F_{105}\! \left(x , y\right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right)+F_{6}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x \right)+F_{116}\! \left(x , y\right)
F_{109}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{6}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{102}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{6}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right)+F_{29}\! \left(x \right)
F_{116}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{125}\! \left(x , y\right)+F_{127}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{18}\! \left(x \right) F_{6}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{138}\! \left(x \right)+F_{139}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{135}\! \left(x , y\right) = \frac{y F_{89}\! \left(x , y\right)-F_{89}\! \left(x , 1\right)}{-1+y}
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{137}\! \left(x , y\right) = \frac{y F_{133}\! \left(x , y\right)-F_{133}\! \left(x , 1\right)}{-1+y}
F_{138}\! \left(x \right) = F_{6}\! \left(x \right) F_{86}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{87}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_6(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_85(x))
Eq(F_5(x), F_6(x)*F_7(x))
Eq(F_6(x), x)
Eq(F_7(x), F_1(x) + F_69(x) + F_70(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0)*F_6(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_38(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_17(x) + F_37(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_6(x))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0) + F_15(x, k_0) + F_9(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_6(x))
Eq(F_15(x, k_0), F_13(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x), F_18(x)*F_6(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_6(x))
Eq(F_21(x), F_1(x) + F_22(x) + F_36(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_18(x)*F_24(x)*F_6(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x) + F_6(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_24(x)*F_6(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_35(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_32(x)*F_6(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_6(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_27(x)*F_6(x))
Eq(F_36(x), F_21(x)*F_6(x))
Eq(F_37(x, k_0), F_11(x, k_0)*F_16(x, k_0))
Eq(F_38(x, k_0), F_39(x) + F_41(x, k_0))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_18(x)*F_26(x))
Eq(F_41(x, k_0), 3*F_30(x) + F_42(x, k_0) + F_68(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_6(x))
Eq(F_43(x, k_0), F_44(x, k_0) + F_67(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_54(x, k_0))
Eq(F_45(x, k_0), F_30(x) + F_46(x, k_0) + F_50(x, k_0) + F_51(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_6(x))
Eq(F_47(x, k_0), F_15(x, k_0) + F_30(x) + F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_44(x, k_0)*F_6(x))
Eq(F_49(x, k_0), F_47(x, k_0)*F_6(x))
Eq(F_50(x, k_0), F_44(x, k_0)*F_6(x))
Eq(F_51(x, k_0), F_16(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_12(x, k_0) + F_51(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_10(x, k_0)*F_6(x))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_18(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_16(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_57(x, k_0) + F_6(x))
Eq(F_60(x, k_0), 2*F_30(x) + F_61(x, k_0) + F_65(x, k_0))
Eq(F_61(x, k_0), F_6(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_57(x, k_0))
Eq(F_64(x, k_0), F_60(x, k_0))
Eq(F_65(x, k_0), F_16(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_29(x) + F_60(x, k_0))
Eq(F_67(x, k_0), F_55(x, k_0))
Eq(F_68(x, k_0), F_16(x, k_0)*F_38(x, k_0))
Eq(F_69(x), F_6(x)*F_7(x))
Eq(F_70(x), F_6(x)*F_71(x))
Eq(F_71(x), F_7(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_6(x)*F_74(x)*F_77(x))
Eq(F_74(x), F_7(x) + F_75(x))
Eq(F_75(x), F_19(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_1(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_6(x)*F_77(x))
Eq(F_80(x), F_78(x) + F_81(x))
Eq(F_81(x), F_30(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_6(x)*F_83(x))
Eq(F_83(x), F_78(x) + F_81(x))
Eq(F_84(x), F_6(x)*F_80(x))
Eq(F_85(x), F_6(x)*F_86(x))
Eq(F_86(x), F_87(x, 1))
Eq(F_87(x, k_0), F_1(x) + F_132(x, k_0) + F_140(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_6(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_1(x) + F_130(x, k_0) + F_90(x, k_0) + F_93(x, k_0) + F_94(x, k_0))
Eq(F_90(x, k_0), F_6(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_10(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), -F_44(x, k_0) + (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_93(x, k_0), F_6(x)*F_89(x, k_0))
Eq(F_94(x, k_0), F_6(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_89(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_122(x, k_0) + F_124(x, k_0) + 2*F_30(x) + F_93(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_18(x)*F_6(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_107(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_59(x, k_0))
Eq(F_101(x, k_0), F_102(x) + F_105(x, k_0))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_6(x))
Eq(F_104(x), F_102(x) + F_6(x))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_101(x, k_0)*F_16(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_66(x, k_0))
Eq(F_108(x, k_0), F_109(x) + F_116(x, k_0))
Eq(F_109(x), F_110(x) + F_114(x) + 2*F_30(x))
Eq(F_110(x), F_111(x)*F_6(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_102(x))
Eq(F_113(x), F_109(x))
Eq(F_114(x), F_115(x)*F_6(x))
Eq(F_115(x), F_109(x) + F_29(x))
Eq(F_116(x, k_0), F_117(x, k_0) + F_121(x, k_0) + 3*F_30(x))
Eq(F_117(x, k_0), F_118(x, k_0)*F_6(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), F_105(x, k_0))
Eq(F_120(x, k_0), F_116(x, k_0))
Eq(F_121(x, k_0), F_108(x, k_0)*F_16(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_6(x)*F_96(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_16(x, k_0))
Eq(F_126(x, k_0), F_125(x, k_0) + F_127(x, k_0) + F_14(x, k_0) + 2*F_30(x))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_18(x)*F_6(x))
Eq(F_129(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_16(x, k_0))
Eq(F_131(x, k_0), F_126(x, k_0) + F_13(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0)*F_6(x))
Eq(F_133(x, k_0), F_1(x) + F_134(x, k_0) + F_136(x, k_0) + F_138(x) + F_139(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_6(x))
Eq(F_135(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_136(x, k_0), F_137(x, k_0)*F_6(x))
Eq(F_137(x, k_0), (k_0*F_133(x, k_0) - F_133(x, 1))/(k_0 - 1))
Eq(F_138(x), F_6(x)*F_86(x))
Eq(F_139(x, k_0), F_133(x, k_0)*F_16(x, k_0))
Eq(F_140(x, k_0), F_16(x, k_0)*F_87(x, k_0))
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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "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": [0, 1], "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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"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], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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": [0, 1], "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, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [0, 1], "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": [0, 1], "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"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/110/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[13,x]+F[4,x]
F[4,x] = F[1,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x] = x
F[13,x] = F[14,x]+F[15,x]+F[170,x]
F[14,x] = 0
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[14,x]+F[168,x]+F[169,x]+F[17,x]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = F[19,x,k[0]]*F[9,x,k[0]]
F[19,x,k[0]] = F[14,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[22,x,k[0]]
F[20,x,k[0]] = F[12,x]*F[21,x,k[0]]
F[21,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[22,x,k[0]] = F[12,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[108,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[26,x,k[0]]+F[27,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]*F[9,x,k[0]]
F[26,x,k[0]] = F[12,x]*F[24,x,k[0]]
F[27,x,k[0]] = F[12,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[52,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[43,x,k[0]]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[33,x]
F[32,x] = F[1,x]+F[12,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[33,x]+F[37,x]
F[37,x] = F[34,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[34,x]
F[42,x] = F[38,x]
F[43,x,k[0]] = 2*F[14,x]+F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[29,x,k[0]]*F[9,x,k[0]]
F[45,x,k[0]] = F[12,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[14,x]+F[25,x,k[0]]+F[47,x,k[0]]+F[48,x,k[0]]
F[47,x,k[0]] = F[12,x]*F[46,x,k[0]]
F[48,x,k[0]] = F[12,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[43,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = 3*F[14,x]+F[107,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]*F[9,x,k[0]]
F[52,x,k[0]] = 2*F[14,x]+F[51,x,k[0]]+F[53,x]+F[64,x,k[0]]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[33,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[58,x]
F[61,x] = F[55,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[12,x]*F[61,x]
F[64,x,k[0]] = F[12,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x]+F[83,x,k[0]]
F[66,x] = F[67,x]
F[67,x] = F[33,x]*F[68,x]
F[68,x] = F[69,x]+F[82,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[1,x]+F[55,x]
F[71,x] = F[12,x]+F[72,x]
F[72,x] = F[14,x]+F[73,x]+F[74,x]
F[73,x] = F[12,x]*F[59,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[12,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[76,x]
F[79,x] = F[72,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[12,x]*F[79,x]
F[82,x] = F[71,x]
F[83,x,k[0]] = F[49,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[33,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]+F[92,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[12,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[9,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[1,x]+F[89,x,k[0]]
F[92,x,k[0]] = 2*F[14,x]+F[93,x,k[0]]+F[99,x,k[0]]
F[93,x,k[0]] = F[12,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[14,x]+F[95,x,k[0]]+F[97,x,k[0]]
F[95,x,k[0]] = F[9,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[59,x]+F[94,x,k[0]]
F[97,x,k[0]] = F[12,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[89,x,k[0]]+F[94,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[12,x]
F[100,x,k[0]] = F[101,x,k[0]]+F[104,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[87,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[101,x,k[0]]*F[12,x]
F[104,x,k[0]] = F[105,x,k[0]]+F[92,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[104,x,k[0]]*F[12,x]
F[107,x,k[0]] = F[12,x]*F[83,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[114,x,k[0]]+F[14,x]+F[165,x,k[0]]+F[166,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[9,x,k[0]]
F[110,x,k[0]] = 2*F[14,x]+F[109,x,k[0]]+F[111,x,k[0]]+F[26,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[12,x]*F[33,x]
F[113,x,k[0]] = F[71,x]+F[86,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[12,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[23,x,k[0]]
F[116,x,k[0]] = 2*F[14,x]+F[117,x,k[0]]+F[118,x,k[0]]+F[120,x,k[0]]+F[121,x,k[0]]
F[117,x,k[0]] = F[109,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[116,x,k[0]]*F[12,x]
F[120,x,k[0]] = F[12,x]*F[23,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]
F[122,x,k[0]] = F[12,x]*F[123,x,k[0]]*F[33,x]
F[123,x,k[0]] = F[124,x]+F[143,x,k[0]]
F[124,x] = F[125,x]+F[71,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[127,x]
F[127,x] = F[12,x]*F[59,x]
F[128,x] = 2*F[14,x]+F[129,x]+F[135,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[131,x]+F[133,x]+F[14,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[130,x]+F[59,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[130,x]+F[59,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[126,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[12,x]*F[137,x]
F[140,x] = F[128,x]+F[141,x]
F[141,x] = F[142,x]
F[142,x] = F[12,x]*F[140,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[86,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]+F[150,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[12,x]*F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[12,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[147,x,k[0]]+F[89,x,k[0]]
F[150,x,k[0]] = 3*F[14,x]+F[151,x,k[0]]+F[157,x,k[0]]
F[151,x,k[0]] = F[12,x]*F[152,x,k[0]]
F[152,x,k[0]] = 2*F[14,x]+F[153,x,k[0]]+F[155,x,k[0]]
F[153,x,k[0]] = F[12,x]*F[154,x,k[0]]
F[154,x,k[0]] = F[152,x,k[0]]+F[94,x,k[0]]
F[155,x,k[0]] = F[12,x]*F[156,x,k[0]]
F[156,x,k[0]] = F[147,x,k[0]]+F[152,x,k[0]]
F[157,x,k[0]] = F[12,x]*F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[162,x,k[0]]
F[159,x,k[0]] = F[145,x,k[0]]+F[160,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[12,x]*F[159,x,k[0]]
F[162,x,k[0]] = F[150,x,k[0]]+F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[12,x]*F[162,x,k[0]]
F[165,x,k[0]] = F[108,x,k[0]]*F[12,x]
F[166,x,k[0]] = F[12,x]*F[167,x,k[0]]
F[167,x,k[0]] = (F[49,x,k[0]]-F[49,x,1])/(-1+k[0])
F[168,x] = F[20,x,1]
F[169,x] = F[22,x,1]
F[170,x] = F[12,x]*F[171,x]
F[171,x] = F[1,x]+F[172,x]+F[206,x]+F[208,x]
F[172,x] = F[12,x]*F[173,x]
F[173,x] = F[171,x]+F[174,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x,1]
F[176,x,k[0]] = F[177,x]*F[33,x]*F[89,x,k[0]]
F[177,x] = F[178,x]+F[181,x]
F[178,x] = F[1,x]+F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[12,x]*F[178,x]
F[181,x] = F[182,x]+F[192,x]
F[182,x] = F[183,x]
F[183,x] = F[12,x]*F[184,x]
F[184,x] = F[185,x]+F[32,x]
F[185,x] = F[182,x]+F[186,x]
F[186,x] = F[14,x]+F[187,x]+F[191,x]
F[187,x] = F[12,x]*F[188,x]
F[188,x] = F[189,x]+F[190,x]
F[189,x] = F[12,x]
F[190,x] = F[186,x]
F[191,x] = F[12,x]*F[182,x]
F[192,x] = F[14,x]+F[193,x]+F[205,x]
F[193,x] = F[12,x]*F[194,x]
F[194,x] = F[195,x]+F[198,x]
F[195,x] = F[179,x]+F[196,x]
F[196,x] = F[197,x]
F[197,x] = F[12,x]*F[179,x]
F[198,x] = F[192,x]+F[199,x]
F[199,x] = 2*F[14,x]+F[200,x]+F[204,x]
F[200,x] = F[12,x]*F[201,x]
F[201,x] = F[202,x]+F[203,x]
F[202,x] = F[196,x]
F[203,x] = F[199,x]
F[204,x] = F[12,x]*F[192,x]
F[205,x] = F[12,x]*F[181,x]
F[206,x] = F[207,x]
F[207,x] = F[12,x]*F[177,x]*F[33,x]
F[208,x] = F[12,x]*F[209,x]
F[209,x] = F[210,x,1]
F[210,x,k[0]] = F[1,x]+F[206,x]+F[211,x,k[0]]+F[214,x,k[0]]+F[261,x,k[0]]
F[211,x,k[0]] = F[12,x]*F[212,x,k[0]]
F[212,x,k[0]] = F[210,x,k[0]]+F[213,x,k[0]]
F[213,x,k[0]] = F[175,x]
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[33,x]*F[9,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[225,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[221,x,k[0]]
F[218,x,k[0]] = F[1,x]+F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]
F[220,x,k[0]] = F[218,x,k[0]]*F[9,x,k[0]]
F[221,x,k[0]] = F[179,x]+F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[12,x]*F[224,x,k[0]]
F[224,x,k[0]] = F[219,x,k[0]]+F[222,x,k[0]]
F[225,x,k[0]] = F[226,x,k[0]]+F[245,x,k[0]]
F[226,x,k[0]] = F[182,x]+F[227,x,k[0]]
F[227,x,k[0]] = F[14,x]+F[228,x,k[0]]+F[240,x,k[0]]
F[228,x,k[0]] = F[12,x]*F[229,x,k[0]]
F[229,x,k[0]] = F[230,x,k[0]]+F[233,x,k[0]]
F[230,x,k[0]] = F[219,x,k[0]]+F[231,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]
F[232,x,k[0]] = F[12,x]*F[219,x,k[0]]
F[233,x,k[0]] = F[227,x,k[0]]+F[234,x,k[0]]
F[234,x,k[0]] = 2*F[14,x]+F[235,x,k[0]]+F[239,x,k[0]]
F[235,x,k[0]] = F[12,x]*F[236,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]+F[238,x,k[0]]
F[237,x,k[0]] = F[231,x,k[0]]
F[238,x,k[0]] = F[234,x,k[0]]
F[239,x,k[0]] = F[12,x]*F[227,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]*F[9,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[59,x]
F[242,x,k[0]] = F[14,x]+F[240,x,k[0]]+F[243,x,k[0]]
F[243,x,k[0]] = F[12,x]*F[244,x,k[0]]
F[244,x,k[0]] = F[219,x,k[0]]+F[242,x,k[0]]
F[245,x,k[0]] = F[192,x]+F[246,x,k[0]]
F[246,x,k[0]] = 2*F[14,x]+F[247,x,k[0]]+F[259,x,k[0]]
F[247,x,k[0]] = F[12,x]*F[248,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]+F[252,x,k[0]]
F[249,x,k[0]] = F[222,x,k[0]]+F[250,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]
F[251,x,k[0]] = F[12,x]*F[222,x,k[0]]
F[252,x,k[0]] = F[246,x,k[0]]+F[253,x,k[0]]
F[253,x,k[0]] = 3*F[14,x]+F[254,x,k[0]]+F[258,x,k[0]]
F[254,x,k[0]] = F[12,x]*F[255,x,k[0]]
F[255,x,k[0]] = F[256,x,k[0]]+F[257,x,k[0]]
F[256,x,k[0]] = F[250,x,k[0]]
F[257,x,k[0]] = F[253,x,k[0]]
F[258,x,k[0]] = F[12,x]*F[246,x,k[0]]
F[259,x,k[0]] = F[12,x]*F[260,x,k[0]]
F[260,x,k[0]] = F[227,x,k[0]]+F[246,x,k[0]]
F[261,x,k[0]] = F[12,x]*F[262,x,k[0]]
F[262,x,k[0]] = (F[210,x,k[0]]*k[0]-F[210,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{12}\! \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_{1}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)+F_{170}\! \left(x \right)
F_{14}\! \left(x \right) = 0
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right)+F_{168}\! \left(x \right)+F_{169}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)
F_{43}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = 3 F_{14}\! \left(x \right)+F_{107}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{33}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{82}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right)+F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{72}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{71}\! \left(x \right)
F_{83}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{93}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{114}\! \left(x , y\right)+F_{14}\! \left(x \right)+F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{71}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{123}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x \right)+F_{143}\! \left(x , y\right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{71}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{14}\! \left(x \right)+F_{129}\! \left(x \right)+F_{135}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{133}\! \left(x \right)+F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{130}\! \left(x \right)+F_{59}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{130}\! \left(x \right)+F_{59}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{126}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{140}\! \left(x \right) = F_{128}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = 3 F_{14}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{159}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = -\frac{F_{49}\! \left(x , 1\right)-F_{49}\! \left(x , y\right)}{-1+y}
F_{168}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{170}\! \left(x \right) = F_{12}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{1}\! \left(x \right)+F_{172}\! \left(x \right)+F_{206}\! \left(x \right)+F_{208}\! \left(x \right)
F_{172}\! \left(x \right) = F_{12}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{171}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x , 1\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x \right) F_{33}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{181}\! \left(x \right)
F_{178}\! \left(x \right) = F_{1}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{12}\! \left(x \right) F_{178}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{192}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{12}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{32}\! \left(x \right)
F_{185}\! \left(x \right) = F_{182}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{14}\! \left(x \right)+F_{187}\! \left(x \right)+F_{191}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right) F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{190}\! \left(x \right)
F_{189}\! \left(x \right) = F_{12}\! \left(x \right)
F_{190}\! \left(x \right) = F_{186}\! \left(x \right)
F_{191}\! \left(x \right) = F_{12}\! \left(x \right) F_{182}\! \left(x \right)
F_{192}\! \left(x \right) = F_{14}\! \left(x \right)+F_{193}\! \left(x \right)+F_{205}\! \left(x \right)
F_{193}\! \left(x \right) = F_{12}\! \left(x \right) F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{198}\! \left(x \right)
F_{195}\! \left(x \right) = F_{179}\! \left(x \right)+F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{12}\! \left(x \right) F_{179}\! \left(x \right)
F_{198}\! \left(x \right) = F_{192}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = 2 F_{14}\! \left(x \right)+F_{200}\! \left(x \right)+F_{204}\! \left(x \right)
F_{200}\! \left(x \right) = F_{12}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{203}\! \left(x \right)
F_{202}\! \left(x \right) = F_{196}\! \left(x \right)
F_{203}\! \left(x \right) = F_{199}\! \left(x \right)
F_{204}\! \left(x \right) = F_{12}\! \left(x \right) F_{192}\! \left(x \right)
F_{205}\! \left(x \right) = F_{12}\! \left(x \right) F_{181}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{12}\! \left(x \right) F_{177}\! \left(x \right) F_{33}\! \left(x \right)
F_{208}\! \left(x \right) = F_{12}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x , 1\right)
F_{210}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{206}\! \left(x \right)+F_{211}\! \left(x , y\right)+F_{214}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{175}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{33}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{179}\! \left(x \right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{182}\! \left(x \right)+F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{228}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{235}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{231}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{234}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{227}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{59}\! \left(x \right)
F_{242}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{240}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{242}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{192}\! \left(x \right)+F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{247}\! \left(x , y\right)+F_{259}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{222}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = 3 F_{14}\! \left(x \right)+F_{254}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{250}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{253}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{246}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{246}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = -\frac{-y F_{210}\! \left(x , y\right)+F_{210}\! \left(x , 1\right)}{-1+y}
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_12(x)*F_3(x))
Eq(F_3(x), F_13(x) + F_4(x))
Eq(F_4(x), F_1(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_15(x) + F_170(x))
Eq(F_14(x), 0)
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_14(x) + F_168(x) + F_169(x) + F_17(x))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), F_19(x, k_0)*F_9(x, k_0))
Eq(F_19(x, k_0), F_14(x) + F_18(x, k_0) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_20(x, k_0), F_12(x)*F_21(x, k_0))
Eq(F_21(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_12(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_108(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_26(x, k_0) + F_27(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0)*F_9(x, k_0))
Eq(F_26(x, k_0), F_12(x)*F_24(x, k_0))
Eq(F_27(x, k_0), F_12(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_52(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_43(x, k_0))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_33(x))
Eq(F_32(x), F_1(x) + F_12(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_33(x) + F_37(x))
Eq(F_37(x), F_34(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_34(x))
Eq(F_42(x), F_38(x))
Eq(F_43(x, k_0), 2*F_14(x) + F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_29(x, k_0)*F_9(x, k_0))
Eq(F_45(x, k_0), F_12(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_14(x) + F_25(x, k_0) + F_47(x, k_0) + F_48(x, k_0))
Eq(F_47(x, k_0), F_12(x)*F_46(x, k_0))
Eq(F_48(x, k_0), F_12(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_43(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_107(x, k_0) + 3*F_14(x) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0)*F_9(x, k_0))
Eq(F_52(x, k_0), 2*F_14(x) + F_51(x, k_0) + F_53(x) + F_64(x, k_0))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_33(x)*F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_58(x))
Eq(F_61(x), F_55(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_61(x))
Eq(F_64(x, k_0), F_12(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x) + F_83(x, k_0))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_33(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_82(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_1(x) + F_55(x))
Eq(F_71(x), F_12(x) + F_72(x))
Eq(F_72(x), F_14(x) + F_73(x) + F_74(x))
Eq(F_73(x), F_12(x)*F_59(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_12(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_76(x))
Eq(F_79(x), F_72(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_12(x)*F_79(x))
Eq(F_82(x), F_71(x))
Eq(F_83(x, k_0), F_49(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_33(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0) + F_92(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_12(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_9(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_1(x) + F_89(x, k_0))
Eq(F_92(x, k_0), 2*F_14(x) + F_93(x, k_0) + F_99(x, k_0))
Eq(F_93(x, k_0), F_12(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_14(x) + F_95(x, k_0) + F_97(x, k_0))
Eq(F_95(x, k_0), F_9(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_59(x) + F_94(x, k_0))
Eq(F_97(x, k_0), F_12(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_89(x, k_0) + F_94(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_12(x))
Eq(F_100(x, k_0), F_101(x, k_0) + F_104(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_87(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_101(x, k_0)*F_12(x))
Eq(F_104(x, k_0), F_105(x, k_0) + F_92(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_104(x, k_0)*F_12(x))
Eq(F_107(x, k_0), F_12(x)*F_83(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_114(x, k_0) + F_14(x) + F_165(x, k_0) + F_166(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_9(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0) + F_111(x, k_0) + 2*F_14(x) + F_26(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_12(x)*F_33(x))
Eq(F_113(x, k_0), F_71(x) + F_86(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_12(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_23(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_118(x, k_0) + F_120(x, k_0) + F_121(x, k_0) + 2*F_14(x))
Eq(F_117(x, k_0), F_109(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_116(x, k_0)*F_12(x))
Eq(F_120(x, k_0), F_12(x)*F_23(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0))
Eq(F_122(x, k_0), F_12(x)*F_123(x, k_0)*F_33(x))
Eq(F_123(x, k_0), F_124(x) + F_143(x, k_0))
Eq(F_124(x), F_125(x) + F_71(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_12(x)*F_59(x))
Eq(F_128(x), F_129(x) + F_135(x) + 2*F_14(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_131(x) + F_133(x) + F_14(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_130(x) + F_59(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_130(x) + F_59(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_126(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_12(x)*F_137(x))
Eq(F_140(x), F_128(x) + F_141(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_12(x)*F_140(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_86(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_150(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_12(x)*F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_12(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_147(x, k_0) + F_89(x, k_0))
Eq(F_150(x, k_0), 3*F_14(x) + F_151(x, k_0) + F_157(x, k_0))
Eq(F_151(x, k_0), F_12(x)*F_152(x, k_0))
Eq(F_152(x, k_0), 2*F_14(x) + F_153(x, k_0) + F_155(x, k_0))
Eq(F_153(x, k_0), F_12(x)*F_154(x, k_0))
Eq(F_154(x, k_0), F_152(x, k_0) + F_94(x, k_0))
Eq(F_155(x, k_0), F_12(x)*F_156(x, k_0))
Eq(F_156(x, k_0), F_147(x, k_0) + F_152(x, k_0))
Eq(F_157(x, k_0), F_12(x)*F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_162(x, k_0))
Eq(F_159(x, k_0), F_145(x, k_0) + F_160(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_12(x)*F_159(x, k_0))
Eq(F_162(x, k_0), F_150(x, k_0) + F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_12(x)*F_162(x, k_0))
Eq(F_165(x, k_0), F_108(x, k_0)*F_12(x))
Eq(F_166(x, k_0), F_12(x)*F_167(x, k_0))
Eq(F_167(x, k_0), -F_49(x, k_0) + (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Eq(F_168(x), F_20(x, 1))
Eq(F_169(x), F_22(x, 1))
Eq(F_170(x), F_12(x)*F_171(x))
Eq(F_171(x), F_1(x) + F_172(x) + F_206(x) + F_208(x))
Eq(F_172(x), F_12(x)*F_173(x))
Eq(F_173(x), F_171(x) + F_174(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x, 1))
Eq(F_176(x, k_0), F_177(x)*F_33(x)*F_89(x, k_0))
Eq(F_177(x), F_178(x) + F_181(x))
Eq(F_178(x), F_1(x) + F_179(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_12(x)*F_178(x))
Eq(F_181(x), F_182(x) + F_192(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_12(x)*F_184(x))
Eq(F_184(x), F_185(x) + F_32(x))
Eq(F_185(x), F_182(x) + F_186(x))
Eq(F_186(x), F_14(x) + F_187(x) + F_191(x))
Eq(F_187(x), F_12(x)*F_188(x))
Eq(F_188(x), F_189(x) + F_190(x))
Eq(F_189(x), F_12(x))
Eq(F_190(x), F_186(x))
Eq(F_191(x), F_12(x)*F_182(x))
Eq(F_192(x), F_14(x) + F_193(x) + F_205(x))
Eq(F_193(x), F_12(x)*F_194(x))
Eq(F_194(x), F_195(x) + F_198(x))
Eq(F_195(x), F_179(x) + F_196(x))
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_12(x)*F_179(x))
Eq(F_198(x), F_192(x) + F_199(x))
Eq(F_199(x), 2*F_14(x) + F_200(x) + F_204(x))
Eq(F_200(x), F_12(x)*F_201(x))
Eq(F_201(x), F_202(x) + F_203(x))
Eq(F_202(x), F_196(x))
Eq(F_203(x), F_199(x))
Eq(F_204(x), F_12(x)*F_192(x))
Eq(F_205(x), F_12(x)*F_181(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_12(x)*F_177(x)*F_33(x))
Eq(F_208(x), F_12(x)*F_209(x))
Eq(F_209(x), F_210(x, 1))
Eq(F_210(x, k_0), F_1(x) + F_206(x) + F_211(x, k_0) + F_214(x, k_0) + F_261(x, k_0))
Eq(F_211(x, k_0), F_12(x)*F_212(x, k_0))
Eq(F_212(x, k_0), F_210(x, k_0) + F_213(x, k_0))
Eq(F_213(x, k_0), F_175(x))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_33(x)*F_9(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_225(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_221(x, k_0))
Eq(F_218(x, k_0), F_1(x) + F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0))
Eq(F_220(x, k_0), F_218(x, k_0)*F_9(x, k_0))
Eq(F_221(x, k_0), F_179(x) + F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_12(x)*F_224(x, k_0))
Eq(F_224(x, k_0), F_219(x, k_0) + F_222(x, k_0))
Eq(F_225(x, k_0), F_226(x, k_0) + F_245(x, k_0))
Eq(F_226(x, k_0), F_182(x) + F_227(x, k_0))
Eq(F_227(x, k_0), F_14(x) + F_228(x, k_0) + F_240(x, k_0))
Eq(F_228(x, k_0), F_12(x)*F_229(x, k_0))
Eq(F_229(x, k_0), F_230(x, k_0) + F_233(x, k_0))
Eq(F_230(x, k_0), F_219(x, k_0) + F_231(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0))
Eq(F_232(x, k_0), F_12(x)*F_219(x, k_0))
Eq(F_233(x, k_0), F_227(x, k_0) + F_234(x, k_0))
Eq(F_234(x, k_0), 2*F_14(x) + F_235(x, k_0) + F_239(x, k_0))
Eq(F_235(x, k_0), F_12(x)*F_236(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0) + F_238(x, k_0))
Eq(F_237(x, k_0), F_231(x, k_0))
Eq(F_238(x, k_0), F_234(x, k_0))
Eq(F_239(x, k_0), F_12(x)*F_227(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0)*F_9(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_59(x))
Eq(F_242(x, k_0), F_14(x) + F_240(x, k_0) + F_243(x, k_0))
Eq(F_243(x, k_0), F_12(x)*F_244(x, k_0))
Eq(F_244(x, k_0), F_219(x, k_0) + F_242(x, k_0))
Eq(F_245(x, k_0), F_192(x) + F_246(x, k_0))
Eq(F_246(x, k_0), 2*F_14(x) + F_247(x, k_0) + F_259(x, k_0))
Eq(F_247(x, k_0), F_12(x)*F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_252(x, k_0))
Eq(F_249(x, k_0), F_222(x, k_0) + F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0))
Eq(F_251(x, k_0), F_12(x)*F_222(x, k_0))
Eq(F_252(x, k_0), F_246(x, k_0) + F_253(x, k_0))
Eq(F_253(x, k_0), 3*F_14(x) + F_254(x, k_0) + F_258(x, k_0))
Eq(F_254(x, k_0), F_12(x)*F_255(x, k_0))
Eq(F_255(x, k_0), F_256(x, k_0) + F_257(x, k_0))
Eq(F_256(x, k_0), F_250(x, k_0))
Eq(F_257(x, k_0), F_253(x, k_0))
Eq(F_258(x, k_0), F_12(x)*F_246(x, k_0))
Eq(F_259(x, k_0), F_12(x)*F_260(x, k_0))
Eq(F_260(x, k_0), F_227(x, k_0) + F_246(x, k_0))
Eq(F_261(x, k_0), F_12(x)*F_262(x, k_0))
Eq(F_262(x, k_0), (-k_0*F_210(x, k_0) + F_210(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": 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"pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[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"}}]}
Specification 3
Strategy pack name: insertion_row_placements_tracked_fusion
Tree: http://permpal.com/tree/111/
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[8,x]
F[4,x] = F[16,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[6,x]
F[15,x] = F[11,x]
F[16,x] = F[17,x]+F[25,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[8,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[23,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]*F[8,x]
F[24,x,k[0]] = (F[20,x,k[0]]*k[0]-F[20,x,1])/(-1+k[0])
F[25,x] = F[26,x]+F[27,x]+F[313,x]
F[26,x] = 0
F[27,x] = F[28,x]*F[8,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[25,x]+F[6,x]
F[30,x] = F[31,x,1]
F[31,x,k[0]] = F[32,x,k[0]]+F[94,x,k[0]]
F[32,x,k[0]] = F[26,x]+F[33,x,k[0]]+F[35,x,k[0]]
F[33,x,k[0]] = F[22,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[32,x,k[0]]+F[6,x]
F[35,x,k[0]] = F[36,x,k[0]]*F[8,x]
F[36,x,k[0]] = F[37,x,k[0]]+F[41,x,k[0]]
F[37,x,k[0]] = F[32,x,k[0]]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[22,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[38,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[50,x,k[0]]
F[42,x,k[0]] = F[26,x]+F[43,x,k[0]]+F[48,x,k[0]]
F[43,x,k[0]] = F[22,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[47,x]*F[8,x]
F[47,x] = F[1,x]+F[45,x]
F[48,x,k[0]] = F[49,x,k[0]]*F[8,x]
F[49,x,k[0]] = F[38,x,k[0]]+F[42,x,k[0]]
F[50,x,k[0]] = F[26,x]+F[51,x,k[0]]+F[72,x,k[0]]+F[74,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[50,x,k[0]]+F[53,x]
F[53,x] = F[26,x]+F[54,x]+F[56,x]
F[54,x] = F[55,x]*F[8,x]
F[55,x] = F[53,x]+F[6,x]
F[56,x] = F[57,x]
F[57,x] = F[5,x]*F[58,x]*F[8,x]
F[58,x] = F[59,x]+F[8,x]
F[59,x] = F[26,x]+F[60,x]+F[64,x]
F[60,x] = F[61,x]*F[8,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]*F[8,x]
F[63,x] = F[1,x]+F[61,x]
F[64,x] = F[65,x]*F[8,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[67,x]+F[8,x]
F[67,x] = F[68,x]
F[68,x] = F[66,x]*F[8,x]
F[69,x] = F[59,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[69,x]*F[8,x]
F[72,x,k[0]] = F[73,x,k[0]]*F[8,x]
F[73,x,k[0]] = F[32,x,k[0]]+F[50,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[5,x]*F[76,x,k[0]]*F[8,x]
F[76,x,k[0]] = F[77,x,k[0]]+F[79,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[79,x,k[0]] = 2*F[26,x]+F[80,x,k[0]]+F[86,x,k[0]]
F[80,x,k[0]] = F[8,x]*F[81,x,k[0]]
F[81,x,k[0]] = F[26,x]+F[82,x,k[0]]+F[84,x,k[0]]
F[82,x,k[0]] = F[22,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[61,x]+F[81,x,k[0]]
F[84,x,k[0]] = F[8,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[38,x,k[0]]+F[81,x,k[0]]
F[86,x,k[0]] = F[8,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[91,x,k[0]]
F[88,x,k[0]] = F[77,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[8,x]*F[88,x,k[0]]
F[91,x,k[0]] = F[79,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[8,x]*F[91,x,k[0]]
F[94,x,k[0]] = F[26,x]+F[95,x,k[0]]+F[97,x,k[0]]+F[99,x,k[0]]
F[95,x,k[0]] = F[22,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[25,x]+F[94,x,k[0]]
F[97,x,k[0]] = -k[0]*(F[98,x,1]-F[98,x,k[0]])/(-1+k[0])
F[98,x,k[0]] = F[31,x,k[0]]*F[8,x]
F[99,x,k[0]] = F[100,x,k[0]]*F[8,x]
F[100,x,k[0]] = F[101,x,k[0]]+F[236,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[117,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]+F[26,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[22,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[8,x]
F[105,x,k[0]] = F[103,x,k[0]]+F[26,x]+F[78,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[8,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[109,x,k[0]]
F[108,x,k[0]] = F[105,x,k[0]]+F[38,x,k[0]]
F[109,x,k[0]] = F[102,x,k[0]]+F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]+F[116,x,k[0]]+F[26,x]
F[111,x,k[0]] = 0
F[112,x,k[0]] = F[113,x,k[0]]*F[8,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]
F[114,x,k[0]] = F[105,x,k[0]]
F[115,x,k[0]] = F[110,x,k[0]]
F[116,x,k[0]] = F[102,x,k[0]]*F[8,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[124,x,k[0]]+F[157,x,k[0]]+F[26,x]
F[118,x,k[0]] = F[119,x,k[0]]*F[22,x,k[0]]
F[119,x,k[0]] = F[120,x]+F[122,x,k[0]]
F[120,x] = F[121,x]+F[26,x]+F[56,x]
F[121,x] = F[6,x]*F[8,x]
F[122,x,k[0]] = F[118,x,k[0]]+F[123,x,k[0]]+F[26,x]+F[74,x,k[0]]
F[123,x,k[0]] = F[32,x,k[0]]*F[8,x]
F[124,x,k[0]] = F[125,x,k[0]]*F[8,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[122,x,k[0]]+F[32,x,k[0]]
F[127,x,k[0]] = F[117,x,k[0]]+F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[130,x,k[0]]+F[133,x,k[0]]+F[134,x,k[0]]+F[26,x]
F[129,x,k[0]] = 0
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[8,x]
F[132,x,k[0]] = F[122,x,k[0]]+F[128,x,k[0]]
F[133,x,k[0]] = F[117,x,k[0]]*F[8,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[5,x]*F[8,x]
F[136,x,k[0]] = F[137,x,k[0]]+F[142,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[8,x]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[8,x]
F[141,x,k[0]] = F[139,x,k[0]]+F[38,x,k[0]]
F[142,x,k[0]] = 3*F[26,x]+F[143,x,k[0]]+F[149,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]*F[8,x]
F[144,x,k[0]] = 2*F[26,x]+F[145,x,k[0]]+F[147,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]*F[8,x]
F[146,x,k[0]] = F[144,x,k[0]]+F[81,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]*F[8,x]
F[148,x,k[0]] = F[139,x,k[0]]+F[144,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[8,x]
F[150,x,k[0]] = F[151,x,k[0]]+F[154,x,k[0]]
F[151,x,k[0]] = F[137,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[151,x,k[0]]*F[8,x]
F[154,x,k[0]] = F[142,x,k[0]]+F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[154,x,k[0]]*F[8,x]
F[157,x,k[0]] = F[158,x,k[0]]*F[8,x]
F[158,x,k[0]] = F[159,x,k[0]]+F[195,x,k[0]]
F[159,x,k[0]] = (-F[160,x,1]*k[0]+F[160,x,k[0]])/(-1+k[0])
F[160,x,k[0]] = F[161,x,k[0]]+F[163,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[22,x,k[0]]*F[38,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]+F[165,x,k[0]]+F[26,x]
F[164,x,k[0]] = F[22,x,k[0]]*F[32,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]*F[8,x]
F[166,x,k[0]] = F[160,x,k[0]]+F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[172,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]+F[170,x,k[0]]+F[26,x]
F[169,x,k[0]] = F[22,x,k[0]]*F[42,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]*F[8,x]
F[171,x,k[0]] = F[161,x,k[0]]+F[168,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[174,x,k[0]]+F[176,x,k[0]]+F[26,x]
F[173,x,k[0]] = F[22,x,k[0]]*F[50,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[8,x]
F[175,x,k[0]] = F[163,x,k[0]]+F[172,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]*F[5,x]*F[8,x]
F[178,x,k[0]] = F[179,x,k[0]]+F[181,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]
F[180,x,k[0]] = F[161,x,k[0]]*F[8,x]
F[181,x,k[0]] = 2*F[26,x]+F[182,x,k[0]]+F[187,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]*F[8,x]
F[183,x,k[0]] = F[184,x,k[0]]+F[185,x,k[0]]+F[26,x]
F[184,x,k[0]] = F[22,x,k[0]]*F[81,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[8,x]
F[186,x,k[0]] = F[161,x,k[0]]+F[183,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[8,x]
F[188,x,k[0]] = F[189,x,k[0]]+F[192,x,k[0]]
F[189,x,k[0]] = F[179,x,k[0]]+F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[191,x,k[0]] = F[189,x,k[0]]*F[8,x]
F[192,x,k[0]] = F[181,x,k[0]]+F[193,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]
F[194,x,k[0]] = F[192,x,k[0]]*F[8,x]
F[195,x,k[0]] = F[196,x,k[0]]+F[215,x,k[0]]
F[196,x,k[0]] = 2*F[26,x]+F[145,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]*F[8,x]
F[198,x,k[0]] = F[148,x,k[0]]+F[199,x,k[0]]
F[199,x,k[0]] = F[196,x,k[0]]+F[200,x,k[0]]
F[200,x,k[0]] = 3*F[26,x]+F[201,x,k[0]]+F[214,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[8,x]
F[202,x,k[0]] = F[203,x,k[0]]+F[211,x,k[0]]
F[203,x,k[0]] = 2*F[26,x]+F[204,x,k[0]]+F[209,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]*F[22,x,k[0]]
F[205,x,k[0]] = F[203,x,k[0]]+F[206,x]
F[206,x] = F[207,x]
F[207,x] = F[208,x]*F[8,x]
F[208,x] = F[206,x]+F[61,x]
F[209,x,k[0]] = F[210,x,k[0]]*F[8,x]
F[210,x,k[0]] = F[203,x,k[0]]+F[81,x,k[0]]
F[211,x,k[0]] = 3*F[26,x]+F[201,x,k[0]]+F[212,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]*F[8,x]
F[213,x,k[0]] = F[144,x,k[0]]+F[211,x,k[0]]
F[214,x,k[0]] = F[199,x,k[0]]*F[8,x]
F[215,x,k[0]] = (-F[216,x,1]*k[0]+F[216,x,k[0]])/(-1+k[0])
F[216,x,k[0]] = 2*F[26,x]+F[217,x,k[0]]+F[231,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]*F[22,x,k[0]]
F[218,x,k[0]] = 2*F[26,x]+F[219,x,k[0]]+F[226,x,k[0]]
F[219,x,k[0]] = F[22,x,k[0]]*F[220,x,k[0]]
F[220,x,k[0]] = F[218,x,k[0]]+F[221,x]
F[221,x] = F[222,x]
F[222,x] = F[223,x]*F[6,x]
F[223,x] = F[224,x]
F[224,x] = F[225,x]*F[63,x]*F[8,x]
F[225,x] = F[1,x]+F[223,x]
F[226,x,k[0]] = F[227,x,k[0]]*F[8,x]
F[227,x,k[0]] = F[228,x,k[0]]+F[229,x,k[0]]
F[228,x,k[0]] = F[218,x,k[0]]+F[32,x,k[0]]
F[229,x,k[0]] = F[230,x,k[0]]
F[230,x,k[0]] = F[6,x]*F[76,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]*F[8,x]
F[232,x,k[0]] = F[233,x,k[0]]+F[234,x,k[0]]
F[233,x,k[0]] = F[163,x,k[0]]+F[216,x,k[0]]
F[234,x,k[0]] = F[235,x,k[0]]
F[235,x,k[0]] = F[178,x,k[0]]*F[6,x]
F[236,x,k[0]] = F[237,x,k[0]]+F[257,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]+F[244,x,k[0]]+F[255,x,k[0]]+F[26,x]
F[238,x,k[0]] = F[22,x,k[0]]*F[239,x,k[0]]
F[239,x,k[0]] = F[240,x]+F[242,x,k[0]]
F[240,x] = F[241,x]
F[241,x] = F[45,x]*F[8,x]
F[242,x,k[0]] = 2*F[26,x]+F[238,x,k[0]]+F[243,x,k[0]]
F[243,x,k[0]] = F[42,x,k[0]]*F[8,x]
F[244,x,k[0]] = F[245,x,k[0]]*F[8,x]
F[245,x,k[0]] = F[246,x,k[0]]+F[247,x,k[0]]
F[246,x,k[0]] = F[242,x,k[0]]+F[42,x,k[0]]
F[247,x,k[0]] = F[237,x,k[0]]+F[248,x,k[0]]
F[248,x,k[0]] = 2*F[26,x]+F[249,x,k[0]]+F[250,x,k[0]]+F[254,x,k[0]]
F[249,x,k[0]] = 0
F[250,x,k[0]] = F[251,x,k[0]]*F[8,x]
F[251,x,k[0]] = F[252,x,k[0]]+F[253,x,k[0]]
F[252,x,k[0]] = F[242,x,k[0]]
F[253,x,k[0]] = F[248,x,k[0]]
F[254,x,k[0]] = F[237,x,k[0]]*F[8,x]
F[255,x,k[0]] = F[256,x,k[0]]*F[8,x]
F[256,x,k[0]] = F[102,x,k[0]]+F[237,x,k[0]]
F[257,x,k[0]] = F[134,x,k[0]]+F[258,x,k[0]]+F[26,x]+F[300,x,k[0]]+F[311,x,k[0]]
F[258,x,k[0]] = F[22,x,k[0]]*F[259,x,k[0]]
F[259,x,k[0]] = F[260,x]+F[297,x,k[0]]
F[260,x] = F[261,x]
F[261,x] = F[262,x,1]
F[262,x,k[0]] = F[263,x,k[0]]
F[263,x,k[0]] = 2*F[26,x]+F[264,x,k[0]]+F[269,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]
F[265,x,k[0]] = F[22,x,k[0]]*F[266,x,k[0]]*F[6,x]*F[8,x]
F[266,x,k[0]] = F[1,x]+F[267,x,k[0]]
F[267,x,k[0]] = F[268,x,k[0]]
F[268,x,k[0]] = F[22,x,k[0]]*F[266,x,k[0]]
F[269,x,k[0]] = F[270,x,k[0]]*F[8,x]
F[270,x,k[0]] = F[271,x,k[0]]+F[274,x,k[0]]
F[271,x,k[0]] = F[263,x,k[0]]+F[272,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0]]
F[273,x,k[0]] = F[267,x,k[0]]*F[8,x]
F[274,x,k[0]] = (-F[275,x,1]*k[0]+F[275,x,k[0]])/(-1+k[0])
F[275,x,k[0]] = F[276,x,k[0]]+F[280,x,k[0]]
F[276,x,k[0]] = F[277,x,k[0]]
F[277,x,k[0]] = F[278,x,k[0]]*F[8,x]
F[278,x,k[0]] = F[279,x,k[0]]
F[279,x,k[0]] = F[22,x,k[0]]*F[267,x,k[0]]
F[280,x,k[0]] = F[281,x,k[0]]
F[281,x,k[0]] = F[282,x,k[0]]*F[8,x]
F[282,x,k[0]] = F[26,x]+F[283,x,k[0]]+F[285,x,k[0]]
F[283,x,k[0]] = F[284,x,k[0]]
F[284,x,k[0]] = F[22,x,k[0]]*F[267,x,k[0]]*F[6,x]
F[285,x,k[0]] = F[286,x,k[0]]*F[8,x]
F[286,x,k[0]] = F[287,x,k[0]]+F[288,x,k[0]]
F[287,x,k[0]] = F[278,x,k[0]]+F[282,x,k[0]]
F[288,x,k[0]] = F[289,x,k[0]]+F[294,x,k[0]]
F[289,x,k[0]] = F[290,x,k[0]]
F[290,x,k[0]] = F[22,x,k[0]]*F[291,x,k[0]]
F[291,x,k[0]] = F[292,x,k[0]]
F[292,x,k[0]] = F[22,x,k[0]]*F[293,x,k[0]]
F[293,x,k[0]] = F[291,x,k[0]]+F[45,x]
F[294,x,k[0]] = F[295,x,k[0]]
F[295,x,k[0]] = F[22,x,k[0]]*F[296,x,k[0]]
F[296,x,k[0]] = (-F[282,x,1]*k[0]+F[282,x,k[0]])/(-1+k[0])
F[297,x,k[0]] = 2*F[26,x]+F[258,x,k[0]]+F[298,x,k[0]]+F[299,x,k[0]]
F[298,x,k[0]] = F[50,x,k[0]]*F[8,x]
F[299,x,k[0]] = 0
F[300,x,k[0]] = F[301,x,k[0]]*F[8,x]
F[301,x,k[0]] = F[302,x,k[0]]+F[303,x,k[0]]
F[302,x,k[0]] = F[297,x,k[0]]+F[50,x,k[0]]
F[303,x,k[0]] = F[257,x,k[0]]+F[304,x,k[0]]
F[304,x,k[0]] = 2*F[26,x]+F[305,x,k[0]]+F[306,x,k[0]]+F[309,x,k[0]]+F[310,x,k[0]]
F[305,x,k[0]] = 0
F[306,x,k[0]] = F[307,x,k[0]]
F[307,x,k[0]] = F[308,x,k[0]]*F[8,x]
F[308,x,k[0]] = F[297,x,k[0]]+F[304,x,k[0]]
F[309,x,k[0]] = F[257,x,k[0]]*F[8,x]
F[310,x,k[0]] = 0
F[311,x,k[0]] = F[312,x,k[0]]*F[8,x]
F[312,x,k[0]] = F[117,x,k[0]]+F[257,x,k[0]]
F[313,x] = F[314,x]*F[8,x]
F[314,x] = F[315,x]+F[379,x]
F[315,x] = F[316,x]+F[327,x]
F[316,x] = F[317,x]
F[317,x] = F[318,x]*F[8,x]
F[318,x] = F[319,x]+F[320,x]
F[319,x] = F[1,x]+F[8,x]
F[320,x] = F[316,x]+F[321,x]
F[321,x] = F[26,x]+F[322,x]+F[326,x]
F[322,x] = F[323,x]*F[8,x]
F[323,x] = F[324,x]+F[325,x]
F[324,x] = F[8,x]
F[325,x] = F[321,x]
F[326,x] = F[316,x]*F[8,x]
F[327,x] = F[26,x]+F[328,x]+F[334,x]
F[328,x] = F[329,x]*F[8,x]
F[329,x] = F[330,x]+F[331,x]
F[330,x] = F[327,x]+F[6,x]
F[331,x] = F[332,x]
F[332,x] = F[333,x]*F[6,x]*F[61,x]
F[333,x] = F[1,x]+F[316,x]
F[334,x] = F[335,x]*F[8,x]
F[335,x] = F[315,x]+F[336,x]
F[336,x] = F[337,x,1]
F[337,x,k[0]] = F[338,x,k[0]]+F[354,x,k[0]]
F[338,x,k[0]] = F[26,x]+F[339,x,k[0]]+F[349,x,k[0]]
F[339,x,k[0]] = F[340,x,k[0]]*F[8,x]
F[340,x,k[0]] = F[341,x,k[0]]+F[342,x,k[0]]
F[341,x,k[0]] = F[267,x,k[0]]+F[272,x,k[0]]
F[342,x,k[0]] = F[338,x,k[0]]+F[343,x,k[0]]
F[343,x,k[0]] = 2*F[26,x]+F[344,x,k[0]]+F[348,x,k[0]]
F[344,x,k[0]] = F[345,x,k[0]]*F[8,x]
F[345,x,k[0]] = F[346,x,k[0]]+F[347,x,k[0]]
F[346,x,k[0]] = F[272,x,k[0]]
F[347,x,k[0]] = F[343,x,k[0]]
F[348,x,k[0]] = F[338,x,k[0]]*F[8,x]
F[349,x,k[0]] = F[22,x,k[0]]*F[350,x,k[0]]
F[350,x,k[0]] = F[351,x,k[0]]+F[61,x]
F[351,x,k[0]] = F[26,x]+F[349,x,k[0]]+F[352,x,k[0]]
F[352,x,k[0]] = F[353,x,k[0]]*F[8,x]
F[353,x,k[0]] = F[267,x,k[0]]+F[351,x,k[0]]
F[354,x,k[0]] = F[26,x]+F[355,x,k[0]]+F[374,x,k[0]]+F[377,x,k[0]]
F[355,x,k[0]] = F[356,x,k[0]]
F[356,x,k[0]] = F[357,x,k[0]]*F[8,x]
F[357,x,k[0]] = F[354,x,k[0]]+F[358,x,k[0]]
F[358,x,k[0]] = F[26,x]+F[359,x,k[0]]+F[361,x,k[0]]
F[359,x,k[0]] = F[22,x,k[0]]*F[360,x,k[0]]
F[360,x,k[0]] = F[358,x,k[0]]+F[6,x]
F[361,x,k[0]] = F[362,x,k[0]]
F[362,x,k[0]] = F[363,x,k[0]]*F[5,x]*F[8,x]
F[363,x,k[0]] = F[22,x,k[0]]+F[364,x,k[0]]
F[364,x,k[0]] = F[26,x]+F[365,x,k[0]]+F[366,x,k[0]]
F[365,x,k[0]] = F[22,x,k[0]]*F[61,x]
F[366,x,k[0]] = F[367,x,k[0]]*F[8,x]
F[367,x,k[0]] = F[368,x,k[0]]+F[371,x,k[0]]
F[368,x,k[0]] = F[22,x,k[0]]+F[369,x,k[0]]
F[369,x,k[0]] = F[370,x,k[0]]
F[370,x,k[0]] = F[368,x,k[0]]*F[8,x]
F[371,x,k[0]] = F[364,x,k[0]]+F[372,x,k[0]]
F[372,x,k[0]] = F[373,x,k[0]]
F[373,x,k[0]] = F[371,x,k[0]]*F[8,x]
F[374,x,k[0]] = F[375,x,k[0]]
F[375,x,k[0]] = F[22,x,k[0]]*F[376,x,k[0]]*F[6,x]
F[376,x,k[0]] = F[316,x]+F[338,x,k[0]]
F[377,x,k[0]] = F[378,x,k[0]]*F[8,x]
F[378,x,k[0]] = -k[0]*(F[337,x,1]-F[337,x,k[0]])/(-1+k[0])
F[379,x] = F[380,x]+F[393,x]
F[380,x] = F[26,x]+F[381,x]+F[391,x]
F[381,x] = F[382,x]*F[8,x]
F[382,x] = F[383,x]+F[384,x]
F[383,x] = F[240,x]+F[45,x]
F[384,x] = F[380,x]+F[385,x]
F[385,x] = 2*F[26,x]+F[386,x]+F[390,x]
F[386,x] = F[387,x]*F[8,x]
F[387,x] = F[388,x]+F[389,x]
F[388,x] = F[240,x]
F[389,x] = F[385,x]
F[390,x] = F[380,x]*F[8,x]
F[391,x] = F[392,x]*F[8,x]
F[392,x] = F[316,x]+F[380,x]
F[393,x] = F[26,x]+F[394,x]+F[404,x]+F[406,x]
F[394,x] = F[395,x]*F[8,x]
F[395,x] = F[396,x]+F[397,x]
F[396,x] = F[260,x]+F[53,x]
F[397,x] = F[393,x]+F[398,x]
F[398,x] = 2*F[26,x]+F[399,x]+F[402,x]+F[403,x]
F[399,x] = F[400,x]
F[400,x] = F[401,x]*F[8,x]
F[401,x] = F[260,x]+F[398,x]
F[402,x] = F[393,x]*F[8,x]
F[403,x] = 0
F[404,x] = F[405,x]*F[8,x]
F[405,x] = F[327,x]+F[393,x]
F[406,x] = F[407,x]
F[407,x] = F[408,x,1]
F[408,x,k[0]] = F[409,x,k[0]]*F[5,x]*F[8,x]
F[409,x,k[0]] = F[410,x,k[0]]+F[412,x,k[0]]
F[410,x,k[0]] = F[411,x,k[0]]
F[411,x,k[0]] = F[22,x,k[0]]*F[61,x]
F[412,x,k[0]] = 2*F[26,x]+F[413,x,k[0]]+F[419,x,k[0]]
F[413,x,k[0]] = F[22,x,k[0]]*F[414,x]
F[414,x] = F[26,x]+F[415,x]+F[417,x]
F[415,x] = F[416,x]*F[8,x]
F[416,x] = F[414,x]+F[61,x]
F[417,x] = F[418,x]*F[8,x]
F[418,x] = F[414,x]+F[61,x]
F[419,x,k[0]] = F[420,x,k[0]]*F[8,x]
F[420,x,k[0]] = F[421,x,k[0]]+F[424,x,k[0]]
F[421,x,k[0]] = F[410,x,k[0]]+F[422,x,k[0]]
F[422,x,k[0]] = F[423,x,k[0]]
F[423,x,k[0]] = F[421,x,k[0]]*F[8,x]
F[424,x,k[0]] = F[412,x,k[0]]+F[425,x,k[0]]
F[425,x,k[0]] = F[426,x,k[0]]
F[426,x,k[0]] = F[424,x,k[0]]*F[8,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
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_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{6}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{25}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{313}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x , 1\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right) F_{8}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{26}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{53}\! \left(x \right)+F_{6}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{5}\! \left(x \right) F_{58}\! \left(x \right) F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)+F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right) F_{8}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right) F_{8}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{66}\! \left(x \right) F_{8}\! \left(x \right)
F_{69}\! \left(x \right) = F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{69}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{73}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{76}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{79}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = -\frac{y \left(F_{98}\! \left(x , 1\right)-F_{98}\! \left(x , y\right)\right)}{-1+y}
F_{98}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{111}\! \left(x , y\right) = 0
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{124}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{122}\! \left(x , y\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{26}\! \left(x \right)+F_{56}\! \left(x \right)
F_{121}\! \left(x \right) = F_{6}\! \left(x \right) F_{8}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{129}\! \left(x , y\right) = 0
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = 3 F_{26}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{144}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = -\frac{F_{160}\! \left(x , 1\right) y -F_{160}\! \left(x , y\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{174}\! \left(x , y\right)+F_{176}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{181}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{182}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{198}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = 3 F_{26}\! \left(x \right)+F_{201}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{204}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right) F_{8}\! \left(x \right)
F_{208}\! \left(x \right) = F_{206}\! \left(x \right)+F_{61}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{210}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = 3 F_{26}\! \left(x \right)+F_{201}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{213}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{215}\! \left(x , y\right) = -\frac{F_{216}\! \left(x , 1\right) y -F_{216}\! \left(x , y\right)}{-1+y}
F_{216}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{217}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{219}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right) F_{6}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right) F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{225}\! \left(x \right) = F_{1}\! \left(x \right)+F_{223}\! \left(x \right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{244}\! \left(x , y\right)+F_{255}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x \right)+F_{242}\! \left(x , y\right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{45}\! \left(x \right) F_{8}\! \left(x \right)
F_{242}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{238}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{249}\! \left(x , y\right)+F_{250}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = 0
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{242}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{248}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{237}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{258}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{300}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x \right)+F_{297}\! \left(x , y\right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{262}\! \left(x , 1\right)
F_{262}\! \left(x , y\right) = F_{263}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{264}\! \left(x , y\right)+F_{269}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{265}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{266}\! \left(x , y\right) F_{6}\! \left(x \right) F_{8}\! \left(x \right)
F_{266}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{267}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{266}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{263}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{267}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{274}\! \left(x , y\right) = -\frac{F_{275}\! \left(x , 1\right) y -F_{275}\! \left(x , y\right)}{-1+y}
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{280}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{278}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{278}\! \left(x , y\right) = F_{279}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{267}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{281}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{282}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{282}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{283}\! \left(x , y\right)+F_{285}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{284}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{267}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{285}\! \left(x , y\right) = F_{286}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{288}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{282}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{289}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{290}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{291}\! \left(x , y\right)
F_{291}\! \left(x , y\right) = F_{292}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{293}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{291}\! \left(x , y\right)+F_{45}\! \left(x \right)
F_{294}\! \left(x , y\right) = F_{295}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = -\frac{F_{282}\! \left(x , 1\right) y -F_{282}\! \left(x , y\right)}{-1+y}
F_{297}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{258}\! \left(x , y\right)+F_{298}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{299}\! \left(x , y\right) = 0
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{301}\! \left(x , y\right) = F_{302}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{257}\! \left(x , y\right)+F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{305}\! \left(x , y\right)+F_{306}\! \left(x , y\right)+F_{309}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = 0
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{308}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{308}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{304}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{257}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{310}\! \left(x , y\right) = 0
F_{311}\! \left(x , y\right) = F_{312}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{312}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right) F_{8}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)+F_{379}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)+F_{327}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right) F_{8}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)+F_{320}\! \left(x \right)
F_{319}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{320}\! \left(x \right) = F_{316}\! \left(x \right)+F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{26}\! \left(x \right)+F_{322}\! \left(x \right)+F_{326}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right) F_{8}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)+F_{325}\! \left(x \right)
F_{324}\! \left(x \right) = F_{8}\! \left(x \right)
F_{325}\! \left(x \right) = F_{321}\! \left(x \right)
F_{326}\! \left(x \right) = F_{316}\! \left(x \right) F_{8}\! \left(x \right)
F_{327}\! \left(x \right) = F_{26}\! \left(x \right)+F_{328}\! \left(x \right)+F_{334}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x \right) F_{8}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)+F_{331}\! \left(x \right)
F_{330}\! \left(x \right) = F_{327}\! \left(x \right)+F_{6}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right) F_{6}\! \left(x \right) F_{61}\! \left(x \right)
F_{333}\! \left(x \right) = F_{1}\! \left(x \right)+F_{316}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right) F_{8}\! \left(x \right)
F_{335}\! \left(x \right) = F_{315}\! \left(x \right)+F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x , 1\right)
F_{337}\! \left(x , y\right) = F_{338}\! \left(x , y\right)+F_{354}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{339}\! \left(x , y\right)+F_{349}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{340}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{340}\! \left(x , y\right) = F_{341}\! \left(x , y\right)+F_{342}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{267}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{342}\! \left(x , y\right) = F_{338}\! \left(x , y\right)+F_{343}\! \left(x , y\right)
F_{343}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{344}\! \left(x , y\right)+F_{348}\! \left(x , y\right)
F_{344}\! \left(x , y\right) = F_{345}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right)+F_{347}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{272}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{343}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = F_{338}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{349}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{350}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{351}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{351}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{349}\! \left(x , y\right)+F_{352}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{353}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{353}\! \left(x , y\right) = F_{267}\! \left(x , y\right)+F_{351}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{355}\! \left(x , y\right)+F_{374}\! \left(x , y\right)+F_{377}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{356}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{357}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{357}\! \left(x , y\right) = F_{354}\! \left(x , y\right)+F_{358}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{359}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{360}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{358}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{361}\! \left(x , y\right) = F_{362}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{363}\! \left(x , y\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{363}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{364}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{365}\! \left(x , y\right)+F_{366}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{61}\! \left(x \right)
F_{366}\! \left(x , y\right) = F_{367}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{367}\! \left(x , y\right) = F_{368}\! \left(x , y\right)+F_{371}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{369}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{370}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{368}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{371}\! \left(x , y\right) = F_{364}\! \left(x , y\right)+F_{372}\! \left(x , y\right)
F_{372}\! \left(x , y\right) = F_{373}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{371}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{374}\! \left(x , y\right) = F_{375}\! \left(x , y\right)
F_{375}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{376}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{376}\! \left(x , y\right) = F_{316}\! \left(x \right)+F_{338}\! \left(x , y\right)
F_{377}\! \left(x , y\right) = F_{378}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{378}\! \left(x , y\right) = -\frac{y \left(F_{337}\! \left(x , 1\right)-F_{337}\! \left(x , y\right)\right)}{-1+y}
F_{379}\! \left(x \right) = F_{380}\! \left(x \right)+F_{393}\! \left(x \right)
F_{380}\! \left(x \right) = F_{26}\! \left(x \right)+F_{381}\! \left(x \right)+F_{391}\! \left(x \right)
F_{381}\! \left(x \right) = F_{382}\! \left(x \right) F_{8}\! \left(x \right)
F_{382}\! \left(x \right) = F_{383}\! \left(x \right)+F_{384}\! \left(x \right)
F_{383}\! \left(x \right) = F_{240}\! \left(x \right)+F_{45}\! \left(x \right)
F_{384}\! \left(x \right) = F_{380}\! \left(x \right)+F_{385}\! \left(x \right)
F_{385}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{386}\! \left(x \right)+F_{390}\! \left(x \right)
F_{386}\! \left(x \right) = F_{387}\! \left(x \right) F_{8}\! \left(x \right)
F_{387}\! \left(x \right) = F_{388}\! \left(x \right)+F_{389}\! \left(x \right)
F_{388}\! \left(x \right) = F_{240}\! \left(x \right)
F_{389}\! \left(x \right) = F_{385}\! \left(x \right)
F_{390}\! \left(x \right) = F_{380}\! \left(x \right) F_{8}\! \left(x \right)
F_{391}\! \left(x \right) = F_{392}\! \left(x \right) F_{8}\! \left(x \right)
F_{392}\! \left(x \right) = F_{316}\! \left(x \right)+F_{380}\! \left(x \right)
F_{393}\! \left(x \right) = F_{26}\! \left(x \right)+F_{394}\! \left(x \right)+F_{404}\! \left(x \right)+F_{406}\! \left(x \right)
F_{394}\! \left(x \right) = F_{395}\! \left(x \right) F_{8}\! \left(x \right)
F_{395}\! \left(x \right) = F_{396}\! \left(x \right)+F_{397}\! \left(x \right)
F_{396}\! \left(x \right) = F_{260}\! \left(x \right)+F_{53}\! \left(x \right)
F_{397}\! \left(x \right) = F_{393}\! \left(x \right)+F_{398}\! \left(x \right)
F_{398}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{399}\! \left(x \right)+F_{402}\! \left(x \right)+F_{403}\! \left(x \right)
F_{399}\! \left(x \right) = F_{400}\! \left(x \right)
F_{400}\! \left(x \right) = F_{401}\! \left(x \right) F_{8}\! \left(x \right)
F_{401}\! \left(x \right) = F_{260}\! \left(x \right)+F_{398}\! \left(x \right)
F_{402}\! \left(x \right) = F_{393}\! \left(x \right) F_{8}\! \left(x \right)
F_{403}\! \left(x \right) = 0
F_{404}\! \left(x \right) = F_{405}\! \left(x \right) F_{8}\! \left(x \right)
F_{405}\! \left(x \right) = F_{327}\! \left(x \right)+F_{393}\! \left(x \right)
F_{406}\! \left(x \right) = F_{407}\! \left(x \right)
F_{407}\! \left(x \right) = F_{408}\! \left(x , 1\right)
F_{408}\! \left(x , y\right) = F_{409}\! \left(x , y\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{409}\! \left(x , y\right) = F_{410}\! \left(x , y\right)+F_{412}\! \left(x , y\right)
F_{410}\! \left(x , y\right) = F_{411}\! \left(x , y\right)
F_{411}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{61}\! \left(x \right)
F_{412}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{413}\! \left(x , y\right)+F_{419}\! \left(x , y\right)
F_{413}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{414}\! \left(x \right)
F_{414}\! \left(x \right) = F_{26}\! \left(x \right)+F_{415}\! \left(x \right)+F_{417}\! \left(x \right)
F_{415}\! \left(x \right) = F_{416}\! \left(x \right) F_{8}\! \left(x \right)
F_{416}\! \left(x \right) = F_{414}\! \left(x \right)+F_{61}\! \left(x \right)
F_{417}\! \left(x \right) = F_{418}\! \left(x \right) F_{8}\! \left(x \right)
F_{418}\! \left(x \right) = F_{414}\! \left(x \right)+F_{61}\! \left(x \right)
F_{419}\! \left(x , y\right) = F_{420}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{420}\! \left(x , y\right) = F_{421}\! \left(x , y\right)+F_{424}\! \left(x , y\right)
F_{421}\! \left(x , y\right) = F_{410}\! \left(x , y\right)+F_{422}\! \left(x , y\right)
F_{422}\! \left(x , y\right) = F_{423}\! \left(x , y\right)
F_{423}\! \left(x , y\right) = F_{421}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{424}\! \left(x , y\right) = F_{412}\! \left(x , y\right)+F_{425}\! \left(x , y\right)
F_{425}\! \left(x , y\right) = F_{426}\! \left(x , y\right)
F_{426}\! \left(x , y\right) = F_{424}\! \left(x , y\right) F_{8}\! \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_8(x))
Eq(F_4(x), F_16(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_6(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), F_17(x) + F_25(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_8(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_23(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0)*F_8(x))
Eq(F_24(x, k_0), (-k_0*F_20(x, k_0) + F_20(x, 1))/(1 - k_0))
Eq(F_25(x), F_26(x) + F_27(x) + F_313(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_28(x)*F_8(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_25(x) + F_6(x))
Eq(F_30(x), F_31(x, 1))
Eq(F_31(x, k_0), F_32(x, k_0) + F_94(x, k_0))
Eq(F_32(x, k_0), F_26(x) + F_33(x, k_0) + F_35(x, k_0))
Eq(F_33(x, k_0), F_22(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_32(x, k_0) + F_6(x))
Eq(F_35(x, k_0), F_36(x, k_0)*F_8(x))
Eq(F_36(x, k_0), F_37(x, k_0) + F_41(x, k_0))
Eq(F_37(x, k_0), F_32(x, k_0) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_22(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_38(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_50(x, k_0))
Eq(F_42(x, k_0), F_26(x) + F_43(x, k_0) + F_48(x, k_0))
Eq(F_43(x, k_0), F_22(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x)*F_8(x))
Eq(F_47(x), F_1(x) + F_45(x))
Eq(F_48(x, k_0), F_49(x, k_0)*F_8(x))
Eq(F_49(x, k_0), F_38(x, k_0) + F_42(x, k_0))
Eq(F_50(x, k_0), F_26(x) + F_51(x, k_0) + F_72(x, k_0) + F_74(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_50(x, k_0) + F_53(x))
Eq(F_53(x), F_26(x) + F_54(x) + F_56(x))
Eq(F_54(x), F_55(x)*F_8(x))
Eq(F_55(x), F_53(x) + F_6(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_5(x)*F_58(x)*F_8(x))
Eq(F_58(x), F_59(x) + F_8(x))
Eq(F_59(x), F_26(x) + F_60(x) + F_64(x))
Eq(F_60(x), F_61(x)*F_8(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x)*F_8(x))
Eq(F_63(x), F_1(x) + F_61(x))
Eq(F_64(x), F_65(x)*F_8(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_67(x) + F_8(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_66(x)*F_8(x))
Eq(F_69(x), F_59(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_69(x)*F_8(x))
Eq(F_72(x, k_0), F_73(x, k_0)*F_8(x))
Eq(F_73(x, k_0), F_32(x, k_0) + F_50(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_5(x)*F_76(x, k_0)*F_8(x))
Eq(F_76(x, k_0), F_77(x, k_0) + F_79(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_79(x, k_0), 2*F_26(x) + F_80(x, k_0) + F_86(x, k_0))
Eq(F_80(x, k_0), F_8(x)*F_81(x, k_0))
Eq(F_81(x, k_0), F_26(x) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_82(x, k_0), F_22(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_61(x) + F_81(x, k_0))
Eq(F_84(x, k_0), F_8(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_38(x, k_0) + F_81(x, k_0))
Eq(F_86(x, k_0), F_8(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_91(x, k_0))
Eq(F_88(x, k_0), F_77(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_8(x)*F_88(x, k_0))
Eq(F_91(x, k_0), F_79(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_8(x)*F_91(x, k_0))
Eq(F_94(x, k_0), F_26(x) + F_95(x, k_0) + F_97(x, k_0) + F_99(x, k_0))
Eq(F_95(x, k_0), F_22(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_25(x) + F_94(x, k_0))
Eq(F_97(x, k_0), -F_98(x, 1) + (-k_0*F_98(x, k_0) + F_98(x, 1))/(1 - k_0))
Eq(F_98(x, k_0), F_31(x, k_0)*F_8(x))
Eq(F_99(x, k_0), F_100(x, k_0)*F_8(x))
Eq(F_100(x, k_0), F_101(x, k_0) + F_236(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_117(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_106(x, k_0) + F_26(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_22(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_8(x))
Eq(F_105(x, k_0), F_103(x, k_0) + F_26(x) + F_78(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_8(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_109(x, k_0))
Eq(F_108(x, k_0), F_105(x, k_0) + F_38(x, k_0))
Eq(F_109(x, k_0), F_102(x, k_0) + F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0) + F_116(x, k_0) + F_26(x))
Eq(F_111(x, k_0), 0)
Eq(F_112(x, k_0), F_113(x, k_0)*F_8(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0))
Eq(F_114(x, k_0), F_105(x, k_0))
Eq(F_115(x, k_0), F_110(x, k_0))
Eq(F_116(x, k_0), F_102(x, k_0)*F_8(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_124(x, k_0) + F_157(x, k_0) + F_26(x))
Eq(F_118(x, k_0), F_119(x, k_0)*F_22(x, k_0))
Eq(F_119(x, k_0), F_120(x) + F_122(x, k_0))
Eq(F_120(x), F_121(x) + F_26(x) + F_56(x))
Eq(F_121(x), F_6(x)*F_8(x))
Eq(F_122(x, k_0), F_118(x, k_0) + F_123(x, k_0) + F_26(x) + F_74(x, k_0))
Eq(F_123(x, k_0), F_32(x, k_0)*F_8(x))
Eq(F_124(x, k_0), F_125(x, k_0)*F_8(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_122(x, k_0) + F_32(x, k_0))
Eq(F_127(x, k_0), F_117(x, k_0) + F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_130(x, k_0) + F_133(x, k_0) + F_134(x, k_0) + F_26(x))
Eq(F_129(x, k_0), 0)
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_8(x))
Eq(F_132(x, k_0), F_122(x, k_0) + F_128(x, k_0))
Eq(F_133(x, k_0), F_117(x, k_0)*F_8(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_5(x)*F_8(x))
Eq(F_136(x, k_0), F_137(x, k_0) + F_142(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_8(x))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_8(x))
Eq(F_141(x, k_0), F_139(x, k_0) + F_38(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_149(x, k_0) + 3*F_26(x))
Eq(F_143(x, k_0), F_144(x, k_0)*F_8(x))
Eq(F_144(x, k_0), F_145(x, k_0) + F_147(x, k_0) + 2*F_26(x))
Eq(F_145(x, k_0), F_146(x, k_0)*F_8(x))
Eq(F_146(x, k_0), F_144(x, k_0) + F_81(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0)*F_8(x))
Eq(F_148(x, k_0), F_139(x, k_0) + F_144(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_8(x))
Eq(F_150(x, k_0), F_151(x, k_0) + F_154(x, k_0))
Eq(F_151(x, k_0), F_137(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_151(x, k_0)*F_8(x))
Eq(F_154(x, k_0), F_142(x, k_0) + F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_154(x, k_0)*F_8(x))
Eq(F_157(x, k_0), F_158(x, k_0)*F_8(x))
Eq(F_158(x, k_0), F_159(x, k_0) + F_195(x, k_0))
Eq(F_159(x, k_0), -F_160(x, 1) - F_160(x, k_0) + (-k_0*F_160(x, k_0) + F_160(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_163(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_22(x, k_0)*F_38(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0) + F_165(x, k_0) + F_26(x))
Eq(F_164(x, k_0), F_22(x, k_0)*F_32(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0)*F_8(x))
Eq(F_166(x, k_0), F_160(x, k_0) + F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_172(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0) + F_170(x, k_0) + F_26(x))
Eq(F_169(x, k_0), F_22(x, k_0)*F_42(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0)*F_8(x))
Eq(F_171(x, k_0), F_161(x, k_0) + F_168(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_174(x, k_0) + F_176(x, k_0) + F_26(x))
Eq(F_173(x, k_0), F_22(x, k_0)*F_50(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_8(x))
Eq(F_175(x, k_0), F_163(x, k_0) + F_172(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0)*F_5(x)*F_8(x))
Eq(F_178(x, k_0), F_179(x, k_0) + F_181(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_180(x, k_0), F_161(x, k_0)*F_8(x))
Eq(F_181(x, k_0), F_182(x, k_0) + F_187(x, k_0) + 2*F_26(x))
Eq(F_182(x, k_0), F_183(x, k_0)*F_8(x))
Eq(F_183(x, k_0), F_184(x, k_0) + F_185(x, k_0) + F_26(x))
Eq(F_184(x, k_0), F_22(x, k_0)*F_81(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_8(x))
Eq(F_186(x, k_0), F_161(x, k_0) + F_183(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_8(x))
Eq(F_188(x, k_0), F_189(x, k_0) + F_192(x, k_0))
Eq(F_189(x, k_0), F_179(x, k_0) + F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_191(x, k_0), F_189(x, k_0)*F_8(x))
Eq(F_192(x, k_0), F_181(x, k_0) + F_193(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0))
Eq(F_194(x, k_0), F_192(x, k_0)*F_8(x))
Eq(F_195(x, k_0), F_196(x, k_0) + F_215(x, k_0))
Eq(F_196(x, k_0), F_145(x, k_0) + F_197(x, k_0) + 2*F_26(x))
Eq(F_197(x, k_0), F_198(x, k_0)*F_8(x))
Eq(F_198(x, k_0), F_148(x, k_0) + F_199(x, k_0))
Eq(F_199(x, k_0), F_196(x, k_0) + F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_214(x, k_0) + 3*F_26(x))
Eq(F_201(x, k_0), F_202(x, k_0)*F_8(x))
Eq(F_202(x, k_0), F_203(x, k_0) + F_211(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_209(x, k_0) + 2*F_26(x))
Eq(F_204(x, k_0), F_205(x, k_0)*F_22(x, k_0))
Eq(F_205(x, k_0), F_203(x, k_0) + F_206(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_208(x)*F_8(x))
Eq(F_208(x), F_206(x) + F_61(x))
Eq(F_209(x, k_0), F_210(x, k_0)*F_8(x))
Eq(F_210(x, k_0), F_203(x, k_0) + F_81(x, k_0))
Eq(F_211(x, k_0), F_201(x, k_0) + F_212(x, k_0) + 3*F_26(x))
Eq(F_212(x, k_0), F_213(x, k_0)*F_8(x))
Eq(F_213(x, k_0), F_144(x, k_0) + F_211(x, k_0))
Eq(F_214(x, k_0), F_199(x, k_0)*F_8(x))
Eq(F_215(x, k_0), -F_216(x, 1) - F_216(x, k_0) + (-k_0*F_216(x, k_0) + F_216(x, 1))/(1 - k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_231(x, k_0) + 2*F_26(x))
Eq(F_217(x, k_0), F_218(x, k_0)*F_22(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0) + F_226(x, k_0) + 2*F_26(x))
Eq(F_219(x, k_0), F_22(x, k_0)*F_220(x, k_0))
Eq(F_220(x, k_0), F_218(x, k_0) + F_221(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_223(x)*F_6(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_225(x)*F_63(x)*F_8(x))
Eq(F_225(x), F_1(x) + F_223(x))
Eq(F_226(x, k_0), F_227(x, k_0)*F_8(x))
Eq(F_227(x, k_0), F_228(x, k_0) + F_229(x, k_0))
Eq(F_228(x, k_0), F_218(x, k_0) + F_32(x, k_0))
Eq(F_229(x, k_0), F_230(x, k_0))
Eq(F_230(x, k_0), F_6(x)*F_76(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0)*F_8(x))
Eq(F_232(x, k_0), F_233(x, k_0) + F_234(x, k_0))
Eq(F_233(x, k_0), F_163(x, k_0) + F_216(x, k_0))
Eq(F_234(x, k_0), F_235(x, k_0))
Eq(F_235(x, k_0), F_178(x, k_0)*F_6(x))
Eq(F_236(x, k_0), F_237(x, k_0) + F_257(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0) + F_244(x, k_0) + F_255(x, k_0) + F_26(x))
Eq(F_238(x, k_0), F_22(x, k_0)*F_239(x, k_0))
Eq(F_239(x, k_0), F_240(x) + F_242(x, k_0))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_45(x)*F_8(x))
Eq(F_242(x, k_0), F_238(x, k_0) + F_243(x, k_0) + 2*F_26(x))
Eq(F_243(x, k_0), F_42(x, k_0)*F_8(x))
Eq(F_244(x, k_0), F_245(x, k_0)*F_8(x))
Eq(F_245(x, k_0), F_246(x, k_0) + F_247(x, k_0))
Eq(F_246(x, k_0), F_242(x, k_0) + F_42(x, k_0))
Eq(F_247(x, k_0), F_237(x, k_0) + F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_250(x, k_0) + F_254(x, k_0) + 2*F_26(x))
Eq(F_249(x, k_0), 0)
Eq(F_250(x, k_0), F_251(x, k_0)*F_8(x))
Eq(F_251(x, k_0), F_252(x, k_0) + F_253(x, k_0))
Eq(F_252(x, k_0), F_242(x, k_0))
Eq(F_253(x, k_0), F_248(x, k_0))
Eq(F_254(x, k_0), F_237(x, k_0)*F_8(x))
Eq(F_255(x, k_0), F_256(x, k_0)*F_8(x))
Eq(F_256(x, k_0), F_102(x, k_0) + F_237(x, k_0))
Eq(F_257(x, k_0), F_134(x, k_0) + F_258(x, k_0) + F_26(x) + F_300(x, k_0) + F_311(x, k_0))
Eq(F_258(x, k_0), F_22(x, k_0)*F_259(x, k_0))
Eq(F_259(x, k_0), F_260(x) + F_297(x, k_0))
Eq(F_260(x), F_261(x))
Eq(F_261(x), F_262(x, 1))
Eq(F_262(x, k_0), F_263(x, k_0))
Eq(F_263(x, k_0), 2*F_26(x) + F_264(x, k_0) + F_269(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0))
Eq(F_265(x, k_0), F_22(x, k_0)*F_266(x, k_0)*F_6(x)*F_8(x))
Eq(F_266(x, k_0), F_1(x) + F_267(x, k_0))
Eq(F_267(x, k_0), F_268(x, k_0))
Eq(F_268(x, k_0), F_22(x, k_0)*F_266(x, k_0))
Eq(F_269(x, k_0), F_270(x, k_0)*F_8(x))
Eq(F_270(x, k_0), F_271(x, k_0) + F_274(x, k_0))
Eq(F_271(x, k_0), F_263(x, k_0) + F_272(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0))
Eq(F_273(x, k_0), F_267(x, k_0)*F_8(x))
Eq(F_274(x, k_0), -F_275(x, 1) - F_275(x, k_0) + (-k_0*F_275(x, k_0) + F_275(x, 1))/(1 - k_0))
Eq(F_275(x, k_0), F_276(x, k_0) + F_280(x, k_0))
Eq(F_276(x, k_0), F_277(x, k_0))
Eq(F_277(x, k_0), F_278(x, k_0)*F_8(x))
Eq(F_278(x, k_0), F_279(x, k_0))
Eq(F_279(x, k_0), F_22(x, k_0)*F_267(x, k_0))
Eq(F_280(x, k_0), F_281(x, k_0))
Eq(F_281(x, k_0), F_282(x, k_0)*F_8(x))
Eq(F_282(x, k_0), F_26(x) + F_283(x, k_0) + F_285(x, k_0))
Eq(F_283(x, k_0), F_284(x, k_0))
Eq(F_284(x, k_0), F_22(x, k_0)*F_267(x, k_0)*F_6(x))
Eq(F_285(x, k_0), F_286(x, k_0)*F_8(x))
Eq(F_286(x, k_0), F_287(x, k_0) + F_288(x, k_0))
Eq(F_287(x, k_0), F_278(x, k_0) + F_282(x, k_0))
Eq(F_288(x, k_0), F_289(x, k_0) + F_294(x, k_0))
Eq(F_289(x, k_0), F_290(x, k_0))
Eq(F_290(x, k_0), F_22(x, k_0)*F_291(x, k_0))
Eq(F_291(x, k_0), F_292(x, k_0))
Eq(F_292(x, k_0), F_22(x, k_0)*F_293(x, k_0))
Eq(F_293(x, k_0), F_291(x, k_0) + F_45(x))
Eq(F_294(x, k_0), F_295(x, k_0))
Eq(F_295(x, k_0), F_22(x, k_0)*F_296(x, k_0))
Eq(F_296(x, k_0), -F_282(x, 1) - F_282(x, k_0) + (-k_0*F_282(x, k_0) + F_282(x, 1))/(1 - k_0))
Eq(F_297(x, k_0), F_258(x, k_0) + 2*F_26(x) + F_298(x, k_0) + F_299(x, k_0))
Eq(F_298(x, k_0), F_50(x, k_0)*F_8(x))
Eq(F_299(x, k_0), 0)
Eq(F_300(x, k_0), F_301(x, k_0)*F_8(x))
Eq(F_301(x, k_0), F_302(x, k_0) + F_303(x, k_0))
Eq(F_302(x, k_0), F_297(x, k_0) + F_50(x, k_0))
Eq(F_303(x, k_0), F_257(x, k_0) + F_304(x, k_0))
Eq(F_304(x, k_0), 2*F_26(x) + F_305(x, k_0) + F_306(x, k_0) + F_309(x, k_0) + F_310(x, k_0))
Eq(F_305(x, k_0), 0)
Eq(F_306(x, k_0), F_307(x, k_0))
Eq(F_307(x, k_0), F_308(x, k_0)*F_8(x))
Eq(F_308(x, k_0), F_297(x, k_0) + F_304(x, k_0))
Eq(F_309(x, k_0), F_257(x, k_0)*F_8(x))
Eq(F_310(x, k_0), 0)
Eq(F_311(x, k_0), F_312(x, k_0)*F_8(x))
Eq(F_312(x, k_0), F_117(x, k_0) + F_257(x, k_0))
Eq(F_313(x), F_314(x)*F_8(x))
Eq(F_314(x), F_315(x) + F_379(x))
Eq(F_315(x), F_316(x) + F_327(x))
Eq(F_316(x), F_317(x))
Eq(F_317(x), F_318(x)*F_8(x))
Eq(F_318(x), F_319(x) + F_320(x))
Eq(F_319(x), F_1(x) + F_8(x))
Eq(F_320(x), F_316(x) + F_321(x))
Eq(F_321(x), F_26(x) + F_322(x) + F_326(x))
Eq(F_322(x), F_323(x)*F_8(x))
Eq(F_323(x), F_324(x) + F_325(x))
Eq(F_324(x), F_8(x))
Eq(F_325(x), F_321(x))
Eq(F_326(x), F_316(x)*F_8(x))
Eq(F_327(x), F_26(x) + F_328(x) + F_334(x))
Eq(F_328(x), F_329(x)*F_8(x))
Eq(F_329(x), F_330(x) + F_331(x))
Eq(F_330(x), F_327(x) + F_6(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_333(x)*F_6(x)*F_61(x))
Eq(F_333(x), F_1(x) + F_316(x))
Eq(F_334(x), F_335(x)*F_8(x))
Eq(F_335(x), F_315(x) + F_336(x))
Eq(F_336(x), F_337(x, 1))
Eq(F_337(x, k_0), F_338(x, k_0) + F_354(x, k_0))
Eq(F_338(x, k_0), F_26(x) + F_339(x, k_0) + F_349(x, k_0))
Eq(F_339(x, k_0), F_340(x, k_0)*F_8(x))
Eq(F_340(x, k_0), F_341(x, k_0) + F_342(x, k_0))
Eq(F_341(x, k_0), F_267(x, k_0) + F_272(x, k_0))
Eq(F_342(x, k_0), F_338(x, k_0) + F_343(x, k_0))
Eq(F_343(x, k_0), 2*F_26(x) + F_344(x, k_0) + F_348(x, k_0))
Eq(F_344(x, k_0), F_345(x, k_0)*F_8(x))
Eq(F_345(x, k_0), F_346(x, k_0) + F_347(x, k_0))
Eq(F_346(x, k_0), F_272(x, k_0))
Eq(F_347(x, k_0), F_343(x, k_0))
Eq(F_348(x, k_0), F_338(x, k_0)*F_8(x))
Eq(F_349(x, k_0), F_22(x, k_0)*F_350(x, k_0))
Eq(F_350(x, k_0), F_351(x, k_0) + F_61(x))
Eq(F_351(x, k_0), F_26(x) + F_349(x, k_0) + F_352(x, k_0))
Eq(F_352(x, k_0), F_353(x, k_0)*F_8(x))
Eq(F_353(x, k_0), F_267(x, k_0) + F_351(x, k_0))
Eq(F_354(x, k_0), F_26(x) + F_355(x, k_0) + F_374(x, k_0) + F_377(x, k_0))
Eq(F_355(x, k_0), F_356(x, k_0))
Eq(F_356(x, k_0), F_357(x, k_0)*F_8(x))
Eq(F_357(x, k_0), F_354(x, k_0) + F_358(x, k_0))
Eq(F_358(x, k_0), F_26(x) + F_359(x, k_0) + F_361(x, k_0))
Eq(F_359(x, k_0), F_22(x, k_0)*F_360(x, k_0))
Eq(F_360(x, k_0), F_358(x, k_0) + F_6(x))
Eq(F_361(x, k_0), F_362(x, k_0))
Eq(F_362(x, k_0), F_363(x, k_0)*F_5(x)*F_8(x))
Eq(F_363(x, k_0), F_22(x, k_0) + F_364(x, k_0))
Eq(F_364(x, k_0), F_26(x) + F_365(x, k_0) + F_366(x, k_0))
Eq(F_365(x, k_0), F_22(x, k_0)*F_61(x))
Eq(F_366(x, k_0), F_367(x, k_0)*F_8(x))
Eq(F_367(x, k_0), F_368(x, k_0) + F_371(x, k_0))
Eq(F_368(x, k_0), F_22(x, k_0) + F_369(x, k_0))
Eq(F_369(x, k_0), F_370(x, k_0))
Eq(F_370(x, k_0), F_368(x, k_0)*F_8(x))
Eq(F_371(x, k_0), F_364(x, k_0) + F_372(x, k_0))
Eq(F_372(x, k_0), F_373(x, k_0))
Eq(F_373(x, k_0), F_371(x, k_0)*F_8(x))
Eq(F_374(x, k_0), F_375(x, k_0))
Eq(F_375(x, k_0), F_22(x, k_0)*F_376(x, k_0)*F_6(x))
Eq(F_376(x, k_0), F_316(x) + F_338(x, k_0))
Eq(F_377(x, k_0), F_378(x, k_0)*F_8(x))
Eq(F_378(x, k_0), -F_337(x, 1) + (-k_0*F_337(x, k_0) + F_337(x, 1))/(1 - k_0))
Eq(F_379(x), F_380(x) + F_393(x))
Eq(F_380(x), F_26(x) + F_381(x) + F_391(x))
Eq(F_381(x), F_382(x)*F_8(x))
Eq(F_382(x), F_383(x) + F_384(x))
Eq(F_383(x), F_240(x) + F_45(x))
Eq(F_384(x), F_380(x) + F_385(x))
Eq(F_385(x), 2*F_26(x) + F_386(x) + F_390(x))
Eq(F_386(x), F_387(x)*F_8(x))
Eq(F_387(x), F_388(x) + F_389(x))
Eq(F_388(x), F_240(x))
Eq(F_389(x), F_385(x))
Eq(F_390(x), F_380(x)*F_8(x))
Eq(F_391(x), F_392(x)*F_8(x))
Eq(F_392(x), F_316(x) + F_380(x))
Eq(F_393(x), F_26(x) + F_394(x) + F_404(x) + F_406(x))
Eq(F_394(x), F_395(x)*F_8(x))
Eq(F_395(x), F_396(x) + F_397(x))
Eq(F_396(x), F_260(x) + F_53(x))
Eq(F_397(x), F_393(x) + F_398(x))
Eq(F_398(x), 2*F_26(x) + F_399(x) + F_402(x) + F_403(x))
Eq(F_399(x), F_400(x))
Eq(F_400(x), F_401(x)*F_8(x))
Eq(F_401(x), F_260(x) + F_398(x))
Eq(F_402(x), F_393(x)*F_8(x))
Eq(F_403(x), 0)
Eq(F_404(x), F_405(x)*F_8(x))
Eq(F_405(x), F_327(x) + F_393(x))
Eq(F_406(x), F_407(x))
Eq(F_407(x), F_408(x, 1))
Eq(F_408(x, k_0), F_409(x, k_0)*F_5(x)*F_8(x))
Eq(F_409(x, k_0), F_410(x, k_0) + F_412(x, k_0))
Eq(F_410(x, k_0), F_411(x, k_0))
Eq(F_411(x, k_0), F_22(x, k_0)*F_61(x))
Eq(F_412(x, k_0), 2*F_26(x) + F_413(x, k_0) + F_419(x, k_0))
Eq(F_413(x, k_0), F_22(x, k_0)*F_414(x))
Eq(F_414(x), F_26(x) + F_415(x) + F_417(x))
Eq(F_415(x), F_416(x)*F_8(x))
Eq(F_416(x), F_414(x) + F_61(x))
Eq(F_417(x), F_418(x)*F_8(x))
Eq(F_418(x), F_414(x) + F_61(x))
Eq(F_419(x, k_0), F_420(x, k_0)*F_8(x))
Eq(F_420(x, k_0), F_421(x, k_0) + F_424(x, k_0))
Eq(F_421(x, k_0), F_410(x, k_0) + F_422(x, k_0))
Eq(F_422(x, k_0), F_423(x, k_0))
Eq(F_423(x, k_0), F_421(x, k_0)*F_8(x))
Eq(F_424(x, k_0), F_412(x, k_0) + F_425(x, k_0))
Eq(F_425(x, k_0), F_426(x, k_0))
Eq(F_426(x, k_0), F_424(x, k_0)*F_8(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 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"pos": [[4, 1]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: insertion_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/112/
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[14,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[13,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[12,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[13,x] = x
F[14,x] = F[15,x]+F[48,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[17,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[13,x]*F[18,x]
F[21,x] = F[22,x]+F[34,x]
F[22,x] = F[23,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]+F[13,x]
F[26,x] = F[22,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[33,x]
F[28,x] = 0
F[29,x] = F[13,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[13,x]
F[32,x] = F[27,x]
F[33,x] = F[13,x]*F[22,x]
F[34,x] = F[28,x]+F[35,x]+F[47,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[19,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[13,x]*F[19,x]
F[40,x] = F[34,x]+F[41,x]
F[41,x] = 2*F[28,x]+F[42,x]+F[46,x]
F[42,x] = F[13,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[38,x]
F[45,x] = F[41,x]
F[46,x] = F[13,x]*F[34,x]
F[47,x] = F[13,x]*F[21,x]
F[48,x] = F[246,x]+F[28,x]+F[49,x]
F[49,x] = F[13,x]*F[50,x]
F[50,x] = F[51,x]+F[71,x]
F[51,x] = F[52,x]+F[61,x]
F[52,x] = F[53,x]
F[53,x] = F[13,x]*F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[13,x]*F[55,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[13,x]*F[58,x]
F[61,x] = F[28,x]+F[62,x]+F[63,x]
F[62,x] = F[13,x]*F[51,x]
F[63,x] = F[13,x]*F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[19,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[13,x]*F[65,x]
F[68,x] = F[61,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[68,x]
F[71,x] = F[227,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[13,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[55,x]^2*F[15,x]
F[76,x] = F[153,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[15,x]*F[55,x]
F[79,x] = F[151,x]+F[80,x]
F[80,x] = F[115,x]+F[28,x]+F[81,x]
F[81,x] = F[13,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[19,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[13,x]*F[83,x]
F[86,x] = F[101,x]+F[87,x]
F[87,x] = F[28,x]+F[88,x]+F[96,x]
F[88,x] = F[13,x]*F[89,x]
F[89,x] = F[37,x]+F[90,x]
F[90,x] = F[87,x]+F[91,x]
F[91,x] = 2*F[28,x]+F[92,x]+F[95,x]
F[92,x] = F[13,x]*F[93,x]
F[93,x] = F[44,x]+F[94,x]
F[94,x] = F[91,x]
F[95,x] = F[13,x]*F[87,x]
F[96,x] = F[13,x]*F[97,x]
F[97,x] = F[56,x]+F[98,x]
F[98,x] = F[28,x]+F[96,x]+F[99,x]
F[99,x] = F[100,x]*F[13,x]
F[100,x] = F[19,x]+F[98,x]
F[101,x] = 2*F[28,x]+F[102,x]+F[114,x]
F[102,x] = F[103,x]*F[13,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]+F[84,x]
F[105,x] = F[106,x]
F[106,x] = F[13,x]*F[84,x]
F[107,x] = F[101,x]+F[108,x]
F[108,x] = 3*F[28,x]+F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[13,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[105,x]
F[112,x] = F[108,x]
F[113,x] = F[101,x]*F[13,x]
F[114,x] = F[13,x]*F[86,x]
F[115,x] = F[116,x]*F[13,x]
F[116,x] = F[117,x]+F[97,x]
F[117,x] = F[118,x]+F[134,x]
F[118,x] = F[119,x]+F[123,x]+F[28,x]
F[119,x] = F[120,x]*F[13,x]
F[120,x] = F[121,x]+F[13,x]
F[121,x] = F[119,x]+F[122,x]+F[28,x]
F[122,x] = F[13,x]*F[56,x]
F[123,x] = F[124,x]*F[13,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[121,x]+F[56,x]
F[126,x] = F[118,x]+F[127,x]
F[127,x] = F[128,x]+F[129,x]+F[133,x]+F[28,x]
F[128,x] = 0
F[129,x] = F[13,x]*F[130,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[121,x]
F[132,x] = F[127,x]
F[133,x] = F[118,x]*F[13,x]
F[134,x] = F[135,x]+F[139,x]+F[150,x]+F[28,x]
F[135,x] = F[13,x]*F[136,x]
F[136,x] = F[137,x]+F[38,x]
F[137,x] = 2*F[28,x]+F[135,x]+F[138,x]
F[138,x] = F[13,x]*F[98,x]
F[139,x] = F[13,x]*F[140,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[137,x]+F[98,x]
F[142,x] = F[134,x]+F[143,x]
F[143,x] = 2*F[28,x]+F[144,x]+F[145,x]+F[149,x]
F[144,x] = 0
F[145,x] = F[13,x]*F[146,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[137,x]
F[148,x] = F[143,x]
F[149,x] = F[13,x]*F[134,x]
F[150,x] = F[117,x]*F[13,x]
F[151,x] = F[152,x]
F[152,x] = F[56,x]^2*F[15,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[55,x]*F[72,x]
F[155,x] = F[156,x,1]
F[156,x,k[0]] = F[157,x,k[0]]+F[225,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]+F[170,x,k[0]]+F[28,x]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[13,x]*F[160,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[166,x,k[0]]
F[161,x,k[0]] = F[157,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[15,x]*F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[10,x,k[0]]*F[165,x,k[0]]
F[165,x,k[0]] = F[1,x]+F[163,x,k[0]]
F[166,x,k[0]] = F[163,x,k[0]]*F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[169,x,k[0]]
F[168,x,k[0]] = F[15,x]*F[165,x,k[0]]
F[169,x,k[0]] = F[157,x,k[0]]+F[80,x]
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[13,x]*F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[222,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[216,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]+F[214,x,k[0]]+F[28,x]
F[175,x,k[0]] = F[13,x]*F[176,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[182,x,k[0]]
F[177,x,k[0]] = F[163,x,k[0]]+F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[180,x,k[0]]+F[28,x]
F[179,x,k[0]] = F[13,x]*F[177,x,k[0]]
F[180,x,k[0]] = F[10,x,k[0]]*F[181,x,k[0]]
F[181,x,k[0]] = F[178,x,k[0]]+F[19,x]
F[182,x,k[0]] = F[174,x,k[0]]+F[183,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]+F[204,x,k[0]]+F[205,x,k[0]]+F[28,x]
F[184,x,k[0]] = F[185,x,k[0]]
F[185,x,k[0]] = F[13,x]*F[186,x,k[0]]*F[203,x]
F[186,x,k[0]] = F[187,x,k[0]]+F[190,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]
F[188,x,k[0]] = F[10,x,k[0]]*F[189,x,k[0]]
F[189,x,k[0]] = F[13,x]+F[187,x,k[0]]
F[190,x,k[0]] = 2*F[28,x]+F[191,x,k[0]]+F[195,x,k[0]]
F[191,x,k[0]] = F[13,x]*F[192,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]+F[194,x,k[0]]
F[193,x,k[0]] = F[187,x,k[0]]
F[194,x,k[0]] = F[190,x,k[0]]
F[195,x,k[0]] = F[10,x,k[0]]*F[196,x,k[0]]
F[196,x,k[0]] = F[190,x,k[0]]+F[197,x]
F[197,x] = F[198,x]+F[202,x]+F[28,x]
F[198,x] = F[13,x]*F[199,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[13,x]
F[201,x] = F[197,x]
F[202,x] = F[13,x]*F[22,x]
F[203,x] = F[1,x]+F[15,x]
F[204,x,k[0]] = F[13,x]*F[182,x,k[0]]
F[205,x,k[0]] = F[10,x,k[0]]*F[206,x,k[0]]
F[206,x,k[0]] = F[183,x,k[0]]+F[207,x]
F[207,x] = F[208,x]
F[208,x] = F[13,x]*F[18,x]*F[209,x]
F[209,x] = F[15,x]+F[210,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[203,x]*F[56,x]
F[212,x] = F[213,x]
F[213,x] = F[13,x]*F[210,x]*F[55,x]
F[214,x,k[0]] = F[10,x,k[0]]*F[215,x,k[0]]
F[215,x,k[0]] = F[15,x]+F[174,x,k[0]]
F[216,x,k[0]] = F[15,x]*F[217,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[220,x,k[0]]+F[28,x]
F[218,x,k[0]] = F[13,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[163,x,k[0]]+F[217,x,k[0]]
F[220,x,k[0]] = F[10,x,k[0]]*F[221,x,k[0]]
F[221,x,k[0]] = F[217,x,k[0]]+F[56,x]
F[222,x,k[0]] = F[157,x,k[0]]+F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]
F[224,x,k[0]] = F[15,x]*F[217,x,k[0]]*F[56,x]
F[225,x,k[0]] = F[226,x,k[0]]
F[226,x,k[0]] = F[15,x]*F[217,x,k[0]]*F[56,x]
F[227,x] = F[228,x]
F[228,x] = F[13,x]*F[229,x]
F[229,x] = F[230,x]+F[236,x]
F[230,x] = F[15,x]*F[231,x]
F[231,x] = F[232,x]+F[51,x]
F[232,x] = F[233,x]*F[56,x]
F[233,x] = F[234,x]+F[235,x]
F[234,x] = F[1,x]+F[52,x]
F[235,x] = F[19,x]+F[61,x]
F[236,x] = F[237,x]+F[238,x]
F[237,x] = F[210,x]*F[51,x]
F[238,x] = F[233,x]*F[239,x]
F[239,x] = F[240,x]+F[72,x]
F[240,x] = F[15,x]*F[241,x]
F[241,x] = F[242,x]+F[244,x]+F[28,x]
F[242,x] = F[13,x]*F[243,x]
F[243,x] = F[241,x]+F[56,x]
F[244,x] = F[13,x]*F[245,x]
F[245,x] = F[241,x]+F[56,x]
F[246,x] = F[13,x]*F[247,x]
F[247,x] = F[248,x,1]
F[248,x,k[0]] = F[215,x,k[0]]+F[249,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[48,x]
F[250,x,k[0]] = F[251,x,k[0]]+F[28,x]+F[366,x,k[0]]+F[369,x,k[0]]
F[251,x,k[0]] = F[13,x]*F[252,x,k[0]]
F[252,x,k[0]] = F[253,x,k[0]]+F[290,x,k[0]]
F[253,x,k[0]] = F[254,x,k[0]]+F[270,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[268,x,k[0]]+F[28,x]
F[255,x,k[0]] = F[13,x]*F[256,x,k[0]]
F[256,x,k[0]] = F[257,x,k[0]]+F[261,x,k[0]]
F[257,x,k[0]] = F[163,x,k[0]]+F[258,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]
F[259,x,k[0]] = F[10,x,k[0]]*F[260,x,k[0]]
F[260,x,k[0]] = F[258,x,k[0]]+F[56,x]
F[261,x,k[0]] = F[262,x,k[0]]+F[265,x,k[0]]
F[262,x,k[0]] = F[263,x,k[0]]
F[263,x,k[0]] = F[10,x,k[0]]*F[264,x,k[0]]
F[264,x,k[0]] = F[262,x,k[0]]+F[52,x]
F[265,x,k[0]] = F[266,x,k[0]]
F[266,x,k[0]] = F[10,x,k[0]]*F[267,x,k[0]]
F[267,x,k[0]] = F[265,x,k[0]]+F[59,x]
F[268,x,k[0]] = F[10,x,k[0]]*F[269,x,k[0]]
F[269,x,k[0]] = F[254,x,k[0]]+F[52,x]
F[270,x,k[0]] = F[271,x,k[0]]+F[272,x,k[0]]+F[28,x]+F[288,x,k[0]]
F[271,x,k[0]] = F[13,x]*F[253,x,k[0]]
F[272,x,k[0]] = F[13,x]*F[273,x,k[0]]
F[273,x,k[0]] = F[274,x,k[0]]+F[281,x,k[0]]
F[274,x,k[0]] = F[275,x,k[0]]+F[278,x,k[0]]
F[275,x,k[0]] = F[276,x,k[0]]
F[276,x,k[0]] = F[10,x,k[0]]*F[277,x,k[0]]
F[277,x,k[0]] = F[19,x]+F[275,x,k[0]]
F[278,x,k[0]] = F[279,x,k[0]]
F[279,x,k[0]] = F[10,x,k[0]]*F[280,x,k[0]]
F[280,x,k[0]] = F[278,x,k[0]]+F[66,x]
F[281,x,k[0]] = F[282,x,k[0]]+F[285,x,k[0]]
F[282,x,k[0]] = F[283,x,k[0]]
F[283,x,k[0]] = F[10,x,k[0]]*F[284,x,k[0]]
F[284,x,k[0]] = F[282,x,k[0]]+F[61,x]
F[285,x,k[0]] = F[286,x,k[0]]
F[286,x,k[0]] = F[10,x,k[0]]*F[287,x,k[0]]
F[287,x,k[0]] = F[285,x,k[0]]+F[69,x]
F[288,x,k[0]] = F[10,x,k[0]]*F[289,x,k[0]]
F[289,x,k[0]] = F[270,x,k[0]]+F[61,x]
F[290,x,k[0]] = F[291,x,k[0]]+F[345,x,k[0]]
F[291,x,k[0]] = F[292,x,k[0]]
F[292,x,k[0]] = F[13,x]*F[293,x,k[0]]
F[293,x,k[0]] = F[294,x,k[0]]+F[299,x,k[0]]
F[294,x,k[0]] = F[295,x,k[0]]
F[295,x,k[0]] = F[15,x]*F[296,x,k[0]]*F[55,x]
F[296,x,k[0]] = F[297,x,k[0]]+F[298,x,k[0]]
F[297,x,k[0]] = F[163,x,k[0]]*F[55,x]
F[298,x,k[0]] = F[163,x,k[0]]*F[165,x,k[0]]
F[299,x,k[0]] = F[300,x,k[0]]+F[308,x,k[0]]
F[300,x,k[0]] = F[301,x,k[0]]+F[303,x,k[0]]
F[301,x,k[0]] = F[302,x,k[0]]
F[302,x,k[0]] = F[163,x,k[0]]*F[210,x]*F[55,x]
F[303,x,k[0]] = F[304,x,k[0]]+F[305,x,k[0]]
F[304,x,k[0]] = F[165,x,k[0]]*F[174,x,k[0]]*F[55,x]
F[305,x,k[0]] = F[156,x,k[0]]+F[306,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]
F[307,x,k[0]] = F[15,x]*F[163,x,k[0]]*F[217,x,k[0]]*F[55,x]
F[308,x,k[0]] = F[309,x,k[0]]+F[310,x,k[0]]
F[309,x,k[0]] = F[291,x,k[0]]*F[55,x]
F[310,x,k[0]] = (-F[311,x,1]*k[0]+F[311,x,k[0]])/(-1+k[0])
F[311,x,k[0]] = F[312,x,k[0]]+F[343,x,k[0]]
F[312,x,k[0]] = F[28,x]+F[313,x,k[0]]+F[327,x,k[0]]
F[313,x,k[0]] = F[314,x,k[0]]
F[314,x,k[0]] = F[13,x]*F[315,x,k[0]]
F[315,x,k[0]] = F[316,x,k[0]]+F[320,x,k[0]]
F[316,x,k[0]] = F[312,x,k[0]]+F[317,x,k[0]]
F[317,x,k[0]] = F[15,x]*F[318,x,k[0]]
F[318,x,k[0]] = F[319,x,k[0]]
F[319,x,k[0]] = F[10,x,k[0]]*F[163,x,k[0]]
F[320,x,k[0]] = F[321,x,k[0]]+F[324,x,k[0]]
F[321,x,k[0]] = F[15,x]*F[322,x,k[0]]
F[322,x,k[0]] = F[318,x,k[0]]+F[323,x,k[0]]
F[323,x,k[0]] = F[163,x,k[0]]^2
F[324,x,k[0]] = F[325,x,k[0]]+F[326,x,k[0]]
F[325,x,k[0]] = F[318,x,k[0]]*F[80,x]
F[326,x,k[0]] = F[157,x,k[0]]*F[163,x,k[0]]
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[13,x]*F[329,x,k[0]]
F[329,x,k[0]] = F[330,x,k[0]]+F[340,x,k[0]]
F[330,x,k[0]] = F[331,x,k[0]]+F[335,x,k[0]]
F[331,x,k[0]] = F[332,x,k[0]]
F[332,x,k[0]] = F[10,x,k[0]]*F[333,x,k[0]]
F[333,x,k[0]] = F[162,x,k[0]]+F[334,x,k[0]]
F[334,x,k[0]] = F[157,x,k[0]]+F[174,x,k[0]]
F[335,x,k[0]] = F[15,x]*F[336,x,k[0]]
F[336,x,k[0]] = F[28,x]+F[337,x,k[0]]+F[339,x,k[0]]
F[337,x,k[0]] = F[13,x]*F[338,x,k[0]]
F[338,x,k[0]] = F[318,x,k[0]]+F[336,x,k[0]]
F[339,x,k[0]] = F[10,x,k[0]]*F[217,x,k[0]]
F[340,x,k[0]] = F[312,x,k[0]]+F[341,x,k[0]]
F[341,x,k[0]] = F[342,x,k[0]]
F[342,x,k[0]] = F[15,x]*F[336,x,k[0]]*F[56,x]
F[343,x,k[0]] = F[344,x,k[0]]
F[344,x,k[0]] = F[15,x]*F[336,x,k[0]]*F[56,x]
F[345,x,k[0]] = F[346,x,k[0]]
F[346,x,k[0]] = F[13,x]*F[347,x,k[0]]
F[347,x,k[0]] = F[348,x,k[0]]+F[354,x,k[0]]
F[348,x,k[0]] = F[349,x,k[0]]
F[349,x,k[0]] = F[15,x]*F[350,x,k[0]]
F[350,x,k[0]] = F[253,x,k[0]]+F[351,x,k[0]]
F[351,x,k[0]] = F[163,x,k[0]]*F[352,x,k[0]]
F[352,x,k[0]] = F[232,x]+F[353,x,k[0]]
F[353,x,k[0]] = F[269,x,k[0]]+F[289,x,k[0]]
F[354,x,k[0]] = F[355,x,k[0]]+F[358,x,k[0]]
F[355,x,k[0]] = F[356,x,k[0]]+F[357,x,k[0]]
F[356,x,k[0]] = F[210,x]*F[253,x,k[0]]
F[357,x,k[0]] = F[173,x,k[0]]*F[353,x,k[0]]
F[358,x,k[0]] = F[233,x]*F[359,x,k[0]]
F[359,x,k[0]] = F[291,x,k[0]]+F[360,x,k[0]]
F[360,x,k[0]] = F[15,x]*F[361,x,k[0]]
F[361,x,k[0]] = 2*F[28,x]+F[362,x,k[0]]+F[364,x,k[0]]
F[362,x,k[0]] = F[13,x]*F[363,x,k[0]]
F[363,x,k[0]] = F[258,x,k[0]]+F[361,x,k[0]]
F[364,x,k[0]] = F[10,x,k[0]]*F[365,x,k[0]]
F[365,x,k[0]] = F[241,x]+F[361,x,k[0]]
F[366,x,k[0]] = -k[0]*(F[367,x,1]-F[367,x,k[0]])/(-1+k[0])
F[367,x,k[0]] = F[13,x]*F[368,x,k[0]]
F[368,x,k[0]] = F[174,x,k[0]]+F[250,x,k[0]]
F[369,x,k[0]] = F[10,x,k[0]]*F[249,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \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_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{13}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)+F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \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_{38}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right)
F_{48}\! \left(x \right) = F_{246}\! \left(x \right)+F_{28}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{71}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{61}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \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_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{28}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{13}\! \left(x \right) F_{51}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{19}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{61}\! \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_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{227}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{13}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{55} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{76}\! \left(x \right) = F_{153}\! \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_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{79}\! \left(x \right) = F_{151}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{115}\! \left(x \right)+F_{28}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{13}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{19}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{13}\! \left(x \right) F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{101}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{28}\! \left(x \right)+F_{88}\! \left(x \right)+F_{96}\! \left(x \right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{37}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{44}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{96}\! \left(x \right) = F_{13}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{56}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{28}\! \left(x \right)+F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{100}\! \left(x \right) = F_{19}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{102}\! \left(x \right)+F_{114}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{13}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{84}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{13}\! \left(x \right) F_{84}\! \left(x \right)
F_{107}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 3 F_{28}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{13}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{105}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{114}\! \left(x \right) = F_{13}\! \left(x \right) F_{86}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{13}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{97}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{134}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)+F_{28}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{13}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{13}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right)+F_{122}\! \left(x \right)+F_{28}\! \left(x \right)
F_{122}\! \left(x \right) = F_{13}\! \left(x \right) F_{56}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{13}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)+F_{56}\! \left(x \right)
F_{126}\! \left(x \right) = F_{118}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)+F_{133}\! \left(x \right)+F_{28}\! \left(x \right)
F_{128}\! \left(x \right) = 0
F_{129}\! \left(x \right) = F_{13}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{121}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)
F_{133}\! \left(x \right) = F_{118}\! \left(x \right) F_{13}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{139}\! \left(x \right)+F_{150}\! \left(x \right)+F_{28}\! \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_{38}\! \left(x \right)
F_{137}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{135}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{13}\! \left(x \right) F_{98}\! \left(x \right)
F_{139}\! \left(x \right) = F_{13}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{137}\! \left(x \right)+F_{98}\! \left(x \right)
F_{142}\! \left(x \right) = F_{134}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{144}\! \left(x \right)+F_{145}\! \left(x \right)+F_{149}\! \left(x \right)
F_{144}\! \left(x \right) = 0
F_{145}\! \left(x \right) = F_{13}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{137}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)
F_{149}\! \left(x \right) = F_{13}\! \left(x \right) F_{134}\! \left(x \right)
F_{150}\! \left(x \right) = F_{117}\! \left(x \right) F_{13}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{56} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{55}\! \left(x \right) F_{72}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{163}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{165}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{80}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{214}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{177}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{186}\! \left(x , y\right) F_{203}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{187}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{191}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{202}\! \left(x \right)+F_{28}\! \left(x \right)
F_{198}\! \left(x \right) = F_{13}\! \left(x \right) F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{13}\! \left(x \right)
F_{201}\! \left(x \right) = F_{197}\! \left(x \right)
F_{202}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{203}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{182}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{15}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{203}\! \left(x \right) F_{56}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{13}\! \left(x \right) F_{210}\! \left(x \right) F_{55}\! \left(x \right)
F_{214}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{174}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{218}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{222}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{217}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{217}\! \left(x , y\right) F_{56}\! \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_{230}\! \left(x \right)+F_{236}\! \left(x \right)
F_{230}\! \left(x \right) = F_{15}\! \left(x \right) F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)+F_{51}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{56}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{235}\! \left(x \right)
F_{234}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{235}\! \left(x \right) = F_{19}\! \left(x \right)+F_{61}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{238}\! \left(x \right)
F_{237}\! \left(x \right) = F_{210}\! \left(x \right) F_{51}\! \left(x \right)
F_{238}\! \left(x \right) = F_{233}\! \left(x \right) F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{72}\! \left(x \right)
F_{240}\! \left(x \right) = F_{15}\! \left(x \right) F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)+F_{28}\! \left(x \right)
F_{242}\! \left(x \right) = F_{13}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{241}\! \left(x \right)+F_{56}\! \left(x \right)
F_{244}\! \left(x \right) = F_{13}\! \left(x \right) F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{241}\! \left(x \right)+F_{56}\! \left(x \right)
F_{246}\! \left(x \right) = F_{13}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x , 1\right)
F_{248}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{28}\! \left(x \right)+F_{366}\! \left(x , y\right)+F_{369}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{252}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)+F_{290}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{268}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{255}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{258}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{263}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{262}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{267}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{59}\! \left(x \right)
F_{268}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{269}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{254}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right)+F_{272}\! \left(x , y\right)+F_{28}\! \left(x \right)+F_{288}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{253}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{281}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)+F_{278}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{275}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{279}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{281}\! \left(x , y\right) = F_{282}\! \left(x , y\right)+F_{285}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{284}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{282}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{285}\! \left(x , y\right) = F_{286}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{285}\! \left(x , y\right)+F_{69}\! \left(x \right)
F_{288}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{289}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{290}\! \left(x , y\right) = F_{291}\! \left(x , y\right)+F_{345}\! \left(x , y\right)
F_{291}\! \left(x , y\right) = F_{292}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{293}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{294}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{295}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{296}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{298}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{165}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{300}\! \left(x , y\right)+F_{308}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{302}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{210}\! \left(x \right) F_{55}\! \left(x \right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{174}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{305}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{306}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{163}\! \left(x , y\right) F_{217}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{308}\! \left(x , y\right) = F_{309}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{291}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{310}\! \left(x , y\right) = -\frac{F_{311}\! \left(x , 1\right) y -F_{311}\! \left(x , y\right)}{-1+y}
F_{311}\! \left(x , y\right) = F_{312}\! \left(x , y\right)+F_{343}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{313}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{314}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{315}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{316}\! \left(x , y\right)+F_{320}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{312}\! \left(x , y\right)+F_{317}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{318}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{319}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{163}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{321}\! \left(x , y\right)+F_{324}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{318}\! \left(x , y\right)+F_{323}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{163}\! \left(x , y\right)^{2}
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)+F_{326}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{318}\! \left(x , y\right) F_{80}\! \left(x \right)
F_{326}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{163}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{329}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)+F_{340}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{331}\! \left(x , y\right)+F_{335}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{332}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{334}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{336}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{337}\! \left(x , y\right)+F_{339}\! \left(x , y\right)
F_{337}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{338}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = F_{318}\! \left(x , y\right)+F_{336}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{217}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{312}\! \left(x , y\right)+F_{341}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{342}\! \left(x , y\right)
F_{342}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{336}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{343}\! \left(x , y\right) = F_{344}\! \left(x , y\right)
F_{344}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{336}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{347}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{348}\! \left(x , y\right)+F_{354}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = F_{349}\! \left(x , y\right)
F_{349}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{350}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{253}\! \left(x , y\right)+F_{351}\! \left(x , y\right)
F_{351}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{352}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{232}\! \left(x \right)+F_{353}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = F_{269}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{355}\! \left(x , y\right)+F_{358}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{356}\! \left(x , y\right)+F_{357}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{210}\! \left(x \right) F_{253}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{353}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{233}\! \left(x \right) F_{359}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{291}\! \left(x , y\right)+F_{360}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{361}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{362}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{363}\! \left(x , y\right)
F_{363}\! \left(x , y\right) = F_{258}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{364}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{241}\! \left(x \right)+F_{361}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = -\frac{y \left(F_{367}\! \left(x , 1\right)-F_{367}\! \left(x , y\right)\right)}{-1+y}
F_{367}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{368}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{249}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_14(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_13(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_11(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_12(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_48(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_13(x)*F_18(x))
Eq(F_21(x), F_22(x) + F_34(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x) + F_13(x))
Eq(F_26(x), F_22(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_33(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_13(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_13(x))
Eq(F_32(x), F_27(x))
Eq(F_33(x), F_13(x)*F_22(x))
Eq(F_34(x), F_28(x) + F_35(x) + F_47(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_19(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_13(x)*F_19(x))
Eq(F_40(x), F_34(x) + F_41(x))
Eq(F_41(x), 2*F_28(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_13(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_38(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_13(x)*F_34(x))
Eq(F_47(x), F_13(x)*F_21(x))
Eq(F_48(x), F_246(x) + F_28(x) + F_49(x))
Eq(F_49(x), F_13(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_71(x))
Eq(F_51(x), F_52(x) + F_61(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_13(x)*F_55(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_13(x)*F_58(x))
Eq(F_61(x), F_28(x) + F_62(x) + F_63(x))
Eq(F_62(x), F_13(x)*F_51(x))
Eq(F_63(x), F_13(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_19(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_13(x)*F_65(x))
Eq(F_68(x), F_61(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_68(x))
Eq(F_71(x), F_227(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_13(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_15(x)*F_55(x)**2)
Eq(F_76(x), F_153(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_15(x)*F_55(x))
Eq(F_79(x), F_151(x) + F_80(x))
Eq(F_80(x), F_115(x) + F_28(x) + F_81(x))
Eq(F_81(x), F_13(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_19(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_13(x)*F_83(x))
Eq(F_86(x), F_101(x) + F_87(x))
Eq(F_87(x), F_28(x) + F_88(x) + F_96(x))
Eq(F_88(x), F_13(x)*F_89(x))
Eq(F_89(x), F_37(x) + F_90(x))
Eq(F_90(x), F_87(x) + F_91(x))
Eq(F_91(x), 2*F_28(x) + F_92(x) + F_95(x))
Eq(F_92(x), F_13(x)*F_93(x))
Eq(F_93(x), F_44(x) + F_94(x))
Eq(F_94(x), F_91(x))
Eq(F_95(x), F_13(x)*F_87(x))
Eq(F_96(x), F_13(x)*F_97(x))
Eq(F_97(x), F_56(x) + F_98(x))
Eq(F_98(x), F_28(x) + F_96(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_13(x))
Eq(F_100(x), F_19(x) + F_98(x))
Eq(F_101(x), F_102(x) + F_114(x) + 2*F_28(x))
Eq(F_102(x), F_103(x)*F_13(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x) + F_84(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_13(x)*F_84(x))
Eq(F_107(x), F_101(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_113(x) + 3*F_28(x))
Eq(F_109(x), F_110(x)*F_13(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_105(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_101(x)*F_13(x))
Eq(F_114(x), F_13(x)*F_86(x))
Eq(F_115(x), F_116(x)*F_13(x))
Eq(F_116(x), F_117(x) + F_97(x))
Eq(F_117(x), F_118(x) + F_134(x))
Eq(F_118(x), F_119(x) + F_123(x) + F_28(x))
Eq(F_119(x), F_120(x)*F_13(x))
Eq(F_120(x), F_121(x) + F_13(x))
Eq(F_121(x), F_119(x) + F_122(x) + F_28(x))
Eq(F_122(x), F_13(x)*F_56(x))
Eq(F_123(x), F_124(x)*F_13(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_121(x) + F_56(x))
Eq(F_126(x), F_118(x) + F_127(x))
Eq(F_127(x), F_128(x) + F_129(x) + F_133(x) + F_28(x))
Eq(F_128(x), 0)
Eq(F_129(x), F_13(x)*F_130(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_121(x))
Eq(F_132(x), F_127(x))
Eq(F_133(x), F_118(x)*F_13(x))
Eq(F_134(x), F_135(x) + F_139(x) + F_150(x) + F_28(x))
Eq(F_135(x), F_13(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_38(x))
Eq(F_137(x), F_135(x) + F_138(x) + 2*F_28(x))
Eq(F_138(x), F_13(x)*F_98(x))
Eq(F_139(x), F_13(x)*F_140(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_137(x) + F_98(x))
Eq(F_142(x), F_134(x) + F_143(x))
Eq(F_143(x), F_144(x) + F_145(x) + F_149(x) + 2*F_28(x))
Eq(F_144(x), 0)
Eq(F_145(x), F_13(x)*F_146(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_137(x))
Eq(F_148(x), F_143(x))
Eq(F_149(x), F_13(x)*F_134(x))
Eq(F_150(x), F_117(x)*F_13(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_15(x)*F_56(x)**2)
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_55(x)*F_72(x))
Eq(F_155(x), F_156(x, 1))
Eq(F_156(x, k_0), F_157(x, k_0) + F_225(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0) + F_170(x, k_0) + F_28(x))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_13(x)*F_160(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_166(x, k_0))
Eq(F_161(x, k_0), F_157(x, k_0) + F_162(x, k_0))
Eq(F_162(x, k_0), F_15(x)*F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_10(x, k_0)*F_165(x, k_0))
Eq(F_165(x, k_0), F_1(x) + F_163(x, k_0))
Eq(F_166(x, k_0), F_163(x, k_0)*F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_169(x, k_0))
Eq(F_168(x, k_0), F_15(x)*F_165(x, k_0))
Eq(F_169(x, k_0), F_157(x, k_0) + F_80(x))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_13(x)*F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_222(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_216(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0) + F_214(x, k_0) + F_28(x))
Eq(F_175(x, k_0), F_13(x)*F_176(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_182(x, k_0))
Eq(F_177(x, k_0), F_163(x, k_0) + F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_180(x, k_0) + F_28(x))
Eq(F_179(x, k_0), F_13(x)*F_177(x, k_0))
Eq(F_180(x, k_0), F_10(x, k_0)*F_181(x, k_0))
Eq(F_181(x, k_0), F_178(x, k_0) + F_19(x))
Eq(F_182(x, k_0), F_174(x, k_0) + F_183(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0) + F_204(x, k_0) + F_205(x, k_0) + F_28(x))
Eq(F_184(x, k_0), F_185(x, k_0))
Eq(F_185(x, k_0), F_13(x)*F_186(x, k_0)*F_203(x))
Eq(F_186(x, k_0), F_187(x, k_0) + F_190(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0))
Eq(F_188(x, k_0), F_10(x, k_0)*F_189(x, k_0))
Eq(F_189(x, k_0), F_13(x) + F_187(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0) + F_195(x, k_0) + 2*F_28(x))
Eq(F_191(x, k_0), F_13(x)*F_192(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0) + F_194(x, k_0))
Eq(F_193(x, k_0), F_187(x, k_0))
Eq(F_194(x, k_0), F_190(x, k_0))
Eq(F_195(x, k_0), F_10(x, k_0)*F_196(x, k_0))
Eq(F_196(x, k_0), F_190(x, k_0) + F_197(x))
Eq(F_197(x), F_198(x) + F_202(x) + F_28(x))
Eq(F_198(x), F_13(x)*F_199(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_13(x))
Eq(F_201(x), F_197(x))
Eq(F_202(x), F_13(x)*F_22(x))
Eq(F_203(x), F_1(x) + F_15(x))
Eq(F_204(x, k_0), F_13(x)*F_182(x, k_0))
Eq(F_205(x, k_0), F_10(x, k_0)*F_206(x, k_0))
Eq(F_206(x, k_0), F_183(x, k_0) + F_207(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_13(x)*F_18(x)*F_209(x))
Eq(F_209(x), F_15(x) + F_210(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_203(x)*F_56(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_13(x)*F_210(x)*F_55(x))
Eq(F_214(x, k_0), F_10(x, k_0)*F_215(x, k_0))
Eq(F_215(x, k_0), F_15(x) + F_174(x, k_0))
Eq(F_216(x, k_0), F_15(x)*F_217(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_220(x, k_0) + F_28(x))
Eq(F_218(x, k_0), F_13(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_163(x, k_0) + F_217(x, k_0))
Eq(F_220(x, k_0), F_10(x, k_0)*F_221(x, k_0))
Eq(F_221(x, k_0), F_217(x, k_0) + F_56(x))
Eq(F_222(x, k_0), F_157(x, k_0) + F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_224(x, k_0), F_15(x)*F_217(x, k_0)*F_56(x))
Eq(F_225(x, k_0), F_226(x, k_0))
Eq(F_226(x, k_0), F_15(x)*F_217(x, k_0)*F_56(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_13(x)*F_229(x))
Eq(F_229(x), F_230(x) + F_236(x))
Eq(F_230(x), F_15(x)*F_231(x))
Eq(F_231(x), F_232(x) + F_51(x))
Eq(F_232(x), F_233(x)*F_56(x))
Eq(F_233(x), F_234(x) + F_235(x))
Eq(F_234(x), F_1(x) + F_52(x))
Eq(F_235(x), F_19(x) + F_61(x))
Eq(F_236(x), F_237(x) + F_238(x))
Eq(F_237(x), F_210(x)*F_51(x))
Eq(F_238(x), F_233(x)*F_239(x))
Eq(F_239(x), F_240(x) + F_72(x))
Eq(F_240(x), F_15(x)*F_241(x))
Eq(F_241(x), F_242(x) + F_244(x) + F_28(x))
Eq(F_242(x), F_13(x)*F_243(x))
Eq(F_243(x), F_241(x) + F_56(x))
Eq(F_244(x), F_13(x)*F_245(x))
Eq(F_245(x), F_241(x) + F_56(x))
Eq(F_246(x), F_13(x)*F_247(x))
Eq(F_247(x), F_248(x, 1))
Eq(F_248(x, k_0), F_215(x, k_0) + F_249(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_48(x))
Eq(F_250(x, k_0), F_251(x, k_0) + F_28(x) + F_366(x, k_0) + F_369(x, k_0))
Eq(F_251(x, k_0), F_13(x)*F_252(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0) + F_290(x, k_0))
Eq(F_253(x, k_0), F_254(x, k_0) + F_270(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_268(x, k_0) + F_28(x))
Eq(F_255(x, k_0), F_13(x)*F_256(x, k_0))
Eq(F_256(x, k_0), F_257(x, k_0) + F_261(x, k_0))
Eq(F_257(x, k_0), F_163(x, k_0) + F_258(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0))
Eq(F_259(x, k_0), F_10(x, k_0)*F_260(x, k_0))
Eq(F_260(x, k_0), F_258(x, k_0) + F_56(x))
Eq(F_261(x, k_0), F_262(x, k_0) + F_265(x, k_0))
Eq(F_262(x, k_0), F_263(x, k_0))
Eq(F_263(x, k_0), F_10(x, k_0)*F_264(x, k_0))
Eq(F_264(x, k_0), F_262(x, k_0) + F_52(x))
Eq(F_265(x, k_0), F_266(x, k_0))
Eq(F_266(x, k_0), F_10(x, k_0)*F_267(x, k_0))
Eq(F_267(x, k_0), F_265(x, k_0) + F_59(x))
Eq(F_268(x, k_0), F_10(x, k_0)*F_269(x, k_0))
Eq(F_269(x, k_0), F_254(x, k_0) + F_52(x))
Eq(F_270(x, k_0), F_271(x, k_0) + F_272(x, k_0) + F_28(x) + F_288(x, k_0))
Eq(F_271(x, k_0), F_13(x)*F_253(x, k_0))
Eq(F_272(x, k_0), F_13(x)*F_273(x, k_0))
Eq(F_273(x, k_0), F_274(x, k_0) + F_281(x, k_0))
Eq(F_274(x, k_0), F_275(x, k_0) + F_278(x, k_0))
Eq(F_275(x, k_0), F_276(x, k_0))
Eq(F_276(x, k_0), F_10(x, k_0)*F_277(x, k_0))
Eq(F_277(x, k_0), F_19(x) + F_275(x, k_0))
Eq(F_278(x, k_0), F_279(x, k_0))
Eq(F_279(x, k_0), F_10(x, k_0)*F_280(x, k_0))
Eq(F_280(x, k_0), F_278(x, k_0) + F_66(x))
Eq(F_281(x, k_0), F_282(x, k_0) + F_285(x, k_0))
Eq(F_282(x, k_0), F_283(x, k_0))
Eq(F_283(x, k_0), F_10(x, k_0)*F_284(x, k_0))
Eq(F_284(x, k_0), F_282(x, k_0) + F_61(x))
Eq(F_285(x, k_0), F_286(x, k_0))
Eq(F_286(x, k_0), F_10(x, k_0)*F_287(x, k_0))
Eq(F_287(x, k_0), F_285(x, k_0) + F_69(x))
Eq(F_288(x, k_0), F_10(x, k_0)*F_289(x, k_0))
Eq(F_289(x, k_0), F_270(x, k_0) + F_61(x))
Eq(F_290(x, k_0), F_291(x, k_0) + F_345(x, k_0))
Eq(F_291(x, k_0), F_292(x, k_0))
Eq(F_292(x, k_0), F_13(x)*F_293(x, k_0))
Eq(F_293(x, k_0), F_294(x, k_0) + F_299(x, k_0))
Eq(F_294(x, k_0), F_295(x, k_0))
Eq(F_295(x, k_0), F_15(x)*F_296(x, k_0)*F_55(x))
Eq(F_296(x, k_0), F_297(x, k_0) + F_298(x, k_0))
Eq(F_297(x, k_0), F_163(x, k_0)*F_55(x))
Eq(F_298(x, k_0), F_163(x, k_0)*F_165(x, k_0))
Eq(F_299(x, k_0), F_300(x, k_0) + F_308(x, k_0))
Eq(F_300(x, k_0), F_301(x, k_0) + F_303(x, k_0))
Eq(F_301(x, k_0), F_302(x, k_0))
Eq(F_302(x, k_0), F_163(x, k_0)*F_210(x)*F_55(x))
Eq(F_303(x, k_0), F_304(x, k_0) + F_305(x, k_0))
Eq(F_304(x, k_0), F_165(x, k_0)*F_174(x, k_0)*F_55(x))
Eq(F_305(x, k_0), F_156(x, k_0) + F_306(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0))
Eq(F_307(x, k_0), F_15(x)*F_163(x, k_0)*F_217(x, k_0)*F_55(x))
Eq(F_308(x, k_0), F_309(x, k_0) + F_310(x, k_0))
Eq(F_309(x, k_0), F_291(x, k_0)*F_55(x))
Eq(F_310(x, k_0), -F_311(x, 1) - F_311(x, k_0) + (k_0*F_311(x, k_0) - F_311(x, 1))/(k_0 - 1))
Eq(F_311(x, k_0), F_312(x, k_0) + F_343(x, k_0))
Eq(F_312(x, k_0), F_28(x) + F_313(x, k_0) + F_327(x, k_0))
Eq(F_313(x, k_0), F_314(x, k_0))
Eq(F_314(x, k_0), F_13(x)*F_315(x, k_0))
Eq(F_315(x, k_0), F_316(x, k_0) + F_320(x, k_0))
Eq(F_316(x, k_0), F_312(x, k_0) + F_317(x, k_0))
Eq(F_317(x, k_0), F_15(x)*F_318(x, k_0))
Eq(F_318(x, k_0), F_319(x, k_0))
Eq(F_319(x, k_0), F_10(x, k_0)*F_163(x, k_0))
Eq(F_320(x, k_0), F_321(x, k_0) + F_324(x, k_0))
Eq(F_321(x, k_0), F_15(x)*F_322(x, k_0))
Eq(F_322(x, k_0), F_318(x, k_0) + F_323(x, k_0))
Eq(F_323(x, k_0), F_163(x, k_0)**2)
Eq(F_324(x, k_0), F_325(x, k_0) + F_326(x, k_0))
Eq(F_325(x, k_0), F_318(x, k_0)*F_80(x))
Eq(F_326(x, k_0), F_157(x, k_0)*F_163(x, k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_13(x)*F_329(x, k_0))
Eq(F_329(x, k_0), F_330(x, k_0) + F_340(x, k_0))
Eq(F_330(x, k_0), F_331(x, k_0) + F_335(x, k_0))
Eq(F_331(x, k_0), F_332(x, k_0))
Eq(F_332(x, k_0), F_10(x, k_0)*F_333(x, k_0))
Eq(F_333(x, k_0), F_162(x, k_0) + F_334(x, k_0))
Eq(F_334(x, k_0), F_157(x, k_0) + F_174(x, k_0))
Eq(F_335(x, k_0), F_15(x)*F_336(x, k_0))
Eq(F_336(x, k_0), F_28(x) + F_337(x, k_0) + F_339(x, k_0))
Eq(F_337(x, k_0), F_13(x)*F_338(x, k_0))
Eq(F_338(x, k_0), F_318(x, k_0) + F_336(x, k_0))
Eq(F_339(x, k_0), F_10(x, k_0)*F_217(x, k_0))
Eq(F_340(x, k_0), F_312(x, k_0) + F_341(x, k_0))
Eq(F_341(x, k_0), F_342(x, k_0))
Eq(F_342(x, k_0), F_15(x)*F_336(x, k_0)*F_56(x))
Eq(F_343(x, k_0), F_344(x, k_0))
Eq(F_344(x, k_0), F_15(x)*F_336(x, k_0)*F_56(x))
Eq(F_345(x, k_0), F_346(x, k_0))
Eq(F_346(x, k_0), F_13(x)*F_347(x, k_0))
Eq(F_347(x, k_0), F_348(x, k_0) + F_354(x, k_0))
Eq(F_348(x, k_0), F_349(x, k_0))
Eq(F_349(x, k_0), F_15(x)*F_350(x, k_0))
Eq(F_350(x, k_0), F_253(x, k_0) + F_351(x, k_0))
Eq(F_351(x, k_0), F_163(x, k_0)*F_352(x, k_0))
Eq(F_352(x, k_0), F_232(x) + F_353(x, k_0))
Eq(F_353(x, k_0), F_269(x, k_0) + F_289(x, k_0))
Eq(F_354(x, k_0), F_355(x, k_0) + F_358(x, k_0))
Eq(F_355(x, k_0), F_356(x, k_0) + F_357(x, k_0))
Eq(F_356(x, k_0), F_210(x)*F_253(x, k_0))
Eq(F_357(x, k_0), F_173(x, k_0)*F_353(x, k_0))
Eq(F_358(x, k_0), F_233(x)*F_359(x, k_0))
Eq(F_359(x, k_0), F_291(x, k_0) + F_360(x, k_0))
Eq(F_360(x, k_0), F_15(x)*F_361(x, k_0))
Eq(F_361(x, k_0), 2*F_28(x) + F_362(x, k_0) + F_364(x, k_0))
Eq(F_362(x, k_0), F_13(x)*F_363(x, k_0))
Eq(F_363(x, k_0), F_258(x, k_0) + F_361(x, k_0))
Eq(F_364(x, k_0), F_10(x, k_0)*F_365(x, k_0))
Eq(F_365(x, k_0), F_241(x) + F_361(x, k_0))
Eq(F_366(x, k_0), -F_367(x, 1) + (k_0*F_367(x, k_0) - F_367(x, 1))/(k_0 - 1))
Eq(F_367(x, k_0), F_13(x)*F_368(x, k_0))
Eq(F_368(x, k_0), F_174(x, k_0) + F_250(x, k_0))
Eq(F_369(x, k_0), F_10(x, k_0)*F_249(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_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, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": 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0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 2], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 1], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], 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"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [1, 0], "pos": [[1, 2], [1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}]]}, "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]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/113/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[152,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[92,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[17,x,k[0]]
F[15,x,k[0]] = F[14,x,k[0]]*F[8,x,k[0]]
F[16,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[17,x,k[0]] = F[11,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x]+F[42,x,k[0]]+F[91,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[8,x,k[0]]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[22,x]*F[32,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[11,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[11,x]*F[26,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[29,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[33,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[33,x]
F[41,x] = F[37,x]
F[42,x,k[0]] = F[11,x]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x]+F[61,x,k[0]]
F[44,x] = F[45,x]
F[45,x] = F[32,x]*F[46,x]
F[46,x] = F[47,x]+F[60,x]
F[47,x] = F[22,x]+F[48,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[50,x]+F[51,x]+F[52,x]
F[50,x] = 0
F[51,x] = F[11,x]*F[27,x]
F[52,x] = F[11,x]*F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[11,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[54,x]
F[57,x] = F[49,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[57,x]
F[60,x] = F[48,x]
F[61,x,k[0]] = F[62,x,k[0]]+F[68,x,k[0]]
F[62,x,k[0]] = 2*F[50,x]+F[19,x,k[0]]+F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[61,x,k[0]]
F[64,x,k[0]] = F[11,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[15,x,k[0]]+F[50,x]+F[66,x,k[0]]+F[67,x,k[0]]
F[66,x,k[0]] = F[11,x]*F[65,x,k[0]]
F[67,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[32,x]*F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[76,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[11,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]*F[8,x,k[0]]
F[75,x,k[0]] = F[1,x]+F[73,x,k[0]]
F[76,x,k[0]] = 2*F[50,x]+F[77,x,k[0]]+F[83,x,k[0]]
F[77,x,k[0]] = F[11,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[50,x]+F[79,x,k[0]]+F[81,x,k[0]]
F[79,x,k[0]] = F[8,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[27,x]+F[78,x,k[0]]
F[81,x,k[0]] = F[11,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[73,x,k[0]]+F[78,x,k[0]]
F[83,x,k[0]] = F[11,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[88,x,k[0]]
F[85,x,k[0]] = F[71,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[11,x]*F[85,x,k[0]]
F[88,x,k[0]] = F[76,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[11,x]*F[88,x,k[0]]
F[91,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[92,x,k[0]] = F[149,x,k[0]]+F[150,x,k[0]]+F[50,x]+F[93,x,k[0]]+F[98,x,k[0]]
F[93,x,k[0]] = F[8,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = 2*F[50,x]+F[16,x,k[0]]+F[93,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[11,x]*F[32,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[48,x]+F[70,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[13,x,k[0]]
F[100,x,k[0]] = 2*F[50,x]+F[101,x,k[0]]+F[102,x,k[0]]+F[104,x,k[0]]+F[105,x,k[0]]
F[101,x,k[0]] = F[93,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[104,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[11,x]*F[32,x]
F[107,x,k[0]] = F[108,x]+F[127,x,k[0]]
F[108,x] = F[109,x]+F[48,x]
F[109,x] = F[110,x]+F[112,x]
F[110,x] = F[111,x]
F[111,x] = F[11,x]*F[27,x]
F[112,x] = 2*F[50,x]+F[113,x]+F[119,x]
F[113,x] = F[11,x]*F[114,x]
F[114,x] = F[115,x]+F[117,x]+F[50,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[27,x]
F[117,x] = F[11,x]*F[118,x]
F[118,x] = F[114,x]+F[27,x]
F[119,x] = F[11,x]*F[120,x]
F[120,x] = F[121,x]+F[124,x]
F[121,x] = F[110,x]+F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[11,x]*F[121,x]
F[124,x] = F[112,x]+F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[11,x]*F[124,x]
F[127,x,k[0]] = F[128,x,k[0]]+F[70,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[134,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[11,x]*F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]
F[132,x,k[0]] = F[11,x]*F[133,x,k[0]]
F[133,x,k[0]] = F[131,x,k[0]]+F[73,x,k[0]]
F[134,x,k[0]] = 3*F[50,x]+F[135,x,k[0]]+F[141,x,k[0]]
F[135,x,k[0]] = F[11,x]*F[136,x,k[0]]
F[136,x,k[0]] = 2*F[50,x]+F[137,x,k[0]]+F[139,x,k[0]]
F[137,x,k[0]] = F[11,x]*F[138,x,k[0]]
F[138,x,k[0]] = F[136,x,k[0]]+F[78,x,k[0]]
F[139,x,k[0]] = F[11,x]*F[140,x,k[0]]
F[140,x,k[0]] = F[131,x,k[0]]+F[136,x,k[0]]
F[141,x,k[0]] = F[11,x]*F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]+F[146,x,k[0]]
F[143,x,k[0]] = F[129,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[146,x,k[0]] = F[134,x,k[0]]+F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[11,x]*F[146,x,k[0]]
F[149,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[150,x,k[0]] = F[11,x]*F[151,x,k[0]]
F[151,x,k[0]] = (F[62,x,k[0]]-F[62,x,1])/(-1+k[0])
F[152,x] = F[11,x]*F[153,x]
F[153,x] = F[1,x]+F[154,x]+F[159,x]+F[162,x]
F[154,x] = F[11,x]*F[155,x]
F[155,x] = F[153,x]+F[156,x]
F[156,x] = 2*F[50,x]+F[157,x]+F[159,x]+F[160,x]
F[157,x] = F[158,x]
F[158,x] = F[11,x]*F[156,x]
F[159,x] = F[11,x]*F[153,x]
F[160,x] = F[161,x]
F[161,x] = F[108,x]*F[11,x]*F[32,x]
F[162,x] = F[11,x]*F[163,x]
F[163,x] = F[18,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{152}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right) F_{32}\! \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_{11}\! \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_{11}\! \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_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \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_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{32}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{60}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = 0
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \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_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{49}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{48}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{50}\! \left(x \right)+F_{66}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{79}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{50}\! \left(x \right)+F_{93}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{70}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x \right)+F_{127}\! \left(x , y\right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{48}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{112}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{113}\! \left(x \right)+F_{119}\! \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_{117}\! \left(x \right)+F_{50}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{27}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right)+F_{27}\! \left(x \right)
F_{119}\! \left(x \right) = F_{11}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{121}\! \left(x \right) = F_{110}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{11}\! \left(x \right) F_{121}\! \left(x \right)
F_{124}\! \left(x \right) = F_{112}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{11}\! \left(x \right) F_{124}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = 3 F_{50}\! \left(x \right)+F_{135}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = 2 F_{50}\! \left(x \right)+F_{137}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{146}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = -\frac{-F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x \right) = F_{11}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{1}\! \left(x \right)+F_{154}\! \left(x \right)+F_{159}\! \left(x \right)+F_{162}\! \left(x \right)
F_{154}\! \left(x \right) = F_{11}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{153}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = 2 F_{50}\! \left(x \right)+F_{157}\! \left(x \right)+F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{11}\! \left(x \right) F_{156}\! \left(x \right)
F_{159}\! \left(x \right) = F_{11}\! \left(x \right) F_{153}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{108}\! \left(x \right) F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{162}\! \left(x \right) = F_{11}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{18}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_152(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_92(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_17(x, k_0))
Eq(F_15(x, k_0), F_14(x, k_0)*F_8(x, k_0))
Eq(F_16(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_17(x, k_0), F_11(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x) + F_42(x, k_0) + F_91(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_8(x, k_0))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_22(x)*F_32(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(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_11(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_11(x)*F_29(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_33(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_33(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x, k_0), F_11(x)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x) + F_61(x, k_0))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_32(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_60(x))
Eq(F_47(x), F_22(x) + F_48(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_50(x) + F_51(x) + F_52(x))
Eq(F_50(x), 0)
Eq(F_51(x), F_11(x)*F_27(x))
Eq(F_52(x), F_11(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_11(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_54(x))
Eq(F_57(x), F_49(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_57(x))
Eq(F_60(x), F_48(x))
Eq(F_61(x, k_0), F_62(x, k_0) + F_68(x, k_0))
Eq(F_62(x, k_0), F_19(x, k_0) + 2*F_50(x) + F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_61(x, k_0))
Eq(F_64(x, k_0), F_11(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_15(x, k_0) + F_50(x) + F_66(x, k_0) + F_67(x, k_0))
Eq(F_66(x, k_0), F_11(x)*F_65(x, k_0))
Eq(F_67(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_32(x)*F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_76(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_11(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0)*F_8(x, k_0))
Eq(F_75(x, k_0), F_1(x) + F_73(x, k_0))
Eq(F_76(x, k_0), 2*F_50(x) + F_77(x, k_0) + F_83(x, k_0))
Eq(F_77(x, k_0), F_11(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_50(x) + F_79(x, k_0) + F_81(x, k_0))
Eq(F_79(x, k_0), F_8(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_27(x) + F_78(x, k_0))
Eq(F_81(x, k_0), F_11(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_73(x, k_0) + F_78(x, k_0))
Eq(F_83(x, k_0), F_11(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_88(x, k_0))
Eq(F_85(x, k_0), F_71(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_11(x)*F_85(x, k_0))
Eq(F_88(x, k_0), F_76(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_11(x)*F_88(x, k_0))
Eq(F_91(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_92(x, k_0), F_149(x, k_0) + F_150(x, k_0) + F_50(x) + F_93(x, k_0) + F_98(x, k_0))
Eq(F_93(x, k_0), F_8(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_16(x, k_0) + 2*F_50(x) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_11(x)*F_32(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_48(x) + F_70(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_13(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_102(x, k_0) + F_104(x, k_0) + F_105(x, k_0) + 2*F_50(x))
Eq(F_101(x, k_0), F_93(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_104(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_11(x)*F_32(x))
Eq(F_107(x, k_0), F_108(x) + F_127(x, k_0))
Eq(F_108(x), F_109(x) + F_48(x))
Eq(F_109(x), F_110(x) + F_112(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_11(x)*F_27(x))
Eq(F_112(x), F_113(x) + F_119(x) + 2*F_50(x))
Eq(F_113(x), F_11(x)*F_114(x))
Eq(F_114(x), F_115(x) + F_117(x) + F_50(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_27(x))
Eq(F_117(x), F_11(x)*F_118(x))
Eq(F_118(x), F_114(x) + F_27(x))
Eq(F_119(x), F_11(x)*F_120(x))
Eq(F_120(x), F_121(x) + F_124(x))
Eq(F_121(x), F_110(x) + F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_11(x)*F_121(x))
Eq(F_124(x), F_112(x) + F_125(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_11(x)*F_124(x))
Eq(F_127(x, k_0), F_128(x, k_0) + F_70(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_134(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_11(x)*F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0))
Eq(F_132(x, k_0), F_11(x)*F_133(x, k_0))
Eq(F_133(x, k_0), F_131(x, k_0) + F_73(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_141(x, k_0) + 3*F_50(x))
Eq(F_135(x, k_0), F_11(x)*F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_139(x, k_0) + 2*F_50(x))
Eq(F_137(x, k_0), F_11(x)*F_138(x, k_0))
Eq(F_138(x, k_0), F_136(x, k_0) + F_78(x, k_0))
Eq(F_139(x, k_0), F_11(x)*F_140(x, k_0))
Eq(F_140(x, k_0), F_131(x, k_0) + F_136(x, k_0))
Eq(F_141(x, k_0), F_11(x)*F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_146(x, k_0))
Eq(F_143(x, k_0), F_129(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_146(x, k_0), F_134(x, k_0) + F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_11(x)*F_146(x, k_0))
Eq(F_149(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_150(x, k_0), F_11(x)*F_151(x, k_0))
Eq(F_151(x, k_0), -F_62(x, k_0) + (-k_0*F_62(x, k_0) + F_62(x, 1))/(1 - k_0))
Eq(F_152(x), F_11(x)*F_153(x))
Eq(F_153(x), F_1(x) + F_154(x) + F_159(x) + F_162(x))
Eq(F_154(x), F_11(x)*F_155(x))
Eq(F_155(x), F_153(x) + F_156(x))
Eq(F_156(x), F_157(x) + F_159(x) + F_160(x) + 2*F_50(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_11(x)*F_156(x))
Eq(F_159(x), F_11(x)*F_153(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_108(x)*F_11(x)*F_32(x))
Eq(F_162(x), F_11(x)*F_163(x))
Eq(F_163(x), F_18(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob", "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], 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