0123_1230_02413_03412
Counting sequence:
1, 1, 2, 6, 22, 87, 352, 1430, 5798, 23426, 94316, 378556, 1515516, 6054635, 24148620, 96188070, 382731270, 1521620430, 6045541260, 24007237620, 95296499220, 378163388070, 1500314043696, 5951292620796, 23604143413852, 93611761666052, 371237683029752, 1472193112497464, 5838188531970872, 23152603464498739, 91819788766267044, 364160352597114374, 1444352359617345990, 5729031023408426006, 22725814079194725772, 90155070263762010052, 357680286139073562532, 1419172918179663812242, 5631344349876720846560, 22347350362114118099220, 88690616004707528770420, 352019961467515257886620, 1397317325029065100480680, 5547035470132500785993160, 22022412378306173945422920, 87439304953428711263334270, 347205098714271877627044120, 1378804691649891843449990748, 5475909846469372530907045788, 21749349903978861824747161356, 86391748940820200155131712056, 343189317302507269681733429256, 1363421873009560572411046310472, 5417029878059339521432646820396, 21524156796910205174053824305952, 85531179529008751866432969070392, 339903490311585189135322655479032, 1350887191143609032782576007191560, 5369258182717249866750914917608048, 21342273678262003578725071312888176, 84839427014487407079155842669532016, 337275558359580324193686544673579331, 1340916009053601790116683615594431956, 5331474202362120356513392827751556550, 21199301603669609468886651859019137350, 84299263975124806152213611817736453350, 335238192210493702445123816856305513100, 1333245646980747783403969065628216188900, 5302654652528409395730434615515264191300, 21091259467909577270535809702239497101850, 83895219157422852460694776400241788073600, 333731325988861022162813453471804744744100, 1327643098867837624538697079228478198617860, 5281896315207553790695721445823502034716460, 21014648251830202797644357099531744852600520, 83613744870625512946431226010307305668916520, 332702529480061711863018308749932324646052520, 1323905538738971014331582637448632416287782090, 5268414829714257745292456811571453087768682920, 20966435599927544017742732138862463110986951540, 83443120898094102156653605114474674720679804340, 332106512997495638523568015396665585176778951140, 1321857987522357748670150303767168145686186577000, 5261534254310052755546844639447027034128996468760, 20944010670636607969865986867495373604774514332120, 83373263763763172565641399287317904223676805022420, 331904335482985591126420189486248539707355009874720, 1321350068318082590359124590740584696455163653250120, 5260673907940546190092708367288151579989290292331400, 20945131215376776565596754598405482456740153982271800, 83395515317508405119282711980573665444518091417734800, 332062564599371794121236619040955192471269047910422800, 1322252685044349541196943758169568495354954225215357200, 5265335287380724883122706659390000845020485414040727150, 20967872215766217521188339978760921219561633430472925800, 83502441658515441287961026799775661854080211234408422300, 332552491470035368491541497599058135181227327922776246300, 1324454962245671758730209889792786069359869365836148174460, 5275090163388861623073051370913519852559298274515240674360, 21010579652718562060848035668248572403257836600696539145320, 83687653838851560973737655695991903180935644621947205953320
Generating function in Maple syntax:
((-2*x^3-8*x^2+6*x-1)*(1-4*x)^(1/2)-8*x^3+18*x^2-8*x+1)/(8*x^4-2*x^3)
Generating function in latex syntax:
\frac{\left(-2 x^{3}-8 x^{2}+6 x -1\right) \sqrt{1-4 x}-8 x^{3}+18 x^{2}-8 x +1}{8 x^{4}-2 x^{3}}
Generating function in sympy syntax:
(-8*x**3 + 18*x**2 - 8*x + sqrt(1 - 4*x)*(-2*x**3 - 8*x**2 + 6*x - 1) + 1)/(8*x**4 - 2*x**3)
Implicit equation for the generating function in Maple syntax:
x^3*(4*x-1)*F(x)^2+(4*x-1)*(2*x^2-4*x+1)*F(x)+x^3+12*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{3} \left(4 x -1\right) F \! \left(x \right)^{2}+\left(4 x -1\right) \left(2 x^{2}-4 x +1\right) F \! \left(x \right)+x^{3}+12 x^{2}-7 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = 4*(2*n+1)/(7+n)*a(n)+2*(5*n+28)/(7+n)*a(3+n)+6*(5*n+13)/(7+n)*a(n+1)-4*(8*n+33)/(7+n)*a(n+2), n >= 4
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(n +4\right) = \frac{4 \left(2 n +1\right) a \! \left(n \right)}{7+n}+\frac{2 \left(5 n +28\right) a \! \left(3+n \right)}{7+n}+\frac{6 \left(5 n +13\right) a \! \left(n +1\right)}{7+n}-\frac{4 \left(8 n +33\right) a \! \left(n +2\right)}{7+n}, \quad n \geq 4
Specification 1
Strategy pack name: all_the_strategies_2_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24028/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[6,x]
F[1,x] = F[2,x]+F[3,x]
F[2,x] = 1
F[3,x] = F[4,x]
F[4,x] = F[1,x]*F[5,x]
F[5,x] = x
F[6,x] = F[7,x]
F[7,x] = F[5,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = -F[36,x]+F[10,x]
F[10,x] = 1/F[5,x]*F[11,x]
F[11,x] = F[12,x]
F[12,x] = -F[3,x]+F[13,x]
F[13,x] = F[14,x]+F[15,x]+F[34,x]
F[14,x] = 0
F[15,x] = F[16,x]*F[5,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[14,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[5,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[20,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]*F[5,x]
F[23,x,k[0]] = F[2,x]+F[24,x,k[0]]+F[31,x,k[0]]+F[33,x,k[0]]
F[24,x,k[0]] = (F[25,x,k[0]]*k[0]-F[25,x,1])/(-1+k[0])
F[26,x,k[0]] = F[2,x]+F[25,x,k[0]]+F[30,x,k[0]]
F[26,x,k[0]] = F[2,x]+F[27,x,k[0]]+F[29,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[5,x]
F[28,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[29,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[21,x,k[0]]*F[23,x,k[0]]
F[33,x,k[0]] = F[22,x,k[0]]
F[34,x] = F[35,x]*F[5,x]
F[35,x] = F[26,x,1]
F[36,x] = 1/F[5,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[47,x]+F[39,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[41,x]
F[41,x] = F[3,x]*F[5,x]
F[42,x] = F[14,x]+F[43,x]+F[46,x]
F[43,x] = F[44,x]*F[5,x]
F[44,x] = F[45,x,1]
F[45,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[46,x] = F[42,x]*F[5,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[49,x]
F[49,x] = F[35,x]*F[5,x]
F[50,x] = F[5,x]*F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = 2*F[14,x]+F[54,x]+F[57,x]
F[54,x] = F[5,x]*F[55,x]
F[55,x] = F[52,x]+F[56,x]
F[56,x] = F[2,x]+F[49,x]
F[57,x] = F[5,x]*F[58,x]
F[58,x] = F[59,x,1]
F[59,x,k[0]] = (F[60,x,k[0]]*k[0]-F[60,x,1])/(-1+k[0])
F[60,x,k[0]] = 2*F[14,x]+F[61,x,k[0]]+F[66,x,k[0]]
F[61,x,k[0]] = F[5,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[2,x]+F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[21,x,k[0]]*F[62,x,k[0]]
F[64,x,k[0]] = F[5,x]*F[65,x,k[0]]
F[65,x,k[0]] = (F[62,x,k[0]]*k[0]-F[62,x,1])/(-1+k[0])
F[66,x,k[0]] = F[5,x]*F[59,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{1}\! \left(x \right) = F_{2}\! \left(x \right)+F_{3}\! \left(x \right)
F_{2}\! \left(x \right) = 1
F_{3}\! \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) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = -F_{3}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{14}\! \left(x \right) = 0
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \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_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x \right) = F_{42}\! \left(x \right) F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{35}\! \left(x \right) F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{5}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{14}\! \left(x \right)+F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{5}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{57}\! \left(x \right) = F_{5}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x , 1\right)
F_{59}\! \left(x , y\right) = -\frac{-y F_{60}\! \left(x , y\right)+F_{60}\! \left(x , 1\right)}{-1+y}
F_{60}\! \left(x , y\right) = 2 F_{14}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = -\frac{-y F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}
F_{66}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{59}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_6(x))
Eq(F_1(x), F_2(x) + F_3(x))
Eq(F_2(x), 1)
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_1(x)*F_5(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)*F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x) - F_36(x))
Eq(F_10(x), F_11(x)/F_5(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x) - F_3(x))
Eq(F_13(x), F_14(x) + F_15(x) + F_34(x))
Eq(F_14(x), 0)
Eq(F_15(x), F_16(x)*F_5(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_14(x) + F_18(x, k_0) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_5(x))
Eq(F_19(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0)*F_5(x))
Eq(F_23(x, k_0), F_2(x) + F_24(x, k_0) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_24(x, k_0), (-k_0*F_25(x, k_0) + F_25(x, 1))/(1 - k_0))
Eq(F_26(x, k_0), F_2(x) + F_25(x, k_0) + F_30(x, k_0))
Eq(F_26(x, k_0), F_2(x) + F_27(x, k_0) + F_29(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_5(x))
Eq(F_28(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_21(x, k_0)*F_26(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_21(x, k_0)*F_23(x, k_0))
Eq(F_33(x, k_0), F_22(x, k_0))
Eq(F_34(x), F_35(x)*F_5(x))
Eq(F_35(x), F_26(x, 1))
Eq(F_36(x), F_37(x)/F_5(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x) - F_47(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_3(x)*F_5(x))
Eq(F_42(x), F_14(x) + F_43(x) + F_46(x))
Eq(F_43(x), F_44(x)*F_5(x))
Eq(F_44(x), F_45(x, 1))
Eq(F_45(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_46(x), F_42(x)*F_5(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_35(x)*F_5(x))
Eq(F_50(x), F_5(x)*F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), 2*F_14(x) + F_54(x) + F_57(x))
Eq(F_54(x), F_5(x)*F_55(x))
Eq(F_55(x), F_52(x) + F_56(x))
Eq(F_56(x), F_2(x) + F_49(x))
Eq(F_57(x), F_5(x)*F_58(x))
Eq(F_58(x), F_59(x, 1))
Eq(F_59(x, k_0), (-k_0*F_60(x, k_0) + F_60(x, 1))/(1 - k_0))
Eq(F_60(x, k_0), 2*F_14(x) + F_61(x, k_0) + F_66(x, k_0))
Eq(F_61(x, k_0), F_5(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_2(x) + F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_21(x, k_0)*F_62(x, k_0))
Eq(F_64(x, k_0), F_5(x)*F_65(x, k_0))
Eq(F_65(x, k_0), (-k_0*F_62(x, k_0) + F_62(x, 1))/(1 - k_0))
Eq(F_66(x, k_0), F_5(x)*F_59(x, k_0))
Pack JSON:
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Specification JSON:
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"tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: all_the_strategies_1_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24029/
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[180,x]+F[4,x]+F[5,x]
F[4,x] = 0
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[178,x]+F[22,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x]+F[15,x,k[0]]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = x
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[17,x,k[0]] = F[11,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[14,x]*F[20,x,k[0]]
F[20,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[21,x,k[0]] = k[0]*x
F[22,x] = F[14,x]*F[23,x]
F[23,x] = F[24,x]+F[86,x]
F[24,x] = F[25,x]+F[27,x]+F[46,x]
F[25,x] = F[26,x,1]
F[26,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[27,x] = F[14,x]*F[28,x]
F[28,x] = F[29,x]+F[38,x]+F[45,x]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[36,x,k[0]]+F[37,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = (F[33,x,k[0]]*k[0]-F[33,x,1])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[14,x]*F[35,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[36,x,k[0]] = F[21,x,k[0]]*F[30,x,k[0]]
F[37,x,k[0]] = F[14,x]*F[30,x,k[0]]
F[38,x] = F[14,x]*F[39,x]
F[39,x] = F[40,x,1]
F[40,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[41,x,k[0]] = F[30,x,k[0]]+F[42,x,k[0]]+F[44,x,k[0]]
F[42,x,k[0]] = F[14,x]*F[43,x,k[0]]
F[43,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[44,x,k[0]] = F[14,x]*F[41,x,k[0]]
F[45,x] = F[14,x]*F[28,x]
F[46,x] = F[47,x]
F[47,x] = -F[85,x]+F[48,x]
F[48,x] = 1/F[14,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = -F[80,x]-F[84,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[14,x]*F[53,x]
F[53,x] = 1/F[14,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = -F[75,x]+F[56,x]
F[56,x] = F[1,x]+F[57,x]+F[64,x]+F[74,x]
F[57,x] = F[14,x]*F[58,x]
F[58,x] = F[59,x,1]
F[59,x,k[0]] = 1/(-1+k[0])*(F[60,x,k[0]]*k[0]-F[60,x,1])
F[60,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[61,x,k[0]]+F[63,x,k[0]]
F[61,x,k[0]] = F[14,x]*F[62,x,k[0]]
F[62,x,k[0]] = 1/(-1+k[0])*(F[60,x,k[0]]*k[0]-F[60,x,1])
F[63,x,k[0]] = F[21,x,k[0]]*F[60,x,k[0]]
F[64,x] = F[14,x]*F[65,x]
F[65,x] = F[56,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[68,x]*F[71,x]
F[68,x] = F[29,x]+F[69,x]
F[69,x] = F[70,x,1]
F[70,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[71,x] = F[1,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[14,x]*F[71,x]
F[74,x] = F[14,x]*F[29,x]
F[75,x] = 1/F[14,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = -F[80,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[56,x]
F[80,x] = -F[84,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[14,x]*F[83,x]
F[83,x] = F[60,x,1]
F[84,x] = F[13,x]
F[85,x] = F[27,x]
F[86,x] = 1/F[14,x]*F[87,x]
F[87,x] = -F[156,x]-F[159,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[90,x]+F[53,x]
F[90,x] = -F[91,x]+F[53,x]
F[91,x] = -F[100,x]+F[92,x]
F[92,x] = 1/F[14,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = -F[99,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[97,x]+F[56,x]
F[97,x] = F[1,x]+F[82,x]+F[98,x]
F[98,x] = F[10,x]*F[14,x]
F[99,x] = -F[12,x]+F[75,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[14,x]
F[102,x] = F[103,x]+F[130,x]
F[103,x] = F[104,x,1]
F[104,x,k[0]] = F[105,x,k[0]]*F[71,x]
F[106,x,k[0]] = F[105,x,k[0]]*F[21,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[122,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[21,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]
F[111,x,k[0]] = F[108,x,k[0]]+F[12,x]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[14,x]
F[114,x,k[0]] = F[115,x]+F[118,x,k[0]]
F[115,x] = F[116,x,1]
F[117,x,k[0]] = F[116,x,k[0]]*F[21,x,k[0]]
F[117,x,k[0]] = F[15,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = -k[0]*(F[108,x,1]-F[108,x,k[0]])/(-1+k[0])
F[120,x,k[0]] = F[121,x,k[0]]*F[14,x]
F[121,x,k[0]] = -k[0]*(F[118,x,1]-F[118,x,k[0]])/(-1+k[0])
F[122,x,k[0]] = F[123,x,k[0]]*F[14,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[126,x,k[0]]+F[128,x,k[0]]+F[4,x]
F[124,x,k[0]] = F[125,x,k[0]]*F[21,x,k[0]]
F[125,x,k[0]] = F[115,x]+F[123,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[127,x,k[0]] = F[123,x,k[0]]*F[14,x]*F[71,x]
F[118,x,k[0]] = 2*F[4,x]+F[128,x,k[0]]+F[129,x,k[0]]
F[129,x,k[0]] = F[114,x,k[0]]*F[21,x,k[0]]
F[130,x] = F[131,x,1]
F[132,x,k[0]] = F[131,x,k[0]]+F[154,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[136,x,k[0]]
F[133,x,k[0]] = F[116,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[132,x,k[0]]*F[14,x]
F[137,x,k[0]] = F[136,x,k[0]]*F[21,x,k[0]]
F[138,x,k[0]] = F[137,x,k[0]]+F[153,x]
F[139,x,k[0]] = F[138,x,k[0]]+F[141,x,k[0]]
F[140,x,k[0]] = F[139,x,k[0]]*F[14,x]
F[141,x,k[0]] = F[140,x,k[0]]+F[151,x]+F[152,x,k[0]]
F[116,x,k[0]] = F[141,x,k[0]]+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[1,x]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[143,x,k[0]]*F[21,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]+F[72,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[150,x,k[0]]+F[4,x]
F[148,x,k[0]] = F[14,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[144,x,k[0]]+F[147,x,k[0]]
F[150,x,k[0]] = F[146,x,k[0]]*F[21,x,k[0]]
F[151,x] = F[13,x]
F[152,x,k[0]] = F[141,x,k[0]]*F[21,x,k[0]]
F[153,x] = F[112,x,1]
F[154,x,k[0]] = F[143,x,k[0]]*F[155,x]
F[155,x] = F[110,x,1]
F[156,x] = F[157,x]
F[157,x] = F[158,x,1]
F[158,x,k[0]] = F[110,x,k[0]]*F[14,x]
F[159,x] = F[160,x]
F[160,x] = F[14,x]*F[161,x]
F[161,x] = F[162,x]+F[177,x]
F[162,x] = F[163,x]
F[163,x] = -F[175,x]+F[164,x]
F[164,x] = 1/F[14,x]*F[165,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]+F[171,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[8,x]
F[170,x] = F[122,x,1]
F[171,x] = F[172,x]
F[172,x] = F[14,x]*F[173,x]
F[173,x] = -F[174,x]+F[28,x]
F[174,x] = F[105,x,1]
F[175,x] = -F[176,x]+F[164,x]
F[176,x] = F[173,x]
F[177,x] = F[88,x]
F[178,x] = F[179,x]
F[179,x] = F[14,x]*F[164,x]
F[180,x] = F[12,x]*F[14,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{180}\! \left(x \right)+F_{4}\! \left(x \right)+F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = 0
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{178}\! \left(x \right)+F_{22}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{86}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{46}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{40}\! \left(x , y\right) = -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{80}\! \left(x \right)-F_{84}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{1}\! \left(x \right)+F_{57}\! \left(x \right)+F_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x , 1\right)
F_{59}\! \left(x , y\right) = -\frac{-y F_{60}\! \left(x , y\right)+F_{60}\! \left(x , 1\right)}{-1+y}
F_{60}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = -\frac{-y F_{60}\! \left(x , y\right)+F_{60}\! \left(x , 1\right)}{-1+y}
F_{63}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{56}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{29}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x , 1\right)
F_{70}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right)
F_{85}\! \left(x \right) = F_{27}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{87}\! \left(x \right) = -F_{156}\! \left(x \right)-F_{159}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{53}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{53}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = \frac{F_{93}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{56}\! \left(x \right)
F_{97}\! \left(x \right) = F_{1}\! \left(x \right)+F_{82}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{99}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{75}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{130}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{71}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{12}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x \right)+F_{118}\! \left(x , y\right)
F_{115}\! \left(x \right) = F_{116}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{15}\! \left(x , y\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) = -\frac{y \left(F_{108}\! \left(x , 1\right)-F_{108}\! \left(x , y\right)\right)}{-1+y}
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{121}\! \left(x , y\right) = -\frac{y \left(F_{118}\! \left(x , 1\right)-F_{118}\! \left(x , y\right)\right)}{-1+y}
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{115}\! \left(x \right)+F_{123}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{118}\! \left(x , y\right) = 2 F_{4}\! \left(x \right)+F_{128}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{130}\! \left(x \right) = F_{131}\! \left(x , 1\right)
F_{132}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{153}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{151}\! \left(x \right)+F_{152}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{1}\! \left(x \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_{143}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{72}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{13}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{153}\! \left(x \right) = F_{112}\! \left(x , 1\right)
F_{154}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{110}\! \left(x , 1\right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x , 1\right)
F_{158}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{14}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{177}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = -F_{175}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = \frac{F_{165}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{171}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{8}\! \left(x \right)
F_{170}\! \left(x \right) = F_{122}\! \left(x , 1\right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{14}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{174}\! \left(x \right)+F_{28}\! \left(x \right)
F_{174}\! \left(x \right) = F_{105}\! \left(x , 1\right)
F_{175}\! \left(x \right) = -F_{176}\! \left(x \right)+F_{164}\! \left(x \right)
F_{176}\! \left(x \right) = F_{173}\! \left(x \right)
F_{177}\! \left(x \right) = F_{88}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{14}\! \left(x \right) F_{164}\! \left(x \right)
F_{180}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_180(x) + F_4(x) + F_5(x))
Eq(F_4(x), 0)
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_178(x) + F_22(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x) + F_15(x, k_0))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_17(x, k_0), F_11(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_14(x)*F_20(x, k_0))
Eq(F_20(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x), F_14(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_86(x))
Eq(F_24(x), F_25(x) + F_27(x) + F_46(x))
Eq(F_25(x), F_26(x, 1))
Eq(F_26(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_27(x), F_14(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_38(x) + F_45(x))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0) + F_36(x, k_0) + F_37(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_14(x)*F_35(x, k_0))
Eq(F_35(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_21(x, k_0)*F_30(x, k_0))
Eq(F_37(x, k_0), F_14(x)*F_30(x, k_0))
Eq(F_38(x), F_14(x)*F_39(x))
Eq(F_39(x), F_40(x, 1))
Eq(F_40(x, k_0), (-k_0*F_41(x, k_0) + F_41(x, 1))/(1 - k_0))
Eq(F_41(x, k_0), F_30(x, k_0) + F_42(x, k_0) + F_44(x, k_0))
Eq(F_42(x, k_0), F_14(x)*F_43(x, k_0))
Eq(F_43(x, k_0), (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_14(x)*F_41(x, k_0))
Eq(F_45(x), F_14(x)*F_28(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) - F_85(x))
Eq(F_48(x), F_49(x)/F_14(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_51(x) - F_80(x) - F_84(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_14(x)*F_53(x))
Eq(F_53(x), F_54(x)/F_14(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) - F_75(x))
Eq(F_56(x), F_1(x) + F_57(x) + F_64(x) + F_74(x))
Eq(F_57(x), F_14(x)*F_58(x))
Eq(F_58(x), F_59(x, 1))
Eq(F_59(x, k_0), (-k_0*F_60(x, k_0) + F_60(x, 1))/(1 - k_0))
Eq(F_60(x, k_0), F_1(x) + F_37(x, k_0) + F_61(x, k_0) + F_63(x, k_0))
Eq(F_61(x, k_0), F_14(x)*F_62(x, k_0))
Eq(F_62(x, k_0), (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_63(x, k_0), F_21(x, k_0)*F_60(x, k_0))
Eq(F_64(x), F_14(x)*F_65(x))
Eq(F_65(x), F_56(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_68(x)*F_71(x))
Eq(F_68(x), F_29(x) + F_69(x))
Eq(F_69(x), F_70(x, 1))
Eq(F_70(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_71(x), F_1(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_14(x)*F_71(x))
Eq(F_74(x), F_14(x)*F_29(x))
Eq(F_75(x), F_76(x)/F_14(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_78(x) - F_80(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_56(x))
Eq(F_80(x), F_81(x) - F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_14(x)*F_83(x))
Eq(F_83(x), F_60(x, 1))
Eq(F_84(x), F_13(x))
Eq(F_85(x), F_27(x))
Eq(F_86(x), F_87(x)/F_14(x))
Eq(F_87(x), -F_156(x) - F_159(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_53(x) - F_90(x))
Eq(F_90(x), F_53(x) - F_91(x))
Eq(F_91(x), -F_100(x) + F_92(x))
Eq(F_92(x), F_93(x)/F_14(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_95(x) - F_99(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_56(x) - F_97(x))
Eq(F_97(x), F_1(x) + F_82(x) + F_98(x))
Eq(F_98(x), F_10(x)*F_14(x))
Eq(F_99(x), -F_12(x) + F_75(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_14(x))
Eq(F_102(x), F_103(x) + F_130(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_104(x, k_0), F_105(x, k_0)*F_71(x))
Eq(F_106(x, k_0), F_105(x, k_0)*F_21(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_122(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_21(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0))
Eq(F_111(x, k_0), F_108(x, k_0) + F_12(x))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_14(x))
Eq(F_114(x, k_0), F_115(x) + F_118(x, k_0))
Eq(F_115(x), F_116(x, 1))
Eq(F_117(x, k_0), F_116(x, k_0)*F_21(x, k_0))
Eq(F_117(x, k_0), F_15(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), -F_108(x, 1) + (-k_0*F_108(x, k_0) + F_108(x, 1))/(1 - k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_14(x))
Eq(F_121(x, k_0), -F_118(x, 1) + (-k_0*F_118(x, k_0) + F_118(x, 1))/(1 - k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_14(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_126(x, k_0) + F_128(x, k_0) + F_4(x))
Eq(F_124(x, k_0), F_125(x, k_0)*F_21(x, k_0))
Eq(F_125(x, k_0), F_115(x) + F_123(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_127(x, k_0), F_123(x, k_0)*F_14(x)*F_71(x))
Eq(F_118(x, k_0), F_128(x, k_0) + F_129(x, k_0) + 2*F_4(x))
Eq(F_129(x, k_0), F_114(x, k_0)*F_21(x, k_0))
Eq(F_130(x), F_131(x, 1))
Eq(F_132(x, k_0), F_131(x, k_0) + F_154(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_136(x, k_0))
Eq(F_133(x, k_0), F_116(x, k_0) + F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_132(x, k_0)*F_14(x))
Eq(F_137(x, k_0), F_136(x, k_0)*F_21(x, k_0))
Eq(F_138(x, k_0), F_137(x, k_0) + F_153(x))
Eq(F_139(x, k_0), F_138(x, k_0) + F_141(x, k_0))
Eq(F_140(x, k_0), F_139(x, k_0)*F_14(x))
Eq(F_141(x, k_0), F_140(x, k_0) + F_151(x) + F_152(x, k_0))
Eq(F_116(x, k_0), F_141(x, k_0) + 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_1(x) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_143(x, k_0)*F_21(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0) + F_72(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_150(x, k_0) + F_4(x))
Eq(F_148(x, k_0), F_14(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_144(x, k_0) + F_147(x, k_0))
Eq(F_150(x, k_0), F_146(x, k_0)*F_21(x, k_0))
Eq(F_151(x), F_13(x))
Eq(F_152(x, k_0), F_141(x, k_0)*F_21(x, k_0))
Eq(F_153(x), F_112(x, 1))
Eq(F_154(x, k_0), F_143(x, k_0)*F_155(x))
Eq(F_155(x), F_110(x, 1))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x, 1))
Eq(F_158(x, k_0), F_110(x, k_0)*F_14(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_14(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_177(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_164(x) - F_175(x))
Eq(F_164(x), F_165(x)/F_14(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x) + F_171(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_8(x))
Eq(F_170(x), F_122(x, 1))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_14(x)*F_173(x))
Eq(F_173(x), -F_174(x) + F_28(x))
Eq(F_174(x), F_105(x, 1))
Eq(F_175(x), F_164(x) - F_176(x))
Eq(F_176(x), F_173(x))
Eq(F_177(x), F_88(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_14(x)*F_164(x))
Eq(F_180(x), F_12(x)*F_14(x))
Pack JSON:
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Specification JSON:
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"strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [4, 1]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 3
Strategy pack name: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24030/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[74,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[1,x]+F[44,x]+F[56,x]+F[7,x]
F[7,x] = F[5,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[41,x,k[0]]+F[43,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[12,x,k[0]] = F[13,x,k[0]]+F[24,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[19,x]+F[22,x,k[0]]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[5,x]
F[21,x] = F[1,x]+F[19,x]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[17,x,k[0]]*F[18,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[31,x,k[0]]
F[25,x,k[0]] = F[19,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x]+F[28,x,k[0]]+F[30,x,k[0]]
F[27,x] = 0
F[28,x,k[0]] = F[29,x,k[0]]*F[5,x]
F[29,x,k[0]] = F[15,x,k[0]]+F[26,x,k[0]]
F[30,x,k[0]] = F[17,x,k[0]]*F[25,x,k[0]]
F[31,x,k[0]] = F[32,x]+F[37,x,k[0]]
F[32,x] = F[27,x]+F[33,x]+F[35,x]
F[33,x] = F[34,x]*F[5,x]
F[34,x] = F[19,x]+F[32,x]
F[35,x] = F[36,x]*F[5,x]
F[36,x] = F[19,x]+F[32,x]
F[37,x,k[0]] = 2*F[27,x]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[5,x]
F[39,x,k[0]] = F[22,x,k[0]]+F[37,x,k[0]]
F[40,x,k[0]] = F[17,x,k[0]]*F[31,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]*F[5,x]
F[42,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[43,x,k[0]] = F[10,x,k[0]]*F[17,x,k[0]]
F[44,x] = F[45,x]*F[5,x]
F[45,x] = F[46,x]+F[50,x]
F[46,x] = F[21,x]+F[47,x]
F[47,x] = F[19,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[47,x]*F[5,x]
F[50,x] = F[36,x]+F[51,x]
F[51,x] = F[32,x]+F[52,x]
F[52,x] = 2*F[27,x]+F[53,x]+F[55,x]
F[53,x] = F[5,x]*F[54,x]
F[54,x] = F[48,x]+F[52,x]
F[55,x] = F[5,x]*F[51,x]
F[56,x] = F[5,x]*F[57,x]
F[57,x] = F[58,x,1]
F[58,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[59,x,k[0]] = F[1,x]+F[60,x,k[0]]+F[61,x,k[0]]+F[73,x,k[0]]
F[60,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[61,x,k[0]] = F[17,x,k[0]]*F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[63,x,k[0]] = F[21,x]+F[64,x,k[0]]
F[64,x,k[0]] = F[15,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[5,x]*F[64,x,k[0]]
F[67,x,k[0]] = F[36,x]+F[68,x,k[0]]
F[68,x,k[0]] = F[26,x,k[0]]+F[69,x,k[0]]
F[69,x,k[0]] = 2*F[27,x]+F[70,x,k[0]]+F[72,x,k[0]]
F[70,x,k[0]] = F[5,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[65,x,k[0]]+F[69,x,k[0]]
F[72,x,k[0]] = F[5,x]*F[68,x,k[0]]
F[73,x,k[0]] = F[5,x]*F[58,x,k[0]]
F[74,x] = F[5,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[1,x]+F[121,x,k[0]]+F[123,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[5,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[85,x,k[0]]
F[79,x,k[0]] = F[1,x]+F[80,x,k[0]]+F[81,x,k[0]]+F[82,x,k[0]]
F[80,x,k[0]] = F[42,x,k[0]]*F[5,x]
F[81,x,k[0]] = F[5,x]*F[78,x,k[0]]
F[82,x,k[0]] = F[17,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[1,x]+F[80,x,k[0]]+F[82,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[14,x,k[0]]*F[5,x]*F[87,x,k[0]]
F[88,x,k[0]] = F[5,x]*F[87,x,k[0]]
F[89,x,k[0]] = F[109,x]+F[110,x]+F[120,x,k[0]]+F[88,x,k[0]]
F[89,x,k[0]] = F[107,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[91,x,k[0]]*k[0]-F[91,x,1])
F[92,x,k[0]] = F[17,x,k[0]]*F[91,x,k[0]]
F[93,x,k[0]] = F[92,x,k[0]]+F[97,x]
F[93,x,k[0]] = F[1,x]+F[94,x,k[0]]+F[95,x,k[0]]
F[94,x,k[0]] = F[10,x,k[0]]*F[5,x]
F[95,x,k[0]] = F[17,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[14,x,k[0]]+F[25,x,k[0]]
F[97,x] = F[1,x]+F[98,x]
F[98,x] = F[5,x]*F[99,x]
F[99,x] = F[1,x]+F[100,x]+F[101,x]
F[100,x] = F[5,x]*F[99,x]
F[101,x] = F[102,x]*F[5,x]
F[102,x] = F[103,x,1]
F[103,x,k[0]] = (F[104,x,k[0]]*k[0]-F[104,x,1])/(-1+k[0])
F[104,x,k[0]] = F[1,x]+F[105,x,k[0]]+F[106,x,k[0]]
F[105,x,k[0]] = F[104,x,k[0]]*F[17,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]*F[5,x]
F[107,x,k[0]] = F[108,x,k[0]]*F[5,x]
F[108,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[109,x] = F[21,x]*F[97,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[21,x]*F[5,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[91,x,1]
F[114,x] = F[115,x]*F[5,x]
F[115,x] = F[116,x,1]
F[116,x,k[0]] = F[117,x,k[0]]+F[118,x,k[0]]
F[117,x,k[0]] = 1/(-1+k[0])*(F[91,x,k[0]]*k[0]-F[91,x,1])
F[118,x,k[0]] = F[119,x,k[0]]*F[5,x]
F[119,x,k[0]] = (F[116,x,k[0]]*k[0]-F[116,x,1])/(-1+k[0])
F[120,x,k[0]] = F[17,x,k[0]]*F[89,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]*F[5,x]
F[122,x,k[0]] = 1/(-1+k[0])*(F[76,x,k[0]]*k[0]-F[76,x,1])
F[123,x,k[0]] = F[17,x,k[0]]*F[76,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)+F_{56}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \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) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{37}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{42}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{43}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right) F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{32}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{5}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{5}\! \left(x \right) F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{5}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{74}\! \left(x \right) = F_{5}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{121}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{5}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)+F_{120}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-y F_{91}\! \left(x , y\right)+F_{91}\! \left(x , 1\right)}{-1+y}
F_{92}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{93}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{95}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{97}\! \left(x \right) = F_{1}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{5}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{5}\! \left(x \right) F_{99}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{5}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x , 1\right)
F_{103}\! \left(x , y\right) = -\frac{-y F_{104}\! \left(x , y\right)+F_{104}\! \left(x , 1\right)}{-1+y}
F_{104}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{108}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{109}\! \left(x \right) = F_{21}\! \left(x \right) F_{97}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{91}\! \left(x , 1\right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{5}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x , 1\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = -\frac{-y F_{91}\! \left(x , y\right)+F_{91}\! \left(x , 1\right)}{-1+y}
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{119}\! \left(x , y\right) = -\frac{-y F_{116}\! \left(x , y\right)+F_{116}\! \left(x , 1\right)}{-1+y}
F_{120}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{122}\! \left(x , y\right) = -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}
F_{123}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{76}\! \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)*F_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_74(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_1(x) + F_44(x) + F_56(x) + F_7(x))
Eq(F_7(x), F_5(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), (-k_0*F_10(x, k_0) + F_10(x, 1))/(1 - k_0))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_41(x, k_0) + F_43(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_12(x, k_0), F_13(x, k_0) + F_24(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_19(x) + F_22(x, k_0))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_5(x))
Eq(F_21(x), F_1(x) + F_19(x))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_17(x, k_0)*F_18(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_31(x, k_0))
Eq(F_25(x, k_0), F_19(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x) + F_28(x, k_0) + F_30(x, k_0))
Eq(F_27(x), 0)
Eq(F_28(x, k_0), F_29(x, k_0)*F_5(x))
Eq(F_29(x, k_0), F_15(x, k_0) + F_26(x, k_0))
Eq(F_30(x, k_0), F_17(x, k_0)*F_25(x, k_0))
Eq(F_31(x, k_0), F_32(x) + F_37(x, k_0))
Eq(F_32(x), F_27(x) + F_33(x) + F_35(x))
Eq(F_33(x), F_34(x)*F_5(x))
Eq(F_34(x), F_19(x) + F_32(x))
Eq(F_35(x), F_36(x)*F_5(x))
Eq(F_36(x), F_19(x) + F_32(x))
Eq(F_37(x, k_0), 2*F_27(x) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_5(x))
Eq(F_39(x, k_0), F_22(x, k_0) + F_37(x, k_0))
Eq(F_40(x, k_0), F_17(x, k_0)*F_31(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0)*F_5(x))
Eq(F_42(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_43(x, k_0), F_10(x, k_0)*F_17(x, k_0))
Eq(F_44(x), F_45(x)*F_5(x))
Eq(F_45(x), F_46(x) + F_50(x))
Eq(F_46(x), F_21(x) + F_47(x))
Eq(F_47(x), F_19(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_47(x)*F_5(x))
Eq(F_50(x), F_36(x) + F_51(x))
Eq(F_51(x), F_32(x) + F_52(x))
Eq(F_52(x), 2*F_27(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_5(x)*F_54(x))
Eq(F_54(x), F_48(x) + F_52(x))
Eq(F_55(x), F_5(x)*F_51(x))
Eq(F_56(x), F_5(x)*F_57(x))
Eq(F_57(x), F_58(x, 1))
Eq(F_58(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_59(x, k_0), F_1(x) + F_60(x, k_0) + F_61(x, k_0) + F_73(x, k_0))
Eq(F_60(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_61(x, k_0), F_17(x, k_0)*F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_63(x, k_0), F_21(x) + F_64(x, k_0))
Eq(F_64(x, k_0), F_15(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_5(x)*F_64(x, k_0))
Eq(F_67(x, k_0), F_36(x) + F_68(x, k_0))
Eq(F_68(x, k_0), F_26(x, k_0) + F_69(x, k_0))
Eq(F_69(x, k_0), 2*F_27(x) + F_70(x, k_0) + F_72(x, k_0))
Eq(F_70(x, k_0), F_5(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_65(x, k_0) + F_69(x, k_0))
Eq(F_72(x, k_0), F_5(x)*F_68(x, k_0))
Eq(F_73(x, k_0), F_5(x)*F_58(x, k_0))
Eq(F_74(x), F_5(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_1(x) + F_121(x, k_0) + F_123(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_5(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_85(x, k_0))
Eq(F_79(x, k_0), F_1(x) + F_80(x, k_0) + F_81(x, k_0) + F_82(x, k_0))
Eq(F_80(x, k_0), F_42(x, k_0)*F_5(x))
Eq(F_81(x, k_0), F_5(x)*F_78(x, k_0))
Eq(F_82(x, k_0), F_17(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_1(x) + F_80(x, k_0) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_14(x, k_0)*F_5(x)*F_87(x, k_0))
Eq(F_88(x, k_0), F_5(x)*F_87(x, k_0))
Eq(F_89(x, k_0), F_109(x) + F_110(x) + F_120(x, k_0) + F_88(x, k_0))
Eq(F_89(x, k_0), F_107(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_91(x, k_0) - F_91(x, 1))/(k_0 - 1))
Eq(F_92(x, k_0), F_17(x, k_0)*F_91(x, k_0))
Eq(F_93(x, k_0), F_92(x, k_0) + F_97(x))
Eq(F_93(x, k_0), F_1(x) + F_94(x, k_0) + F_95(x, k_0))
Eq(F_94(x, k_0), F_10(x, k_0)*F_5(x))
Eq(F_95(x, k_0), F_17(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_14(x, k_0) + F_25(x, k_0))
Eq(F_97(x), F_1(x) + F_98(x))
Eq(F_98(x), F_5(x)*F_99(x))
Eq(F_99(x), F_1(x) + F_100(x) + F_101(x))
Eq(F_100(x), F_5(x)*F_99(x))
Eq(F_101(x), F_102(x)*F_5(x))
Eq(F_102(x), F_103(x, 1))
Eq(F_103(x, k_0), (-k_0*F_104(x, k_0) + F_104(x, 1))/(1 - k_0))
Eq(F_104(x, k_0), F_1(x) + F_105(x, k_0) + F_106(x, k_0))
Eq(F_105(x, k_0), F_104(x, k_0)*F_17(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0)*F_5(x))
Eq(F_107(x, k_0), F_108(x, k_0)*F_5(x))
Eq(F_108(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_109(x), F_21(x)*F_97(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_21(x)*F_5(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_91(x, 1))
Eq(F_114(x), F_115(x)*F_5(x))
Eq(F_115(x), F_116(x, 1))
Eq(F_116(x, k_0), F_117(x, k_0) + F_118(x, k_0))
Eq(F_117(x, k_0), (-k_0*F_91(x, k_0) + F_91(x, 1))/(1 - k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_5(x))
Eq(F_119(x, k_0), (-k_0*F_116(x, k_0) + F_116(x, 1))/(1 - k_0))
Eq(F_120(x, k_0), F_17(x, k_0)*F_89(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0)*F_5(x))
Eq(F_122(x, k_0), (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_123(x, k_0), F_17(x, k_0)*F_76(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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"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, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "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], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": 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{"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"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], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 3]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, 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"pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 3], [1, 4], [2, 0], [2, 2], [3, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"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": 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"RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "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, 0], [1, 1]]}, {"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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"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"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "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, 0], [1, 1]]}, {"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": [{"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, 0], [0, 1]]}, {"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"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24031/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[1,x]+F[140,x]+F[5,x]
F[5,x] = F[14,x]*F[6,x]
F[6,x] = F[62,x]+F[7,x]
F[7,x] = F[1,x]+F[5,x]+F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[29,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]+F[18,x]
F[16,x] = F[17,x]
F[17,x] = F[10,x]*F[14,x]
F[18,x] = F[19,x]+F[20,x]+F[24,x]
F[19,x] = 0
F[20,x] = F[14,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[12,x]
F[23,x] = F[18,x]
F[24,x] = F[14,x]*F[25,x]
F[25,x] = F[12,x]+F[26,x]
F[26,x] = F[19,x]+F[24,x]+F[27,x]
F[27,x] = F[14,x]*F[28,x]
F[28,x] = F[12,x]+F[26,x]
F[29,x] = F[25,x]+F[30,x]
F[30,x] = F[31,x]+F[53,x]
F[31,x] = F[19,x]+F[27,x]+F[32,x]
F[32,x] = F[14,x]*F[33,x]
F[33,x] = F[25,x]+F[34,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[19,x]+F[36,x]+F[44,x]+F[48,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[40,x]
F[40,x] = F[12,x]+F[38,x]
F[41,x] = 2*F[19,x]+F[36,x]+F[42,x]
F[42,x] = F[14,x]*F[43,x]
F[43,x] = F[26,x]+F[41,x]
F[44,x] = F[14,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[26,x]
F[47,x] = F[35,x]
F[48,x] = F[14,x]*F[49,x]
F[49,x] = F[26,x]+F[50,x]
F[50,x] = F[19,x]+F[36,x]+F[48,x]+F[51,x]
F[51,x] = F[14,x]*F[52,x]
F[52,x] = F[26,x]+F[50,x]
F[53,x] = F[19,x]+F[48,x]+F[54,x]+F[59,x]
F[54,x] = F[14,x]*F[55,x]
F[55,x] = F[26,x]+F[56,x]
F[56,x] = F[19,x]+F[48,x]+F[54,x]+F[57,x]
F[57,x] = F[14,x]*F[58,x]
F[58,x] = F[26,x]+F[56,x]
F[59,x] = F[14,x]*F[60,x]
F[60,x] = F[46,x]+F[61,x]
F[61,x] = F[53,x]
F[62,x] = F[125,x]+F[138,x]+F[19,x]+F[63,x]
F[63,x] = F[14,x]*F[64,x]
F[64,x] = F[65,x,1]
F[66,x,k[0]] = F[121,x,k[0]]+F[65,x,k[0]]
F[66,x,k[0]] = F[6,x]+F[67,x,k[0]]
F[67,x,k[0]] = F[119,x,k[0]]+F[19,x]+F[68,x,k[0]]+F[93,x,k[0]]+F[95,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]*F[70,x,k[0]]
F[69,x,k[0]] = k[0]*x
F[70,x,k[0]] = F[1,x]+F[68,x,k[0]]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[14,x]*F[72,x,k[0]]
F[72,x,k[0]] = (F[70,x,k[0]]*k[0]-F[70,x,1])/(-1+k[0])
F[73,x,k[0]] = F[14,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x]+F[76,x,k[0]]
F[75,x] = F[11,x]+F[25,x]
F[76,x,k[0]] = F[77,x,k[0]]+F[85,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[69,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[1,x]+F[78,x,k[0]]
F[81,x,k[0]] = F[19,x]+F[82,x,k[0]]+F[84,x,k[0]]
F[82,x,k[0]] = F[69,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[12,x]+F[81,x,k[0]]
F[84,x,k[0]] = F[14,x]*F[77,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[89,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[14,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[78,x,k[0]]+F[86,x,k[0]]
F[89,x,k[0]] = 2*F[19,x]+F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[14,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[81,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = F[14,x]*F[85,x,k[0]]
F[93,x,k[0]] = F[14,x]*F[94,x,k[0]]
F[94,x,k[0]] = -k[0]*(F[67,x,1]-F[67,x,k[0]])/(-1+k[0])
F[95,x,k[0]] = F[14,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[108,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[102,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[78,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[69,x,k[0]]
F[101,x,k[0]] = F[12,x]+F[99,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[81,x,k[0]]
F[103,x,k[0]] = 2*F[19,x]+F[104,x,k[0]]+F[106,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[69,x,k[0]]
F[105,x,k[0]] = F[103,x,k[0]]+F[26,x]
F[106,x,k[0]] = F[107,x,k[0]]*F[14,x]
F[107,x,k[0]] = F[103,x,k[0]]+F[99,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[113,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[86,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[14,x]
F[112,x,k[0]] = F[110,x,k[0]]+F[99,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[89,x,k[0]]
F[114,x,k[0]] = 3*F[19,x]+F[115,x,k[0]]+F[117,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[14,x]
F[116,x,k[0]] = F[103,x,k[0]]+F[114,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[14,x]
F[118,x,k[0]] = F[110,x,k[0]]+F[114,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[14,x]*F[67,x,k[0]]
F[121,x,k[0]] = F[1,x]+F[122,x,k[0]]+F[124,x,k[0]]+F[8,x]
F[122,x,k[0]] = F[123,x,k[0]]*F[69,x,k[0]]
F[123,x,k[0]] = F[75,x]+F[97,x,k[0]]
F[124,x,k[0]] = F[14,x]*F[66,x,k[0]]
F[125,x] = F[126,x]*F[14,x]
F[126,x] = F[127,x]+F[75,x]
F[127,x] = F[128,x]+F[132,x]
F[128,x] = F[12,x]+F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]*F[14,x]
F[131,x] = F[12,x]+F[129,x]
F[132,x] = F[133,x]+F[26,x]
F[133,x] = 2*F[19,x]+F[134,x]+F[136,x]
F[134,x] = F[135,x]*F[14,x]
F[135,x] = F[133,x]+F[26,x]
F[136,x] = F[137,x]*F[14,x]
F[137,x] = F[129,x]+F[133,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[62,x]
F[140,x] = F[14,x]*F[141,x]
F[141,x] = F[142,x,1]
F[142,x,k[0]] = F[1,x]+F[143,x,k[0]]+F[144,x,k[0]]+F[146,x,k[0]]
F[143,x,k[0]] = F[142,x,k[0]]*F[69,x,k[0]]
F[144,x,k[0]] = F[14,x]*F[145,x,k[0]]
F[145,x,k[0]] = (F[142,x,k[0]]*k[0]-F[142,x,1])/(-1+k[0])
F[146,x,k[0]] = F[14,x]*F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]+F[246,x,k[0]]
F[148,x,k[0]] = F[1,x]+F[149,x,k[0]]+F[212,x,k[0]]+F[213,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[69,x,k[0]]
F[150,x,k[0]] = F[151,x]+F[159,x,k[0]]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[1,x]+F[16,x]
F[153,x] = F[12,x]+F[154,x]
F[154,x] = F[155,x]+F[19,x]+F[27,x]
F[155,x] = F[14,x]*F[156,x]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[12,x]
F[158,x] = F[154,x]
F[159,x,k[0]] = F[160,x,k[0]]+F[195,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[78,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]+F[164,x,k[0]]+F[19,x]
F[162,x,k[0]] = F[163,x,k[0]]*F[69,x,k[0]]
F[163,x,k[0]] = F[16,x]+F[161,x,k[0]]
F[164,x,k[0]] = F[14,x]*F[165,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[77,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]+F[186,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[19,x]+F[82,x,k[0]]
F[168,x,k[0]] = F[14,x]*F[169,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]+F[77,x,k[0]]
F[170,x,k[0]] = F[167,x,k[0]]+F[171,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]+F[177,x,k[0]]+F[181,x,k[0]]+F[19,x]
F[172,x,k[0]] = F[173,x,k[0]]*F[69,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[38,x]
F[174,x,k[0]] = 2*F[19,x]+F[172,x,k[0]]+F[175,x,k[0]]
F[175,x,k[0]] = F[14,x]*F[176,x,k[0]]
F[176,x,k[0]] = F[174,x,k[0]]+F[81,x,k[0]]
F[177,x,k[0]] = F[14,x]*F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[180,x,k[0]]
F[179,x,k[0]] = F[81,x,k[0]]
F[180,x,k[0]] = F[171,x,k[0]]
F[181,x,k[0]] = F[14,x]*F[182,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]+F[81,x,k[0]]
F[183,x,k[0]] = F[172,x,k[0]]+F[181,x,k[0]]+F[184,x,k[0]]+F[19,x]
F[184,x,k[0]] = F[14,x]*F[185,x,k[0]]
F[185,x,k[0]] = F[183,x,k[0]]+F[81,x,k[0]]
F[186,x,k[0]] = F[181,x,k[0]]+F[187,x,k[0]]+F[19,x]+F[192,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[69,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[26,x]
F[189,x,k[0]] = F[181,x,k[0]]+F[187,x,k[0]]+F[19,x]+F[190,x,k[0]]
F[190,x,k[0]] = F[14,x]*F[191,x,k[0]]
F[191,x,k[0]] = F[189,x,k[0]]+F[81,x,k[0]]
F[192,x,k[0]] = F[14,x]*F[193,x,k[0]]
F[193,x,k[0]] = F[179,x,k[0]]+F[194,x,k[0]]
F[194,x,k[0]] = F[186,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]+F[81,x,k[0]]
F[196,x,k[0]] = F[19,x]+F[197,x,k[0]]+F[199,x,k[0]]+F[204,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]*F[69,x,k[0]]
F[198,x,k[0]] = F[154,x]+F[196,x,k[0]]
F[199,x,k[0]] = F[14,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[81,x,k[0]]
F[201,x,k[0]] = F[19,x]+F[199,x,k[0]]+F[202,x,k[0]]+F[92,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]*F[69,x,k[0]]
F[203,x,k[0]] = F[201,x,k[0]]+F[26,x]
F[204,x,k[0]] = F[14,x]*F[205,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]+F[207,x,k[0]]
F[206,x,k[0]] = F[86,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]
F[208,x,k[0]] = 2*F[19,x]+F[209,x,k[0]]+F[90,x,k[0]]
F[209,x,k[0]] = F[14,x]*F[210,x,k[0]]
F[210,x,k[0]] = F[206,x,k[0]]+F[211,x,k[0]]
F[211,x,k[0]] = F[208,x,k[0]]
F[212,x,k[0]] = F[14,x]*F[147,x,k[0]]
F[213,x,k[0]] = F[14,x]*F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]+F[9,x]
F[215,x,k[0]] = F[165,x,k[0]]+F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[85,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[237,x,k[0]]
F[218,x,k[0]] = 2*F[19,x]+F[219,x,k[0]]+F[90,x,k[0]]
F[219,x,k[0]] = F[14,x]*F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]+F[85,x,k[0]]
F[221,x,k[0]] = F[218,x,k[0]]+F[222,x,k[0]]
F[222,x,k[0]] = 2*F[19,x]+F[223,x,k[0]]+F[228,x,k[0]]+F[232,x,k[0]]
F[223,x,k[0]] = F[14,x]*F[224,x,k[0]]
F[224,x,k[0]] = F[174,x,k[0]]+F[225,x,k[0]]
F[225,x,k[0]] = 3*F[19,x]+F[223,x,k[0]]+F[226,x,k[0]]
F[226,x,k[0]] = F[14,x]*F[227,x,k[0]]
F[227,x,k[0]] = F[225,x,k[0]]+F[89,x,k[0]]
F[228,x,k[0]] = F[14,x]*F[229,x,k[0]]
F[229,x,k[0]] = F[230,x,k[0]]+F[231,x,k[0]]
F[230,x,k[0]] = F[89,x,k[0]]
F[231,x,k[0]] = F[222,x,k[0]]
F[232,x,k[0]] = F[14,x]*F[233,x,k[0]]
F[233,x,k[0]] = F[234,x,k[0]]+F[89,x,k[0]]
F[234,x,k[0]] = 2*F[19,x]+F[223,x,k[0]]+F[232,x,k[0]]+F[235,x,k[0]]
F[235,x,k[0]] = F[14,x]*F[236,x,k[0]]
F[236,x,k[0]] = F[234,x,k[0]]+F[89,x,k[0]]
F[237,x,k[0]] = 2*F[19,x]+F[232,x,k[0]]+F[238,x,k[0]]+F[243,x,k[0]]
F[238,x,k[0]] = F[14,x]*F[239,x,k[0]]
F[239,x,k[0]] = F[189,x,k[0]]+F[240,x,k[0]]
F[240,x,k[0]] = 2*F[19,x]+F[232,x,k[0]]+F[238,x,k[0]]+F[241,x,k[0]]
F[241,x,k[0]] = F[14,x]*F[242,x,k[0]]
F[242,x,k[0]] = F[240,x,k[0]]+F[89,x,k[0]]
F[243,x,k[0]] = F[14,x]*F[244,x,k[0]]
F[244,x,k[0]] = F[230,x,k[0]]+F[245,x,k[0]]
F[245,x,k[0]] = F[237,x,k[0]]
F[246,x,k[0]] = F[19,x]+F[247,x,k[0]]+F[248,x,k[0]]+F[250,x,k[0]]+F[252,x,k[0]]
F[247,x,k[0]] = F[246,x,k[0]]*F[69,x,k[0]]
F[248,x,k[0]] = F[14,x]*F[249,x,k[0]]
F[249,x,k[0]] = (F[65,x,k[0]]*k[0]-F[65,x,1])/(-1+k[0])
F[250,x,k[0]] = F[14,x]*F[251,x,k[0]]
F[251,x,k[0]] = F[126,x]+F[96,x,k[0]]
F[252,x,k[0]] = F[253,x,k[0]]
F[253,x,k[0]] = F[14,x]*F[246,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{62}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{53}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)+F_{36}\! \left(x \right)+F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{26}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{26}\! \left(x \right)
F_{47}\! \left(x \right) = F_{35}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{26}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right)+F_{36}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{26}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)+F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{26}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)+F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{26}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{53}\! \left(x \right)
F_{62}\! \left(x \right) = F_{125}\! \left(x \right)+F_{138}\! \left(x \right)+F_{19}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x , 1\right)
F_{66}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{68}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = y x
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{68}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}
F_{73}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x \right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{y \left(F_{67}\! \left(x , 1\right)-F_{67}\! \left(x , y\right)\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = 3 F_{19}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{1}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{75}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{132}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{26}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{134}\! \left(x \right)+F_{136}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{14}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right)+F_{26}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{14}\! \left(x \right)
F_{137}\! \left(x \right) = F_{129}\! \left(x \right)+F_{133}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{140}\! \left(x \right) = F_{14}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x , 1\right)
F_{142}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = -\frac{-y F_{142}\! \left(x , y\right)+F_{142}\! \left(x , 1\right)}{-1+y}
F_{146}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{246}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{212}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x \right)+F_{159}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{153}\! \left(x \right) = F_{12}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{19}\! \left(x \right)+F_{27}\! \left(x \right)
F_{155}\! \left(x \right) = F_{14}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{12}\! \left(x \right)
F_{158}\! \left(x \right) = F_{154}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{164}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{161}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{177}\! \left(x , y\right)+F_{181}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{174}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{14}\! \left(x \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_{179}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{181}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{192}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{186}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{197}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{154}\! \left(x \right)+F_{196}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{202}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{209}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{208}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{219}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{223}\! \left(x , y\right)+F_{228}\! \left(x , y\right)+F_{232}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = 3 F_{19}\! \left(x \right)+F_{223}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{223}\! \left(x , y\right)+F_{232}\! \left(x , y\right)+F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{234}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{232}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{232}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{242}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{237}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{247}\! \left(x , y\right)+F_{248}\! \left(x , y\right)+F_{250}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{246}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = -\frac{-y F_{65}\! \left(x , y\right)+F_{65}\! \left(x , 1\right)}{-1+y}
F_{250}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{126}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{246}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_140(x) + F_5(x))
Eq(F_5(x), F_14(x)*F_6(x))
Eq(F_6(x), F_62(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_5(x) + F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_29(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x) + F_18(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_10(x)*F_14(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_24(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_14(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_12(x))
Eq(F_23(x), F_18(x))
Eq(F_24(x), F_14(x)*F_25(x))
Eq(F_25(x), F_12(x) + F_26(x))
Eq(F_26(x), F_19(x) + F_24(x) + F_27(x))
Eq(F_27(x), F_14(x)*F_28(x))
Eq(F_28(x), F_12(x) + F_26(x))
Eq(F_29(x), F_25(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_53(x))
Eq(F_31(x), F_19(x) + F_27(x) + F_32(x))
Eq(F_32(x), F_14(x)*F_33(x))
Eq(F_33(x), F_25(x) + F_34(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_19(x) + F_36(x) + F_44(x) + F_48(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_14(x)*F_40(x))
Eq(F_40(x), F_12(x) + F_38(x))
Eq(F_41(x), 2*F_19(x) + F_36(x) + F_42(x))
Eq(F_42(x), F_14(x)*F_43(x))
Eq(F_43(x), F_26(x) + F_41(x))
Eq(F_44(x), F_14(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_26(x))
Eq(F_47(x), F_35(x))
Eq(F_48(x), F_14(x)*F_49(x))
Eq(F_49(x), F_26(x) + F_50(x))
Eq(F_50(x), F_19(x) + F_36(x) + F_48(x) + F_51(x))
Eq(F_51(x), F_14(x)*F_52(x))
Eq(F_52(x), F_26(x) + F_50(x))
Eq(F_53(x), F_19(x) + F_48(x) + F_54(x) + F_59(x))
Eq(F_54(x), F_14(x)*F_55(x))
Eq(F_55(x), F_26(x) + F_56(x))
Eq(F_56(x), F_19(x) + F_48(x) + F_54(x) + F_57(x))
Eq(F_57(x), F_14(x)*F_58(x))
Eq(F_58(x), F_26(x) + F_56(x))
Eq(F_59(x), F_14(x)*F_60(x))
Eq(F_60(x), F_46(x) + F_61(x))
Eq(F_61(x), F_53(x))
Eq(F_62(x), F_125(x) + F_138(x) + F_19(x) + F_63(x))
Eq(F_63(x), F_14(x)*F_64(x))
Eq(F_64(x), F_65(x, 1))
Eq(F_66(x, k_0), F_121(x, k_0) + F_65(x, k_0))
Eq(F_66(x, k_0), F_6(x) + F_67(x, k_0))
Eq(F_67(x, k_0), F_119(x, k_0) + F_19(x) + F_68(x, k_0) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0)*F_70(x, k_0))
Eq(F_69(x, k_0), k_0*x)
Eq(F_70(x, k_0), F_1(x) + F_68(x, k_0) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_14(x)*F_72(x, k_0))
Eq(F_72(x, k_0), (-k_0*F_70(x, k_0) + F_70(x, 1))/(1 - k_0))
Eq(F_73(x, k_0), F_14(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x) + F_76(x, k_0))
Eq(F_75(x), F_11(x) + F_25(x))
Eq(F_76(x, k_0), F_77(x, k_0) + F_85(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_69(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_1(x) + F_78(x, k_0))
Eq(F_81(x, k_0), F_19(x) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_82(x, k_0), F_69(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_12(x) + F_81(x, k_0))
Eq(F_84(x, k_0), F_14(x)*F_77(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_89(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_14(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_78(x, k_0) + F_86(x, k_0))
Eq(F_89(x, k_0), 2*F_19(x) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_14(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_81(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), F_14(x)*F_85(x, k_0))
Eq(F_93(x, k_0), F_14(x)*F_94(x, k_0))
Eq(F_94(x, k_0), -F_67(x, 1) + (-k_0*F_67(x, k_0) + F_67(x, 1))/(1 - k_0))
Eq(F_95(x, k_0), F_14(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_108(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_102(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_78(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_69(x, k_0))
Eq(F_101(x, k_0), F_12(x) + F_99(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_81(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_106(x, k_0) + 2*F_19(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_69(x, k_0))
Eq(F_105(x, k_0), F_103(x, k_0) + F_26(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_14(x))
Eq(F_107(x, k_0), F_103(x, k_0) + F_99(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_113(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_86(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_14(x))
Eq(F_112(x, k_0), F_110(x, k_0) + F_99(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_89(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_117(x, k_0) + 3*F_19(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_14(x))
Eq(F_116(x, k_0), F_103(x, k_0) + F_114(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_14(x))
Eq(F_118(x, k_0), F_110(x, k_0) + F_114(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_14(x)*F_67(x, k_0))
Eq(F_121(x, k_0), F_1(x) + F_122(x, k_0) + F_124(x, k_0) + F_8(x))
Eq(F_122(x, k_0), F_123(x, k_0)*F_69(x, k_0))
Eq(F_123(x, k_0), F_75(x) + F_97(x, k_0))
Eq(F_124(x, k_0), F_14(x)*F_66(x, k_0))
Eq(F_125(x), F_126(x)*F_14(x))
Eq(F_126(x), F_127(x) + F_75(x))
Eq(F_127(x), F_128(x) + F_132(x))
Eq(F_128(x), F_12(x) + F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)*F_14(x))
Eq(F_131(x), F_12(x) + F_129(x))
Eq(F_132(x), F_133(x) + F_26(x))
Eq(F_133(x), F_134(x) + F_136(x) + 2*F_19(x))
Eq(F_134(x), F_135(x)*F_14(x))
Eq(F_135(x), F_133(x) + F_26(x))
Eq(F_136(x), F_137(x)*F_14(x))
Eq(F_137(x), F_129(x) + F_133(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_62(x))
Eq(F_140(x), F_14(x)*F_141(x))
Eq(F_141(x), F_142(x, 1))
Eq(F_142(x, k_0), F_1(x) + F_143(x, k_0) + F_144(x, k_0) + F_146(x, k_0))
Eq(F_143(x, k_0), F_142(x, k_0)*F_69(x, k_0))
Eq(F_144(x, k_0), F_14(x)*F_145(x, k_0))
Eq(F_145(x, k_0), (-k_0*F_142(x, k_0) + F_142(x, 1))/(1 - k_0))
Eq(F_146(x, k_0), F_14(x)*F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + F_246(x, k_0))
Eq(F_148(x, k_0), F_1(x) + F_149(x, k_0) + F_212(x, k_0) + F_213(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_69(x, k_0))
Eq(F_150(x, k_0), F_151(x) + F_159(x, k_0))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_1(x) + F_16(x))
Eq(F_153(x), F_12(x) + F_154(x))
Eq(F_154(x), F_155(x) + F_19(x) + F_27(x))
Eq(F_155(x), F_14(x)*F_156(x))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_12(x))
Eq(F_158(x), F_154(x))
Eq(F_159(x, k_0), F_160(x, k_0) + F_195(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_78(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0) + F_164(x, k_0) + F_19(x))
Eq(F_162(x, k_0), F_163(x, k_0)*F_69(x, k_0))
Eq(F_163(x, k_0), F_16(x) + F_161(x, k_0))
Eq(F_164(x, k_0), F_14(x)*F_165(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_77(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0) + F_186(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_19(x) + F_82(x, k_0))
Eq(F_168(x, k_0), F_14(x)*F_169(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_77(x, k_0))
Eq(F_170(x, k_0), F_167(x, k_0) + F_171(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0) + F_177(x, k_0) + F_181(x, k_0) + F_19(x))
Eq(F_172(x, k_0), F_173(x, k_0)*F_69(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_38(x))
Eq(F_174(x, k_0), F_172(x, k_0) + F_175(x, k_0) + 2*F_19(x))
Eq(F_175(x, k_0), F_14(x)*F_176(x, k_0))
Eq(F_176(x, k_0), F_174(x, k_0) + F_81(x, k_0))
Eq(F_177(x, k_0), F_14(x)*F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_180(x, k_0))
Eq(F_179(x, k_0), F_81(x, k_0))
Eq(F_180(x, k_0), F_171(x, k_0))
Eq(F_181(x, k_0), F_14(x)*F_182(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0) + F_81(x, k_0))
Eq(F_183(x, k_0), F_172(x, k_0) + F_181(x, k_0) + F_184(x, k_0) + F_19(x))
Eq(F_184(x, k_0), F_14(x)*F_185(x, k_0))
Eq(F_185(x, k_0), F_183(x, k_0) + F_81(x, k_0))
Eq(F_186(x, k_0), F_181(x, k_0) + F_187(x, k_0) + F_19(x) + F_192(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_69(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_26(x))
Eq(F_189(x, k_0), F_181(x, k_0) + F_187(x, k_0) + F_19(x) + F_190(x, k_0))
Eq(F_190(x, k_0), F_14(x)*F_191(x, k_0))
Eq(F_191(x, k_0), F_189(x, k_0) + F_81(x, k_0))
Eq(F_192(x, k_0), F_14(x)*F_193(x, k_0))
Eq(F_193(x, k_0), F_179(x, k_0) + F_194(x, k_0))
Eq(F_194(x, k_0), F_186(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0) + F_81(x, k_0))
Eq(F_196(x, k_0), F_19(x) + F_197(x, k_0) + F_199(x, k_0) + F_204(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0)*F_69(x, k_0))
Eq(F_198(x, k_0), F_154(x) + F_196(x, k_0))
Eq(F_199(x, k_0), F_14(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_81(x, k_0))
Eq(F_201(x, k_0), F_19(x) + F_199(x, k_0) + F_202(x, k_0) + F_92(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0)*F_69(x, k_0))
Eq(F_203(x, k_0), F_201(x, k_0) + F_26(x))
Eq(F_204(x, k_0), F_14(x)*F_205(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_207(x, k_0))
Eq(F_206(x, k_0), F_86(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0))
Eq(F_208(x, k_0), 2*F_19(x) + F_209(x, k_0) + F_90(x, k_0))
Eq(F_209(x, k_0), F_14(x)*F_210(x, k_0))
Eq(F_210(x, k_0), F_206(x, k_0) + F_211(x, k_0))
Eq(F_211(x, k_0), F_208(x, k_0))
Eq(F_212(x, k_0), F_14(x)*F_147(x, k_0))
Eq(F_213(x, k_0), F_14(x)*F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0) + F_9(x))
Eq(F_215(x, k_0), F_165(x, k_0) + F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_85(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_237(x, k_0))
Eq(F_218(x, k_0), 2*F_19(x) + F_219(x, k_0) + F_90(x, k_0))
Eq(F_219(x, k_0), F_14(x)*F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0) + F_85(x, k_0))
Eq(F_221(x, k_0), F_218(x, k_0) + F_222(x, k_0))
Eq(F_222(x, k_0), 2*F_19(x) + F_223(x, k_0) + F_228(x, k_0) + F_232(x, k_0))
Eq(F_223(x, k_0), F_14(x)*F_224(x, k_0))
Eq(F_224(x, k_0), F_174(x, k_0) + F_225(x, k_0))
Eq(F_225(x, k_0), 3*F_19(x) + F_223(x, k_0) + F_226(x, k_0))
Eq(F_226(x, k_0), F_14(x)*F_227(x, k_0))
Eq(F_227(x, k_0), F_225(x, k_0) + F_89(x, k_0))
Eq(F_228(x, k_0), F_14(x)*F_229(x, k_0))
Eq(F_229(x, k_0), F_230(x, k_0) + F_231(x, k_0))
Eq(F_230(x, k_0), F_89(x, k_0))
Eq(F_231(x, k_0), F_222(x, k_0))
Eq(F_232(x, k_0), F_14(x)*F_233(x, k_0))
Eq(F_233(x, k_0), F_234(x, k_0) + F_89(x, k_0))
Eq(F_234(x, k_0), 2*F_19(x) + F_223(x, k_0) + F_232(x, k_0) + F_235(x, k_0))
Eq(F_235(x, k_0), F_14(x)*F_236(x, k_0))
Eq(F_236(x, k_0), F_234(x, k_0) + F_89(x, k_0))
Eq(F_237(x, k_0), 2*F_19(x) + F_232(x, k_0) + F_238(x, k_0) + F_243(x, k_0))
Eq(F_238(x, k_0), F_14(x)*F_239(x, k_0))
Eq(F_239(x, k_0), F_189(x, k_0) + F_240(x, k_0))
Eq(F_240(x, k_0), 2*F_19(x) + F_232(x, k_0) + F_238(x, k_0) + F_241(x, k_0))
Eq(F_241(x, k_0), F_14(x)*F_242(x, k_0))
Eq(F_242(x, k_0), F_240(x, k_0) + F_89(x, k_0))
Eq(F_243(x, k_0), F_14(x)*F_244(x, k_0))
Eq(F_244(x, k_0), F_230(x, k_0) + F_245(x, k_0))
Eq(F_245(x, k_0), F_237(x, k_0))
Eq(F_246(x, k_0), F_19(x) + F_247(x, k_0) + F_248(x, k_0) + F_250(x, k_0) + F_252(x, k_0))
Eq(F_247(x, k_0), F_246(x, k_0)*F_69(x, k_0))
Eq(F_248(x, k_0), F_14(x)*F_249(x, k_0))
Eq(F_249(x, k_0), (-k_0*F_65(x, k_0) + F_65(x, 1))/(1 - k_0))
Eq(F_250(x, k_0), F_14(x)*F_251(x, k_0))
Eq(F_251(x, k_0), F_126(x) + F_96(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0))
Eq(F_253(x, k_0), F_14(x)*F_246(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": 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_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [3, 0], 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[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[4, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[3, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[4, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[3, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24032/
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[11,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[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]*F[8,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x] = F[15,x]
F[15,x] = F[11,x]*F[16,x]
F[16,x] = F[121,x]+F[17,x]+F[7,x]
F[17,x] = F[11,x]*F[18,x]
F[18,x] = F[19,x]+F[43,x]
F[19,x] = 1/F[11,x]*F[20,x]
F[20,x] = -F[22,x]-F[5,x]+F[21,x]
F[21,x] = 1/F[11,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]+F[25,x]+F[42,x]
F[24,x] = 0
F[25,x] = F[11,x]*F[26,x]
F[26,x] = -F[7,x]+F[27,x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = F[1,x]+F[29,x,k[0]]+F[31,x,k[0]]+F[32,x,k[0]]
F[29,x,k[0]] = F[11,x]*F[30,x,k[0]]
F[30,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[31,x,k[0]] = F[13,x,k[0]]*F[28,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[7,x]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[13,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[33,x,k[0]]+F[37,x,k[0]]+F[41,x,k[0]]
F[37,x,k[0]] = F[11,x]*F[38,x,k[0]]
F[38,x,k[0]] = 1/(-1+k[0])*(F[39,x,k[0]]*k[0]-F[39,x,1])
F[39,x,k[0]] = F[37,x,k[0]]+F[40,x,k[0]]+F[8,x,k[0]]
F[40,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[41,x,k[0]] = F[11,x]*F[36,x,k[0]]
F[42,x] = F[11,x]*F[7,x]
F[43,x] = 1/F[11,x]*F[44,x]
F[44,x] = -F[80,x]-F[90,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[49,x]+F[47,x]
F[47,x] = 1/F[11,x]*F[48,x]
F[48,x] = F[26,x]
F[49,x] = -F[50,x]+F[47,x]
F[50,x] = -F[76,x]+F[51,x]
F[51,x] = 1/F[11,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[73,x]+F[54,x]
F[54,x] = -F[72,x]+F[55,x]
F[55,x] = F[1,x]+F[56,x]+F[59,x]+F[70,x]
F[56,x] = F[11,x]*F[57,x]
F[57,x] = F[58,x,1]
F[58,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[11,x]*F[64,x]
F[64,x] = F[65,x]+F[68,x]+F[69,x]+F[7,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[67,x,1]
F[67,x,k[0]] = 1/(-1+k[0])*(F[39,x,k[0]]*k[0]-F[39,x,1])
F[68,x] = F[11,x]*F[64,x]
F[69,x] = F[11,x]*F[64,x]
F[70,x] = F[11,x]*F[71,x]
F[71,x] = F[62,x]+F[7,x]
F[72,x] = F[23,x]+F[5,x]
F[73,x] = -F[5,x]+F[74,x]
F[74,x] = -F[75,x]+F[55,x]
F[75,x] = F[26,x]
F[76,x] = F[77,x,1]
F[77,x,k[0]] = F[34,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[11,x]*F[79,x,k[0]]
F[79,x,k[0]] = -k[0]*(F[77,x,1]-F[77,x,k[0]])/(-1+k[0])
F[80,x] = F[81,x]
F[81,x] = F[11,x]*F[82,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[84,x,k[0]]+F[87,x,k[0]]
F[84,x,k[0]] = F[5,x]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[13,x,k[0]]*F[83,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[11,x]*F[89,x,k[0]]
F[89,x,k[0]] = (F[83,x,k[0]]*k[0]-F[83,x,1])/(-1+k[0])
F[90,x] = F[91,x]
F[91,x] = F[11,x]*F[92,x]
F[92,x] = F[120,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = -F[96,x]+F[95,x]
F[95,x] = F[111,x]+F[96,x]
F[96,x] = 1/F[11,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[14,x]+F[99,x]
F[99,x] = F[100,x]*F[11,x]
F[100,x] = F[101,x,1]
F[101,x,k[0]] = F[102,x,k[0]]+F[109,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[105,x,k[0]]+F[106,x,k[0]]+F[24,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[11,x]
F[104,x,k[0]] = F[102,x,k[0]]+F[84,x,k[0]]
F[105,x,k[0]] = F[102,x,k[0]]*F[13,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[11,x]
F[107,x,k[0]] = (F[108,x,k[0]]-F[108,x,1])/(-1+k[0])
F[108,x,k[0]] = -k[0]*(F[85,x,1]-F[85,x,k[0]])/(-1+k[0])
F[109,x,k[0]] = F[11,x]*F[110,x,k[0]]
F[110,x,k[0]] = (F[101,x,k[0]]*k[0]-F[101,x,1])/(-1+k[0])
F[111,x] = F[112,x]
F[112,x] = F[113,x,1]
F[113,x,k[0]] = F[114,x,k[0]]+F[116,x,k[0]]+F[24,x]
F[114,x,k[0]] = F[11,x]*F[115,x,k[0]]
F[115,x,k[0]] = 1/(-1+k[0])*(F[113,x,k[0]]*k[0]-F[113,x,1])
F[116,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[117,x,k[0]] = F[116,x,k[0]]+F[118,x,k[0]]+F[33,x,k[0]]
F[118,x,k[0]] = F[11,x]*F[119,x,k[0]]
F[119,x,k[0]] = 1/(-1+k[0])*(F[117,x,k[0]]*k[0]-F[117,x,1])
F[120,x] = F[45,x]
F[121,x] = F[122,x]
F[122,x] = F[11,x]*F[95,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_{11}\! \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_{11}\! \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_{12}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
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_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{121}\! \left(x \right)+F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{43}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)-F_{5}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{7}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{44}\! \left(x \right) = -F_{80}\! \left(x \right)-F_{90}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{26}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)+F_{7}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x , 1\right)
F_{67}\! \left(x , y\right) = -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{62}\! \left(x \right)+F_{7}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{55}\! \left(x \right)
F_{75}\! \left(x \right) = F_{26}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = -\frac{y \left(F_{77}\! \left(x , 1\right)-F_{77}\! \left(x , y\right)\right)}{-1+y}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = -\frac{-y F_{83}\! \left(x , y\right)+F_{83}\! \left(x , 1\right)}{-1+y}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{120}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{111}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{11}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x , 1\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{F_{108}\! \left(x , 1\right)-F_{108}\! \left(x , y\right)}{-1+y}
F_{108}\! \left(x , y\right) = -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}
F_{109}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = -\frac{-y F_{101}\! \left(x , y\right)+F_{101}\! \left(x , 1\right)}{-1+y}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x , 1\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = -\frac{-y F_{113}\! \left(x , y\right)+F_{113}\! \left(x , 1\right)}{-1+y}
F_{116}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = -\frac{-y F_{117}\! \left(x , y\right)+F_{117}\! \left(x , 1\right)}{-1+y}
F_{120}\! \left(x \right) = F_{45}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{11}\! \left(x \right) F_{95}\! \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_11(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_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0)*F_8(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)*F_16(x))
Eq(F_16(x), F_121(x) + F_17(x) + F_7(x))
Eq(F_17(x), F_11(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_43(x))
Eq(F_19(x), F_20(x)/F_11(x))
Eq(F_20(x), F_21(x) - F_22(x) - F_5(x))
Eq(F_21(x), F_22(x)/F_11(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_42(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_27(x) - F_7(x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), F_1(x) + F_29(x, k_0) + F_31(x, k_0) + F_32(x, k_0))
Eq(F_29(x, k_0), F_11(x)*F_30(x, k_0))
Eq(F_30(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_31(x, k_0), F_13(x, k_0)*F_28(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_7(x))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_13(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_33(x, k_0) + F_37(x, k_0) + F_41(x, k_0))
Eq(F_37(x, k_0), F_11(x)*F_38(x, k_0))
Eq(F_38(x, k_0), (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_37(x, k_0) + F_40(x, k_0) + F_8(x, k_0))
Eq(F_40(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_41(x, k_0), F_11(x)*F_36(x, k_0))
Eq(F_42(x), F_11(x)*F_7(x))
Eq(F_43(x), F_44(x)/F_11(x))
Eq(F_44(x), F_45(x) - F_80(x) - F_90(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_49(x))
Eq(F_47(x), F_48(x)/F_11(x))
Eq(F_48(x), F_26(x))
Eq(F_49(x), F_47(x) - F_50(x))
Eq(F_50(x), F_51(x) - F_76(x))
Eq(F_51(x), F_52(x)/F_11(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) - F_73(x))
Eq(F_54(x), F_55(x) - F_72(x))
Eq(F_55(x), F_1(x) + F_56(x) + F_59(x) + F_70(x))
Eq(F_56(x), F_11(x)*F_57(x))
Eq(F_57(x), F_58(x, 1))
Eq(F_58(x, k_0), (-k_0*F_28(x, k_0) + F_28(x, 1))/(1 - k_0))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_11(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_68(x) + F_69(x) + F_7(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_67(x, 1))
Eq(F_67(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_68(x), F_11(x)*F_64(x))
Eq(F_69(x), F_11(x)*F_64(x))
Eq(F_70(x), F_11(x)*F_71(x))
Eq(F_71(x), F_62(x) + F_7(x))
Eq(F_72(x), F_23(x) + F_5(x))
Eq(F_73(x), -F_5(x) + F_74(x))
Eq(F_74(x), F_55(x) - F_75(x))
Eq(F_75(x), F_26(x))
Eq(F_76(x), F_77(x, 1))
Eq(F_77(x, k_0), F_34(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_11(x)*F_79(x, k_0))
Eq(F_79(x, k_0), -F_77(x, 1) + (k_0*F_77(x, k_0) - F_77(x, 1))/(k_0 - 1))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_11(x)*F_82(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_84(x, k_0) + F_87(x, k_0))
Eq(F_84(x, k_0), F_5(x) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_13(x, k_0)*F_83(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_11(x)*F_89(x, k_0))
Eq(F_89(x, k_0), (-k_0*F_83(x, k_0) + F_83(x, 1))/(1 - k_0))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_11(x)*F_92(x))
Eq(F_92(x), F_120(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_95(x) - F_96(x))
Eq(F_95(x), F_111(x) + F_96(x))
Eq(F_96(x), F_97(x)/F_11(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_14(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_11(x))
Eq(F_100(x), F_101(x, 1))
Eq(F_101(x, k_0), F_102(x, k_0) + F_109(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_105(x, k_0) + F_106(x, k_0) + F_24(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_11(x))
Eq(F_104(x, k_0), F_102(x, k_0) + F_84(x, k_0))
Eq(F_105(x, k_0), F_102(x, k_0)*F_13(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_11(x))
Eq(F_107(x, k_0), -F_108(x, k_0) + (k_0*F_108(x, k_0) - F_108(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), -F_85(x, 1) + (-k_0*F_85(x, k_0) + F_85(x, 1))/(1 - k_0))
Eq(F_109(x, k_0), F_11(x)*F_110(x, k_0))
Eq(F_110(x, k_0), (-k_0*F_101(x, k_0) + F_101(x, 1))/(1 - k_0))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x, 1))
Eq(F_113(x, k_0), F_114(x, k_0) + F_116(x, k_0) + F_24(x))
Eq(F_114(x, k_0), F_11(x)*F_115(x, k_0))
Eq(F_115(x, k_0), (k_0*F_113(x, k_0) - F_113(x, 1))/(k_0 - 1))
Eq(F_116(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_117(x, k_0), F_116(x, k_0) + F_118(x, k_0) + F_33(x, k_0))
Eq(F_118(x, k_0), F_11(x)*F_119(x, k_0))
Eq(F_119(x, k_0), (k_0*F_117(x, k_0) - F_117(x, 1))/(k_0 - 1))
Eq(F_120(x), F_45(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_11(x)*F_95(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": 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_and_col_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 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, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[2, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 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"requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}], "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, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [1, 2], [2, 0], [3, 2]], [[4, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"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, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 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, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 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, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}], "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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, 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