1032_2301
Counting sequence:
1, 1, 2, 6, 22, 86, 340, 1340, 5254, 20518, 79932, 311028, 1209916, 4707964, 18330728, 71429176, 278586182, 1087537414, 4249391468, 16618640836, 65048019092, 254814326164, 998953992728, 3919041821896, 15385395144092, 60438585676636, 237563884988120, 934311596780040, 3676495517376184, 14474185732012088, 57011153530262480, 224656915621201776, 885652912419210822, 3492861836026915782, 13780479845245611084, 54388113081432337380, 214729932989712917668, 848052809484541707556, 3350334574655466140216, 13239822072430180232232, 52335808270599440879284, 206934571189982074002548, 818425886045480073365896, 3237673398479042349060632, 12811192923571669467870664, 50704290989642196738527048, 200721767558683308700217776, 794758327136359419952519952, 3147480247103506996680796444, 12467371711588974170827212188, 49393251191799570968275635832, 195721323613651013964116220008, 775681930753017847189773247816, 3074691375740439617836809788744, 12189592067181565816702419563248, 48333049189844665620128143125968, 191674487676565550273850199554424, 760234106384599142912931614646008, 3015721572748589992463595600401200, 11964485381977151314836595373090960, 47473780481353767802050510461474416, 188394767873878618122620614886243696, 747717213262848575274466080605467552, 2967958428851480386917331132533607136, 11782259592346823520686656131742782022, 46778706886870096588550881954439021894, 185744202455399051984941117140485426188, 737612707907218431744486755161165283876, 2929451267263567016070637982850089264452, 11635570442457473175795713890168152798404, 46220155055609632689452725735280292076408, 183618435592218742042711461696686422730216, 729526765909664873244748736973027445604932, 2898712749488697136757456372292134404034564, 11518796733262965478081905854113416167753128, 45776865583236473399203960989099899119494776, 181937009594320978873736215406788995917525032, 723154688965889751097101396443192826411889064, 2874588225169330729910266250097039087510781168, 11427560208426660761216674193001922526450403536, 45432226748523983679867488376304124899523401012, 180636860154887532842333974035976978875788303284, 718256924308840704281727251872444612431548985768, 2856167234882640332177000885696057331411192948216, 11358398642653256630400822038234943728547172796632, 45173065721576308057178968529470878470010061869784, 179667842488623618336093016334593779472760809719248, 714642491229551839105935178063714692911965481155696, 2842722058240330382759816822753037594153543736276232, 11308537787442034315752841106800792975560381040259464, 44988801505636138725613585002139650894736930818859728, 178989582482503853042943703302031527717732898643340656, 712157265987568127773494228152764511315128648488823312, 2833664093821898191595666210009358256743525029610686224, 11275728828895114632325888269455044211548265118705668448, 44870838790971390745360943764893423662680647193816689696, 178569214591821033028866839352551169428060985661714360092, 710675533602207732686301380136130771528525107574404678684, 2828512285392854707326223033551336688181493890435185846968, 11258130303537041119524653026082830440762998748471762960936, 44812126024908558505907621010943168569218082391894548561192
Generating function in Maple syntax:
1/(-4*x+1)^(1/2)*(3*x-1)/(2*x-1)
Generating function in latex syntax:
\frac{3 x -1}{\sqrt{-4 x +1}\, \left(2 x -1\right)}
Generating function in sympy syntax:
(3*x - 1)/(sqrt(1 - 4*x)*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(4*x-1)*(2*x-1)^2*F(x)^2+(3*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) \left(2 x -1\right)^{2} F \! \left(x \right)^{2}+\left(3 x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+3) = 12*(1+2*n)/(n+3)*a(n)-2*(16+13*n)/(n+3)*a(n+1)+(19+9*n)/(n+3)*a(n+2), n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n +3\right) = \frac{12 \left(1+2 n \right) a \! \left(n \right)}{n +3}-\frac{2 \left(16+13 n \right) a \! \left(n +1\right)}{n +3}+\frac{\left(19+9 n \right) a \! \left(n +2\right)}{n +3}, \quad n \geq 3
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/215/
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[0,x]+F[4,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[28,x]+F[3,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]] = F[10,x,k[0]]+F[16,x]+F[26,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = F[10,x,k[0]]*F[5,x]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[16,x] = F[17,x]*F[5,x]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = F[19,x,k[0]]+F[24,x,k[0]]+F[7,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[23,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[22,x,k[0]]
F[21,x,k[0]] = F[19,x,k[0]]*F[5,x]
F[22,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[23,x,k[0]] = F[18,x,k[0]]*F[5,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[5,x]
F[25,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[26,x,k[0]] = F[27,x,k[0]]*F[5,x]
F[27,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[28,x] = F[17,x]*F[5,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{0}\! \left(x \right)+F_{4}\! \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_{28}\! \left(x \right)+F_{3}\! \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) = F_{10}\! \left(x , y\right)+F_{16}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \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)*F_5(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_28(x) + F_3(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), F_10(x, k_0) + F_16(x) + F_26(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), F_10(x, k_0)*F_5(x))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_16(x), F_17(x)*F_5(x))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), F_19(x, k_0) + F_24(x, k_0) + F_7(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_23(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_22(x, k_0))
Eq(F_21(x, k_0), F_19(x, k_0)*F_5(x))
Eq(F_22(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_23(x, k_0), F_18(x, k_0)*F_5(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_5(x))
Eq(F_25(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), F_27(x, k_0)*F_5(x))
Eq(F_27(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_28(x), F_17(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.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_isolated", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 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0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 2, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: row_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/216/
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[9,x]
F[3,x] = F[1,x]+F[241,x]+F[4,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[194,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]*F[9,x]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[13,x,k[0]]+F[239,x,k[0]]+F[240,x,k[0]]
F[12,x,k[0]] = F[11,x,k[0]]*F[9,x]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[14,x,k[0]] = F[1,x]+F[15,x]+F[222,x,k[0]]+F[236,x]+F[237,x,k[0]]+F[238,x,k[0]]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[17,x,k[0]]*F[18,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[1,x]+F[104,x]+F[16,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[9,x]
F[20,x,k[0]] = F[1,x]+F[209,x,k[0]]+F[21,x,k[0]]+F[235,x,k[0]]+F[35,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x]+F[26,x,k[0]]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[9,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[30,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[17,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[34,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[17,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[24,x]+F[30,x,k[0]]
F[34,x,k[0]] = F[26,x,k[0]]*F[9,x]
F[35,x,k[0]] = F[36,x,k[0]]*F[9,x]
F[36,x,k[0]] = F[1,x]+F[170,x,k[0]]+F[173,x,k[0]]+F[176,x,k[0]]+F[37,x,k[0]]+F[49,x,k[0]]
F[37,x,k[0]] = F[17,x,k[0]]*F[38,x,k[0]]
F[38,x,k[0]] = F[39,x]+F[43,x,k[0]]
F[39,x] = F[23,x]+F[40,x]
F[40,x] = F[24,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[40,x]*F[9,x]
F[43,x,k[0]] = F[26,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[30,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = 2*F[31,x]+F[46,x,k[0]]+F[48,x,k[0]]
F[46,x,k[0]] = F[17,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[41,x]+F[45,x,k[0]]
F[48,x,k[0]] = F[44,x,k[0]]*F[9,x]
F[49,x,k[0]] = F[50,x,k[0]]*F[9,x]
F[50,x,k[0]] = F[1,x]+F[228,x,k[0]]+F[234,x,k[0]]+F[51,x,k[0]]+F[52,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]*F[50,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]*F[9,x]
F[53,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[19,x,k[0]]+F[219,x]+F[221,x]+F[54,x]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[1,x]+F[214,x]+F[217,x]+F[218,x]+F[56,x]+F[82,x]
F[56,x] = F[57,x,1]
F[57,x,k[0]] = F[17,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x]+F[67,x,k[0]]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[1,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[60,x]*F[9,x]
F[63,x] = F[61,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]*F[9,x]
F[66,x] = F[61,x]+F[64,x]
F[67,x,k[0]] = F[68,x,k[0]]+F[76,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[72,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[17,x,k[0]]*F[71,x,k[0]]
F[71,x,k[0]] = F[1,x]+F[69,x,k[0]]
F[72,x,k[0]] = F[31,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[17,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[61,x]+F[72,x,k[0]]
F[75,x,k[0]] = F[68,x,k[0]]*F[9,x]
F[76,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = 2*F[31,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[17,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[64,x]+F[77,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]*F[9,x]
F[81,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[82,x] = F[83,x]*F[9,x]
F[83,x] = F[84,x,1]
F[84,x,k[0]] = F[1,x]+F[212,x,k[0]]+F[213,x,k[0]]+F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[84,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]*F[9,x]
F[87,x,k[0]] = F[1,x]+F[206,x,k[0]]+F[207,x]+F[208,x]+F[210,x]+F[88,x,k[0]]
F[88,x,k[0]] = F[17,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[1,x]+F[205,x,k[0]]+F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[17,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[60,x]+F[68,x,k[0]]
F[92,x,k[0]] = F[9,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[1,x]+F[202,x,k[0]]+F[203,x]+F[94,x,k[0]]+F[95,x,k[0]]
F[94,x,k[0]] = F[17,x,k[0]]*F[93,x,k[0]]
F[95,x,k[0]] = F[9,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[1,x]+F[111,x,k[0]]+F[112,x]+F[113,x]+F[90,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[9,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[104,x]+F[57,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[84,x,k[0]]*F[9,x]
F[100,x,k[0]] = F[101,x,k[0]]*F[9,x]
F[101,x,k[0]] = (F[98,x,k[0]]*k[0]-F[98,x,1])/(-1+k[0])
F[102,x,k[0]] = F[103,x,k[0]]*F[9,x]
F[103,x,k[0]] = (F[87,x,k[0]]*k[0]-F[87,x,1])/(-1+k[0])
F[104,x] = F[105,x]*F[9,x]
F[105,x] = F[106,x]+F[60,x]
F[106,x] = F[107,x]+F[24,x]
F[107,x] = F[108,x]+F[110,x]+F[31,x]
F[108,x] = F[109,x]*F[9,x]
F[109,x] = F[107,x]+F[61,x]
F[110,x] = F[106,x]*F[9,x]
F[111,x,k[0]] = F[87,x,k[0]]*F[9,x]
F[112,x] = F[92,x,1]
F[113,x] = F[114,x,1]
F[114,x,k[0]] = F[115,x,k[0]]*F[17,x,k[0]]
F[115,x,k[0]] = F[1,x]+F[104,x]+F[114,x,k[0]]+F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[9,x]
F[117,x,k[0]] = F[1,x]+F[118,x,k[0]]+F[119,x,k[0]]+F[179,x,k[0]]+F[186,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]*F[9,x]
F[119,x,k[0]] = F[120,x,k[0]]*F[9,x]
F[120,x,k[0]] = F[1,x]+F[121,x]+F[123,x]+F[136,x,k[0]]+F[178,x,k[0]]+F[179,x,k[0]]
F[121,x] = F[122,x,1]
F[122,x,k[0]] = F[115,x,k[0]]*F[9,x]
F[123,x] = F[124,x]*F[9,x]
F[124,x] = F[125,x,1]
F[125,x,k[0]] = F[1,x]+F[126,x,k[0]]+F[134,x,k[0]]+F[135,x,k[0]]+F[90,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]*F[9,x]
F[127,x,k[0]] = F[1,x]+F[128,x,k[0]]+F[130,x,k[0]]+F[132,x,k[0]]+F[57,x,k[0]]+F[99,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[9,x]
F[129,x,k[0]] = 1/(-1+k[0])*(F[127,x,k[0]]*k[0]-F[127,x,1])
F[130,x,k[0]] = F[131,x,k[0]]*F[9,x]
F[131,x,k[0]] = (F[96,x,k[0]]*k[0]-F[96,x,1])/(-1+k[0])
F[132,x,k[0]] = F[133,x,k[0]]*F[9,x]
F[133,x,k[0]] = (F[125,x,k[0]]*k[0]-F[125,x,1])/(-1+k[0])
F[134,x,k[0]] = F[9,x]*F[96,x,k[0]]
F[135,x,k[0]] = F[125,x,k[0]]*F[9,x]
F[136,x,k[0]] = F[137,x,k[0]]*F[9,x]
F[137,x,k[0]] = F[1,x]+F[114,x,k[0]]+F[116,x,k[0]]+F[138,x]+F[145,x]+F[153,x]
F[138,x] = F[139,x,1]
F[139,x,k[0]] = F[140,x,k[0]]*F[17,x,k[0]]
F[140,x,k[0]] = F[1,x]+F[141,x,k[0]]+F[143,x,k[0]]+F[37,x,k[0]]+F[49,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]*F[9,x]
F[142,x,k[0]] = (F[140,x,k[0]]*k[0]-F[140,x,1])/(-1+k[0])
F[143,x,k[0]] = F[144,x,k[0]]*F[9,x]
F[144,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[145,x] = F[146,x,1]
F[146,x,k[0]] = F[147,x,k[0]]*F[9,x]
F[147,x,k[0]] = F[1,x]+F[104,x]+F[148,x]+F[152,x]+F[16,x,k[0]]+F[19,x,k[0]]
F[148,x] = F[149,x]*F[9,x]
F[149,x] = F[1,x]+F[104,x]+F[150,x]+F[151,x]+F[56,x]+F[82,x]
F[150,x] = F[100,x,1]
F[151,x] = F[102,x,1]
F[152,x] = F[111,x,1]
F[153,x] = F[154,x]*F[9,x]
F[154,x] = F[1,x]+F[155,x]+F[168,x]+F[169,x]+F[172,x]+F[175,x]
F[155,x] = F[156,x]*F[9,x]
F[156,x] = F[157,x]+F[39,x]
F[157,x] = F[158,x]+F[163,x]
F[158,x] = F[159,x]+F[61,x]
F[159,x] = F[160,x]+F[162,x]+F[31,x]
F[160,x] = F[161,x]*F[9,x]
F[161,x] = F[159,x]+F[24,x]
F[162,x] = F[158,x]*F[9,x]
F[163,x] = F[159,x]+F[164,x]
F[164,x] = 2*F[31,x]+F[165,x]+F[167,x]
F[165,x] = F[166,x]*F[9,x]
F[166,x] = F[164,x]+F[41,x]
F[167,x] = F[163,x]*F[9,x]
F[168,x] = F[49,x,1]
F[169,x] = F[170,x,1]
F[170,x,k[0]] = F[171,x,k[0]]*F[9,x]
F[171,x,k[0]] = (F[36,x,k[0]]*k[0]-F[36,x,1])/(-1+k[0])
F[172,x] = F[173,x,1]
F[173,x,k[0]] = F[174,x,k[0]]*F[9,x]
F[174,x,k[0]] = (F[147,x,k[0]]*k[0]-F[147,x,1])/(-1+k[0])
F[175,x] = F[176,x,1]
F[176,x,k[0]] = F[177,x,k[0]]*F[9,x]
F[177,x,k[0]] = (F[20,x,k[0]]*k[0]-F[20,x,1])/(-1+k[0])
F[178,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[179,x,k[0]] = F[17,x,k[0]]*F[180,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]+F[71,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[61,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[185,x,k[0]]+F[31,x]
F[183,x,k[0]] = F[184,x,k[0]]*F[9,x]
F[184,x,k[0]] = F[182,x,k[0]]+F[69,x,k[0]]
F[185,x,k[0]] = F[17,x,k[0]]*F[181,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]*F[9,x]
F[187,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[188,x,k[0]]+F[190,x,k[0]]+F[192,x,k[0]]+F[194,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]*F[9,x]
F[189,x,k[0]] = 1/(-1+k[0])*(F[117,x,k[0]]*k[0]-F[117,x,1])
F[190,x,k[0]] = F[191,x,k[0]]*F[9,x]
F[191,x,k[0]] = 1/(-1+k[0])*(F[120,x,k[0]]*k[0]-F[120,x,1])
F[192,x,k[0]] = F[193,x,k[0]]*F[9,x]
F[193,x,k[0]] = 1/(-1+k[0])*(F[187,x,k[0]]*k[0]-F[187,x,1])
F[194,x,k[0]] = F[17,x,k[0]]*F[195,x,k[0]]
F[195,x,k[0]] = F[180,x,k[0]]+F[196,x,k[0]]
F[196,x,k[0]] = F[181,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[64,x]
F[198,x,k[0]] = 2*F[31,x]+F[199,x,k[0]]+F[201,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]*F[9,x]
F[200,x,k[0]] = F[182,x,k[0]]+F[198,x,k[0]]
F[201,x,k[0]] = F[17,x,k[0]]*F[197,x,k[0]]
F[202,x,k[0]] = F[127,x,k[0]]*F[9,x]
F[203,x] = F[204,x]*F[9,x]
F[204,x] = F[158,x]+F[23,x]
F[205,x,k[0]] = F[89,x,k[0]]*F[9,x]
F[206,x,k[0]] = F[125,x,k[0]]*F[9,x]
F[207,x] = F[35,x,1]
F[208,x] = F[209,x,1]
F[209,x,k[0]] = F[147,x,k[0]]*F[9,x]
F[210,x] = F[211,x]*F[9,x]
F[211,x] = F[20,x,1]
F[212,x,k[0]] = F[9,x]*F[98,x,k[0]]
F[213,x,k[0]] = F[84,x,k[0]]*F[9,x]
F[214,x] = F[215,x]*F[9,x]
F[215,x] = F[216,x,1]
F[216,x,k[0]] = 1/(-1+k[0])*(F[127,x,k[0]]*k[0]-F[127,x,1])
F[217,x] = F[130,x,1]
F[218,x] = F[132,x,1]
F[219,x] = F[220,x]*F[9,x]
F[220,x] = F[1,x]+F[104,x]+F[112,x]+F[113,x]+F[148,x]+F[152,x]
F[221,x] = F[222,x,1]
F[222,x,k[0]] = F[17,x,k[0]]*F[223,x,k[0]]
F[223,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[194,x,k[0]]+F[224,x,k[0]]+F[226,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]*F[9,x]
F[225,x,k[0]] = 1/(-1+k[0])*(F[115,x,k[0]]*k[0]-F[115,x,1])
F[226,x,k[0]] = F[227,x,k[0]]*F[9,x]
F[227,x,k[0]] = 1/(-1+k[0])*(F[223,x,k[0]]*k[0]-F[223,x,1])
F[228,x,k[0]] = F[229,x,k[0]]*F[9,x]
F[229,x,k[0]] = F[1,x]+F[203,x]+F[230,x,k[0]]+F[232,x,k[0]]+F[37,x,k[0]]+F[49,x,k[0]]
F[230,x,k[0]] = F[231,x,k[0]]*F[9,x]
F[231,x,k[0]] = (F[229,x,k[0]]*k[0]-F[229,x,1])/(-1+k[0])
F[232,x,k[0]] = F[233,x,k[0]]*F[9,x]
F[233,x,k[0]] = (F[53,x,k[0]]*k[0]-F[53,x,1])/(-1+k[0])
F[234,x,k[0]] = F[50,x,k[0]]*F[9,x]
F[235,x,k[0]] = F[20,x,k[0]]*F[9,x]
F[236,x] = F[211,x]*F[9,x]
F[237,x,k[0]] = F[187,x,k[0]]*F[9,x]
F[238,x,k[0]] = F[120,x,k[0]]*F[9,x]
F[239,x,k[0]] = F[137,x,k[0]]*F[9,x]
F[240,x,k[0]] = F[11,x,k[0]]*F[17,x,k[0]]
F[241,x] = F[242,x]*F[9,x]
F[242,x] = F[243,x,1]
F[243,x,k[0]] = F[1,x]+F[244,x,k[0]]+F[37,x,k[0]]+F[49,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]*F[9,x]
F[245,x,k[0]] = F[1,x]+F[246,x,k[0]]+F[263,x,k[0]]+F[265,x,k[0]]+F[37,x,k[0]]
F[246,x,k[0]] = F[247,x,k[0]]*F[9,x]
F[247,x,k[0]] = F[156,x]+F[248,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]+F[43,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[258,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]+F[254,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]
F[252,x,k[0]] = F[17,x,k[0]]*F[253,x,k[0]]
F[253,x,k[0]] = F[251,x,k[0]]+F[61,x]
F[254,x,k[0]] = 2*F[31,x]+F[255,x,k[0]]+F[257,x,k[0]]
F[255,x,k[0]] = F[17,x,k[0]]*F[256,x,k[0]]
F[256,x,k[0]] = F[159,x]+F[254,x,k[0]]
F[257,x,k[0]] = F[250,x,k[0]]*F[9,x]
F[258,x,k[0]] = F[254,x,k[0]]+F[259,x,k[0]]
F[259,x,k[0]] = 3*F[31,x]+F[260,x,k[0]]+F[262,x,k[0]]
F[260,x,k[0]] = F[17,x,k[0]]*F[261,x,k[0]]
F[261,x,k[0]] = F[164,x]+F[259,x,k[0]]
F[262,x,k[0]] = F[258,x,k[0]]*F[9,x]
F[263,x,k[0]] = F[264,x,k[0]]*F[9,x]
F[264,x,k[0]] = (F[50,x,k[0]]*k[0]-F[50,x,1])/(-1+k[0])
F[265,x,k[0]] = F[266,x,k[0]]*F[9,x]
F[266,x,k[0]] = (F[245,x,k[0]]*k[0]-F[245,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{241}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{194}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{239}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{222}\! \left(x , y\right)+F_{236}\! \left(x \right)+F_{237}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{209}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{235}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{170}\! \left(x , y\right)+F_{173}\! \left(x , y\right)+F_{176}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{39}\! \left(x \right) = F_{23}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{24}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{40}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{50}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{228}\! \left(x , y\right)+F_{234}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{219}\! \left(x \right)+F_{221}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{214}\! \left(x \right)+F_{217}\! \left(x \right)+F_{218}\! \left(x \right)+F_{56}\! \left(x \right)+F_{82}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{57}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{1}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right) F_{9}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{64}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right) F_{9}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{84}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{212}\! \left(x , y\right)+F_{213}\! \left(x , y\right)+F_{85}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{206}\! \left(x , y\right)+F_{207}\! \left(x \right)+F_{208}\! \left(x \right)+F_{210}\! \left(x \right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{205}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{60}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{202}\! \left(x , y\right)+F_{203}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{111}\! \left(x , y\right)+F_{112}\! \left(x \right)+F_{113}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x \right)+F_{57}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{101}\! \left(x , y\right) = -\frac{-y F_{98}\! \left(x , y\right)+F_{98}\! \left(x , 1\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{103}\! \left(x , y\right) = -\frac{-y F_{87}\! \left(x , y\right)+F_{87}\! \left(x , 1\right)}{-1+y}
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{9}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{60}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{24}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{110}\! \left(x \right)+F_{31}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{9}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right)+F_{61}\! \left(x \right)
F_{110}\! \left(x \right) = F_{106}\! \left(x \right) F_{9}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{112}\! \left(x \right) = F_{92}\! \left(x , 1\right)
F_{113}\! \left(x \right) = F_{114}\! \left(x , 1\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{114}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{121}\! \left(x \right)+F_{123}\! \left(x \right)+F_{136}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{121}\! \left(x \right) = F_{122}\! \left(x , 1\right)
F_{122}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{9}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x , 1\right)
F_{125}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{128}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{132}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{129}\! \left(x , y\right) = -\frac{-y F_{127}\! \left(x , y\right)+F_{127}\! \left(x , 1\right)}{-1+y}
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{131}\! \left(x , y\right) = -\frac{-y F_{96}\! \left(x , y\right)+F_{96}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{133}\! \left(x , y\right) = -\frac{-y F_{125}\! \left(x , y\right)+F_{125}\! \left(x , 1\right)}{-1+y}
F_{134}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{138}\! \left(x \right)+F_{145}\! \left(x \right)+F_{153}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x , 1\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{141}\! \left(x , y\right)+F_{143}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{142}\! \left(x , y\right) = -\frac{-y F_{140}\! \left(x , y\right)+F_{140}\! \left(x , 1\right)}{-1+y}
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{144}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{145}\! \left(x \right) = F_{146}\! \left(x , 1\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{148}\! \left(x \right)+F_{152}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{9}\! \left(x \right)
F_{149}\! \left(x \right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{150}\! \left(x \right)+F_{151}\! \left(x \right)+F_{56}\! \left(x \right)+F_{82}\! \left(x \right)
F_{150}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{151}\! \left(x \right) = F_{102}\! \left(x , 1\right)
F_{152}\! \left(x \right) = F_{111}\! \left(x , 1\right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{9}\! \left(x \right)
F_{154}\! \left(x \right) = F_{1}\! \left(x \right)+F_{155}\! \left(x \right)+F_{168}\! \left(x \right)+F_{169}\! \left(x \right)+F_{172}\! \left(x \right)+F_{175}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{9}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{39}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{163}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{61}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{162}\! \left(x \right)+F_{31}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{9}\! \left(x \right)
F_{161}\! \left(x \right) = F_{159}\! \left(x \right)+F_{24}\! \left(x \right)
F_{162}\! \left(x \right) = F_{158}\! \left(x \right) F_{9}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{165}\! \left(x \right)+F_{167}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{9}\! \left(x \right)
F_{166}\! \left(x \right) = F_{164}\! \left(x \right)+F_{41}\! \left(x \right)
F_{167}\! \left(x \right) = F_{163}\! \left(x \right) F_{9}\! \left(x \right)
F_{168}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{170}\! \left(x , 1\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{171}\! \left(x , y\right) = -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}
F_{172}\! \left(x \right) = F_{173}\! \left(x , 1\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{174}\! \left(x , y\right) = -\frac{-y F_{147}\! \left(x , y\right)+F_{147}\! \left(x , 1\right)}{-1+y}
F_{175}\! \left(x \right) = F_{176}\! \left(x , 1\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{177}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{178}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{181}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{188}\! \left(x , y\right)+F_{190}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{189}\! \left(x , y\right) = -\frac{-y F_{117}\! \left(x , y\right)+F_{117}\! \left(x , 1\right)}{-1+y}
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{191}\! \left(x , y\right) = -\frac{-y F_{120}\! \left(x , y\right)+F_{120}\! \left(x , 1\right)}{-1+y}
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{193}\! \left(x , y\right) = -\frac{-y F_{187}\! \left(x , y\right)+F_{187}\! \left(x , 1\right)}{-1+y}
F_{194}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{64}\! \left(x \right)
F_{198}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{200}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{197}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{9}\! \left(x \right)
F_{204}\! \left(x \right) = F_{158}\! \left(x \right)+F_{23}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{89}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{207}\! \left(x \right) = F_{35}\! \left(x , 1\right)
F_{208}\! \left(x \right) = F_{209}\! \left(x , 1\right)
F_{209}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{9}\! \left(x \right)
F_{211}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{212}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{9}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x , 1\right)
F_{216}\! \left(x , y\right) = -\frac{-y F_{127}\! \left(x , y\right)+F_{127}\! \left(x , 1\right)}{-1+y}
F_{217}\! \left(x \right) = F_{130}\! \left(x , 1\right)
F_{218}\! \left(x \right) = F_{132}\! \left(x , 1\right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right) F_{9}\! \left(x \right)
F_{220}\! \left(x \right) = F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{112}\! \left(x \right)+F_{113}\! \left(x \right)+F_{148}\! \left(x \right)+F_{152}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x , 1\right)
F_{222}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{194}\! \left(x , y\right)+F_{224}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{225}\! \left(x , y\right) = -\frac{-y F_{115}\! \left(x , y\right)+F_{115}\! \left(x , 1\right)}{-1+y}
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{227}\! \left(x , y\right) = -\frac{-y F_{223}\! \left(x , y\right)+F_{223}\! \left(x , 1\right)}{-1+y}
F_{228}\! \left(x , y\right) = F_{229}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{203}\! \left(x \right)+F_{230}\! \left(x , y\right)+F_{232}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{231}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{231}\! \left(x , y\right) = -\frac{-y F_{229}\! \left(x , y\right)+F_{229}\! \left(x , 1\right)}{-1+y}
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{233}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{234}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{235}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{236}\! \left(x \right) = F_{211}\! \left(x \right) F_{9}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{239}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{240}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right) F_{9}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x , 1\right)
F_{243}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{244}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{245}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{246}\! \left(x , y\right)+F_{263}\! \left(x , y\right)+F_{265}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{247}\! \left(x , y\right) = F_{156}\! \left(x \right)+F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{254}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{255}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{159}\! \left(x \right)+F_{254}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{250}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{258}\! \left(x , y\right) = F_{254}\! \left(x , y\right)+F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = 3 F_{31}\! \left(x \right)+F_{260}\! \left(x , y\right)+F_{262}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{261}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{164}\! \left(x \right)+F_{259}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{263}\! \left(x , y\right) = F_{264}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{264}\! \left(x , y\right) = -\frac{-y F_{50}\! \left(x , y\right)+F_{50}\! \left(x , 1\right)}{-1+y}
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{266}\! \left(x , y\right) = -\frac{-y F_{245}\! \left(x , y\right)+F_{245}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_9(x))
Eq(F_3(x), F_1(x) + F_241(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_194(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_9(x))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_13(x, k_0) + F_239(x, k_0) + F_240(x, k_0))
Eq(F_12(x, k_0), F_11(x, k_0)*F_9(x))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x) + F_222(x, k_0) + F_236(x) + F_237(x, k_0) + F_238(x, k_0))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_17(x, k_0)*F_18(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_1(x) + F_104(x) + F_16(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_9(x))
Eq(F_20(x, k_0), F_1(x) + F_209(x, k_0) + F_21(x, k_0) + F_235(x, k_0) + F_35(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x) + F_26(x, k_0))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_9(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_30(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_17(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_34(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_17(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_24(x) + F_30(x, k_0))
Eq(F_34(x, k_0), F_26(x, k_0)*F_9(x))
Eq(F_35(x, k_0), F_36(x, k_0)*F_9(x))
Eq(F_36(x, k_0), F_1(x) + F_170(x, k_0) + F_173(x, k_0) + F_176(x, k_0) + F_37(x, k_0) + F_49(x, k_0))
Eq(F_37(x, k_0), F_17(x, k_0)*F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x) + F_43(x, k_0))
Eq(F_39(x), F_23(x) + F_40(x))
Eq(F_40(x), F_24(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_40(x)*F_9(x))
Eq(F_43(x, k_0), F_26(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_30(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), 2*F_31(x) + F_46(x, k_0) + F_48(x, k_0))
Eq(F_46(x, k_0), F_17(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_41(x) + F_45(x, k_0))
Eq(F_48(x, k_0), F_44(x, k_0)*F_9(x))
Eq(F_49(x, k_0), F_50(x, k_0)*F_9(x))
Eq(F_50(x, k_0), F_1(x) + F_228(x, k_0) + F_234(x, k_0) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0)*F_50(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0)*F_9(x))
Eq(F_53(x, k_0), F_1(x) + F_16(x, k_0) + F_19(x, k_0) + F_219(x) + F_221(x) + F_54(x))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_1(x) + F_214(x) + F_217(x) + F_218(x) + F_56(x) + F_82(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_57(x, k_0), F_17(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x) + F_67(x, k_0))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_1(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_60(x)*F_9(x))
Eq(F_63(x), F_61(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x)*F_9(x))
Eq(F_66(x), F_61(x) + F_64(x))
Eq(F_67(x, k_0), F_68(x, k_0) + F_76(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_72(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_17(x, k_0)*F_71(x, k_0))
Eq(F_71(x, k_0), F_1(x) + F_69(x, k_0))
Eq(F_72(x, k_0), F_31(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_17(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_61(x) + F_72(x, k_0))
Eq(F_75(x, k_0), F_68(x, k_0)*F_9(x))
Eq(F_76(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), 2*F_31(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_17(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_64(x) + F_77(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0)*F_9(x))
Eq(F_81(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_82(x), F_83(x)*F_9(x))
Eq(F_83(x), F_84(x, 1))
Eq(F_84(x, k_0), F_1(x) + F_212(x, k_0) + F_213(x, k_0) + F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_84(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0)*F_9(x))
Eq(F_87(x, k_0), F_1(x) + F_206(x, k_0) + F_207(x) + F_208(x) + F_210(x) + F_88(x, k_0))
Eq(F_88(x, k_0), F_17(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_1(x) + F_205(x, k_0) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_17(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_60(x) + F_68(x, k_0))
Eq(F_92(x, k_0), F_9(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_1(x) + F_202(x, k_0) + F_203(x) + F_94(x, k_0) + F_95(x, k_0))
Eq(F_94(x, k_0), F_17(x, k_0)*F_93(x, k_0))
Eq(F_95(x, k_0), F_9(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_1(x) + F_111(x, k_0) + F_112(x) + F_113(x) + F_90(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_9(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_104(x) + F_57(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_84(x, k_0)*F_9(x))
Eq(F_100(x, k_0), F_101(x, k_0)*F_9(x))
Eq(F_101(x, k_0), (-k_0*F_98(x, k_0) + F_98(x, 1))/(1 - k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_9(x))
Eq(F_103(x, k_0), (-k_0*F_87(x, k_0) + F_87(x, 1))/(1 - k_0))
Eq(F_104(x), F_105(x)*F_9(x))
Eq(F_105(x), F_106(x) + F_60(x))
Eq(F_106(x), F_107(x) + F_24(x))
Eq(F_107(x), F_108(x) + F_110(x) + F_31(x))
Eq(F_108(x), F_109(x)*F_9(x))
Eq(F_109(x), F_107(x) + F_61(x))
Eq(F_110(x), F_106(x)*F_9(x))
Eq(F_111(x, k_0), F_87(x, k_0)*F_9(x))
Eq(F_112(x), F_92(x, 1))
Eq(F_113(x), F_114(x, 1))
Eq(F_114(x, k_0), F_115(x, k_0)*F_17(x, k_0))
Eq(F_115(x, k_0), F_1(x) + F_104(x) + F_114(x, k_0) + F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0)*F_9(x))
Eq(F_117(x, k_0), F_1(x) + F_118(x, k_0) + F_119(x, k_0) + F_179(x, k_0) + F_186(x, k_0))
Eq(F_118(x, k_0), F_117(x, k_0)*F_9(x))
Eq(F_119(x, k_0), F_120(x, k_0)*F_9(x))
Eq(F_120(x, k_0), F_1(x) + F_121(x) + F_123(x) + F_136(x, k_0) + F_178(x, k_0) + F_179(x, k_0))
Eq(F_121(x), F_122(x, 1))
Eq(F_122(x, k_0), F_115(x, k_0)*F_9(x))
Eq(F_123(x), F_124(x)*F_9(x))
Eq(F_124(x), F_125(x, 1))
Eq(F_125(x, k_0), F_1(x) + F_126(x, k_0) + F_134(x, k_0) + F_135(x, k_0) + F_90(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0)*F_9(x))
Eq(F_127(x, k_0), F_1(x) + F_128(x, k_0) + F_130(x, k_0) + F_132(x, k_0) + F_57(x, k_0) + F_99(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_9(x))
Eq(F_129(x, k_0), (-k_0*F_127(x, k_0) + F_127(x, 1))/(1 - k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_9(x))
Eq(F_131(x, k_0), (-k_0*F_96(x, k_0) + F_96(x, 1))/(1 - k_0))
Eq(F_132(x, k_0), F_133(x, k_0)*F_9(x))
Eq(F_133(x, k_0), (-k_0*F_125(x, k_0) + F_125(x, 1))/(1 - k_0))
Eq(F_134(x, k_0), F_9(x)*F_96(x, k_0))
Eq(F_135(x, k_0), F_125(x, k_0)*F_9(x))
Eq(F_136(x, k_0), F_137(x, k_0)*F_9(x))
Eq(F_137(x, k_0), F_1(x) + F_114(x, k_0) + F_116(x, k_0) + F_138(x) + F_145(x) + F_153(x))
Eq(F_138(x), F_139(x, 1))
Eq(F_139(x, k_0), F_140(x, k_0)*F_17(x, k_0))
Eq(F_140(x, k_0), F_1(x) + F_141(x, k_0) + F_143(x, k_0) + F_37(x, k_0) + F_49(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0)*F_9(x))
Eq(F_142(x, k_0), (-k_0*F_140(x, k_0) + F_140(x, 1))/(1 - k_0))
Eq(F_143(x, k_0), F_144(x, k_0)*F_9(x))
Eq(F_144(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_145(x), F_146(x, 1))
Eq(F_146(x, k_0), F_147(x, k_0)*F_9(x))
Eq(F_147(x, k_0), F_1(x) + F_104(x) + F_148(x) + F_152(x) + F_16(x, k_0) + F_19(x, k_0))
Eq(F_148(x), F_149(x)*F_9(x))
Eq(F_149(x), F_1(x) + F_104(x) + F_150(x) + F_151(x) + F_56(x) + F_82(x))
Eq(F_150(x), F_100(x, 1))
Eq(F_151(x), F_102(x, 1))
Eq(F_152(x), F_111(x, 1))
Eq(F_153(x), F_154(x)*F_9(x))
Eq(F_154(x), F_1(x) + F_155(x) + F_168(x) + F_169(x) + F_172(x) + F_175(x))
Eq(F_155(x), F_156(x)*F_9(x))
Eq(F_156(x), F_157(x) + F_39(x))
Eq(F_157(x), F_158(x) + F_163(x))
Eq(F_158(x), F_159(x) + F_61(x))
Eq(F_159(x), F_160(x) + F_162(x) + F_31(x))
Eq(F_160(x), F_161(x)*F_9(x))
Eq(F_161(x), F_159(x) + F_24(x))
Eq(F_162(x), F_158(x)*F_9(x))
Eq(F_163(x), F_159(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_167(x) + 2*F_31(x))
Eq(F_165(x), F_166(x)*F_9(x))
Eq(F_166(x), F_164(x) + F_41(x))
Eq(F_167(x), F_163(x)*F_9(x))
Eq(F_168(x), F_49(x, 1))
Eq(F_169(x), F_170(x, 1))
Eq(F_170(x, k_0), F_171(x, k_0)*F_9(x))
Eq(F_171(x, k_0), (-k_0*F_36(x, k_0) + F_36(x, 1))/(1 - k_0))
Eq(F_172(x), F_173(x, 1))
Eq(F_173(x, k_0), F_174(x, k_0)*F_9(x))
Eq(F_174(x, k_0), (-k_0*F_147(x, k_0) + F_147(x, 1))/(1 - k_0))
Eq(F_175(x), F_176(x, 1))
Eq(F_176(x, k_0), F_177(x, k_0)*F_9(x))
Eq(F_177(x, k_0), (-k_0*F_20(x, k_0) + F_20(x, 1))/(1 - k_0))
Eq(F_178(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_179(x, k_0), F_17(x, k_0)*F_180(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0) + F_71(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_61(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_185(x, k_0) + F_31(x))
Eq(F_183(x, k_0), F_184(x, k_0)*F_9(x))
Eq(F_184(x, k_0), F_182(x, k_0) + F_69(x, k_0))
Eq(F_185(x, k_0), F_17(x, k_0)*F_181(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0)*F_9(x))
Eq(F_187(x, k_0), F_1(x) + F_10(x, k_0) + F_188(x, k_0) + F_190(x, k_0) + F_192(x, k_0) + F_194(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0)*F_9(x))
Eq(F_189(x, k_0), (k_0*F_117(x, k_0) - F_117(x, 1))/(k_0 - 1))
Eq(F_190(x, k_0), F_191(x, k_0)*F_9(x))
Eq(F_191(x, k_0), (k_0*F_120(x, k_0) - F_120(x, 1))/(k_0 - 1))
Eq(F_192(x, k_0), F_193(x, k_0)*F_9(x))
Eq(F_193(x, k_0), (k_0*F_187(x, k_0) - F_187(x, 1))/(k_0 - 1))
Eq(F_194(x, k_0), F_17(x, k_0)*F_195(x, k_0))
Eq(F_195(x, k_0), F_180(x, k_0) + F_196(x, k_0))
Eq(F_196(x, k_0), F_181(x, k_0) + F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_64(x))
Eq(F_198(x, k_0), F_199(x, k_0) + F_201(x, k_0) + 2*F_31(x))
Eq(F_199(x, k_0), F_200(x, k_0)*F_9(x))
Eq(F_200(x, k_0), F_182(x, k_0) + F_198(x, k_0))
Eq(F_201(x, k_0), F_17(x, k_0)*F_197(x, k_0))
Eq(F_202(x, k_0), F_127(x, k_0)*F_9(x))
Eq(F_203(x), F_204(x)*F_9(x))
Eq(F_204(x), F_158(x) + F_23(x))
Eq(F_205(x, k_0), F_89(x, k_0)*F_9(x))
Eq(F_206(x, k_0), F_125(x, k_0)*F_9(x))
Eq(F_207(x), F_35(x, 1))
Eq(F_208(x), F_209(x, 1))
Eq(F_209(x, k_0), F_147(x, k_0)*F_9(x))
Eq(F_210(x), F_211(x)*F_9(x))
Eq(F_211(x), F_20(x, 1))
Eq(F_212(x, k_0), F_9(x)*F_98(x, k_0))
Eq(F_213(x, k_0), F_84(x, k_0)*F_9(x))
Eq(F_214(x), F_215(x)*F_9(x))
Eq(F_215(x), F_216(x, 1))
Eq(F_216(x, k_0), (k_0*F_127(x, k_0) - F_127(x, 1))/(k_0 - 1))
Eq(F_217(x), F_130(x, 1))
Eq(F_218(x), F_132(x, 1))
Eq(F_219(x), F_220(x)*F_9(x))
Eq(F_220(x), F_1(x) + F_104(x) + F_112(x) + F_113(x) + F_148(x) + F_152(x))
Eq(F_221(x), F_222(x, 1))
Eq(F_222(x, k_0), F_17(x, k_0)*F_223(x, k_0))
Eq(F_223(x, k_0), F_1(x) + F_10(x, k_0) + F_194(x, k_0) + F_224(x, k_0) + F_226(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0)*F_9(x))
Eq(F_225(x, k_0), (k_0*F_115(x, k_0) - F_115(x, 1))/(k_0 - 1))
Eq(F_226(x, k_0), F_227(x, k_0)*F_9(x))
Eq(F_227(x, k_0), (k_0*F_223(x, k_0) - F_223(x, 1))/(k_0 - 1))
Eq(F_228(x, k_0), F_229(x, k_0)*F_9(x))
Eq(F_229(x, k_0), F_1(x) + F_203(x) + F_230(x, k_0) + F_232(x, k_0) + F_37(x, k_0) + F_49(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0)*F_9(x))
Eq(F_231(x, k_0), (-k_0*F_229(x, k_0) + F_229(x, 1))/(1 - k_0))
Eq(F_232(x, k_0), F_233(x, k_0)*F_9(x))
Eq(F_233(x, k_0), (-k_0*F_53(x, k_0) + F_53(x, 1))/(1 - k_0))
Eq(F_234(x, k_0), F_50(x, k_0)*F_9(x))
Eq(F_235(x, k_0), F_20(x, k_0)*F_9(x))
Eq(F_236(x), F_211(x)*F_9(x))
Eq(F_237(x, k_0), F_187(x, k_0)*F_9(x))
Eq(F_238(x, k_0), F_120(x, k_0)*F_9(x))
Eq(F_239(x, k_0), F_137(x, k_0)*F_9(x))
Eq(F_240(x, k_0), F_11(x, k_0)*F_17(x, k_0))
Eq(F_241(x), F_242(x)*F_9(x))
Eq(F_242(x), F_243(x, 1))
Eq(F_243(x, k_0), F_1(x) + F_244(x, k_0) + F_37(x, k_0) + F_49(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0)*F_9(x))
Eq(F_245(x, k_0), F_1(x) + F_246(x, k_0) + F_263(x, k_0) + F_265(x, k_0) + F_37(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0)*F_9(x))
Eq(F_247(x, k_0), F_156(x) + F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_43(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_258(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0) + F_254(x, k_0))
Eq(F_251(x, k_0), F_252(x, k_0))
Eq(F_252(x, k_0), F_17(x, k_0)*F_253(x, k_0))
Eq(F_253(x, k_0), F_251(x, k_0) + F_61(x))
Eq(F_254(x, k_0), F_255(x, k_0) + F_257(x, k_0) + 2*F_31(x))
Eq(F_255(x, k_0), F_17(x, k_0)*F_256(x, k_0))
Eq(F_256(x, k_0), F_159(x) + F_254(x, k_0))
Eq(F_257(x, k_0), F_250(x, k_0)*F_9(x))
Eq(F_258(x, k_0), F_254(x, k_0) + F_259(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0) + F_262(x, k_0) + 3*F_31(x))
Eq(F_260(x, k_0), F_17(x, k_0)*F_261(x, k_0))
Eq(F_261(x, k_0), F_164(x) + F_259(x, k_0))
Eq(F_262(x, k_0), F_258(x, k_0)*F_9(x))
Eq(F_263(x, k_0), F_264(x, k_0)*F_9(x))
Eq(F_264(x, k_0), (-k_0*F_50(x, k_0) + F_50(x, 1))/(1 - k_0))
Eq(F_265(x, k_0), F_266(x, k_0)*F_9(x))
Eq(F_266(x, k_0), (-k_0*F_245(x, k_0) + F_245(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion_isolated", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], 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[], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 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": [[1, 0], [1, 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, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 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": [[1, 0], [1, 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, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/217/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[368,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[228,x]+F[229,x]+F[7,x]
F[7,x] = F[3,x]*F[8,x]
F[8,x] = F[1,x]+F[125,x]+F[26,x]+F[40,x]+F[9,x]
F[9,x] = F[10,x]*F[3,x]
F[10,x] = F[1,x]+F[11,x]+F[226,x]+F[227,x]
F[11,x] = F[12,x]*F[3,x]
F[12,x] = F[1,x]+F[13,x]+F[154,x]+F[162,x]+F[83,x]
F[13,x] = F[14,x]*F[3,x]
F[14,x] = F[1,x]+F[15,x]+F[220,x]+F[225,x]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[17,x,k[0]] = F[1,x]+F[131,x,k[0]]+F[18,x,k[0]]+F[219,x,k[0]]+F[9,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[19,x,k[0]] = F[1,x]+F[184,x,k[0]]+F[197,x,k[0]]+F[20,x,k[0]]+F[215,x,k[0]]+F[217,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]
F[21,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[22,x,k[0]] = F[1,x]+F[213,x,k[0]]+F[214,x,k[0]]+F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]*F[3,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[25,x,k[0]] = F[1,x]+F[125,x]+F[174,x,k[0]]+F[175,x,k[0]]+F[26,x]+F[40,x]
F[26,x] = F[27,x]*F[3,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[3,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[3,x]*F[34,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x] = F[36,x]+F[37,x]+F[39,x]
F[36,x] = 0
F[37,x] = F[3,x]*F[38,x]
F[38,x] = F[29,x]+F[35,x]
F[39,x] = F[3,x]*F[31,x]
F[40,x] = F[3,x]*F[41,x]
F[41,x] = F[42,x,1]
F[42,x,k[0]] = F[1,x]+F[160,x]+F[161,x]+F[173,x,k[0]]+F[43,x,k[0]]+F[45,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]*F[52,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[140,x]+F[173,x,k[0]]+F[43,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[3,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[140,x]+F[156,x]+F[158,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[52,x,k[0]]
F[48,x,k[0]] = F[1,x]+F[140,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[3,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[1,x]+F[133,x,k[0]]+F[172,x,k[0]]+F[51,x,k[0]]+F[62,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]*F[53,x,k[0]]
F[52,x,k[0]] = k[0]*x
F[53,x,k[0]] = F[28,x]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[58,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[52,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[58,x,k[0]] = F[36,x]+F[59,x,k[0]]+F[61,x,k[0]]
F[59,x,k[0]] = F[52,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[29,x]+F[58,x,k[0]]
F[61,x,k[0]] = F[3,x]*F[54,x,k[0]]
F[62,x,k[0]] = F[3,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[1,x]+F[166,x,k[0]]+F[168,x,k[0]]+F[170,x,k[0]]+F[64,x,k[0]]+F[78,x,k[0]]
F[64,x,k[0]] = F[52,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x]+F[71,x,k[0]]
F[66,x] = F[28,x]+F[67,x]
F[67,x] = F[29,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[3,x]*F[70,x]
F[70,x] = F[29,x]+F[68,x]
F[71,x,k[0]] = F[54,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[58,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = 2*F[36,x]+F[74,x,k[0]]+F[76,x,k[0]]
F[74,x,k[0]] = F[52,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[68,x]+F[73,x,k[0]]
F[76,x,k[0]] = F[3,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[58,x,k[0]]+F[73,x,k[0]]
F[78,x,k[0]] = F[3,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[1,x]+F[164,x,k[0]]+F[165,x,k[0]]+F[80,x,k[0]]+F[81,x,k[0]]
F[80,x,k[0]] = F[52,x,k[0]]*F[79,x,k[0]]
F[81,x,k[0]] = F[3,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[1,x]+F[154,x]+F[162,x]+F[47,x,k[0]]+F[49,x,k[0]]+F[83,x]
F[83,x] = F[3,x]*F[84,x]
F[84,x] = F[85,x,1]
F[85,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[148,x,k[0]]+F[150,x,k[0]]+F[152,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[52,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x]+F[92,x,k[0]]
F[88,x] = F[34,x]+F[89,x]
F[89,x] = F[32,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[3,x]*F[89,x]
F[92,x,k[0]] = F[101,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]
F[95,x,k[0]] = F[52,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[1,x]+F[94,x,k[0]]
F[97,x,k[0]] = F[100,x,k[0]]+F[36,x]+F[98,x,k[0]]
F[98,x,k[0]] = F[52,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[32,x]+F[97,x,k[0]]
F[100,x,k[0]] = F[3,x]*F[93,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[97,x,k[0]]
F[102,x,k[0]] = 2*F[36,x]+F[103,x,k[0]]+F[105,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[52,x,k[0]]
F[104,x,k[0]] = F[102,x,k[0]]+F[90,x]
F[105,x,k[0]] = F[101,x,k[0]]*F[3,x]
F[106,x,k[0]] = F[107,x,k[0]]*F[3,x]
F[107,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[109,x,k[0]]+F[134,x,k[0]]+F[147,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[52,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[3,x]
F[110,x,k[0]] = F[1,x]+F[111,x,k[0]]+F[120,x,k[0]]+F[129,x]+F[130,x]+F[132,x]
F[111,x,k[0]] = F[112,x,k[0]]*F[52,x,k[0]]
F[112,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[115,x,k[0]]+F[128,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[52,x,k[0]]
F[114,x,k[0]] = F[34,x]+F[93,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[3,x]
F[116,x,k[0]] = F[1,x]+F[117,x,k[0]]+F[118,x,k[0]]+F[127,x,k[0]]+F[26,x]
F[117,x,k[0]] = F[116,x,k[0]]*F[52,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[3,x]
F[119,x,k[0]] = F[1,x]+F[111,x,k[0]]+F[120,x,k[0]]+F[125,x]+F[26,x]+F[40,x]
F[120,x,k[0]] = F[121,x,k[0]]*F[3,x]
F[121,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[122,x,k[0]]+F[123,x,k[0]]+F[124,x,k[0]]
F[122,x,k[0]] = F[3,x]*F[85,x,k[0]]
F[123,x,k[0]] = F[119,x,k[0]]*F[3,x]
F[124,x,k[0]] = F[121,x,k[0]]*F[3,x]
F[125,x] = F[126,x,1]
F[126,x,k[0]] = F[3,x]*F[82,x,k[0]]
F[127,x,k[0]] = F[3,x]*F[85,x,k[0]]
F[128,x,k[0]] = F[112,x,k[0]]*F[3,x]
F[129,x] = F[62,x,1]
F[130,x] = F[131,x,1]
F[131,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[132,x] = F[133,x,1]
F[133,x,k[0]] = F[3,x]*F[50,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[3,x]
F[135,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[136,x,k[0]]+F[138,x,k[0]]+F[140,x]+F[86,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[3,x]
F[137,x,k[0]] = (F[135,x,k[0]]*k[0]-F[135,x,1])/(-1+k[0])
F[138,x,k[0]] = F[139,x,k[0]]*F[3,x]
F[139,x,k[0]] = (F[110,x,k[0]]*k[0]-F[110,x,1])/(-1+k[0])
F[140,x] = F[141,x]*F[3,x]
F[141,x] = F[142,x]+F[34,x]
F[142,x] = F[143,x]+F[29,x]
F[143,x] = F[144,x]+F[146,x]+F[36,x]
F[144,x] = F[145,x]*F[3,x]
F[145,x] = F[143,x]+F[32,x]
F[146,x] = F[142,x]*F[3,x]
F[147,x,k[0]] = F[107,x,k[0]]*F[3,x]
F[148,x,k[0]] = F[149,x,k[0]]*F[3,x]
F[149,x,k[0]] = (F[85,x,k[0]]*k[0]-F[85,x,1])/(-1+k[0])
F[150,x,k[0]] = F[151,x,k[0]]*F[3,x]
F[151,x,k[0]] = (F[119,x,k[0]]*k[0]-F[119,x,1])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]*F[3,x]
F[153,x,k[0]] = (F[121,x,k[0]]*k[0]-F[121,x,1])/(-1+k[0])
F[154,x] = F[155,x]*F[3,x]
F[155,x] = F[1,x]+F[140,x]+F[156,x]+F[158,x]+F[160,x]+F[161,x]
F[156,x] = F[157,x,1]
F[157,x,k[0]] = F[135,x,k[0]]*F[3,x]
F[158,x] = F[159,x,1]
F[159,x,k[0]] = F[110,x,k[0]]*F[3,x]
F[160,x] = F[115,x,1]
F[161,x] = F[128,x,1]
F[162,x] = F[163,x]*F[3,x]
F[163,x] = F[121,x,1]
F[164,x,k[0]] = F[3,x]*F[42,x,k[0]]
F[165,x,k[0]] = F[3,x]*F[79,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[3,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[63,x,k[0]]*k[0]-F[63,x,1])
F[168,x,k[0]] = F[169,x,k[0]]*F[3,x]
F[169,x,k[0]] = 1/(-1+k[0])*(F[46,x,k[0]]*k[0]-F[46,x,1])
F[170,x,k[0]] = F[171,x,k[0]]*F[3,x]
F[171,x,k[0]] = (F[50,x,k[0]]*k[0]-F[50,x,1])/(-1+k[0])
F[172,x,k[0]] = F[3,x]*F[46,x,k[0]]
F[173,x,k[0]] = F[3,x]*F[63,x,k[0]]
F[174,x,k[0]] = F[22,x,k[0]]*F[3,x]
F[175,x,k[0]] = F[176,x,k[0]]*F[52,x,k[0]]
F[176,x,k[0]] = F[1,x]+F[177,x,k[0]]+F[178,x,k[0]]+F[213,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[3,x]
F[178,x,k[0]] = F[179,x,k[0]]*F[3,x]
F[179,x,k[0]] = F[1,x]+F[180,x,k[0]]+F[182,x,k[0]]+F[184,x,k[0]]+F[197,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]*F[3,x]
F[181,x,k[0]] = 1/(-1+k[0])*(F[176,x,k[0]]*k[0]-F[176,x,1])
F[182,x,k[0]] = F[183,x,k[0]]*F[3,x]
F[183,x,k[0]] = 1/(-1+k[0])*(F[179,x,k[0]]*k[0]-F[179,x,1])
F[184,x,k[0]] = F[185,x,k[0]]*F[3,x]
F[185,x,k[0]] = F[1,x]+F[186,x,k[0]]+F[187,x,k[0]]+F[211,x,k[0]]+F[212,x,k[0]]
F[186,x,k[0]] = F[185,x,k[0]]*F[3,x]
F[187,x,k[0]] = F[188,x,k[0]]*F[3,x]
F[188,x,k[0]] = F[1,x]+F[140,x]+F[184,x,k[0]]+F[189,x,k[0]]+F[195,x,k[0]]+F[197,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[3,x]
F[190,x,k[0]] = 1/(-1+k[0])*(F[191,x,k[0]]*k[0]-F[191,x,1])
F[191,x,k[0]] = F[1,x]+F[174,x,k[0]]+F[175,x,k[0]]+F[192,x]+F[193,x]+F[194,x]
F[192,x] = F[117,x,1]
F[193,x] = F[155,x]*F[3,x]
F[194,x] = F[3,x]*F[84,x]
F[195,x,k[0]] = F[196,x,k[0]]*F[3,x]
F[196,x,k[0]] = 1/(-1+k[0])*(F[188,x,k[0]]*k[0]-F[188,x,1])
F[197,x,k[0]] = F[198,x,k[0]]*F[52,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[205,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[57,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[29,x]
F[201,x,k[0]] = F[202,x,k[0]]+F[204,x,k[0]]+F[36,x]
F[202,x,k[0]] = F[203,x,k[0]]*F[3,x]
F[203,x,k[0]] = F[201,x,k[0]]+F[55,x,k[0]]
F[204,x,k[0]] = F[200,x,k[0]]*F[52,x,k[0]]
F[205,x,k[0]] = F[200,x,k[0]]+F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]+F[68,x]
F[207,x,k[0]] = 2*F[36,x]+F[208,x,k[0]]+F[210,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]*F[3,x]
F[209,x,k[0]] = F[201,x,k[0]]+F[207,x,k[0]]
F[210,x,k[0]] = F[206,x,k[0]]*F[52,x,k[0]]
F[211,x,k[0]] = F[191,x,k[0]]*F[3,x]
F[212,x,k[0]] = F[185,x,k[0]]*F[52,x,k[0]]
F[213,x,k[0]] = F[199,x,k[0]]*F[52,x,k[0]]
F[214,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[215,x,k[0]] = F[216,x,k[0]]*F[3,x]
F[216,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[217,x,k[0]] = F[218,x,k[0]]*F[3,x]
F[218,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[219,x,k[0]] = F[179,x,k[0]]*F[52,x,k[0]]
F[220,x] = F[221,x,1]
F[221,x,k[0]] = F[222,x,k[0]]*F[3,x]
F[222,x,k[0]] = F[1,x]+F[13,x]+F[213,x,k[0]]+F[223,x,k[0]]+F[224,x,k[0]]
F[223,x,k[0]] = F[191,x,k[0]]*F[3,x]
F[224,x,k[0]] = F[188,x,k[0]]*F[3,x]
F[225,x] = F[14,x]*F[3,x]
F[226,x] = F[3,x]*F[8,x]
F[227,x] = F[10,x]*F[3,x]
F[228,x] = F[12,x]*F[3,x]
F[229,x] = F[230,x]*F[3,x]
F[230,x] = F[1,x]+F[231,x]+F[366,x]+F[367,x]
F[231,x] = F[232,x,1]
F[232,x,k[0]] = F[233,x,k[0]]*F[52,x,k[0]]
F[233,x,k[0]] = F[1,x]+F[232,x,k[0]]+F[234,x,k[0]]+F[237,x,k[0]]
F[234,x,k[0]] = F[235,x,k[0]]*F[3,x]
F[235,x,k[0]] = F[1,x]+F[126,x,k[0]]+F[229,x]+F[236,x,k[0]]+F[51,x,k[0]]
F[236,x,k[0]] = F[3,x]*F[42,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]*F[3,x]
F[238,x,k[0]] = F[1,x]+F[173,x,k[0]]+F[239,x]+F[43,x,k[0]]+F[45,x,k[0]]
F[239,x] = F[240,x]*F[3,x]
F[240,x] = F[1,x]+F[241,x]+F[254,x]+F[256,x]
F[241,x] = F[242,x,1]
F[242,x,k[0]] = F[243,x,k[0]]*F[3,x]
F[243,x,k[0]] = F[244,x,k[0]]+F[248,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]+F[57,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]+F[32,x]
F[246,x,k[0]] = F[247,x,k[0]]
F[247,x,k[0]] = F[245,x,k[0]]*F[52,x,k[0]]
F[248,x,k[0]] = F[200,x,k[0]]+F[249,x,k[0]]
F[249,x,k[0]] = F[143,x]+F[250,x,k[0]]
F[250,x,k[0]] = 2*F[36,x]+F[251,x,k[0]]+F[253,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]*F[3,x]
F[252,x,k[0]] = F[246,x,k[0]]+F[250,x,k[0]]
F[253,x,k[0]] = F[249,x,k[0]]*F[52,x,k[0]]
F[254,x] = F[255,x]*F[3,x]
F[255,x] = F[185,x,1]
F[256,x] = F[257,x,1]
F[257,x,k[0]] = F[258,x,k[0]]*F[3,x]
F[258,x,k[0]] = (F[259,x,k[0]]*k[0]-F[259,x,1])/(-1+k[0])
F[259,x,k[0]] = F[1,x]+F[260,x,k[0]]+F[261,x,k[0]]+F[364,x,k[0]]
F[260,x,k[0]] = F[259,x,k[0]]*F[52,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]*F[3,x]
F[262,x,k[0]] = F[1,x]+F[111,x,k[0]]+F[120,x,k[0]]+F[263,x]+F[338,x]
F[263,x] = F[264,x]*F[3,x]
F[264,x] = F[1,x]+F[239,x]+F[265,x]+F[276,x]+F[277,x]
F[265,x] = F[266,x]*F[3,x]
F[266,x] = F[1,x]+F[267,x]+F[268,x]+F[270,x]+F[273,x]
F[267,x] = F[64,x,1]
F[268,x] = F[269,x]*F[3,x]
F[269,x] = F[79,x,1]
F[270,x] = F[271,x]*F[3,x]
F[271,x] = F[272,x,1]
F[272,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[273,x] = F[274,x]*F[3,x]
F[274,x] = F[275,x,1]
F[275,x,k[0]] = (F[48,x,k[0]]*k[0]-F[48,x,1])/(-1+k[0])
F[276,x] = F[45,x,1]
F[277,x] = F[278,x]*F[3,x]
F[278,x] = F[1,x]+F[267,x]+F[268,x]+F[279,x]+F[333,x]+F[336,x]
F[279,x] = F[280,x]*F[3,x]
F[280,x] = F[1,x]+F[267,x]+F[281,x]+F[320,x]+F[323,x]+F[327,x]+F[330,x]
F[281,x] = F[282,x,1]
F[282,x,k[0]] = F[283,x,k[0]]*F[52,x,k[0]]
F[283,x,k[0]] = F[284,x,k[0]]+F[302,x,k[0]]
F[284,x,k[0]] = F[285,x,k[0]]+F[290,x,k[0]]
F[285,x,k[0]] = F[28,x]+F[286,x,k[0]]
F[286,x,k[0]] = F[287,x,k[0]]+F[94,x,k[0]]
F[287,x,k[0]] = F[288,x,k[0]]
F[288,x,k[0]] = F[289,x,k[0]]*F[52,x,k[0]]
F[289,x,k[0]] = F[287,x,k[0]]+F[29,x]
F[290,x,k[0]] = F[291,x,k[0]]+F[31,x]
F[291,x,k[0]] = F[292,x,k[0]]+F[297,x,k[0]]
F[292,x,k[0]] = F[293,x,k[0]]+F[295,x,k[0]]+F[36,x]
F[293,x,k[0]] = F[294,x,k[0]]*F[3,x]
F[294,x,k[0]] = F[292,x,k[0]]+F[94,x,k[0]]
F[295,x,k[0]] = F[296,x,k[0]]*F[52,x,k[0]]
F[296,x,k[0]] = F[292,x,k[0]]+F[32,x]
F[297,x,k[0]] = 2*F[36,x]+F[298,x,k[0]]+F[300,x,k[0]]
F[298,x,k[0]] = F[299,x,k[0]]*F[3,x]
F[299,x,k[0]] = F[287,x,k[0]]+F[297,x,k[0]]
F[300,x,k[0]] = F[301,x,k[0]]*F[52,x,k[0]]
F[301,x,k[0]] = F[297,x,k[0]]+F[35,x]
F[302,x,k[0]] = F[290,x,k[0]]+F[303,x,k[0]]
F[303,x,k[0]] = F[304,x]+F[309,x,k[0]]
F[304,x] = F[305,x]+F[90,x]
F[305,x] = 2*F[36,x]+F[306,x]+F[308,x]
F[306,x] = F[3,x]*F[307,x]
F[307,x] = F[305,x]+F[35,x]
F[308,x] = F[3,x]*F[304,x]
F[309,x,k[0]] = F[310,x,k[0]]+F[315,x,k[0]]
F[310,x,k[0]] = 2*F[36,x]+F[311,x,k[0]]+F[313,x,k[0]]
F[311,x,k[0]] = F[3,x]*F[312,x,k[0]]
F[312,x,k[0]] = F[292,x,k[0]]+F[310,x,k[0]]
F[313,x,k[0]] = F[314,x,k[0]]*F[52,x,k[0]]
F[314,x,k[0]] = F[310,x,k[0]]+F[90,x]
F[315,x,k[0]] = 3*F[36,x]+F[316,x,k[0]]+F[318,x,k[0]]
F[316,x,k[0]] = F[3,x]*F[317,x,k[0]]
F[317,x,k[0]] = F[297,x,k[0]]+F[315,x,k[0]]
F[318,x,k[0]] = F[319,x,k[0]]*F[52,x,k[0]]
F[319,x,k[0]] = F[305,x]+F[315,x,k[0]]
F[320,x] = F[321,x,1]
F[321,x,k[0]] = F[3,x]*F[322,x,k[0]]
F[322,x,k[0]] = 1/(-1+k[0])*(F[79,x,k[0]]*k[0]-F[79,x,1])
F[323,x] = F[3,x]*F[324,x]
F[324,x] = F[325,x,1]
F[325,x,k[0]] = (F[326,x,k[0]]*k[0]-F[326,x,1])/(-1+k[0])
F[326,x,k[0]] = 1/(-1+k[0])*(F[63,x,k[0]]*k[0]-F[63,x,1])
F[327,x] = F[3,x]*F[328,x]
F[328,x] = F[329,x,1]
F[329,x,k[0]] = (F[169,x,k[0]]*k[0]-F[169,x,1])/(-1+k[0])
F[330,x] = F[3,x]*F[331,x]
F[331,x] = F[332,x,1]
F[332,x,k[0]] = (F[171,x,k[0]]*k[0]-F[171,x,1])/(-1+k[0])
F[333,x] = F[3,x]*F[334,x]
F[334,x] = F[335,x,1]
F[335,x,k[0]] = 1/(-1+k[0])*(F[46,x,k[0]]*k[0]-F[46,x,1])
F[336,x] = F[3,x]*F[337,x]
F[337,x] = F[171,x,1]
F[338,x] = F[3,x]*F[339,x]
F[339,x] = F[1,x]+F[340,x]+F[341,x]+F[342,x]+F[362,x]
F[340,x] = F[177,x,1]
F[341,x] = F[178,x,1]
F[342,x] = F[3,x]*F[343,x]
F[343,x] = F[1,x]+F[241,x]+F[254,x]+F[344,x]+F[351,x]
F[344,x] = F[345,x,1]
F[345,x,k[0]] = F[3,x]*F[346,x,k[0]]
F[346,x,k[0]] = F[1,x]+F[192,x]+F[229,x]+F[347,x,k[0]]+F[349,x,k[0]]+F[350,x,k[0]]
F[347,x,k[0]] = F[348,x,k[0]]*F[52,x,k[0]]
F[348,x,k[0]] = (F[116,x,k[0]]*k[0]-F[116,x,1])/(-1+k[0])
F[349,x,k[0]] = F[151,x,k[0]]*F[3,x]
F[350,x,k[0]] = F[149,x,k[0]]*F[3,x]
F[351,x] = F[352,x,1]
F[352,x,k[0]] = F[3,x]*F[353,x,k[0]]
F[353,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[136,x,k[0]]+F[138,x,k[0]]+F[239,x]+F[354,x,k[0]]
F[354,x,k[0]] = F[3,x]*F[355,x,k[0]]
F[355,x,k[0]] = F[141,x]+F[356,x,k[0]]
F[356,x,k[0]] = F[357,x,k[0]]+F[93,x,k[0]]
F[357,x,k[0]] = F[287,x,k[0]]+F[358,x,k[0]]
F[358,x,k[0]] = 2*F[36,x]+F[359,x,k[0]]+F[361,x,k[0]]
F[359,x,k[0]] = F[360,x,k[0]]*F[52,x,k[0]]
F[360,x,k[0]] = F[143,x]+F[358,x,k[0]]
F[361,x,k[0]] = F[3,x]*F[357,x,k[0]]
F[362,x] = F[3,x]*F[363,x]
F[363,x] = F[262,x,1]
F[364,x,k[0]] = F[3,x]*F[365,x,k[0]]
F[365,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[345,x,k[0]]+F[352,x,k[0]]+F[86,x,k[0]]
F[366,x] = F[234,x,1]
F[367,x] = F[237,x,1]
F[368,x] = F[3,x]*F[369,x]
F[369,x] = F[1,x]+F[239,x]+F[370,x]+F[376,x]
F[370,x] = F[3,x]*F[371,x]
F[371,x] = F[1,x]+F[228,x]+F[372,x]+F[374,x]+F[7,x]
F[372,x] = F[373,x,1]
F[373,x,k[0]] = F[3,x]*F[44,x,k[0]]
F[374,x] = F[3,x]*F[375,x]
F[375,x] = F[176,x,1]
F[376,x] = F[3,x]*F[377,x]
F[377,x] = F[1,x]+F[129,x]+F[130,x]+F[132,x]+F[9,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{368}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{228}\! \left(x \right)+F_{229}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{125}\! \left(x \right)+F_{26}\! \left(x \right)+F_{40}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{3}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{226}\! \left(x \right)+F_{227}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{154}\! \left(x \right)+F_{162}\! \left(x \right)+F_{83}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{220}\! \left(x \right)+F_{225}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{219}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{184}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{215}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{213}\! \left(x , y\right)+F_{214}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{125}\! \left(x \right)+F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{3}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{3}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{3}\! \left(x \right) F_{31}\! \left(x \right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x \right)+F_{161}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{156}\! \left(x \right)+F_{158}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{133}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = y x
F_{53}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{166}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{64}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{66}\! \left(x \right) = F_{28}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{29}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{3}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{29}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{68}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{154}\! \left(x \right)+F_{162}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{3}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{85}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{88}\! \left(x \right) = F_{34}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{32}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{3}\! \left(x \right) F_{89}\! \left(x \right)
F_{92}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{36}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{111}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{129}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{93}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{127}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{111}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{125}\! \left(x \right)+F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{122}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x , 1\right)
F_{126}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{129}\! \left(x \right) = F_{62}\! \left(x , 1\right)
F_{130}\! \left(x \right) = F_{131}\! \left(x , 1\right)
F_{131}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x , 1\right)
F_{133}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{138}\! \left(x , y\right)+F_{140}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{137}\! \left(x , y\right) = -\frac{-y F_{135}\! \left(x , y\right)+F_{135}\! \left(x , 1\right)}{-1+y}
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{139}\! \left(x , y\right) = -\frac{-y F_{110}\! \left(x , y\right)+F_{110}\! \left(x , 1\right)}{-1+y}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{3}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{34}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{29}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{146}\! \left(x \right)+F_{36}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{3}\! \left(x \right)
F_{145}\! \left(x \right) = F_{143}\! \left(x \right)+F_{32}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right) F_{3}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{151}\! \left(x , y\right) = -\frac{-y F_{119}\! \left(x , y\right)+F_{119}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{153}\! \left(x , y\right) = -\frac{-y F_{121}\! \left(x , y\right)+F_{121}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{3}\! \left(x \right)
F_{155}\! \left(x \right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{156}\! \left(x \right)+F_{158}\! \left(x \right)+F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x , 1\right)
F_{157}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x , 1\right)
F_{159}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{160}\! \left(x \right) = F_{115}\! \left(x , 1\right)
F_{161}\! \left(x \right) = F_{128}\! \left(x , 1\right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{3}\! \left(x \right)
F_{163}\! \left(x \right) = F_{121}\! \left(x , 1\right)
F_{164}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{167}\! \left(x , y\right) = -\frac{-y F_{63}\! \left(x , y\right)+F_{63}\! \left(x , 1\right)}{-1+y}
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{169}\! \left(x , y\right) = -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{171}\! \left(x , y\right) = -\frac{-y F_{50}\! \left(x , y\right)+F_{50}\! \left(x , 1\right)}{-1+y}
F_{172}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{180}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{181}\! \left(x , y\right) = -\frac{-y F_{176}\! \left(x , y\right)+F_{176}\! \left(x , 1\right)}{-1+y}
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{183}\! \left(x , y\right) = -\frac{-y F_{179}\! \left(x , y\right)+F_{179}\! \left(x , 1\right)}{-1+y}
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{185}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{186}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{211}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{184}\! \left(x , y\right)+F_{189}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{190}\! \left(x , y\right) = -\frac{-y F_{191}\! \left(x , y\right)+F_{191}\! \left(x , 1\right)}{-1+y}
F_{191}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)+F_{192}\! \left(x \right)+F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{192}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{155}\! \left(x \right) F_{3}\! \left(x \right)
F_{194}\! \left(x \right) = F_{3}\! \left(x \right) F_{84}\! \left(x \right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{196}\! \left(x , y\right) = -\frac{-y F_{188}\! \left(x , y\right)+F_{188}\! \left(x , 1\right)}{-1+y}
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{204}\! \left(x , y\right)+F_{36}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{68}\! \left(x \right)
F_{207}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{208}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{209}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{206}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{212}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{216}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{218}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{219}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{220}\! \left(x \right) = F_{221}\! \left(x , 1\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{222}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{213}\! \left(x , y\right)+F_{223}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{224}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{225}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{226}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{227}\! \left(x \right) = F_{10}\! \left(x \right) F_{3}\! \left(x \right)
F_{228}\! \left(x \right) = F_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right) F_{3}\! \left(x \right)
F_{230}\! \left(x \right) = F_{1}\! \left(x \right)+F_{231}\! \left(x \right)+F_{366}\! \left(x \right)+F_{367}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x , 1\right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{232}\! \left(x , y\right)+F_{234}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{235}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{229}\! \left(x \right)+F_{236}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{239}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right) F_{3}\! \left(x \right)
F_{240}\! \left(x \right) = F_{1}\! \left(x \right)+F_{241}\! \left(x \right)+F_{254}\! \left(x \right)+F_{256}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x , 1\right)
F_{242}\! \left(x , y\right) = F_{243}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{248}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{32}\! \left(x \right)
F_{246}\! \left(x , y\right) = F_{247}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{245}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{143}\! \left(x \right)+F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{251}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{249}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right) F_{3}\! \left(x \right)
F_{255}\! \left(x \right) = F_{185}\! \left(x , 1\right)
F_{256}\! \left(x \right) = F_{257}\! \left(x , 1\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{258}\! \left(x , y\right) = -\frac{-y F_{259}\! \left(x , y\right)+F_{259}\! \left(x , 1\right)}{-1+y}
F_{259}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{260}\! \left(x , y\right)+F_{261}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{259}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{262}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{111}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{263}\! \left(x \right)+F_{338}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right) F_{3}\! \left(x \right)
F_{264}\! \left(x \right) = F_{1}\! \left(x \right)+F_{239}\! \left(x \right)+F_{265}\! \left(x \right)+F_{276}\! \left(x \right)+F_{277}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right) F_{3}\! \left(x \right)
F_{266}\! \left(x \right) = F_{1}\! \left(x \right)+F_{267}\! \left(x \right)+F_{268}\! \left(x \right)+F_{270}\! \left(x \right)+F_{273}\! \left(x \right)
F_{267}\! \left(x \right) = F_{64}\! \left(x , 1\right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{3}\! \left(x \right)
F_{269}\! \left(x \right) = F_{79}\! \left(x , 1\right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right) F_{3}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x , 1\right)
F_{272}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{273}\! \left(x \right) = F_{274}\! \left(x \right) F_{3}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x , 1\right)
F_{275}\! \left(x , y\right) = -\frac{-y F_{48}\! \left(x , y\right)+F_{48}\! \left(x , 1\right)}{-1+y}
F_{276}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right) F_{3}\! \left(x \right)
F_{278}\! \left(x \right) = F_{1}\! \left(x \right)+F_{267}\! \left(x \right)+F_{268}\! \left(x \right)+F_{279}\! \left(x \right)+F_{333}\! \left(x \right)+F_{336}\! \left(x \right)
F_{279}\! \left(x \right) = F_{280}\! \left(x \right) F_{3}\! \left(x \right)
F_{280}\! \left(x \right) = F_{1}\! \left(x \right)+F_{267}\! \left(x \right)+F_{281}\! \left(x \right)+F_{320}\! \left(x \right)+F_{323}\! \left(x \right)+F_{327}\! \left(x \right)+F_{330}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x , 1\right)
F_{282}\! \left(x , y\right) = F_{283}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{302}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{285}\! \left(x , y\right)+F_{290}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{286}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{288}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{289}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{290}\! \left(x , y\right) = F_{291}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{291}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{297}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{293}\! \left(x , y\right)+F_{295}\! \left(x , y\right)+F_{36}\! \left(x \right)
F_{293}\! \left(x , y\right) = F_{294}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{294}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{296}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{32}\! \left(x \right)
F_{297}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{298}\! \left(x , y\right)+F_{300}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{299}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{299}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{297}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{302}\! \left(x , y\right) = F_{290}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x \right)+F_{309}\! \left(x , y\right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{90}\! \left(x \right)
F_{305}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{306}\! \left(x \right)+F_{308}\! \left(x \right)
F_{306}\! \left(x \right) = F_{3}\! \left(x \right) F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{305}\! \left(x \right)+F_{35}\! \left(x \right)
F_{308}\! \left(x \right) = F_{3}\! \left(x \right) F_{304}\! \left(x \right)
F_{309}\! \left(x , y\right) = F_{310}\! \left(x , y\right)+F_{315}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{311}\! \left(x , y\right)+F_{313}\! \left(x , y\right)
F_{311}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{292}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{314}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{310}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{315}\! \left(x , y\right) = 3 F_{36}\! \left(x \right)+F_{316}\! \left(x , y\right)+F_{318}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{317}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{315}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{319}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = F_{305}\! \left(x \right)+F_{315}\! \left(x , y\right)
F_{320}\! \left(x \right) = F_{321}\! \left(x , 1\right)
F_{321}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = -\frac{-y F_{79}\! \left(x , y\right)+F_{79}\! \left(x , 1\right)}{-1+y}
F_{323}\! \left(x \right) = F_{3}\! \left(x \right) F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{325}\! \left(x , 1\right)
F_{325}\! \left(x , y\right) = -\frac{-y F_{326}\! \left(x , y\right)+F_{326}\! \left(x , 1\right)}{-1+y}
F_{326}\! \left(x , y\right) = -\frac{-y F_{63}\! \left(x , y\right)+F_{63}\! \left(x , 1\right)}{-1+y}
F_{327}\! \left(x \right) = F_{3}\! \left(x \right) F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x , 1\right)
F_{329}\! \left(x , y\right) = -\frac{-y F_{169}\! \left(x , y\right)+F_{169}\! \left(x , 1\right)}{-1+y}
F_{330}\! \left(x \right) = F_{3}\! \left(x \right) F_{331}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x , 1\right)
F_{332}\! \left(x , y\right) = -\frac{-y F_{171}\! \left(x , y\right)+F_{171}\! \left(x , 1\right)}{-1+y}
F_{333}\! \left(x \right) = F_{3}\! \left(x \right) F_{334}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x , 1\right)
F_{335}\! \left(x , y\right) = -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}
F_{336}\! \left(x \right) = F_{3}\! \left(x \right) F_{337}\! \left(x \right)
F_{337}\! \left(x \right) = F_{171}\! \left(x , 1\right)
F_{338}\! \left(x \right) = F_{3}\! \left(x \right) F_{339}\! \left(x \right)
F_{339}\! \left(x \right) = F_{1}\! \left(x \right)+F_{340}\! \left(x \right)+F_{341}\! \left(x \right)+F_{342}\! \left(x \right)+F_{362}\! \left(x \right)
F_{340}\! \left(x \right) = F_{177}\! \left(x , 1\right)
F_{341}\! \left(x \right) = F_{178}\! \left(x , 1\right)
F_{342}\! \left(x \right) = F_{3}\! \left(x \right) F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = F_{1}\! \left(x \right)+F_{241}\! \left(x \right)+F_{254}\! \left(x \right)+F_{344}\! \left(x \right)+F_{351}\! \left(x \right)
F_{344}\! \left(x \right) = F_{345}\! \left(x , 1\right)
F_{345}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{346}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{192}\! \left(x \right)+F_{229}\! \left(x \right)+F_{347}\! \left(x , y\right)+F_{349}\! \left(x , y\right)+F_{350}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{348}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = -\frac{-y F_{116}\! \left(x , y\right)+F_{116}\! \left(x , 1\right)}{-1+y}
F_{349}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{350}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x , 1\right)
F_{352}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{353}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{138}\! \left(x , y\right)+F_{239}\! \left(x \right)+F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{355}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{141}\! \left(x \right)+F_{356}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{357}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{287}\! \left(x , y\right)+F_{358}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{359}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{360}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{143}\! \left(x \right)+F_{358}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{357}\! \left(x , y\right)
F_{362}\! \left(x \right) = F_{3}\! \left(x \right) F_{363}\! \left(x \right)
F_{363}\! \left(x \right) = F_{262}\! \left(x , 1\right)
F_{364}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{345}\! \left(x , y\right)+F_{352}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{366}\! \left(x \right) = F_{234}\! \left(x , 1\right)
F_{367}\! \left(x \right) = F_{237}\! \left(x , 1\right)
F_{368}\! \left(x \right) = F_{3}\! \left(x \right) F_{369}\! \left(x \right)
F_{369}\! \left(x \right) = F_{1}\! \left(x \right)+F_{239}\! \left(x \right)+F_{370}\! \left(x \right)+F_{376}\! \left(x \right)
F_{370}\! \left(x \right) = F_{3}\! \left(x \right) F_{371}\! \left(x \right)
F_{371}\! \left(x \right) = F_{1}\! \left(x \right)+F_{228}\! \left(x \right)+F_{372}\! \left(x \right)+F_{374}\! \left(x \right)+F_{7}\! \left(x \right)
F_{372}\! \left(x \right) = F_{373}\! \left(x , 1\right)
F_{373}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{374}\! \left(x \right) = F_{3}\! \left(x \right) F_{375}\! \left(x \right)
F_{375}\! \left(x \right) = F_{176}\! \left(x , 1\right)
F_{376}\! \left(x \right) = F_{3}\! \left(x \right) F_{377}\! \left(x \right)
F_{377}\! \left(x \right) = F_{1}\! \left(x \right)+F_{129}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{9}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_368(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_228(x) + F_229(x) + F_7(x))
Eq(F_7(x), F_3(x)*F_8(x))
Eq(F_8(x), F_1(x) + F_125(x) + F_26(x) + F_40(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_3(x))
Eq(F_10(x), F_1(x) + F_11(x) + F_226(x) + F_227(x))
Eq(F_11(x), F_12(x)*F_3(x))
Eq(F_12(x), F_1(x) + F_13(x) + F_154(x) + F_162(x) + F_83(x))
Eq(F_13(x), F_14(x)*F_3(x))
Eq(F_14(x), F_1(x) + F_15(x) + F_220(x) + F_225(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_17(x, k_0), F_1(x) + F_131(x, k_0) + F_18(x, k_0) + F_219(x, k_0) + F_9(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_19(x, k_0), F_1(x) + F_184(x, k_0) + F_197(x, k_0) + F_20(x, k_0) + F_215(x, k_0) + F_217(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x))
Eq(F_21(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_22(x, k_0), F_1(x) + F_213(x, k_0) + F_214(x, k_0) + F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0)*F_3(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_25(x, k_0), F_1(x) + F_125(x) + F_174(x, k_0) + F_175(x, k_0) + F_26(x) + F_40(x))
Eq(F_26(x), F_27(x)*F_3(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_3(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_3(x)*F_34(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_39(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_3(x)*F_38(x))
Eq(F_38(x), F_29(x) + F_35(x))
Eq(F_39(x), F_3(x)*F_31(x))
Eq(F_40(x), F_3(x)*F_41(x))
Eq(F_41(x), F_42(x, 1))
Eq(F_42(x, k_0), F_1(x) + F_160(x) + F_161(x) + F_173(x, k_0) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0)*F_52(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_140(x) + F_173(x, k_0) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_140(x) + F_156(x) + F_158(x) + F_47(x, k_0) + F_49(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_52(x, k_0))
Eq(F_48(x, k_0), F_1(x) + F_140(x) + F_47(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_3(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_1(x) + F_133(x, k_0) + F_172(x, k_0) + F_51(x, k_0) + F_62(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0)*F_53(x, k_0))
Eq(F_52(x, k_0), k_0*x)
Eq(F_53(x, k_0), F_28(x) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_58(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_52(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_58(x, k_0), F_36(x) + F_59(x, k_0) + F_61(x, k_0))
Eq(F_59(x, k_0), F_52(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_29(x) + F_58(x, k_0))
Eq(F_61(x, k_0), F_3(x)*F_54(x, k_0))
Eq(F_62(x, k_0), F_3(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_1(x) + F_166(x, k_0) + F_168(x, k_0) + F_170(x, k_0) + F_64(x, k_0) + F_78(x, k_0))
Eq(F_64(x, k_0), F_52(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x) + F_71(x, k_0))
Eq(F_66(x), F_28(x) + F_67(x))
Eq(F_67(x), F_29(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_3(x)*F_70(x))
Eq(F_70(x), F_29(x) + F_68(x))
Eq(F_71(x, k_0), F_54(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_58(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), 2*F_36(x) + F_74(x, k_0) + F_76(x, k_0))
Eq(F_74(x, k_0), F_52(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_68(x) + F_73(x, k_0))
Eq(F_76(x, k_0), F_3(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_58(x, k_0) + F_73(x, k_0))
Eq(F_78(x, k_0), F_3(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_1(x) + F_164(x, k_0) + F_165(x, k_0) + F_80(x, k_0) + F_81(x, k_0))
Eq(F_80(x, k_0), F_52(x, k_0)*F_79(x, k_0))
Eq(F_81(x, k_0), F_3(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_1(x) + F_154(x) + F_162(x) + F_47(x, k_0) + F_49(x, k_0) + F_83(x))
Eq(F_83(x), F_3(x)*F_84(x))
Eq(F_84(x), F_85(x, 1))
Eq(F_85(x, k_0), F_1(x) + F_106(x, k_0) + F_148(x, k_0) + F_150(x, k_0) + F_152(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_52(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x) + F_92(x, k_0))
Eq(F_88(x), F_34(x) + F_89(x))
Eq(F_89(x), F_32(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_3(x)*F_89(x))
Eq(F_92(x, k_0), F_101(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0))
Eq(F_95(x, k_0), F_52(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_1(x) + F_94(x, k_0))
Eq(F_97(x, k_0), F_100(x, k_0) + F_36(x) + F_98(x, k_0))
Eq(F_98(x, k_0), F_52(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_32(x) + F_97(x, k_0))
Eq(F_100(x, k_0), F_3(x)*F_93(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_97(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_105(x, k_0) + 2*F_36(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_52(x, k_0))
Eq(F_104(x, k_0), F_102(x, k_0) + F_90(x))
Eq(F_105(x, k_0), F_101(x, k_0)*F_3(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_3(x))
Eq(F_107(x, k_0), F_1(x) + F_108(x, k_0) + F_109(x, k_0) + F_134(x, k_0) + F_147(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_52(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_3(x))
Eq(F_110(x, k_0), F_1(x) + F_111(x, k_0) + F_120(x, k_0) + F_129(x) + F_130(x) + F_132(x))
Eq(F_111(x, k_0), F_112(x, k_0)*F_52(x, k_0))
Eq(F_112(x, k_0), F_1(x) + F_113(x, k_0) + F_115(x, k_0) + F_128(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_52(x, k_0))
Eq(F_114(x, k_0), F_34(x) + F_93(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_3(x))
Eq(F_116(x, k_0), F_1(x) + F_117(x, k_0) + F_118(x, k_0) + F_127(x, k_0) + F_26(x))
Eq(F_117(x, k_0), F_116(x, k_0)*F_52(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_3(x))
Eq(F_119(x, k_0), F_1(x) + F_111(x, k_0) + F_120(x, k_0) + F_125(x) + F_26(x) + F_40(x))
Eq(F_120(x, k_0), F_121(x, k_0)*F_3(x))
Eq(F_121(x, k_0), F_1(x) + F_113(x, k_0) + F_122(x, k_0) + F_123(x, k_0) + F_124(x, k_0))
Eq(F_122(x, k_0), F_3(x)*F_85(x, k_0))
Eq(F_123(x, k_0), F_119(x, k_0)*F_3(x))
Eq(F_124(x, k_0), F_121(x, k_0)*F_3(x))
Eq(F_125(x), F_126(x, 1))
Eq(F_126(x, k_0), F_3(x)*F_82(x, k_0))
Eq(F_127(x, k_0), F_3(x)*F_85(x, k_0))
Eq(F_128(x, k_0), F_112(x, k_0)*F_3(x))
Eq(F_129(x), F_62(x, 1))
Eq(F_130(x), F_131(x, 1))
Eq(F_131(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_132(x), F_133(x, 1))
Eq(F_133(x, k_0), F_3(x)*F_50(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_3(x))
Eq(F_135(x, k_0), F_1(x) + F_106(x, k_0) + F_136(x, k_0) + F_138(x, k_0) + F_140(x) + F_86(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_3(x))
Eq(F_137(x, k_0), (-k_0*F_135(x, k_0) + F_135(x, 1))/(1 - k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_3(x))
Eq(F_139(x, k_0), (-k_0*F_110(x, k_0) + F_110(x, 1))/(1 - k_0))
Eq(F_140(x), F_141(x)*F_3(x))
Eq(F_141(x), F_142(x) + F_34(x))
Eq(F_142(x), F_143(x) + F_29(x))
Eq(F_143(x), F_144(x) + F_146(x) + F_36(x))
Eq(F_144(x), F_145(x)*F_3(x))
Eq(F_145(x), F_143(x) + F_32(x))
Eq(F_146(x), F_142(x)*F_3(x))
Eq(F_147(x, k_0), F_107(x, k_0)*F_3(x))
Eq(F_148(x, k_0), F_149(x, k_0)*F_3(x))
Eq(F_149(x, k_0), (-k_0*F_85(x, k_0) + F_85(x, 1))/(1 - k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_3(x))
Eq(F_151(x, k_0), (-k_0*F_119(x, k_0) + F_119(x, 1))/(1 - k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_3(x))
Eq(F_153(x, k_0), (-k_0*F_121(x, k_0) + F_121(x, 1))/(1 - k_0))
Eq(F_154(x), F_155(x)*F_3(x))
Eq(F_155(x), F_1(x) + F_140(x) + F_156(x) + F_158(x) + F_160(x) + F_161(x))
Eq(F_156(x), F_157(x, 1))
Eq(F_157(x, k_0), F_135(x, k_0)*F_3(x))
Eq(F_158(x), F_159(x, 1))
Eq(F_159(x, k_0), F_110(x, k_0)*F_3(x))
Eq(F_160(x), F_115(x, 1))
Eq(F_161(x), F_128(x, 1))
Eq(F_162(x), F_163(x)*F_3(x))
Eq(F_163(x), F_121(x, 1))
Eq(F_164(x, k_0), F_3(x)*F_42(x, k_0))
Eq(F_165(x, k_0), F_3(x)*F_79(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_3(x))
Eq(F_167(x, k_0), (-k_0*F_63(x, k_0) + F_63(x, 1))/(1 - k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_3(x))
Eq(F_169(x, k_0), (-k_0*F_46(x, k_0) + F_46(x, 1))/(1 - k_0))
Eq(F_170(x, k_0), F_171(x, k_0)*F_3(x))
Eq(F_171(x, k_0), (-k_0*F_50(x, k_0) + F_50(x, 1))/(1 - k_0))
Eq(F_172(x, k_0), F_3(x)*F_46(x, k_0))
Eq(F_173(x, k_0), F_3(x)*F_63(x, k_0))
Eq(F_174(x, k_0), F_22(x, k_0)*F_3(x))
Eq(F_175(x, k_0), F_176(x, k_0)*F_52(x, k_0))
Eq(F_176(x, k_0), F_1(x) + F_177(x, k_0) + F_178(x, k_0) + F_213(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_3(x))
Eq(F_178(x, k_0), F_179(x, k_0)*F_3(x))
Eq(F_179(x, k_0), F_1(x) + F_180(x, k_0) + F_182(x, k_0) + F_184(x, k_0) + F_197(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0)*F_3(x))
Eq(F_181(x, k_0), (k_0*F_176(x, k_0) - F_176(x, 1))/(k_0 - 1))
Eq(F_182(x, k_0), F_183(x, k_0)*F_3(x))
Eq(F_183(x, k_0), (k_0*F_179(x, k_0) - F_179(x, 1))/(k_0 - 1))
Eq(F_184(x, k_0), F_185(x, k_0)*F_3(x))
Eq(F_185(x, k_0), F_1(x) + F_186(x, k_0) + F_187(x, k_0) + F_211(x, k_0) + F_212(x, k_0))
Eq(F_186(x, k_0), F_185(x, k_0)*F_3(x))
Eq(F_187(x, k_0), F_188(x, k_0)*F_3(x))
Eq(F_188(x, k_0), F_1(x) + F_140(x) + F_184(x, k_0) + F_189(x, k_0) + F_195(x, k_0) + F_197(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_3(x))
Eq(F_190(x, k_0), (k_0*F_191(x, k_0) - F_191(x, 1))/(k_0 - 1))
Eq(F_191(x, k_0), F_1(x) + F_174(x, k_0) + F_175(x, k_0) + F_192(x) + F_193(x) + F_194(x))
Eq(F_192(x), F_117(x, 1))
Eq(F_193(x), F_155(x)*F_3(x))
Eq(F_194(x), F_3(x)*F_84(x))
Eq(F_195(x, k_0), F_196(x, k_0)*F_3(x))
Eq(F_196(x, k_0), (k_0*F_188(x, k_0) - F_188(x, 1))/(k_0 - 1))
Eq(F_197(x, k_0), F_198(x, k_0)*F_52(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_205(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_57(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_29(x))
Eq(F_201(x, k_0), F_202(x, k_0) + F_204(x, k_0) + F_36(x))
Eq(F_202(x, k_0), F_203(x, k_0)*F_3(x))
Eq(F_203(x, k_0), F_201(x, k_0) + F_55(x, k_0))
Eq(F_204(x, k_0), F_200(x, k_0)*F_52(x, k_0))
Eq(F_205(x, k_0), F_200(x, k_0) + F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0) + F_68(x))
Eq(F_207(x, k_0), F_208(x, k_0) + F_210(x, k_0) + 2*F_36(x))
Eq(F_208(x, k_0), F_209(x, k_0)*F_3(x))
Eq(F_209(x, k_0), F_201(x, k_0) + F_207(x, k_0))
Eq(F_210(x, k_0), F_206(x, k_0)*F_52(x, k_0))
Eq(F_211(x, k_0), F_191(x, k_0)*F_3(x))
Eq(F_212(x, k_0), F_185(x, k_0)*F_52(x, k_0))
Eq(F_213(x, k_0), F_199(x, k_0)*F_52(x, k_0))
Eq(F_214(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_215(x, k_0), F_216(x, k_0)*F_3(x))
Eq(F_216(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_217(x, k_0), F_218(x, k_0)*F_3(x))
Eq(F_218(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_219(x, k_0), F_179(x, k_0)*F_52(x, k_0))
Eq(F_220(x), F_221(x, 1))
Eq(F_221(x, k_0), F_222(x, k_0)*F_3(x))
Eq(F_222(x, k_0), F_1(x) + F_13(x) + F_213(x, k_0) + F_223(x, k_0) + F_224(x, k_0))
Eq(F_223(x, k_0), F_191(x, k_0)*F_3(x))
Eq(F_224(x, k_0), F_188(x, k_0)*F_3(x))
Eq(F_225(x), F_14(x)*F_3(x))
Eq(F_226(x), F_3(x)*F_8(x))
Eq(F_227(x), F_10(x)*F_3(x))
Eq(F_228(x), F_12(x)*F_3(x))
Eq(F_229(x), F_230(x)*F_3(x))
Eq(F_230(x), F_1(x) + F_231(x) + F_366(x) + F_367(x))
Eq(F_231(x), F_232(x, 1))
Eq(F_232(x, k_0), F_233(x, k_0)*F_52(x, k_0))
Eq(F_233(x, k_0), F_1(x) + F_232(x, k_0) + F_234(x, k_0) + F_237(x, k_0))
Eq(F_234(x, k_0), F_235(x, k_0)*F_3(x))
Eq(F_235(x, k_0), F_1(x) + F_126(x, k_0) + F_229(x) + F_236(x, k_0) + F_51(x, k_0))
Eq(F_236(x, k_0), F_3(x)*F_42(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0)*F_3(x))
Eq(F_238(x, k_0), F_1(x) + F_173(x, k_0) + F_239(x) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_239(x), F_240(x)*F_3(x))
Eq(F_240(x), F_1(x) + F_241(x) + F_254(x) + F_256(x))
Eq(F_241(x), F_242(x, 1))
Eq(F_242(x, k_0), F_243(x, k_0)*F_3(x))
Eq(F_243(x, k_0), F_244(x, k_0) + F_248(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0) + F_57(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0) + F_32(x))
Eq(F_246(x, k_0), F_247(x, k_0))
Eq(F_247(x, k_0), F_245(x, k_0)*F_52(x, k_0))
Eq(F_248(x, k_0), F_200(x, k_0) + F_249(x, k_0))
Eq(F_249(x, k_0), F_143(x) + F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0) + F_253(x, k_0) + 2*F_36(x))
Eq(F_251(x, k_0), F_252(x, k_0)*F_3(x))
Eq(F_252(x, k_0), F_246(x, k_0) + F_250(x, k_0))
Eq(F_253(x, k_0), F_249(x, k_0)*F_52(x, k_0))
Eq(F_254(x), F_255(x)*F_3(x))
Eq(F_255(x), F_185(x, 1))
Eq(F_256(x), F_257(x, 1))
Eq(F_257(x, k_0), F_258(x, k_0)*F_3(x))
Eq(F_258(x, k_0), (-k_0*F_259(x, k_0) + F_259(x, 1))/(1 - k_0))
Eq(F_259(x, k_0), F_1(x) + F_260(x, k_0) + F_261(x, k_0) + F_364(x, k_0))
Eq(F_260(x, k_0), F_259(x, k_0)*F_52(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0)*F_3(x))
Eq(F_262(x, k_0), F_1(x) + F_111(x, k_0) + F_120(x, k_0) + F_263(x) + F_338(x))
Eq(F_263(x), F_264(x)*F_3(x))
Eq(F_264(x), F_1(x) + F_239(x) + F_265(x) + F_276(x) + F_277(x))
Eq(F_265(x), F_266(x)*F_3(x))
Eq(F_266(x), F_1(x) + F_267(x) + F_268(x) + F_270(x) + F_273(x))
Eq(F_267(x), F_64(x, 1))
Eq(F_268(x), F_269(x)*F_3(x))
Eq(F_269(x), F_79(x, 1))
Eq(F_270(x), F_271(x)*F_3(x))
Eq(F_271(x), F_272(x, 1))
Eq(F_272(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_273(x), F_274(x)*F_3(x))
Eq(F_274(x), F_275(x, 1))
Eq(F_275(x, k_0), (-k_0*F_48(x, k_0) + F_48(x, 1))/(1 - k_0))
Eq(F_276(x), F_45(x, 1))
Eq(F_277(x), F_278(x)*F_3(x))
Eq(F_278(x), F_1(x) + F_267(x) + F_268(x) + F_279(x) + F_333(x) + F_336(x))
Eq(F_279(x), F_280(x)*F_3(x))
Eq(F_280(x), F_1(x) + F_267(x) + F_281(x) + F_320(x) + F_323(x) + F_327(x) + F_330(x))
Eq(F_281(x), F_282(x, 1))
Eq(F_282(x, k_0), F_283(x, k_0)*F_52(x, k_0))
Eq(F_283(x, k_0), F_284(x, k_0) + F_302(x, k_0))
Eq(F_284(x, k_0), F_285(x, k_0) + F_290(x, k_0))
Eq(F_285(x, k_0), F_28(x) + F_286(x, k_0))
Eq(F_286(x, k_0), F_287(x, k_0) + F_94(x, k_0))
Eq(F_287(x, k_0), F_288(x, k_0))
Eq(F_288(x, k_0), F_289(x, k_0)*F_52(x, k_0))
Eq(F_289(x, k_0), F_287(x, k_0) + F_29(x))
Eq(F_290(x, k_0), F_291(x, k_0) + F_31(x))
Eq(F_291(x, k_0), F_292(x, k_0) + F_297(x, k_0))
Eq(F_292(x, k_0), F_293(x, k_0) + F_295(x, k_0) + F_36(x))
Eq(F_293(x, k_0), F_294(x, k_0)*F_3(x))
Eq(F_294(x, k_0), F_292(x, k_0) + F_94(x, k_0))
Eq(F_295(x, k_0), F_296(x, k_0)*F_52(x, k_0))
Eq(F_296(x, k_0), F_292(x, k_0) + F_32(x))
Eq(F_297(x, k_0), F_298(x, k_0) + F_300(x, k_0) + 2*F_36(x))
Eq(F_298(x, k_0), F_299(x, k_0)*F_3(x))
Eq(F_299(x, k_0), F_287(x, k_0) + F_297(x, k_0))
Eq(F_300(x, k_0), F_301(x, k_0)*F_52(x, k_0))
Eq(F_301(x, k_0), F_297(x, k_0) + F_35(x))
Eq(F_302(x, k_0), F_290(x, k_0) + F_303(x, k_0))
Eq(F_303(x, k_0), F_304(x) + F_309(x, k_0))
Eq(F_304(x), F_305(x) + F_90(x))
Eq(F_305(x), F_306(x) + F_308(x) + 2*F_36(x))
Eq(F_306(x), F_3(x)*F_307(x))
Eq(F_307(x), F_305(x) + F_35(x))
Eq(F_308(x), F_3(x)*F_304(x))
Eq(F_309(x, k_0), F_310(x, k_0) + F_315(x, k_0))
Eq(F_310(x, k_0), F_311(x, k_0) + F_313(x, k_0) + 2*F_36(x))
Eq(F_311(x, k_0), F_3(x)*F_312(x, k_0))
Eq(F_312(x, k_0), F_292(x, k_0) + F_310(x, k_0))
Eq(F_313(x, k_0), F_314(x, k_0)*F_52(x, k_0))
Eq(F_314(x, k_0), F_310(x, k_0) + F_90(x))
Eq(F_315(x, k_0), F_316(x, k_0) + F_318(x, k_0) + 3*F_36(x))
Eq(F_316(x, k_0), F_3(x)*F_317(x, k_0))
Eq(F_317(x, k_0), F_297(x, k_0) + F_315(x, k_0))
Eq(F_318(x, k_0), F_319(x, k_0)*F_52(x, k_0))
Eq(F_319(x, k_0), F_305(x) + F_315(x, k_0))
Eq(F_320(x), F_321(x, 1))
Eq(F_321(x, k_0), F_3(x)*F_322(x, k_0))
Eq(F_322(x, k_0), (k_0*F_79(x, k_0) - F_79(x, 1))/(k_0 - 1))
Eq(F_323(x), F_3(x)*F_324(x))
Eq(F_324(x), F_325(x, 1))
Eq(F_325(x, k_0), (-k_0*F_326(x, k_0) + F_326(x, 1))/(1 - k_0))
Eq(F_326(x, k_0), (k_0*F_63(x, k_0) - F_63(x, 1))/(k_0 - 1))
Eq(F_327(x), F_3(x)*F_328(x))
Eq(F_328(x), F_329(x, 1))
Eq(F_329(x, k_0), (-k_0*F_169(x, k_0) + F_169(x, 1))/(1 - k_0))
Eq(F_330(x), F_3(x)*F_331(x))
Eq(F_331(x), F_332(x, 1))
Eq(F_332(x, k_0), (-k_0*F_171(x, k_0) + F_171(x, 1))/(1 - k_0))
Eq(F_333(x), F_3(x)*F_334(x))
Eq(F_334(x), F_335(x, 1))
Eq(F_335(x, k_0), (k_0*F_46(x, k_0) - F_46(x, 1))/(k_0 - 1))
Eq(F_336(x), F_3(x)*F_337(x))
Eq(F_337(x), F_171(x, 1))
Eq(F_338(x), F_3(x)*F_339(x))
Eq(F_339(x), F_1(x) + F_340(x) + F_341(x) + F_342(x) + F_362(x))
Eq(F_340(x), F_177(x, 1))
Eq(F_341(x), F_178(x, 1))
Eq(F_342(x), F_3(x)*F_343(x))
Eq(F_343(x), F_1(x) + F_241(x) + F_254(x) + F_344(x) + F_351(x))
Eq(F_344(x), F_345(x, 1))
Eq(F_345(x, k_0), F_3(x)*F_346(x, k_0))
Eq(F_346(x, k_0), F_1(x) + F_192(x) + F_229(x) + F_347(x, k_0) + F_349(x, k_0) + F_350(x, k_0))
Eq(F_347(x, k_0), F_348(x, k_0)*F_52(x, k_0))
Eq(F_348(x, k_0), (-k_0*F_116(x, k_0) + F_116(x, 1))/(1 - k_0))
Eq(F_349(x, k_0), F_151(x, k_0)*F_3(x))
Eq(F_350(x, k_0), F_149(x, k_0)*F_3(x))
Eq(F_351(x), F_352(x, 1))
Eq(F_352(x, k_0), F_3(x)*F_353(x, k_0))
Eq(F_353(x, k_0), F_1(x) + F_113(x, k_0) + F_136(x, k_0) + F_138(x, k_0) + F_239(x) + F_354(x, k_0))
Eq(F_354(x, k_0), F_3(x)*F_355(x, k_0))
Eq(F_355(x, k_0), F_141(x) + F_356(x, k_0))
Eq(F_356(x, k_0), F_357(x, k_0) + F_93(x, k_0))
Eq(F_357(x, k_0), F_287(x, k_0) + F_358(x, k_0))
Eq(F_358(x, k_0), F_359(x, k_0) + 2*F_36(x) + F_361(x, k_0))
Eq(F_359(x, k_0), F_360(x, k_0)*F_52(x, k_0))
Eq(F_360(x, k_0), F_143(x) + F_358(x, k_0))
Eq(F_361(x, k_0), F_3(x)*F_357(x, k_0))
Eq(F_362(x), F_3(x)*F_363(x))
Eq(F_363(x), F_262(x, 1))
Eq(F_364(x, k_0), F_3(x)*F_365(x, k_0))
Eq(F_365(x, k_0), F_1(x) + F_106(x, k_0) + F_345(x, k_0) + F_352(x, k_0) + F_86(x, k_0))
Eq(F_366(x), F_234(x, 1))
Eq(F_367(x), F_237(x, 1))
Eq(F_368(x), F_3(x)*F_369(x))
Eq(F_369(x), F_1(x) + F_239(x) + F_370(x) + F_376(x))
Eq(F_370(x), F_3(x)*F_371(x))
Eq(F_371(x), F_1(x) + F_228(x) + F_372(x) + F_374(x) + F_7(x))
Eq(F_372(x), F_373(x, 1))
Eq(F_373(x, k_0), F_3(x)*F_44(x, k_0))
Eq(F_374(x), F_3(x)*F_375(x))
Eq(F_375(x), F_176(x, 1))
Eq(F_376(x), F_3(x)*F_377(x))
Eq(F_377(x), F_1(x) + F_129(x) + F_130(x) + F_132(x) + F_9(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], 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[0, 6]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 6]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 6]]}, {"patt": [0, 1], "pos": [[0, 6], [0, 6]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 5], [0, 5]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 5], [0, 5]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 5]]}, {"patt": [1, 0, 2], "pos": [[0, 5], [0, 5], [0, 6]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 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[0, 1], [0, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 4], [0, 2], [0, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 5], [0, 5], [0, 4], [0, 5]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 5], [0, 6], [0, 4], [0, 5]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 5], [0, 6], [0, 5], [0, 5]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 0, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 4
Strategy pack name: col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/218/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[290,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[183,x]+F[217,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[166,x,k[0]]+F[265,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[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[254,x,k[0]]+F[264,x,k[0]]
F[15,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[16,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[18,x]+F[230,x,k[0]]+F[232,x,k[0]]+F[252,x]+F[253,x,k[0]]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[22,x,k[0]]+F[66,x]
F[22,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[144,x,k[0]]+F[24,x,k[0]]+F[251,x,k[0]]+F[38,x,k[0]]
F[24,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[11,x]*F[26,x]
F[29,x,k[0]] = F[30,x,k[0]]+F[33,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[20,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[1,x]+F[30,x,k[0]]
F[33,x,k[0]] = F[34,x]+F[35,x,k[0]]+F[37,x,k[0]]
F[34,x] = 0
F[35,x,k[0]] = F[20,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[27,x]+F[33,x,k[0]]
F[37,x,k[0]] = F[11,x]*F[29,x,k[0]]
F[38,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[39,x,k[0]] = F[1,x]+F[245,x,k[0]]+F[247,x,k[0]]+F[249,x,k[0]]+F[40,x,k[0]]+F[52,x,k[0]]
F[40,x,k[0]] = F[20,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x]+F[46,x,k[0]]
F[42,x] = F[26,x]+F[43,x]
F[43,x] = F[27,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[11,x]*F[43,x]
F[46,x,k[0]] = F[29,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[33,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = 2*F[34,x]+F[49,x,k[0]]+F[51,x,k[0]]
F[49,x,k[0]] = F[20,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = F[44,x]+F[48,x,k[0]]
F[51,x,k[0]] = F[11,x]*F[47,x,k[0]]
F[52,x,k[0]] = F[11,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[1,x]+F[238,x,k[0]]+F[244,x,k[0]]+F[54,x,k[0]]+F[55,x,k[0]]
F[54,x,k[0]] = F[20,x,k[0]]*F[53,x,k[0]]
F[55,x,k[0]] = F[11,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[22,x,k[0]]+F[229,x]+F[231,x]+F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[1,x]+F[181,x]+F[182,x]+F[183,x]+F[217,x]+F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[61,x,1]
F[61,x,k[0]] = 1/(-1+k[0])*(F[62,x,k[0]]*k[0]-F[62,x,1])
F[62,x,k[0]] = F[1,x]+F[158,x,k[0]]+F[180,x,k[0]]+F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[64,x,k[0]] = F[11,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[1,x]+F[117,x,k[0]]+F[119,x,k[0]]+F[146,x]+F[66,x]+F[76,x]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[1,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[11,x]*F[68,x]
F[71,x] = F[27,x]+F[72,x]
F[72,x] = F[34,x]+F[73,x]+F[75,x]
F[73,x] = F[11,x]*F[74,x]
F[74,x] = F[69,x]+F[72,x]
F[75,x] = F[11,x]*F[71,x]
F[76,x] = F[77,x,1]
F[77,x,k[0]] = F[11,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[154,x,k[0]]+F[156,x,k[0]]+F[66,x]+F[79,x,k[0]]
F[79,x,k[0]] = F[20,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[81,x]+F[86,x,k[0]]
F[81,x] = F[68,x]+F[82,x]
F[82,x] = F[69,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[69,x]+F[83,x]
F[86,x,k[0]] = F[87,x,k[0]]+F[95,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[91,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[20,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[1,x]+F[88,x,k[0]]
F[91,x,k[0]] = F[34,x]+F[92,x,k[0]]+F[94,x,k[0]]
F[92,x,k[0]] = F[20,x,k[0]]*F[93,x,k[0]]
F[93,x,k[0]] = F[69,x]+F[91,x,k[0]]
F[94,x,k[0]] = F[11,x]*F[87,x,k[0]]
F[95,x,k[0]] = F[91,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = 2*F[34,x]+F[97,x,k[0]]+F[99,x,k[0]]
F[97,x,k[0]] = F[20,x,k[0]]*F[98,x,k[0]]
F[98,x,k[0]] = F[83,x]+F[96,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[100,x,k[0]] = F[91,x,k[0]]+F[96,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[1,x]+F[103,x,k[0]]+F[104,x,k[0]]+F[152,x,k[0]]+F[153,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[20,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[105,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[141,x,k[0]]+F[142,x]+F[143,x]+F[150,x]
F[106,x,k[0]] = F[107,x,k[0]]*F[20,x,k[0]]
F[107,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[110,x,k[0]]+F[140,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[20,x,k[0]]
F[109,x,k[0]] = F[68,x]+F[87,x,k[0]]
F[110,x,k[0]] = F[11,x]*F[111,x,k[0]]
F[111,x,k[0]] = F[1,x]+F[112,x,k[0]]+F[113,x,k[0]]+F[121,x,k[0]]+F[133,x]
F[112,x,k[0]] = F[111,x,k[0]]*F[20,x,k[0]]
F[113,x,k[0]] = F[11,x]*F[114,x,k[0]]
F[114,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[115,x,k[0]]+F[116,x]+F[118,x]+F[77,x,k[0]]
F[115,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[116,x] = F[117,x,1]
F[117,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[118,x] = F[119,x,1]
F[119,x,k[0]] = F[120,x,k[0]]*F[20,x,k[0]]
F[120,x,k[0]] = F[1,x]+F[117,x,k[0]]+F[119,x,k[0]]+F[66,x]
F[121,x,k[0]] = F[11,x]*F[122,x,k[0]]
F[122,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[123,x,k[0]]+F[125,x,k[0]]+F[127,x,k[0]]+F[79,x,k[0]]
F[123,x,k[0]] = F[11,x]*F[124,x,k[0]]
F[124,x,k[0]] = (F[122,x,k[0]]*k[0]-F[122,x,1])/(-1+k[0])
F[125,x,k[0]] = F[11,x]*F[126,x,k[0]]
F[126,x,k[0]] = (F[114,x,k[0]]*k[0]-F[114,x,1])/(-1+k[0])
F[127,x,k[0]] = F[11,x]*F[128,x,k[0]]
F[128,x,k[0]] = (F[129,x,k[0]]*k[0]-F[129,x,1])/(-1+k[0])
F[129,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[130,x,k[0]]+F[131,x,k[0]]+F[132,x,k[0]]
F[130,x,k[0]] = F[11,x]*F[122,x,k[0]]
F[131,x,k[0]] = F[11,x]*F[114,x,k[0]]
F[132,x,k[0]] = F[11,x]*F[129,x,k[0]]
F[133,x] = F[11,x]*F[134,x]
F[134,x] = F[135,x]+F[26,x]
F[135,x] = F[136,x]+F[69,x]
F[136,x] = F[137,x]+F[139,x]+F[34,x]
F[137,x] = F[11,x]*F[138,x]
F[138,x] = F[136,x]+F[27,x]
F[139,x] = F[11,x]*F[135,x]
F[140,x,k[0]] = F[107,x,k[0]]*F[11,x]
F[141,x,k[0]] = F[11,x]*F[129,x,k[0]]
F[142,x] = F[38,x,1]
F[143,x] = F[144,x,1]
F[144,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[145,x,k[0]] = F[1,x]+F[146,x]+F[19,x,k[0]]+F[22,x,k[0]]+F[66,x]+F[76,x]
F[146,x] = F[11,x]*F[147,x]
F[147,x] = F[1,x]+F[142,x]+F[143,x]+F[148,x]+F[149,x]+F[150,x]
F[148,x] = F[106,x,1]
F[149,x] = F[141,x,1]
F[150,x] = F[11,x]*F[151,x]
F[151,x] = F[23,x,1]
F[152,x,k[0]] = F[11,x]*F[78,x,k[0]]
F[153,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[154,x,k[0]] = F[11,x]*F[155,x,k[0]]
F[155,x,k[0]] = (F[78,x,k[0]]*k[0]-F[78,x,1])/(-1+k[0])
F[156,x,k[0]] = F[11,x]*F[157,x,k[0]]
F[157,x,k[0]] = (F[105,x,k[0]]*k[0]-F[105,x,1])/(-1+k[0])
F[158,x,k[0]] = F[11,x]*F[159,x,k[0]]
F[159,x,k[0]] = F[1,x]+F[160,x,k[0]]+F[161,x,k[0]]+F[163,x,k[0]]+F[165,x,k[0]]+F[166,x,k[0]]
F[160,x,k[0]] = F[11,x]*F[61,x,k[0]]
F[161,x,k[0]] = F[11,x]*F[162,x,k[0]]
F[162,x,k[0]] = 1/(-1+k[0])*(F[65,x,k[0]]*k[0]-F[65,x,1])
F[163,x,k[0]] = F[11,x]*F[164,x,k[0]]
F[164,x,k[0]] = 1/(-1+k[0])*(F[159,x,k[0]]*k[0]-F[159,x,1])
F[165,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[20,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[174,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]+F[90,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]+F[69,x]
F[170,x,k[0]] = F[171,x,k[0]]+F[173,x,k[0]]+F[34,x]
F[171,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[172,x,k[0]] = F[170,x,k[0]]+F[88,x,k[0]]
F[173,x,k[0]] = F[169,x,k[0]]*F[20,x,k[0]]
F[174,x,k[0]] = F[169,x,k[0]]+F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[83,x]
F[176,x,k[0]] = 2*F[34,x]+F[177,x,k[0]]+F[179,x,k[0]]
F[177,x,k[0]] = F[11,x]*F[178,x,k[0]]
F[178,x,k[0]] = F[170,x,k[0]]+F[176,x,k[0]]
F[179,x,k[0]] = F[175,x,k[0]]*F[20,x,k[0]]
F[180,x,k[0]] = F[168,x,k[0]]*F[20,x,k[0]]
F[181,x] = F[161,x,1]
F[182,x] = F[163,x,1]
F[183,x] = F[11,x]*F[184,x]
F[184,x] = F[1,x]+F[185,x]+F[200,x]+F[201,x]+F[204,x]
F[185,x] = F[186,x,1]
F[186,x,k[0]] = F[187,x,k[0]]*F[20,x,k[0]]
F[187,x,k[0]] = F[188,x]+F[193,x,k[0]]
F[188,x] = F[189,x]+F[42,x]
F[189,x] = F[190,x]+F[43,x]
F[190,x] = F[191,x]+F[44,x]
F[191,x] = F[192,x]
F[192,x] = F[11,x]*F[190,x]
F[193,x,k[0]] = F[194,x,k[0]]+F[46,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]+F[47,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]+F[48,x,k[0]]
F[196,x,k[0]] = 3*F[34,x]+F[197,x,k[0]]+F[199,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]*F[20,x,k[0]]
F[198,x,k[0]] = F[191,x]+F[196,x,k[0]]
F[199,x,k[0]] = F[11,x]*F[195,x,k[0]]
F[200,x] = F[12,x,1]
F[201,x] = F[202,x,1]
F[202,x,k[0]] = F[11,x]*F[203,x,k[0]]
F[203,x,k[0]] = (F[53,x,k[0]]*k[0]-F[53,x,1])/(-1+k[0])
F[204,x] = F[205,x,1]
F[205,x,k[0]] = F[20,x,k[0]]*F[206,x,k[0]]
F[206,x,k[0]] = F[167,x,k[0]]+F[207,x,k[0]]
F[207,x,k[0]] = F[174,x,k[0]]+F[208,x,k[0]]
F[208,x,k[0]] = F[175,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = F[210,x]+F[213,x,k[0]]
F[210,x] = F[211,x]
F[211,x] = F[11,x]*F[212,x]
F[212,x] = F[210,x]+F[83,x]
F[213,x,k[0]] = 3*F[34,x]+F[214,x,k[0]]+F[216,x,k[0]]
F[214,x,k[0]] = F[11,x]*F[215,x,k[0]]
F[215,x,k[0]] = F[176,x,k[0]]+F[213,x,k[0]]
F[216,x,k[0]] = F[20,x,k[0]]*F[209,x,k[0]]
F[217,x] = F[218,x,1]
F[218,x,k[0]] = F[11,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[134,x]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]+F[29,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]+F[225,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[20,x,k[0]]*F[224,x,k[0]]
F[224,x,k[0]] = F[222,x,k[0]]+F[69,x]
F[225,x,k[0]] = 2*F[34,x]+F[226,x,k[0]]+F[228,x,k[0]]
F[226,x,k[0]] = F[20,x,k[0]]*F[227,x,k[0]]
F[227,x,k[0]] = F[136,x]+F[225,x,k[0]]
F[228,x,k[0]] = F[11,x]*F[221,x,k[0]]
F[229,x] = F[230,x,1]
F[230,x,k[0]] = F[11,x]*F[65,x,k[0]]
F[231,x] = F[232,x,1]
F[232,x,k[0]] = F[20,x,k[0]]*F[233,x,k[0]]
F[233,x,k[0]] = F[1,x]+F[165,x,k[0]]+F[166,x,k[0]]+F[234,x,k[0]]+F[236,x,k[0]]
F[234,x,k[0]] = F[11,x]*F[235,x,k[0]]
F[235,x,k[0]] = 1/(-1+k[0])*(F[120,x,k[0]]*k[0]-F[120,x,1])
F[236,x,k[0]] = F[11,x]*F[237,x,k[0]]
F[237,x,k[0]] = 1/(-1+k[0])*(F[233,x,k[0]]*k[0]-F[233,x,1])
F[238,x,k[0]] = F[11,x]*F[239,x,k[0]]
F[239,x,k[0]] = F[1,x]+F[133,x]+F[240,x,k[0]]+F[242,x,k[0]]+F[40,x,k[0]]+F[52,x,k[0]]
F[240,x,k[0]] = F[11,x]*F[241,x,k[0]]
F[241,x,k[0]] = (F[239,x,k[0]]*k[0]-F[239,x,1])/(-1+k[0])
F[242,x,k[0]] = F[11,x]*F[243,x,k[0]]
F[243,x,k[0]] = (F[56,x,k[0]]*k[0]-F[56,x,1])/(-1+k[0])
F[244,x,k[0]] = F[11,x]*F[53,x,k[0]]
F[245,x,k[0]] = F[11,x]*F[246,x,k[0]]
F[246,x,k[0]] = (F[39,x,k[0]]*k[0]-F[39,x,1])/(-1+k[0])
F[247,x,k[0]] = F[11,x]*F[248,x,k[0]]
F[248,x,k[0]] = (F[145,x,k[0]]*k[0]-F[145,x,1])/(-1+k[0])
F[249,x,k[0]] = F[11,x]*F[250,x,k[0]]
F[250,x,k[0]] = (F[23,x,k[0]]*k[0]-F[23,x,1])/(-1+k[0])
F[251,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[252,x] = F[11,x]*F[151,x]
F[253,x,k[0]] = F[11,x]*F[159,x,k[0]]
F[254,x,k[0]] = F[11,x]*F[255,x,k[0]]
F[255,x,k[0]] = F[1,x]+F[117,x,k[0]]+F[119,x,k[0]]+F[256,x]+F[261,x]+F[262,x]
F[256,x] = F[257,x,1]
F[257,x,k[0]] = F[20,x,k[0]]*F[258,x,k[0]]
F[258,x,k[0]] = F[1,x]+F[257,x,k[0]]+F[259,x,k[0]]+F[260,x,k[0]]+F[66,x]
F[259,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[260,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[261,x] = F[259,x,1]
F[262,x] = F[11,x]*F[263,x]
F[263,x] = F[39,x,1]
F[264,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[265,x,k[0]] = F[11,x]*F[266,x,k[0]]
F[266,x,k[0]] = F[267,x,k[0]]+F[278,x,k[0]]
F[267,x,k[0]] = F[268,x,k[0]]+F[272,x,k[0]]
F[268,x,k[0]] = F[269,x,k[0]]+F[90,x,k[0]]
F[269,x,k[0]] = F[27,x]+F[270,x,k[0]]
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[20,x,k[0]]*F[269,x,k[0]]
F[272,x,k[0]] = F[169,x,k[0]]+F[273,x,k[0]]
F[273,x,k[0]] = F[136,x]+F[274,x,k[0]]
F[274,x,k[0]] = 2*F[34,x]+F[275,x,k[0]]+F[277,x,k[0]]
F[275,x,k[0]] = F[11,x]*F[276,x,k[0]]
F[276,x,k[0]] = F[270,x,k[0]]+F[274,x,k[0]]
F[277,x,k[0]] = F[20,x,k[0]]*F[273,x,k[0]]
F[278,x,k[0]] = F[272,x,k[0]]+F[279,x,k[0]]
F[279,x,k[0]] = F[175,x,k[0]]+F[280,x,k[0]]
F[280,x,k[0]] = F[281,x]+F[286,x,k[0]]
F[281,x] = 2*F[34,x]+F[282,x]+F[284,x]
F[282,x] = F[11,x]*F[283,x]
F[283,x] = F[136,x]+F[281,x]
F[284,x] = F[11,x]*F[285,x]
F[285,x] = F[281,x]+F[83,x]
F[286,x,k[0]] = 3*F[34,x]+F[287,x,k[0]]+F[289,x,k[0]]
F[287,x,k[0]] = F[11,x]*F[288,x,k[0]]
F[288,x,k[0]] = F[274,x,k[0]]+F[286,x,k[0]]
F[289,x,k[0]] = F[20,x,k[0]]*F[280,x,k[0]]
F[290,x] = F[11,x]*F[291,x]
F[291,x] = F[292,x,1]
F[292,x,k[0]] = F[1,x]+F[293,x,k[0]]+F[40,x,k[0]]+F[52,x,k[0]]
F[293,x,k[0]] = F[11,x]*F[294,x,k[0]]
F[294,x,k[0]] = (F[292,x,k[0]]*k[0]-F[292,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{290}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{183}\! \left(x \right)+F_{217}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{265}\! \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_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{254}\! \left(x , y\right)+F_{264}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)+F_{230}\! \left(x , y\right)+F_{232}\! \left(x , y\right)+F_{252}\! \left(x \right)+F_{253}\! \left(x , y\right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{251}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{245}\! \left(x , y\right)+F_{247}\! \left(x , y\right)+F_{249}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{26}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{238}\! \left(x , y\right)+F_{244}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{229}\! \left(x \right)+F_{231}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{181}\! \left(x \right)+F_{182}\! \left(x \right)+F_{183}\! \left(x \right)+F_{217}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x , 1\right)
F_{61}\! \left(x , y\right) = -\frac{-y F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}
F_{62}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{158}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{146}\! \left(x \right)+F_{66}\! \left(x \right)+F_{76}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{27}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{34}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{77}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{156}\! \left(x , y\right)+F_{66}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{81}\! \left(x \right) = F_{68}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{69}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{69}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{69}\! \left(x \right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{83}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{152}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{141}\! \left(x , y\right)+F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{150}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{68}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)+F_{121}\! \left(x , y\right)+F_{133}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{118}\! \left(x \right) = F_{119}\! \left(x , 1\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{127}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = -\frac{-y F_{122}\! \left(x , y\right)+F_{122}\! \left(x , 1\right)}{-1+y}
F_{125}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = -\frac{-y F_{114}\! \left(x , y\right)+F_{114}\! \left(x , 1\right)}{-1+y}
F_{127}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = -\frac{-y F_{129}\! \left(x , y\right)+F_{129}\! \left(x , 1\right)}{-1+y}
F_{129}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{114}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{129}\! \left(x , y\right)
F_{133}\! \left(x \right) = F_{11}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{26}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{69}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{139}\! \left(x \right)+F_{34}\! \left(x \right)
F_{137}\! \left(x \right) = F_{11}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{136}\! \left(x \right)+F_{27}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right) F_{135}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{129}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{143}\! \left(x \right) = F_{144}\! \left(x , 1\right)
F_{144}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{146}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{66}\! \left(x \right)+F_{76}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{1}\! \left(x \right)+F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{148}\! \left(x \right)+F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{148}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{149}\! \left(x \right) = F_{141}\! \left(x , 1\right)
F_{150}\! \left(x \right) = F_{11}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{152}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{156}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{158}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{163}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = -\frac{-y F_{65}\! \left(x , y\right)+F_{65}\! \left(x , 1\right)}{-1+y}
F_{163}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = -\frac{-y F_{159}\! \left(x , y\right)+F_{159}\! \left(x , 1\right)}{-1+y}
F_{165}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{69}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{173}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{83}\! \left(x \right)
F_{176}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{181}\! \left(x \right) = F_{161}\! \left(x , 1\right)
F_{182}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{183}\! \left(x \right) = F_{11}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{1}\! \left(x \right)+F_{185}\! \left(x \right)+F_{200}\! \left(x \right)+F_{201}\! \left(x \right)+F_{204}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x , 1\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x \right)+F_{193}\! \left(x , y\right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{42}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{43}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{44}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{11}\! \left(x \right) F_{190}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{197}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{191}\! \left(x \right)+F_{196}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{195}\! \left(x , y\right)
F_{200}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{201}\! \left(x \right) = F_{202}\! \left(x , 1\right)
F_{202}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{204}\! \left(x \right) = F_{205}\! \left(x , 1\right)
F_{205}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x \right)+F_{213}\! \left(x , y\right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{11}\! \left(x \right) F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{210}\! \left(x \right)+F_{83}\! \left(x \right)
F_{213}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{214}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{209}\! \left(x , y\right)
F_{217}\! \left(x \right) = F_{218}\! \left(x , 1\right)
F_{218}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{134}\! \left(x \right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{69}\! \left(x \right)
F_{225}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{226}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{225}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{221}\! \left(x , y\right)
F_{229}\! \left(x \right) = F_{230}\! \left(x , 1\right)
F_{230}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{231}\! \left(x \right) = F_{232}\! \left(x , 1\right)
F_{232}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{234}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = -\frac{-y F_{120}\! \left(x , y\right)+F_{120}\! \left(x , 1\right)}{-1+y}
F_{236}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = -\frac{-y F_{233}\! \left(x , y\right)+F_{233}\! \left(x , 1\right)}{-1+y}
F_{238}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)+F_{240}\! \left(x , y\right)+F_{242}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = -\frac{-y F_{239}\! \left(x , y\right)+F_{239}\! \left(x , 1\right)}{-1+y}
F_{242}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = -\frac{-y F_{56}\! \left(x , y\right)+F_{56}\! \left(x , 1\right)}{-1+y}
F_{244}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{247}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = -\frac{-y F_{145}\! \left(x , y\right)+F_{145}\! \left(x , 1\right)}{-1+y}
F_{249}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}
F_{251}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{252}\! \left(x \right) = F_{11}\! \left(x \right) F_{151}\! \left(x \right)
F_{253}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{159}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{256}\! \left(x \right)+F_{261}\! \left(x \right)+F_{262}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x , 1\right)
F_{257}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{258}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{257}\! \left(x , y\right)+F_{259}\! \left(x , y\right)+F_{260}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{259}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{261}\! \left(x \right) = F_{259}\! \left(x , 1\right)
F_{262}\! \left(x \right) = F_{11}\! \left(x \right) F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{264}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{266}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{267}\! \left(x , y\right)+F_{278}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{268}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{269}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{270}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{269}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{274}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{275}\! \left(x , y\right)+F_{277}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{273}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{272}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{281}\! \left(x \right)+F_{286}\! \left(x , y\right)
F_{281}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{282}\! \left(x \right)+F_{284}\! \left(x \right)
F_{282}\! \left(x \right) = F_{11}\! \left(x \right) F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{136}\! \left(x \right)+F_{281}\! \left(x \right)
F_{284}\! \left(x \right) = F_{11}\! \left(x \right) F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{281}\! \left(x \right)+F_{83}\! \left(x \right)
F_{286}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{287}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{288}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{286}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{280}\! \left(x , y\right)
F_{290}\! \left(x \right) = F_{11}\! \left(x \right) F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x , 1\right)
F_{292}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{293}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{294}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = -\frac{-y F_{292}\! \left(x , y\right)+F_{292}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_290(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_183(x) + F_217(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_166(x, k_0) + F_265(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_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_254(x, k_0) + F_264(x, k_0))
Eq(F_15(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_16(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x) + F_230(x, k_0) + F_232(x, k_0) + F_252(x) + F_253(x, k_0))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_1(x) + F_19(x, k_0) + F_22(x, k_0) + F_66(x))
Eq(F_22(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_144(x, k_0) + F_24(x, k_0) + F_251(x, k_0) + F_38(x, k_0))
Eq(F_24(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_11(x)*F_26(x))
Eq(F_29(x, k_0), F_30(x, k_0) + F_33(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_20(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_1(x) + F_30(x, k_0))
Eq(F_33(x, k_0), F_34(x) + F_35(x, k_0) + F_37(x, k_0))
Eq(F_34(x), 0)
Eq(F_35(x, k_0), F_20(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_27(x) + F_33(x, k_0))
Eq(F_37(x, k_0), F_11(x)*F_29(x, k_0))
Eq(F_38(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_39(x, k_0), F_1(x) + F_245(x, k_0) + F_247(x, k_0) + F_249(x, k_0) + F_40(x, k_0) + F_52(x, k_0))
Eq(F_40(x, k_0), F_20(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x) + F_46(x, k_0))
Eq(F_42(x), F_26(x) + F_43(x))
Eq(F_43(x), F_27(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_11(x)*F_43(x))
Eq(F_46(x, k_0), F_29(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_33(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), 2*F_34(x) + F_49(x, k_0) + F_51(x, k_0))
Eq(F_49(x, k_0), F_20(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), F_44(x) + F_48(x, k_0))
Eq(F_51(x, k_0), F_11(x)*F_47(x, k_0))
Eq(F_52(x, k_0), F_11(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_1(x) + F_238(x, k_0) + F_244(x, k_0) + F_54(x, k_0) + F_55(x, k_0))
Eq(F_54(x, k_0), F_20(x, k_0)*F_53(x, k_0))
Eq(F_55(x, k_0), F_11(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_19(x, k_0) + F_22(x, k_0) + F_229(x) + F_231(x) + F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_181(x) + F_182(x) + F_183(x) + F_217(x) + F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_61(x, 1))
Eq(F_61(x, k_0), (k_0*F_62(x, k_0) - F_62(x, 1))/(k_0 - 1))
Eq(F_62(x, k_0), F_1(x) + F_158(x, k_0) + F_180(x, k_0) + F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_64(x, k_0), F_11(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_1(x) + F_117(x, k_0) + F_119(x, k_0) + F_146(x) + F_66(x) + F_76(x))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_1(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_11(x)*F_68(x))
Eq(F_71(x), F_27(x) + F_72(x))
Eq(F_72(x), F_34(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_11(x)*F_74(x))
Eq(F_74(x), F_69(x) + F_72(x))
Eq(F_75(x), F_11(x)*F_71(x))
Eq(F_76(x), F_77(x, 1))
Eq(F_77(x, k_0), F_11(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_1(x) + F_101(x, k_0) + F_154(x, k_0) + F_156(x, k_0) + F_66(x) + F_79(x, k_0))
Eq(F_79(x, k_0), F_20(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x) + F_86(x, k_0))
Eq(F_81(x), F_68(x) + F_82(x))
Eq(F_82(x), F_69(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_69(x) + F_83(x))
Eq(F_86(x, k_0), F_87(x, k_0) + F_95(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_91(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_20(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_1(x) + F_88(x, k_0))
Eq(F_91(x, k_0), F_34(x) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_92(x, k_0), F_20(x, k_0)*F_93(x, k_0))
Eq(F_93(x, k_0), F_69(x) + F_91(x, k_0))
Eq(F_94(x, k_0), F_11(x)*F_87(x, k_0))
Eq(F_95(x, k_0), F_91(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), 2*F_34(x) + F_97(x, k_0) + F_99(x, k_0))
Eq(F_97(x, k_0), F_20(x, k_0)*F_98(x, k_0))
Eq(F_98(x, k_0), F_83(x) + F_96(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_100(x, k_0), F_91(x, k_0) + F_96(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_1(x) + F_103(x, k_0) + F_104(x, k_0) + F_152(x, k_0) + F_153(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_20(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_11(x))
Eq(F_105(x, k_0), F_1(x) + F_106(x, k_0) + F_141(x, k_0) + F_142(x) + F_143(x) + F_150(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_20(x, k_0))
Eq(F_107(x, k_0), F_1(x) + F_108(x, k_0) + F_110(x, k_0) + F_140(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_20(x, k_0))
Eq(F_109(x, k_0), F_68(x) + F_87(x, k_0))
Eq(F_110(x, k_0), F_11(x)*F_111(x, k_0))
Eq(F_111(x, k_0), F_1(x) + F_112(x, k_0) + F_113(x, k_0) + F_121(x, k_0) + F_133(x))
Eq(F_112(x, k_0), F_111(x, k_0)*F_20(x, k_0))
Eq(F_113(x, k_0), F_11(x)*F_114(x, k_0))
Eq(F_114(x, k_0), F_1(x) + F_108(x, k_0) + F_115(x, k_0) + F_116(x) + F_118(x) + F_77(x, k_0))
Eq(F_115(x, k_0), F_105(x, k_0)*F_11(x))
Eq(F_116(x), F_117(x, 1))
Eq(F_117(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_118(x), F_119(x, 1))
Eq(F_119(x, k_0), F_120(x, k_0)*F_20(x, k_0))
Eq(F_120(x, k_0), F_1(x) + F_117(x, k_0) + F_119(x, k_0) + F_66(x))
Eq(F_121(x, k_0), F_11(x)*F_122(x, k_0))
Eq(F_122(x, k_0), F_1(x) + F_101(x, k_0) + F_123(x, k_0) + F_125(x, k_0) + F_127(x, k_0) + F_79(x, k_0))
Eq(F_123(x, k_0), F_11(x)*F_124(x, k_0))
Eq(F_124(x, k_0), (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_125(x, k_0), F_11(x)*F_126(x, k_0))
Eq(F_126(x, k_0), (-k_0*F_114(x, k_0) + F_114(x, 1))/(1 - k_0))
Eq(F_127(x, k_0), F_11(x)*F_128(x, k_0))
Eq(F_128(x, k_0), (-k_0*F_129(x, k_0) + F_129(x, 1))/(1 - k_0))
Eq(F_129(x, k_0), F_1(x) + F_108(x, k_0) + F_130(x, k_0) + F_131(x, k_0) + F_132(x, k_0))
Eq(F_130(x, k_0), F_11(x)*F_122(x, k_0))
Eq(F_131(x, k_0), F_11(x)*F_114(x, k_0))
Eq(F_132(x, k_0), F_11(x)*F_129(x, k_0))
Eq(F_133(x), F_11(x)*F_134(x))
Eq(F_134(x), F_135(x) + F_26(x))
Eq(F_135(x), F_136(x) + F_69(x))
Eq(F_136(x), F_137(x) + F_139(x) + F_34(x))
Eq(F_137(x), F_11(x)*F_138(x))
Eq(F_138(x), F_136(x) + F_27(x))
Eq(F_139(x), F_11(x)*F_135(x))
Eq(F_140(x, k_0), F_107(x, k_0)*F_11(x))
Eq(F_141(x, k_0), F_11(x)*F_129(x, k_0))
Eq(F_142(x), F_38(x, 1))
Eq(F_143(x), F_144(x, 1))
Eq(F_144(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_145(x, k_0), F_1(x) + F_146(x) + F_19(x, k_0) + F_22(x, k_0) + F_66(x) + F_76(x))
Eq(F_146(x), F_11(x)*F_147(x))
Eq(F_147(x), F_1(x) + F_142(x) + F_143(x) + F_148(x) + F_149(x) + F_150(x))
Eq(F_148(x), F_106(x, 1))
Eq(F_149(x), F_141(x, 1))
Eq(F_150(x), F_11(x)*F_151(x))
Eq(F_151(x), F_23(x, 1))
Eq(F_152(x, k_0), F_11(x)*F_78(x, k_0))
Eq(F_153(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_154(x, k_0), F_11(x)*F_155(x, k_0))
Eq(F_155(x, k_0), (-k_0*F_78(x, k_0) + F_78(x, 1))/(1 - k_0))
Eq(F_156(x, k_0), F_11(x)*F_157(x, k_0))
Eq(F_157(x, k_0), (-k_0*F_105(x, k_0) + F_105(x, 1))/(1 - k_0))
Eq(F_158(x, k_0), F_11(x)*F_159(x, k_0))
Eq(F_159(x, k_0), F_1(x) + F_160(x, k_0) + F_161(x, k_0) + F_163(x, k_0) + F_165(x, k_0) + F_166(x, k_0))
Eq(F_160(x, k_0), F_11(x)*F_61(x, k_0))
Eq(F_161(x, k_0), F_11(x)*F_162(x, k_0))
Eq(F_162(x, k_0), (k_0*F_65(x, k_0) - F_65(x, 1))/(k_0 - 1))
Eq(F_163(x, k_0), F_11(x)*F_164(x, k_0))
Eq(F_164(x, k_0), (k_0*F_159(x, k_0) - F_159(x, 1))/(k_0 - 1))
Eq(F_165(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_20(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_174(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0) + F_90(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_69(x))
Eq(F_170(x, k_0), F_171(x, k_0) + F_173(x, k_0) + F_34(x))
Eq(F_171(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_172(x, k_0), F_170(x, k_0) + F_88(x, k_0))
Eq(F_173(x, k_0), F_169(x, k_0)*F_20(x, k_0))
Eq(F_174(x, k_0), F_169(x, k_0) + F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_83(x))
Eq(F_176(x, k_0), F_177(x, k_0) + F_179(x, k_0) + 2*F_34(x))
Eq(F_177(x, k_0), F_11(x)*F_178(x, k_0))
Eq(F_178(x, k_0), F_170(x, k_0) + F_176(x, k_0))
Eq(F_179(x, k_0), F_175(x, k_0)*F_20(x, k_0))
Eq(F_180(x, k_0), F_168(x, k_0)*F_20(x, k_0))
Eq(F_181(x), F_161(x, 1))
Eq(F_182(x), F_163(x, 1))
Eq(F_183(x), F_11(x)*F_184(x))
Eq(F_184(x), F_1(x) + F_185(x) + F_200(x) + F_201(x) + F_204(x))
Eq(F_185(x), F_186(x, 1))
Eq(F_186(x, k_0), F_187(x, k_0)*F_20(x, k_0))
Eq(F_187(x, k_0), F_188(x) + F_193(x, k_0))
Eq(F_188(x), F_189(x) + F_42(x))
Eq(F_189(x), F_190(x) + F_43(x))
Eq(F_190(x), F_191(x) + F_44(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_11(x)*F_190(x))
Eq(F_193(x, k_0), F_194(x, k_0) + F_46(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0) + F_47(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0) + F_48(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_199(x, k_0) + 3*F_34(x))
Eq(F_197(x, k_0), F_198(x, k_0)*F_20(x, k_0))
Eq(F_198(x, k_0), F_191(x) + F_196(x, k_0))
Eq(F_199(x, k_0), F_11(x)*F_195(x, k_0))
Eq(F_200(x), F_12(x, 1))
Eq(F_201(x), F_202(x, 1))
Eq(F_202(x, k_0), F_11(x)*F_203(x, k_0))
Eq(F_203(x, k_0), (-k_0*F_53(x, k_0) + F_53(x, 1))/(1 - k_0))
Eq(F_204(x), F_205(x, 1))
Eq(F_205(x, k_0), F_20(x, k_0)*F_206(x, k_0))
Eq(F_206(x, k_0), F_167(x, k_0) + F_207(x, k_0))
Eq(F_207(x, k_0), F_174(x, k_0) + F_208(x, k_0))
Eq(F_208(x, k_0), F_175(x, k_0) + F_209(x, k_0))
Eq(F_209(x, k_0), F_210(x) + F_213(x, k_0))
Eq(F_210(x), F_211(x))
Eq(F_211(x), F_11(x)*F_212(x))
Eq(F_212(x), F_210(x) + F_83(x))
Eq(F_213(x, k_0), F_214(x, k_0) + F_216(x, k_0) + 3*F_34(x))
Eq(F_214(x, k_0), F_11(x)*F_215(x, k_0))
Eq(F_215(x, k_0), F_176(x, k_0) + F_213(x, k_0))
Eq(F_216(x, k_0), F_20(x, k_0)*F_209(x, k_0))
Eq(F_217(x), F_218(x, 1))
Eq(F_218(x, k_0), F_11(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_134(x) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0) + F_29(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0) + F_225(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_20(x, k_0)*F_224(x, k_0))
Eq(F_224(x, k_0), F_222(x, k_0) + F_69(x))
Eq(F_225(x, k_0), F_226(x, k_0) + F_228(x, k_0) + 2*F_34(x))
Eq(F_226(x, k_0), F_20(x, k_0)*F_227(x, k_0))
Eq(F_227(x, k_0), F_136(x) + F_225(x, k_0))
Eq(F_228(x, k_0), F_11(x)*F_221(x, k_0))
Eq(F_229(x), F_230(x, 1))
Eq(F_230(x, k_0), F_11(x)*F_65(x, k_0))
Eq(F_231(x), F_232(x, 1))
Eq(F_232(x, k_0), F_20(x, k_0)*F_233(x, k_0))
Eq(F_233(x, k_0), F_1(x) + F_165(x, k_0) + F_166(x, k_0) + F_234(x, k_0) + F_236(x, k_0))
Eq(F_234(x, k_0), F_11(x)*F_235(x, k_0))
Eq(F_235(x, k_0), (k_0*F_120(x, k_0) - F_120(x, 1))/(k_0 - 1))
Eq(F_236(x, k_0), F_11(x)*F_237(x, k_0))
Eq(F_237(x, k_0), (k_0*F_233(x, k_0) - F_233(x, 1))/(k_0 - 1))
Eq(F_238(x, k_0), F_11(x)*F_239(x, k_0))
Eq(F_239(x, k_0), F_1(x) + F_133(x) + F_240(x, k_0) + F_242(x, k_0) + F_40(x, k_0) + F_52(x, k_0))
Eq(F_240(x, k_0), F_11(x)*F_241(x, k_0))
Eq(F_241(x, k_0), (-k_0*F_239(x, k_0) + F_239(x, 1))/(1 - k_0))
Eq(F_242(x, k_0), F_11(x)*F_243(x, k_0))
Eq(F_243(x, k_0), (-k_0*F_56(x, k_0) + F_56(x, 1))/(1 - k_0))
Eq(F_244(x, k_0), F_11(x)*F_53(x, k_0))
Eq(F_245(x, k_0), F_11(x)*F_246(x, k_0))
Eq(F_246(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_247(x, k_0), F_11(x)*F_248(x, k_0))
Eq(F_248(x, k_0), (-k_0*F_145(x, k_0) + F_145(x, 1))/(1 - k_0))
Eq(F_249(x, k_0), F_11(x)*F_250(x, k_0))
Eq(F_250(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_251(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_252(x), F_11(x)*F_151(x))
Eq(F_253(x, k_0), F_11(x)*F_159(x, k_0))
Eq(F_254(x, k_0), F_11(x)*F_255(x, k_0))
Eq(F_255(x, k_0), F_1(x) + F_117(x, k_0) + F_119(x, k_0) + F_256(x) + F_261(x) + F_262(x))
Eq(F_256(x), F_257(x, 1))
Eq(F_257(x, k_0), F_20(x, k_0)*F_258(x, k_0))
Eq(F_258(x, k_0), F_1(x) + F_257(x, k_0) + F_259(x, k_0) + F_260(x, k_0) + F_66(x))
Eq(F_259(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_260(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_261(x), F_259(x, 1))
Eq(F_262(x), F_11(x)*F_263(x))
Eq(F_263(x), F_39(x, 1))
Eq(F_264(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_265(x, k_0), F_11(x)*F_266(x, k_0))
Eq(F_266(x, k_0), F_267(x, k_0) + F_278(x, k_0))
Eq(F_267(x, k_0), F_268(x, k_0) + F_272(x, k_0))
Eq(F_268(x, k_0), F_269(x, k_0) + F_90(x, k_0))
Eq(F_269(x, k_0), F_27(x) + F_270(x, k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_20(x, k_0)*F_269(x, k_0))
Eq(F_272(x, k_0), F_169(x, k_0) + F_273(x, k_0))
Eq(F_273(x, k_0), F_136(x) + F_274(x, k_0))
Eq(F_274(x, k_0), F_275(x, k_0) + F_277(x, k_0) + 2*F_34(x))
Eq(F_275(x, k_0), F_11(x)*F_276(x, k_0))
Eq(F_276(x, k_0), F_270(x, k_0) + F_274(x, k_0))
Eq(F_277(x, k_0), F_20(x, k_0)*F_273(x, k_0))
Eq(F_278(x, k_0), F_272(x, k_0) + F_279(x, k_0))
Eq(F_279(x, k_0), F_175(x, k_0) + F_280(x, k_0))
Eq(F_280(x, k_0), F_281(x) + F_286(x, k_0))
Eq(F_281(x), F_282(x) + F_284(x) + 2*F_34(x))
Eq(F_282(x), F_11(x)*F_283(x))
Eq(F_283(x), F_136(x) + F_281(x))
Eq(F_284(x), F_11(x)*F_285(x))
Eq(F_285(x), F_281(x) + F_83(x))
Eq(F_286(x, k_0), F_287(x, k_0) + F_289(x, k_0) + 3*F_34(x))
Eq(F_287(x, k_0), F_11(x)*F_288(x, k_0))
Eq(F_288(x, k_0), F_274(x, k_0) + F_286(x, k_0))
Eq(F_289(x, k_0), F_20(x, k_0)*F_280(x, k_0))
Eq(F_290(x), F_11(x)*F_291(x))
Eq(F_291(x), F_292(x, 1))
Eq(F_292(x, k_0), F_1(x) + F_293(x, k_0) + F_40(x, k_0) + F_52(x, k_0))
Eq(F_293(x, k_0), F_11(x)*F_294(x, k_0))
Eq(F_294(x, k_0), (-k_0*F_292(x, k_0) + F_292(x, 1))/(1 - 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": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion_isolated", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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3]], [[1, 0], [1, 1], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": 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"pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": 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[[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"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": [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, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 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, 1], [0, 1]]}, {"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, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/219/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[150,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[14,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[105,x,k[0]]+F[149,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[14,x]
F[11,x,k[0]] = F[1,x]+F[105,x,k[0]]+F[119,x,k[0]]+F[12,x,k[0]]+F[15,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[14,x] = x
F[15,x,k[0]] = F[14,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = F[18,x]+F[77,x,k[0]]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]+F[36,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[35,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[29,x,k[0]]
F[22,x,k[0]] = F[23,x]+F[26,x,k[0]]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[23,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[31,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[30,x,k[0]]
F[29,x,k[0]] = k[0]*x
F[30,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[34,x,k[0]]+F[6,x]
F[32,x,k[0]] = F[29,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[24,x]+F[31,x,k[0]]
F[34,x,k[0]] = F[14,x]*F[26,x,k[0]]
F[35,x,k[0]] = F[14,x]*F[19,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[47,x,k[0]]+F[6,x]+F[72,x,k[0]]
F[37,x,k[0]] = F[29,x,k[0]]*F[38,x,k[0]]
F[38,x,k[0]] = F[39,x]+F[42,x,k[0]]
F[39,x] = F[24,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[39,x]
F[42,x,k[0]] = F[31,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = 2*F[6,x]+F[44,x,k[0]]+F[46,x,k[0]]
F[44,x,k[0]] = F[29,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[40,x]+F[43,x,k[0]]
F[46,x,k[0]] = F[14,x]*F[42,x,k[0]]
F[47,x,k[0]] = F[14,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x]+F[50,x,k[0]]
F[49,x] = F[9,x,1]
F[50,x,k[0]] = F[51,x,k[0]]+F[52,x,k[0]]+F[6,x]+F[69,x,k[0]]+F[71,x,k[0]]
F[51,x,k[0]] = F[29,x,k[0]]*F[48,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[14,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[21,x,k[0]]+F[55,x,k[0]]+F[6,x]+F[67,x,k[0]]
F[55,x,k[0]] = F[14,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[6,x]+F[61,x,k[0]]+F[62,x,k[0]]+F[64,x,k[0]]
F[57,x,k[0]] = F[29,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x]+F[60,x,k[0]]
F[59,x] = F[23,x]+F[39,x]
F[60,x,k[0]] = F[26,x,k[0]]+F[42,x,k[0]]
F[61,x,k[0]] = F[14,x]*F[50,x,k[0]]
F[62,x,k[0]] = F[14,x]*F[63,x,k[0]]
F[63,x,k[0]] = -k[0]*(F[56,x,1]-F[56,x,k[0]])/(-1+k[0])
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[14,x]*F[66,x,k[0]]
F[66,x,k[0]] = -k[0]*(F[54,x,1]-F[54,x,k[0]])/(-1+k[0])
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[14,x]*F[54,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[14,x]*F[56,x,k[0]]
F[71,x,k[0]] = F[14,x]*F[50,x,k[0]]
F[72,x,k[0]] = F[14,x]*F[73,x,k[0]]
F[73,x,k[0]] = (F[74,x,k[0]]-F[74,x,1])/(-1+k[0])
F[74,x,k[0]] = F[6,x]+F[70,x,k[0]]+F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[19,x,k[0]]*F[29,x,k[0]]
F[76,x,k[0]] = F[53,x,k[0]]
F[77,x,k[0]] = F[116,x,k[0]]+F[118,x,k[0]]+F[6,x]+F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[14,x]*F[77,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[14,x]*F[81,x,k[0]]
F[81,x,k[0]] = F[102,x,k[0]]+F[104,x,k[0]]+F[105,x,k[0]]+F[6,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[14,x]*F[84,x,k[0]]
F[84,x,k[0]] = -k[0]*(F[85,x,1]-F[85,x,k[0]])/(-1+k[0])
F[85,x,k[0]] = F[6,x]+F[86,x,k[0]]+F[88,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[85,x,k[0]]
F[88,x,k[0]] = F[14,x]*F[81,x,k[0]]
F[89,x,k[0]] = F[29,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]+F[94,x,k[0]]
F[91,x,k[0]] = F[1,x]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[29,x,k[0]]*F[91,x,k[0]]
F[94,x,k[0]] = F[95,x]+F[98,x,k[0]]
F[95,x] = F[96,x]
F[96,x] = F[14,x]*F[97,x]
F[97,x] = F[1,x]+F[95,x]
F[98,x,k[0]] = F[101,x,k[0]]+F[6,x]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[14,x]
F[100,x,k[0]] = F[92,x,k[0]]+F[98,x,k[0]]
F[101,x,k[0]] = F[29,x,k[0]]*F[94,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[14,x]
F[103,x,k[0]] = -k[0]*(F[81,x,1]-F[81,x,k[0]])/(-1+k[0])
F[104,x,k[0]] = F[14,x]*F[77,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[29,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[90,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[94,x,k[0]]
F[108,x,k[0]] = F[109,x]+F[112,x,k[0]]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[14,x]
F[111,x] = F[109,x]+F[95,x]
F[112,x,k[0]] = 2*F[6,x]+F[113,x,k[0]]+F[115,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[14,x]
F[114,x,k[0]] = F[112,x,k[0]]+F[98,x,k[0]]
F[115,x,k[0]] = F[108,x,k[0]]*F[29,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[14,x]*F[85,x,k[0]]
F[118,x,k[0]] = F[17,x,k[0]]*F[29,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[14,x]
F[120,x,k[0]] = F[121,x,k[0]]+F[137,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[126,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[91,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[24,x]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[123,x,k[0]]*F[29,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[94,x,k[0]]
F[127,x,k[0]] = F[128,x]+F[133,x,k[0]]
F[128,x] = F[129,x]+F[131,x]+F[6,x]
F[129,x] = F[130,x]*F[14,x]
F[130,x] = F[128,x]+F[24,x]
F[131,x] = F[132,x]*F[14,x]
F[132,x] = F[128,x]+F[95,x]
F[133,x,k[0]] = 2*F[6,x]+F[134,x,k[0]]+F[136,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[14,x]
F[135,x,k[0]] = F[124,x,k[0]]+F[133,x,k[0]]
F[136,x,k[0]] = F[127,x,k[0]]*F[29,x,k[0]]
F[137,x,k[0]] = F[126,x,k[0]]+F[138,x,k[0]]
F[138,x,k[0]] = F[108,x,k[0]]+F[139,x,k[0]]
F[139,x,k[0]] = F[140,x]+F[145,x,k[0]]
F[140,x] = 2*F[6,x]+F[141,x]+F[143,x]
F[141,x] = F[14,x]*F[142,x]
F[142,x] = F[128,x]+F[140,x]
F[143,x] = F[14,x]*F[144,x]
F[144,x] = F[109,x]+F[140,x]
F[145,x,k[0]] = 3*F[6,x]+F[146,x,k[0]]+F[148,x,k[0]]
F[146,x,k[0]] = F[14,x]*F[147,x,k[0]]
F[147,x,k[0]] = F[133,x,k[0]]+F[145,x,k[0]]
F[148,x,k[0]] = F[139,x,k[0]]*F[29,x,k[0]]
F[149,x,k[0]] = F[14,x]*F[17,x,k[0]]
F[150,x] = F[14,x]*F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x,1]
F[153,x,k[0]] = F[74,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{150}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{18}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = y x
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{40}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{55}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{60}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right)+F_{39}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{y \left(F_{56}\! \left(x , 1\right)-F_{56}\! \left(x , y\right)\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = -\frac{F_{74}\! \left(x , 1\right)-F_{74}\! \left(x , y\right)}{-1+y}
F_{74}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{88}\! \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_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{1}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{103}\! \left(x , y\right) = -\frac{y \left(F_{81}\! \left(x , 1\right)-F_{81}\! \left(x , y\right)\right)}{-1+y}
F_{104}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x \right)+F_{112}\! \left(x , y\right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{109}\! \left(x \right)+F_{95}\! \left(x \right)
F_{112}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{115}\! \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_{112}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x \right)+F_{133}\! \left(x , y\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{131}\! \left(x \right)+F_{6}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{14}\! \left(x \right)
F_{130}\! \left(x \right) = F_{128}\! \left(x \right)+F_{24}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{14}\! \left(x \right)
F_{132}\! \left(x \right) = F_{128}\! \left(x \right)+F_{95}\! \left(x \right)
F_{133}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x \right)+F_{145}\! \left(x , y\right)
F_{140}\! \left(x \right) = 2 F_{6}\! \left(x \right)+F_{141}\! \left(x \right)+F_{143}\! \left(x \right)
F_{141}\! \left(x \right) = F_{14}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{128}\! \left(x \right)+F_{140}\! \left(x \right)
F_{143}\! \left(x \right) = F_{14}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{109}\! \left(x \right)+F_{140}\! \left(x \right)
F_{145}\! \left(x , y\right) = 3 F_{6}\! \left(x \right)+F_{146}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{150}\! \left(x \right) = F_{14}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x , 1\right)
F_{153}\! \left(x , y\right) = F_{74}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_150(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_14(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_105(x, k_0) + F_149(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_14(x))
Eq(F_11(x, k_0), F_1(x) + F_105(x, k_0) + F_119(x, k_0) + F_12(x, k_0) + F_15(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x))
Eq(F_13(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_14(x), x)
Eq(F_15(x, k_0), F_14(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_18(x) + F_77(x, k_0))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0) + F_36(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_35(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_29(x, k_0))
Eq(F_22(x, k_0), F_23(x) + F_26(x, k_0))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_23(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_31(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_30(x, k_0))
Eq(F_29(x, k_0), k_0*x)
Eq(F_30(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_34(x, k_0) + F_6(x))
Eq(F_32(x, k_0), F_29(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_24(x) + F_31(x, k_0))
Eq(F_34(x, k_0), F_14(x)*F_26(x, k_0))
Eq(F_35(x, k_0), F_14(x)*F_19(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_47(x, k_0) + F_6(x) + F_72(x, k_0))
Eq(F_37(x, k_0), F_29(x, k_0)*F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x) + F_42(x, k_0))
Eq(F_39(x), F_24(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_39(x))
Eq(F_42(x, k_0), F_31(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_46(x, k_0) + 2*F_6(x))
Eq(F_44(x, k_0), F_29(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_40(x) + F_43(x, k_0))
Eq(F_46(x, k_0), F_14(x)*F_42(x, k_0))
Eq(F_47(x, k_0), F_14(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x) + F_50(x, k_0))
Eq(F_49(x), F_9(x, 1))
Eq(F_50(x, k_0), F_51(x, k_0) + F_52(x, k_0) + F_6(x) + F_69(x, k_0) + F_71(x, k_0))
Eq(F_51(x, k_0), F_29(x, k_0)*F_48(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_14(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_21(x, k_0) + F_55(x, k_0) + F_6(x) + F_67(x, k_0))
Eq(F_55(x, k_0), F_14(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_6(x) + F_61(x, k_0) + F_62(x, k_0) + F_64(x, k_0))
Eq(F_57(x, k_0), F_29(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x) + F_60(x, k_0))
Eq(F_59(x), F_23(x) + F_39(x))
Eq(F_60(x, k_0), F_26(x, k_0) + F_42(x, k_0))
Eq(F_61(x, k_0), F_14(x)*F_50(x, k_0))
Eq(F_62(x, k_0), F_14(x)*F_63(x, k_0))
Eq(F_63(x, k_0), -F_56(x, 1) + (-k_0*F_56(x, k_0) + F_56(x, 1))/(1 - k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_14(x)*F_66(x, k_0))
Eq(F_66(x, k_0), -F_54(x, 1) + (-k_0*F_54(x, k_0) + F_54(x, 1))/(1 - k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_14(x)*F_54(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_14(x)*F_56(x, k_0))
Eq(F_71(x, k_0), F_14(x)*F_50(x, k_0))
Eq(F_72(x, k_0), F_14(x)*F_73(x, k_0))
Eq(F_73(x, k_0), -F_74(x, k_0) + (-k_0*F_74(x, k_0) + F_74(x, 1))/(1 - k_0))
Eq(F_74(x, k_0), F_6(x) + F_70(x, k_0) + F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_19(x, k_0)*F_29(x, k_0))
Eq(F_76(x, k_0), F_53(x, k_0))
Eq(F_77(x, k_0), F_116(x, k_0) + F_118(x, k_0) + F_6(x) + F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_14(x)*F_77(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_14(x)*F_81(x, k_0))
Eq(F_81(x, k_0), F_102(x, k_0) + F_104(x, k_0) + F_105(x, k_0) + F_6(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_14(x)*F_84(x, k_0))
Eq(F_84(x, k_0), -F_85(x, 1) + (k_0*F_85(x, k_0) - F_85(x, 1))/(k_0 - 1))
Eq(F_85(x, k_0), F_6(x) + F_86(x, k_0) + F_88(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_85(x, k_0))
Eq(F_88(x, k_0), F_14(x)*F_81(x, k_0))
Eq(F_89(x, k_0), F_29(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0) + F_94(x, k_0))
Eq(F_91(x, k_0), F_1(x) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_29(x, k_0)*F_91(x, k_0))
Eq(F_94(x, k_0), F_95(x) + F_98(x, k_0))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_14(x)*F_97(x))
Eq(F_97(x), F_1(x) + F_95(x))
Eq(F_98(x, k_0), F_101(x, k_0) + F_6(x) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_14(x))
Eq(F_100(x, k_0), F_92(x, k_0) + F_98(x, k_0))
Eq(F_101(x, k_0), F_29(x, k_0)*F_94(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_14(x))
Eq(F_103(x, k_0), -F_81(x, 1) + (k_0*F_81(x, k_0) - F_81(x, 1))/(k_0 - 1))
Eq(F_104(x, k_0), F_14(x)*F_77(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_29(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_90(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_94(x, k_0))
Eq(F_108(x, k_0), F_109(x) + F_112(x, k_0))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_14(x))
Eq(F_111(x), F_109(x) + F_95(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0) + 2*F_6(x))
Eq(F_113(x, k_0), F_114(x, k_0)*F_14(x))
Eq(F_114(x, k_0), F_112(x, k_0) + F_98(x, k_0))
Eq(F_115(x, k_0), F_108(x, k_0)*F_29(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_14(x)*F_85(x, k_0))
Eq(F_118(x, k_0), F_17(x, k_0)*F_29(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0)*F_14(x))
Eq(F_120(x, k_0), F_121(x, k_0) + F_137(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_126(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_91(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_24(x))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_123(x, k_0)*F_29(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_94(x, k_0))
Eq(F_127(x, k_0), F_128(x) + F_133(x, k_0))
Eq(F_128(x), F_129(x) + F_131(x) + F_6(x))
Eq(F_129(x), F_130(x)*F_14(x))
Eq(F_130(x), F_128(x) + F_24(x))
Eq(F_131(x), F_132(x)*F_14(x))
Eq(F_132(x), F_128(x) + F_95(x))
Eq(F_133(x, k_0), F_134(x, k_0) + F_136(x, k_0) + 2*F_6(x))
Eq(F_134(x, k_0), F_135(x, k_0)*F_14(x))
Eq(F_135(x, k_0), F_124(x, k_0) + F_133(x, k_0))
Eq(F_136(x, k_0), F_127(x, k_0)*F_29(x, k_0))
Eq(F_137(x, k_0), F_126(x, k_0) + F_138(x, k_0))
Eq(F_138(x, k_0), F_108(x, k_0) + F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x) + F_145(x, k_0))
Eq(F_140(x), F_141(x) + F_143(x) + 2*F_6(x))
Eq(F_141(x), F_14(x)*F_142(x))
Eq(F_142(x), F_128(x) + F_140(x))
Eq(F_143(x), F_14(x)*F_144(x))
Eq(F_144(x), F_109(x) + F_140(x))
Eq(F_145(x, k_0), F_146(x, k_0) + F_148(x, k_0) + 3*F_6(x))
Eq(F_146(x, k_0), F_14(x)*F_147(x, k_0))
Eq(F_147(x, k_0), F_133(x, k_0) + F_145(x, k_0))
Eq(F_148(x, k_0), F_139(x, k_0)*F_29(x, k_0))
Eq(F_149(x, k_0), F_14(x)*F_17(x, k_0))
Eq(F_150(x), F_14(x)*F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x, 1))
Eq(F_153(x, k_0), F_74(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 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