1032_1302_304152
Counting sequence:
1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742, 15521467648875090, 85249942588971314, 469286147871837366, 2588758890960637798, 14308406109097843626, 79228031819993134650, 439442782615614361662, 2441263009246175852478, 13582285614213903189954, 75672545337796460900418, 422158527806921249683014, 2358045034996817096518614, 13186762229969911326195738, 73825509266803210054176714, 413744003711584755242223438, 2321083025362608992223726894, 13033522069997514889215092274, 73252943452863199223393858898, 412061442720070604908289934294, 2319824936637513933714881477958, 13070393952625514917631908633482, 73696580719034769214303906556250, 415831259625127007215514095957086, 2347928652146955633301765770354078, 13265947508553602309369175431365026, 75000761566763827145224941186411618, 424283543233691838260433080620759398, 2401593774673792297361446179037614006, 13601477343632400527767268213048769018, 77073779272885977020023254295915628266, 436971024085954796290610303307461466990, 2478653831690076100088720298283149489422, 14066584046529013725085103560520804574738, 79866310879834163229292594665706543602034, 453663534693850195686460667123382923500278, 2578058682623181189697966937739368886054694, 14656630568593973333973106198029483323909994, 83358894098787816613549314525130317456485498, 474286255370429617942243026791925684793786494, 2699569581623203904920541044702174725512879998, 15371234811776523868650878005698910430202961794, 87554469522958377138755995490746080739109617794, 498882798426402159521454478141768350193090899078, 2843576412546208340221194074583339359985310934934, 16213364962102490366103878328244865647555172888538, 92473905425478965452483914141593657771802288922122, 527593095000024778151982091136956400377574686254990, 3010988607092394896417597701043924930186940754864366, 17188802682090899672500146128332285575668045969848818, 98153364535215963782323163906086831829355773017417106, 560640532892262603354460063484591577003970621211357718, 3203172665681192346622816544900896002595156529621124358, 18305841793760424680154621430418780681523533531801673546, 104642864530896737207618717893521194008008527581735690138, 598325164943559373744948766984500352935799706039116059806, 3421920651494217703361052849648731678676812561507875200350, 19575145529594373004334767968613012138269718700842042196322, 112005653162512670274733777484363842197180560245702246829218, 641021117519290914746964286173070817630839957398566690647974, 3669440419831969958422546258088530756063025637290340831875958, 21009716690579236401887583574543083549904081973832685742784954, 120318172177646736618696901545023201244745795730675271890072874, 689177081897978391122217856003853830119110923264764010082913198, 3948362055340350140680020802666740519613808824287558217299724494, 22624953370904018901353934671727048802325911161238183811407020498, 129670474901504706381997527787278405431429527321160644877245020594, 743319221158994216085862924952269488154648087794223144216228112694, 4261757226338042831158975959521897325919311779789998586036272373478, 24438774057583613278048926220772229870922406873153001513488741966634, 140167018025129185868954119576724414060673174921691765624010117079738, 804056104197892430009502735476119485683292523144621098692933804429502, 4613169566706958265933076228065878936195669326617529466206880481490750, 26471802968334898948028447644814364935937000278105670111952646786369346, 151927783773762708731069683108992436724172801785658343831948253505777858, 872085458815060952612778117624832287371627646645575624352952264741298886, 5006655111336460402472381082547036154743871773943263346408958078720471894
Generating function in Maple syntax:
-1/2*x+3/2-1/2*(x^2-6*x+1)^(1/2)
Generating function in latex syntax:
-\frac{x}{2}+\frac{3}{2}-\frac{\sqrt{x^{2}-6 x +1}}{2}
Generating function in sympy syntax:
-x/2 - sqrt(x**2 - 6*x + 1)/2 + 3/2
Implicit equation for the generating function in Maple syntax:
F(x)^2+(x-3)*F(x)+2 = 0
Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{2}+\left(x -3\right) F \! \left(x \right)+2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(n+2) = -(n-1)/(n+2)*a(n)+3*(2*n+1)/(n+2)*a(n+1), n >= 2
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(n +2\right) = -\frac{\left(n -1\right) a \! \left(n \right)}{n +2}+\frac{3 \left(2 n +1\right) a \! \left(n +1\right)}{n +2}, \quad n \geq 2
Specification 1
Strategy pack name: point_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23989/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[17,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[13,x]*F[14,x]
F[11,x] = 1/F[0,x]/F[13,x]*F[12,x]
F[12,x] = F[5,x]
F[13,x] = x
F[14,x] = F[0,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[11,x]*F[13,x]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = F[19,x,k[0]]+F[46,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[43,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[27,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[28,x,k[0]]
F[23,x,k[0]] = F[0,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[0,x]*F[13,x]*F[30,x,k[0]]
F[31,x,k[0]] = F[27,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[19,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[25,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[24,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[38,x,k[0]] = F[37,x,k[0]]+F[42,x,k[0]]
F[39,x,k[0]] = F[13,x]*F[38,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[41,x,k[0]] = F[24,x,k[0]]+F[40,x,k[0]]
F[41,x,k[0]] = F[0,x]+F[20,x,k[0]]
F[42,x,k[0]] = F[19,x,k[0]]+F[4,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[13,x]*F[45,x,k[0]]
F[45,x,k[0]] = -k[0]*(F[18,x,1]-F[18,x,k[0]])/(-1+k[0])
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[11,x]*F[13,x]*F[19,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{13}\! \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_{46}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{y \left(F_{18}\! \left(x , 1\right)-F_{18}\! \left(x , y\right)\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{19}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_17(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_13(x)*F_14(x))
Eq(F_11(x), F_12(x)/(F_0(x)*F_13(x)))
Eq(F_12(x), F_5(x))
Eq(F_13(x), x)
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_11(x)*F_13(x))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), F_19(x, k_0) + F_46(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_43(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_27(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_28(x, k_0))
Eq(F_23(x, k_0), F_0(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_0(x)*F_13(x)*F_30(x, k_0))
Eq(F_31(x, k_0), F_27(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_19(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_25(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_24(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_38(x, k_0), F_37(x, k_0) + F_42(x, k_0))
Eq(F_39(x, k_0), F_13(x)*F_38(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_41(x, k_0), F_24(x, k_0) + F_40(x, k_0))
Eq(F_41(x, k_0), F_0(x) + F_20(x, k_0))
Eq(F_42(x, k_0), F_19(x, k_0) + F_4(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_13(x)*F_45(x, k_0))
Eq(F_45(x, k_0), -F_18(x, 1) + (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_11(x)*F_13(x)*F_19(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"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 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": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, 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"pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[1, 2], [1, 1], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": 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[[{"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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_placements_tracked_fusion
Tree: http://permpal.com/tree/23990/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[126,x]+F[9,x]
F[9,x] = F[10,x]+F[122,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[25,x,k[0]]
F[20,x,k[0]] = F[2,x]*F[21,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[21,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = -F[0,x]+F[27,x]
F[27,x] = 1/F[13,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x,k[0]] = F[17,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[13,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[43,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[41,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[38,x,k[0]]
F[35,x,k[0]] = F[22,x,k[0]]*F[36,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[0,x]*F[2,x]
F[38,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = F[17,x,k[0]]*F[2,x]
F[40,x,k[0]] = F[0,x]*F[30,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[0,x]*F[2,x]*F[21,x,k[0]]*F[22,x,k[0]]
F[43,x,k[0]] = F[108,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[47,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[2,x]*F[22,x,k[0]]*F[36,x]
F[47,x,k[0]] = F[48,x,k[0]]+F[99,x,k[0]]
F[48,x,k[0]] = F[2,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[13,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[62,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[58,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[57,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[13,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[22,x,k[0]]+F[54,x,k[0]]
F[57,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[58,x,k[0]] = F[59,x,k[0]]+F[61,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[11,x]*F[2,x]*F[22,x,k[0]]
F[61,x,k[0]] = -k[0]*(F[49,x,1]-F[49,x,k[0]])/(-1+k[0])
F[62,x,k[0]] = F[63,x,k[0]]+F[65,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[2,x]*F[53,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[11,x]*F[22,x,k[0]]*F[68,x]
F[68,x] = -F[2,x]+F[26,x]
F[69,x,k[0]] = -k[0]*(F[70,x,1]-F[70,x,k[0]])/(-1+k[0])
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[13,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[80,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[77,x,k[0]]
F[74,x,k[0]] = F[49,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[2,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[17,x,k[0]]+F[49,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[2,x]*F[49,x,k[0]]
F[79,x,k[0]] = F[68,x]*F[76,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]+F[83,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[2,x]*F[74,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[85,x,k[0]]
F[84,x,k[0]] = F[49,x,k[0]]*F[6,x]
F[85,x,k[0]] = F[76,x,k[0]]*F[86,x]
F[86,x] = 1/F[0,x]*F[87,x]
F[87,x] = -F[98,x]+F[88,x]
F[88,x] = -F[96,x]+F[89,x]
F[89,x] = -F[92,x]+F[90,x]
F[90,x] = 1/F[13,x]*F[91,x]
F[91,x] = F[68,x]
F[92,x] = F[36,x]+F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[2,x]^2
F[95,x] = F[0,x]*F[68,x]
F[96,x] = F[97,x]
F[97,x] = F[2,x]*F[36,x]
F[98,x] = F[2,x]*F[6,x]
F[99,x,k[0]] = F[0,x]*F[100,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]+F[49,x,k[0]]
F[102,x,k[0]] = F[101,x,k[0]]+F[107,x]
F[103,x,k[0]] = F[102,x,k[0]]+F[105,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]*F[24,x,k[0]]
F[104,x,k[0]] = F[49,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[2,x]^2*F[21,x,k[0]]
F[107,x] = F[6,x]+F[86,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[2,x]*F[21,x,k[0]]
F[111,x,k[0]] = F[110,x,k[0]]*F[21,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[113,x,k[0]] = F[112,x,k[0]]+F[120,x,k[0]]
F[114,x,k[0]] = F[113,x,k[0]]+F[116,x,k[0]]
F[115,x,k[0]] = F[114,x,k[0]]*F[13,x]
F[115,x,k[0]] = F[17,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[118,x,k[0]]
F[117,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[0,x]*F[21,x,k[0]]*F[22,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[49,x,k[0]]
F[121,x,k[0]] = F[2,x]*F[22,x,k[0]]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[11,x]*F[2,x]
F[124,x] = F[125,x]+F[6,x]
F[125,x] = F[49,x,1]
F[126,x] = F[127,x]+F[129,x]
F[127,x] = F[128,x]
F[128,x] = F[10,x]*F[2,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[11,x]*F[68,x]
F[131,x] = F[132,x]+F[140,x]
F[132,x] = F[133,x]
F[133,x] = F[13,x]*F[134,x]
F[134,x] = F[135,x]+F[138,x]
F[135,x] = F[136,x]*F[2,x]
F[136,x] = F[107,x]+F[137,x]
F[137,x] = F[37,x]
F[138,x] = F[139,x]*F[68,x]
F[139,x] = F[136,x]+F[27,x]
F[140,x] = F[70,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{126}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{122}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{22}\! \left(x , y\right) F_{36}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{y \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y\right)\right)}{-1+y}
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = -\frac{y \left(F_{49}\! \left(x , 1\right)-F_{49}\! \left(x , y\right)\right)}{-1+y}
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{22}\! \left(x , y\right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{26}\! \left(x \right)
F_{69}\! \left(x , y\right) = -\frac{y \left(F_{70}\! \left(x , 1\right)-F_{70}\! \left(x , y\right)\right)}{-1+y}
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{68}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{85}\! \left(x , y\right) = F_{76}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{87}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{68}\! \left(x \right)
F_{92}\! \left(x \right) = F_{36}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{95}\! \left(x \right) = F_{0}\! \left(x \right) F_{68}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{98}\! \left(x \right) = F_{2}\! \left(x \right) F_{6}\! \left(x \right)
F_{99}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{100}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{107}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{2} \left(x \right)^{2} F_{21}\! \left(x , y\right)
F_{107}\! \left(x \right) = F_{6}\! \left(x \right)+F_{86}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{2}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{6}\! \left(x \right)
F_{125}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{129}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{13}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{138}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{2}\! \left(x \right)
F_{136}\! \left(x \right) = F_{107}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{37}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{68}\! \left(x \right)
F_{139}\! \left(x \right) = F_{136}\! \left(x \right)+F_{27}\! \left(x \right)
F_{140}\! \left(x \right) = F_{70}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_126(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_122(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_25(x, k_0))
Eq(F_20(x, k_0), F_2(x)*F_21(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_21(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), -F_0(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_13(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x, k_0), F_17(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_13(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_43(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_41(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_38(x, k_0))
Eq(F_35(x, k_0), F_22(x, k_0)*F_36(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_0(x)*F_2(x))
Eq(F_38(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), F_17(x, k_0)*F_2(x))
Eq(F_40(x, k_0), F_0(x)*F_30(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_0(x)*F_2(x)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_43(x, k_0), F_108(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_47(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_2(x)*F_22(x, k_0)*F_36(x))
Eq(F_47(x, k_0), F_48(x, k_0) + F_99(x, k_0))
Eq(F_48(x, k_0), F_2(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_13(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_62(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_58(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_57(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_13(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_22(x, k_0) + F_54(x, k_0))
Eq(F_57(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_58(x, k_0), F_59(x, k_0) + F_61(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_11(x)*F_2(x)*F_22(x, k_0))
Eq(F_61(x, k_0), -F_49(x, 1) + (k_0*F_49(x, k_0) - F_49(x, 1))/(k_0 - 1))
Eq(F_62(x, k_0), F_63(x, k_0) + F_65(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_2(x)*F_53(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_11(x)*F_22(x, k_0)*F_68(x))
Eq(F_68(x), -F_2(x) + F_26(x))
Eq(F_69(x, k_0), -F_70(x, 1) + (k_0*F_70(x, k_0) - F_70(x, 1))/(k_0 - 1))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_13(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_80(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_77(x, k_0))
Eq(F_74(x, k_0), F_49(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_2(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_17(x, k_0) + F_49(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_2(x)*F_49(x, k_0))
Eq(F_79(x, k_0), F_68(x)*F_76(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0) + F_83(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_2(x)*F_74(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_85(x, k_0))
Eq(F_84(x, k_0), F_49(x, k_0)*F_6(x))
Eq(F_85(x, k_0), F_76(x, k_0)*F_86(x))
Eq(F_86(x), F_87(x)/F_0(x))
Eq(F_87(x), F_88(x) - F_98(x))
Eq(F_88(x), F_89(x) - F_96(x))
Eq(F_89(x), F_90(x) - F_92(x))
Eq(F_90(x), F_91(x)/F_13(x))
Eq(F_91(x), F_68(x))
Eq(F_92(x), F_36(x) + F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_2(x)**2)
Eq(F_95(x), F_0(x)*F_68(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_2(x)*F_36(x))
Eq(F_98(x), F_2(x)*F_6(x))
Eq(F_99(x, k_0), F_0(x)*F_100(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0) + F_49(x, k_0))
Eq(F_102(x, k_0), F_101(x, k_0) + F_107(x))
Eq(F_103(x, k_0), F_102(x, k_0) + F_105(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0)*F_24(x, k_0))
Eq(F_104(x, k_0), F_49(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_2(x)**2*F_21(x, k_0))
Eq(F_107(x), F_6(x) + F_86(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_2(x)*F_21(x, k_0))
Eq(F_111(x, k_0), F_110(x, k_0)*F_21(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_113(x, k_0), F_112(x, k_0) + F_120(x, k_0))
Eq(F_114(x, k_0), F_113(x, k_0) + F_116(x, k_0))
Eq(F_115(x, k_0), F_114(x, k_0)*F_13(x))
Eq(F_115(x, k_0), F_17(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_118(x, k_0))
Eq(F_117(x, k_0), F_17(x, k_0) + F_22(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_0(x)*F_21(x, k_0)*F_22(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_49(x, k_0))
Eq(F_121(x, k_0), F_2(x)*F_22(x, k_0))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_11(x)*F_2(x))
Eq(F_124(x), F_125(x) + F_6(x))
Eq(F_125(x), F_49(x, 1))
Eq(F_126(x), F_127(x) + F_129(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_10(x)*F_2(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_11(x)*F_68(x))
Eq(F_131(x), F_132(x) + F_140(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_13(x)*F_134(x))
Eq(F_134(x), F_135(x) + F_138(x))
Eq(F_135(x), F_136(x)*F_2(x))
Eq(F_136(x), F_107(x) + F_137(x))
Eq(F_137(x), F_37(x))
Eq(F_138(x), F_139(x)*F_68(x))
Eq(F_139(x), F_136(x) + F_27(x))
Eq(F_140(x), F_70(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "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": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[1, 0], [1, 0], [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": [1, 0, 2], "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": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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