1032_1302_243051
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_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/23985/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[0,x]*F[23,x]*F[7,x]
F[7,x] = F[4,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[23,x]
F[12,x,k[0]] = F[13,x,k[0]]+F[26,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[24,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[22,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[21,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]^2*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[14,x,k[0]]*F[23,x]
F[23,x] = x
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[14,x,k[0]]*F[23,x]*F[7,x]
F[26,x,k[0]] = F[23,x]*F[27,x,k[0]]
F[27,x,k[0]] = (F[12,x,k[0]]*k[0]-F[12,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_{3}\! \left(x \right) = F_{23}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{0}\! \left(x \right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{12}\! \left(x , y\right)+F_{12}\! \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))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_0(x)*F_23(x)*F_7(x))
Eq(F_7(x), F_4(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_23(x))
Eq(F_12(x, k_0), F_13(x, k_0) + F_26(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_24(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_22(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_21(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)**2*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_14(x, k_0)*F_23(x))
Eq(F_23(x), x)
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_14(x, k_0)*F_23(x)*F_7(x))
Eq(F_26(x, k_0), F_23(x)*F_27(x, k_0))
Eq(F_27(x, k_0), (-k_0*F_12(x, k_0) + F_12(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [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": [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": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 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": [[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": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 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": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], 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"pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, "rule_class": "EquivalenceRule"}, {"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]]}, {"patt": [0], "pos": [[2, 0]]}]}], "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": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "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"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "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": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}]}
Specification 2
Strategy pack name: point_and_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/23986/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x,1]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[12,x]*F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[12,x]*F[16,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[23,x,k[0]]+F[43,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[38,x,k[0]]
F[20,x,k[0]] = F[0,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[26,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]+F[32,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[12,x]*F[22,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[23,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[29,x,k[0]]^2*F[12,x]
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[34,x,k[0]] = F[26,x,k[0]]*F[33,x,k[0]]
F[19,x,k[0]] = F[34,x,k[0]]+F[35,x]
F[35,x] = F[0,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[7,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[12,x]*F[40,x,k[0]]
F[40,x,k[0]] = (F[41,x,k[0]]*k[0]-F[41,x,1])/(-1+k[0])
F[41,x,k[0]] = F[14,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[43,x,k[0]] = F[12,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[19,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[12,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x]+F[51,x,k[0]]+F[52,x,k[0]]
F[48,x] = 1/F[12,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = -F[0,x]+F[4,x]
F[51,x,k[0]] = F[26,x,k[0]]*F[47,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[12,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[12,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]+F[61,x,k[0]]
F[58,x,k[0]] = F[12,x]*F[57,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[41,x,k[0]] = F[4,x]+F[59,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[26,x,k[0]]*F[41,x,k[0]]
F[62,x,k[0]] = F[12,x]*F[61,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[19,x,k[0]] = F[0,x]+F[63,x,k[0]]+F[64,x,k[0]]
F[64,x,k[0]] = F[19,x,k[0]]*F[26,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_{12}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{22}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{23}\! \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_{29}\! \left(x , y\right)^{2} F_{12}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_12(x)*F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_12(x)*F_16(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_23(x, k_0) + F_43(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_38(x, k_0))
Eq(F_20(x, k_0), F_0(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_26(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_27(x, k_0) + F_32(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_12(x)*F_22(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_23(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_12(x)*F_29(x, k_0)**2)
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_34(x, k_0), F_26(x, k_0)*F_33(x, k_0))
Eq(F_19(x, k_0), F_34(x, k_0) + F_35(x))
Eq(F_35(x), F_0(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_7(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_12(x)*F_40(x, k_0))
Eq(F_40(x, k_0), (-k_0*F_41(x, k_0) + F_41(x, 1))/(1 - k_0))
Eq(F_41(x, k_0), F_14(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_43(x, k_0), F_12(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_19(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_12(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_48(x), F_49(x)/F_12(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), -F_0(x) + F_4(x))
Eq(F_51(x, k_0), F_26(x, k_0)*F_47(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_12(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_12(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0) + F_61(x, k_0))
Eq(F_58(x, k_0), F_12(x)*F_57(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_41(x, k_0), F_4(x) + F_59(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_26(x, k_0)*F_41(x, k_0))
Eq(F_62(x, k_0), F_12(x)*F_61(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_19(x, k_0), F_0(x) + F_63(x, k_0) + F_64(x, k_0))
Eq(F_64(x, k_0), F_19(x, k_0)*F_26(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": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_and_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:
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0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], 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[1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 1], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 2], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"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, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 2], [0, 1], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": 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1], [2, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"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]]}], "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": [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", "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": [[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]]}], "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": [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", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "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 3
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/23987/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[7,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[0,x]*F[12,x]*F[15,x]
F[15,x] = 1/F[12,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]
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]]+F[37,x]
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[4,x]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[12,x]*F[29,x,k[0]]*F[4,x]
F[30,x,k[0]] = F[12,x]*F[29,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[32,x,k[0]] = F[23,x,k[0]]+F[31,x,k[0]]+F[58,x,k[0]]
F[32,x,k[0]] = F[33,x]+F[43,x,k[0]]
F[33,x] = F[0,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[17,x]+F[37,x]
F[37,x] = F[38,x]+F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[9,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[15,x]
F[43,x,k[0]] = F[44,x,k[0]]+F[55,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[26,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[23,x,k[0]]+F[47,x,k[0]]+F[52,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[12,x]*F[46,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = F[23,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[49,x,k[0]]^2*F[12,x]
F[52,x,k[0]] = F[12,x]*F[53,x,k[0]]
F[54,x,k[0]] = F[26,x,k[0]]*F[53,x,k[0]]
F[54,x,k[0]] = F[43,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[12,x]*F[57,x,k[0]]
F[57,x,k[0]] = -k[0]*(F[20,x,1]-F[20,x,k[0]])/(-1+k[0])
F[58,x,k[0]] = F[12,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[32,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[63,x]+F[67,x,k[0]]
F[63,x] = 1/F[12,x]*F[64,x]
F[64,x] = -F[65,x]-F[9,x]+F[7,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[15,x]
F[68,x,k[0]] = F[12,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[20,x,k[0]] = F[43,x,k[0]]+F[69,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_{12}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \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_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \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)+F_{37}\! \left(x \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_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{9}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{46}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{49}\! \left(x , y\right)^{2} F_{12}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}
F_{58}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{64}\! \left(x \right) = -F_{65}\! \left(x \right)-F_{9}\! \left(x \right)+F_{7}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{69}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_7(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_0(x)*F_12(x)*F_15(x))
Eq(F_15(x), F_16(x)/F_12(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0) + F_37(x))
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_4(x))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_12(x)*F_29(x, k_0)*F_4(x))
Eq(F_30(x, k_0), F_12(x)*F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_32(x, k_0), F_23(x, k_0) + F_31(x, k_0) + F_58(x, k_0))
Eq(F_32(x, k_0), F_33(x) + F_43(x, k_0))
Eq(F_33(x), F_0(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_17(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_15(x))
Eq(F_43(x, k_0), F_44(x, k_0) + F_55(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_26(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_23(x, k_0) + F_47(x, k_0) + F_52(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_12(x)*F_46(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), F_23(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_12(x)*F_49(x, k_0)**2)
Eq(F_52(x, k_0), F_12(x)*F_53(x, k_0))
Eq(F_54(x, k_0), F_26(x, k_0)*F_53(x, k_0))
Eq(F_54(x, k_0), F_43(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_12(x)*F_57(x, k_0))
Eq(F_57(x, k_0), -F_20(x, 1) + (-k_0*F_20(x, k_0) + F_20(x, 1))/(1 - k_0))
Eq(F_58(x, k_0), F_12(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_32(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x) + F_67(x, k_0))
Eq(F_63(x), F_64(x)/F_12(x))
Eq(F_64(x), -F_65(x) + F_7(x) - F_9(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_15(x))
Eq(F_68(x, k_0), F_12(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_20(x, k_0), F_43(x, k_0) + F_69(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": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob", "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": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 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": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 1], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 1], [4, 0], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 1], [4, 1], [4, 0], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[4, 1], [4, 1], [4, 1], [4, 0], [4, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[3, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1], [4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [3, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 0], [3, 1], [3, 1]]}, {"patt": [1, 0, 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"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]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "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": [[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]]}], "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": [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", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "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 4
Strategy pack name: insertion_point_row_placements_tracked_fusion
Tree: http://permpal.com/tree/23988/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[163,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[13,x]*F[2,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[21,x]
F[17,x] = -F[2,x]+F[18,x]
F[18,x] = -F[0,x]+F[19,x]
F[19,x] = 1/F[4,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = F[22,x,1]
F[23,x,k[0]] = F[17,x]+F[22,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[38,x]
F[25,x,k[0]] = F[203,x,k[0]]+F[24,x,k[0]]
F[26,x,k[0]] = F[202,x,k[0]]+F[25,x,k[0]]
F[27,x,k[0]] = F[26,x,k[0]]*F[35,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[29,x,k[0]] = F[196,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[42,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[37,x,k[0]]
F[32,x,k[0]] = F[2,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]*F[36,x,k[0]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[37,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]^2*F[4,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[38,x]
F[42,x,k[0]] = F[43,x,k[0]]+F[44,x,k[0]]
F[43,x,k[0]] = F[2,x]^2*F[33,x,k[0]]
F[44,x,k[0]] = F[36,x,k[0]]*F[38,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[4,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[190,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[33,x,k[0]]+F[45,x,k[0]]
F[50,x,k[0]] = F[45,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[4,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[108,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[67,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[64,x,k[0]]
F[56,x,k[0]] = F[45,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[33,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[2,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[35,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[58,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[2,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[36,x,k[0]]+F[58,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[2,x]*F[59,x,k[0]]
F[66,x,k[0]] = F[45,x,k[0]]*F[58,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[87,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[75,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[4,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[73,x,k[0]]
F[72,x,k[0]] = F[45,x,k[0]]+F[65,x,k[0]]
F[73,x,k[0]] = F[69,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[17,x]*F[59,x,k[0]]
F[75,x,k[0]] = F[58,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[35,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[85,x,k[0]]
F[79,x,k[0]] = F[14,x]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x]+F[82,x,k[0]]+F[84,x,k[0]]
F[81,x] = 0
F[82,x,k[0]] = F[4,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[33,x,k[0]]+F[80,x,k[0]]
F[84,x,k[0]] = F[35,x,k[0]]*F[79,x,k[0]]
F[85,x,k[0]] = F[2,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[36,x,k[0]]+F[79,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[93,x,k[0]]
F[88,x,k[0]] = F[59,x,k[0]]*F[89,x]
F[89,x] = -F[2,x]+F[90,x]
F[90,x] = -F[0,x]+F[91,x]
F[91,x] = 1/F[4,x]*F[92,x]
F[92,x] = F[2,x]
F[93,x,k[0]] = F[58,x,k[0]]*F[94,x,k[0]]
F[95,x,k[0]] = F[36,x,k[0]]*F[94,x,k[0]]
F[96,x,k[0]] = F[107,x,k[0]]+F[95,x,k[0]]
F[97,x,k[0]] = F[105,x,k[0]]+F[96,x,k[0]]
F[98,x,k[0]] = F[100,x,k[0]]+F[97,x,k[0]]
F[99,x,k[0]] = F[4,x]*F[98,x,k[0]]
F[99,x,k[0]] = F[45,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[33,x,k[0]]
F[102,x,k[0]] = F[33,x,k[0]]*F[36,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[32,x,k[0]]
F[104,x,k[0]] = F[36,x,k[0]]*F[45,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[32,x,k[0]]
F[106,x,k[0]] = F[36,x,k[0]]*F[76,x,k[0]]
F[107,x,k[0]] = F[33,x,k[0]]*F[89,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[111,x,k[0]]
F[110,x,k[0]] = F[22,x,k[0]]+F[32,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[33,x,k[0]]*F[7,x]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[4,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[161,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[118,x,k[0]]
F[117,x,k[0]] = F[113,x,k[0]]+F[22,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = F[13,x]*F[22,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[150,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]+F[127,x]
F[123,x,k[0]] = F[122,x,k[0]]+F[126,x,k[0]]
F[124,x,k[0]] = F[123,x,k[0]]+F[23,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]*F[35,x,k[0]]
F[125,x,k[0]] = F[22,x,k[0]]
F[126,x,k[0]] = F[17,x]*F[36,x,k[0]]
F[127,x] = -F[17,x]+F[128,x]
F[128,x] = -F[149,x]+F[129,x]
F[129,x] = 1/F[4,x]*F[130,x]
F[130,x] = -F[131,x]-F[81,x]+F[17,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[137,x]
F[133,x] = F[134,x]+F[14,x]
F[134,x] = F[131,x]+F[135,x]+F[81,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[134,x]+F[2,x]
F[137,x] = F[138,x]+F[140,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[2,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[146,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[2,x]^2
F[145,x] = F[0,x]*F[17,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[134,x]*F[2,x]
F[148,x] = F[133,x]*F[17,x]
F[149,x] = F[17,x]+F[2,x]
F[151,x,k[0]] = F[150,x,k[0]]+F[160,x,k[0]]
F[152,x,k[0]] = F[151,x,k[0]]+F[158,x,k[0]]
F[153,x,k[0]] = F[119,x,k[0]]+F[152,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]*F[4,x]
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = -k[0]*(F[156,x,1]-F[156,x,k[0]])/(-1+k[0])
F[156,x,k[0]] = F[157,x,k[0]]*F[4,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[22,x,k[0]]
F[158,x,k[0]] = F[121,x,k[0]]+F[159,x,k[0]]
F[159,x,k[0]] = F[17,x]*F[33,x,k[0]]
F[160,x,k[0]] = F[21,x]*F[33,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x]*F[59,x,k[0]]
F[163,x] = F[144,x]+F[164,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[180,x]
F[167,x] = F[168,x]*F[2,x]
F[168,x] = F[169,x]+F[171,x]
F[169,x] = F[170,x]
F[170,x] = F[0,x]*F[14,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[59,x,1]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[4,x]
F[175,x] = F[176,x]+F[178,x]
F[176,x] = F[177,x]*F[2,x]
F[177,x] = F[172,x]+F[2,x]
F[178,x] = F[179,x]*F[7,x]
F[179,x] = F[13,x]+F[177,x]
F[180,x] = F[181,x]*F[185,x]
F[181,x] = -F[2,x]+F[182,x]
F[182,x] = -F[0,x]+F[183,x]
F[183,x] = 1/F[4,x]*F[184,x]
F[184,x] = F[2,x]
F[185,x] = F[186,x]+F[188,x]
F[186,x] = F[187,x]
F[187,x] = F[0,x]*F[13,x]
F[188,x] = F[177,x]+F[189,x]
F[189,x] = F[173,x]+F[7,x]
F[190,x,k[0]] = F[191,x,k[0]]*F[33,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]+F[194,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]+F[36,x,k[0]]
F[193,x,k[0]] = F[2,x]+F[45,x,k[0]]
F[194,x,k[0]] = F[193,x,k[0]]+F[195,x,k[0]]
F[195,x,k[0]] = F[51,x,k[0]]+F[7,x]
F[196,x,k[0]] = F[197,x,k[0]]+F[199,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[43,x,k[0]]
F[198,x,k[0]] = F[36,x,k[0]]*F[38,x]*F[76,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[201,x,k[0]]
F[200,x,k[0]] = F[2,x]*F[33,x,k[0]]*F[89,x]
F[201,x,k[0]] = F[36,x,k[0]]*F[38,x]*F[94,x,k[0]]
F[202,x,k[0]] = F[193,x,k[0]]*F[38,x]
F[203,x,k[0]] = F[2,x]^2*F[36,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{163}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{21}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{35}\! \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_{4}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{2}\! \left(x \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_{35}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = y x
F_{36}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{2} \left(x \right)^{2} F_{33}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{38}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{81}\! \left(x \right) = 0
F_{82}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{2}\! \left(x \right)
F_{93}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{89}\! \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_{111}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{32}\! \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_{33}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{161}\! \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_{113}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{127}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{127}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{130}\! \left(x \right) = -F_{131}\! \left(x \right)-F_{81}\! \left(x \right)+F_{17}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{137}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{14}\! \left(x \right)
F_{134}\! \left(x \right) = F_{131}\! \left(x \right)+F_{135}\! \left(x \right)+F_{81}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{134}\! \left(x \right)+F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{140}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{145}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{134}\! \left(x \right) F_{2}\! \left(x \right)
F_{148}\! \left(x \right) = F_{133}\! \left(x \right) F_{17}\! \left(x \right)
F_{149}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = -\frac{y \left(F_{156}\! \left(x , 1\right)-F_{156}\! \left(x , y\right)\right)}{-1+y}
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{163}\! \left(x \right) = F_{144}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{180}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{2}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{171}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{59}\! \left(x , 1\right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{178}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{2}\! \left(x \right)
F_{177}\! \left(x \right) = F_{172}\! \left(x \right)+F_{2}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{7}\! \left(x \right)
F_{179}\! \left(x \right) = F_{13}\! \left(x \right)+F_{177}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{185}\! \left(x \right)
F_{181}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = \frac{F_{184}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{184}\! \left(x \right) = F_{2}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{188}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right)
F_{188}\! \left(x \right) = F_{177}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{173}\! \left(x \right)+F_{7}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{196}\! \left(x , y\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_{43}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{38}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{33}\! \left(x , y\right) F_{89}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{38}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{2} \left(x \right)^{2} F_{36}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_163(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_13(x)*F_2(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_21(x))
Eq(F_17(x), F_18(x) - F_2(x))
Eq(F_18(x), -F_0(x) + F_19(x))
Eq(F_19(x), F_20(x)/F_4(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), F_22(x, 1))
Eq(F_23(x, k_0), F_17(x) + F_22(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_38(x))
Eq(F_25(x, k_0), F_203(x, k_0) + F_24(x, k_0))
Eq(F_26(x, k_0), F_202(x, k_0) + F_25(x, k_0))
Eq(F_27(x, k_0), F_26(x, k_0)*F_35(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_4(x))
Eq(F_29(x, k_0), F_196(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_42(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_37(x, k_0))
Eq(F_32(x, k_0), F_2(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0)*F_36(x, k_0))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_37(x, k_0), F_33(x, k_0)*F_36(x, k_0)*F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x)**2)
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_38(x))
Eq(F_42(x, k_0), F_43(x, k_0) + F_44(x, k_0))
Eq(F_43(x, k_0), F_2(x)**2*F_33(x, k_0))
Eq(F_44(x, k_0), F_36(x, k_0)*F_38(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_4(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_190(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_33(x, k_0) + F_45(x, k_0))
Eq(F_50(x, k_0), F_45(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_4(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_108(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_67(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_64(x, k_0))
Eq(F_56(x, k_0), F_45(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_33(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_2(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_35(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_58(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_2(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_36(x, k_0) + F_58(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_2(x)*F_59(x, k_0))
Eq(F_66(x, k_0), F_45(x, k_0)*F_58(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_87(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_75(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_4(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_73(x, k_0))
Eq(F_72(x, k_0), F_45(x, k_0) + F_65(x, k_0))
Eq(F_73(x, k_0), F_69(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_17(x)*F_59(x, k_0))
Eq(F_75(x, k_0), F_58(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_35(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_85(x, k_0))
Eq(F_79(x, k_0), F_14(x) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_81(x), 0)
Eq(F_82(x, k_0), F_4(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_33(x, k_0) + F_80(x, k_0))
Eq(F_84(x, k_0), F_35(x, k_0)*F_79(x, k_0))
Eq(F_85(x, k_0), F_2(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_36(x, k_0) + F_79(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_93(x, k_0))
Eq(F_88(x, k_0), F_59(x, k_0)*F_89(x))
Eq(F_89(x), -F_2(x) + F_90(x))
Eq(F_90(x), -F_0(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_4(x))
Eq(F_92(x), F_2(x))
Eq(F_93(x, k_0), F_58(x, k_0)*F_94(x, k_0))
Eq(F_95(x, k_0), F_36(x, k_0)*F_94(x, k_0))
Eq(F_96(x, k_0), F_107(x, k_0) + F_95(x, k_0))
Eq(F_97(x, k_0), F_105(x, k_0) + F_96(x, k_0))
Eq(F_98(x, k_0), F_100(x, k_0) + F_97(x, k_0))
Eq(F_99(x, k_0), F_4(x)*F_98(x, k_0))
Eq(F_99(x, k_0), F_45(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_33(x, k_0))
Eq(F_102(x, k_0), F_33(x, k_0)*F_36(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_32(x, k_0))
Eq(F_104(x, k_0), F_36(x, k_0)*F_45(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_32(x, k_0))
Eq(F_106(x, k_0), F_36(x, k_0)*F_76(x, k_0))
Eq(F_107(x, k_0), F_33(x, k_0)*F_89(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_111(x, k_0))
Eq(F_110(x, k_0), F_22(x, k_0) + F_32(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_33(x, k_0)*F_7(x))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_4(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_161(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_113(x, k_0) + F_22(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), F_13(x)*F_22(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_150(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0) + F_127(x))
Eq(F_123(x, k_0), F_122(x, k_0) + F_126(x, k_0))
Eq(F_124(x, k_0), F_123(x, k_0) + F_23(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0)*F_35(x, k_0))
Eq(F_125(x, k_0), F_22(x, k_0))
Eq(F_126(x, k_0), F_17(x)*F_36(x, k_0))
Eq(F_127(x), F_128(x) - F_17(x))
Eq(F_128(x), F_129(x) - F_149(x))
Eq(F_129(x), F_130(x)/F_4(x))
Eq(F_130(x), -F_131(x) + F_17(x) - F_81(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_137(x))
Eq(F_133(x), F_134(x) + F_14(x))
Eq(F_134(x), F_131(x) + F_135(x) + F_81(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_134(x) + F_2(x))
Eq(F_137(x), F_138(x) + F_140(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_2(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_146(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_2(x)**2)
Eq(F_145(x), F_0(x)*F_17(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_134(x)*F_2(x))
Eq(F_148(x), F_133(x)*F_17(x))
Eq(F_149(x), F_17(x) + F_2(x))
Eq(F_151(x, k_0), F_150(x, k_0) + F_160(x, k_0))
Eq(F_152(x, k_0), F_151(x, k_0) + F_158(x, k_0))
Eq(F_153(x, k_0), F_119(x, k_0) + F_152(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0)*F_4(x))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), -F_156(x, 1) + (k_0*F_156(x, k_0) - F_156(x, 1))/(k_0 - 1))
Eq(F_156(x, k_0), F_157(x, k_0)*F_4(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_22(x, k_0))
Eq(F_158(x, k_0), F_121(x, k_0) + F_159(x, k_0))
Eq(F_159(x, k_0), F_17(x)*F_33(x, k_0))
Eq(F_160(x, k_0), F_21(x)*F_33(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x)*F_59(x, k_0))
Eq(F_163(x), F_144(x) + F_164(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_180(x))
Eq(F_167(x), F_168(x)*F_2(x))
Eq(F_168(x), F_169(x) + F_171(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_0(x)*F_14(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_59(x, 1))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_4(x))
Eq(F_175(x), F_176(x) + F_178(x))
Eq(F_176(x), F_177(x)*F_2(x))
Eq(F_177(x), F_172(x) + F_2(x))
Eq(F_178(x), F_179(x)*F_7(x))
Eq(F_179(x), F_13(x) + F_177(x))
Eq(F_180(x), F_181(x)*F_185(x))
Eq(F_181(x), F_182(x) - F_2(x))
Eq(F_182(x), -F_0(x) + F_183(x))
Eq(F_183(x), F_184(x)/F_4(x))
Eq(F_184(x), F_2(x))
Eq(F_185(x), F_186(x) + F_188(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_0(x)*F_13(x))
Eq(F_188(x), F_177(x) + F_189(x))
Eq(F_189(x), F_173(x) + F_7(x))
Eq(F_190(x, k_0), F_191(x, k_0)*F_33(x, k_0))
Eq(F_191(x, k_0), F_192(x, k_0) + F_194(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0) + F_36(x, k_0))
Eq(F_193(x, k_0), F_2(x) + F_45(x, k_0))
Eq(F_194(x, k_0), F_193(x, k_0) + F_195(x, k_0))
Eq(F_195(x, k_0), F_51(x, k_0) + F_7(x))
Eq(F_196(x, k_0), F_197(x, k_0) + F_199(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_43(x, k_0))
Eq(F_198(x, k_0), F_36(x, k_0)*F_38(x)*F_76(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_201(x, k_0))
Eq(F_200(x, k_0), F_2(x)*F_33(x, k_0)*F_89(x))
Eq(F_201(x, k_0), F_36(x, k_0)*F_38(x)*F_94(x, k_0))
Eq(F_202(x, k_0), F_193(x, k_0)*F_38(x))
Eq(F_203(x, k_0), F_2(x)**2*F_36(x, k_0))
Pack JSON:
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Specification JSON:
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